TRANSPORTATION ENGINEERING
ONLINE LAB MANUAL Oregon State University: Kate Hunter-Zaworski Portland State University: Julia Fowler Kent Lall University of Idaho: Ty Bardwell Patrick Bird Steven Dahl Cheryl Gussenhoven Michael Kyte Melissa Lines Mark Lovejoy Josh Nelson
About the Manual This web site (http://www.webs1.uidaho.edu/niatt_labmanual/index.htm (http://www.webs1.uidaho.edu/niatt_labmanual/index.htm)) is a laboratory manual that is designed to supplement the average junior-level course in transportation engineering. Laboratory exercises are presented for most of the major topics addressed in undergraduate transportation engineering. Practicing engineers and educational entities view these topics as the most important ones that civil engineering graduates need to understand. The lab manual includes a vast collection of help resources, to assist you in completing the laboratory exercises, and to increase your understanding of these important topics. Each chapter includes:
discussions of the important theories and concepts. demonstrations of many of the concepts. information about how these concepts are applied in professional practice. example problems with solutions. links to other web sites, for more information on the topic. a glossary of terms specific to that topic.
While this list might sound extensive, and it is, this manual is not meant to be a substitute for lectures or for texts. Additional topics will likely be covered in class, and your text may contain more detail in its descriptions of certain concepts or calculations. This lab manual is the product of two years of collaboration between Oregon State University, Portland State University, and the University of Idaho. All of the individuals who made contributions to this lab manual, both great and small, are listed below.
Oregon State University: Kate Hunter-Zaworski Portland State University: Julia Fowler Kent Lall University of Idaho: Ty Bardwell Patrick Bird Steven Dahl Cheryl Gussenhoven Michael Kyte Melissa Lines Mark Lovejoy Josh Nelson The development of this lab manual was funded by:
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About the Manual This web site (http://www.webs1.uidaho.edu/niatt_labmanual/index.htm (http://www.webs1.uidaho.edu/niatt_labmanual/index.htm)) is a laboratory manual that is designed to supplement the average junior-level course in transportation engineering. Laboratory exercises are presented for most of the major topics addressed in undergraduate transportation engineering. Practicing engineers and educational entities view these topics as the most important ones that civil engineering graduates need to understand. The lab manual includes a vast collection of help resources, to assist you in completing the laboratory exercises, and to increase your understanding of these important topics. Each chapter includes:
discussions of the important theories and concepts. demonstrations of many of the concepts. information about how these concepts are applied in professional practice. example problems with solutions. links to other web sites, for more information on the topic. a glossary of terms specific to that topic.
While this list might sound extensive, and it is, this manual is not meant to be a substitute for lectures or for texts. Additional topics will likely be covered in class, and your text may contain more detail in its descriptions of certain concepts or calculations. This lab manual is the product of two years of collaboration between Oregon State University, Portland State University, and the University of Idaho. All of the individuals who made contributions to this lab manual, both great and small, are listed below.
Oregon State University: Kate Hunter-Zaworski Portland State University: Julia Fowler Kent Lall University of Idaho: Ty Bardwell Patrick Bird Steven Dahl Cheryl Gussenhoven Michael Kyte Melissa Lines Mark Lovejoy Josh Nelson The development of this lab manual was funded by:
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Learning More This lab manual contains a tremendous amount of valuable information that is available to you at any time. To use this information most effectively, however, you should probably develop a strategy. Normally, you will be asked by b y your instructor to complete a laboratory labora tory exercise exerci se from this manual. manual . We recommend that you first read the laboratory exercise and then review the related information in that chapter before you begin working. For example, let’s say that the lab exercise asked you to write a formal evaluation of the current signal timing conditions at a given signal. You could begin with an overview of the topic, under the Introduction button. Next, you could review all of the relevant concepts under the Theory & Concepts button, and then see how these concepts are applied in practice, under the Professional Practice button. Finally, you could work an example problem or two, under the Example Problems button, to guarantee that you fully understand the concepts. At any time, feel free to access the Related Links or the Glossary of Terms. Even though this web site is called a lab manual, it can be much more. You can use this lab manual as a supplemental text at any time. If you are having trouble with a particular concept in class, you can always review that concept in the lab manual, view the Excel demonstration of that concept, and work an example problem. We hope that this lab manual will contribute positively to your education in the field of transportation engineering. We intend to update the site periodically, and add even more content in the future. Please help us improve this educational resource, by filling out the evaluation form under "feedback", on the opening page. Tell us what you liked or didn’t like about the lab manual, and anything that you think we should add or change. Thank you for participating in this project.
Acknowledgements Contributors: This lab manual is the product of two years of collaboration between Oregon State University, Portland State University, and the University of Idaho. All of the individuals who made contributions to this lab manual, both great and small, are listed below. Oregon State University: Kate Hunter-Zaworski Portland State University: Julia Fowler Kent Lall University of Idaho: Ty Bardwell Patrick Bird ii
Steven Dahl Cheryl Gussenhoven Michael Kyte Melissa Lines Mark Lovejoy Josh Nelson
Funding: The development of this lab manual was funded by:
Acknowledgements: The developers would like to thank the following agencies and organizations for their assistance in the development of this lab manual: American Association of State Highway and Transportation Officials (AASHTO), Idaho Transportation Department (ITD), Institute of Transportation Engineers (ITE), Oregon Department of Transportation (ODOT), Transportation Research Board (TRB), U.S. Department of Transportation (USDOT).
Quoted Material: The material in the Professional Practice modules of this lab manual was excerpted from the following publications, with permission: A Policy on Geometric Design of Highways and Streets , 1994, American Association of State Highway and Transportation Officials. Idaho Transportation Department Traffic Manual , 1995, Idaho Transportation Department. Manual of Traffic Signal Design , 2nd Edition, © 1991 Institute of Transportation Engineers. Special Report 209: Highway Capacity Manual , Third Edition, copyright 1998 by the Transportation Research Board, National Research Council, Washington, D.C. Traffic Engineering Handbook , © 1992, Institute of Transportation Engineers. Transportation Planning Handbook , © 1992, Institute of Transportation Engineers. (Note: ITE's Traffic Engineering and Transportation Planning Handbooks will be available in updated versions in October, 1999.)
Accessibility: The developers of these materials have made a special effort to make these materials accessible and available to people with disabilities, who use assistive or enhanced computer technology.
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Table of Contents 1.
Bus Service Planning ................................................................................................................ 1 1.1.
Introduction ........................................................................................................................... 1
1.2. Lab Exercises ........................................................................................................................ 1 1.2.1. Lab Exercise One: Bus Service Planning ...................................................................1 1.3. Theory and Concepts ............................................................................................................. 2 1.3.1. Evaluation of Demand ................................................................................................ 2 1.3.2. Route and Network Structures ................................................................................... 2 1.3.3. Fare Structure and Payment Options .......................................................................... 3 1.3.4. Preliminary Schedule Design ..................................................................................... 4 1.3.5. Final Schedule Design and Blocking ......................................................................... 5 1.3.6. Importance of Layover Times .................................................................................... 6 1.4. Professional Practice ............................................................................................................. 6 1.4.1. Cycle Time ................................................................................................................. 7 1.4.2. Route Cycle Times ..................................................................................................... 7 1.4.3. Terminal Points .......................................................................................................... 8 1.4.4. Intermediate Time Points ........................................................................................... 8 1.4.5. Blocking ..................................................................................................................... 8 1.5. Example Problems.................................................................................................................9 1.5.1. Cycle Time and Number of Vehicles ......................................................................... 9 1.5.2. Vehicle Blocking ...................................................................................................... 10 1.6.
2.
Glossary ............................................................................................................................... 11
Capacity and Level of Service (LOS) Analysis .................................................................... 13 2.1.
Introduction ......................................................................................................................... 13
2.2. Lab Exercises ...................................................................................................................... 13 2.2.1. Lab Exercise: Freeway Analysis .............................................................................. 13 2.3. Theory and Concepts ........................................................................................................... 15 2.3.1. Basic Freeway Section and Ideal Freeway Conditions ............................................ 15 2.3.2. Free-Flow Speed and Flow Rate .............................................................................. 15 2.3.3. Level of Service Criteria .......................................................................................... 16 2.3.4. Determining Flow Rate [d]....................................................................................... 18 2.3.5. Peak Hour Factor ...................................................................................................... 18 2.3.6. Heavy Vehicle Adjustment Factor [d]......................................................................19 2.3.7. Free-Flow Speed Adjustment [d] ............................................................................. 20 2.3.8. Determining Level of Service and Density [d] ........................................................ 21 2.3.9. Applications [d] ........................................................................................................ 22 2.4. Professional Practice ........................................................................................................... 22 2.4.1. Basic Freeway Section and Ideal Freeway Conditions ............................................ 23 2.4.2. Determining Flow Rate ............................................................................................ 23 2.4.3. Free-Flow Speed and Flow Rate .............................................................................. 23 2.4.4. Free-Flow Speed Adjustment ................................................................................... 24 2.4.5. LOS Criteria and Capacity ....................................................................................... 24 2.4.6. Determining LOS and Density ................................................................................. 25 2.5. Example Problems...............................................................................................................25 2.5.1. Peak Hour Factor ...................................................................................................... 25 iv
2.5.2. 2.5.3. 2.5.4. 2.5.5. 2.5.6. 2.6.
3.
Heavy Vehicle Adjustment Factor ........................................................................... 26 Calculating Flow Rate .............................................................................................. 27 Free-Flow Speed Adjustment ................................................................................... 27 Determining LOS and Density ................................................................................. 28 Design Application ................................................................................................... 29
Glossary ............................................................................................................................... 31
Geometric Design....................................................................................................................32 3.1.
Introduction ......................................................................................................................... 32
3.2. Lab Exercises ...................................................................................................................... 32 3.2.1. Lab Exercise One: Geometric Design ...................................................................... 32 3.3. Theory and Concepts ........................................................................................................... 34 3.3.1. Brake Reaction Time ................................................................................................ 34 3.3.2. Braking Distance [d] ................................................................................................ 34 3.3.3. Stopping Sight Distance [d] ..................................................................................... 36 3.3.4. Decision Sight Distance ........................................................................................... 36 3.3.5. Passing Sight Distance [d] ........................................................................................ 37 3.3.6. Horizontal Alignment ............................................................................................... 40 3.3.7. Superelevation and Side-Friction ............................................................................. 40 3.3.8. Minimum Radius Calculations [d] ........................................................................... 41 3.3.9. Design Iterations....................................................................................................... 42 3.3.10. Horizontal Curve Sight Distance [d] ........................................................................42 3.3.11. Transition Segments ................................................................................................. 43 3.3.12. Vertical Alignment ................................................................................................... 43 3.3.13. Ascending Grades ..................................................................................................... 44 3.3.14. Descending Grades ................................................................................................... 45 3.3.15. Vertical Curves ......................................................................................................... 46 3.3.16. Crest Vertical Curves [d] .......................................................................................... 47 3.3.17. Sag Vertical Curves [d] ............................................................................................ 48 3.4. Example Problems...............................................................................................................50 3.4.1. Stopping Sight Distance ........................................................................................... 50 3.4.2. Passing Sight Distance ............................................................................................. 51 3.4.3. Horizontal Curve Radius Calculations ..................................................................... 52 3.4.4. Horizontal Curve Sight Distance .............................................................................. 53 3.4.5. Transition Segments ................................................................................................. 53 3.4.6. Ascending Grades ..................................................................................................... 54 3.4.7. Crest Vertical Curves ............................................................................................... 54 3.4.8. Sag Vertical Curves .................................................................................................. 55 3.5.
4.
Glossary ............................................................................................................................... 56
Parking Lot Design ................................................................................................................. 58 4.1.
Introduction ......................................................................................................................... 58
4.2. Lab Exercises ...................................................................................................................... 58 4.2.1. Lab Exercise One: Facility Analysis and Design ..................................................... 58 4.3. Theory and Concepts ........................................................................................................... 59 4.3.1. Parking Studies ......................................................................................................... 59 4.3.2. Adequacy Analysis ................................................................................................... 62 4.3.3. Parking Facility Design Process ............................................................................... 62 4.3.4. Entrance Considerations ........................................................................................... 63 v
4.3.5. 4.3.6. 4.3.7. 4.3.8.
Internal Considerations ............................................................................................. 63 Parking Stall Layout Considerations ........................................................................ 64 Exit Considerations .................................................................................................. 67 ADAAG Requirements ............................................................................................ 67
4.4. Professional Practice ........................................................................................................... 68 4.4.1. Parking Studies ......................................................................................................... 68 4.4.2. Types of Facilities .................................................................................................... 69 4.4.3. Types of Operation ................................................................................................... 69 4.4.4. Operational Design Elements ................................................................................... 69 4.4.5. Change of Mode Parking .......................................................................................... 70 4.4.6. Downtown Areas ...................................................................................................... 72 4.4.7. Location .................................................................................................................... 72 4.4.8. Off-Street Zoning ..................................................................................................... 72 4.4.9. Design of Off-Street Facilities ................................................................................. 73 4.4.10. Supplemental Specifications and Implementation ................................................... 74 4.5. Example Problems...............................................................................................................75 4.5.1. Adequacy Analysis ................................................................................................... 75 4.5.2. Space Requirements ................................................................................................. 76 4.6.
5.
Glossary ............................................................................................................................... 77
Roadway Design......................................................................................................................79 5.1.
Introduction ......................................................................................................................... 79
5.2. Lab Exercises ...................................................................................................................... 79 5.2.1. Lab Exercise One: Roadway Design ........................................................................ 79 5.3. Theory and Concepts ........................................................................................................... 80 5.3.1. Route Selection and Alignment ................................................................................ 80 5.3.2. Surveys and Maps .................................................................................................... 81 5.3.3. Design Controls and Criteria .................................................................................... 82 5.3.4. Vertical Profile [d].................................................................................................... 83 5.3.5. Cross Section Elements [d] ...................................................................................... 84 5.3.6. Cut and Fill Sections ................................................................................................ 85 5.3.7. Earthwork [d] ........................................................................................................... 86 5.3.8. Designing Bike Lanes .............................................................................................. 87 5.4. Professional Practice ........................................................................................................... 88 5.4.1. Route Selection......................................................................................................... 88 5.4.2. Surveys and Maps .................................................................................................... 89 5.4.3. Design Controls and Criteria .................................................................................... 89 5.4.4. Horizontal and Vertical Alignment .......................................................................... 90 5.4.5. Cross Sections .......................................................................................................... 90 5.5. Example Problems...............................................................................................................91 5.5.1. Traffic Volume ......................................................................................................... 91 5.5.2. Vertical Alignment ................................................................................................... 91 5.5.3. Cross Sections .......................................................................................................... 92 5.6.
6.
Glossary ............................................................................................................................... 93
Signal Timing Design ............................................................................................................. 94 6.1.
Introduction ......................................................................................................................... 94
6.2.
Lab Exercises ...................................................................................................................... 94 vi
6.2.1.
Lab Exercise One: Signal Timing and LOS ............................................................. 94
6.3. Theory and Concepts ........................................................................................................... 95 6.3.1. Basic Timing Elements ............................................................................................ 95 6.3.2. Queuing Theory [d] .................................................................................................. 96 6.3.3. Design Process Outline ............................................................................................ 97 6.3.4. Intergreen Time [d] .................................................................................................. 98 6.3.5. Pedestrian Crossing Time, Minimum Green Interval [d] ....................................... 100 6.3.6. Saturation Flow Rate and Capacity [d] .................................................................. 101 6.3.7. Peak Hour Volume, Peak Hour Factor, Design Flow Rate .................................... 102 6.3.8. Critical Movement or Lane [d] ............................................................................... 103 6.3.9. Cycle Length Determination [d]............................................................................. 103 6.3.10. Green Split Calculations [d] ................................................................................... 104 6.3.11. Timing Adjustments ............................................................................................... 105 6.3.12. Computing Delay and LOS [d] .............................................................................. 105 6.4. Professional Practice ......................................................................................................... 106 6.4.1. Design Process Outline .......................................................................................... 107 6.4.2. Intergreen Time ...................................................................................................... 107 6.4.3. Pedestrian Crossing Time, Minimum Green Time ................................................ 109 6.4.4. Capacity/Saturation Flow Rate ............................................................................... 110 6.4.5. Peak Hour Volume, Design Flow Rate, PHF ......................................................... 111 6.4.6. Critical Movement or Lane .................................................................................... 112 6.4.7. Cycle Length Determination .................................................................................. 113 6.4.8. Green Split Calculations ......................................................................................... 114 6.4.9. Timing Adjustments ............................................................................................... 114 6.4.10. Computing Delay and LOS, Operational Analysis Outline ................................... 115 6.5. Example Problems.............................................................................................................116 6.5.1. Intergreen Time ...................................................................................................... 116 6.5.2. Pedestrian Crossing Time, Minimum Green Interval ............................................ 117 6.5.3. Capacity/Saturation Flow Rate ............................................................................... 118 6.5.4. Peak Hour Volume, Design Flow Rate, PHF ......................................................... 118 6.5.5. Critical Movement or Lane .................................................................................... 119 6.5.6. Cycle Length Determination .................................................................................. 120 6.5.7. Green Split Calculations ......................................................................................... 121 6.5.8. Timing Adjustments ............................................................................................... 121 6.5.9. Computing Delay and LOS .................................................................................... 122 6.6.
7.
Glossary ............................................................................................................................. 122
Traffic Flow Theory ............................................................................................................. 125 7.1.
Introduction ....................................................................................................................... 125
7.2. Lab Exercises .................................................................................................................... 125 7.2.1. Lab Exercise One: Flow Models [d] ...................................................................... 125 7.2.2. Lab Exercise Two: Shock Waves/Queue Formation ............................................. 126 7.3. Theory and Concepts ......................................................................................................... 126 7.3.1. Types of Traffic Flow............................................................................................. 126 7.3.2. Traffic Flow Parameters ......................................................................................... 127 7.3.3. Speed-Flow-Density Relationship .......................................................................... 128 7.3.4. Special Speed & Density Conditions ..................................................................... 129 7.3.5. Greenshield’s Model [d] ......................................................................................... 129 7.3.6. Time-Space Diagrams [d] ...................................................................................... 131 vii
7.3.7. 7.3.8.
Shock Waves [d] .................................................................................................... 132 Queuing Theory ...................................................................................................... 133
7.4. Professional Practice ......................................................................................................... 133 7.4.1. Traffic Flow Parameters ......................................................................................... 134 7.4.2. Speed-Flow-Density Relationships ........................................................................ 136 7.4.3. Greenshields' Model ............................................................................................... 138 7.4.4. Shock Waves and Continuum Flow Models .......................................................... 138 7.4.5. Queuing Theory ...................................................................................................... 141 7.5. Example Problems.............................................................................................................142 7.5.1. Greenshield's Model ............................................................................................... 143 7.5.2. Shock Waves .......................................................................................................... 143 7.5.3. Traffic Flow Model ................................................................................................ 146 7.6.
8.
Glossary ............................................................................................................................. 147
Travel Demand Forecasting ................................................................................................ 149 8.1.
Introduction ....................................................................................................................... 149
8.2. Lab Exercises .................................................................................................................... 149 8.2.1. Lab Exercise 1: The Gravity Model ....................................................................... 149 8.2.2. Lab Exercise 2: Cross-Classification ..................................................................... 151 8.3. Theory and Concepts ......................................................................................................... 151 8.3.1. Overview of the TDF Process ................................................................................ 152 8.3.2. Description of the Study Area ................................................................................ 152 8.3.3. Trip Generation Analysis ....................................................................................... 155 8.3.4. Multiple Regression Analysis ................................................................................ 156 8.3.5. Experience Based Analysis .................................................................................... 157 8.3.6. Trip Distribution Analysis ...................................................................................... 157 8.3.7. The Logit Model ..................................................................................................... 157 8.3.8. The Gravity Model ................................................................................................. 158 8.3.9. Modal Choice Analysis .......................................................................................... 158 8.3.10. Trip Assignment Analysis ...................................................................................... 159 8.3.11. Results .................................................................................................................... 160 8.4. Professional Practice ......................................................................................................... 160 8.4.1. Zones and Zoning ................................................................................................... 161 8.4.2. Networks and Nodes .............................................................................................. 161 8.4.3. Trip Generation Analysis ....................................................................................... 161 8.4.4. Trip Distribution ..................................................................................................... 162 8.4.5. Modal Choice ......................................................................................................... 164 8.4.6. Trip Assignment ..................................................................................................... 164 8.4.7. Model Calibration and Validation .......................................................................... 165 8.5. Example Problems.............................................................................................................166 8.5.1. Cross Classification ................................................................................................ 166 8.5.2. Gravity Model ........................................................................................................ 170 8.5.3. Logit Model ............................................................................................................ 173 8.5.4. Traffic Assignment ................................................................................................. 174 8.6.
Glossary ............................................................................................................................. 176
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1. Bus Service Planning 1.1.
Introduction
Public transit systems serve many useful functions in the modern world. When designed properly, public transit can provide an efficient and convenient alternative to private passenger vehicles. Reducing the use of private automobiles has several benefits, not the least of which are reduced congestion in transportation networks and fewer harmful chemical emissions. The principle problem facing transit engineers is the development of transit systems that encourage patronage, provide dependable and efficient service, and are operable within the budgetary and political constraints that exist within their districts. Bus service is the most common form of public transit. Its popularity is based on its flexibility, expandability, and low cost. Since the bus service planning process can be long and complex, it is often done with the help of computer software that can try millions of potential route structures, service schedules, and employee schedules. This chapter will introduce most of the important concepts in bus service planning, but will fall short of being a comprehensive guide to the subject. Once you are in practice, your transportation district and transit authority will be able to provide you with procedures and guidelines that have been developed from years of experience in the area.
1.2.
Lab Exercises
This exercise will help increase your understanding of Bus Service Planning, by presenting a more complicated problem that requires more thorough analysis.
1.2.1.
Lab Exercise One: Bus Service Planning
Your city is considering a new weekday bus route. Your task will be to study the route and determine the cost of providing this service. You will present your results in a brief report to the city manager, who must then make a decision on the feasibility of this service. Your instructor will provide the specific information on the route, including the points to be served by the route and other relevant information. This assignment is divided into several parts:
What street segments should be included in this service? How long does it take to travel this route during different periods of the day? How many vehicles are required to provide service on this route? How many bus drivers will be required to operate this service?
Tasks To Be Completed As you complete the following tasks, consider what information will be useful to the city manager, who must decide on the feasibility of this service. Task 1. Your instructor will assign an area in your city that is to be served by a new public transit route. You should visit the area and document the key areas to be served and the street segments that are appropriate for bus operations.
1
Task 2. Based on your site visit, determine the length of the route, the average running speed of the bus during both the peak and off-peak periods, the bus stops that should be included along the route, the terminal points on the route, the times of operation, and the headways that should be provided. Task 3. Calculate the number of vehicles required in order to provide this service during the different service periods. Task 4. Prepare a headway sheet showing the schedule. Task 5. Determine the vehicle blocks necessary to serve this schedule. Task 6 . If the average driver cost per hour is $80 (including fringe benefits and overhead), what is the total annual operating cost for this service (assume 255 weekdays per year). Task 7. Prepare a brief report summarizing the results of your work, including documentation of your site visit, computations, results, and conclusions.
1.3.
Theory and Concepts
A course in transportation engineering would not be complete without discussing some elements of Bus Service Planning. Most junior level courses introduce several aspects of Bus Service Planning, including the topics listed below. To begin learning about Bus Service Planning, just click on the link of your choice.
1.3.1.
Evaluation of Demand
Whether you are contemplating the addition of new routes to an existing bus transit system, or developing an entirely new bus system in a community, you’ll need to estimate the number of users that your new routes will service. Once you have estimated where and when the demand will be present, you can design your bus transit system to service that demand. As discussed in the chapter entitled "Travel Demand Forecasting," you can divide the area that you want to service into regions and conduct trip generation, trip distribution, and mode split analyses of the region with your proposed route structure in place. This will give you an estimate of the number of users that will decide to use your new bus route(s) instead of their current means of transportation. Once you have this information, you can use existing traffic data and microanalysis of the regions to determine when the peak travel periods are and what specific destinations are the most common. For example, if you knew that a school was present in zone "A" and that zone "B" was primarily residential, you might deduce that a high demand for travel from zone "A" to zone "B" would exist around 3:00 PM. Having a firm understanding of the demand for bus service in both the spatial and temporal dimensions will make the remainder of the bus service planning process much easier.
1.3.2.
Route and Network Structures
A network is a system of routes. Routes are individual paths that are taken by transit vehicles. Routes include a spatial element -the streets and stops that are serviced along the way, and a temporal element- the time that the bus will arrive and depart from each stop or station. 2
Selecting a network structure is a complicated task, for which there is not a simple solution. There are, however, a few network structures that have become very common. Grid networks are common in large cities. These systems tend to be centered on the central business district with few routes venturing far outside the central business district (CBD). Grid networks make extensive use of the existing roadways. Where traffic is heavy, deep within the CBD, one or more exclusive bus lanes may be required in order to provide buses with adequate freedom to move. Exclusive bus lanes increase the capacity of the system by reducing delays caused by interfering traffic, but the exclusive bus lanes also reduce the capacity of roadways to handle private traffic and parking. Radial networks are also frequently found in modern cities. These systems contain linear routes from the CBD to outlying suburbs. Commuters who live in the suburbs and work in the central business district are well served by radial networks, but those who want inter-suburb transportation are not well served, unless there are direct lines connecting each of the suburbs. Exclusive bus lanes are occasionally included on radial routes as well. Many modern cities employ transit systems that are a combination of the grid and radial networks. These networks transport individuals to and from the suburbs using radial routes and then provide transportation within the CBD via a grid network. The route structure should serve the needs of the population; therefore, each community’s needs require special consideration.
1.3.3.
Fare Structure and Payment Options
Bus service planning encompasses not only the calculation of where and when buses will arrive, but also how much each passenger will be required to pay and how the payment will be received. Poorly designed fare schedules and fare collection procedures can be a source of significant confusion and delay. The amount that passengers must pay for a particular trip can be calculated in several ways.
A city may choose to adopt a uniform fare for all routes in the transit network. While this rate structure is simple, it also penalizes those who travel short distances on the network. A more equitable solution would be to adjust the fare based on the distance the user traveled on the network, but this system is prohibitively complex. Many transit authorities have decided on a compromise that charges users based on the number of zones that they travel through on a given route. Travel from zone "A" to zone "E" would cost the user more than the shorter trip from zone "A" to zone "C." This system is reasonably simple and much more equitable than the uniform fare system.
Fare collection is another complicated issue, for which several solutions have been devised.
The driver can collect fares from each boarding passenger. While simple, this system causes large delays at every stop, as the driver must interact with each passenger as they board. To reduce delay, fare collection machines that accept payment from the passengers are commonly installed near the bus door. These machines allow the bus driver to focus on driving, and accelerate the boarding process considerably. Finally, fare card programs are becoming more and more common. These systems allow the transit user to purchase a magnetic card with a predetermined value. The fare is deducted when the passenger swipes the card through a reader at the bus door. This system is very efficient. In 3
addition, it allows the transit authority to monitor the transportation habits of the cardholders by automatically recording the routes, stops, and times at which each card is used.
1.3.4.
Preliminary Schedule Design
Designing a schedule can be quite complicated, so preliminary schedule design will be portrayed here in the form of an example. Consider a transit route that connects a residential neighborhood to a central business district. The distance between the neighborhood and the downtown area is 5 miles. The transit vehicles average 12 miles per hour between the two terminal points. The goal is to provide transit service every 15 minutes along the route. The first step is to determine the time required to travel from one end of the route to the other. The one-way trip time is given in the equation below: One-Way Trip Time = Route Length / Average Operating Speed One-Way Trip Time = 5 miles / 12 mph One-Way Trip Time = 25 minutes The total round-trip time is twice the one-way trip time, or 50 minutes. The next step is to determine the number of vehicles required in order to operate at the desired level of service. Now suppose that the desired headway is 15 minutes. That is, the frequency of service is one vehicle every 15 minutes. How many vehicles would be required to provide this service? Number of Vehicles Required = Total Round Trip Time / Headway Number of Vehicles Required = 50 minutes / (15 min/vehicle) Number of Vehicles Required = 3.33 or 4 The revised round-trip time can now be calculated. Revised Round Trip Time = (Number of Vehicles) × (Headway) Revised Round Trip Time = (4 vehicles) × (15 minutes/vehicle) Revised Round Trip Time = 60 minutes This leaves 10 minutes for recovery and layover time, since the actual round-trip running time is 50 minutes. The capacity of the route can also be determined. Capacity = (Vehicles) × (Capacity/Vehicle) Capacity = (4 vehicles/hour) × (75 passengers/vehicle) Capacity = 300 passengers/hour Now suppose that the forecasted demand for this transit route is 400 passengers per hour at the peak loading point. We need to re-estimate the required vehicles because the capacity calculated above is insufficient to carry this projected demand. # Vehicles = (400 passengers/hour) / (75 passengers/vehicle) # Vehicles = 5.33 vehicles/hour Headway = 60 minutes / 5.33 vehicles 4
Headway = 11.25 = 10 minutes/vehicle Note that we use an even “clock headway” of 10 minutes, rather than the cumbersome and potentially confusing value of 11.25 minutes that we initially calculated. # Vehicles = (50 minutes + 10 minutes) / (10 minutes/vehicle) # Vehicles = 6 At this point, we have completed the preliminary calculations in schedule design. The final computations involve the development of the schedule and the vehicle 'blocks.' These computations are presented in the 'final schedule design and blocking' discussion.
1.3.5.
Final Schedule Design and Blocking
The final computations in schedule design will produce a summary of the activity that will occur on the route during the period in question. We’ll continue our example problem, which was introduced in the 'preliminary schedule design' section, to illustrate the steps and the desired result. Our preliminary schedule design conclusions were that we needed 6 vehicles running with 10-minute headways to service the demand of 400 passengers/hour between ‘A’ and ‘B’. Let’s assume that these calculations were meant for the morning peak-period of 7:00 a.m. through 9:00 a.m. First, we list the departure times from ‘A’ for each vehicle during the peak-period. Leave ‘A’
7:00
7:10
7:20
7:30
7:40
7:50
8:00
8:10
8:20
8:30
8:40
8:50
Next, since we know that it takes 25 minutes for each vehicle to proceed from ‘A’ to ‘B’, we can record the arrival times. Including 5-minutes of layover time at each terminal ‘A’ and ‘B’, we can include the departure times as well. Notice that the work so far has been vehicle-independent. We are only recording the times at which these events should occur, not which vehicle should be at each station at these times. Leave ‘A’
Arrive ‘B’
Leave ‘B’
Arrive ‘A’
7:00 7:10 7:20 7:30 7:40 7:50 8:00 8:10 8:20 8:30 8:40 8:50
7:25 7:35 7:45 7:55 8:05 8:15 8:25 8:35 8:45 8:55 9:05 9:15
7:30 7:40 7:50 8:00 8:10 8:20 8:30 8:40 8:50 9:00 9:10 9:20
7:55 8:05 8:15 8:25 8:35 8:45 8:55 9:05 9:15 9:25 9:35 9:45
Now that we have a schedule of times, we can try to link together these times into routes that specific vehicles can follow. For example, if a vehicle were to leave ‘A’ at 7:00, it would arrive at ‘A’ again at 7:55. This vehicle could then start again with the 8:00 shift. Extending this process leads to the table below. 5
Vehicle
Leave ‘A’
Arrive ‘B’
Leave ‘B’
Arrive ‘A’
1 2 3 4 5 6 1 2 3 4 5 6
7:00 7:10 7:20 7:30 7:40 7:50 8:00 8:10 8:20 8:30 8:40 8:50
7:25 7:35 7:45 7:55 8:05 8:15 8:25 8:35 8:45 8:55 9:05 9:15
7:30 7:40 7:50 8:00 8:10 8:20 8:30 8:40 8:50 9:00 9:10 9:20
7:55 8:05 8:15 8:25 8:35 8:45 8:55 9:05 9:15 9:25 9:35 9:45
At this point, we can prepare the final vehicle block summary. This summary simply indicates the times that each vehicle will be in service and the vehicle block that the vehicle will be assigned to. Vehicle
Vehicle Block
Time Block
Time In Service
A B C D E F Total
1 2 3 4 5 6
7:00-8:55 7:10-9:05 7:20-9:15 7:30-9:25 7:40-9:35 7:50-9:45
1:55 1:55 1:55 1:55 1:55 1:55 11:30
The tables that have been developed in this section are the ultimate result of schedule design.
1.3.6.
Importance of Layover Times
Layover, while mentioned only casually in the schedule design discussion, is an important part of the schedule. The layover period serves a variety of functions. First, it provides a window of time to compensate for vehicles that are running ahead of or behind schedule. The layover can be extended or shortened in order to keep vehicles on schedule. Next, the layover time provides an opportunity for drivers to relax and prepare for the next run. In fact, labor unions usually require layovers periods that are a certain percentage of the cycle length. Finally, layover periods can be used to change drivers, or for other administrative purposes.
1.4.
Professional Practice
In order to supplement your knowledge about the various concepts within Bus Service Planning, and in order to give you a glimpse of how these various topics are discussed in the professional environment, we have included selected excerpts from professional design manuals.
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1.4.1.
Cycle Time
The following excerpt was taken from the Transit Cooperative Research Program (TCRP) Report 30, page 19.
Cycle time is the number of minutes needed to make a round trip on the route, including layover/recovery time. Cycle time is important for several reasons, including playing a part in the formula used for determining the number of vehicles needed to provide a given level of service on a route. Since cycle time equals the number of minutes needed to make a round trip, including the layover/recovery time, the scheduler determines the amount of time it takes to operate or "run" from one end of the route to the other and back, then adds layover/recovery time to yield the cycle time. Minimum vs. Available Cycle Time
For many agencies, on some or all routes, the amount of layover/recovery time is often determined by labor agreement or agency policy. These agreements or policies dictate a minimum number of minutes that must be built into the schedule for layover/recovery. Minimum cycle time is the number of minutes scheduled for a vehicle to make a round trip, including a minimum layover/recovery time as dictated by labor agreement or agency policy . . . . However, maintaining a constant headway . . . will, in most cases, result in a cycle time other than the minimum cycle time for the vehicles operating that route . . . . The resulting cycle time (which includes the additional layover/recovery time) necessary to maintain the 30-minute headways is now called the available cycle time. In the optimal case, the minimum cycle time would be the same as the available cycle time. However, maintaining fixed, clock multiple headways often makes that impossible.
1.4.2.
Route Cycle Times
The following excerpt was taken from the Transit Cooperative Research Program (TCRP) Report 30, page 4.
Cycle time is the time it takes to drive a round trip on a route plus any time that the operator and vehicle are scheduled to take a break (layover and/or recovery time) before starting out on another trip. Typical service standards attempt to maximize the length of the route design per cycle time, while providing for the minimum amount of layover/recovery time allowed. Maximizing route length per cycle time utilizes equipment and labor power most effectively. However, other considerations make this optimization difficult to achieve. Other considerations that make optimization of labor and equipment difficult include:
the need to maintain consistent time between vehicles on a route (headway). adjusting for changes in ridership and traffic during the day (for example, rush hour vs. non rush hour). planning for vehicles to arrive at common locations so that passengers may make transfers to other routes (timed transfers).
These considerations often require additional layover/recovery time beyond the minimum allowed. 7
1.4.3.
Terminal Points
The following excerpt was taken from the Transit Cooperative Research Program (TCRP) Report 30, page 16.
Terminal points are considered the "ends" of a line or route. These are the locations where vehicles generally begin and/or end their trips and operators usually take their layovers. For that reason, locations where there is safe parking and restrooms close by are considered desirable locations for terminal points. How many terminal points are usually on a route?
Loop routes that operate only in one direction generally have only one terminal point. A basic end-to-end route with bi-directional service and no branches or short turns generally has two terminal points, one located at each end of the route. Routes with more complex patterns generally have more than two terminal points.
1.4.4.
Intermediate Time Points
The following excerpt was taken from the Transit Cooperative Research Program (TCRP) Report 30, page 21.
Intermediate time points are locations along the route, between the terminals, that indicate when the vehicle will be there. The term "node" is commonly used in computerized scheduling systems to denote a time point. Generally speaking, on public timetables, these intermediate time points, or nodes, are timed to be between 6 and 10 minutes apart. In theory, when intermediate time points are too close together, there is a greater risk that the operator may arrive early and have to wait or "dwell" at that point to stay on schedule, causing passengers to become impatient. When time points are more than 10 minutes apart, some agencies believe that customers are more likely to be confused about when a vehicle will arrive at a particular stop, given the differences in individual operator driving habits. Where are intermediate time points typically located?
Physical location considerations also affect the selection of intermediate time points. Major intersections that are widely recognized and possess good pedestrian amenities like sidewalks and actuated traffic signals make good time points. It is a good idea to locate intermediate time points at major trip generator locations such as shopping centers, hospitals, and government buildings. Time points are also useful at locations where time is critical, such as major employment centers and intersecting bus routes or rail centers.
1.4.5.
Blocking
The following excerpt was taken from the Transit Cooperative Research Program (TCRP) Report 30, page 38.
8
What is "blocking"? Blocking is the process of developing vehicle assignments. These assignments, or blocks, describe a series of trips that are "hooked" together and assigned to a single vehicle. The vehicle trips that are linked together as part of the block may cover more than one route and may also involve more than one operator during the course of the vehicle workday. However, the block refers to the work assignment for only a single vehicle for a single service workday.
Why is blocking important? Blocking is a critical element in the scheduling process because it serves as the basis for both the costs associated with operating the revenue service vehicle as well as influencing the cost associated with work assignments for operators.
1.5.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic.
1.5.1.
Cycle Time and Number of Vehicles
You have just designed a route that requires 65 minutes to travel round trip without any layover/recovery time at the route terminals. Your boss indicates that a layover/recovery period of at least 5% of the round trip time must be included at either end of the route. Adjust the cycle time to include the layover/recovery time and determine the number of vehicles that will be required to service this route if the required headway is 15 minutes.
Solution First, you’ll need to adjust the cycle time so that it includes the necessary layover/recovery periods. C = Travel Time + Layover / Recovery Time C = 65 minutes + 65 × (10%) = 71.5 minutes C = 72 minutes (rounded to the next whole number) Next, you’ll need to determine the number of vehicles that are required. Number of Vehicles = Cycle Time / Headway Number of Vehicles = 72 / 15 = 4.8 vehicles Number of Vehicles = 5 vehicles (rounded to the next whole number) Since the number of vehicles and the headway are set, we should solve for the new cycle time and determine what layover/recovery period is actually provided. Cycle Time = Number of Vehicles × Headway Cycle Time = 5 × 15 = 75 minutes
9
Since the actual travel time is 65 minutes and the total cycle time is 75 minutes, the total layover/recovery period for each bus is 10 minutes, or 5 minutes at each end. The layover/recovery period at each end is, therefore, 7.6% of the travel time and the number of vehicles that are required is 5.
1.5.2.
Vehicle Blocking
A two terminal bus route has the following characteristics during the evening peak period (4-6 PM):
cycle time = 90 minutes layover/recovery time = 5 minutes at each terminal number of vehicles = 6 headway = 15 minutes.
Develop a vehicle block summary for this time period.
Solution The easiest place to start is with the departures. Develop a table that indicates when vehicles should depart from the first terminal. Leave TP #1
4:00
4:15
4:30
4:45
5:00
5:15
5:30
5:45
Next, determine the travel time between terminals. Cycle Time = 90 minutes Layover/Recovery time = 10 minutes total Travel Time = 80 minutes Travel Time between terminals = 40 minutes Now that we know that the travel time between terminals is 40 minutes and the layover/recovery time is 5 minutes at each terminal, we can develop a table of arrivals and departures for both terminals. Leave TP #1
Arrive TP #2
Leave TP #2
Arrive TP #1
4:00 4:15 4:30 4:45 5:00 5:15 5:30 5:45
4:40 4:55 5:10 5:25 5:40 5:55 6:10 6:25
4:45 5:00 5:15 5:30 5:45 6:00 6:15 6:30
5:25 5:40 5:55 6:10 6:25 6:40 6:55 7:10
Now we can hook the trips together and form the initial vehicle blocks.
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Vehicle
Leave TP Arrive TP #2 Leave TP #2 Arrive TP
1 4:00* 4:40 2 4:15* 4:55 3 4:30* 5:10 4 4:45* 5:25 5 5:00* 5:40 6 5:15* 5:55 1 5:30 6:10 2 5:45 6:25 * Vehicle enters service ** Vehicle leaves service
4:45 5:00 5:15 5:30 5:45 6:00 6:15 6:30
5:25 5:40 5:55** 6:10** 6:25** 6:40** 6:55** 7:10**
Now we can create the final block summary. Vehicle 1 2 3 4 5 6 Total
1.6.
Time Block Time in Service 4:00 – 6:55 2:55 4:15 – 7:10 2:55 4:30 – 5:55 1:25 4:45 – 6:10 1:25 5:00 – 6:25 1:25 5:15 – 6:40 1:25 11:30
Glossary
Blocking: assigning trips to vehicles so that each vehicle works continuously and proper headways are maintained. Cycle Time: the total time required to complete a full cycle. The cycle time includes the running time and the layover/recovery time. Exclusive Bus Lanes: roadway lanes that are meant to be used by buses only. These lanes reduce conflicts with passenger cars and other traffic. Fare: the amount of money that is charged for riding a transit vehicle. Headway: the time that should elapse between consecutive buses arriving at stations or terminal points. Layover/Recovery Time: the time that transit vehicles should remain stationary at each terminal point. The layover/recovery time is used for resting, administrative purposes, and for maintaining proper headways. Network: a system of routes. Operating Speed: the average speed at which a transit vehicle can traverse the route in question, including intermediate stops. Policy Headway: the headway set by the local transit authority. Route a specific physical path that a transit vehicle follows. 11
Running Time: the portion of the cycle time that is spent traveling, not in layover/recovery. Schedule: the temporal path that a transit vehicle follows, or a listing of times at which the transit vehicle should be located at various places. Terminal Point: a point at the end of the route, or any other designated point, at which the transit vehicle may enter or leave service or remain stationary for a few moments for layover/recovery. There are normally two terminal points on linear routes, one at each end. Travel Time: see Running Time above. Vehicle Block Summary: a table listing the time intervals that each vehicle will be in service and also listing the total time that each vehicle will be in service.
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2. Capacity and Level of Service (LOS) Analysis 2.1.
Introduction
The number of vehicles on our highways increases every year, and transportation engineers are often faced with the challenge of designing modifications to existing facilities that will service the increased demand. As part of this work, the engineers must evaluate the capacity of the existing and proposed systems. In addition, engineers are often required to justify the expense of modifying or adding facilities by looking at the current and potential levels of service. Capacity and Level of Service (LOS) are closely related and can be easily confused. To help clarify the difference between the two, imagine a phone booth that contains ten people. The phone booth obviously has a capacity of ten or more people, but it’s likely that the level of service (quality of service) would be unanimously unacceptable. Capacity is a measure of the demand that a highway can potentially service, while level of service (LOS) is a measure of the highway’s operating conditions under a given demand.
Traffic engineers use capacity and level of service analyses to:
Determine the number and width of lanes needed for new facilities or for expanding existing facilities. Assess service levels and operational characteristics of existing facilities that are being considered for upgrading. Identify traffic and roadway changes needed for new developments. Provide base values for determining changes in fuel consumption, air pollutant emissions, roaduser costs, and noise associated with proposed roadway changes.
Capacity and level of service (LOS) are fundamental concepts that are used repeatedly in professional practice. Because of their obvious importance, this chapter is designed to introduce the undergraduate engineering student to capacity and level of service (LOS).
2.2.
Lab Exercises
This exercise will help increase your understanding of Capacity and LOS Analysis, by presenting a more complicated problem that requires more thorough analysis.
2.2.1.
Lab Exercise: Freeway Analysis
Your State Department of Transportation (DOT) has been given funding for the construction of a new freeway to relieve the congestion on the existing freeway that extends through the downtown section of your community. Construction of the new freeway will begin this year and is expected to take a minimum of three years to complete. In the interim, the DOT has decided to evaluate the most congested section of the existing freeway for immediate improvements that would keep traffic flow at less than capacity on this section while the new freeway is under construction. Your supervisor has given you the task of determining the most economical improvements for the existing freeway, so that operations do not exceed capacity for the next several years. This 3,000-foot section of existing freeway has the following characteristics:
an interchange density of 1 per mile free-flow speeds of 58 mph on the upgrade and 62 mph on the downgrade carries 1600 vehicles per hour during the peak hour (in one direction) on a grade of 5% four asphalt-paved lanes (two in each direction) 13
11-foot lanes with 1-foot right shoulder lateral clearance to a concrete barrier, a 4-foot median with a concrete barrier PHF = 0.85 11% trucks, 4% buses and no RVs the total right-of-way consists of 64 feet
This assignment is divided into the following parts: 1. What is the existing LOS on this 3,000-foot section of freeway? 2. Given that the anticipated rate of annual growth in traffic volume in the area is expected to be 15%, what will the LOS be in three years? 3. What are possible improvements (and their estimated costs) that can be made to the existing freeway to delay capacity flow conditions for three years, given that the existing right-of-way cannot be expanded?
Tasks to be Completed As you complete the following tasks, you will determine the most economical improvements that can be implemented on the existing freeway to delay the onset of capacity flow operations. Task 1. Calculate the free-flow speed and convert volume (vph) to flow rate (pcphpl) for the existing freeway, in both directions (upgrade and downgrade). You will first need to calculate the upgrade and downgrade heavy-vehicle adjustment factors in order to convert volume to flow rate. For selecting the driver population adjustment factor, you can assume that the traffic is mostly commuters who are familiar with the freeway. Using your calculated free-flow speed, construct an appropriate speed-flow curve of the same shape as the typical curves on the free-flow speed versus flow rate graph. The curve should intercept the y-axis at your calculated free-flow speed. The LOS for the upgrade and downgrade can be determined directly from the graph. Task 2. Using the anticipated growth rate of 15% per year, determine what the traffic volume and flow rate will be in three years. Then repeat all of the steps in Task 1 except for calculation of the free-flow speed to determine what the LOS will be in three years. How many years will it be until the upgrade section is operating close to capacity? Task 3. Given that the right-of-way cannot exceed a total of 64 feet, develop possible improvements that will forestall capacity operations on this section of freeway. At a minimum, you should evaluate the effects of changing lane widths, lateral clearances and number of lanes (specifically in the upgrade direction). Setting up a spreadsheet program to calculate free-flow speed and flow rate will make this task relatively straightforward. Task 4. Estimating costs may prove to be the most challenging part of this exercise. What you need to keep in mind is that the term "estimated" means just that - an estimate. The purpose of this exercise is simply to introduce you to the costs associated with highway improvement projects. Possible resources include cost data manuals (such as the RS Means Cost Manuals), government transportation offices, and the civil engineering department at your university. Task 5. You are to present the data from Tasks 1 through 4 in a report that includes, at a minimum,
1. a summary of existing conditions and LOS, 2. a description of when the freeway will reach capacity with no improvements, 3. a list of possible improvements and the respective effects on LOS, and 14
4. your recommended improvement(s) and estimated costs to implement your recommendation. Remember to note any assumptions in your report.
2.3.
Theory and Concepts
Evaluating the capacity and LOS of a roadway probably seems like a daunting task. In reality, the calculations are really quite simple. The Theory and Concept links that are located below should help you navigate through the process with ease. Topics followed by the characters '[d]' include an Excel demonstration.
2.3.1.
Basic Freeway Section and Ideal Freeway Conditions
A basic freeway section is a segment where there are no interruptions to the flow of traffic. Interruptions to traffic flow occur when vehicles enter or leave the freeway. Therefore, a basic freeway section is one where on or off ramps are not present for at least 1500 feet upstream and downstream of the section. In addition to uninterrupted conditions, the "ideal" basic freeway section is defined as having the following characteristics:
Each lane is 12 feet wide. There is 6 feet of clearance between the outside and the inside edges of the freeway and the nearest obstruction that would distract or influence a motorist. All vehicles are passenger cars (no trucks, buses, or recreational vehicles). Ten or more lanes (in urban areas only). Interchanges are spaced every 2 miles or more. The drivers are regular and familiar users of the freeway section. The terrain is level, with grades no greater than 2%.
Together, these conditions represent the "highest" (ideal) type of freeway section, which is one with a free-flow speed of 70 mph or higher and a capacity of 2400 passenger cars per hour per lane (pcphpl).
2.3.2.
Free-Flow Speed and Flow Rate
An understanding of the relationship between speed and flow rate is the key to determining capacity and LOS for a specific freeway section. In general, freeways are designed to accommodate relatively large numbers of vehicles at higher speeds than other roadways. Free-flow speed is the term used to describe the average speed that a motorist would travel if there were no congestion or other adverse conditions (such as bad weather). The "highest" (ideal) type of basic freeway section is one in which the free-flow speed is 70 mph or higher. Flow rate is defined as the rate at which traffic traverses a freeway segment, in vehicles per hour or passenger cars per hour. Free-flow speed is actually defined as the speed that occurs when density and flow are zero. Of course, observing zero density and flow doesn’t make much sense. The following scenario illustrates the relationship between Free-flow Speed and Flow Rate. Imagine that you are the only motorist on a section of freeway that you travel frequently, the weather is good and you are driving at a speed that is comfortable for that particular section, say 70 mph. Studies have shown that as long as the number of vehicles traveling per hour per lane on your 15
section of freeway does not exceed a flow rate of 1300, you will likely continue traveling at 70 mph. (This assumes all passenger cars - no trucks, buses or recreational vehicles). Your speed will start to decrease once the flow rate exceeds 1300 passenger cars per hour per lane (approximately 22 cars per minute, or about 1 car every 3 seconds). If you were traveling at 65 mph, your speed wouldn’t decrease until a flow rate of 1450 passenger cars per hour per lane (pcphpl) has been reached. The relationship is shown below.
2.3.3.
Level of Service Criteria
Six levels of service have been defined for roadways and have been given letter designations of A through F. LOS A represents the best level of service and LOS F represents the worst. The following table lists the criteria for each LOS, based on the free-flow speed. Level of Maximum Density Minimum Speed Maximum Service Service (pc/mi/ln) (mph) Flow Rate (pcphpl) Free-Flow Speed = 70 mph A 10 70.0 700 B 16 70.0 1,120 C 24 68.0 1,632 D 32 64.0 2,048 E 45 53.0 2,400 F var var var Free-Flow Speed = 65 mph A B C D E F
10 16 24 32 45 Var
65.0 65.0 64.5 62.0 52.0 var
650 1,040 1,548 1,984 2,350 var 16
Maximum (v/c)* Ratio
0.29 0.47 0.68 0.85 1.00 var
0.28 0.44 0.66 0.84 1.00 var
(continuation of table which at previous page) Level of Maximum Density Minimum Speed Maximum Service Service (pc/mi/ln) (mph) Flow Rate (pcphpl) Free-Flow Speed = 60 mph
A B C D E F
10 16 24 32 45 var
A 10 B 16 C 24 D 32 E 45 F var *See Terms and Definitions
60.0 600 60.0 960 60.5 1,440 58.0 1,856 51.0 2,300 var var Free-Flow Speed = 55 mph 55.0 550 55.0 880 55.0 1,320 54.5 1,744 50.0 2,250 var var
Maximum (v/c)* Ratio
0.26 0.42 0.63 0.81 1.00 var
0.24 0.39 0.59 0.78 1.00 var
To illustrate where each LOS falls with respect to speed and flow rate, the chart below shows speed versus flow rate with corresponding levels of service A through E. LOS F lies beyond LOS E. The value of the slope of each line that separates the levels of service is the maximum density for that level of service.
For example, the line drawn for LOS E extends from the end of the free-flow speed lines to the origin and has a slope of 45.0 pc/mi/ln. Service flow rate E is the value that corresponds to the maximum flow rate, or capacity. Service flows C or D are usually used for most design or planning purposes because these levels of service are more acceptable to roadway users. Note that the flow rate at capacity for a free-flow speed of 70 mph is 2400 pcphpl. This capacity represents ideal traffic and roadway conditions. Also note that the value of capacity varies with the free-flow speed. 17
2.3.4.
Determining Flow Rate [d]
Determining the LOS for a basic freeway section involves two steps: 1. Adjusting a count or estimate of the hourly volume of vehicles to account for the effects of prevailing traffic conditions. This module addresses step one. 2. Adjusting the free-flow speed for the prevailing design conditions of that section. The module "Free-Flow Speed Adjustment" addresses step two. The hourly volume (in vehicles per hour) is changed to an equivalent passenger-car flow rate by allowing for the effects of heavy vehicles (buses, trucks and recreational vehicles) on traffic flow, the variation of traffic flow during the hour, and the characteristics of the driver population. The passenger-car equivalent flow rate is then reported on a per lane basis. Passenger-car equivalents in passenger car per hour per lane (pcphpl) are determined using the following equation:
v PHF N Vf f Where v p V PHF f HV f p
= 15-minute passenger-car equivalent flow rate (pcphpl) = hourly volume (vph) = peak-hour factor = heavy-vehicle adjustment factor = driver population factor
Values for the driver population factor, fp, range from 0.85 to 1.0. In general, the value of 1.0 is used to reflect commuter traffic. Use of a lower value reflects more recreational traffic. The peak hour and heavy-vehicle adjustment factors are described in their respective modules. The demonstration for this module uses values derived from the peak-hour and heavy-vehicle adjustment factor modules.
2.3.5.
Peak Hour Factor
Traffic engineers focus on the peak-hour traffic volume in evaluating capacity and other parameters because it represents the most critical time period. And, as any motorist who travels during the morning or evening rush hours knows, it’s the period during which traffic volume is at its highest. The analysis of level of service is based on peak rates of flow occurring within the peak hour because substantial short-term fluctuations typically occur during an hour. Common practice is to use a peak 15-minute rate of flow. Flow rates are usually expressed in vehicles per hour, not vehicles per 15 minutes. The relationship between the peak 15-minute flow rate and the full hourly volume is given by the peak-hour factor (PHF) as shown in the following equation:
volume PHF Peak rateHourly of low whitin the hour If 15-minute periods are used, the PHF is computed as:
PHF 4 VV Where 18
V V15
= peak-hour volume (vph) = volume during the peak 15 minutes of flow (veh/15 minutes)
Typical peak-hour factors for freeways range between 0.80 and 0.95. Lower factors are more typical for rural freeways or off-peak conditions. Higher factors are typical of urban and suburban peak-hour conditions.
2.3.6.
Heavy Vehicle Adjustment Factor [d]
Determining the adjustment factor for the presence of heavy vehicles is a two-step process: 1. Finding passenger-car equivalents for trucks, buses and recreational vehicles 2. Using the equivalent values and the percentage of each type to compute the adjustment factor, using the following equation:
f 1 PE 11 PE 1 Where f HV ET ER PT, PR
= heavy-vehicle adjustment factor = passenger-car equivalents for trucks and/or buses = passenger-car equivalents for recreational vehicles = proportion of trucks or buses and RVs in the traffic stream.
Finding ET and ER There are two methods for finding values of ET and ER and the choice of methods depends on the freeway grade conditions.
Method 1: If an extended length of freeway contains a number of upgrades, downgrades and level segments, but no one grade is long enough or steep enough to have a significant impact on traffic operations, finding E T and E R is relatively straightforward. ET and ER are shown in the following table for extended general segments where no one grade equal to or greater than 3 percent is longer than 1/4 mile, or longer than 1/2 mile for grades less than 3 percent.
CATEGORY E T Trucks and Buses Combined E R (RVs)
LEVEL 1.5 1.2
TYPE OF TERRAIN ROLLING MOUNTAINOUS 3.0 6.0 2.0 4.0
Method 2: There are three tables you can use to find ET and ER for isolated specific up and down grades: 1. The first table is used to find the passenger car equivalent for trucks and buses on upgrades that are more than 1/2 mile for grades less than 3 percent or 1/4 mile for grades of 3 percent or more. 2. The second table is used to find the passenger car equivalent for recreational vehicles on upgrades that are more than 1/2 mile for grades less than 3 percent or 1/4 mile for grades of 3 percent or more. 19
3. The third table is used to find the passenger car equivalent for trucks and buses on downgrades that are more than 4 miles for grades of 4 percent or more.
2.3.7.
Free-Flow Speed Adjustment [d]
Determining the LOS for a basic freeway section involves two steps: 1. Adjusting a count or estimate of the hourly volume of vehicles to account for the effects of prevailing traffic conditions. See the module "Determining Flow Rate" for information on Step One. 2. Adjusting the free-flow speed for the prevailing design conditions of that section. This module addresses the second step. The free-flow speed of a freeway section can be obtained directly by field measurement. If field measurements are not feasible, the free-flow speed can be estimated by the following equation, which accounts for the effects of physical characteristics: FFS = 70 – f LW – f LC – f N - f ID Where FSS f LW f LC f N f ID
= estimated free-flow speed = adjustment for lane width = adjustment for right-shoulder lateral clearance = adjustment for number of lanes = adjustment for interchange density
The adjustment factors can be obtained from the tables below. Table 1. Adjustment Factors for Lane Width Lane Width (ft) Reduction in Free-Flow Speed, f LW (mph) ≥ 12
0.0 2.0 6.5
11 10
Table 2. Adjustment Factors for Right-Shoulder Lateral Clearance Reduction in Free-Flow Speed, f LC (mph) Right Shoulder Lateral Clearance (ft) Lanes in One Direction ≥6
5 4 3 2 1 0
2 0.0 0.6 1.2 1.8 2.4 3.0 3.6
20
3 0.0 0.4 0.8 1.2 1.6 2.0 2.4
4 0.0 0.2 0.4 0.6 0.8 1.0 1.2
Table 3. Adjustment Factors for Number of Lanes Reduction in Free-Flow Speed, f N Number of Lanes (One Direction) ≥5
0.0 1.5 3.0 4.5
4 3 2
Table 4. Adjustment Factors for Interchange Density Reduction in Free-Flow Speed, f ID Interchanges per Mile ≤ 0.50
0.0 1.3 2.5 3.7 5.0 6.3 7.5
0.75 1.00 1.25 1.50 1.75 2.00
2.3.8.
Determining Level of Service and Density [d]
Once you have made the appropriate adjustments to the free-flow speed and have calculated the equivalent passenger-car flow rate, determining LOS for a basic freeway section is as simple as looking at the table given in the module "Level of Service Criteria and Capacity", or at the graph below.
If your free-flow speed calculation resulted in a speed other than 70, 65, 60 or 55 mph, you would construct the appropriate curve on the graph below. The curve would have the same general shape as those shown and would intersect the y-axis at the estimated (or measured) free-flow speed. The red line in the figure below presents an example of a curve drawn for an estimated free-flow speed of 63 mph.
21
Vehicle density is calculated by the following equation:
D vS where D v p S
2.3.9.
= density (pc/mi/ln), = flow rate (pcphpl), and = average passenger-car speed (mph).
Applications [d]
The methodology presented in the modules for this section may be used for the following applications: 1. Operational analysis. Known or projected design and traffic variables are used to estimate LOS, speed, and density of the traffic stream, as demonstrated in the module entitled "Determining Level of Service and Density". This application is used to evaluate impacts of alternative designs. 2. Design analysis. A forecasted demand volume, known design standards and a desired LOS are used to determine the appropriate number of lanes needed for a basic freeway section. The demonstration associated with this module uses a design approach. 3. Planning analysis. A desired LOS is used to determine the number of lanes needed. The difference between a planning analysis and a design analysis is that the design standards and the specifics of the demand volume may not be known. This application is beyond the scope of this training module.
2.4.
Professional Practice
In order to supplement your knowledge about the various concepts within Capacity and LOS Analysis, and to give you a glimpse of how these various topics are discussed in the professional environment, we have included selected excerpts from professional design manuals. 22
2.4.1.
Basic Freeway Section and Ideal Freeway Conditions
The following excerpt was taken from Chapter 3, page 3-1, of the 1997 revision of the Highway Capacity Manual published by the Transportation Research Board.
A freeway may be defined as a divided highway with full control of access and two or more lanes for the exclusive use of traffic in each direction. Freeways provide uninterrupted flow. There are no signalized or stop-controlled at-grade intersections, and direct access to and from adjacent property is not permitted. Access to and from the freeway is limited to ramp locations. Opposing directions of flow are continuously separated by a raised barrier, an at-grade median, or a raised traffic island. Operating conditions on a freeway primarily result from interactions among vehicles and drivers in the traffic stream and between vehicles and their drivers and the geometric characteristics of the freeway. Operations can also be affected by environmental conditions, such as weather or lighting conditions, by pavement conditions, and by the occurrence of traffic incidents.
2.4.2.
Determining Flow Rate
The following excerpt was taken from Chapter 3, pages 3-14 and 3-15, of the 1997 revision of the Highway Capacity Manual published by the Transportation Research Board.
The hourly flow rate must reflect the effects of heavy vehicles, the temporal variation of traffic flow during an hour, and the characteristics of the driver population. These effects are reflected by adjusting hourly volume counts or estimates, typically reported in vehicles per hour (vph), to arrive at an equivalent passenger-car flow rate in passenger cars per hour (pcph). The equivalent passenger-car flow rate is calculated using the heavy-vehicle and peak-hour adjustment factors and is reported on a per lane basis, or in passenger cars per hour per lane... Heavy Vehicle Adjustment Factor
Freeway traffic volumes that include a mix of vehicle types must be adjusted to an equivalent flow rate expressed in passenger cars per hour per lane. This adjustment is made using the factor fHV. Adjustments for the presence of heavy vehicles in the traffic stream apply for three vehicle types: trucks, buses, and RVs. There is no evidence to indicate any differences in performance characteristics between the truck and bus populations on freeways, so trucks and buses are treated identically.
2.4.3.
Free-Flow Speed and Flow Rate
The following excerpt was taken from Chapter 3, page 3-3, of the 1997 revision of the Highway Capacity Manual published by the Transportation Research Board.
All recent freeway studies indicate that speed on freeways is insensitive to flow if the flow is low to moderate. This is reflected in Figure 3-2 [reproduced in the Theory and Concept section entitled Free-Flow Speed and Flow Rate], which shows speed to be constant for flows up to 1,300 pcphpl for a 70-mph free-flow speed. For freeways with a lower free-flow speed, the region over which speed is insensitive to flow extends to even higher flow rates. Thus, free-flow speed is easily measured in the field as the average speed of passenger cars when flow rates are less than 1,300 23
pcphpl. Field determination of free-flow speed is easily accomplished by performing travel time or spot speed studies during periods of low flows. Note that although Figure 3-2 shows only curves for free-flow speeds of 75,70, 65, 60, and 55 mph, curves representing any free-flow speed between 75 and 55 mph can be obtained by interpolation. Also, the speed-flow curve representing a 75-mph [not shown in the figure included with this chapter] free-flow speed, which corresponds with the recent increase in the posted speed limit on many rural freeway sections throughout the United States, shown by a dashed line, is not based on empirical field research but was created by extrapolation from the 70-mph free-flow speed curve. Capacity at free-flow speeds greater than or equal to 70 mph is considered to be 2,400 pcphpl.
2.4.4.
Free-Flow Speed Adjustment
The following excerpt was taken from Chapter 3, pages 3-4 and 3-5, of the 1997 revision of the Highway Capacity Manual published by the Transportation Research Board.
Recent research has found that the free-flow speed on a freeway depends on the traffic and roadway conditions present on a given facility. These conditions are described in the following sections. Lane Width and Lateral Clearance
When lane widths are less than 12 feet, drivers are forced to travel closer to one another laterally than they would normally desire. The effect of restricted lateral clearance is similar. When objects are located too close to the edge of the median and roadside lanes, drivers in these lanes will shy away from them, positioning themselves further from the lane edge. This restricted lateral clearance has the same effect as narrow lanes: it forces drivers closer together laterally. Drivers have been found to compensate by reducing their speed. The closeness of objects has been found to have a greater effect on drivers in the right shoulder lane than on those in the median lane. Drivers in the median lane appear to be unaffected by lateral clearance when minimum clearance is 2 feet, whereas drivers in the right shoulder lane are affected when lateral clearance is less than 6 feet... Number of Lanes
The number of lanes on a freeway section influences free-flow speed. As the number of lanes increases, so does the opportunity for drivers to position themselves to avoid slow-moving traffic. In typical freeway driving, traffic tends to be distributed across lanes according to speed. Traffic in the median lane or lanes typically moves faster than in the lane adjacent to the right shoulder...
2.4.5.
LOS Criteria and Capacity
The following excerpt regarding LOS F was taken from Chapter 3, page 3-10, of the 1997 revision of the Highway Capacity Manual published by the Transportation Research Board.
LOS F describes breakdowns in vehicular flow. Such conditions generally exist within queues forming behind breakdown points. Such breakdowns occur for a number of reasons:
Traffic incidents cause a temporary reduction in the capacity of a short segment, so that the number of vehicles arriving at the point is greater than the number of vehicles that can move through it. 24
Points of recurring congestion exist, such as merge or weaving areas and lane drops where the number of vehicles arriving is greater than the number of vehicles discharged. In forecasting situations, any location where the projected peak-hour (or other) flow rate exceeds the estimated capacity of the location presents a problem.
Note that in all cases, breakdown occurs when the ratio of demand to actual capacity or the ratio of forecast demand to estimated capacity exceeds 1.00. Operations immediately downstream of such a point, however, are generally at or near capacity, and downstream operations improve (assuming that there are no additional downstream bottlenecks) as discharging vehicles move away from the bottleneck.
2.4.6.
Determining LOS and Density
The following excerpt was taken from Chapter 3, page 3-22, of the 1997 revision of the Highway Capacity Manual published by the Transportation Research Board.
The level of service on a basic freeway section can be determined directly from Figure 3-4 (this figure is presented in Theory and Concepts, Determining LOS and Density) on the basis of the freeflow speed and the flow rate. The procedure is as follows: Step 1. Define and segment the freeway section as appropriate. Step 2. On the basis of the measured or estimated free-flow speed on the freeway segment, construct an appropriate speed-flow curve of the same shape as the typical curves shown in Figure 3-2. The curve should intercept the y-axis at the free-flow speed. Step 3. On the basis of the flow rate, v p, read up to the free-flow speed curve identified in Step 2 and determine the average passenger-car speed and level of service corresponding to that point. Step 4. Determine the density of flow as
D
Where D v p S
= density (pc/mi/ln), = flow rate (pcphpl), and = average passenger-car speed (mph).
The level of service can also be determined using the density ranges provided in Table 3-1 [this table is presented in Theory and Concepts, LOS Criteria].
2.5.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable roadway design concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic.
2.5.1.
Peak Hour Factor
The results of a traffic count taken between 5:00 p.m. and 6:00 p.m. are given below: 25
Time Interval 5:00-5:15 5:15-5:30 5:30-5:45 5:45-6:00
Volume (vehicles)
p.m. p.m. p.m. p.m.
900 1000 1200 850
5:00-6:00 p.m.
3950 total vehicles
The peak hour factor needs to be determined for this section of freeway.
Solution The equation for calculating the peak hour factor for 15-minute periods is as follows:
PHF 4 VV Where V V15
= peak-hour volume (vph) – 3950 = volume during the peak 15 minutes of flow (veh/15 minutes) – 1200
Therefore,
PHF 43950 1200 0.82 2.5.2.
Heavy Vehicle Adjustment Factor
A six lane freeway has a flow of 3500 vehicles. This flow consists of 180 trucks per hour, 200 RVs per hour, 350 passenger buses per hour and the remainder of passenger. Calculate the heavy vehicle adjustment factor for a ½ mile section of this freeway that has a +4% grade.
Solution The percentage of trucks is 5% [(180/3500) × 100], buses is 10% [(350/3500) × 100] and RVs is 6%. The heavy vehicle adjustment factor is calculated using the following equation:
f 1 PE 11 PE 1 ET ER PT PR
= passenger-car equivalents for trucks and/or buses = 3.0 (see “Passenger-Car Equivalents For Trucks And Buses On Specific Upgrades” excel demonstration ) = passenger-car equivalents for recreational vehicles = 2.0 (see “Passenger-Car Equivalents For Trucks And Buses On Specific Upgrades” excel demonstration ) = proportion of trucks/buses in the traffic stream = 5 + 10 = 15%. = proportion of RVs in the traffic stream = 6%
Therefore,
f 1 0.153 11 0.062 1 0.74 26
2.5.3.
Calculating Flow Rate
A four-lane highway (two lanes in each direction) has a 2,500-vph peak-hour volume that includes mostly commuter traffic, 5% trucks and 6% buses. The section of highway that we are interested in is in rolling terrain. The peak-hour factor has been determined by earlier studies to be 0.95. What is the passenger-car equivalent (or service) flow rate for this section of freeway?
Solution The equation for calculating the passenger-car equivalent flow rate is:
v PHF N Vf f V PHF f HV
= peak hour volume (vph) = 2,500 = peak-hour factor = 0.95 = heavy-vehicle adjustment factor
1 1 f 1 PE 1 PE 1 1 0.05 0.063 102 1 0.82 (for ET and ER , use the small table for extended general freeway segments) f p v p
= driver population factor = 1.0 for commuter traffic = 15-minute passenger-car equivalent flow rate (pcphpl)
v 0.95 22500 0.82 1 1.605 2.5.4.
Free-Flow Speed Adjustment
An existing six-lane freeway in an urban area has the following physical characteristics:
11-ft lanes 2-ft lateral clearance on outer shoulders interchange density of 1 interchange per mile.
Calculate the free-flow speed for this section of freeway.
Solution When actual field measurements aren’t available, free-flow speed is estimated by the following equation, which utilizes the tables given in the Free-Flow Speed Adjustment theory and concept subject: FFS = 70 – f LW – f LC – f N – f ID where f LW f LC
= adjustment for lane width = 2.0 = adjustment for right-shoulder lateral clearance = 1.6 27
f N f ID FSS
= adjustment for number of lanes = 3.0 = adjustment for interchange density = 2.5 = estimated free-flow speed = 70 – 2.0 – 1.6 – 3.0 – 2.5 = 60.9 mph
2.5.5.
Determining LOS and Density
An existing freeway has the following characteristics:
8 lanes Carries a flow of 4000 vph Trucks make up 8% and RVs 2% of the flow 12-foot lane widths Interchange density is less than 0.5 per mile Obstructions within 4 feet of the outside edges of the freeway PHF is 0.95
We are interested in determining the existing LOS and density as well as the maximum service flow rate at capacity (LOS E) for a two-mile section of this freeway with a grade of +4%
Solution In order to determine the existing LOS using the applicable graph or table, we need to calculate (1) the service flow rate and (2) the adjusted free-flow speed. 1. The service (or passenger-car equivalent) flow rate calculation is as follows:
v PHF N Vf f V PHF f HV
= hourly peak hour volume (vph) = 4,000 = peak-hour factor = 0.95 = heavy-vehicle adjustment factor =
f 1 PE 11 PE 1 1 0.086 11 0.023 1 0.69 f p v p
= driver population factor = 1.0 (assumed) = 15-minute passenger-car equivalent flow rate (pcphpl)
v 0.95 44000 0.69 1 1.526 2. The free-flow speed calculation is as follows: FFS = 70 – f LW – f LC – f N - f ID Where f LW f LC f N f ID
= adjustment for lane width = 0 = adjustment for right-shoulder lateral clearance = 0.4 = adjustment for number of lanes = 1.5 = adjustment for interchange density = 0 28
FSS
= estimated free-flow speed = 70 – 0 – 0.4 – 1.5 – 0 = 68.1 mph
We then draw the free-flow speed curve of 68.1 mph on the graph as shown below.
At the flow rate of 1526 pcphpl, the LOS is C. Density is calculated as:
D vS Where v p S D
= flow rate (pcphpl) = 1,526, and = average passenger-car speed (mph) = 67 (from the graph) and = density (pc/mi/ln) = 23.7 pc/mi/ln.
The flow at capacity can be taken from the graph above, at the end of the red line as 2380 pcphpl.
2.5.6.
Design Application
A new 1-1/2 mile section of freeway is going to be built in an urban area with the following characteristics:
5% grade 1.5 interchanges per mile Uphill traffic volume of 3080 vehicles per hour 5% trucks, no buses and 2% RVs Estimated peak hour factor if 0.95 Full shoulders 12-foot-wide lanes
How many lanes will be required to provide LOS C for the uphill direction? If we assume the same traffic and design components, will the downhill lane requirement be the same?
Solution We want to solve the following equation: 29
N v PHFV f f Where: V PHF f HV f p
= hourly volume (vph) = 3,080 = peak-hour factor = 0.95 = heavy-vehicle adjustment factor (equation shown below) = driver population factor = 1.0 for commuter traffic
1 f 1 PE 1 PE 1 (for ET and ER use the applicable passenger-car equivalent tables) For the uphill section,
1 f 10.059 1 0.024.51 0.68 For the downhill section,
f 1 0.051.511 0.021.2 1 0.97 The value for vP can be interpolated from the table or the graph given in the module entitled "Level of Service Criteria and Capacity" after we've adjusted the free flow speed. Adjusted Free-flow speed = FFS = 70 – f LW – f LC – f N – f ID Where f LW f LC f N f ID FFS
= adjustment for lane width = 0 = adjustment for right-shoulder lateral clearance = 0 = adjustment for number of lanes (we'll assume 3 lanes to begin with and come back to check to see if it agrees with our final solution) = 3.0 = adjustment for interchange density = 5 = estimated free-flow speed = 70 – 0 – 0 – 3.0 – 5 = 62
By interpolation, the maximum service flow rate (vP) for LOS C at a free-flow speed of 62 mph is 1480 pcphpl. Therefore, for the uphill section: N = 3080 / (1480 × 0.95 × 0.68 × 1) = 3.2 or 4 lanes Checking the free-flow speed: 70 – 0 – 0 – 1.5 – 5 = 63.5 And the maximum service flow rate for LOS C for a free-flow speed of 63.5 mph is approximately 1520 vph. Let's confirm that 4 lanes is still appropriate:
30
N = 3080 / (1520 × 0.95 × 0.68 × 1) = 3.1 or 4 lanes (always round up). For the downhill section, and going back to the 3 lane assumption because the heavy vehicle adjustment factor is quite a bit larger: N = 3080 / (1480 × 0.95 × 0.97 × 1) = 2.3 or, rounding up, 3 lanes are needed in the downhill direction.
2.6.
Glossary
Basic Freeway Section: Freeway segments that are outside of the influence of ramps or weaving sections. Capacity: The maximum number of vehicles that can reasonably be expected to traverse over a specific section of roadway, in one direction, during a given time period and under the prevailing conditions. This is expressed in passengers cars per hour per lane (pcphpl). Design Conditions: The physical qualities of a basic freeway section such as lane width, shoulder clearances and density of interchanges (on and off ramps). Density: The number of vehicles in a one-mile segment of one lane of traffic. Flow rate: The rate, in vehicles per hour or passenger cars per hour, at which traffic traverses a freeway segment. Free-flow speed: The speed of traffic flow that is unaffected by upstream or downstream conditions. Ideally, free-flow speed is the speed that occurs when density and flow are zero. Level of Service (LOS): A measure of the operating conditions of a basic freeway section. There are six categories – A through F – with F being the least desirable. Peak-hour factor: The ratio of the number of vehicles during the peak hour to four times the number of vehicles entering the traffic stream during the peak 15-minute period. Traffic conditions: The qualities of traffic such as traffic speed, density, vehicle types and traffic flow rate. V/C ratio: The proportion of the facility’s capacity being utilized by current or projected traffic. v/c = rate of flow/capacity.
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3. Geometric Design 3.1.
Introduction
There are an infinite number of ways to get from point A to point B. Geometric design is the aspect of transportation engineering that deals with selecting the best path between those points. A good geometric design will balance operational efficiency, comfort, safety, convenience, cost, environmental impact, and aesthetics. Geometric Design can be a difficult process, and many professionals rely on the assistance of design manuals. The American Association of State Highway and Transportation Officials has published a design manual entitled: A Policy on Geometric Design of Highways and Streets, which provides engineers with a guide to geometric design that is based on years of practical experience and research. This chapter is designed to help the undergraduate engineer in his/her studies of the more quantifiable aspects of geometric design. Our focus here is on the geometric aspect, or the actual shape of the roadway.
3.2.
Lab Exercises
This exercise will help increase your understanding of Geometric Design, by presenting a more complicated problem that requires more thorough analysis.
3.2.1.
Lab Exercise One: Geometric Design
A section of an existing two-lane rural highway will be modified, requiring the connection of two intersecting one-percent grades with a vertical curve. (See Figure 1). You have been asked to determine the length of the vertical curve necessary so that sufficient sight distance is provided along this vertical curve for one vehicle to safely pass another.
This assignment is divided into several parts:
How much distance is required for one vehicle to safely pass another vehicle and return again to the travel lane? What is the overall sight distance required with consideration given to an oncoming vehicle? What length of vertical curve is required to accommodate this sight distance? How do your computations compare with the AASHTO design standard? 32
Tasks To Be Completed As you complete the following tasks, you will determine the required sight distance for passing and the required length of the vertical curve connecting the two grades. Task 1. Consider the following situation. Vehicles are traveling along a two-lane rural highway. The speed limit on the highway is 55 miles per hour. A passenger car is following a slower vehicle traveling at 45 miles per hour. The passenger car would like to travel at the speed limit of 55 miles per hour. Describe the tasks that must be performed by the driver of the passenger car in order to safely pass the slower vehicle. These tasks should be defined in terms of both the decisions and the maneuvers to be made by the driver, from the decision to pass to the maneuver back into the travel lane. Task 2. Identify the key events relating to this passing maneuver on a time-distance diagram. Plot distance on the y-axis and time on the x-axis. Sketch the key events (without regard for computations yet) relating both the lead (slower) vehicle and the following (faster) vehicle. Task 3. Calculate the kinematic characteristics (position, velocity, and acceleration) of both the passing and the passed vehicles for each stage of the passing maneuver that you identified in Task 1. What distance is traveled by each vehicle during these stages? What is the resultant position of the vehicles at each stage? How much time does each stage consume? Task 4. Now consider the effects of an oncoming vehicle. What distance is traveled by the oncoming vehicle during the relevant stages of the passing maneuver? In determining this distance, you should identify the point of the passing maneuver that can be described as the point of no return for the passing driver. Task 5. Using a spreadsheet program, prepare a time-distance plot of the three vehicles involved in this passing maneuver. This should provide a visual check for you to make sure that your assumptions and calculations are correct. Task 6. Integrate the results of Tasks 1 through 5 above to calculate the required passing sight distance for the passing vehicle. How do your results compare with the AASHTO model and design information? Why do you suppose that these differences exist? (Note: the standards used by AASHTO are based on certain kinematic assumptions and simplifications, as well as field measurements performed a number of years ago; your standard should reflect both your own reasoning regarding the passing maneuver as well as a clear documentation of this logic). Task 7. The grades of the section for which you need to design the vertical curve are both one percent. Using the relationships between sight distance and the length of the vertical curve, compute the minimum length of the vertical curve required to accommodate this passing maneuver. If the required length of the curve is more than 2000 feet, then a no-passing zone should be established for the curve. If the length of the curve is less than 2000 feet, then a passing zone can be established. Task 8. Prepare a brief report summarizing the results of your work.
Assumptions The following data will be useful to you in this problem. 1. The acceleration rate for the passing vehicle is 1.47 miles per hour per second. 33
2. The perception/reaction time for a passing maneuver is 1 second. 3. Safe following distance is assumed to be 2 seconds. 4. Minimum clearance between the passing vehicle and the opposing vehicle is 1 second.
3.3.
Theory and Concepts
A course in transportation engineering wouldn't be complete without discussing some elements of Geometric Design. Most junior level courses cover several aspects of Geometric Design, including the topics listed below. As these discussions are only meant to supplement your learning experience, please don't forget to read your textbook. To begin learning about these Geometric Design principles, just click on the link of your choice. Topics followed by the characters '[d]' include an Excel demonstration.
3.3.1.
Brake Reaction Time
The brake reaction time is the amount of time that elapses between the recognition of an object or hazard in the roadway and the application of the brakes. The length of the brake reaction time varies widely between individual drivers. An alert driver may react in less than 1 second, while other drivers may require up to 3.5 seconds. The brake reaction time depends on an extensive list of variables, including:
driver characteristics such as attitude, level of fatigue, and experience. environmental conditions such as the clarity of the atmosphere and the time of day the properties of the hazard or object itself, such as size, color and movement.
To make highways reasonably safe, the engineer must provide a continuous sight distance (see the stopping sight distance module) equal to or greater than the stopping sight distance. As an integral part of the stopping sight distance, a value for the brake reaction time must be assumed. Extensive research has shown that 90% of the driving population can react in 2.5 seconds or less. The brake reaction time normally used in design, therefore, is 2.5 seconds. The distance traveled during the brake reaction time can be calculated by multiplying the vehicle's initial speed by the brake reaction time. Both the brake reaction time and the braking distance are used in the calculation of the stopping sight distance. Therefore, it is suggested that you read the braking distance module before proceeding to the stopping sight distance module.
3.3.2.
Braking Distance [d]
The braking distance is the distance that a vehicle travels while slowing to a complete stop. The braking distance is a function of several variables. First, the slope (grade) of the roadway will affect the braking distance. If you are going uphill, gravity assists you in your attempts to stop and reduces the braking distance. Similarly, gravity works against you when you are descending and will increase your braking distance. Next, the frictional resistance between the roadway and your tires can influence your braking distance. If you have old tires on a wet road, chances are you'll require more distance to stop than if you have new tires on a dry road. The last parameter that we will consider is your initial velocity. Obviously, the higher your speed the longer it will take you to stop, given a constant deceleration. The equation used to calculate the braking distance is a child of a more general equation from classical mechanics. The parent equation is given below. 34
V V 2 a d Where: Vf Vo a d
= Final velocity = Initial velocity = Acceleration rate = Distance traversed during acceleration
When calculating the braking distance, we assume the final velocity will be zero. Based on this, the equation can be manipulated to solve for the distance traversed during braking.
V d 2a Notice that the distance will be positive as long as a negative acceleration rate is used. The acceleration of a braking vehicle depends on the frictional resistance and the grade of the road. From our knowledge of the frictional force, we know that the acceleration due to friction can be calculated by multiplying the coefficient of friction by the acceleration due to gravity. Similarly, we know from inclined plane problems that a portion of the car's weight will act in a direction parallel to the surface of the road. The acceleration due to gravity multiplied by the grade of the road will give us an estimate of the acceleration caused by the slope of the road. The final formula for the braking distance is given below. Notice how the acceleration rate is calculated by multiplying the acceleration due to gravity by the sum of the coefficient of friction and grade of the road.
V d 2gf G Where: d g G V f
= Braking Distance (ft) = Acceleration due to gravity (32.2 ft/sec2) = Roadway grade as a percentage; for 2% use 0.02 = Initial vehicle speed (ft/sec) = Coefficient of friction between the tires and the roadway
The braking distance and the brake reaction time are both essential parts of the stopping sight distance calculations. In order to ensure that the stopping sight distance provided is adequate, we need a more in-depth understanding of the frictional force. The value of the coefficient of friction is a difficult thing to determine. The frictional force between your tires and the roadway is highly variable and depends on the tire pressure, tire composition, and tread type. The frictional force also depends on the condition of the pavement surface. The presence of moisture, mud, snow, or ice can greatly reduce the frictional force that is stopping you. In addition, the coefficient of friction is lower at higher speeds. Since the coefficient of friction for wet pavement is lower than the coefficient of friction for dry pavement, the wet pavement conditions are used in the stopping sight distance calculations. This provides a reasonable margin of safety, regardless of the roadway surface conditions. The table below gives a few values for the frictional coefficient under wet roadway surface conditions (AASHTO, 1984). 35
3.3.3.
Design Speed (mph)
Coefficient of Friction (f)
20 30 40 60
0.40 0.35 0.32 0.29
Stopping Sight Distance [d]
(Note: If you feel uncomfortable with your understanding of brake reaction time or braking distance, you might want to review those topics before continuing with Stopping Sight Distance.)
The stopping sight distance is the sum of the braking distance and the distance traversed during the brake reaction time. In other words, it is the length of roadway that should be visible ahead of you, in order to ensure that you will be able to stop if there is an object in your path. For example, let us say that you are negotiating a horizontal curve in a highway when you notice an object 200 feet ahead of you. If the distance you travel during your brake reaction time is 100 feet and your braking distance is 130 feet, you will not be able to avoid the collision. If the horizontal curve were not as tight, you would be able to see the object at a distance of 250 feet, which would allow you to stop 20 feet short of the object. A properly designed roadway will provide the minimum stopping sight distance at every point along its length. In order to calculate the actual sight distance based on the geometry of the roadway, some assumptions are necessary. The main assumptions are the height of the driver's eyes above the roadway surface and the height of the object or hazard. In geometric design, these values are 3.5 feet and 0.5 feet, respectively. This represents a reasonable worst-case scenario. To include the stopping sight distance in your design, calculate the stopping sight distance for a vehicle traveling on your roadway at the design speed, and then make sure the actual sight distance that you provide is at least as great as the stopping sight distance.
Trucks and Busses Trucks and busses require longer braking distances than passenger cars, but their stopping sight distances are not considered in most designs. This is because the driver's eyes are higher and their sight distance is consequently increased. The drivers of these vehicles also tend to be more experienced and more alert. The net effect is that large vehicles can avoid obstacles even though the road was not specifically designed with them in mind. The engineer must decide when large vehicles may need extra sight distances and provide these distances where necessary.
3.3.4.
Decision Sight Distance
Normally, the stopping sight distance is an adequate sight distance for roadway design. However, there are cases where it may not be appropriate. In areas where information about navigation or hazards must be observed by the driver, or where the driver’s visual field is cluttered, the stopping sight distance may not be adequate. In addition, there are avoidance maneuvers that are far safer than stopping, but require more planning by the driver. These may not be possible if the minimum stopping sight distance is used for design. In these instances, the proper sight distance to use is the decision sight distance.
36
The decision sight distance is the distance traversed while recognizing an object or hazard, plotting an avoidance course, and making the necessary maneuvers. Unlike the stopping sight distance, the decision sight distance is quite complex. Various design values for the decision sight distance have been developed from research. The table below gives a few values for the decision sight distance (AASHTO, 1994). Design Speed (km/h) 50 80 90 110
Decision Sight Distance (meters) Stop Rural Road 75 155 185 265
Stop Urban Road 160 300 360 455
Adjustment Rural Road 145 230 275 335
Adjustment Suburban Road 160 275 320 390
Adjustment Urban Road 200 315 360 435
It is up to the engineer to decide when to use the decision sight distance. Providing the extra sight distance will probably increase the cost of a project, but it will also increase safety. The decision sight distance should be provided in those areas that need the extra margin of safety, but it isn’t needed continuously in those areas that don't contain potential hazards.
3.3.5.
Passing Sight Distance [d]
While passing is not an event that is a major factor in the design of four-lane highways, it is a critical component of two-lane highway design. The capacity of a two-lane roadway is greatly increased if a large percentage of the roadway's length can be used for passing. On the other hand, providing a sufficient passing sight distance over large portions of the roadway can be very expensive. Simply put, the passing sight distance is the length of roadway that the driver of the passing vehicle must be able to see initially, in order to make a passing maneuver safely. Our real goal is to provide most drivers with a sight distance that gives them a feeling of safety and that encourages them to pass slower vehicles. Calculating the passing sight distance required for a given roadway is best accomplished using a simple model. The model that is normally used incorporates three vehicles, and is based on six assumptions: 1) The vehicle being passed travels at a constant speed throughout the passing maneuver. 2) The passing vehicle follows the slow vehicle into the passing section. 3) Upon entering the passing section, the passing vehicle requires some time to perceive that the opposing lane is clear and to begin accelerating. 4) While in the left lane, the passing vehicle travels at an average speed that is 10 mph faster than the vehicle being passed. 5) An opposing vehicle is coming toward the passing vehicle. 6) There is an adequate clearance distance between the passing vehicle and the opposing vehicle when the passing vehicle returns to the right lane. Under these assumptions, the passing sight distance can be divided into four quantifiable portions: d1 - The distance the passing vehicle travels while contemplating the passing maneuver, and while accelerating to the point of encroachment on the left lane. 37
d2 - The length of roadway that is traversed by the passing vehicle while it occupies the left lane. d3 - The clearance distance between the passing vehicle and the opposing vehicle when the passing vehicle returns to the right lane. d4 - The distance that the opposing vehicle travels during the final 2/3 of the period when the passing vehicle is in the left lane. Because the purpose of these specific distances might not be obvious at this point, a short discussion of each of these distances can be found below. In addition, figure 1.0 below gives a graphical explanation of these distances.
Figure 1.0: Diagram of Passing Sight Distance Components Source: AASHTO, 1994
d1- The perception-reaction-acceleration distance isn't hard to understand or to justify. The only aspect of this distance that might be confusing is the simultaneous nature of the perception and acceleration. Some drivers will begin accelerating before they enter the passing section and will continue to accelerate while they scan the opposing lane for traffic. These drivers tend to accelerate at a reduced rate. Other drivers will avoid accelerating until they have determined that the opposing lane is clear, but they will accelerate at a higher rate once they have decided to pass. The net effect is that the perception-reaction-acceleration distance is identical for both types of drivers. The distance d1 and the corresponding time t1 were measured for several different passing vehicle speeds. More recent research has confirmed that the accepted values are conservative. See table 1.0. d2- The distance traveled during the occupancy of the left lane is also easy to understand. Since the speed of the passing vehicle was assumed to be 10 mph faster than the overtaken vehicle, all we need to know to calculate the distance d2 is the time that the passing vehicle occupies the left lane. Values for this time interval were measured for several different passing vehicle speeds. These measured values were then used to develop design values for d2. See table 1.0. d3- The clearance distance might not seem necessary at first, but for now let’s take it on faith that an opposing vehicle is necessary. If this is the case, a maneuver that feels safe will require that a certain length of roadway is present between the passing vehicle and the opposing vehicle when the passing vehicle returns to the relative safety of the right lane. The clearance distance that drivers require depends on their personality. A timid driver might require several hundred feet of clearance distance, while a more aggressive driver might consider exchanging side mirrors a perfectly acceptable practice. Studies have shown that the clearance distance is normally between 100 and 300 feet. See table 1.0. d4- The opposing vehicle encroachment distance is the distance that seems to be the most troubling for students. Let us picture a passing section that is terminated by a sharp reduction in grade, which prevents the passing driver from seeing any vehicles beyond the end of the passing section. Let us also assume that the length of the passing section is equal to the sum of the distances d1 and d2. Our 38
passing vehicle driver could pass the slower vehicle before leaving the passing section, but she might be flirting with destiny in doing so. Her principal problem is that she can't see if there are any opposing vehicles beyond the passing section that might conflict with her during the maneuver. The question now is, how much extra sight distance would she need to feel secure that an opposing vehicle would not conflict with her while she is in the left lane? If we assume that she can abort her maneuver if an opposing vehicle appears during the interval t1 or during the first third of the interval t2, we can reduce the sight distance that we need to provide. Let’s say that we make the passing section length equal to the passing sight distance as defined in reality (d = d1 + d 2 + d 3 + d4). If an opposing vehicle appears just after the first third of the interval t2 is over, the passing car can still safely pass the slower car and return to the right lane before the opposing car becomes a threat. This is because the opposing vehicle is a distance 2/3 × d2 +d3 + d 4 away from the passing vehicle. By the time that the passing vehicle has traveled the remaining 2/3 × d2 and returned to the right lane, the opposing car will have traveled d4, and the clearance distance d3 will separate them. This is why we add the distances d3 and d4 to the passing sight distance. The distance d4 is calculated by multiplying the speed of the opposing vehicle (normally assumed to be the speed of the passing vehicle) by 2/3 × t2. The table below summarizes the results of field observations directed toward quantifying the various aspects of the passing sight distance (AASHTO, 1994).
Speed Group (km/h)
50-65
66-80
81-95
96-110
Average Passing Speed (km/h)
56.2
70.0
84.5
99.8
Initial Maneuver:
Average acceleration (km/h/s)
2.25
2.30
2.37
2.41
Time (s)
3.6
4.0
4.3
4.5
Distance Traveled (m)
45
65
90
110
Occupation of the Left Lane:
Time (s)
9.3
10.0
10.7
11.3
Distance Traveled (m)
145
195
250
315
55
75
90
Clearance Length:
Distance Traveled (m)
30 Opposing Vehicle:
Distance Traveled (m)
95
130
165
210
Total Distance (m)
315
445
580
725
Now that we know how to calculate the required passing sight distance, how do we calculate the actual passing sight distance that we have provided in our geometric design? To do this, we simply assume that the driver's eyes are at a height of 3.5 ft from the road surface and the opposing vehicle is 4.25 ft tall. The actual passing sight distance is the length of roadway ahead over which an object 4.25 ft tall would be visible, if your eyes were at an elevation of 3.5 ft. 39
3.3.6.
Horizontal Alignment
Horizontal alignment is a broad term that encompasses several aspects of transportation engineering. In this discussion, we will focus on the design of horizontal curves. The key steps in the design of horizontal curves are listed below. This will serve as a guide, as you explore the remaining topics within the horizontal alignment section of geometric design. 1. 2. 3. 4. 5.
Determine a reasonable maximum superelevation rate. Decide upon a maximum side-friction factor. Calculate the minimum radius for your horizontal curve. Iterate and test several different radii until you are satisfied with your design. Make sure that the stopping sight distance is provided throughout the length of your curve. Adjust your design if necessary. 6. Design the transition segments. Now that you have a feel for the general design procedure, you can begin to explore the various steps within the procedure in greater detail. Feel free to return to this guide whenever you wish - it isn't hard to lose sight of the greater plan while battling the details.
3.3.7.
Superelevation and Side-Friction
Most highways will change directions several times over the course of their lengths. These changes may be in a horizontal plane, in a vertical plane, or in both. The engineer is often charged with designing curves that accommodate these transitions, and consequently must have a good understanding of the physics involved. The superelevation of the highway cross-section and the side-friction factor are two of the most crucial components in the design of horizontal curves. The superelevation is normally discussed in terms of the superelevation rate, which is the rise in the roadway surface elevation as you move from the inside to the outside edge of the road. For example, a superelevation rate of 10% implies that the roadway surface elevation increases by 1 ft for every 10 ft of roadway width. The sidefriction factor is simply the coefficient of friction between the design vehicle's tires and the roadway. Whenever a body changes directions, it does so because of the application of an unbalanced force. In the special case of a body moving in a circular path, the force required to keep that body traveling in a circular path is called the centripetal force. When vehicles travel over a horizontal curve, it is this centripetal force that keeps the vehicles from sliding to the outside edge of the curve. In the simplest case, where the road is not banked, the entire centripetal force is provided by the friction between the vehicle's tires and the roadway. If we add some side-slope or superelevation to the cross-section of the roadway, some of the centripetal force can be provided by the weight of the car itself. High rates of superelevation that make cornering more comfortable during the summer by requiring less frictional force, can make winter driving ponderous by causing slow-moving vehicles to slip downhill toward the inside of the curve. Because of this, there are practical maximum limits for the rate of superelevation. In areas where ice and snow are expected, a superelevation rate of 8% seems to be a conservative maximum value. In areas that are not plagued by ice and snow, a maximum superelevation rate of 10-12% seems to be a practical limit. Both modern construction techniques and driver comfort limit the maximum superelevation rate to 12%. 40
The side-friction factor has practical upper limits as well. As was discussed in the braking distance module, the coefficient of friction is a function of several variables, including the pavement type and the vehicle speed. In every case, the side-friction factor that is used in design should be well below the side-friction factor of impending release. In addition to the safety concerns, drivers don't feel comfortable if the roadway seems to rely heavily on the frictional force. Several studies aimed at determining the maximum side-friction factors that are comfortable for drivers have been conducted. Some of the results from these studies are tabulated below. (AASHTO, 1994) Speed (km/h)
Comfortable Side-Friction Factor
40 50 55-80 > 110
0.21 0.18 0.15 < 0.10
The side-friction factors that are employed in the design of horizontal curves should accommodate the safety and comfort of the intended users. The module on horizontal curve minimum radii will bring the effects of the superelevation rate and the side-friction factor together. Both of these concepts contribute to the final alignment of horizontal curves.
3.3.8.
Minimum Radius Calculations [d]
Calculating the minimum radius for a horizontal curve is based on three factors: the design speed, the superelevation, and the side-friction factor (see superelevation and sidefriction factor modules). The minimum radius serves not only as a constraint on the geometric design of the roadway, but also as a starting point from which a more refined curve design can be produced. For a given speed, the curve with the smallest radius is also the curve that requires the most centripetal force. The maximum achievable centripetal force is obtained when the superelevation rate of the road is at its maximum practical value, and the side-friction factor is at its maximum value as well. Any increase in the radius of the curve beyond this minimum radius will allow you to reduce the side-friction factor, the superelevation rate, or both. Using the equations for circular motion, friction, and inclined plane relationships, the following equation has been derived.
V R 127e f 100 Where: R min V emax f max
= Minimum radius of the curve (m) = Design velocity of the vehicles (km/h) = Maximum superelevation rate as a percent = Maximum side-friction factor
This equation allows the engineer to calculate the minimum radius for a horizontal curve based on the design speed, the superelevation rate, and the side friction factor.
41
3.3.9.
Design Iterations
In many ways, horizontal alignment is an art form. The goal is to produce a horizontal curve that is comfortable and safe to use, and also cost efficient and aesthetically pleasing. The first step is to calculate the radius of the horizontal curve. We can calculate the radius for any combination of superelevation and side-friction factors using the equation below.
V R 127 e f 100 Where: R V e f
= The radius of the curve (m) = Design velocity of the vehicles (km/h) = Cross-section superelevation rate as a percent = Side-friction factor
As long as the radius of your curve is above the minimum radius as described in the minimum radius module, and as long as you haven't exceeded the practical values for the superelevation or for the side-friction factor, you know that your design is acceptable. You will probably need to test several different curve radii before you select your final design. While iterating, you also need to consider other factors: the cost, environmental impacts, sight distances, and, of course, the aesthetic consequences of your curve. Most surveying books contain a complete chapter on the layout of horizontal curves, and consequently, we won't delve into the surveying issues. Please refer to your surveying texts for this information.
3.3.10.
Horizontal Curve Sight Distance [d]
Once you have a radius that seems to connect the two previously disjointed sections of roadway safely and comfortably, you need to make sure that you have provided an adequate stopping sight distance throughout your horizontal curve. Sight distance can be the controlling aspect of horizontal curve design where obstructions are present near the inside of the curve. To determine the actual sight distance that you have provided, you need to consider that the driver can only see the portion of the roadway ahead that is not hidden by the obstruction. In addition, at the instant the driver is in a position to see a hazard in the roadway ahead, there should be a length of roadway between the vehicle and the hazard that is greater than or equal to the stopping sight distance. See figure 1.0 below.
Figure 1.0: Sight Distance 42
Because the sight obstructions for each curve will be different, no general method for calculating the sight distance has been developed. If you do have a specific obstruction in mind, however, there is an equation that might be helpful. This equation involves the stopping sight distance, the degree of the curve, and the location of the obstruction.
SD cos M 5730 1 D 200 Where: M D S R
= Distance from the center of the inside lane to the obstruction (ft.) = Degree of the curve. Where R = 5730 / D = Stopping sight distance (ft) = Radius of the curve (ft)
Once your rough design has been adjusted to accommodate the sight distance restrictions, and you are satisfied with the aesthetic and financial consequences of your superelevation scheme, you can begin to polish your design into its final form.
3.3.11.
Transition Segments
Often, horizontal curves are more comfortable and more aesthetically pleasing if the change in roadway cross-section and curvature is effected over a short transitional segment. The gradual change in curvature is produced by using a spiral curve. The radius of the spiral curve starts at infinity and is gradually reduced to the radius of the circular curve that you designed originally. Adding the spiral curve causes the centripetal acceleration to build up gradually, which is more comfortable for vehicle occupants. The equation commonly employed to calculate the minimum length of the spiral transition segment is given below.
3. 1 5 v L R C Where: L v R C
= Minimum length of the spiral curve (ft) = Speed (mph) = Circular curve radius (ft) = Centripetal acceleration development rate (usually between 1 and 3 ft/sec3)
The other purpose of the transition segment is to gradually change the cross-section of the roadway from normal to superelevated. This can be accomplished by rotating the cross-section around any line parallel to the roadway. The engineer should keep water drainage in mind while considering all of the available cross-section options. Opinions vary as to how fast the pavement cross-section should change, but most people agree that the change in curvature and the change in cross-section should occur in concert with one another. You should look at your local geometric design policy for more specific information regarding transition segments.
3.3.12.
Vertical Alignment
The topics discussed under vertical alignment can be divided into two categories: the design of highway sections that have ascending or descending grades, and the design of vertical curves that connect these segments of ascending and descending grades. 43
Grade is a measure of the inclination, or slope, of the roadway. It is defined as the rise over the run. In other words, a 10% grade simply means that the elevation of the roadway increases by 10 feet for every 100 feet of horizontal distance. The issues that surround the design of inclined roadway sections revolve around safety and level of service. Vertical curves, however, are slightly more complicated. The best feature of the vertical curve, in its purest form, is that it doesn't require any changes in the roadway cross-section. In this respect, vertical curves are easier to design than horizontal curves. On the other hand, vertical curves have a parabolic shape instead of the simple circular shape of the pure horizontal curve. Because this makes certain calculations more involved, we will spend more time explaining issues that we would otherwise leave for surveying texts. The general discussion regarding vertical curves covers the geometry of simple vertical curves. The discussions pertaining to sag and crest vertical curves include more specific information related to the design of these curves.
3.3.13.
Ascending Grades
Efficiency and safety govern the design of ascending grades. Research has shown that the frequency of collisions increases dramatically when vehicles traveling more than 10 mph below the average traffic speed are present in the traffic stream. This 10 mph differential is, therefore, a bounding value in the design of ascending grades. Research has also shown that most passenger cars are essentially unaffected by grades below 4-5%. Large commercial vehicles and recreational vehicles, on the other hand, are extremely sensitive to changes in grade. Design engineers do have some basic guidelines regarding the maximum upgrade for certain design speeds. Some of these recommended values are tabulated below (AASHTO, 1994). Note that these maximum upgrades are tolerable but not desirable, so they should not be used as targets for design. Design Speed (km/h)
Maximum Grade (%)
50 60 80 110
7-8 intermediate intermediate 5
Let’s return to our discussion of the speed differential. For each grade, there is a critical length at which the design vehicles (trucks, RVs) will obtain the 10 mph differential. The figure below can be used to find the critical length for some common grades (AASHTO, 1984).
44
As long as the length of your ascending grade is below the critical length, you will be able to maintain a reasonable level of safety, and large vehicles will not aggravate the traffic flow. The general design process is this: design your roadway so that the ascending grades achieve the necessary change in elevation while not violating the maximum grade guidelines and not reducing the speed of trucks to more than 10 mph below the traffic's running speed. This can be done any number of ways, including a stepped approach with level sections between grades. While the standards above should be the design goal, it is not always economically or physically possible to meet them. In these cases, climbing lanes may relieve some of the excess restriction. Climbing lanes are extra lanes that are reserved for slow vehicles. They allow faster vehicles to overtake slow vehicles safely and therefore increase the level of service for the highway. According to AASHTO, a climbing lane can be justified if all three of the criteria below are satisfied. 1. Upgrade traffic flow rate in excess of 200 vehicles per hour. 2. Upgrade truck flow rate in excess of 20 vehicles per hour. 3. One of the following conditions exists: A 15 km/h or greater speed reduction is expected for a typical heavy truck. Level-of-service E or F exists on the grade. A reduction of two or more levels of service is experienced when moving from the approach segment to the grade.
Climbing lanes are becoming more and more common on two-lane highways. They are rarely used on multilane and divided-multilane highways, because these roadways currently accommodate the casual passing of slow vehicles.
3.3.14.
Descending Grades
Descending grades pose an entirely new set of problems for the design engineer. Instead of worrying about reductions in speed, the engineer must be concerned about unbridled increases in speed. The potential consequences of runaway vehicles are evident when you consider a highly populated area that is located at the base of a long, steep grade. To avoid catastrophes created by runaway vehicles, runaway vehicle ramps are often designed and included at critical locations along the grade. The location of runaway ramps depends on the geometry of the roadway and the topography of the surrounding terrain. Logically, a ramp should exist before each turn that cannot be negotiated at runaway speeds. Ramps should also be placed along straight stretches of roadway, wherever unreasonable speeds might be obtained. In addition, the ramps should be located on the right side of the road whenever possible, because opposing traffic or other vehicles may not realize that the truck is in trouble and be able to yield in time. Runaway ramps are normally designed so that they can stop a truck moving at a speed of at least 80 mph. Note that this is only a minimum speed and extra ramp length should be provided if the potential for greater entrance speeds exists. The ramp should also be wide enough to service more than one vehicle at a time. There are several different ramp types that can be employed to stop runaway vehicles. Figure 1.0 illustrates the various types of ramps that are commonly used.
45
Figure 1.0: Common Runaway Vehicle Ramps Along with the runaway ramp considerations, the engineer should give some thought to including a slow vehicle lane on downgrades. Trucks often use their lower gears and crawl down descending grades, to minimize the use of their brakes. Including a slow vehicle lane will provide faster traffic with a safe path for overtaking slow vehicles, and the extra lane may also provide endangered vehicles with an escape route if they discover a runaway in their rear-view mirror.
3.3.15.
Vertical Curves
In highway design, most vertical curves are equal-tangent curves, which mean that the horizontal distance from the center of the curve to the end of the curve is identical in both directions. Unequaltangent vertical curves, which are simply equal-tangent curves that have been attached to one another, are used only infrequently. Because of its overwhelming popularity, we will limit our discussion to the geometry of the equal-tangent parabolic curve. In highway design, the grades of the disjointed segments of roadway are normally known before any vertical curve calculations are initiated. In addition, the design speed of the roadway, the stopping sight distance, and the decision sight distance are also well established. The first step in the design of a vertical curve is the calculation of the curve length, which is the length of the curve as it would appear when projected on the x-axis. (See figure 1.0 below). Because the stopping sight distance should always be adequate, the length of the curve is normally dependent upon the stopping sight distance. Occasionally, as with any other section of a highway, the decision sight distance is a more appropriate sight distance. In these instances, the decision sight distance governs the length of the vertical curve. The curve length calculations are slightly different for sag and crest vertical curves, and are covered separately in those sections of this chapter. Let’s assume that you have already calculated the appropriate length (L) for your curve. At this point you would probably want to develop the actual shape of the curve for your design documents. Refer to figure 1.0 throughout the following discussion. The first step in developing the profile for your curve is to find the center of your curve. The location of the center-point is where the disjointed segments of the roadway would have intersected, had they been allowed to do so. In other words, draw lines tangent to your roadway segments and see where those lines intersect. This intersection is normally called the vertical point of intersection (VPI). 46
Figure 1.0: Vertical Curve The vertical point of curvature (VPC) and the vertical point of tangency (VPT) are located a horizontal distance of L/2 from the VPI. The VPC is generally designated as the origin for the curve and is located on the approaching roadway segment. The VPT serves as the end of the vertical curve and is located at the point where the vertical curve connects with the departing roadway segment. In other words, the VPC and VPT are the points along the roadway where the vertical curve begins and ends. One you have located the VPI, VPC, and VPT, you are ready to develop the shape of your curve. The equation that calculates the elevation at every point along an equal-tangent parabolic vertical curve is shown below.
A x Y VPCy B x 200 L Where: Y VPCy B A L x
= Elevation of the curve at a distance x from the VPC (ft) = Elevation of the VPC (ft) = Slope of the approaching roadway, or the roadway that intersects the VPC = The change in grade between the disjointed segments (From 2% to -2% would be a change of -4% or -4) = Length of the curve (ft) = Horizontal distance from the VPC (ft) (Varied from 0 to L for graphing.)
At this point, you have everything that you need to develop the shape of a simple equal-tangent vertical curve. The procedure above will work for both sag and crest vertical curves.
3.3.16.
Crest Vertical Curves [d]
Crest vertical curves are curves that connect inclined sections of roadway, forming a crest, and they are relatively easy to design. As you know from the module entitled ‘Vertical Curves,’ we only need to find an appropriate length for the curve that will accommodate the correct sight distance. The stopping sight distance is usually the controlling sight distance, but the decision sight distance or even the passing sight distance could be used if desired. The passing sight distance is rarely ever used as the design sight distance, because it demands long, gentle curvatures that are expensive and difficult to construct. The sight distance and the length of the curve can be related to each other in one of two ways. The first possibility is that the sight distance is less than the length of the curve. Alternatively, the length of the curve could be less than the sight distance. See figure 1.0.
47
Figure 1.0: Sight Distance Possibilities In any case, there are equations that relate these two parameters to the change in grade for both possible conditions. The designer must double-check that the equation that is used agrees with its own assumptions. For example, if the equation that is based on sight distances that are less than the curve length produces a curve length that is less than the sight distance, you know that the result is invalid. The equations that are normally used to calculate the lengths of crest vertical curves are given below. If S > L then
200 h h L 2S A If S < L then
A S L 100 2h 2h Where: L S A h1 h2
= Length of the crest vertical curve (ft) = Sight distance (ft) = The change in grades (|G2-G1| as a percent) = Height of the driver's eyes above the ground (ft) = Height of the object above the roadway (ft)
The heights in the calculations above should be those that correspond to the sight distance of interest. For the stopping sight distance, h1 = 3.5 ft and h2 = 0.5 ft. For the passing sight distance, h1 = 3.5 ft and h2 = 4.25 ft. While the sight distance has been portrayed as the only parameter that affects the design of vertical curves, this isn't entirely true. Vertical curves should also be comfortable for the driver, aesthetically pleasing, safe, and capable of facilitating proper drainage. In the special case of crest vertical curves, it just so happens that a curve designed with adequate sight distances in mind is usually aesthetically pleasing and comfortable for the driver. In addition, drainage is rarely a special concern for crest vertical curves.
3.3.17.
Sag Vertical Curves [d]
Sag vertical curves are curves that connect descending grades, forming a bowl or sag. Designing them is is very similar to the design of crest vertical curves. Once again, the sight distance is the 48
parameter that is normally employed to find the length of the curve. When designing a sag vertical curve, however, the engineer must pay special attention to the comfort of the drivers. Sag vertical curves are characterized by a positive change in grade, which means that vehicles traveling over sag vertical curves are accelerated upward. Because of the inertia of the driver's body, this upward acceleration feels like a downward thrust. When this perceived thrust and gravity combine, drivers can experience discomfort. The length of sag vertical curves, which is the only parameter that we need for design, is determined by considering drainage, driver comfort, aesthetics, and sight distance. Once again, the aesthetics and driver comfort concerns are normally automatically resolved when the curve is designed with adequate sight distance in mind. Driver comfort, for example, requires a curve length that is approximately 50% of the curve length required for the sight distance. Drainage may be a problem if the curve is quite long and flat, or if the sag is within a cut. For more information on these secondary concerns, see your local design manuals. The theory behind the sight distance calculations for sag vertical curves is only slightly different from that for crest vertical curves. Sag vertical curves normally present drivers with a commanding view of the roadway during the daylight hours, but unfortunately, they truncate the forward spread of the driver's headlights at night. Because the sight distance is restricted after dark, the headlight beams are the focus of the sight distance calculations. For sight distance calculations, a 1° upward divergence of the beam is normally assumed. In addition, the headlights of the vehicle are assumed to reside 2 ft above the roadway surface. As with crest vertical curves, these assumptions lead to two possible configurations, one in which the sight distance is greater than the curve length, and one in which the opposite is true. The figure below illustrates these possibilities.
As with crest vertical curves, each possibility has a different design equation. All that you need to do, therefore, is make sure that the results from the equation that you use are consistent with that equation's assumptions. For example, if you employ the equation that assumes the sight distance is greater than the curve length, you should make sure that the resulting curve length is less than the sight distance. The equations for each possibility are given below. If S > L then
L 2S 200H AS tan B If S < L then
A S L 200H S tan B 49
Where: L S B H A
= Curve length (ft) = Sight distance (ft) (normally the stopping sight distance) = Beam upward divergence (°) (normally assumed as 1°) = Height of the headlights (ft) (normally assumed as 2 ft) = Change in grade (|G2-G1| as a percent)
The stopping sight distance is normally the controlling sight distance for sag vertical curves. At decision points, the roadway should be illuminated by other means so that the sight distance of the driver is extended. Where possible, increased curve length may also be provided. Highway overpasses or other obstacles can occasionally reduce the sight distance on sag vertical curves. In these instances, separate equations should be used to determine the correct curve length. These equations are readily available in design manuals. At this point, you have all of the information that you need to develop the precise layout of your vertical curve. The parabolic curve calculations are identical for sag and crest vertical curves. Just remember to use the appropriate positive or negative values for the participating grades.
3.4.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable Geometric Design concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic.
3.4.1.
Stopping Sight Distance
While descending a -7% grade at a speed of 90 km/h, George notices a large object in the roadway ahead of him. Without thinking about any alternatives, George stabs his brakes and begins to slow down. Assuming that George is so paralyzed with fear that he won't engage in an avoidance maneuver, calculate the minimum distance at which George must have seen the object in order to avoid colliding with it. You can assume that the roadway surface is concrete and that the surface is wet. You can also assume that George has a brake reaction time of 0.9 seconds because he is always alert on this stretch of the road.
Solution First, we need to calculate the distance that George traveled during his brake reaction time. This is done using the equation D = V × T from physics. Since George's brake reaction time was 0.9 seconds and his velocity was 25 m/sec (90 km/h), the distance he traveled during his brake reaction time was 22.5 meters. Second, we need to calculate the distance George will travel while braking. This is done using the equation shown below.
V d 2gf G Where: 50
V g f
= George's Velocity, 25 m/sec (90 km/h) = Acceleration due to gravity, 9.81 m/sec2 = Coefficient of friction, 0.29 (we'll use the value for 96 km/h (60 mph) just to be conservative) = The grade of the road, -0.07 (-7%)
G
Solving the equation yields a distance of 145 meters. Summing the distance traveled while braking and the distance traveled during the brake reaction time yields a total stopping sight distance of 168 meters, which is about 15.2 meters short of two football fields. George needed to be about 168 meters away from the object at the instant he first saw it in order to avoid a collision.
3.4.2.
Passing Sight Distance
A vehicle moving at a speed of 50 mph is slowing traffic on a two-lane highway. What passing sight distance is necessary, in order for a passing maneuver to be carried out safely? Calculate the passing sight distance by hand, and then compare it to the values recommended by AASHTO. In your calculations, assume that the following variables have the values given:
Passing vehicle driver's perception/reaction time = 2.5 sec Passing vehicle's acceleration rate = 1.47 mph/sec Initial speed of passing vehicle = 50 mph Passing speed of passing vehicle = 60 mph Speed of slow vehicle = 50 mph Speed of opposing vehicle = 60 mph Length of passing vehicle = 22 ft Length of slow vehicle = 22 ft Clearance distance between passing and slow vehicles at lane change = 20 ft Clearance distance between passing and slow vehicles at lane re-entry = 20 ft Clearance distance between passing and opposing vehicles at lane re-entry = 250 ft
You should also assume that the passing vehicle accelerates to passing speed before moving into the left lane.
Solution The first step in calculating the passing sight distance is the calculation of the distance D1. This distance includes the distance traveled during the perception/reaction time and the distance traveled while accelerating to the passing speed. The distance traveled during the perception reaction time is computed using D = V × T from physics, where V = 73.3 f./sec (50 mph) and T = 2.5 seconds. Solving for D yields a value of 183.3 feet. The distance traveled during the acceleration portion of D1 is computed using the equation , where Vf = 88 ft/sec (60 mph), Vi = 73.3 f./sec (50 mph), and A = 2.155 ft/sec/sec (1.47 mph/sec). Solving for D yields a value of 550.1 feet. The total distance D1 is 183.3 + 550.1 = 733.4 feet.
V V 2AD
The second portion of the passing sight distance is the distance D2, which is defined as the distance that the passing vehicle travels while in the left lane. This distance can be calculated in the following way. While in the left lane, the passing vehicle must traverse the clearance distance between itself and the slow vehicle, the length of the slow vehicle, the length of itself, and the length of the clearance 51
distance between itself and the slow vehicle at lane re-entry. The time it takes the passing vehicle to traverse these distances relative to the slow vehicle can be computed from the equation D = V × T, where D = 84 ft (20 ft + 22 ft + 22 ft + 20 ft) and V = 14.67 ft/sec (10 mph = relative speed of passing vehicle with reference point on the slow vehicle). Solving for the time T2 yields a value of 5.7 seconds. The real distance traveled by the passing vehicle during the time T2 is calculated using D = V × T, where V = 88 ft./sec. (60 mph) and T = 5.7 seconds. Solving for D yields the distance D2 or 501.6 ft. The distance D3 is the clearance distance between the passing vehicle and the opposing vehicle at the moment the passing vehicle returns to the right lane. This distance was given as 250 ft. The distance D4 is the final component of the passing sight distance and is defined as the distance the opposing vehicle travels during 66% of the time that the passing vehicle is in the left lane. This distance is computed using D = V × T, where V = 88 ft./sec. (60 mph) and T = 3.7 seconds (5.7 × 66%). Solving for D yields a value of 325.6 ft. for D4. The total passing sight distance is, therefore, D1 + D2 + D3 + D4 or 1811 ft. The passing sight distance recommended by AASHTO for speeds within the 50 mph - 60 mph range is 1900 ft. Our approximation came within 100 ft. of the values recommended by AASHTO.
3.4.3.
Horizontal Curve Radius Calculations
A new transportation engineer is charged with the design of a horizontal curve for the Queen's Highway in Canada. His final design calls for a curve with a radius of 520 meters. Would you sign your name to his plans? Assume that the design speed for the Queen's highway is 110 km/h. You can also assume that snow and ice will be present on the roadway from time to time (it's Canada).
Solution The first step in a review of his plans would be to make sure that the curve radius as designed is greater than the minimum curve radius. For a design speed of 110 km/h, the comfortable sidefriction factor is 0.10. In addition, since the roadway will be covered with snow and ice from time to time, the maximum superelevation rate is 8%. With this information we can go ahead and calculate the minimum curve radius using the equation below.
V R 127e f 100 Where: R min V emax f max
= Minimum radius (m) = Design speed, 110 km/hr = Maximum superelevation rate, 8% = Maximum side-friction factor, 0.10
Substituting and solving yields a minimum radius of 530 meters. The 520 meter radius that is called for in the plans would probably work, but it might be uncomfortable for the vehicle occupants. A larger radius would be more appropriate.
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3.4.4.
Horizontal Curve Sight Distance
A large grain elevator is located 40 feet from the centerline of a two-lane highway, which has 12-foot wide lanes. The elevator is situated on the inside of a horizontal curve with a radius of 500 feet. Assuming that the elevator is the only sight restriction on the curve, what is the minimum sight distance along the curve?
Solution The first thing that we need to do is calculate the distance from the edge of the grain elevator to the center of the nearest lane. This turns out to be 40 - 6 = 34 ft. Next, we need to calculate the degree of the curve using the equation R = 5730/D. The degree of the curve turns out to be 11.46°. The last step involves solving for the sight distance using the equation below.
SD M 5730 1 cos D 200 Where: M D
= Distance from the center of the inside lane to the obstruction, 34 ft = Degree of the curve, 11.46°.
Where R = 5730 / D S= R=
Sight distance (ft) Radius of the curve, 500 ft
Substituting the values for the variables and solving for the sight distance yields a sight distance of 371 feet. You might want to change the position of the elevator and see how it affects the sight distance.
3.4.5.
Transition Segments
After designing a horizontal curve with a radius of 1910 feet for a highway with a design speed of 70 mph, your final task is to design the transition segments. Your local design code requires that any superelevation within the curve be run-off over a distance equal to or greater than the distance a vehicle would travel in two seconds at your design speed. In addition, the spiral curves must have the minimum length given by the equation below.
3. 1 5 v L R C Where: L v R C
= Minimum length of the spiral curve (ft.) = Speed (mph) = Circular curve radius (ft.) = Centripetal acceleration development rate (usually between 1 and 3 ft/sec3)
If you use a centripetal acceleration development rate of 2 ft/sec3, what is the minimum length of your transition segments?
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Solution We'll calculate the required length of your transition segments based on the superelevation restrictions first. At 70 mph (102.6 ft/s) you would travel a distance of 205.2 feet in two seconds. Your transition segments should, therefore, slowly change the cross-section of the road over the course of 205.2 feet. The minimum length of the spiral curve is investigated by substituting the correct values into the equation below.
3. 1 5 v L R C Where: L v R C
= Minimum length of the spiral curve (ft) = Design speed, 70 mph = Circular curve radius, 1910 ft = Centripetal acceleration development rate, 2 ft/sec3
Solving for the curve length yields a minimum spiral curve length of 282.8 ft. Since you are required to have a 282.8 foot-long spiral curve, you should gradually change the road cross-section from its normal state to the superelevated state over 282.8 ft. Your transition segments should be 282.8 feet long.
3.4.6.
Ascending Grades
If a highway with traffic normally running at 65 mph has an inclined section with a 3% grade, how much can the elevation of the roadway increase before the speed of the larger vehicles is reduced to 55 mph?
Solution Looking at the table in the Ascending Grades module, we can see that a 3% grade causes a reduction in speed of 10 mph after 1400 feet. To find the exact increase in the elevation of the highway we would need to employ some simple trigonometry. But, since the angle of a 3% grade is small, we can just estimate the elevation increase by multiplying the length of the grade by the grade itself. This yields 1400 × 0.03 = 42 ft. The elevation of the roadway can only be increased by about 42 feet before heavy vehicles are reduced to a speed of 55 mph.
3.4.7.
Crest Vertical Curves
You have been instructed to design a crest vertical curve that will connect a highway segment with a 3% grade to an adjoining segment with a -1% grade. Assume that the minimum stopping sight distance for the highway is 540 feet. If the elevation of the VPC is 1500 ft, what will the elevation of the curve be at L/2?
Solution The first step in the analysis is to find the length of the crest vertical curve. The grade changes from 3% to -1%, which is a change of -4% or A = |-4%|. In addition, for the stopping sight distance h1 = 3.5 ft and h2 = 0.5 ft. Since we know S = 540 ft, we can go ahead and solve for the length of the crest vertical curve. 54
If S > L then (invalid because L > S)
200 h h L 2S A If S < L then
A S L 100 2h 2h Where: L S A h1 h2
= Length of the crest vertical curve (ft) = Sight distance, 540 ft = The change in grades, |-4%| = Height of the driver's eyes above the ground, 3.5 ft = Height of the object above the roadway, 0.5 ft
The curve length calculated from the 'S < L' equation was 877.5 feet, which is greater than the sight distance of 540 feet. To find the elevation of the curve at a horizontal distance of L/2 from the VPC, we need to use the equation below.
A x Y VPCy B x 200 L Where: Y VPCy B A x
= Elevation of the curve at a distance x from the VPC (ft) = Elevation of the VPC, 1500 ft = Slope of the approaching roadway, or the roadway that intersects the VPC, 0.03 = The change in grade between the disjointed segments, -4 (From 3% to -1% would be a change of -4%) = L/2 = 877.5 ft / 2 = 438.75 ft
The equation above yields a curve elevation of 1508.8 feet at a distance L/2 from the VPC.
3.4.8.
Sag Vertical Curves
If a stopping sight distance of 400 ft. is to be maintained on a sag vertical curve with tangent grades of -3% and 0%, what should the length of the curve be? Assume a headlight beam upward divergence angle of 1°.
Solution Since we know everything that we need to know to solve this problem, we'll jump straight into the equations. If S > L then
L 2S 200H AS tan B 55
If S < L then (invalid because L < S)
A S L 200H S tan B Where: L S B H A
= Curve length (ft) = Sight distance, 400 f. = Beam upward divergence, 1° = Height of the headlights, 2 ft (assumed as 2 ft) = Change in grade, 3% (|G2-G1| as a percent)
Solving the equations above results in a curve length of 201 feet. You can find the elevation of any point along the curve once you have the curve length. See the crest vertical curve example problem.
3.5.
Glossary
Acceleration Development Rate: The rate at which the centripetal acceleration necessary to negotiate a horizontal curve is developed on the transition segment leading up to the curve. Actual Sight Distance: The sight distance provided by the highway as designed. Brake Reaction Time: The elapsed time between recognition of an object in roadway ahead and application of the brakes. Braking Distance: The distance traveled while braking to a complete stop. Centripetal Force: The force required to keep an object moving in a circular path. The centripetal force is always normal to the direction of the object. Coefficient of Friction: A dimensionless parameter that quantifies the resistance to sliding at the interface of two surfaces. Crest (vertical) Curve: A curve that connects a segment of roadway with a segment of roadway that has a more negative grade. (uphill to level, uphill to downhill...) Decision Sight Distance: The sight distance that should be provided wherever drivers are forced to make decisions or are forced to cope with large amounts of information. (Also see 'pre-maneuver time') Design Speed: The speed at which a vehicle should be able to traverse a roadway safely under favorable environmental conditions. Grade (roadway): The slope of the roadway surface. Grade is expressed as the change in elevation per 100 feet of horizontal distance. Horizontal Alignment: The part of geometric design involved with designing the shape of the roadway within the horizontal plane.
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Length (vertical curve): The horizontal distance from one end of the vertical curve to the other, or the horizontal distance between the VPC and the VPT. Passing Sight Distance: The sight distance required for drivers to feel comfortable about making a passing maneuver. Pre-Maneuver Time: The time required for a driver to process information relative to a hazard, plot an avoidance course, and initiate the required avoidance maneuver. Sag (vertical) Curve: A vertical curve that connects a segment of roadway with a segment of roadway that has a more positive grade. (downhill to level, downhill to uphill...) Side-Friction Factor: The dimensionless factor used to describe the frictional resistance to slippage normal to the direction of travel. Sight Distance: The length of roadway ahead over which an object of a specific height is continuously visible to the driver. Stopping Sight Distance, (Minimum): The distance required for a driver to react to a hazard in the roadway ahead and bring his/her vehicle to a complete stop. The sum of the distance required to stop the car and the distance traveled during the break reaction time. Superelevation: Inclined roadway cross-section that employs the weight of a vehicle in the generation of the necessary centripetal force for curve negotiation. Superelevation Rate: The slope of the roadway cross-section. For example, a 10 ft wide roadway with a superelevation rate of 10% would be 1 ft higher on one side than it is on the other. Tangent Grade: A grade that shares a common slope with the end of a vertical curve. Vertical Alignment: The portion of geometric design that deals with the shape of the roadway in the vertical plane. Vertical Curve: A parabolic curve used to provide a gradual change in grade between roadway segments with differing grades.
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4. Parking Lot Design 4.1.
Introduction
Off-street parking is an important part of the transportation system. It is an efficient means of storing vehicles while they aren’t in use, and it causes little disruption to the neighboring roadways. Additionally, since parking is the terminal or destination for a trip, the availability of off-street parking can affect the attractiveness of destinations as well as transportation modes. The attractiveness of a destination is reduced if there is a delay or difficulty in parking. The use of transit systems is increased in areas where parking is scarce. To be efficient, the transportation system must include adequate parking facilities at all places that attract trips. Off-street parking plays an important role in the efficiency of the overall transportation system. This chapter is designed to help the undergraduate engineering student understand the fundamentals of planning and designing off-street parking.
4.2.
Lab Exercises
This exercise will help increase your understanding of Parking Lot Design, by presenting a more complicated problem that requires more thorough analysis.
4.2.1.
Lab Exercise One: Facility Analysis and Design
A local off-street parking facility might be inadequate. You have been asked to evaluate the adequacy of the parking facility. If your results show that the facility is inadequate, you are to propose suitable modifications and/or additions that will correct the problem. You should prepare a brief report that summarizes your analysis and any proposed modifications to the facility. Your instructor will designate the off-street parking facility and provide any additional information that might be needed.
Tasks to be Completed Task 1: Develop an inventory of the parking facility including:
the location, condition, type, and number of parking spaces, any time limits, hours of availability and other restrictions, and the geometry of the spaces and other features.
Task 2: Estimate the peak parking period for the facility and complete an accumulation count study for the facility during that period. Using your results, develop an accumulation graph. Task 3: Perform a simplified license plate survey and estimate the average length of time that vehicles are parked at the facility during the peak parking period. Task 4: Using the information from the first three tasks, calculate the probability that an incoming car will not find a parking space during the peak parking period. Determine whether or not the probability of rejection is acceptable. Task 5: If the current parking facility is inadequate, design modifications and/or additions that will correct the problem. Your goal is to suggest the most economical solution. Report any assumptions that you make.
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4.3.
Theory and Concepts
Many facets of parking are interrelated. Parking programs usually evolve from parking studies that determine the supply of parking and the current demand, as well as estimates of future parking demand. Parking facility planning and design requires a determination of the number of spaces needed, the proper location for these spaces, and a workable layout with acceptable operating controls. In addition, other factors need to be considered, such as characteristics of the transportation system and users, transportation attractions and generators, and transportation operations. To start learning more about Parking Lot Design, select a topic from the list below.
4.3.1.
Parking Studies
Studies must be conducted to collect the required information about the capacity and use of existing parking facilities. In addition, information about the demand for parking is needed. Parking studies may be restricted to a particular traffic producer or attractor, such as a store, or they may encompass an entire region, such as a central business district. Before parking studies can be initiated, the study area must be defined. A cordon line is drawn to delineate the study area. It should include traffic generators and a periphery, including all points within an appropriate walking distance. The survey area should also include any area that might be impacted by the parking modifications. The boundary should be drawn to facilitate cordon counts by minimizing the number of entrance and exit points. Once the study area has been defined, there are several different types of parking studies that may be required. These study types are listed below and discussed in detail in the remaining paragraphs.
Inventory of Parking Facilities Accumulation Counts Duration and Turnover Surveys User Information Surveys Land Use Method of Determining Demand
Inventory of Parking Facilities:
Information is collected on the current condition of parking facilities. This includes:
the location, condition, type, and number of parking spaces. parking rates if appropriate. These are often related to trip generation or other land use considerations. time limits, hours of availability and any other restrictions. layout of spaces: geometry and other features such as crosswalks and city services. ownership of the off-street facilities.
Accumulation Counts:
These are conducted to obtain data on the number of vehicles parked in a study area during a specific period of time. First, the number of vehicles already in that area are counted or estimated. Then the number of vehicles entering and exiting during that specified period are noted, and added or subtracted from the accumulated number of vehicles. Accumulation data are normally summarized by time period for the entire study area. The occupancy can be calculated by taking accumulation/total spaces. Peaking characteristics can be determined by graphing the accumulation 59
data by time of day. The accumulation graph usually includes cumulative arrival and cumulative departure graphs as well.
Above Figures taken from: Khisty, C. and M. Kyte, Lab and Field Manual for Transportation Engineering, Prentice Hall, Englewood Cliffs, NJ, 1991. Duration and Turnover Surveys:
The accumulation study does not provide information on parking duration, turnover or parking violations. This information requires a license plate survey, which is often very expensive. Instead, modifications are often made to the field data collection protocols. Note that there is usually a tradeoff between data collection costs and study accuracy. Spending more time and money may increase accuracy, but at what point does the incremental change in accuracy become too expensive? 60
In planning a license plate survey, assume that each patrolling observer can check about four spaces per minute. The first observer will be slower, because all the license plate numbers will have to be recorded, but subsequent observers will be able to work much faster. The form shown below can be used for a license plate survey. Parking turnover is the rate of use of a facility. It is determined by dividing the number of available parking spaces into the number of vehicles parked in those spaces in a stated time period. Table1. Typical License Plate Survey Field Form for Curbside Survey Street_______Side____Study Date_________________ Data Collector_________From_____________________ To ________________ Direction of Travel ___________ Space No
Space Desc.
Time at beginning of Patrol 8:00
8:30
9:00
9:30
10:00
10:30
11:00
11:30
User Information Surveys:
Individual users can provide valuable information that is not attainable with license plate surveys. The two major methods for collecting these data are parking interviews and postcard studies. For the parking interviews, drivers are interviewed right in the parking lot. The interviews can gather information about origin and destination, trip purpose, and trip frequency. The postage paid postcard surveys requests the same information as in the parking interview. Return rates average about 35%, and may include bias. The bias can take two forms. Drivers will sometimes overestimate their parking needs in order to encourage the surveyors to recommend additional parking. Or, they may file false reports that they feel are more socially acceptable. Land Use Method of Determining Demand:
Parking generation rates can be used to estimate the demand for parking.
Tabulate the type and intensity of land uses throughout the study area. Based on reported parking generation rates, estimate the number of parking spaces needed for each unit of land use. Determine the demand for parking from questionnaires. A rule of thumb is to overestimate the demand for parking by about 10 %. If the analysis suggests that the parking demand for a particular facility will be 500 spaces, then the design should be for 550 spaces.
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4.3.2.
Adequacy Analysis
The adequacy of a parking facility can be measured by calculating the probability that an entering vehicle will not be able to find a parking space. A high probability of rejection (not finding a space) may indicate that expansion of the parking facility is warranted. The probability of rejection can be calculated by comparing the traffic load to the number of parking stalls as shown below. First, the traffic load is estimated using: A=Q×T Where: A Q T
= traffic load, = incoming vehicle flow rate, and = the average parking duration.
Make sure that your units of time cancel each other. If you give Q in vehicles per hour, then use T in units of hours. Next, calculate the probability of rejection using the following formula:
AM! P 1A A A 2 M! Where: P A M
= the probability of rejection, = the traffic load, and = the number of parking stalls.
If the probability of rejection is high, you may want to consider adding more parking stalls to the parking facility.
4.3.3.
Parking Facility Design Process
The goal in designing off-street parking facilities is to maximize the number of spaces provided, while allowing vehicles to park with only one distinct maneuver. It would be nice to present a step-by-step procedure for reaching this goal, but it isn’t that simple. Parking lot design requires balancing a variety of concerns. For example, you might decide on a nice layout for your parking lot, only to realize that you haven’t provided any spaces for persons with disabilities. The next iteration would correct this error, but might very well create another problem. You simply have to hammer out all of the kinks, until you end up with a design that satisfies all of your criteria. One way to start is to imagine that you are parking your own car in a lot. What maneuvers would you need to make? Knowing that, what needs to be included in the design to make sure all those maneuvers are possible? Use the following list of maneuvers to guide your thinking. 1. Vehicle enters from street (space provided by entry driveway). 62
2. Vehicle searches for a parking stall (space provided by circulation and /or access aisles). 3. Vehicle enters the stall (space provided by the access aisle). 4. Vehicle is parked (stall designed to accommodate the vehicle’s length and width plus space to open vehicle doors). 5. Pedestrians access the building or destination (usually via the aisles). 6. Vehicle exits the parking stall (space provided by the access aisle). 7. Vehicle searches for an exit (space provided by the access and circulation aisles). 8. Vehicle enters the street network (space provided by the exit driveways).
4.3.4.
Entrance Considerations
The first maneuver that a parking vehicle will make involves leaving the street and entering the off-street parking lot. This maneuver, while simple, requires some careful thought by the parking lot designer. Analysis of the demand for parking may indicate that there are periods during the day in which a large number of vehicles want to enter the parking facility at roughly the same time. The entrance to the parking lot must be able to handle the entering traffic without forcing vehicles to wait in the street, because stagnant vehicles will reduce the capacity of the adjacent street. To avoid conflicts with other traffic, entrances should be located as far from intersections and conflict points as possible. Multiple entrances may ease access and reduce restriction on the adjacent roadways. Years of experience have produced general entrance dimensions that seem to work. The basic nominal design width for a two-way driveway serving commercial land use is 30 ft., with 15 feet radii. With greater volumes such as at a shopping center, a 36-ft driveway may be appropriate. It should be marked with two exit lanes (each 10 or 11 ft wide) and a single entry lane (14-16 ft wide) to accommodate the off-tracking path of entering vehicles. Larger commercial facilities such as regional shopping centers may require twin entry and exit lanes separated by a 4-12 foot median. Many areas of the country have specific regulations or guidelines for the design of access facilities. It is important that the local and state regulations concerning access management are followed when designing access to off-street parking facilities.
4.3.5.
Internal Considerations
There are two major internal maneuvers that the parking lot designer must consider, vehicles searching for an open stall and vehicles searching for an exit. These internal maneuvers require space, which is space that cannot be used for parking. Off-street parking facilities normally operate in one of two ways. The first and most common operation is ‘self-parking’, in which the driver maneuvers the vehicle through the parking lot. The second operation is ‘attendant parking’, in which parking attendants maneuver the vehicle through the parking lot. Parking facilities that use ‘self-parking’ must normally include larger aisles, as individuals unfamiliar with the parking facility may require extra room to maneuver. Attendant parking is normally more expensive to operate than self-parking. Tollbooths and other restrictions at entrances or exits also affect the internal operation of parking facilities. Tollbooths require reservoir space within the parking facility for vehicles that are waiting. In general, 2-3 spaces per lane are required at entrances to self-parking lots where a ticket needs to be acquired. At exits, a much larger reservoir should be provided, because toll collection requires extra time. 63
Finally, in areas where winter snowfall is common, consideration of the snowfall removal operation should be included in the design process. Adequate space must be provided for snow removal equipment to maneuver.
4.3.6.
Parking Stall Layout Considerations
The objective of the layout design is to maximize the number of stalls, while following the guidelines below.
The layout of the parking facility must be flexible enough to adapt to future changes in vehicle dimensions. The stall and aisle dimensions must be compatible with the type of operation planned for the facility.
The critical dimensions are the width and length of stalls, the width of aisles, the angle of parking, and the radius of turns. All of these dimensions are related to the vehicle dimensions and performance characteristics. In recent years there have been a number of changes in vehicle dimensions. The popularity of minivans and sport utility vehicles has had an impact on the design of parking facilities. For the near future, a wide mix of vehicle sizes should be anticipated. There are three approaches for handling the layout: 1. Design all spaces for large-size vehicles (about 6 feet wide and 17-18 ft long). 2. Design some of the spaces for large vehicles and some for small vehicles (these are about 5 ft wide and 14-15 ft long). 3. Provide a layout with intermediate dimensions (too small for large vehicles and too big for small vehicles). For design, it is customary to work with stalls and aisles in combinations called "modules". A complete module is one access aisle servicing a row of parking on each side of the aisle. The width of an aisle is usually 12 to 26 feet depending on the angle at which the parking stalls are oriented. Stall Width
For simplicity, the stall width is measured perpendicular to the vehicle, not parallel to the aisle. If the stall is placed at an angle of less than 90°, then the width parallel to the aisle will increase while the width perpendicular to the vehicle will remain the same. Stall Length
The length of the stall should be large enough to accommodate most of the vehicles. The length of the stall refers to the longitudinal dimension of the stall. When the stall is rotated an angle of less than 90°, the stall depth perpendicular to the aisle increases up to 1 foot or more. It should be noted that the effective stall depth depends on the boundary conditions of the module, which could include walls on each side of the module, curbs with or without overhang, or drive-in versus back-in operations. For parking at angles of less than 90°, front bumper overhangs beyond the curbing are generally reduced with decreasing angle and, for example, drop to about 2 feet at 45° angles. The Table 8-3 below gives the standard dimensions for several different layouts as defined by Figure 8-4.
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Table 8-3 and Figure 8-4 where taken from: Weant, R.A. and Levinson, H.S., Parking, Eno Foundation, 1990, page 161. Interlock Module
A special type of module, the interlock, is possible at angles below 90°. There are two types of interlock. The most common, and preferable, type is the bumper-to-bumper arrangement. The second type, the "herringbone" interlock, can be used at 45° and is produced by adjacent sides having one way movements in the same direction. This arrangement requires the bumper of one car to face the fender of another car. Figure 8-3 shows several different module layouts that are commonly used.
Comparing Angle Efficiencies
The relative efficiencies of various parking angles can be compared by looking at the number of square feet required per car space (including the prorated area of the access aisle and entrances). Where the size and shape of the tract is appropriate, both the 90° and the 60° parking layouts tend to require the smallest area per car space. In typical lot layouts for large size vehicles, the average overall area required (including cross aisles and entrances) ranges between 310 and 330 square feet/car. A very flat angle layout is significantly less efficient than other angles.
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One-Way Aisles
There are many conditions where one-way aisles are desirable. With parking angles less than 90°, drivers can be restricted to certain directions. However, the angle should usually be no greater than 75°. Drivers may be tempted to enter the parking aisles and stalls from the wrong direction when the stall angle is too large. Adjacent aisles generally have opposite driving directions.
4.3.7.
Exit Considerations
The last maneuver that a vehicle will make in a parking facility involves leaving the facility and entering the adjacent street network. Inefficiencies in this part of the parking process can lead to reduced capacity in both the parking facility and the adjacent street network. As was discussed in the section entitled ‘Entrance Considerations,’ access and egress points should be located as far as possible from any conflicting points on the adjacent street network. This normally means that entrances and exits are placed ‘mid-block.’ Multiple exit lanes may be required, so that right-turning vehicles can avoid waiting for left-turning vehicles at the exit. If the flow rate of departing vehicles is low, or if the adjacent street is one-way, a single lane may be sufficient. The type of parking facility also impacts the exit design. Facilities that have tollbooths near the exits will require multiple exit lanes. They may also require that a large portion of the parking lot be devoted to lanes for vehicles waiting to pay at the tollbooths.
4.3.8.
ADAAG Requirements
The Americans with Disabilities Act Accessibility Guidelines for Buildings and Facilities (ADAAG) specifies the number and dimensions of accessible parking spaces. Where possible, the accessible parking spaces should be provided on the accessible path to the facility entrance and also minimize the distance traveled. Total Parking in Lot
Required Minimum Number Of Accessible Spaces
1 to 25 26 to 50 51 to 75 76 to 100 100 to 150 151 to 200 201 to 300 301 to 400 401 to 500 501 to 1000
1 2 3 4 5 6 7 8 9 2 percent of total
1001 and over
20 plus 1 for each 100 over 1000
One in eight accessible spaces, but not less than one, should be "van accessible". These spaces should be 96 in (2440mm) wide. Parking access aisles need to be part of the accessible path to the building. Two adjacent accessible spaces may share a common access aisle. The access aisle should be 5 feet wide. Parking spaces and access aisles should be level, with surface slopes not greater than 1:50 (2%) in all directions. 67
4.4.
Professional Practice
In order to supplement your knowledge about the various concepts within Parking Lot Design, and in order to give you a glimpse of how these various topics are discussed in the professional environment, we have included selected excerpts from professional design manuals.
4.4.1.
Parking Studies
The following excerpts were taken from the1992 edition of the Transportation Planning Handbook, published by the Institute of Transportation Engineers (p. 199-400).
Parking Studies (p. 199) Parking studies are used to evaluate the current supply of parking or to plan for future parking needs. Some parking studies are only concerned with the adequacy of parking for a particular need, such as a shopping mall, office building, or a sports facility. Other studies are designed to evaluate the parking conditions in an area to establish time limits, parking rates, and the need for additional parking. Some studies are used to aid operational analyses in relation to removal or modification of curb parking. Still others are required to evaluate residential parking impacted by encroachment from outside parkers. There are a wide variety of other specialized studies to meet specific needs.
Supply and Demand (p. 400) Parking supply is merely the number and location of all parking spaces in the study area. The supply is defined by the parking inventory described earlier in this chapter (under inventories). Supply is much easier to quantify than is demand because it is a physical count. Demand, on the other hand, is an estimate of the number of drivers who wish to park in the study area at any given time. Supply is generally constant, although there can be some changes during the day (e.g., tow away zones during peak hours, part-time loading zones, etc.). Demand varies by time. In fact, one of the elements to be defined in the study is the time of peak demand. In some areas there may be multiple peaks because of the differing uses within the study area. A simple example is an office complex. The peak employee accumulation may be by 9:00 A.M., while the peak client or visitor accumulation may be 11:30 A.M. or 2:30 P.M. Deliveries or service personnel may peak at still different times. Current demand may be estimated in those study areas where supply greatly exceeds demand by merely counting the accumulated vehicles at various times of the day. However, when the demand reaches 85 percent or more of the supply, it may not represent the true demand because there may be additional demand that is not present because of the lack of adequate parking.
User Characteristics User characteristics analyses are made to assist in parking management in an area. Such studies are used in establishing time-limit parking, employee parking, loading zones, etc. Information is obtained on the magnitude of the various segments of the parking demand. In other words, the study is used to project the demand for short-term parking (15 to 20 minutes); for errands at banks, pharmacies, dry cleaners, etc.; for limited parking (1 to 2 hours) covering short-term shopping or business appointments; for longer term parking (8 hours or more) for employees in the area.
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4.4.2.
Types of Facilities
The following excerpt was taken from the1992 edition of the Transportation Planning Handbook, published by the Institute of Transportation Engineers (p. 175).
Off-street facilities range from the parking pad, carport, or garage of a single-family home to lots or garages serving large parking generators such as shopping centers, airports, and sporting events. Most off-street parking is accommodated in ‘free’ facilities (technically this is a misnomer, since all parking carries a cost which is reflected in the price of a home, the rent of a retail or commercial building, the price of a product, etc). However, this term is used to distinguish from those types of commercial facilities which charge a specific fee to the driver. . . . Unfortunately, a large supply of parking also is provided at the curb, along streets. The use of streets for curb parking exacts a heavy toll in accidents and congestion (along the more heavily traveled routes). While most curb parking is free and open to the general public, the use of parking meters in business areas converts the street curb to a charge, or revenue producing, operation. Additionally, some curb spaces are limited to specific users such as bus stops and loading zones for trucks, taxis, or passenger pickup/drop-off.
4.4.3.
Types of Operation
The following excerpt was taken from the1992 edition of the Traffic Engineering Handbook, published by the Institute of Transportation Engineers (pp. 204-205).
Most of the so-called public parking facilities represent a more centralized and general-purpose use. Parkers usually have a choice of several destinations. Much of the time they also have a choice of alternate places to park. A facility open to the general public usually needs to attract parkers if investment in its construction is to be justified. When the facility is revenue-financed, the need is obvious. Even when the parking is free, justification is needed for the expenditure of benefit district assessment funds, parking meter revenue, or other public funds used to acquire land and to construct and operate the facility. The design of a general-purpose parking facility must take into consideration the type of proposed operation – with attendants, by self parking, or with a combination of the two. The most economical operation occurs where patrons park their own cars. In heavily used facilities where patrons pay for parking, it is sometimes feasible to utilize attendants to park the cars after the patron pulls into the lot. This also frequently occurs in older parking garages. Some facilities can operate on both systems, with certain areas reserved for self-parkers and other areas served by attendants. . . . A basic factor in design of a parking facility is the expected use by type of parker or type of generator being served. Parking duration can be either short-term or long term, or a combination of both. Design dimensions are often larger in facilities for short-term parkers because of the high turnover rate and the need to provide easy access and circulation. . . .
4.4.4.
Operational Design Elements
The following excerpt was taken from the1992 edition of the Traffic Engineering Handbook, published by the Institute of Transportation Engineers (pp. 204-205).
The design of a parking facility is very strongly influenced by its intended operation. The basic design elements and their associated operational features may be identified in successive steps as follows: 69
1. 2. 3. 4. 5. 6. 7. 8. 9.
Vehicular access from the street system (entry driveway); Search for a parking stall (circulation and/or access aisles); Maneuver space to enter the stall (access aisles); Sufficient stall size to accommodate the vehicle’s length and width plus space to open car doors wide enough to enter and leave vehicle (stall dimensions); Pedestrian access to and from the facility boundary (usually via the aisles) and vertically by stairs, escalators, or elevators in multilevel facilities; Maneuver space to exit form the parking stall (access aisles); Routing to leave facility (access and circulation aisles); Vehicular egress to the street system (exit driveway); and Any revenue-control system (may involve elements of entry, exit, or both).
The simplest form of off-street parking is a single stall at home. Assuming a straight driveway, steps 1 and 8 above use the same lane and curb cut, and step 9 does not apply. Steps 2 and 7 are rudimentary. Thus, a driveway serving a one-car parking stall or garage cannot be considered as representing a second parking space, if such parking would block continuous access to the basic stall. Step 6 usually involves backing out into the public street or alley, as part of steps 7 and 8. Herein lies the essential difference between low-volume parking and what generally should be practiced in facilities designed to handle more than a few cars. Except along alleys, the larger lots should have all parking and unparking maneuvers contained off-street. Frequent backing of cars across sidewalks and into public streets increases congestion and creates hazards. For the large facilities, and particularly garages, an operational concept necessarily precedes structural, architectural, and other design elements. The concept begins with the question, "What do we plan to serve?" From answers to this question, design features emerge such as user ease of access, security, vehicle circulation and walk patterns, signing, lighting, and equipment needs.
4.4.5.
Change of Mode Parking
The following excerpts were taken from the1992 edition of the Transportation Planning Handbook, published by the Institute of Transportation Engineers (pp. 183-184).
. . . There are two general types of park and ride lots: (1) a change from the private vehicle to some form of public transportation such as bus, rapid transit, or suburban rail and (2) carpooling.
Transit Stations The interfaces are the following:
Pedestrian or walk-in-traffic Private automobile park-and-ride or pickup/drop-off Transit transfers such as bus to bus, or bus to rail Taxi
For most locations, there are two elements to the park-and-ride function: (1) long-term, all day commuter parking, which represents the major consideration, and (2) short-term spaces that are desirable to encourage midday shopper, sporting event, or other personal trip usage of the transit facility during off peak periods. These spaces would typically be used from 4 to 6 hours. Efficiency of land use is enhanced by combining the P/D operation with the short-term space needs. Thus, a very short time limit during the A.M. and P.M. peak transit activity, such as 5 to 10 minutes, is imposed on a limited number of spaces adjacent to the station. These spaces are then available for 70
intermediate-term parking during the balance of the day. The major P/D problem involves the pickup element in the evening, when motorists arrive and temporarily park while awaiting arrival of the commuter train or express bus. . . .Additional planning elements of the transit terminal include loading/unloading spaces for buses and waiting areas for taxis. The important parking characteristics of a transit station include the number of P/D spaces needed versus the number of long-term spaces. Reliable estimators for the number of P/D spaces, on a peroriginating-daily-passenger basis, are needed but have not been identified. Three studies in the Chicago area found a range of 0.05 to 0.07 (average 0.06) spaces per originating passenger; however, additional research on this parking demand is needed in other cities. . . . The parking space demand per originating passenger at various types of terminals is given in Table 6.9 (not included here) and suggests a need of about one space per three passengers. The Chicago area developed a method of estimating current and future parking demand at each station, using data from ticket sales by mail: 1. Determine the natural service area (NSA) by geographic zones having boundaries defined by existing patterns of user origins and expected future development. 2. Calculate the current NSA. 3. Calculate the current NSA parking demand. 4. Project ridership growth. 5. Determine the future NSA.
Fringe Parking Change-of-mode parking facilities can be located at the outer edges of the CBD, or at more remote distances. Those located near CBDs are served by local or special shuttle buses. Those located farther away are typically served by express buses, rapid transit, and/or suburban rail. An ITE committee found that bus-serviced lots have the greatest usage close to the CBD, with a smaller peak at the 11- to 13- mile range. Rail lots have the greatest usage in the range from 5 to 15 miles from the CBD. Most bus-serviced lots have transit times greater than automobile travel times, whereas those with rail typically have shorter travel times. Most change-of-mode lots have transit service for 14 or more hours per day, and peak-hour transit service headways of 25 minutes or less. In the Cleveland fringe, buses were reported operating with 5-minute headways during the peak hours. Locational factors for parking facilities were identified by Ellis, Bennett, and Rassam: 1. Fringe parking facilities should be located in transportation corridors so that they intercept home to work trips destined to the CBD at a point where there is sufficient density of traffic demand that high-quality transit service may be offered. 2. To the extent feasible, facilities should be located on land that is already used for parking or in low-grade nonresidential use. 3. Such facilities should be located on sites compatible with land uses and activities in the immediately adjacent area. 4. Potential joint-use aspects of a facility should be considered. 5. Trade-offs in the scale of the facility (such as the level of transit service as opposed to its neighborhood impacts and the ease of access) should be considered.
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4.4.6.
Downtown Areas
The following excerpt was taken from the1992 edition of the Transportation Planning Handbook, published by the Institute of Transportation Engineers (p. 177).
Looking at CBDs in general, the following relationships are typical: 1. On-street (curb) parking is related to city population, typically decreasing to about 10 percent of total supply in cities over 250,000 population. 2. The demand for long-term, work purpose parking increases with population size, ranging from 20 percent of total parkers for cities under 100,000 to over 30 percent for cities approaching 1 million or more population. 3. The average walking distance increases with city size. 4. The parking duration varies by trip purpose and population size. Work trip and residential parking exhibit the longest durations, while durations for all trip purposes increase with city size. 5. The parking turnover at the curb is usually three to four times greater than for off-street spaces. At all facilities, turnover is influenced by the type of parker, the rate structure, local regulations, and enforcement levels. Furthermore, larger cities generally experience lower parking turnover than smaller cities. 6. Parking accumulation peaks between 11:00 A.M. and 2:00 P.M. in the average CBD; however, different trip purposes exhibit unique accumulation patterns. The peak accumulation seldom exceeds 85 percent of the total parking supply, even though parts of the area are severely deficient in parking supply (location is the key factor). Peak accumulation tends to increase with population size, but at a diminishing rate.
4.4.7.
Location
The following excerpt was taken from the1992 edition of the Transportation Planning Handbook, published by the Institute of Transportation Engineers (p. 199).
Key Factors To assure optimum use, general-purpose parking facilities must be properly located. Whether free or commercial, the public purpose of a parking lot or garage is to enhance local economic values, and/or reduce street congestion. Factors that determine appropriate locations for individual facilities include amount and type of parking shortages, type of nearby generators, facility-user considerations (whether long-term or short-term), development costs, and street system elements, such as capacity, directional flows, and turn restrictions. The total parking system of an area should be considered as it relates to balancing of supply to needs and the street access network. Most work on parking facility location involves CBD areas. However, other needs exist in outlying business areas, in older apartment areas with severe parking shortages, and at universities.
4.4.8.
Off-Street Zoning
The following excerpt was taken from the1992 edition of the Transportation Planning Handbook, published by the Institute of Transportation Engineers (p. 403).
Many jurisdictions have zoning regulations that specify the level of parking that must be provided for various land uses. Data may be obtained from the Institute of Transportation Engineers publication "Parking Generation" or by making observations of peak parking demand at similar 72
land uses to that under consideration. Peak periods vary for differing land uses. Peak residential demand occurs in the early morning hours. Some restaurants peak at lunchtime while others peak in the early evening. Office buildings peak in midmorning while shopping centers peak around noon on Saturdays.
4.4.9.
Design of Off-Street Facilities
The following excerpts were taken from the1992 edition of the Traffic Engineering Handbook, published by the Institute of Transportation Engineers (pp. 205-215).
Elements of Good Design (pp. 205-206) In designing any off-street parking facility, the elements of customer service, convenience, and safety with minimum interference to street traffic flow must receive high priority. Drivers desire to park their vehicles as close to their destination as possible. The accessibility, ease of entering, circulating, parking, unparking, and exiting are important factors. Good dimensions and internal circulation are more important than a few additional spaces. Better sight distances, maneuverability, traffic flow, parking ease, and circulation are the results of well-organized, adequately designed lot or garage.
Site Characteristics Factors such as site dimensions, topography, and adjacent street profiles affect the design of offstreet parking facilities. The relation of the site to the surrounding street system will affect the location of entry and exit points and the internal circulation pattern.
Access Location External factors such as traffic controls and volumes on adjacent streets must be considered -- particularly the location of driveways or garage ramps. It is desirable to avoid locating access or egress points where vehicles entering or leaving the site would conflict with large numbers of pedestrians. Similarly, street traffic volumes, turning restrictions, and one-way postings may limit points at which entrances and exits can logically be placed. It is important to investigate these factors at the beginning of design. Driveways should be located to provide maximum storage space and distance form controlled intersections. . . .
General Elements and Layout Alternatives (p. 212) Because of their lack of walls or cover, parking lots have no ventilation problems, and lighting is sometimes provided by relatively tall poles, thus affording high efficiencies and minimizing the number of poles. Generally, lots have clear sight lines and offer a feeling of greater security than in a more confined space. Lots are not restricted on vehicle heights and thus afford access to both commercial and emergency vehicles. . . . Generally, the layout of a parking lot seeks to strike a balance among maximizing capacity, maneuverability, and circulation. . . . The general advantages of 90° parking, as compared with lesser angles, are: 1. Most common and understandable; 73
2. 3. 4. 5. 6. 7. 8.
Can sometimes be better fitted into buildings; Generally most efficient if site is sufficiently large; Uses two-way movement (can allow short, dead-end aisles); Allows unparking in either direction. Thus it can minimize travel distances and internal conflict; Does not require any aisle directional signs or markings; Wide aisles often provide room to pass vehicles stopped and waiting for an unparking vehicle; Wide aisles increase separation for pedestrians walking in the aisle and between moving vehicles; 9. Wide aisles increase clearance from other traffic in the aisle, during unparking maneuvers; 10. Fewer total aisles (hence easier to locate parked vehicle). Several advantages and disadvantages of angle parking (usually 45° to 75° ), are: 1. 2. 3. 4.
Easiest in which to park Can be adapted to almost any width of site by varying the angle; Requires slightly deeper stalls but much narrower aisles and modules; Drivers must unpark and proceed in original direction; hence producing greater out-of-way travel and conflict; 5. Unused triangles at end of parking aisles reduce overall efficiency; 6. To avoid long travel, additional cross aisles for one-way travel are required, which adds to gross area used per car parked; 7. Difficult to sign one-way aisles.
Wheel Stops and Speed Bumps (p. 215) In general, the ends of parking stalls within lots can be marked in a satisfactory fashion by only a paint line. Wheel stop blocks in the interior of a lot have disadvantages, for they may interfere with and present a hazard to people walking between cars, provide traps for blowing debris, and interfere with snow plowing in northern climates. . . . Wheel stops are often used along the side boundaries of a lot, where large landscaped areas extend beyond the edge of pavement and an occasional override would present no significant hazard.
4.4.10.
Supplemental Specifications and Implementation
The following excerpts were taken from the1992 edition of the Transportation Planning Handbook, published by the Institute of Transportation Engineers (pp. 190-191).
To be effective, a zoning code must specify the number of required spaces and must contain sufficient controls to ensure that all the parking is convenient and usable.
Relation to Site and Joint Use Zoning can aid sound community development if it causes all owners to provide adequate off-street parking and loading facilities for their property. Each building may have its own parking lot or garage, or the development of consolidated, common-use parking facilities may be more practical and desirable in a business area. However, zoning should apply to business districts (including the CBD) to the extent that each developer is required to contribute their fair share of the acquisition and development cost for the parking needed to serve their property. This can be done by cash contributions to an area parking fund in an amount equal to the estimated cost of providing the specified number of spaces. 74
Stall Sizes and Access Good driveway design is particularly important for the higher volume commercial driveways. In areas with high pedestrian activity, it is good practice to restrict driveway widths and radii and to meet sidewalk grades and a short distance in form the curb, thus creating a short hump. Such measures ensure vehicular entry and exit at low speeds. In all other areas, use of greater widths, large radii, and flat driveway slopes frequently requiring step-down curbs is desirable to speed up the entry and exit of vehicles and thus increase ease and capacity of access. The recommended stall and access dimensions for zoning or local administrative regulations are covered in Chapter 7 of the Traffic Engineering Handbook , and in the ITE Committee 5D-8 Recommended Practice.
4.5.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic.
4.5.1.
Adequacy Analysis
Over the course of an 8-hour day, 96 vehicles enter a local electronics store’s parking lot. The parking lot has 5 spaces and the average customer stays in the grocery store for 15 minutes. Calculate the probability that an incoming car will be rejected.
Solution First, we need to calculate the incoming flow rate. This is done as follows: Q = 96 vehicles / 8 hours Q = 12 vehicles/hour Since we know the average vehicle is parked for 15 minutes, or 0.25 hours, we can calculate the traffic load as follows. A=Q×T A = 12 vehicles/hour × 0.25 hours A = 3 vehicle Now that we have the traffic load, we can find the probability of rejection using the equation below.
AM! P 1A A A 2 M! Where: P A M
= the probability of rejection, = the traffic load, and = the number of parking stalls.
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3120 P 13 3 3 3 3 0.11 2 6 24 120 Each entering vehicle has an 11% chance of being rejected. As a result, the electronics store loses one out of each 10 customers entering their lot.
4.5.2.
Space Requirements
A new sandwich shop is nearing completion and a parking lot needs to be designed. The storeowners anticipate that, on the average 12-hour day, 360 vehicles will visit the sandwich shop. The owners also anticipate that the average vehicle will remain parked for 10 minutes. How many parking spaces need to be provided in order to guarantee that no more than 1 vehicle in 50 will be unable to find a parking space?
Solution First, we need to determine the traffic load. The incoming flow rate is calculated as shown below. Q = 360 vehicles / 12 hours Q = 30 vehicles/hour The average parking duration is 10 minutes or 0.167 hours. The traffic load is calculated as shown below. A = 30 vehicles/hour × 0.167 hours A=5 The maximum probability of rejection is 1 in 50, or 0.02. Using the probability of rejection equation, we can solve for the number of spaces required.
AM! P 1A A A 2 M! Where: P A M
= the probability of rejection (0.02), = the traffic load (5), and = the number of parking stalls.
Solving the equation for M yields a value of 10. The parking lot at the sandwich shop must have at least 10 spaces, in order to meet the owner’s expectations. Note that we have used average parking rates in this analysis. The sandwich shop’s particular situation could dictate that more spaces are required. For example, say that the shop serves 80% of its customers between 11 A.M and 2 P.M. The majority of the customers are arriving during a much shorter time frame than the 12 hours that we used to find the incoming flow rate. In this case, more parking spaces would be required.
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4.6.
Glossary
Accessible Path: a barrier-free path that persons with mobility or sensory impairments can safely follow without obstacles or obstructions. Accessible paths are at least 5 feet wide and level. Aisle: the portion of the parking lot devoted to providing immediate access to the parking stalls. The recommended aisle width is dependent on the parking angle. A parking angle of 45 o requires an aisle width of 12 feet for a 9.0-foot stall, and a 90o parking angle requires an aisle width of 26 feet for a 9.0-foot stall. These dimensions lead to wall to wall distances of 47 feet for 45o and 63 feet for 90o. CBD: Central Business District, typically ranging from an average size of 27 blocks (10,000-25,000 population cities) to over 200 blocks (cities over 1,000,000 population). CBD Core: the heart of business, commercial, financial and administrative activity. Typically ranges in size from an average of 7 blocks (10,000-25,000 population cities) to over 60 blocks (cities over 1,000,000 population). CBD Fringe: the area immediately surrounding the CBD, usually within 2-3 blocks. Change of Mode: the transfer from one form of transportation to another. A park and ride lot is an example of a change of mode, where an auto driver parks the vehicle and rides public transportation for the remainder of the trip. Cordon Count: the simultaneous counting of all traffic entering and leaving a given area such as a CBD. It is generally a manual vehicle classification count, supplemented with automatic traffic recorder counts. Duration: the length of time a vehicle remains in one parking space. Long Term Parking: parking with a duration of three hours or more. Module: a complete module is one access aisle, servicing a row of parking on each side of the aisle. Both the access aisle and the parking stalls serviced by that aisle are part of the module. Outlying Business District: commercial area generally removed by a mile or more from a central CBD. Parking Accumulation: the total number of vehicles parked in a specific area (usually segregated by type of parking facility) at a specific time. Parking Demand: the number of vehicles with drivers desiring to park at a specific location or in a general area. It is usually expressed as the number of vehicles during the peak-parking hour. Parking Space or Stall: an area large enough to accommodate one parked vehicle with unrestricted access (no blockage by another parked vehicle). Parking Supply: the number of spaces available for use, usually classified by on-street curb (metered and unmetered), lot and garage. Further differentiation of the types of parking is useful, such as those available to the general public, and private spaces earmarked for a specific purpose such as loading. 77
Parking Volume: the total number of vehicles that park in a study area during a specific length of time. Partial Module: one access aisle combined with a single one-side row of parking. Short Term Parking: parking with a duration of three hours or less. Stall Length: The longitudinal dimension of the stall, normally 18.5 feet. Stall Width: The width of each parking space as measured crosswise to the vehicle. The most common width is 8.5 to 9.0 feet. Study Period: the time during which the parking study is conducted, usually between 10:00 A.M. and 6:00 P.M. Increasing emphasis, however, is being placed on inclusion of the morning and evening periods within the length of the study. Certain uses, such a theatres, may peak in the evening hours, while residential parking demand peaks around 3:00 A.M. Trip Purpose: the primary reason for the individual’s journey to the study area. Typical purposes include shopping, working, business, and recreation. Turning Radii: The radius of the circle that is traveled by the design vehicle when completing a turn. Large turning radii should be provided. These are a function of the parking angle and end island design, but in general the turning radii should be at least 18 feet. Turnover: the number of different vehicles parked at a specific parking space or facility during the study period. Parking turnover measures utilization. Van Accessible: a parking space that is at least 8 feet wide, with a minimum access aisle of 5 feet along the right side of the parking space.
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5. Roadway Design 5.1.
Introduction
Roadway Design consists of many steps, beginning with route selection and ending with highway construction. These steps include (but are not necessarily limited to):
Route selection Surveys and preparation of maps Determining design controls and criteria Calculating horizontal and vertical curve parameters (addressed in the Geometric Design chapter) Selecting appropriate cross-section elements and their parameters (lane and shoulder widths, slopes, etc.) Drawing roadway profiles and cross sections Developing traffic signal plans (addressed in the Signal Timing Design chapter) Specifying earthwork quantities (excavation and/or fill requirements)
This chapter addresses all of the elements listed above. There are three additional elements of roadway design not discussed in this chapter that are equally important:
Evaluating potential environmental impacts Determining pavement characteristics Preparing preliminary, intermediate and final cost estimates
As you can see, Roadway Design can be a long and complicated process. This chapter is designed to help the undergraduate engineering student understand the major aspects of this complex topic.
5.2.
Lab Exercises
This exercise will help increase your understanding of Roadway Design, by presenting a more complicated problem that requires more thorough analysis.
5.2.1.
Lab Exercise One: Roadway Design
In this lab exercise, you will be required to define the best alignment for a highway connecting two or more separate points on a topographical map. The topographical map may be supplied by your instructor, or you may be asked to find an appropriate map on your own. Your instructor will select the points that must be connected by your roadway. Your design should:
avoid damaging areas that are environmentally sensitive. include plots of the vertical profile of your roadway and existing points on the ground. obey AASHTO or local geometric design guidelines for setting grades, vertical curves, sight distances, and drainage requirements. include end area profiles (cut and fill) and complete earthwork calculations, using an appropriate shrinkage factor.
Your final design should be accompanied by a brief report that summarizes the details and features of your selected design. 79
Tasks to be Completed Task 1. Acquire a topographic map of a suitable area. Discuss possible ‘terminal’ points with your instructor and define any areas that are environmentally sensitive or especially hazardous. Task 2. Develop an optimum roadway alignment. Review AASHTO and/or local guidelines to check for grades, vertical curves, sight distances, or drainage requirements that are not met by the selected alignment. Modify as necessary. Task 3. Prepare a vertical profile diagram of the ground and centerline for the selected route by following the rules listed below.
State distances in feet from the end of the project. Round horizontal distances to nearest 50 ft. Calculate elevations along the alignment at every 100-ft station.
Task 4. At 100-ft stations, prepare cross-section diagrams of the ground and superimpose a highway cross-section template. Calculate cut and fill areas. Section lengths and average end areas may be used to calculate the cut and fill volumes. Task 5. Complete the earthwork calculations using an appropriate shrinkage factor. Prepare a masshaul diagram and determine whether you will have to borrow or waste any material in order to complete the project. Attempt to balance cut and fills.
5.3.
Theory and Concepts
The topics shown below are some of the nuts and bolts of basic roadway design. Additionally, because bike lanes have become a fundamental piece of most roadway construction or reconstruction projects, we've included a brief discussion on their basic design. Topics followed by the characters '[d]' include an Excel demonstration.
5.3.1.
Route Selection and Alignment
Two of the most important considerations in selecting the route for a proposed highway are 1. the physical features of the area and 2. how these features relate to the geometric design controls. Physical features that affect route selection include topography, ground (soil) conditions, and surrounding land use. Any possible environmental impacts posed by construction of a new highway must also be considered. First, the highway designer reviews topographic, geologic and soil maps as well as available aerial photographs of the area. The designer looks for conditions that will require sudden changes in alignment. For example, areas that would necessitate connecting long straight sections with sharp curves should be avoided. Areas that are subject to floods or avalanches make highway construction difficult, expensive and/or unsafe. Highway alignment is influenced by terrain. In general, the terrain or topography of an area is classified as level, rolling or mountainous. In level terrain, selection of an alignment is influenced by factors such as the cost of right-of-way, land use, waterways that may require expensive 80
bridging, existing roads, railroads, and subgrade conditions. In rolling terrain, a number of factors need to be considered, including: grade and curvature, depths of cut and heights of fill, drainage structures, and number of bridges. Grades are the greatest challenge in mountainous country.
Flat
Rolling
Mountainous
Typically, several preliminary maps are drawn showing various alignments. Selection of an alignment is a trial and error process, as the proposed alignments are checked for compliance with the horizontal and vertical control criteria. The selection of the final alignment is based on a comparison of costs and environmental and social impacts.
5.3.2.
Surveys and Maps
Acquisition of land for highway right of way requires a cadastral survey to establish existing property lines and to establish and mark (monument) new boundaries. Cadastral land surveyors identify and establish monuments that document the legal boundaries between public and private lands. A topographic survey is made to establish the configuration of the ground and the location of natural and man-made objects. A located centerline survey is generally made after the topographic survey is completed and alternative alignments have been evaluated. The final alignment is determined and then a survey of the centerline of the planned highway is conducted. Many different types of maps are produced in the course of designing a highway. The most common include:
Location or Vicinity Maps present the highway location in relation to surrounding physical features. Topographic Maps illustrate elevation with the use of contour lines and spot elevations. Planimetric Maps show features such as roads, buildings, water, fences, vegetation, bridges, railroads. Detail Base Maps, generally produced at scales ranging from 1:200 to 1:1000, combine features of the topographic and planimetric maps, and illustrate the following:
utilities (above and below ground) recorded survey monuments exposed geologic features section corners, property corners, right of way monuments and other pertinent boundaries or corners proposed highway alignment features such as stations, bearings, and curve data
Keep in mind that each jurisdiction probably has its own map requirements and map terminology. Examples of planimetric and cadastral survey maps are shown below.
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Planimetric Map
5.3.3.
Cadastral Survey
Design Controls and Criteria
The physical design of a new highway is controlled by many factors. This module addresses factors common to most of the functional classifications.
Design Speed "Design speed is the maximum safe speed that can be maintained over a specified section of a highway when conditions are so favorable that the design features of the highway govern." (AASHTO, 1990). The selection of a suitable design speed will depend on the terrain and functional class of the highway. Typical design speeds for freeways range from 50 mph to 70 mph depending on the terrain type (level, rolling or mountainous).
Traffic Volume The traffic engineer’s measure or indicator of traffic volume is the average daily traffic (ADT). The ADT is the volume that results from dividing a traffic count obtained during a given time period by the number of days in that time period. For example, given a traffic count of 52,800 vehicles that was taken over a continuous period of 30 days, the ADT for this count equals 1,760 vehicles (52,800 divided by 30). Another commonly used measure of traffic volume is the annual average daily traffic (AADT), which is determined by dividing a count of the total yearly traffic volume by 365. The ADT and the AADT are not the same and it’s important to be aware of the time period when calculating the ADT.
Design Hour Volume The DHV is a two-way traffic volume that is determined by multiplying the ADT by a percentage called the K-factor. Values for K typically range from 8 to 12% for urban facilities and 12 to 18% for rural facilities. Neither the AADT nor the ADT indicate the variations in traffic volumes that occur on an hourly basis during the day, specifically high traffic volumes that occur during the peak hour of travel. The traffic engineer has to balance the desire to provide an adequate level of service (LOS) for the peak hour traffic volume with proposing a design in which the highway capacity would only be utilized for a few hours of the year. This is where the design hour volume (DHV) comes in. 82
Directional Design Hour Volume The directional design hour volume (DDHV) is the one-way volume in the predominant direction of travel in the design hour, expressed as a percentage of the two-way DHV. For rural and suburban roads, the directional distribution factor (D) ranges from 55 to 80 percent. A factor of approximately 50 percent is used for urban highways. Keep in mind that the directional distribution can change during the day. For example, traffic volume heading into the central business district is usually higher than outbound traffic in the morning, but the reverse is true during the afternoon peak hour. In summary, DDHV = ADT (or AADT) × K × D.
Vehicle Characteristics Traffic engineers design highways that will accommodate all classes of vehicles. Width and height, overhangs and minimum turning paths at intersections are important parameters to have at hand during the design process. AASHTO states that the vehicle which should be used in designing for normal operations is the largest one that represents a significant percentage of the traffic for the design year.
Geometric Design Elements Major elements of the highway design include stopping sight distance, passing sight distance, and horizontal and vertical alignment. These elements are all addressed in the chapter "Geometric Design".
5.3.4.
Vertical Profile [d]
The vertical profile of a highway is made up of straight lines (grade lines) and curves, as shown in the following figure.
The curves joining the grade lines are called vertical curves, and their function is to make a smooth transition from one grade to another. Details of designing sag and crest vertical curves are presented in the chapter "Geometric Design". During or after completion of the detail base map (see Surveys and Maps), the traffic engineer prepares a vertical profile of the alignment. Information needed to create a vertical profile includes the vertical curve data and the elevations of the existing ground surface along the chosen route. The first step is to draw the existing ground level along the centerline of the proposed alignment, with elevation data on the vertical scale. Then draw the centerline of the alignment on the profile, as shown below:
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At a minimum, data included with the centerline are the elevation and stations of all points of intersection and the lengths of vertical curves. The Excel demonstration provided with this concept uses station notation and elevation information to develop a vertical crest curve and the accompanying information.
5.3.5.
Cross Section Elements [d]
Roadway cross sections include the elements shown below.
Travel Lanes Historically, 10-foot lanes were standard for "first-class" paved highways. Today, public agencies prefer lane widths of 12 feet for designing freeways and major traffic arterials. For two-lane highways, a 24-foot wide roadway is necessary for buses and commercial vehicles to have sufficient clearance. As demonstrated in the module on Capacity and Level of Service, lane width affects highway capacity. Anything less than 12 feet tends to reduce speed. However, there are instances when existing rights of way and development will control lane widths. These situations must be carefully evaluated in order to develop the safest design. The number of lanes is determined by estimates of traffic volumes and lane capacity, as discussed in the Capacity and Level of Service module. 84
Slopes usually fall in both directions from the centerline of two-lane highways. Each half of a divided roadway is sloped individually and may be crowned separately as well. Drivers barely perceive cross slopes up to 2 percent; 1.5 to 2 percent are common cross slope values. Values greater than 2 percent can be unsafe.
Shoulders The shoulder is the portion of the roadway between the outer edge of the traveled lane and the inside edge of the ditch, gutter, curb, slope or median (in divided roadways). As drivers, we all know the benefits of having adequate shoulder widths when our cars break down. Shoulders also provide lateral support for pavement subbase, base and surface courses. Shoulder widths are usually determined by the traffic volume and the percent of heavy vehicles. Shoulders vary in width from 2 feet to 6 feet on non-freeway roadways and from 4 feet to 10 feet on freeways or other major roads. Shoulders are sloped so that fluids drain away from the traveled roadway. In general, asphalt or concrete-paved shoulders are sloped from 2 to 6 percent, gravel shoulders from 4 to 6 percent and turf shoulders at about 8 percent.
Sideslopes The purpose of sideslopes is to provide a transition from the roadway shoulder to the original ground surface. Foreslopes extend from the shoulder edge to a drainage ditch or directly to the ground surface, depending on the terrain. Backslopes extend from the outside edge of the drainage ditch to ground surface or to the "cut" surface of a roadside. AASHTO states that foreslopes steeper than 3:1 (33%) are recommended only where conditions do not permit the use of flatter slopes. Backslopes steeper than 3:1 may be difficult to maintain and need to be evaluated with regard to slope stability.
5.3.6.
Cut and Fill Sections
Cut Sections A detailed engineering soils analysis of a proposed highway alignment is a crucial part of the highway design process. The results of the soils analysis are used to develop the design details of cut sections such as depth and slope of the cut. The engineer has to keep in mind that the volume of excavation increases significantly as the depth of the cut increases, and therefore usually tries to avoid excessive cut depths. Cut slopes are rarely steeper than 2:1 (2 units horizontal to 1 unit vertical or about 27 degrees from horizontal) except in very competent materials such as solid rock. AASHTO recommends that cut slopes steeper than 3:1 be evaluated with regard to soil stability and traffic safety.
Fill Sections The greatest amount of roadway construction in rural areas occurs on fill. In flat terrain, the highway pavement should be elevated several feet above the original ground surface to aid drainage. Slopes for fill should be determined in accordance with the guidelines discussed under Cross Section Elements. It is desirable to keep the height of the fill section to 30 feet or less, with 20 feet being a preferred maximum. With fill heights greater than 20 feet, it may be more economical to build a bridge, depending on the topography.
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5.3.7.
Earthwork [d]
One important aspect of roadway design is determining the amount of earthwork necessary on a project. Earthwork includes the excavation of existing earth material and any placement of fill material required for constructing the embankment. The manual method for determining earth excavation and embankment amounts involves three steps: cross sections of the proposed highway are placed on the original ground cross sections, the areas in cut and the areas in fill are calculated, and the volumes between the sections are computed. Cut and fill are the terms that are usually used for the areas of the section; the terms excavation and embankment generally refer to volumes. The methods used to manually calculate cut and fill areas are presented in most surveying textbooks. Mass diagrams (or mass-haul diagrams) are plots of the cumulative volumes of cut and fill along an alignment. Typically, the mass diagram is plotted below a profile of the route, with the ordinate at any station representing the sum of the volumes of cut and fill up to that station. An example of a mass diagram is shown below, with its associated profile. Steps used to create a mass diagram are presented in the Excel demonstration included with this page. The most economical way to handle the distribution of earthwork volumes can be determined from the diagram.
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The rising curve on the mass diagram indicates excavation and a descending curve indicates embankment. If a horizontal line is drawn to intersect the diagram at two points, excavation and embankment (adjusted for shrinkage) will be equal between the two stations represented by the points of intersection. Such a horizontal line is called a balance line, because the excavation balances the embankment between the two points at its ends. Since the ordinates represent the cumulative volume of excavation and embankment, the total volumes of excavation and embankment will be equal where the final ordinate equals the initial ordinate. If the final ordinate is greater than the initial ordinate, there is an excess of excavation (as shown in this mass diagram); if it is less than the initial ordinate, the volume of embankment is the greater and additional material must be obtained to complete the embankment. Highway engineers strive to balance the amount of cut and fill during a highway construction project to avoid costly hauling of materials.
5.3.8.
Designing Bike Lanes
The Intermodal Surface Transportation Efficiency Act (ISTEA) places increased importance on the use of the bicycle as a viable transportation mode, and calls on each state Department of Transportation to encourage its use. AASHTO's Guide for the Development of Bicycle Facilities is the basic reference for bicycle facility designers. It has been adopted, in part or in its entirety, by many state and local governments. The AASHTO bicycle guidelines state "all new highways, except those where bicyclists will be legally prohibited, should be designed and constructed under the assumption that they will be used by bicyclists." On existing multi-lane arterials and collectors with relatively high motor vehicle volumes and/or significant truck/bus traffic, a right (curb) lane wider than 12 feet is desirable to better accommodate both bicyclists and motor vehicles in the same travel lane. AASHTO and the National Advisory Committee on Uniform Traffic Control Devices suggest reducing the inside vehicle lanes from 12 feet to 11 feet for the purpose of widening the right-hand lane for bicycle use. The AASHTO bicycle guidelines recommend a "usable" curb lane width of 14 feet on road segments where parking is not permitted in the curb lane. Usable width generally cannot be measured from curb face to lane stripe, because adjustments must be made for drainage grates (even the "bicycle safe" ones) and longitudinal joints between pavement and gutter sections. For instance, on those road segments where no parking is allowed but drainage grates and the longitudinal joints are located 18 inches from the curb face, the travel lane (from joint line to lane stripe) should be 14 feet in width, reflecting the unsuitability of bicycle riding on the outside 18 inches of the roadway. If parking is permitted in the curb lane, then the minimum width of the curb lane, from curb face to through travel lane is 14 feet, with 15 feet being the desirable width. In this design situation, the lane width is measured from the curb face, since parked motor vehicles can occupy the curb flag (gutter section). Conversely, when bicycles travel directly adjacent to a curb, they cannot safely operate in the gutter section. Wide curb lanes are not striped or generally promoted as "bicycle routes", but are often all that is needed to accommodate bicycle travel. An example of a 151/2-foot curb lane is shown below.
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Bicycle lanes are constructed when it is desirable to delineate available road space for preferential use by bicyclists or motorists and to provide for more predictable movements by each. Bicycle lane markings can increase a bicyclist's confidence that motorists will not stray into his/her path of travel. Likewise, passing motorists are less likely to swerve to the left out of their lane to avoid bicyclists on their right. Bike lanes are generally established on urban arterials and sometimes on urban collector streets. Bicycle lanes are delineated by painted lane markings. They should always be one-way facilities and carry traffic in the same direction as adjacent motor vehicle traffic. Twoway bicycle lanes on one side of the roadway are unacceptable because they promote riding against the flow of motor vehicle traffic. Wrong-way riding is a major cause of bicycle accidents. Bicycle lanes on one-way streets should be on the right of the street, except in areas where a bicycle lane on the left will decrease the number of conflicts (e.g., those caused by heavy bus traffic).
5.4.
Professional Practice
In order to supplement your knowledge about the various concepts within roadway design, and in order to give you a glimpse of how these various topics are discussed in the professional environment, we have included selected excerpts from professional design manuals.
5.4.1.
Route Selection
The following excerpt was taken from page 226 of the 1990 edition of AASHTO's A Policy on Geometric Design of Highways and Streets.
The topography of the land traversed has an influence on the alignment of roads and streets. Topography does affect horizontal alignment, but it is more evident in the effect on vertical alignment. To characterize variations, engineers generally separate topography into three classifications according to terrain. Level terrain is that condition where highway sight distances, as governed by both horizontal and vertical restrictions, are generally long or could be made to be so without construction difficulty or major expense. Rolling terrain is that condition where the natural slopes consistently rise above and fall below the road or street grade and where occasional steep slopes offer some restriction to normal horizontal and vertical roadway alignment.
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Mountainous terrain is that condition where longitudinal and transverse changes in the elevation of the ground with respect to the road or street are abrupt and where benching and side hill excavation are frequently required to obtain horizontal and vertical alignment. Terrain classification pertains to the general character of a specific route corridor. Routes in valleys or passes or mountainous areas that have all the characteristics of roads or streets traversing level or rolling terrain should be classified as level or rolling. In general, rolling terrain generates steeper grades, causing trucks to reduce speeds below those of passenger cars, and mountainous terrain aggravates the situation, resulting in some trucks operating at crawl speeds.
5.4.2.
Surveys and Maps
The following excerpt was taken from pages 1-2 of the 1996 Oregon Department of Transportation Highway Design Manual.
Before a control traverse is run in the field, careful planning and research must be done. The county surveyor's office contains a wealth of knowledge about existing monumentation along the course of the project i.e., public land survey corners, property corners, GPS monuments, etc. Roadway Engineering in Salem, Oregon has on file all of the right of way maps, transit notes and asconstructed plans. For help with general orientation of a project, a 7.5 minute or 15 minute quad sheet is helpful. The quad sheet will also show section corners that have been found or reset, to assist with your field search. With the above information in hand, some careful planning about the project is the next step. Identify what will be used for the control of this project i.e., NGS or NOAA control monuments, new GPS control points, existing right of way monuments or random traverse points with solar observation for basis of bearing. Identify which public land survey corners will be tied on the project. No less than 2 corners per township will be tied unless it is determined that there is insufficient monumentation along the project to meet this requirement. Public land survey corners will be tied on each end of the project.
Cadastral Survey Acquisition of land for highway right of way requires a cadastral survey to establish existing property lines and to establish and monument new boundaries. This work must be done in compliance with the laws of the State of Oregon....
Topographical Survey The topographic survey is made to establish the configuration of the ground and the location of natural and man-made objects. A planimetric map made by Photogrammetry will be of value, but some field survey work is usually necessary to complete the topographic map.
5.4.3.
Design Controls and Criteria
Driver performance is one of the roadway design criteria that is not quantifiable, but is important. The following excerpt on driver performance was taken from page 42 of the 1990 edition of AASHTO's A Policy on Geometric Design of Highways and Streets.
An appreciation of driver performance is essential to proper highway design and operation. Design suitability rests as much on the ability of the highway to be used safely and efficiently as on any 89
other criterion. When drivers use a highway designed to be compatible with their capabilities and limitations, their performance is aided. When a design is incompatible with the attributes of drivers, the chances for driver errors increase, and accidents and inefficient operation often result. At the start of the 20th century, approximately 4 percent of American's population was 65 years of age or older. Persons 65 years of age or older accounted for 15 percent of the driving age population in 1986, and will increase to 22 percent by the year 2030. Elderly drivers and pedestrians are a significant and rapidly growing segment of the traffic stream with a variety of age-related sensory-motor impairments. As a group, they have the potential to adversely affect the highway system's safety and efficiency... Thus, designers and engineers should be aware of the problems and requirements of the elderly, and consider applying applicable measures to aid their performance.
5.4.4.
Horizontal and Vertical Alignment
The following excerpt about the combination of horizontal and vertical alignments in roadway design was taken from page 297 of the 1990 edition of AASHTO's A Policy on Geometric Design of Highways and Streets.
Coordination of horizontal alignment and profile should not be left to chance but should begin with preliminary design, during which stage adjustments can readily be made. Although a specific order of study for all highways cannot be stated, a general procedure applicable to most facilities can be outlined. The designer should use working drawings of a size, scale and arrangement so that he can study long, continuous stretches of highway in both plan and profile and visualize the whole in three dimensions. Working drawings should be of sufficiently small scale, generally 1 inch = 100 feet or 1 inch = 200 feet with the profile plotted jointly with the plan. A continuous roll of plan-profile paper usually is suitable for this purpose. After study of the horizontal alignment and profile in preliminary form, adjustments in each, or both, can be made jointly to obtain the desired coordination. At this stage the designer should not be concerned with line calculations other than known major controls. The study should be made largely on the basis of a graphical analysis... The coordination of horizontal alignment and profile from the viewpoint of appearance usually can be accomplished visually on the preliminary working drawings. Generally, this visual method results in a satisfactory product when done by an experienced designer. This means of analysis may be supplemented by models or perspective sketches at locations where the effect of certain combinations of line and grade are questionable.
5.4.5.
Cross Sections
The following excerpt was taken from page 328 of the 1990 edition of AASHTO's A Policy on Geometric Design of Highways and Streets.
Two-lane and wider undivided pavements on tangents or on flat curves have a crown or high point in the middle and slope downward toward both edges. The downward cross slope may be a plane or curved section or a combination of the two. With plane cross slopes, there is a cross slope break at the crown line and a uniform slope on each side. Curved cross sections usually are parabolic, with a slightly rounded surface at the crown line and increasing cross slope toward the pavement edge. 90
Because the rate of crown slope is variable, the parabolic section is described by the crown height, i.e., the vertical drop from the center crown line to the pavement edge. The advantage of the curved section lies in the fact that the cross slope steepens toward the pavement edge, thereby facilitating drainage. The disadvantages are that curved sections are more difficult to construct, the cross slope of the outer lanes may be excessive, and warping of pavement areas at intersections may be awkward or difficult to construct. On divided highways, each one-way pavement may be crowned separately, as on two-lane highways, or it may have a unidirectional slope across the entire width of pavement, which is almost always downward to the outer edge. Where freeze-thaw conditions are a problem, each pavement of a divided highway should be crowned separately.
5.5.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable roadway design concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic.
5.5.1.
Traffic Volume
Consider a rural highway with a projected 20-year AADT of 40,000 vpd. For the type of highway and region in question, it is known that peak-hour traffic currently is approximately 20% of the AADT, and that the peak direction generally carries 65% of the peak-hour traffic. What is the DDHV?
Solution An approximate DDHV could be estimated as DDHV = AADT×K×D. K is the percentage of the AADT that occurs in the peak hour and D is the directional distribution percentage. Therefore, DDHV = 40,000 × 0.20 × 0.65 = 4000 vph
5.5.2.
Vertical Alignment
A highway design includes the intersection of a +5.8% grade with a –2.9% grade at station 1052+75 at elevation 100.50 feet above sea level. Calculate the center line elevation along this highway for every 100-ft station on a parabolic vertical curve of 600-ft length. You’ll need to use concepts introduced in the Geometric Design Chapter.
Solution The VPC is at station 1052+75 – 3+00 = 1049+75 The elevation of the VPC equals the elevation of the VPI minus ½ of the curve length times the initial grade = 100.50 - (300 × 0.058) = 83.10 feet. The VPT is at station 1052+75 + 3+00 = 1055+75 The elevation of the VPT equals the elevation of the VPI minus ½ of the curve length times the second grade = 100.50 - (300 × 0.029) = 91.80 feet. 91
The equation for a parabolic vertical curve is y = (r / 2) * x2 + g1 * x + (elevation of VPC) where y = station elevation, r = rate of change of the grade of the curve [(g2 - g1) / (length of curve in stations)] and x = stations beyond the VPC. First, r = (-2.9 - 5.8) / 6 = -1.45% per station. The computations are shown in the following table. Station
x
x2
(r/2) * x2
g1 * x
1049+75 1050+75 1051+75 1052+75 1053+75 1054+75 1055+75
0 1 2 3 4 5 6
0 1 4 9 16 25 36
0 -0.73 -2.90 -6.53 -11.60 -18.13 -26.10
0.00 5.80 11.60 17.40 23.20 29.00 34.80
5.5.3.
Elevation VPC 83.10 83.10 83.10 83.10 83.10 83.10 83.10
Elevation Curve 83.10 88.18 91.80 93.98 94.70 93.98 91.80
Cross Sections
Right-of-way width is the sum of the cross section elements such as the number of lanes, shoulders, ditches, and sideslopes. Determine the minimum width of the right of way for a four lane rural highway (two lanes in each direction) with the following dimensions:
12–foot lanes at a slope of 2% 6-foot shoulders at a slope of 6:1 Ditch width is 2 feet 10-foot foreslopes at a slope of 3:1 15-foot backslopes at a slope of 3:1.
The dimensions are measured along the surface of the element.
Solution Using the pythagorean theorem, the width required for 4 lanes is 4 × (12 / (12 + 0.022) × 1/2) = 48 feet. Using the same procedure for the remaining elements: Shoulder width = 2 × (6 / (12 + (1/6) × 2) × 1/2) = 11.8 feet Ditch width = 2 × 2 = 4 feet Foreslope width = 2 × (10 / (12 + (1/3) × 2) × 1/2) = 19 feet Backslope width = 2 × (15 / (12 + (1/3) × 2) × 1/2) = 28.5 feet Total width = 48 + 11.8 + 4 + 19 + 28.5 = 111.3 feet
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5.6.
Glossary
AADT: Annual average daily traffic determined by dividing a count of the total yearly traffic volume by 365. Units are vehicles per day. ADT: Average daily traffic that results from dividing a traffic count obtained during a given time period by the number of days in that time period. Cadastral Survey: A survey that identifies the legal boundaries between public and private lands. Design Speed: The maximum safe speed that can be maintained when conditions permit the design features of the highway to govern. D: Directional distribution. The percentage of the two-way traffic volume traveling in the direction of interest, expressed as a decimal. DHV: Design hour volume. The two-way traffic volume that is determined by multiplying the ADT by a percentage factor called the K-factor (see below). DDHV: Directional design hour volume expressed as vehicles per hour. Functional Class: The classification of roadways by operational status such as freeway, arterial, collectors and local. K-factor: The proportion of daily traffic occurring during the peak hour, expressed as a decimal. For design purposes, K represents the proportion of AADT occurring during the thirtieth highest peak hour of the year. Located Centerline Survey: A survey of the centerline of a planned or existing highway. Planimetric Map: Illustrates features such as roads, buildings, water, fences, vegetation, bridges, railroads. Stations: Points along a line (usually a survey line) of equal distance designated either in feet or meters. Points at multiples of 100 meters or feet are typically called full stations. Topographic Map: Illustrates elevation with the use of contour lines and spot elevations. Topographic Survey: A survey that establishes the configuration of the ground and the location of natural and man-made objects.
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6. Signal Timing Design 6.1.
Introduction
There are innumerable locations around the country where roads intersect. Conflicting traffic movements cannot share the same space at the same time. Because of their ability to separate traffic movements in time, traffic signals are one of the most common regulatory fixtures found at intersections. Since traffic signals are so common, professional engineers are often expected to know the basics of Signal Timing Design. Signal Timing Design, at its simplest level, involves finding the appropriate duration for all of the various signal indications. The design process involves assembling the results of several independent calculations. This chapter introduces the fundamentals of Signal Timing Design by discussing each step of the process in detail.
6.2.
Lab Exercises
This exercise will help increase your understanding of Signal Timing Design, by presenting a more complicated problem that requires more thorough analysis.
6.2.1.
Lab Exercise One: Signal Timing and LOS
Your assignment is to determine the level of service (LOS) at which a local intersection is functioning during its peak period. If the measured LOS is unacceptable, you are to propose changes to the signal-timing plan that would correct the problem or show why an easy solution does not exist. Your instructor may select an intersection in your area for this analysis, or you may be allowed to select an intersection. In addition, your instructor may indicate specific movements that are of particular interest.
Tasks to be Completed Task 1. Measure and record the dimensions of the study intersection. Prepare a dimensioned drawing of the facility. Task 2. During the peak period, record the average lengths of the various signal indications. You should record enough information to accurately describe the current signal-timing plan for the intersection. Task 3. During the peak period, record the number of vehicles passing through the intersection within each of the various movements. Make sure you record enough information to complete the required LOS computations. Task 4. Determine the LOS of the various intersection movements using the information you have collected. Record any interesting observations. Task 5. If the LOS analysis reveals a problem, propose a new signal-timing plan that would correct the problem or show why an easy solution does not exist.
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Task 6. Prepare a brief report that outlines your work and summarizes your conclusions and proposals.
6.3.
Theory and Concepts
Signal timing design incorporates several calculations that seem, at first, to be completely independent. The results of these calculations, however, are all pieces of a larger puzzle, which is assembled at a later stage. The concepts that are the most crucial to signal timing design are listed below. Simply click on the links to explore these concepts.
6.3.1.
Basic Timing Elements
Signalized intersections permit conflicting traffic movements to proceed efficiently and safely through space that is common to those movements. This is accomplished by separating the individual movements in time rather than in space. The various movements are collected and allowed to move in turn, or in phases. Each phase of a signal cycle is devoted to only one collection of movements. These movements are those that can proceed concurrently without any major conflict. For example, the straight-through and right-turn movements of a street can be permitted to use an intersection simultaneously without any danger to the motorists involved. This might be one phase of a multi-phase cycle. Some movements are allowed to proceed during a phase even though they cause conflicts. Pedestrians are commonly allowed to proceed across intersections even though right-turn movements are occurring. These movements are called permitted, while protected movements are those without any conflicts. In any case, the movements at an intersection can be grouped, and then these groups can be served during separate phases. The basic timing elements within each phase include the green interval, the effective green time, the yellow or amber interval, the all-red interval, the intergreen interval, the pedestrian WALK interval, and the pedestrian crossing interval. Each of these elements is described below.
The green interval is the period of the phase during which the green signal is illuminated. The yellow or amber interval is the portion of the phase during which the yellow light is illuminated. The effective green time is contained within the green interval and the amber interval. The effective green time, for a phase, is the time during which vehicles are actually discharging through the intersection. The all-red interval is the period following the yellow interval in which all of the intersection's signals are red. The intergreen interval is simply the interval between the end of green for one phase and the beginning of green for another phase. It is the sum of the yellow and all-red intervals. The pedestrian WALK interval is the portion of time during which the pedestrian signal says WALK. This period usually lasts around 4-7 seconds and is completely encompassed within the green interval for vehicular traffic. Some pedestrian movements in large cities are separate phases unto themselves. Finally, the pedestrian crossing time is the time required for a pedestrian to cross the intersection. This is used to calculate the intergreen interval and the minimum green time for each phase. 95
This brief look at the basic signal timing elements should help you navigate through the rest of the signal timing design concepts. Please remember to visit the glossary if you aren't sure about a definition.
6.3.2.
Queuing Theory [d]
Queuing theory provides the design engineer with a traffic flow model that can be used in the design of signalized intersections. Consider a simple situation in which traffic is arriving at an intersection approach in a uniform manner, with equal and constant headways between each vehicle. This constant flow rate is shown in the figure below.
Figure 1: Constant Arrival Flow During the red interval for the approach, vehicles cannot depart from the intersection and consequently, a queue of vehicles is formed. When the signal changes to green, the vehicles depart at the saturation flow rate until the standing queue is cleared. Once the queue is cleared, the departure flow rate is equal to the arrival flow rate. Figure 2 illustrates this behavior..
Figure 2: Departure Flow or Service Flow versus Time The combined effect of the arrival and departure flow rates is illustrated by graphing queue length versus time. During the red interval, the line of vehicles waiting at the intersection begins to increase. The queue reaches its maximum length at the end of the red interval. When the signal changes to green, the queue begins to clear as vehicles depart from the intersection at the saturation flow rate. See the figure below.
Figure 3: Queue Length versus Time
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There is another graph that allows us to glean even more information from our model. Imagine a plot where the x-axis is time and the y-axis contains the vehicle numbers according to the order of their arrival. Vehicle one would be the first vehicle to arrive during the red interval and would be the lowest vehicle on the y-axis. If you were to plot the arrival and departure (service) times for each vehicle, you would get a triangle as shown in figure 4 below.
Figure 4: Vehicles versus Time While this graph may not seem informative at first, a second look reveals its insights. For a given time, the difference between the arrival pattern and the service pattern is the queue length. For a given vehicle, the difference between the service pattern and the arrival pattern is the vehicle delay. In addition, the area of the triangle is equivalent to the total delay for all of the vehicles. See figure 5 below.
Figure 5: Graph Properties As you would expect, the first vehicle to be stopped by the red signal experiences the most delay. In addition, the queue is longest just before the green interval begins. Queuing theory provides a foundation for the optimization of signal timing.
6.3.3.
Design Process Outline
This page is meant to guide you through the design process. Knowing a little more about how these various concepts are used together will make the individual concepts easier to understand. Pre-Design Data Collection:
The design of signal timing schemes is a fairly simple, though multi-step process. First, you need to know most of the roadway conditions surrounding the intersection you are working on. This includes the number of lanes, the width of the lanes, the width of the intersection, the width of the shoulders, and more. Second, you need to have information regarding the composition of the traffic, such as the percentage of busses and the percentage of trucks within the traffic stream. You also need to know the peak hour volumes and peak fifteen-minute volumes for all of the various movements. 97
The Design Process:
The basic steps in the design process (assuming you are using Webster's method – see Cycle Length Determination module) are listed below. While this particular listing is oriented toward Webster's method, most of the other methods incorporate the same concepts, but in a slightly different way. 1. 2. 3. 4. 5.
Decide on a phasing plan. Calculate the length of the intergreen period for each phase of your cycle. Calculate the minimum green time for each phase based on the pedestrian crossing time. Calculate or measure the saturation flow rate for each approach or lane. Calculate the design flow rate for each approach or lane using the peak hour volume and peak hour factor. 6. Find the critical movements or lanes, and calculate the critical flow ratios. 7. Calculate the optimum cycle length. 8. Allocate the available green time using the critical flow ratios from step six. 9. Calculate the capacity of the intersection approaches or lanes. 10. Check the capacities/design flow rates and green intervals/minimum green intervals. Adjust your cycle timing scheme if necessary. Even though this outline is tailored for Webster's method, you'll find that most of the other design methods involve many of the same calculations. Refer to this roadmap frequently as you proceed through this chapter, so that you can see how each calculation is related to the design process.
6.3.4.
Intergreen Time [d]
The intergreen period of a phase consists of both the yellow (amber) indication and the all-red indication (if applicable). This phase is governed by three separate concepts: stopping distance, intersection clearance time, and pedestrian crossing time, if there are no pedestrian signals. The yellow signal indication serves as a warning to drivers that another phase will soon be receiving the right-of-way. The intergreen interval, therefore, should be long enough to allow cars that are greater than the stopping distance away from the stop-bar to brake easily to a stop. The intergreen interval should also allow vehicles that are already beyond the point-of-no-return to continue through the intersection safely. This issue is called the"dilemma zone" concept. If the intergreen time is too short, only those vehicles that are close to the intersection will be able to continue through the intersection safely. In addition, only vehicles that are reasonably distant will have adequate time to react to the signal and stop. Those who are in between will be caught in the "dilemma zone," and won’t have enough time to stop or safely cross the intersection. Figure 1 shows this situation graphically.
Figure 1: Dilemma Zone The only responsible thing to do, it seems, is to eliminate the dilemma zone. This would allow any vehicle, regardless of its location, to be able to safely stop or, alternatively, safely proceed during the intergreen period. This is done by making sure that any vehicle closer to the intersection than its minimum braking distance can safely proceed through the intersection without accelerating or speeding. 98
First, we calculate the minimum safe stopping distance. The equation for this distance is given below and a more detailed discussion of this distance can be found in the geometric design portion of this website. Minimum Safe Stopping Distance:
1. 4 7 V SD 1.47V t 30 fG Where: SD Vo tr f G
= Min. safe stopping dist. (ft) = Initial velocity (mph) = Perception/Reaction time (sec) = Coefficient of friction = Grade, as a percentage
Next, we calculate the time required for a vehicle to travel the minimum safe stopping distance and to clear the intersection. This is simple kinematics as well. Intersection Clearance Time:
T SD1.47L VW Where: T Vo L SD W
= Intersection clearance time (sec) = Initial velocity (mph) = Length of the vehicle (ft) = Min. safe stopping dist. (ft) = Width of the intersection (ft)
Now that you’ve determined the first two elements of the intergreen period length—stopping distance and intersection clearance time—you need to consider the pedestrians. The intergreen time for intersections that have signalized pedestrian movements is the same as the intersection clearance time. If you have an intersection where the pedestrian movements are not regulated by a separate pedestrian signal, you need to protect these movements by providing enough intergreen time for a pedestrian to cross the intersection. In other words, if a pedestrian begins to cross the street just as the signal turns yellow for the vehicular traffic, he/she must be able to cross the street safely before the next phase of the cycle begins. The formula for this calculation is shown below. Pedestrian Crossing Time:
PCT WV Where: PCT
= Pedestrian crossing time (sec) 99
W V
= Width of the intersection (feet) = Velocity of the pedestrian (usually 4 ft/sec)
Once you have considered the safety of both the vehicular traffic and the pedestrian traffic for the given phase, you can choose the intergreen time. The intergreen time is equal to whichever is larger, the pedestrian crossing time or the intersection clearance time. As you know, the intergreen period is composed of the yellow interval and the all-red interval. The allocation of the intergreen time to these separate intervals is a question that is answered best by referring you to your local codes. In some areas, the yellow time has been standardized for several speeds. This would make the all-red time the difference between the standard yellow time and the intergreen time. One other option is to allocate all of the intergreen period as calculated to the yellow interval. You could then tack on an all-red period as a little extra safety. This, however, might increase delay at your intersection.
6.3.5.
Pedestrian Crossing Time, Minimum Green Interval [d]
The pedestrian crossing time serves as a constraint on the green time allocated to each phase of a cycle. Pedestrians can safely cross an intersection as long as there are not any conflicting movements occurring at the same time. (Permitted left and right turns are common exceptions to this rule.) This allows pedestrians to cross the intersection in both the green interval and the intergreen interval. Thus, the sum of the green interval and the intergreen interval lengths, for each phase, must be large enough to accommodate the pedestrian movements that occur during that phase. At this point, two separate conditions arise. If you have an intersection in which the pedestrian movements are not assisted by a pedestrian signal, you need to make sure that the green interval that you provide for vehicles will service the pedestrians as well. In this case, the minimum green interval length is somewhere between 4 and 7 seconds. You already took care of the pedestrian crossing time considerations when you calculated the intergreen period length. (See the module on the intergreen period.) If, on the other hand, you plan to provide a pedestrian signal, you need to calculate the pedestrian crossing time as described below. This will not only give you the information you need to program the pedestrian signal, but it will also allow you to find the minimum green interval for your vehicular movements as well. We only need a few assumptions to calculate the pedestrian crossing time. Assumptions:
The WALK signal will be illuminated for approximately 7 seconds. A pedestrian will begin to cross the street just as the DON'T WALK signal begins to flash. Pedestrians walk at an average pace of 4 feet/second. The WALK interval must be completely encompassed by the green interval of the accompanying vehicle movements.
Calculations: The total time required for the pedestrian movements (T) is the sum of the WALK allowance (Z) and the time required for a person to traverse the crosswalk (R). 100
R = (width of intersection, in feet) / (4 ft/sec) T = Z + R The pedestrian crossing time governs the minimum green time for the accompanying phase in the following way. If the time it takes the pedestrian to traverse the crosswalk (R) is greater than the intergreen time (I), the remainder of the time (Z+R-I) must be provided by the green interval. Therefore, the minimum green interval length (gmin) for each phase can be calculated using the equation below. gmin = T - intergreen time (I)
or
gmin = Z + R – I
If the above equation results in a minimum green interval that is less than the WALK time (Z), the minimum green interval length is equal to the WALK time (Z). gmin = Z You now have the minimum length of the green interval for the vehicular movements, as governed by the pedestrian movements. The WALK interval for the pedestrians is whatever you assumed, and the DON'T WALK flashes for the remainder of the green and intergreen intervals. Many design manuals suggest that the distance the pedestrian is assumed to travel can be reduced to the distance between the curb and the center of the farthest lane. On another note, if the vehicular traffic requires an extended green period, feel free to let the pedestrains partake of the extra time as well.
6.3.6.
Saturation Flow Rate and Capacity [d]
Saturation Flow Rate
Saturation Flow Rate can be defined with the following scenario: Assume that an intersection’s approach signal was to stay green for an entire hour, and the traffic was as dense as could reasonably be expected. The number of vehicles that would pass through the intersection during that hour is the saturation flow rate. Obviously, certain aspects of the traffic and the roadway will effect the saturation flow rate of your approach. If your approach has very narrow lanes, traffic will naturally provide longer gaps between vehicles, which will reduce your saturation flow rate. If you have large numbers of turning movements, or large numbers of trucks and busses, your saturation flow rate will be reduced. Put another way, the saturation flow rate (s) for a lane group is the maximum number of vehicles from that lane group that can pass through the intersection during one hour of continuous green under the prevailing traffic and roadway conditions. The saturation flow rate is normally given in terms of straight-through passenger cars per hour of green. Most design manuals and textbooks provide tables that give common values for trucks and turning movements in terms of passenger car units (pcu). Determining the saturation flow rate can be a somewhat complicated matter. The saturation flow rate depends on roadway and traffic conditions, which can vary substantially from one region to another. It’s possible that someone in the area has already completed a measurement of the saturation flow rate for an approach similar to yours. If not, you'll need to measure it in the field. One other possibility, which is used quite frequently, is to assume an ideal value for the saturation flow rate and adjust it for the prevailing conditions using adjustment factors. A saturation flow rate 101
of 1900 vehicles/hour/lane, which corresponds to a saturation headway of about 1.9 seconds, is a fairly common nominal value. Design manuals usually provide adjustment factors that take parameters such as lane-width, lan e-width, pedestrian traffic, traf fic, and traffic composition compositio n into account. Capacity
Capacity is an adjustment of the saturation flow rate that takes the real signal timing into account, since most signals are not allowed to permit the continuous movement of one phase for an hour. If your approach has 30 minutes of green per hour, you could deduce that the actual capacity of your approach is about half of the saturation flow rate. The capacity, therefore, is the maximum hourly flow of vehicles that can be discharged through the intersection from the lane group in question under the prevailing traffic, roadway, and signalization conditions. The formula for calculating capacity (c) is given below.
c Cg s Where: c g C s
= capacity (pcu/hour) = Effective green time for the phase in question (sec) = Cycle length (sec) = Saturation flow rate (pcu/hour)
Capacity can be calculated on several levels, depending on the amount of information you want to obtain. You could calculate the capacity for each individual lane, or you could lump the lanes together and find the capacity of an entire approach. You need to decide what makes sense for your situation. Capacity can be used as a reference to gauge the current operation of the intersection. For example, let us assume that you know the current flow rate for a lane group and you also know the capacity of that lane group. If the current flow rate is 10% of the capacity, you would be inclined to think that too much green time has been allocated to that particular lane group. You'll see other uses for capacity as you explore the remaining signal timing design concepts.
6.3.7.
Peak Hour Volume, Peak Hour Factor, Design Flow Rate
Peak Hour Volume Volume
The peak hour volume is the volume of traffic that uses the approach, lane, or lane group in question during the hour of the day that observes the highest traffic volumes for that intersection. For example, rush hour might be the peak hour h our for certain interstate int erstate acceleration ramps. The peak hour volume would be the volume of passenger car units that used the ramps during rush hour. Notice the conversion to passenger car units. The peak hour volume is normally given in terms of passenger car units, since changing turning all vehicles into passenger car units makes these volume calculations more representative of what is actually going on. The peak hour flow rate is also given in passenger car units/hour. Sometimes these two terms are used interchangeably because they are identical numerically.
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Peak Hour Factor Factor
The peak hour factor (PHF) is derived from the peak hour volume. It is simply the ratio of the peak hour volume to four times the peak fifteen-minute volume. For example, during the peak hour, there will probably be a fifteen-minute period in which the traffic volume is more dense than during the remainder of the hour. That is the peak fifteen minutes, and the volume of traffic that uses the approach, lane, or lane group during those fifteen minutes is the peak fifteen-minute volume. The peak hour factor is given giv en below. Peak Hour Factor:
Peak hour volume PHF 4 Peak Peak ifteen ifteen minute nute volume volume Design Flow Rate
The design flow rate or the actual flow rate, for an approach, lane, or lane group is the peak hour volume (flow rate) for that entity divided by the peak hour factor. A simpler way to arrive at the design flow rate is to multiply the peak fifteen-minute volume by 4. However you derive the figure, most calculations, such as those that measure the current use of intersection capacity, require the actual flow rate (design flow rate).
6.3.8.
Critical Movement or Lane [d]
While each phase of a cycle can service several movements or lanes, some of these lanes will inevitably require requir e more time than others to discharge disch arge their queue. For example, the right-turn movement of an approach may service two cars while the straight-through movement is required to service 30 cars. The net effect is that the right-turn movement will be finished long before the straight-through movement. What might seem to be an added complexity is really an opening for simplicity. If each phase is long enough to discharge the vehicles in the most demanding lane or movement, then all of the vehicles in the movements or lanes with lower time requirements will be discharged as well. This allows the engineer to focus on one movement per phase instead of all the movements in each phase. The movement or lane for a given phase that requires the most green time is known as the critical movement or critical lane. The critical movement or lane for each phase can be determined using flow ratios. The flow ratio is the design (or actual) flow rate divided by the saturation flow rate. The movement or lane with the highest flow ratio is the critical movement or critical lane. You will see how this concept is applied in the cycle length and green split discussions.
6.3.9.
Cycle Length Determination [d]
Once you know the total cycle length, you can subtract the length of the amber and all-red periods from the total cycle length and end up with the total time available for green signal indications. Efficiency dictates that the cycle length should be long enough to serve all of the critical movements, but no longer. If the cycle is too short, there will be so many phase changes during an hour that the time lost due to these changes will be high compared to the usable green time. But if the cycle is too long, delays will be lengthened, as vehicles wait for their turn to discharge through the intersection. Figure 1 provides a graphical portrayal of this phenomenon.
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Figure 1: Cycle Length versus Delay Several methods for solving this optimization problem have already been developed, but Webster’s equation is the most prevalent. Webster's equation, which minimizes intersection delay, gives the optimum cycle length as a function fu nction of the lost times and the critical flow ratios. Many design manuals use Webster's equation as the basis for their design and only make minor adjustments to suit their purposes. Webster's equation is shown below.
C 1.15L ∑V5 s Where: Co L V/s
= Optimum cycle length (sec) = Sum of the lost time for all phases, usually taken as the sum of the intergreen periods (sec) = Ratio of the design flow rate to the saturation flow rate for for the critical approach or lane in each phase
After you have calculated the optimum cycle length, you should increase it to the nearest multiple of 5. For example, if you calculate a cycle length of 62 seconds, bump it up to 65 seconds. Once you have done this, you are ready to go. If you know the intergreen times for all of the phases, you can then calculate the total available green time and allocate it to the various phases based on their critical movements. (See the module entitled green split determination.)
6.3.10.
Green Split Calculations [d]
Once you have the total cycle length, you can determine the length of time that is available for green signal indications by subtracting the intergreen periods from the total cycle length. But, the result is useless unless you know how to allocate it to all of the phases of the cycle. As explained in the module about critical movement analysis, the critical movements or lanes are used to distribute the available green time among all of the phases. The flow ratio for a movement or lane is the actual (design) flow rate, for that entity, divided by the saturation flow rate. The critical flow ratio, which is the one that is important for this calculation, is the flow ratio for the critical movement or lane. Green time is allocated using a ratio equation. Each phase is given a portion of the available green time that is consistent with the ratio of its critical flow ratio to the sum of all the critical flow ratios. This calculation is simple to do and hard to say, which makes it refreshingly different from most of the other calculations we encounter in engineering. 104
The proportion of the available green time that should be allocated to phase "i" can be found using the following equation:
Vs g ∑ V G s Where: gi = The length of the green interval for phase "i" (sec) (V/s)i = The critical flow ratio for phase "i" GT = The available green time for the cycle (sec) You now have the length of the green interval for each phase of your cycle. At this point, you might want to look at the timing adjustments module.
6.3.11.
Timing Adjustments
Once you have calculated the lengths of the minimum green intervals, green intervals, and intergreen intervals, as well as the design flow rates and capacities for each of your phases; it is time to ask yourself whether or not your results actually work. The first and most obvious check involves the green intervals. Check the length of the green interval for each phase. If it is not greater than the length of the phase's minimum green interval, you need to bump up the cycle length and add green time to that phase until the green interval is equal to or greater than the minimum. The second check involves capacity. If the capacity of a particular phase is below the design flow rate for that phase, you should back-calculate the effective green time that would allow the phase to run at the design flow rate. Once again, simply increasing the cycle length and allocating more time to the green interval of the troubled phase will solve the problem. Webster noted that the cycle length can vary between 0.75Co and 1.5Co without adding much delay, so don't worry too much about adding a second or two to the nominal cycle length.
6.3.12.
Computing Delay and LOS [d]
One way to check an existing or planned signal timing scheme is to calculate the delay experienced by those who are using, or who will use, the intersection. The delay experienced by the average vehicle can be directly related to a level of service (LOS). The LOS categories, which are listed below, contain information about the progression of traffic under the delay conditions that they represent. This allows you, as a designer or evaluator, to visualize and understand the traffic flow conditions surrounding an intersection, even though the intersection might still be on the drawing board. The first step in the LOS analysis is to calculate the average delay per vehicle for various portions of the intersection. You might be interested in the LOS of an entire approach, or alternatively, you might be interested in the LOS of each individual lane. The equation for the average vehicle delay is given below.
105
Average Stopped Delay Per Vehicle:
gC 0. 3 8C1 d 1 g X 173X X 1 X1 16 XC 12 C Where: d C g/C g X V c
= Average stopped delay per vehicle for the lane or lane group of interest (sec) = cycle length (sec) = green ratio for the lane or lane group = The effective green time for the lane or lane group (sec) = V/c ratio for the lane group = The actual or design flow rate for the lane or lane group (pcu/hour) = Capacity of the lane group (pcu/hour)
This equation predicts the average stopped delay per vehicle by assuming a random arrival pattern for approaching vehicles. The first term of the equation accounts for uniform delay, or the delay that occurs if arrival demand in the lane group is uniformly distributed over time. The second term of the equation accounts for the incremental delay of random arrivals over uniform arrivals, and for the additional delay due to cycle failures. As was mentioned before, the level of service for signalized intersections is defined in terms of average stopped delay per vehicle. This delay is directly related to the driver's level of discomfort, frustration, fuel consumption, and loss of travel time. The following paragraphs describe the various LOS categories.
Level of Service A: Operations with low delay, or delays of less than 5.0 seconds per vehicle. This LOS is reached when most of the oncoming vehicles enter the signal during the green phase, and the driving conditions are ideal in all other respects as well. Level of Service B: Operations with delays between 5.1 and 15.0 seconds per vehicle. This LOS implies good progression, with some vehicles arriving during the red phase. Level of Service C: Operations with delays between 15.1 and 25.0 seconds per vehicle. This LOS witnesses longer cycle lengths and fair progression. Level of Service D: Operations with delays between 25.1 and 40.0 seconds per vehicle. At this LOS, congestion is noticeable and longer delays may result from a combination of unfavorable progression, long cycle lengths, and high V/c ratios. Level of Service E: Operations with delay between 40.1 and 60.0 seconds per vehicle. This LOS is considered unacceptable by most drivers. This occurs under over-saturated intersection conditions (V/c ratios over 1.0), and can also be attributed to long cycle lengths and poor progression. As you can see by now, the LOS illuminates the qualitative aspects of signal operation.
6.4.
Professional Practice
Engineering can occasionally seem like a double major. You are expected to learn the theories and concepts while in school, and then how things are actually done while on the job. In an effort to bring these two aspects of engineering together for you, we have included excerpts from real design 106
manuals and other professional references as used by professional engineers. This allows you to learn about the theory, but also to see how that theory is really applied. The professional practice materials were taken from several different design manuals and references. The code in your area may differ somewhat from the excerpts presented here, and consequently, you should not reference these aids for any legitimate design work.
6.4.1.
Design Process Outline
The following excerpts were taken from the 1991 Manual of Traffic Signal Design, 2nd Edition, published by the Institute of Transportation Engineers (pp. 139-140) General Considerations
The functional objective of signal timing is to alternate the right-of-way among the various phases in such a way as to:
provide for the orderly movement of traffic. minimize average delay to vehicles and pedestrians. reduce the potential for accident-producing conflicts. maximize the capacity of each intersection approach.
Unfortunately, these desirable attributes are not compatible. For example, delay may be minimized by using as few phases as possible and the shortest practical cycle length. To reduce accident potential requires fewer conflicts. Therefore, multiple phases and longer cycles are indicated. Maximizing approach capacity requires the minimum number of phases to service the demand. Accordingly, it is necessary to exercise engineering judgment to achieve the best possible compromise among these objectives. Timing for Pre-timed Control
There are several fundamental aspects of developing timing settings for pretimed signal control. Some of there fundamentals are also applicable to actuated signal timing. The essential elements include:
Number of timing plans. Phase change intervals (yellow change plus all-red clearance) Pedestrian timing requirements (including decision whether or not to use pedestrian indications) Cycle length calculations Split calculations Flashing operation
To function effectively, pre-timed signal operations must take into account a number of local intersection variables and hardware characteristics. It is therefore difficult to set forth comprehensive guidelines to fit all possible situations. In many situations, it is desirable to monitor the initial operations and adjust the timing settings to reflect the unique character of the intersection and traffic flow.
6.4.2.
Intergreen Time
The following excerpt was taken from section 12-306.2 of the 1995 Idaho Transportation Department Traffic Manual.
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Vehicle Signal Change Interval
A vehicle signal change interval is that period of time in a traffic signal cycle between conflicting green intervals. It is the time required to terminate one green indication before initiating a conflicting green indication characterized by either a yellow interval or a yellow and all-red interval. At the present time, there is considerable discussion of proper timing for change interval with no recommended national practice adopted at this time. The Idaho Motor Vehicle Code permits vehicles to enter the intersection on a yellow indication termed as a permissive yellow rule. These vehicles have lawfully entered the intersection and accordingly are permitted to clear the intersection on the remaining yellow interval, an all-red interval, or subsequent green indication. It should also be noted that Idaho Code permits vehicles to enter the intersection on a green indication only after yielding the right-of-way to vehicles lawfully within the intersection. However, drivers are not always that observant of vehicles entering the intersection, particularly at the far side of an intersection, which can lead to a conflict between the two vehicles. The recommended formula for determining an appropriate change interval is:
Y R t 2 a V2 G g W V L Where: Y R t V a g G W L
= length of the yellow interval = length of the all-red interval = driver perception/reaction perception/rea ction time, recommended at 1.0 seconds. = velocity of approaching vehicle in feet/second, recommended that the 85 percentile signal approach speed or the posted speed limit, converted to feet/second, be used. = vehicle deceleration rate, recommended as 10 feet per second2. = acceleration due to gravity at 32 feet per second2. = grade of the signal approach in percent divided by 100 or 2 percent is 0.02. A downhill grade results in a negative term, i.e., -2 Gg. = width of intersection measured in feet from the near side stop line to the far edge of the conflicting traffic lane along the vehicle path. = length of vehicle on clearance, recommended as 20 feet for passenger cars.
The above formula will determine the total change interval composed of a yellow interval and allred interval. The recommended minimum yellow intervals for traffic signals on the state highway system in Idaho are as follows:
Approach Speed
Standard Yellow Interval
All-Red Clearance Interval
25 mph
3.2 sec
Optional
30 mph
3.2 sec
Optional
35 mph
3.2 sec
Optional
40 mph
4.0 sec
Required
45 mph
4.0 sec
Required
50 mph
4.0 sec
Required
55 mph
4.0 sec
Required
> 55 mph
5.0 sec
Required
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The all-red clearance interval is determined by computing the change interval, "Y+R," noted above and subtracting the standard yellow interval. The yellow interval has been standardized to present the drivers the same yellow interval at comparable intersections. Additional clearance time is then provided by adding an all-red a ll-red interval for a longer lon ger change interval. interval . It should be recognized that longer change intervals detract from the available intersection green time and are only needed if there are potential vehicle or vehicle-pedestrian conflicts between signal phases. Note that the term (W+L)/V provides additional clearance time for a vehicle to clear the intersection conflict zone. However, it is desirable to set a minimum yellow interval based on engineering judgment and then adjust the change interval using an all-red interval if needed. An all-red interval may be desirable at an intersection to provide additional time for a vehicle to clear the intersection before there are conflicts with pedestrians or other vehicles. The need for an all-red interval must consider a number of factors as follows:
Sight distance between vehicles or vehicle/pedestrian conflicts. Phasing of signal indications resulting in location of clearing vehicle versus conflicting vehicle or pedestrian movements. Width of intersection or length of turning path of vehicle. Start up delay of a conflicting pedestrian or vehicle movement plus the time to reach a point of conflict with the clearing vehicle. Speed of the approaching vehicle. Required intersection clearance for a protected left-turn movement relative to position in intersection versus conflicting pedestrians or vehicles. Field observation of intersection operations relative to vehicle conflicts with only a yellow interval and intersection accidents attributable to vehicle change interval.
The all-red intervals should not be less than 0.5 seconds and would normally be limited to 2.0 seconds. The determination of the all-red interval should be based on the factors noted above, calculated values, intersection observations, vehicle clearance practices at comparable intersections, and engineer judgment.
6.4.3.
Pedestrian Crossing Time, Minimum Green Time
The following excerpt was taken from the 1990 Manual of Traffic Signal Design, Second Edition, published by by the Institute Institute of Transportati Transportation on Engineers Engineers (pp. 144-145). 144-145). Pedestrian Timing Requirements Requirements
Pedestrian movements across signalized intersections are typically accommodated by one of the following operational options:
Pedestrians cross the street with the parallel vehicular green indication (no pedestrian signal display). Pedestrian movements are controlled by a concurrent separate pedestrian signal display. Pedestrians move on an exclusive phase while all vehicular traffic is stopped.
The essential factor in any of these options is to provide adequate time for the pedestrian to enter the intersection (walk interval) and to safely cross the street (pedestrian clearance interval). In cases where there are no separate pedestrian displays and the pedestrian moves concurrently with 109
vehicular traffic on the parallel street, the time allocated to vehicular traffic must consider the time required for pedestrians to react to the vehicular green indication and move across the street. When separate pedestrian displays (WALK, DONT WALK) are used, the minimum WALK interval generally ranges from 4 to 7 seconds (as recommended by the MUTCD 4D-7). This allows the pedestrian ample opportunity to leave the curb before the pedestrian clearance interval commences. Various research studies have indicated that when there are fewer than 10 pedestrians per cycle, the lower 4 second sec ond WALK interval is usually adequate. The MUTCD mandates that a pedestrian clearance interval always be provided where pedestrian indications are used. During this interval, a flashing DONT WALK indication is displayed long enough to allow the pedestrian to travel from the curb to the center of the farthest travel lane before opposing vehicles receive a green indication. Some agencies terminate the flashing DONT WALK and display a steady DONT WALK at the onset of the yellow vehicular change interval. This encourages those pedestrians still in the crosswalk to complete the crossing without delay. The calculation of the pedestrian clearance time therefore includes the yellow change interval. That is, the pedestrian clearance time equals the flashing DONT WALK plus the yellow change interval. . . . The typical walking speed of 4 ft/s, as cited in the MUTCD, is assumed to represent the "normal" pedestrian. There are, however, various categories within the general population that walk at a slower rate. For example, some female pedestrians walk slower than some male pedestrians; very young children, the elderly, and the handicapped also walk at a slower rate. Research on pedestrian characteristics verify that over 60% of all pedestrians move slower than 4 ft/s and 15% walk at or below 3.5 ft/s. Although this may imply that the lower walking speed (3.5 ft/s) should be used in calculating the pedestrian timing, timing , many engineers argue that the slower rate creates cre ates longer cycle lengths, ultimately resulting in longer vehicular delays.
6.4.4.
Capacity/Saturation Flow Rate
The following excerpts were taken from the 1994 Highway Capacity Manual, published by the Transportation Research Board.
Capacity at signalized intersections is based upon the concept of saturation flow and saturation flow rate. Saturation flow rate is given the symbol s and is expressed in units of vehicles per hour of effective green time (vphg) for a given lane group. The flow ratio for a given lane group is defined as the ratio of the actual or projected demand flow rate for the lane group (vi) to the saturation flow rate (si). The flow ratio is given the symbol (v/s)i (for lane group i). The capacity of a given lane group may be stated as
c s gC where; ci si gi/C
= capacity of lane group i, vph, = saturation flow rate for lane group i, vphg, = effective green ratio for lane group i. 110
Saturation flow rate is defined as the flow rate per lane at which vehicles can pass through a signalized intersection in such a stable moving queue. By definition, it is computed as
s 3600 h where; s = saturation flow rate (vphgpl), h = saturation headway (sec), 3,600 = number of seconds per hour.
6.4.5.
Peak Hour Volume, Design Flow Rate, PHF
The following excerpts were taken from the 1994 Highway Capacity Manual, published by the Transportation Research Board. Peak Hour and Design Hour
Capacity and other traffic analyses focus on the peak hour of traffic volume, because it represents the most critical period for operations and has the highest capacity requirements. The peak hour volume, however, is not a constant value from day to day or from season to season. If the highest hourly volumes for a given location were listed in descending order, a large variation in the data would be observed, depending on the type of route and facility under study. Rural and recreational routes often show a wide variation in peak-hour volumes. Several extremely high volumes occur on a few selected weekends or other peak periods, and traffic during the rest of the year is at much lower volumes, even during the peak hour. This occurs because the traffic stream consists of few daily or frequent users; the major component of traffic is generated by seasonal recreational activities and special events. Urban routes, on the other hand, show little variation in peak-hour. . . . The relationship between the 15-min flow rate and the full hourly volume is given by the peak hour factor, defined in Part A of this chapter (see below). Whether the design hour was measured, established from the analysis of peaking patterns, or based on modeled demand, the peak-hour factor (PHF) is applied to determine design hour flow rates. Peak-hour factors in urban areas generally range between 0.80 and 0.98. Lower values signify greater variability of flow within the subject hour, and higher values signify little flow variation. Peak-hour factors over 0.95 are often indicative of high traffic volumes, sometimes with capacity constraints on flow during the peak hour. (Description of PHF from Part A, as referred to above.)
Peak rates of flow are related to hourly volumes through the use of the peak-hour factor. This factor is defined as the ratio of total hourly volume to the peak rate of flow within the hour:
volume PHF Peak rate ofHourly low within the hour 111
If 15-min periods are used, the PHF may be computed as
PHF 4VV Where PHF V V15
= peak-hour factor, = hourly volume (vph), and = volume during the peak 15 min of the peak hour (veh/15 min).
Where the peak-hour factor is known, it may be used to convert a peak-hour volume to a peak rate of flow, as follows (equation 2-3):
v PHFV Where v V PHF
= rate of flow for a peak 15-min period (vph), = peak-hour volume (vph), and = peak-hour factor.
Equation 2-3 need not be used to estimate peak flow rates where traffic counts are available. The chosen count interval must allow the identification of the maximum 15-min flow period. The rate may then be directly computed as 4 times the maximum 15-min count. Many of the procedures use this conversion to allow computations to focus on the peak flow period within the peak hour.
6.4.6.
Critical Movement or Lane
The following excerpt was taken from the 1995 Canadian Capacity Guide for Signalized Intersections, Second Edition, published by the Institute for Transportation Engineers (District 7 Canada), (p. 46.)
Critical Lanes The analysis and evaluation of signalized intersections, including most planning tasks, proceed on a lane-by-lane basis. Not all the lanes, however, are equally important. Normally, in every phase there is only one lane for which the relationship between the arrival flow and saturation flow results in the longest green interval requirement. Such lanes are called critical lanes. The number of critical lanes equals the number of phases in a cycle and, together, they have a decisive influence on the cycle time. A critical lane can be recognized by the highest flow ratio in a given phase: ycrit j = max (yij) = max (qij /Sij) Where: 112
ycrit j yij qij Sij
= flow ratio for the critical lane in phase j = flow ratio for lane i in phase j = arrival flow in lane i discharging in phase j (pcu/h) = saturation flow in lane i discharging in phase j (pcu/h). . . .
6.4.7.
Cycle Length Determination
The following excerpt was taken from section 12-306.3 of the 1995 Idaho Transportation Department Traffic Manual. Cycle Length
Cycle length is composed of the total signal time to serve all of the signal phases including the green time plus any change interval. Longer cycles will accommodate more vehicles per hour but that will also produce higher average delays. The best way is to use the shortest practical cycle length that will serve the traffic demand. Vehicles at a signal installation do not instantaneously enter the intersection. Early studies by Greenshields found that the first vehicle had a starting delay of 3.7 seconds to enter the intersection with subsequent vehicles requiring an average of 2.1 seconds each. Generally, vehicles will pass over an approach detector with a headway of 2 to 2.5 seconds. For general calculation purposes, an average time of 2.5 seconds per vehicle to enter the intersection is a conservative value. This value can be used to estimate signal timing for planning purposes. The cycle length includes the green time plus the vehicle signal change interval for each phase totaled to include all signal phases. A number of methods have been used to determine cycle lengths as outlined in the Highway Capacity Manual, ITE Manual on Traffic Signal Design, and ITE Transportation and Traffic Engineering Handbook. Webster provided the basic empirical formula that would minimize intersection delay as follows:
5 L 5 C 1.1.0 ∑ Y Where: C L ΣYi
= optimum cycle length in seconds adjusted usually to the next highest 5 second interval. Cycle lengths in the range of 0.75C to 1.5C do not significantly increase delay. = Unusable time per cycle in seconds usually taken as a sum of the vehicle signal change intervals. = critical lane volume each phase/saturation flow
The saturation flow will be between 1500 and 1800 vehicles per hour. Refer to Highway Capacity Manual. The "Y" value should be computed for each phase and totaled to arrive at ΣYi for all phases. Note: The traffic volumes used should be the predicted volumes at time of signal turn-on. The volumes should also be the peak hour or peak fifteen-minute period for the cycle determination. When the cycle length has been determined the vehicle signal changes are deducted giving the total cycle green time which can be proportioned to each signal phase on the basis of critical lane 113
volumes. The individual signal phase times are then the proportioned time plus the vehicle change interval on each phase. To ensure that critical lane volumes are adequately served, a capacity check should be computed for each green interval.
6.4.8.
Green Split Calculations
This excerpt was taken from the1995 Canadian Capacity Guide for Signalized Intersections, Second Edition, published by the Institute for Transportation Engineers (District 7 - Canada), (p. 58). Green Intervals by Balancing Flow Ratios
This procedure uses flow ratios for the critical lanes. First, the total time available in the cycle for the allocation of green intervals is determined as:
∑ g c ∑ I Where: Σg j
c I j
= total green time available in the cycle (s) = selected cycle time (s) (See the explanation below.) = intergreen period following phase j (s).
This total available green time is allocated in proportion to the flow ratio of the critical lane for the corresponding phase and the intersection flow ratio: g j =
y j
g j
Y
Where: g j y j Σg j Y
= green interval for phase j (s) = flow ratio for the critical lane in phase j = total green time available in the cycle (s) = intersection flow ratio (sum of the critical flow ratios for all phases).
(Explanation for selected cycle time) The Canadians list several different methods for calculating the total cycle time. The engineer is supposed to select the method that suits his/her purposes best.
6.4.9.
Timing Adjustments
The following excerpt was taken from section 12-306.3 of the 1995 Idaho Transportation Department Traffic Manual. (This is a continuation of the CYCLE LENGTH discussion that was visited in the "cycle length determination" professional practice page.)
To ensure that critical lane volumes are adequately served, a capacity check should be computed for each green interval. This can be done by making the following computations for each phase: 114
1. For each signal phase, determine the critical lane. 2. Then for each signal phase, determine in that critical lane the vehicles served per cycle. 3. That phase minimum green time would be as follows: Phase Minimum Green Interval = Vehicles per cycle × 1.1 × 2.1 sec + 3.7 sec 1.1 sec provides a 10% increase for capacity traffic fluctuations 2.1 sec is the average headway per vehicle 3.7 sec is the time delay to start a traffic queue 4. The total cycle length equals the sum of the phase minimum green intervals determined in item no. 3. The minimum green interval should be less than green intervals determined above, under the Webster method. If not, the cycle length should be increased with additional time allocated to those phases not meeting the capacity criteria. (The Webster method portion, as referred to, was not included on this page.)
6.4.10.
Computing Delay and LOS, Operational Analysis Outline
The theory and concepts module on this topic covered the LOS grades and their corresponding traffic flow descriptions, and also presented a simple formula for the calculation of the delay. This module discusses the longer and more complex process for calculating the delay and LOS of an existing intersection. The excerpt below gives an overview of the process used in operational analysis. Your text probably contains a detailed description of this process, and you would be wise to look it over. The following excerpt was taken from the 1994 edition of the Highway Capacity Manual, published by the Transportation Research Board. Operational Analysis
Operational analysis results in the determination of capacity and level of service for each lane group as well as the level of service for the intersection as a whole. It requires that detailed information be provided concerning geometric, traffic, and signalization conditions at the intersection. These may be known for existing cases or projected for future situations. Because the operational analysis of signalized intersections is complex, it is divided into five distinct modules, as follows: 1. Input Module: All required information upon which subsequent computations are based is defined. The module includes all necessary data on intersection geometry, traffic volumes and conditions, and signalization. It is used to provide a convenient summary for the remainder of the analysis. 2. Volume Adjustment Module: Demand volumes are generally stated in terms of vehicles per hour for a peak hour. The volume adjustment module converts these to flow rates for a peak 15min analysis period and accounts for the effects of lane distribution. The definition of lane groups for analysis also takes place in this module. 3. Saturation Flow Rate Module: The saturation flow rate is computed for each of the lane groups established for analysis. The flow rate is based upon adjustment of an "ideal" saturation flow rate to reflect a variety of prevailing conditions. 115
4. Capacity Analysis Module: Volumes and saturation flow rates are manipulated to compute the capacity and v/c ratios for each lane group and the critical v/c ratio for the intersection. 5. LOS Module: Delay is estimated for each lane group established for analysis. Delay measures are aggregated for approaches and for the intersection as a whole, and levels of service are determined.
6.5.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic.
6.5.1.
Intergreen Time
On your way home from work a light turns yellow ahead of you. You are too close to the intersection to stop without a heroic effort, so you proceed toward the intersection, assuming that you'll get through it before the opposing phase is unleashed. To your surprise, the intersection signal turns red before you have made it to the stop-bar. Luckily you clear the intersection, but unfortunately, the local sheriff witnessed your maneuver. As part of your plea for mercy, you mention that the signal seems to have an inadequate intergreen period that produces a dilemma zone. Your plea doesn't work and you resolve to dispute the matter in court. You return to the intersection and measure the intergreen time, using a stopwatch. It turns out to be 6 seconds. You also note the speed limit (50 mph in this case), the width of the intersection (around 60 feet), and your car's length (18 feet). The approach to the intersection is level, and you assume that the coefficient of friction is around 0.5. Because you were only paying casual attention to the road when the incident occurred, you decide to use 1 second as your perception reaction time. Can you successfully argue that a dilemma zone exists? If one exists, what should be done to the intergreen time to fix the problem?
Solution The first step in this analysis is to calculate the minimum stopping distance you had under the given circumstances. The minimum safe stopping distance can be calculated using the formula below.
1.47V SD 1.47V t 30 f G Placing the given information into the equation yields:
1.4750 SD 1.47 501 30 0.5 0 Solving this equation gives us a stopping distance of 434 feet. Next you must calculate the time required to traverse the sum of the stopping distance, intersection width, and one car length. This will give you the intergreen time that is necessary for a car to safely pass through the intersection from the point-of-no-return. The intersection clearance time is given by the equation below. 116
T SD1.47L VW Placing the given information into the equation yields:
18 60 T 434 1.4750 Solving this equation gives us an intersection clearance time of 7 seconds. Since the intersection clearance time provided was only 6 seconds, and a full 7 seconds is required for a car to safely pass through the intersection from the point-of-no-return, your claim that a dilemma zone exists is well founded. To fix the problem, the city should increase the intergreen time by 1 second.
6.5.2.
Pedestrian Crossing Time, Minimum Green Interval
A senior citizen using a crosswalk at a local intersection was struck by a vehicle. Following the incident, a number of other citizens complained that the allocated pedestrian crossing time was insufficient at the intersection. You have been asked to evaluate the situation. You estimate the width of the intersection as 60 ft and the average pedestrian’s pace as 4 ft/sec. You also record the WALK time (10 sec), concurrent green interval length (14 sec), and the intergreen time (6 sec). Can you prove that the green interval given to the concurrent vehicular movement was insufficient based on the pedestrian crossing time? If this pedestrian movement has an extremely low flow rate, which is why this incident didn't happened before, how would you correct the safety problem without increasing the delay observed by the vehicular movements?
Solution The first step in this solution is to calculate the time required for a person to cross the intersection. This time can be calculated from the equation below.
width of intersection R walking speed of person Substituting the given information into this equation, we get a crossing time (R) of 15 seconds. Next, the total time that should be devoted to pedestrians is calculated by adding the WALK time (Z) to the crossing time (R). This gives us a required pedestrian total time of 25 seconds. Adding the vehicular green interval length (14 sec) and intergreen times (6 sec) that were provided gives us a value of 20 seconds. Since the pedestrian phase requires 25 seconds and is currently only given a total time of 20 seconds, conflicting traffic will begin moving a full 5 seconds before the last pedestrian has made it to safety. No wonder this incident occurred. This problem could be remedied by increasing the length of the vehicular movement's green interval by 5 seconds. You might want to prove this using the equation g = Z + R - I. One way to alleviate the problem without increasing the cycle length is to reduce the WALK time that is given to the pedestrians by 5 seconds. This would bring the required pedestrian total time to the 20 seconds that is currently provided. This option is only available because the pedestrian flow rate is very low for this intersection.
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6.5.3.
Capacity/Saturation Flow Rate
Your first assignment as a transportation engineer is to design a small signalized intersection. One step in this design process requires that you find the saturation flow rate for the eastern approach. You decide to try and calculate the saturation flow rate from field observations of an approach that is part of an intersection very similar to yours. After recording the departure headways of the first few discharging vehicles for several different cycles, you calculate the average headway and get a value of 2.1 seconds. Calculate the saturation flow rate. If the eastern approach to your intersection has an estimated green time of 20 seconds and the total cycle length will be around 45 seconds, what is the approximate capacity for the eastern approach?
Solution Since we know, from queuing theory, that the vehicles in a queue will discharge at the saturation flow rate, we can take the average headway of those vehicles and convert it into the saturation flow rate. Since one vehicle entered the intersection every 2.1 seconds when the queue was discharging, 3600/2.1 vehicles would enter the intersection in an hour if the queue were long enough and the approach was given a green signal for an entire hour. Therefore, our saturation flow rate is 1714 veh/hr. Since we weren't given any information to the contrary, we will assume that these vehicles were all passenger cars and call our saturation flow rate 1714 pcu/hr. To find the capacity, we first need to calculate the green ratio (g/C). If the length of the green interval (g) is 20 seconds and the cycle length (C) is about 45 seconds, the green ratio will be about 0.44. Capacity is the product of the green ratio and the saturation flow rate. In this case, the capacity of the eastern approach would be about 760 pcu/hr.
6.5.4.
Peak Hour Volume, Design Flow Rate, PHF
It is commonly known in your area that the heaviest traffic flow rates occur between 4:00 PM and 6:30 PM. Your assignment for the day is to find the peak hour volume, peak hour factor (PHF), and the actual or design flow rate for an existing one-lane approach. To do this, you obtain a clickcounter and position yourself at the intersection. For each fifteen-minute interval, you record the numbers of right-turns, left-turns, straight-through trucks, and straight-through passenger cars. Your tabulated values are as shown below.
Time Interval
Left Turns
Right Turns
ST Trucks
ST Cars
4:00-4:15 4:15-4:30 4:30-4:45 4:45-5:00 5:00-5:15 5:15-5:30 5:30-5:45 5:45-6:00 6:00-6:15 6:15-6:30
5 6 4 7 10 9 14 12 10 9
10 15 7 16 13 12 15 12 9 12
6 8 10 8 6 12 8 10 8 4
30 26 35 40 49 55 65 50 39 30
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If a truck is equal to 1.5 passenger cars and a right-turn is as well, and if a left-turn is equal to 2.5 passenger cars, then the n calculate the peak hour ho ur volume, peak hour factor fact or (PHF), and the actual (design) (design ) flow rate for this approach.
Solution The first step in this solution is to find the total traffic volume for each 15 minute period in terms of passenger car units. This is done by multiplying the number of trucks by 1.5, the number of right turns by 1.5, and the number of left turns by 2.5. We then add these three numbers and the volume of straight-through cars together to get the total volume of traffic serviced in each interval. Once we have this, we can locate the hour with the highest volume and the 15 minute interval with the highest volume. The peak hour is shown in blue below with the peak 15 minute period shown in a darker shade of blue.
Time Interval
Interval Volume (pcu)
4:00-4:15 4:15-4:30 4:30-4:45 4:45-5:00 5:00-5:15 5:15-5:30 5:30-5:45 5:45-6:00 6:00-6:15 6:15-6:30
67 76 71 94 10 3 11 4 13 5 11 3 90 77
The peak hour volume is just the sum of the volumes of the four 15 minute intervals within the peak hour (464 pcu). The peak 15 minute volume is 135 pcu in this case. The peak hour factor (PHF) is found by dividing the peak hour volume by four times the peak 15 minute volume.
464 0.86 PHF 4135 The actual (design) flow rate can be calculated by dividing the peak hour volume by the PHF, 464/0.86 = 540 pcu/hr, or by multiplying the peak 15 minute volume by four, 4×135 = 540 pcu/hr.
6.5.5.
Critical Movement or Lane
As a transportation engineer about to embark on the cycle length and green split calculations, you need to find the critical lane for each phase of a two-phase signal cycle. In this example problem we will only focus on one phase. phas e. The approaches that are serviced service d in this phase ph ase will have two lanes, one servicing left-turns and straight-through traffic, and the other servicing right-turns and straight-through traffic. The design flow rates and saturation flow rates for each lane are given below.
Lane Description
Design Flow Rate
North-bound L,S
600 pcu/hr
1200 pcu/hr
North-bound R,S
500 pcu/hr
1700 pcu/hr
South-bound L,S
450 pcu/hr
1330 pcu/hr
South-bound R,S
720 pcu/hr
1600 pcu/hr
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Saturation Flow Rate
Which lane is the critical lane for this phase, and what is the critical flow ratio for this phase?
Solution The critical lane is the lane that requires the most time to service its queue. It can be found by locating the lane with the highest flow ratio (V/s). Simply calculate the flow ratio for each lane by dividing the design flow rate by the saturation flow rate. Then find the lane with the largest flow ratio.
Lane Description
Flow Ratio
North-bound L S North-bound R,S South-bound L,S South-bound R,S
0.5 0.294 0 .3 3 8 0.45
It looks like the north-bound left-turn and straight-through lane is the critical lane for this phase. The critical flow ratio rati o is just the flow ratio for the th e critical lane (0.5).
6.5.6.
Cycle Length Determination
As part of a signal design team, you have been assigned to find the optimum cycle length for a three-phase cycle. Field observations and calculations by yourself and others are the basis for your work. So far, you know the critical flow ratio for each phase and the intergreen time for each phase. Calculate the optimum cycle length for your signal, given the critical flow ratios and intergreen times below. What would the optimum cycle length be if all of the critical flow ratios were near zero?
Phase Number
Critical Flow Ratio
Intergreen Time
1 2 3
0.233 0.13 0.256
6 sec 4 sec 7 sec
Solution Webster's optimum cycle length equation, which is shown below, has two variables on the righthand side. These are the total cycle lost time (L) which is usually taken as the sum of all the intergreen times, and the sum of all the critical flow ratios (Σ(V/s)).
C 11.5L∑V5 s In this case, the sum of the intergreen period lengths is 17 seconds (L=17). The sum of the critical flow ratios is 0.619. When we substitute these values into the equation above we obtain an optimum cycle length of 80 seconds. If all of the critical flow ratios were very near zero, the denominator in Webster's equation would approach unity and the optimum cycle length would be 31 seconds.
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6.5.7.
Green Split Calculations
Assuming that both of the critical movements in a two-phase cycle have the same saturation flow rate, what percentage of the available green time would each phase receive, given the design flow rates for the critical movements listed below?
Situation Number
Phase 1 Flow Rate (pcu/hr)
Phase 2 Flow Rate (pcu/hr)
1 2 3 4
5 00 4 00 90 1 00
25 0 10 0 30 80
Solution The available green time is allocated based on the ratio of the critical flow ratios to the sum of the critical flow ratios. However, in this case we can simplify the calculations because the saturation flow rate is assumed to be identical for both of the critical movements. This means that the green time is allocated according to the ratios of the design flow rates to the sum of the design flow rates. This simplification is shown below.
Vs G g ∑ V s g G∑VV
simplifies to
Since we weren't given the available green time, we'll forget about it and focus on the ratios. For situation number one, the design flow rate for the critical movement in phase one was 500 pce/hr while the critical design flow rate for phase two was 250 pcu/hr. The sum of these flow rates is 750 pcu/hr. Hence, phase one will receive 67% (500/750) of the available green time, while phase two will receive 33% (250/750). The results are tabulated below.
Situation Number 1 2 3 4
6.5.8.
Phase 1 Flow Rate Phase 2 Flow Rate (pcu/hr) (pcu/hr) 50 0 40 0 90 10 0
2 50 1 00 30 80
Phase 1 % of G
Phase 2 % of G
67 80 75 56
33 20 25 44
Timing Adjustments
You have just finished allocating the available green time to a two-phase cycle. The actual (design) flow rates for the two critical lanes are 350 pcu/hr and 700 pcu/hr respectively. The optimum cycle length was 55 seconds and of the available green time, 14 seconds were allocated to phase one (350 pcu/hour) and 27 seconds were allocated to phase two (700 pcu/hr). Both phases have intergreen intervals of 6 seconds. The lengths of the pedestrian WALK intervals for phases one and two are 10 seconds and 16 seconds respectively. The width of the intersection for phases one and two is 48 ft and 68 ft respectively. Assume the saturation flow rate is 1900 pcu/hr for both lanes. Does this timing scheme require any adjustments? If so, what should the final signal timing plan be? 121
Solution The first thing we will check is the capacities of the two critical lanes. We'll calculate the capacities by multiplying the green ratio (g/C) by the saturation flow rate (s). For phase one, the green ratio is 14/55 and the saturation flow rate is 1900 pcu/hr. This gives a capacity of 484 pcu/hr, which is more than adequate to handle the 350 pcu/hr design flow rate. Phase two has a capacity of 933 pcu/hr, which is also more than adequate to handle its design flow rate. Next, we will check the minimum length of the green interval based on pedestrian movements. In phase one, the WALK interval is 10 seconds long and the crossing time is 48 ft/(4 ft/s), or 12 seconds. The total time required for pedestrians is 22 seconds. The vehicular movement provides only 14 seconds of green and 6 seconds of intergreen. Thus, the total time before the next phase begins is only 20 seconds. To remedy this, two seconds should be added to both the total cycle time and the green interval for phase number one. Pedestrians in phase number two receive 16 seconds of WALK time and require 68 ft/(4 ft/sec) = 17 seconds of crossing time. The total time required for the pedestrians in phase number two is, therefore, 33 seconds. The green interval and intergreen interval for phase number two add up to 33 seconds, which perfectly matches the pedestrian crossing time. As it turns out, phase one's green interval needed to be increased by two seconds in order to serve the pedestrian movements. The total cycle length and phase one's green interval were both increased by two seconds, while all the other signal timing variables were left untouched.
6.5.9.
Computing Delay and LOS
Because several complaints have been received from local drivers, you have been assigned to determine the level of service for a one-lane approach at a local signalized intersection. The cycle length is 80 seconds, and 30 seconds of effective green time are enjoyed by the approach in question. The actual flow rate of traffic through the approach is 400 pcu/hr and the saturation flow rate for the approach is 1750 pcu/hr. What is the LOS for this approach?
Solution Before we can calculate the delay for the approach, we need to know the green ratio (g/C), the capacity (c), and the ratio V/c (X). The green ratio for this approach is 30/80 or 0.375. The capacity is (g/C) × s which equals 0.375 × 1750 or 656 pce/hr. The ratio V/c is 400/656 or 0.609. The average vehicle delay is given by the equation below.
g 0. 3 8C1 C d 1 g X 173X X 1 X1 16 XC 12 C By placing the values calculated above into the equation, we obtain an average vehicle delay of 23 seconds. This corresponds to the level of service grade "C".
6.6.
Glossary
Actual Flow Rate: The design flow rate, or the maximum flow that is expected to use the intersection. See the theory and concepts modules on peak hour volume, design flow rate, and PHF. All-red interval: Any portion of a signal cycle in which a red indication is observed by all approaches. 122
Approach: The portion of an intersection leg that is used by traffic approaching the intersection. Capacity: The maximum number of vehicles that can reasonably be expected to pass over a given roadway or section of roadway, in one direction, during a given time period and under the prevailing roadway, traffic, and signalization conditions. Change interval: Identical to the intergreen interval. Clearance interval: Identical to the all-red interval. Critical Flow Ratio: The flow ratio of the critical lane group within a phase. The actual or design flow rate for the critical movement divided by the saturation flow rate for that movement. Critical Movement or Lane: The lane or movement for each phase, depending on how you choose to subdivide you intersection, that requires the most green time. Critical Volume: A volume, or combination of volumes, which produces the greatest utilization of capacity for the street or lane in question, given in terms of passenger car units per hour per lane or mixed vehicles per hour per lane. Cycle: A complete sequence of signal indications. Each phase has been serviced and the cycle is beginning again. Cycle Length: The time required for one full cycle of signal indications, given in seconds. Delay: The stopped time per vehicle (in seconds per vehicle), usually calculated separately for each lane group. Design Flow Rate: Identical to the actual flow rate. Effective Green Time: The green time that is actually used by traffic. Some lost time occurs initially while traffic responds to the green signal and begins to accelerate. Some time is also lost during the intergreen period as vehicles stop in anticipation of the next phase. Flow Rate: The rate, in vehicles per hour or passenger car units per hour, at which traffic is entering an intersection. Flow Ratio: The ratio of the actual flow rate to the saturation flow rate. Green Interval: The portion of a signal phase in which the green signal is illuminated. Green Ratio: The ratio of the effective green time to the cycle length. Green Time: The length of the green interval and its change interval, given in seconds. Hourly Volume: The number of mixed vehicles that traverse a given section of lane or roadway during an hour. Intergreen: The time interval between the end of a green indication for one phase and the beginning of green for the next phase. 123
Intersection Flow Ratio: The sum of all the critical flow ratios--one from each phase. Lane Group: Any group of lanes. Lanes can be combined during the signal timing design process in order to simplify the calculations. Legs (intersection): The portions of the intersecting streets or roadways that are within close proximity to the actual intersection. Level of Service (LOS): A measure of the operating conditions of an intersection. See the theory and concepts modules for more detail. Lost Time: The time during a given phase in which traffic could be discharging through the intersection, but is not. This is the period during the green interval and change intervals that is not used by discharging traffic. Passenger Car Units: A unit of measure whereby large trucks and turning movements are converted to passenger cars using multiplication factors. This allows you to deal with mixed traffic streams more accurately than if you had assumed all vehicles were created equal. Peak-Hour: The hour of the day that observes the largest utilization of capacity, or the hour of the day in which the largest number of vehicles use the intersection approach or lane of interest. Peak-Hour Factor: The ratio of the number of vehicles entering an approach during the peak hour to four times the number of vehicles entering during the peak 15 minute period. In the absence of field information, a value of 0.85 is normally used. Pedestrian Crossing Time: The time that is required for a pedestrian to cross the intersection. Phase: The portion of the cycle that is devoted to servicing a given traffic movement. Phase Sequence: The predetermined order in which the phases of a cycle occur. Queue: A closely spaced collection of vehicles. Roadway Conditions: The physical aspects of the roadway, such as lane-width, number of lanes, easements, bike lanes, shoulder width, and any other aspect of the roadway. Saturation Flow Rate: The maximum number of vehicles from a lane group that would pass through the intersection in one hour under the prevailing traffic and roadway conditions if the lane group was given a continuous green signal for that hour. This assumes that there is a continuous queue of vehicles with minimal headways. Signalization Conditions: All the various aspects of the signal system, including timing, phasing, actuation, and so on. Split: A percentage of a cycle length allocated to each of the various phases in a signal cycle. Traffic Conditions: The qualities of traffic, such as traffic speed, density, vehicle types, and traffic flow rate.
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7. Traffic Flow Theory 7.1.
Introduction
Traffic Flow Theory is a tool that helps transportation engineers understand and express the properties of traffic flow. At any given time, there are millions of vehicles on our roadways. These vehicles interact with each other and impact the overall movement of traffic, or the traffic flow. Whether the task is evaluating the capacity of existing roadways or designing new roadways, most transportation engineering projects begin with an evaluation of the traffic flow. Therefore, the transportation engineer needs to have a firm understanding of the theories behind Traffic Flow Analysis. This chapter is designed to help the undergraduate engineering student understand the fundamentals of Traffic Flow Theory.
7.2.
Lab Exercises
These exercises will help increase your understanding of Traffic Flow Theory, by presenting more complicated problems that require more thorough analysis.
7.2.1.
Lab Exercise One: Flow Models [d]
The attached data sets reflect field data taken at two sites in Huskytown. You are an engineering intern and you have been asked by your supervisor to analyze the data and prepare a brief report documenting any conclusions and recommendations that you have. Using “7.2.1. Data Set One” and “7.2.1. Data Set Two” data sets, analyze the data. Assume Greenshield's model for space mean speed as a function of density.
Tasks to be Completed Task 1. Using regression to determine the theoretical equation that describes the speed as a function of density:
Plot the actual data and theoretical data and describe any correlation. Report all the important statistical results of the regression analysis.
Task 2. Using histograms, calculate and graph the following:
flow speed occupancy
Task 3. Using any analysis tools, plot:
flow versus occupancy flow versus density speed versus flow speed versus density
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Task 4. Write up a report stating the information specified above, as well as your own conclusions about the data provided.
7.2.2.
Lab Exercise Two: Shock Waves/Queue Formation
A freeway in Thrillville with two lanes in one direction has a capacity of 2000 vphpl under normal stable flow conditions. On a particular morning, one of these lanes becomes blocked by a small accident for 15 minutes, beginning at 7 a.m. The arrival pattern of vehicles is as follows: Time/Flow (vph) 7-8 a.m./4000 8-9 a.m./3900 9-10 a.m./3500
After 10 a.m / 2800 This assignment is divided into two cases: (a) the capacity of this section reduces to 1800 vphpl under unstable or forced flow conditions, (b) the capacity of the section remains 2000 vphpl under forced flow conditions. Please determine the following for each case above: 1. How long a queue will be established due to this blockage? 2. When will the maximum queue occur? 3. How long will it take to dissipate the queue from the time of the breakdown?
Tasks to be Completed Task 1. Identify the type of problem and use the appropriate analytical tools to answer the questions. State your analysis approach. Task 2. Clearly lay out your solution and write up your solution in a brief report. Make sure that you clearly label any and all graphs that you use as part of your solution.
7.3.
Theory and Concepts
A course in transportation engineering wouldn't be complete without discussing some elements of Traffic Flow Theory. Most junior level courses cover several aspects of Traffic Flow Theory, including the topics listed below. To begin learning about Traffic Flow Theory, just click on the link of your choice. Topics followed by the characters '[d]' include an Excel demonstration.
7.3.1.
Types of Traffic Flow
Traffic flow can be divided into two primary types. Understanding what type of flow is occurring in a given situation will help you decide which analysis methods and descriptions are the most relevant.
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The first type is called uninterrupted flow , and is flow regulated by vehicle-vehicle interactions and interactions between vehicles and the roadway. For example, vehicles traveling on an interstate highway are participating in uninterrupted flow. The second type of traffic flow is called interrupted flow. Interrupted flow is flow regulated by an external means, such as a traffic signal. Under interrupted flow conditions, vehicle-vehicle interactions and vehicle-roadway interactions play a secondary role in defining the traffic flow.
7.3.2.
Traffic Flow Parameters
Traffic flow is a difficult phenomenon to describe without the use of a common set of terms. The following paragraphs will introduce most of the common terms that are used in discussions about traffic flow.
Speed (v) The speed of a vehicle is defined as the distance it travels per unit of time. Most of the time, each vehicle on the roadway will have a speed that is somewhat different from those around it. In quantifying the traffic flow, the average speed of the traffic is the significant variable. The average speed, called the space mean speed, can be found by averaging the individual speeds of all of the vehicles in the study area.
Volume Volume is simply the number of vehicles that pass a given point on the roadway in a specified period of time. By counting the number of vehicles that pass a point on the roadway during a 15minute period, you can arrive at the 15-minute volume. Volume is commonly converted directly to flow (q), which is a more useful parameter.
Flow (q) Flow is one of the most common traffic parameters. Flow is the rate at which vehicles pass a given point on the roadway, and is normally given in terms of vehicles per hour. The 15-minute volume can be converted to a flow by multiplying the volume by four. If our 15-minute volume were 100 cars, we would report the flow as 400 vehicles per hour. For that 15-minute interval of time, the vehicles were crossing our designated point at a rate of 400 vehicles/hour.
Peak Hour Factor (PHF) The ratio of the hourly flow rate (q60) divided by the peak 15 minute rate of flow expressed as an hourly flow (q15).
PHF
Density (k) Density refers to the number of vehicles present on a given length of roadway. Normally, density is reported in terms of vehicles per mile or vehicles per kilometer. High densities indicate that individual vehicles are very close together, while low densities imply greater distances between vehicles. Headway, spacing, gap, and clearance are all various measures for describing the space between vehicles. These parameters are discussed in the paragraphs below and are shown graphically in figure 1.0. 127
Headway (h) Headway is a measure of the temporal space between two vehicles. Specifically, the headway is the time that elapses between the arrival of the leading vehicle and the following vehicle at the designated test point. You can measure the headway between two vehicles by starting a chronograph when the front bumper of the first vehicle crosses the selected point, and subsequently recording the time that the second vehicle’s front bumper crosses over the designated point. Headway is usually reported in units of seconds.
Spacing (s) Spacing is the physical distance, usually reported in feet or meters, between the front bumper of the leading vehicle and the front bumper of the following vehicle. Spacing complements headway, as it describes the same space in another way. Spacing is the product of speed and headway.
Gap (g) Gap is very similar to headway, except that it is a measure of the time that elapses between the departure of the first vehicle and the arrival of the second at the designated test point. Gap is a measure of the time between the rear bumper of the first vehicle and the front bumper of the second vehicle, where headway focuses on front-to-front times. Gap is usually reported in units of seconds.
Clearance (c) Clearance is similar to spacing, except that the clearance is the distance between the rear bumper of the leading vehicle and the front bumper of the following vehicle. The clearance is equivalent to the spacing minus the length of the leading vehicle. Clearance, like spacing, is usually reported in units of feet or meters. Figure 1.0: Explanation of Parameters
7.3.3.
Speed-Flow-Density Relationship
Speed, flow, and density are all related to each other. The relationships between speed and density are not difficult to observe in the real world, while the effects of speed and density on flow are not quite as apparent. Under uninterrupted flow conditions, speed, density, and flow are all related by the following equation: q=k×v Where 128
q v k
= Flow (vehicles/hour) = Speed (miles/hour, kilometers/hour) = Density (vehicles/mile, vehicles/kilometer)
Because flow is the product of speed and density, the flow is equal to zero when one or both of these terms is zero. It is also possible to deduce that the flow is maximized at some critical combination of speed and density. Two common traffic conditions illustrate these points. The first is the modern traffic jam, where traffic densities are very high and speeds are very low. This combination produces a very low flow. The second condition occurs when traffic densities are very low and drivers can obtain free flow speed without any undue stress caused by other vehicles on the roadway. The extremely low density compensates for the high speeds, and the resulting flow is very low.
7.3.4.
Special Speed & Density Conditions
The discussion of the speed-flow-density relationship mentioned several speed-density conditions. Two of these conditions are extremely significant and have been given special names.
Free Flow Speed This is the mean speed that vehicles will travel on a roadway when the density of vehicles is low. Under low-density conditions, drivers no longer worry about other vehicles. They subsequently proceed at speeds that are controlled by the performance of their vehicles, the conditions of the roadway, and the posted speed limit.
Jam Density Extremely high densities can bring traffic on a roadway to a complete stop. The density at which traffic stops is called the jam density.
7.3.5.
Greenshield’s Model [d]
Greenshield was able to develop a model of uninterrupted traffic flow that predicts and explains the trends that are observed in real traffic flows. While Greenshield’s model is not perfect, it is fairly accurate and relatively simple. Greenshield made the assumption that, under uninterrupted flow conditions, speed and density are linearly related. This relationship is expressed mathematically and graphically below. See figure 1.0. v = A - B × k Where: v A, B k
= speed (miles/hour, kilometers/hour) = constants determined from field observations = density (vehicles/mile, vehicles/kilometer)
As noted above, you can determine the values of the constants A and B through field observations. This is normally done by collecting velocity and density data in the field, plotting the data, and then 129
using linear regression to fit a line through the data points. The constant A represents the free flow speed, while A/B represents the jam density. Figure 1.0: Speed vs. Density
Inserting Greenshield’s speed-density relationship into the general speed-flow-density relationship yields the following equations: q = (A – B × k) × k
or
q = A × k – B × k 2
Where: q A, B k
= flow (vehicles/hour) = constants = density (vehicles/mile, vehicles/kilometer) Figure 2.0: Flow vs. Density
This new relationship between flow and density provides an avenue for finding the density at which the flow is maximized.
setting
0
d A 2 B k d A k 2 B
Therefore, at the density given above, the flow will be maximized. Substituting this maximized value of k into the original speed-density relationship yields the speed at which the flow is maximized.
A or v A v A B2 B 2 130
This indicates that the maximum flow occurs when traffic is flowing at half of free-flow speed (A). Substituting the optimum speed and density into the speed-flow-density relationship yields the maximum flow.
A A A q 2 2 B or q 4B Figure 3.0 shows the relationship between flow and speed graphically. Figure 3.0: Flow vs. Speed
As you can see, Greenshield’s model is quite powerful. The following can be derived from Greenshield’s model:
When the density is zero, the flow is zero because there are no vehicles on the roadway. As the density increases, the flow also increases to some maximum flow conditions. When the density reaches a maximum, generally called jam density, the flow must be zero because the vehicles tend to line up end to end (parking lot conditions).
As the density increases the flow increases to some maximum value, but a continual increase in density will cause the flow to decrease until jam density and zero flow conditions are reached.
7.3.6.
Time-Space Diagrams [d]
A time–space diagram is commonly used to solve a number of transportation- related problems. Typically, time is drawn on the horizontal axis and distance from a reference point on the vertical axis. The trajectories of individual vehicles in motion are portrayed in this diagram by sloping lines, and stationary vehicles are represented by horizontal lines. The slope of the line represents the speed of the vehicle. Curved portions of the trajectories represent vehicles undergoing speed changes such as deceleration. Diagrams that show the position of individual vehicles in time and in space are very useful for understanding traffic flow. These diagrams are especially useful for discussions of shock waves and wave propagation. The time-space diagram is a graph that describes the relationship between the location of vehicles in a traffic stream and the time as the vehicles progress along the highway. The following diagram is an example of a time-space diagram. 131
Time-space diagrams are created by plotting the position of each vehicle, given as a distance from a reference point, against time. The first vehicle will probably start at the origin, while the vehicles that follow won’t reach the reference point until slightly later times. Reductions in speed cause the slopes of the lines to flatten, while increases in speed cause the slopes to become greater. Acceleration causes the time-space curve for the accelerating vehicle to bend until the new speed is attained. Curves that cross indicate that the vehicles both shared the same position at the same time. Unless passing is permitted, crossed curves indicate collisions.
7.3.7.
Shock Waves [d]
Shock waves that occur in traffic flow are very similar to the waves produced by dropping stones in water. A shock wave propagates along a line of vehicles in response to changing conditions at the front of the line. Shock waves can be generated by collisions, sudden increases in speed caused by entering free flow conditions, or by a number of other means. Basically, a shock wave exists whenever the traffic conditions change. The equation that is used to estimate the propagation velocity of shock waves is given below.
v qk qk Where vsw q b qa k b k a
= propagation velocity of shock wave (miles/hour) = flow prior to change in conditions (vehicles/hour) = flow after change in conditions (vehicles/hour) = traffic density prior to change in conditions (vehicles/mile) = traffic density after change in conditions (vehicles/mile)
Note the magnitude and direction of the shock wave. (+) Shock wave is travelling in same direction as traffic stream. (-) Shock wave is traveling upstream or against the traffic stream. For example, let’s assume that an accident has occurred and that the flow after the accident is reduced to zero. Initially, the flow was several vehicles per hour. Also, the density is much greater after the accident. Substituting these values into the shock wave equation yields a negative (-) propagation velocity. This means that the shock wave is traveling against the traffic. If you could 132
look down on this accident, you would see a wave front, at which vehicles began to slow from their initial speed, passing from vehicle to vehicle back up the traffic stream. The first car would notice the accident first, followed an instant later by the second car. Each vehicle begins slowing after its driver recognizes that the preceding vehicle is slowing.
7.3.8.
Queuing Theory
Greenshield’s model was developed to aid our understanding of uninterrupted flow. Unfortunately, Greenshield’s model is unable to cope with the added complexities that are generated under interrupted flow conditions. Interrupted flow requires an understanding of Queuing Theory, which is an entirely separate model of traffic flow. Queuing Theory can be used to analyze the flow of traffic on the approach to and through an intersection controlled by a traffic signal. This is accomplished by analyzing the cumulative passage of vehicles as a function of time. The queuing diagram for interrupted flow shows the flow on one intersection approach. Traffic is stopped from time t1 to t2 during the red signal interval. At the start of the green interval (t2), traffic begins to leave the intersection at the saturation flow rate (qG), and continues until the queue is exhausted. Thereafter, the departure rate D(t), equals the arrival rate, A(t), until t3, which is the beginning of the next red signal. At this point, the process starts over. For further information on Queing Theory, consult the chapter entitled "Signal Timing Design."
Queuing Diagram for Interrupted Flow Papacostas , C.S. and Prevedouros, P.D., Transportation Engineering and Planning, 2 nd Edition, Prentice Hall, Englewood Cliffs, New Jersey, 1993
7.4.
Professional Practice
In order to supplement your knowledge about the various concepts within Traffic Flow Theory, and in order to give you a glimpse of how these various topics are discussed in the professional environment, we have included selected excerpts from professional design aids. The Transportation Research Board maintains an Internet website to provide information on all facets of the transportation industry. The professional practice material in this module is excerpted from TRB’s updated Special Report on Traffic Flow Theory, which is published on their website.
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7.4.1.
Traffic Flow Parameters
The following excerpt is taken from Chapter 2 (pp. 5-11) of the Transportation Research Board Special Report on Traffic Flow Theory, published on the website http://www.tfhrc.gov/its/tft/tft.htm .
In general, traffic streams are not uniform, but vary over both space and time. Because of that, measurement of the variables of interest for traffic flow theory is in fact the sampling of a random variable. . . . In reality, the traffic characteristics that are labeled as flow, speed, and concentration are parameters of statistical distributions, not absolute numbers. Flow Rates
Flow rates are collected directly through point measurements, and by definition require measurement over time. They cannot be estimated from a single snapshot of a length of road. Flow rates and time headways are related to each other as follows. Flow rate, q, is the number of vehicles counted, divided by the elapsed time, T:
q NT . . . Flow rates are usually expressed in terms of vehicles per hour, although the actual measurement interval can be much less. Concern has been expressed, however, about the sustainability of high volumes measured over very short intervals (such as 30 seconds or one minute) when investigating high rates of flow. The 1985 Highway Capacity Manual (HCM 1985) suggests using at least 15minute intervals, although there are also situations in which the detail provided by five minute or one minute data is valuable. . . . Speeds
Measurement of the speed of an individual vehicle requires observation over both time and space. ... In the literature, the distinction has frequently been made between different ways of calculating the average speed of a set of vehicles. . . . The first way of calculating speeds, namely taking the arithmetic mean of the observation,
1 u N u is termed the time mean speed because it is an average of observations taken over time. The second term that is used in the literature is space mean speed, but unfortunately there are a variety of definitions for it, not all of which are equivalent. . . . Regardless of the particular definition put forward for space mean speed, all authors agree that for computations involving mean speeds to be theoretically correct, it is necessary to ensure that one has measured space mean speed, rather than time mean speed. . . . Under conditions of stop-and-go traffic, as along a signalized street or a badly congested freeway, it is important to distinguish between these two mean speeds. For freely flowing freeway traffic, however, there will not be any significant difference between the two. . . . When there is great variability of speeds, as for example at the time of breakdown from uncongested to stop and go conditions, there will be considerable difference between the two. Wardrop (1952) provided an example of this kind (albeit along what must certainly have been a signalized roadway – Western Avenue, Greenford, Middlesex, England), in which speeds ranged from a low of 8 km/h to a high of 100 km/h. The space mean speed was 48.6 km/h; the time mean 134
speed 54.0 km/h. . . . For relatively uniform flow and speeds, the two mean speeds are likely to be equivalent for practical purposes. Nevertheless, it is still appropriate to specify which type of averaging has been done, and perhaps to specify the amount of variability in the speeds (which can provide an indication of how similar the two are likely to be). . . . At least for freeways, the practical significance of the difference between space mean speed and time mean speed is minimal. However, it is important to note that for traffic flow theory purists, the only ‘correct’ way to measure average travel velocity is to calculate space-mean speed directly. Only a few freeway traffic management systems acquire speed information directly, since to do so requires pairs of presence detectors at each of the detector stations on the roadway, and that is more expensive than using single loops. Those systems that do not measure speeds, because they have only single-loop detector stations, sometimes calculate speeds from flow and occupancy data, using a method first identified by Athol (1965). . . . Concentration
Concentration has in the past been used as a synonym for density. For example, Gerlough and Huber (1975, 10) wrote, "Although concentration (the number of vehicles per unit length) implies measurement along a distance." In this chapter, it seems more useful to use ‘concentration’ as a broader term encompassing both density and occupancy. The first is a measure of concentration over space; the second measure concentration over time of the same vehicle stream. Density can be measured only along a length. If only point measurements are available, density needs to be calculated, either from occupancy or from speed and flow. Gerlough and Huber wrote (in the continuation of the quote in the previous paragraph), that " . . .traffic engineers have traditionally estimated concentration from point measurements, using the relationship
k uq . . . The difficulty with using this equation to estimate density is that the equation is strictly correct only under some very restricted conditions, or in the limit as both the space and time measurement intervals approach zero. If neither of those situations holds, then use of the equation to calculate density can give misleading results, which would not agree with empirical measurements. These issues are important, because this equation has often been uncritically applied to situations that exceed its validity . . . . Real traffic flows, however, are not only made up of finite vehicles surrounded by real spaces, but are inherently stochastic (Newell 1982). Measured values are averages taken from samples, and are therefore themselves random variables. Measured flows are taken over an interval of time, at a particular place. Measured densities are taken over space at a particular time. Only for stationary processes (in the statistical sense) will the time and space intervals be able to represent conditions at the same point in the time-space plane. Hence it is likely that any measurements that are taken of flow and density (and space mean speed) will not be very good estimates of the expected values that would be defined at the point of interest in the time space plane. . . . Speeds within a lane are relatively constant during uncongested flow. Hence the estimation of density from occupancy measurements is probably reasonable during those traffic conditions, but not during congested conditions. . . . In short, once congestion sets in, there is probably no good way to estimate density; it would have to be measured.
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Temporal concentration (occupancy) can be measured only over a short section (shorter than the minimum vehicle length), with presence detectors, and does not make sense over a long section. Perhaps because the concept of density has been a part of traffic measurement since at least the 1930’s, there has been a consensus that density was to be preferred over occupancy as the measure of vehicular concentration. . . . It would be fair to say that the majority opinion at present remains in favor of density, but that a minority view is that occupancy should begin to enter theoretical work instead of density. There are two principal reasons put forward by the minority for making more use of occupancy. The first is that there should be improved correspondence between theoretical and practical work on freeways. If freeway traffic management makes extensive use of a variable that freeway theory ignores, the profession is the poorer. The second reason is that density, as vehicles per length of road ignores the effects of vehicle length and traffic composition. Occupancy, on the other hand, is directly affected by both of these variables, and therefore gives a more reliable indicator of the amount of a road being used by vehicles. There are also good reasons put forward by the majority for the continued use of density in theoretical work. Not least is that it is theoretically useful in their work in a way that occupancy is not. . . .
7.4.2.
Speed-Flow-Density Relationships
The following excerpt is taken from Chapter 2 (pp. 20-26) of the Transportation Research Board Special Report on Traffic Flow Theory, published on the website http://www.tfhrc.gov/its/tft/tft.htm . Speed-Density Model
This subsection deals with mathematical models for the
u u 1 kk speed-density relationship, going back to as early as 1935. Greenshields’ (1935) linear model of speed and density was mentioned in the previous section. . . . The most interesting aspect of this particular model is that its empirical basis consisted of half a dozen points in one cluster near freeflow speed, and a single observation under congested conditions. . . . The linear relationship comes from connecting the cluster with the single point. . . . What is surprising is not that such simple analytical methods were used in 1935, but that their results (the linear speed-density model) have continued to be so widely accepted for so long. While there have been studies that claimed to have confirmed this model they tended to have similarly sparse portions of the full range of data, usually omitting both the lowest flows and flow in the range near capacity. . . . A second early model was that put forward by Greenberg (1959), showing a logarithmic relationship:
u clnkk His paper showed the fit of the model to two data sets, both of which visually looked very reasonable. However, the first data set was derived from speed and headway data on individual vehicles, which "was then separated into speed classes and the average headway was calculated for each speed class". In other words, the vehicles that appear in one data point(speed class) may not even have been traveling together! While a density can always be calculated as the reciprocal of 136
average headway, when that average is taken over vehicles that may well not have been traveling together, it is not clear what that density is meant to represent. . . . Duncan (1976, 1979) showed that the tree step procedure of (1) calculating density from speed and flow data, (2) fitting a speed-density function to that data, and then (3) transforming the speeddensity function into a speed-flow function results in a curve that does not fit the original speedflow data particularly well. . . . Duncan’s 1979 paper expanded on the difficulties to show that minor changes in the speed-density function led to major changes in the speed-flow function. This result suggests the need for further caution in using this method of double transformations to calibrate a speed-flow curve. . . . The car-following models gave rise to four of the speed-density models tested by Drake et al. The results of their testing suggest that the speed-density models are not particularly good. Logic says that if the consequences of a set of premises are shown to be false, then one (at least) of the premises is not valid. It is possible, then, that the car-following models are not valid for freeways. This is not surprising, as they were not developed for this context. Flow-Concentration Model
Although Gerlough and Huber did not give the topic of flow-concentration models such extensive treatment as they gave the speed-concentration models, they nonetheless thought this topic to be very important. . . . Edie was perhaps the first to point out that empirical flow-concentration data frequently have discontinuities in the vicinity of what would be maximum flow, and to suggest that therefore discontinuous curves might be needed for this relationship. . . . Koshi et al. (1983) gave an empirically-based discussion of the flow-density relationship, in which they suggested that a reverse lambda shape was the best description of the data. . . . These authors also investigated the implications of this phenomenon for car-following models, as well as for wave propagation. . . . there appears to be strong evidence that traffic operations on a freeway can move from one branch of the curve to the other without going all the way around the capacity point. This is an aspect of traffic behavior that none of the mathematical models . . . either explain or lead one to expect. Nonetheless, the phenomenon has been at least implicitly recognized since Lighthill and Witham’s (1955) discussion of shock waves in traffic, which assumes instantaneous jumps from one branch to the other on a speed-flow or flow-occupancy curve. As well, queuing models (e.g. Newell 1982) imply that immediately upstream from the back end of a queue there must be points where the speed is changing rapidly from the uncongested branch of the speed-flow curve to that of the congested branch. It would be beneficial if flow-concentration (and speed-flow) models explicitly took this possibility into account. One of the conclusions of the paper by Hall et al. (1986), . . . is that an inverted ‘V’ shape is a plausible representation of the flow-occupancy relationship. Although that conclusion was based on limited data from near Toronto, Hall and Gunter (1986) supported it with data from a larger number of stations. Banks (1989) tested their proposition using data from the San Diego area, and confirmed the suggestion of the inverted ‘V’. He also offered a mathematical statement of this proposition and a behavioral interpretation of it (p. 58): The inverted-V model implies that drivers maintain a roughly constant average time gap between their front bumper and back bumper of the vehicle in front of them, provided their speed is less than some critical value. Once their speed 137
reaches this critical value (which is as fast as they want to go), they cease to be sensitive to vehicle spacing. . . .
7.4.3.
Greenshields' Model
The following excerpt is taken from Chapter 2 (pp. 17-20) of the Transportation Research Board Special Report on Traffic Flow Theory, published on the website http://www.tfhrc.gov/its/tft/tft.htm . Speed-Flow Model
The problem for traffic flow theory is that these curves are empirically derived. There is not really any theory that would explain these particular shapes, except perhaps for Edie et al. (1980), who propose qualitative flow regimes that relate well to these curves. The task that lies ahead for traffic flow theorists is to develop a consistent set of equations that can replicate this reality. . . . It is instructive to review the history of depictions of speed-flow curves in light of this current understanding. Probably the seminal work on this topic was the paper by Greenshields in 1935, in which he derived the following parabolic equation for the speed-flow curve on the basis of a linear speed-density relationship together with the equation, flow = speed × density:
u q k u u where uf is the free-flow speed, and k j is the jam density. . . . In short, Greenshields’ model dominated the field for over 50 years, despite at least three problems. The most fundamental is that Greenshields did not work with freeway data. Yet his result for a single lane of traffic was adopted directly for freeway conditions. (This of course was not his doing.) The second problem is that by current standards of research the method of analysis of the data, with overlapping groups and averaging prior to curve-fitting, would not be acceptable. The third problem is that despite the fact that most people have used a model that was based on holiday traffic, current work focuses on regular commuters who are familiar with the road, to better ascertain what a road is capable of carrying. . . . Speed-flow models are now recognized to be important for freeway management strategies, and will be of fundamental importance for ITS implementation of alternate routing; hence there is currently considerably more work on this topic than on the remaining two bivariate topics. . . . Hence, it is sensible to turn to discussion of speed-concentration models, and to deal with any other speed-flow models as a consequence of speed-concentration work, which is the way they were developed.
7.4.4.
Shock Waves and Continuum Flow Models
The following excerpt is taken from Chapter 5 (pp. 1-4) of the Transportation Research Board Special Report on Traffic Flow Theory, published on the website http://www.tfhrc.gov/its/tft/tft.htm .
Since the conservation equation describes flow and density as a function of distance and time, one can immediately see that continuum modeling is superior to input-output models used in practice (which are only one dimensional, because they essentially ignore space). In addition, because flow is assumed to be a function of density, continuum models have a second major advantage, (e.g. compressibility). The simple continuum model referred to in this text consists of the conservation equation and the equation of state (speed-density or flow density relationship). If these equations are solved together with the basic traffic flow equation (flow equals density times speed), then we 138
can obtain speed, flow, density at any time and point of the roadway. Knowing these basic traffic flow variables we know the state of the traffic system and can derive measures of effectiveness, such as delays stops, total travel, travel time, and others that allow engineers to evaluate how well the system is performing. . . . A shock wave is a discontinuity of flow or density, and has the physical implication that cars change speeds abruptly without time to accelerate or decelerate. This is an unnatural behavior that could be eliminated by considering high order continuum models. These models add a momentum equation that accounts for the acceleration and inertia characteristics of traffic mass. In this manner, shock waves are smoothed out and the equilibrium assumption is removed. . . . In spite of this improvement, the most widely known high order models still require an equilibrium speed-density relationship. . . .
u 2u kk ∂k∂x ∂k∂t 0 . . . where u f represents the free flow speed and k j the jam density . . . is a first order quasi-linear, partial differential equation which can be solved by the method of characteristics. . . . In practical terms, the solution . . . suggests that:
The density k is a constant along a family of curves called characteristics or waves; a wave represents the motion (propagation) of a change in flow and density along the roadway. The characteristics are straight lines emanating from the boundaries of the time-space domain. The slope of the characteristics is:
dx f k kf k dq dt dk
This implies that the characteristics have slope equal to the tangent of the flow-density curve at the point representing the flow conditions at the boundary from which the characteristic emanates. The density at any point x,t of the time space domain is found by drawing the proper characteristic passing through that point. The characteristics carry the value of density (and flow) at the boundary from which they emanate. When two characteristic lines intersect, then density at this point should have two values which is physically unrealizable; this discrepancy is explained by the generation of shock waves. In short, when two characteristics intersect, a shock wave is generated and the characteristics terminate. A shock then represents a mathematical discontinuity (abrupt change) in k, q, or u. The speed of the shock wave is:
u qk q k . . . where k d , qd represent downstream and k u , qu upstream flow conditions. In the flow concentration curve, the shock wave speed is represented by the slope of the line connecting the two flow conditions (i.e., upstream and downstream). It should be noted that when uw is positive, the shock wave moves downstream with respect to the roadway; conversely, when uw is negative, the shock is moving upstream. Furthermore, the mere fact that a difference exists in flow conditions upstream and downstream of a point does not imply 139
that a shock wave is present unless the characteristics intersect. Generally this occurs only when the downstream density is higher than upstream. When density downstream is lower than upstream, we have diffusion of flow similar to that observed when a queue is discharging. When downstream density is higher than upstream, then shock waves are generated and queues are generally being built even though they might be moving downstream. Figure 5.2 , taken from Gerlough and Huber (1975), demonstrates the use of traffic waves in identifying the occurrence of a shock wave and following its trajectory. The process follows the steps of the solution of the conservation equation as outlined above. The top of the figure represents a glow-concentration curve; the bottom figure represents trajectories of the traffic waves. On theq-k curve, point A represents a situation where traffic flows at near capacity implying that speed is well below the free-flow speed. Point B represents an uncongested condition where traffic flows at a higher speed because of the lower density. Tangents at points A and B represent the wave velocities of these two situations. The areas where conditions A and B prevail are shown by the characteristics drawn in the bottom of Figure 5.2. This figure assumes that the faster flow of point B occurs later in time than that of point A; therefore, the characteristics (waves) of point B will eventually intersect with those of point A. The intersection of these two sets of waves has a slope equal to the chord connecting the two points on the q-k curve, and this intersection represents the path of the shock wave shown at the bottom of Figure 5.2. It is necessary to clarify that the waves of the time-space diagram of Figure 5.2 are not the trajectories of vehicles but lines of constant flow and speed showing the propagation of conditions A and B. The velocities of individual vehicles within A and B are higher because the speed of the traffic stream is represented by the line connecting the origin with A and B in the q-k curve. Figure 5.2 Shock Wave Formation Resulting from the Solution of the Conservation Equation
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7.4.5.
Queuing Theory
The following excerpt is taken from Chapter 5 (pg. 6 ) of the Transportation Research Board Special Report on Traffic Flow Theory, published on the website http://www.tfhrc.gov/its/tft/tft.htm .
Consider a single-lane queue at the beginning of the effective green at a signalized intersection. If the number of cars in the queue (i.e., the queue size) at this time is x and the average space headway is h, then the estimated queue length (i.e., the space occupied by the x cars) is xh. Suppose now that shortly after the beginning of green, N 1 cars join the queue while N are discharged in front. Then following the same logic, the queue length should be [x + (N 1-N 2 )]h. However, generally this is not the case, since shortly after the commencement of green the queue length is growing regardless of the net difference N 1 – N 2; for instance, if N 1 = N 2 the effective queue size continues to be x, but the queue length can no longer be estimated from the product xh. Clearly the average space headway is a function of time because of compressibility (i.e., the changing density within the queue in both time and space). This observation leads to the conclusion that although input-output analysis can be used for describing the evolution of queuing situation in time, they yield crude estimation of another important state variable (i.e., the queue length). For fixed-time control such approximations may suffice, but when further accuracy or realism is required, more rigorous modeling is necessary. Another disadvantage of input-output analysis is that the assumption of compact queues leads to miscalculations of the queue size itself and therefore results in miscalculations of delays (Michalopoulos and Pisharody 1981). The simple continuum model offers the advantage of taking compressibility into account (pp. 9-11)
A major benefit of the continuum modeling is the fact that compressibility is built into the state equations since speed or flow is assumed to be a function of density. This suggests that as groups of cars enter areas of higher density, the continuum models exhibit platoon compression characteristics; conversely, when they enter areas of lower density we observe diffusion or dispersion. This phenomenon has been shown analytically in Michalopoulos and Pisharody (1980), where it is demonstrated that by using continuum models we do not have to rely on empirical dispersion models such as the ones employed today in most signal control packages. The result is a more realistic and elegant modeling that should lead to more effective control. The advantage of the analytical results presented thus far is that they visually depict the effects of downstream disturbances on upstream flow. Thus they provide a good insight on the formation and dissipation of queues and congestion in time and space in both freeways and arterials; further, they can be used to demonstrate that platoon dispersion and compression are inherent in this modeling. . . . The disadvantage of the analytical solution lies in the oversimplifications needed in the derivations. These include simple initial flow conditions, as well as arrival and departure patterns, absence of sinks or sources, and uncomplicated flow-concentration relationships. Most importantly, complexities frequently encountered in real situations such as turning lanes, side streets, or freeway entrances and exits cannot be treated analytically with ease. As in similar problems of compressible flow, these difficulties can be resolved by developing numerical solutions for the state equations. Clearly, a numerical methodology is needed for numerical implementation of the conservation equation in practical situations. This allows for inclusion of complexities one is likely to encounter in practice (turning lanes, sinks and sources, spillbacks, etc.) treatment of realistic arrival and departure patterns, more complicated u-k models, as well as inclusion of empirical considerations. 141
Numerical computation of k, u, and q proceeds by discretizing the roadway under consideration into small increments Δ x (in the order of 9 to 45 meters) and updating the values of these traffic flow variables on each node of the discretized network at consecutive time increments Δt (in the order of one second or so). . . . . . . It should be emphasized that this discretization is not physical and is only performed for computational purposes. . . . density on any node j except the boundary ones . . . at the next time step n+1 is computed from density in the immediately adjacent cells (both upstream and downstream j-1 and j+1 respectively) at the current time step n according to the relationship:
1 ∆t ∆t k k k q q 2 2∆x 2 q q in which: k jn, q jn to Δt, Δx g jn g jn
= density and flow rate on node j at t = t o+n Δt = the initial time = the time and space increments respectively such that Δt/Δx > free flow speed. = is the generation (dissipation) rate at node j at t = to+nΔt; if no sinks or sources exist = 0 and the last term . . . vanishes.
Once the density is determined, the speed at t+ Δt (i.e., at n+1) is obtained from the equilibrium speed density relationship ue(k), i.e.,
u u k For instance, for the Greenshields (1934) linear model,
k u u 1 k where u f is the free flow speed and k jam the jam density… if an analytical expression is not available, then u can easily be obtained numerically from the u-k curve. Finally, flow at t+ Δt is obtained from the fundamental relationship:
q k u . . . It can be demonstrated (Michalopoulos 1988) that measures of effectiveness such as delays, stops, total travel, etc., can be derived from k, u, and q. . . . In conclusion it is noted that more accurate numerical methods can be developed for solving the conservation Equation 9; such methods are not recommended as they lead to sharp shocks which are unrealizable in practice. . . .
7.5.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic. 142
7.5.1.
Greenshield's Model
Inspection of a freeway data set reveals a free flow speed of 60 mph, a jam density of 180 vehicles per mile per lane, and an observed maximum flow of 2000 vehicles per hour. Determine the linear equation for velocity for these conditions, and determine the speed and density at maximum flow conditions. How do the theoretical and observed conditions compare?
Solution
v v kv k mph 60 k 600.333k v 60 180 q v k q 60k 0.333k dq 60 20.333k dk 60 = 2(0.333)k k = 90 = k j/2 half of jam density
60 90 30 mph v half of free low speed v 60 180 2 q v k q 3090 2700 vph 2000h The theoretical value does not account for the field conditions that influence maximum flow.
7.5.2.
Shock Waves
A slow moving truck drives along the roadway at 10 MPH. The existing conditions on the roadway before the truck enters are shown at point 1 below: 40 mph, flow of 1000 vehicles per hour, and density of 25 vehicles per mile. The truck enters the roadway and causes a queue of vehicles to build, giving the characteristics of point 2 below: flow of 1200 vehicles per hour and a density of 120 vehicles per mile. Using the information provided below, find the velocity of the shockwave at the front and back of the platoon.
143
Point 1: Normal flow ( us = 40 MPH, k=25 veh/mi, q= 1000 vph.) Point 2: Slow Truck: ( us = 10 MPH, k=120 veh/mi, q= 1200 vph.)
Solution Figures 3.6.2 and 3.6.3, shown below, illustrate the behavior of the vehicles that are impacted by the shockwave. The speed of the shockwave in front of the truck at point A-A ( q b= 0, k b = 0) can be found by substituting the correct values into the general shockwave equation. Upon substitution, as shown below, we find that the shockwave is moving at the same speed as the truck, or 10 MPH downstream with reference to a stationary point on the roadway.
1200 10 MPH u 00 120
144
Solving for the speed of the shockwave at the end of the platoon (B-B) is accomplished by substituting the correct values into the general shockwave equation. qa= 1000 vph, k a=25 vpm q b= 1200 vph, k b =120 vpm
The (+) sign indicates that the shockwave is moving downstream with respect to a fixed observer. A-A moves forward relative to the roadway at 10 MPH B-B moves forward relative to the roadway at 2.1 MPH Platoon Growth: 10 - 2.1 =
7.9 MPH
Problem adapted from: Papacostas, C.S., and Prevedourous P.D., Transportation Engineering and Planning, 2nd Edition, Prentice Hall, pages 151-157 145
7.5.3.
Traffic Flow Model
A study of freeway flow at a particular site has resulted in a calibrated speed-density relationship, as follows: Us= 57.5 (1 - 0.008k) From this relationship: a. Find the free-flow speed and jam density b. Derive the equations describing flow versus speed and flow versus density. c. Determine the capacity of the site mathematically
Solution A) To solve for free-flow speed and jam density: us = 57.5 – 0.46k Notice that this equation is linear with respect to space mean speed and density and is of the form of Greenshield’s equation. Greenshield’s equation:
u u k
Free flow speed uf = 57.5 MPH To calculate jam density:
0.46 gives k = 125 vpm j
B) To derive the equations for flow as a function of density: q= us × k q = 57.5k - 0.46k 2 vph gives flow as a function of density (note that it is a quadratic in k) To derive flow as a function of speed: 0.46k = 57.5 - us
k 57.0.546 u 125 0.u46 u u q u 125 0.46 125u 0.46 vph note that it is a quadratic in u C) To determine the capacity of the site: Need to determine the maximum flow:
dq 57.5 0.462 k 0 dk 57.5 0.46 2k 146
57.5 62.5 veh per mile k density at maximum low k 0.462 q 57.5k 0.46k q 57.562.50.4662.5 q 3593.75 1796.875 q 1796.875 veh/hour q speed at maxium flow = um = 57.5 – 0.46 × (62.5) = 28.75 mph
7.6.
Glossary
Density: the number of vehicles occupying a road lane per unit length at a given instant. Flow: the number of vehicles passing a point per unit of time; often called volume when the time unit is one hour. Gap: the time interval between the passage of consecutive vehicles moving in the same stream, measured between the rear of the lead vehicle and the front of the following vehicle. Headway: the time interval between passage of consecutive vehicles moving in the same stream, measured between corresponding points (e.g. front bumper) on successive vehicles. Interrupted Flow: occurs when flow is periodically interrupted by external fixtures, primarily traffic control devices. Jam Density: the density when speed and flow are zero. PHF (Peak Hour Factor): This describes the relationship between hourly volume and the maximum rate of flow within the hour: PHF = hourly volume/maximum rate of flow. For the 15 minute periods, PHF = volume / [4 x (maximum 15 minute volume within the hour)] Shockwaves: Shockwaves occur as a result of differences in flow and density which occur when there are constrictions in traffic flow. These constrictions are called bottlenecks. The speed of growth of the ensuing queue is the shockwave, and is the difference in flow divided by the difference in density. Space Mean Speed: the arithmetic mean of the speed of those vehicles occupying a given length of road at a given instant. Spacing: the distance between vehicles moving in the same lane, measured between corresponding points ( front to front ) of consecutive vehicles. Speed: the time rate of change of distance. Time Mean Speed: the arithmetic mean of the speed of vehicles passing a point during a given time interval.
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Travel Time: the total time required for a vehicle to travel from one point to another over a specified route under prevailing conditions. Uninterrupted Flow: occurs when vehicles traversing a length of roadway are not required to stop by any cause external to the traffic stream, such as traffic control devices. Volume: Traffic volume is the most basic and widely used parameter in traffic engineering, vehicles per mile, or vehicles per kilometer.
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8. Travel Demand Forecasting 8.1.
Introduction
Travel Demand Forecasting is a key component of the transportation engineer’s technical repertoire. It allows the engineer to predict the volume of traffic that will use a given transportation element in the future, whether that element is an existing highway or a potential light-rail route. Like many other ‘predictive’ sciences, Travel Demand Forecasting is continually evolving. Special refinements based on experience and research are proposed each year, but the general ideology behind Travel Demand Forecasting has remained relatively untouched. The travel demand forecasting process can be confusing. This chapter is designed to introduce the fundamentals of Travel Demand Forecasting to undergraduate engineering students by dividing the process into manageable steps.
8.2.
Lab Exercises
These exercises will help increase your understanding of Travel Demand Forecasting, by presenting more complicated problems that require more thorough analysis.
8.2.1.
Lab Exercise 1: The Gravity Model
The four-zone city of Wocsom’s trip generation characteristics are shown below, in addition to a travel network for the city. There are two major activities in this lab assignment: a. Use the trip generation information provided to distribute the trips between the four zones. b. Using the results of the trip distribution analysis and the results of the network analysis, assign the trips to the various links.
The four-zone city has the following productions and attractions:
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Zone
Productions
Attractions
A B C D
1000 2000 3000 4000
3000 3000 2000 2000
Travel Time (min) Zone
A
B
C
D
A B C D
2 5 7 10
5 3 8 12
7 8 2 11
10 12 11 3
Travel Time (min)
Fij
2 3 5 7 8 11 12
3.0 2.5 2.3 1.5 1.2 0.95 0.90
Tasks to be Completed Task 1. Distribute the trips for the city of Wocsom using the gravity model. Use the given data to develop a trip table for the four-zone city of Wocsom. Task 2. Find the shortest path from nodes A,B,C, and D to all other nodes and intersections. Task 3. Using the trip table (veh/hr) below, load the network and find the total volume on each link assuming all or nothing assignment.
From\ To
A
B
C
D
A B C D
-30 90 60
50 -80 70
40 80 -50
20 10 20 --
Task 4. Using the trip table resulting from the gravity model above, load the network and find the total volume on each link, assuming all or nothing assignment. Task 5. Prepare a brief report documenting your analysis, and be sure to explain the differences and similarities in the results of Task 3 and Task 4.
Assumptions For your analysis using the gravity model, assume the socioeconomic factor K ij=1.0.
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8.2.2.
Lab Exercise 2: Cross-Classification
Twenty households in the city of Scoretown were sampled for household income, autos per household and trips produced.
Households
Trips
Income(dollars)
Autos
1 2 3 4 5
2 4 10 5 5
4000 6000 17,000 11,000 4,500
0 0 2 0 1
6 7 8 9 10
15 7 4 6 13
17,000 9,500 9,000 7,000 19,000
3 1 0 1 3
11 12 13 14 15
8 9 9 11 10
18,000 21,000 7,000 11,000 11,000
1 1 2 2 2
16 17 18 19 20
11 12 8 8 9
13,000 15,000 11,000 13,000 15,000
2 2 1 1 1
Tasks to be Completed Task 1. Develop matrices relating income to automobiles available. Task 2. Draw a graph relating trips per household to income. Task 3. Using the results of tasks 1 and 2, calculate how many trips a household with an income of $10,000, owning one auto, will make per day? Task 4. Perform a similar analysis for the same household, but with an additional vehicle. Task 5. Prepare a brief report documenting your analysis of the data for Scoretown, and the impact of increased auto ownership on travel demand patterns. Task 6. Prepare a 3-5 page report discussing the important issues involved in managing and even reducing travel demand, as measured by vehicle miles driven for the city of Scoretown or your own community.
8.3.
Theory and Concepts
Travel Demand Forecasting can seem like a long and daunting process when viewed as a whole. It is much easier to approach when broken into small steps. The discussions below should help you develop a basic understanding of the Travel Demand Forecasting process. 151
8.3.1.
Overview of the TDF Process
Travel Demand Forecasting is a multi-stage process, and there are several different techniques that can be used at each stage. Generally, Travel Demand Forecasting involves five interrelated tasks. 1. Break the area that requires prediction of future travel demand into study zones that can be accurately described by a few variables. 2. Calculate the number of trips starting in each zone for a particular trip purpose. (Trip Generation Analysis ) 3. Produce a table of the number of trips starting in each zone and ending up in each other zone. (Trip Distribution Analysis ) 4. Complete the allocation of the various trips among the available transportation systems (bus, train, pedestrian, and private vehicles). (Modal Choice Analysis ) 5. Identify the specific routes on each transportation system that will be selected by the travelers. (Trip Assignment Analysis ) Once these five steps have been completed, the transportation engineer will have a clear picture of the projected travel demand for an existing or proposed transportation system.
8.3.2.
Description of the Study Area
Study Boundary
Before forecasting the travel for an urban area or region, the planner must clearly define the exact area to be considered. These areas may be defined by the urban growth boundary (UGB) , county lines or town centers. The planning area generally includes all the developed land, plus undeveloped land that the area will encompass in the next 20 to 30 years. The cordon line denotes the boundary of the planning area. In addition to considering future growth, the establishment of the cordon line might take into account political jurisdictions, census area boundaries, and natural boundaries. The cordon line should intersect a minimum number of roads. Zones
The study area must then be divided into analysis units, or zones. This will enable the planner to link information about activities, travel, and transportation to the physical locations in the study area. The transportation analysis zones (TAZ) vary in size depending on the density or nature of the development. In an urban area the TAZ may be as small as a city block, but in rural areas the TAZ may be as large as 10 or more square miles. The zones attempt to encompass homogeneous urban activities, which are all residential, all commercial, or all industrial. Zones are designed to be relatively homogeneous traffic generators and are sized so that only 10-15% of the trips are intrazonal. An important consideration in establishing zones is their compatibility with the transportation network. As a general rule, the network should form the boundaries of the zones. A study area that has been divided into zones is shown below.
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Links and Nodes
Normally, a simple representation of the geometry of the available transportation systems is included on the map of the study area. A system of links and nodes, or a network, indicates roadways and other transportation routes. Links represent sections of roadway (or railway etc.) that are homogeneous, while nodes are simply points at which links meet. Usually, transit networks are developed independently of truck and automobile networks. In the network description, zone centroids (centers of activity) are identified; they are connected to nodes by imaginary links called centroid connectors. Centroids are used as the points as which trips are "loaded" onto the network. A diagram of a transportation network is shown below. 153
The figures on this page came from: Garber, N.J. and Hoel, L.A., Traffic and Highway Engineering, Revised 2nd Edition, PWS, Pacific Grove, CA. 1999. Pg. 499 and 501
154
8.3.3.
Trip Generation Analysis
Once the study area has been broken into zones, the next task involves quantifying the number of trips that each zone will produce or attract. The number of trips to and from an area or zone is related to the land use activities of the zone and the socioeconomic characteristics of the tripmakers. There are at least three characteristics of land use and trip-makers that are important. The density or intensity of the land use is important. Many studies begin by determining the number of dwellings, employees, or tenants per acre. The intensity can be related to an average number of trips per day, based on experience with the type of land use at hand. Next, the social and economic character of the users can influence the number of trips that are expected. Character attributes like average family income, education, and car ownership influence the number of trips that will be produced by a zone. Finally, location plays an important role in trip production and attraction. Street congestion, parking, and other environmental attributes can increase or decrease the number of trips that an area produces or attracts. The three major techniques used for Trip Generation Analysis are Cross-Classification, Multiple Regression Analysis, and Experience Based Analysis. Each of these techniques is discussed as a separate concept within this section.
Cross-Classification The three major techniques used for Trip Generation Analysis are Cross-Classification, Multiple Regression Analysis, and Experience Based Analysis. Cross-Classification procedures measure the changes in one variable (trips) when other variables (land use etc.) are accounted for. CrossClassification resembles multiple regression techniques. Cross-Classification is essentially non parametric, since no account is taken of the distribution of the individual values. One problem with the Cross-Classification technique is that the "independent" variables may not be truly independent, and the resultant relationships and predictions may well be invalid. The FHWA Trip Production Model uses Cross-Classification and has the following sub-models. a. Income sub-model: reflects the distribution of households within various income categories (e.g. high, medium and low). b. Auto ownership sub-model: relates the household income to auto ownership. c. Trip production sub-model: establishes the relationship between the trips made by each household and the independent variables. d. Trip purpose sub-model: relates the trip purposes to income in such a manner that the trip productions can be divided among various purposes. These models are developed using origindestination travel surveys. A considerable amount of research and development has focused on the area of disaggregate models for improved travel demand forecasting. The difference between the aggregate and disaggregate techniques is mainly in the data efficiency. Aggregate models are usually based upon home interview origin and destination data that has been aggregated into zones; then the "average" zonal productions and attractions are derived. The disaggregate approach is based on large samples of household types and travel behaviors and uses data directly. There are savings in the amount of data required and some of the data can be transferred to other applications. The disaggregate approach expresses non-linear relationships and is more easily understood. The tables shown below show several steps of a cross-classification analysis. 155
The above figures are from: Paul Wright, Highway Engineering , 6th ed. Wiley, 1996.pp55, 56, and 58
8.3.4.
Multiple Regression Analysis
The three major techniques used for Trip Generation Analysis are Cross-Classification, Multiple Regression Analysis, and Experience Based Analysis. Multiple Regression Analysis is based on trip generation as a function of one or more independent variables. The approach is mathematical and all of the variables are considered random, and with normal distributions. For example, consider the following equation: Ti = 0.34 (P) + 0.21 (DU) + 0.12 (A) A j = 57.2 + 0.87 (E) Where: Ti A j P DU A E
= Total number of trips produced in zone I = Total number of trips attracted in zone j = Total Population for zone I = Total number of dwelling units for zone I = Total number of automobiles in zone I = Total employment in zone j
156
Multiple Regression Analysis is relatively simple to understand. First, data regarding the actual number of productions and attractions is coupled with data about the area that is thought to impact the production and attraction of trips. For instance, the total population is believed to impact the number of trips produced. If we know the number of trips produced and the population for the present and a few time periods in the past, it is possible to develop a relationship between these parameters using statistical regression. Once we are satisfied with the relationship that has been developed, we can extrapolate into the future by plugging the future population into our relationship and solving for the number of productions. The process is called Multiple Regression, because there are normally several variables that impact trip production and attraction.
8.3.5.
Experience Based Analysis
The three major techniques used for Trip Generation Analysis are Cross-Classification, Multiple Regression Analysis, and Experience Based Analysis. Experience Based Analysis, one of the most commonly used techniques, is founded primarily on experience. The Institute of Transportation Engineer’s Manual of Trip Generation is one of the best sources of generalized trip generation rates. The manual is a compilation of data from all over North America on many different types of land uses. Within the manual, productions and attractions for each type of land use are related to some measurable variable. For example, a shopping center might produce a certain number of trips for each employee. Simply asking for the employment roster would allow a transportation engineer to estimate the total number of trips that are generated by the shopping center employees. To establish local credibility, a survey of similar land uses in the area may also need to be conducted.
8.3.6.
Trip Distribution Analysis
Once the trip productions and attractions for each zone are computed, the trips can be distributed among the zones using Trip Distribution Models. Trip Distribution has traditionally been based on the gravity model, but other models are gaining popularity as well. This module will discuss the logit model and the gravity model.
8.3.7.
The Logit Model
The logit model, which will be discussed again later in the Mode Choice module, has been used by the Portland, Oregon metropolitan area. The probability of selecting a particular destination zone is based on the number of trip attractions estimated for that destination zone, relative to the total attractions in all possible destination zones. The probability is applied to trip productions estimated for the origin zone, making it conceptually similar to the gravity model.
e P ∑ e where Pij Vij A j tij Z
= probability of trips from zone i choosing destination j = where a and b are parameters to be estimated = trip attractions estimated for zone j = highway travel time to zone j from zone i = total number of zones
A a t bt
Multiplying the probability of traveling from zone i to zone j by the number of trips produced by zone i will yield the number of trips produced by zone i that will travel to zone j. 157
8.3.8.
The Gravity Model
The gravity model is much like Newton's theory of gravity. The gravity model assumes that the trips produced at an origin and attracted to a destination are directly proportional to the total trip productions at the origin and the total attractions at the destination. The calibrating term or "friction factor" (F) represents the reluctance or impedance of persons to make trips of various duration or distances. The general friction factor indicates that as travel times increase, travelers are increasingly less likely to make trips of such lengths. Calibration of the gravity model involves adjusting the friction factor. The socioeconomic adjustment factor is an adjustment factor for individual trip interchanges. An important consideration in developing the gravity model is "balancing" productions and attractions. Balancing means that the total productions and attractions for a study area are equal. Standard form of gravity model
AFK P T ∑ AFK Where: Tij Pi A j
= trips produced at i and attracted at j = total trip production at i = total trip attraction at j
Fij
= a calibration term for interchange ij, (friction factor) or travel time factor (
C K ij i n
= calibration factor for the friction factor = a socioeconomic adjustment factor for interchange ij = origin zone = number of zones
F
)
Before the gravity model can be used for prediction of future travel demand, it must be calibrated. Calibration is accomplished by adjusting the various factors within the gravity model until the model can duplicate a known base year’s trip distribution. For example, if you knew the trip distribution for the current year, you would adjust the gravity model so that it resulted in the same trip distribution as was measured for the current year.
8.3.9.
Modal Choice Analysis
After completing the Trip Distribution Analysis, we need to determine what transportation system each of those travelers will use. Mode choice models estimate how many people will use public transit and how many will use private automobiles. The most common form of the mode choice model is the logit model. The logit mode choice relationship states that the probability of choosing a particular mode for a given trip is based on the relative values of a number of factors such as cost, level of service, and travel time. The most difficult part of employing the logit mode choice model is estimating the parameters for the variables in the utility function. The estimation is often accomplished using one or more multivariate statistical analysis programs to optimize the accuracy of estimates of the coefficients of several independent variables. In regions where there are several alternative modes available, the mode choice model may require a special form called the "nested" logit. This form attempts to represent the choices presented to the 158
traveler in a more structured manner. Nesting is necessary when there are major competing alternatives within, as well as between, principal modes.
Logit Model
U e P ∑ eU Where: Pit Uit U jt
= probability of individual t choosing mode i = utility of mode i to individual t = utility of mode j to individual t
For example: Uauto U bus Uwalk TT TC
8.3.10.
= 1.0 - 0.1 (TTauto) - 0.05 (TCauto) = - 0.1 (TT bus) - 0.05 (TC bus) = - 0.5 - 0.1 (TTwalk ) = travel time by mode in minutes = travel cost by mode in dollars
Trip Assignment Analysis
Once you have determined the number of trips that will enter and leave each zone, as well as the transportation modes that the travelers will use, you can identify the exact roadways or routes that will be selected for each trip. Trip assignment involves assigning traffic to a transportation network such as roads and streets or a transit network. Traffic is assigned to available transit or roadway routes using a mathematical algorithm that determines the amount of traffic as a function of time, volume, capacity, or impedance factor. There are three common methods for trip assignment: all or nothing, diversion, and capacity restraint. All-or-Nothing
All-or-nothing is often referred to as the minimum path algorithm. The minimum path, or tree, represents the minimum time path between two zone centroids and is assigned all of the traffic volume between the zones in question. As volumes and travel times increase, the results of this method become more unreliable. As an example of this method, imagine that zones A and B are connected by ten separate routes. Route 3.0 has the shortest travel time which means that, according to this model, all trips from A to B will use route 3.0. Diversion is the allocation of trips to two or more possible routes in a designated proportion that depends on some specified criterion. In most cases the criterion that is used is time, although some also use distance and generalized cost. Diversion is very similar to the all-or-nothing’ method, except that portions of the total number of trips are allocated to different routes, with fewer trips being given to those routes with longer travel times.
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Capacity Restraint
Many different capacity restraint equations have been developed and tested and are available for use. There are two basic characteristics common to capacity restraint models; (i) they are non-linear relationships and (ii) they use the volume-capacity ratio or v/c as a common factor. The underlying premise of a capacity restraint model is that the travel time on any link is related to the traffic volume on that link. This is analogous to the level of service (LOS) criterion, where LOS A corresponds to a low v/c and a higher vehicle speed. LOS E and the corresponding v/c = 1 represents capacity. Capacity restraint models assign traffic to possible routes in an iterative manner: 1. A portion of the total traffic volume is assigned to the link with the shortest travel time. 2. Travel times for all possible links are calculated again, since volumes have changed. 3. Another portion of the traffic volume remaining to be assigned is allocated to the link that now has the shortest travel time. 4. The travel time for all links are calculated and revised if changes result. 5. The process of incremental assignments, followed by calculation of revised shortest travel times, by link, continues until all trips have been assigned. The capacity restraint model used by FHWA is applied in an iterative manner. The adjusted link speed and/or its associated travel impedance is computed using the following capacity restraint function:
V T T 10.15C Where: T To V C
= balance travel time (at which traffic V can travel on a highway segment) = free flow travel time: observed travel time (at practical capacity) times 0.87 = assigned volume = practical capacity
8.3.11.
Results
Once you have completed the trip assignment analysis, you have a picture of the volume of traffic that each element of your transportation system can expect to service in the future. This gives you insight into the ramifications of changing the transportation system. For example, widening a highway will increase capacity and shift more traffic onto that highway in the future. Using travel demand forecasting, you can explore the impacts of alternatives before their construction.
8.4.
Professional Practice
The Transportation Planning Handbook serves as the primary source for information concerning Travel Demand Forecasting. Published by the Institute of Transportation Engineers, this manual serves as a general reference for professional engineers. It has been developed extensively to encompass all aspects of planning and provides essential knowledge for the transportation engineer. We referenced the 1992 publication of the Transportation Planning Handbook because it is generally accepted as "the" authority on planning in the professional realm of engineering. For more a extensive analysis the Institute of Transportation Engineers also publishes a Travel Demand 160
Forecasting manual. This manual provides in-depth analyses for various aspects of travel demand and impact studies and is also frequently referenced in the professional arena.
8.4.1.
Zones and Zoning
The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (pp. 100-102).
Data processing of information describing the urban area and the transportation system requires identifying that information with a numerical code to facilitate automated retrieval. To do this the area being studied is divided into small geographic areas called zones, and the boundaries of each zone are drawn on a base map of convenient scale. A unique numerical code, usually consecutive starting with number one, is assigned to each zone. . . . The time, cost, and capacity for computer processing dictate that there should usually not be more than 1,000 analysis zones. . . . In large metropolitan areas, the recommended limitation on the number of zones may yield zones that are too large for detailed transportation analysis. The approach that has been chosen by some agencies to overcome this difficulty is to define zones that are small enough to perform the most detailed analysis anticipated. These small zones are aggregated to larger zones of an appropriate size for analyses requiring less detail.
8.4.2.
Networks and Nodes
The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (pp. 102-103).
The transportation system is represented by a network of lines; each road and transit route is drawn as a line on a map or overlay at the same scale as the zone map. The intersections of the transportation lines are called nodes. Each node is assigned a unique number, starting with a number somewhat greater than the highest zone number. . . . The two node numbers at the ends of any link identify that link. A roadway is defined by the links along its path. The links are stored in the computer according to their identifying node numbers. Transit routes are identified and stored in a similar manner, as the string or series of node numbers along the transit route. For transit routes operating on roadways, the string of node numbers identifies the roadway nodes traversed by the transit route. (p. 103) The characteristics of the roadway represented by each link are coded as attributes of that link. The attributes usually include the length of the link (in miles), the vehicle capacity of the roadway, and the speed or time of movement along the link. Depending on the computer program being used, other attributes of the link or activity along the link may also be coded, such as adjacent land use, character of the area in which the link is located, whether parking is permitted, and the classification of the facility that the link represents.
8.4.3.
Trip Generation Analysis
The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (pp. 108-112). Trip Generation Models
(p. 110) There are two kinds of trip generation models: production models and attraction models. Trip production models estimate the number of home-based trips to and from zones where trip makers reside. Trip attraction models estimate the number of home-based trips to and from each 161
zone at the non-home end of the trip. Different production and attraction models are used for each trip purpose. Special generation models are used to estimate nonhome-based, truck, taxi, and external trips. Cross-Classification
Over time the profession has come to understand that considerable predictive power and accuracy can be gained by disaggregate analysis of influential variables. . . . This means that the models use factors describing individual sample units (e.g., persons, households or workplaces) rather than an average value of each factor for each analysis zone. The result is trip generation models with trip rates for sample units having specific characteristics, such as households of one, two, or more family members, owning one, two, or more vehicles. These models are based on the trip rates for individual sample households having those particular discrete characteristics. . . . (p. 112) Most trip production models are two- or three-way cross-classification tables with the dependent variable being trips per household or trips per person. The independent variables are most often income, auto ownership, and household size. . . . Virtually all of the trip attraction models use employment and an identifier of location as independent variables. Multiple Regression
(p. 110) Early trip generation models were commonly developed by regression analysis because of its power and simplicity. The independent variables in such models were usually zonal averages of the various factors of influence. Trip generation equations developed by regression are still used by some planning agencies, more commonly for attraction models than for production models. This is because only zonal averages of trip attracting characteristics are usually available since most travel surveys do not survey at trip destinations. Obtaining more detailed data for individual attraction zones requires a survey of trip attractors, such as a workplace survey. Experience Based
(p. 108) Early travel forecasting used extrapolation of past trends to estimate future travel. Such an approach is still used occasionally for estimating future traffic on a single facility, in a relatively isolated area, where only moderate and uniform growth or change in development pattern is anticipated. One level of sophistication that can be added to trend analysis to respond to anticipated growth is comparing the past traffic trend to the trend of development during the same period. This provides understanding of how traffic on the subject facility will respond to expected development changes. That relationship between the two trends is incorporated subjectively in the trend forecast.
8.4.4.
Trip Distribution
The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (pp. 112-114).
Trip distribution models connect the trip origins and destination estimated by the trip generation models to create estimated trips. Different trip distribution models are developed for each of the trip purposes for which trip generation has been estimated. The trip distribution models found most often in practice today are "gravity models," so named because of their basis in Newton’s law. . . . The measure of separation between zones most commonly used for trip distribution is roadway travel time, calculated from the computerized transportation networks. Most transportation planning efforts use peak-period travel times as a measure of zonal separation for home-based work and 162
home-based school models. . . . Recent studies have tried to incorporate travel cost and transit travel time into the separation measure. Cost has been considered in an attempt to estimate effects on trip distribution of parking costs, vehicle operating costs, and tolls. Logit Model
Other trip distribution models that have been used include "opportunity" models and logit models, both of which estimate the probability that travelers will accept various destination options available. The logit formulation has recently been used for the Portland, Oregon metropolitan area. As shown in Figure 4.20, the probability of selecting a particular destination zone is based on the number of trip attractions estimated for that destination zone relative to the total attractions in all possible destination zones. The probability is applied to trip productions estimated for the origin zone, making it conceptually similar to the gravity model. Gravity model
Those models generally estimate the distribution of trips to be proportional to the number of trip ends estimated by the trip generation models and inversely proportional to a measure of separation between the origin and destination zones. The gravity model has achieved virtually universal use because of its simplicity, its accuracy and due to its support from the U.S. Department of Transportation. . . . Developing a gravity model is a trial-and-error process that requires considerable care. This process, often called calibration, identifies the appropriate decay function or "friction factor", that represents the reluctance or impedance of persons to make trips of various durations or distances. . . . The adjustments are made incrementally with successive iterations of the model until the trip length frequency distribution produced by the model closely matches the frequency distribution from the travel survey or demonstrates an acceptable shape and average trip length. An important consideration in developing trip distribution models is "balancing" productions and attractions. One aspect of balance is to assure that the total productions equal the total attractions in the study area for each trip purpose. Deciding whether the productions or attractions should be the control total depends on whether there is greater confidence in the production (usually population) growth estimate or the attraction (usually employment) growth estimate. It is not unreasonable to average the two (production and attraction) trip estimates. The productions and/or attractions for all zones must then be factored so that their sum matches the control total. . . . (p. 114) At each iteration of the gravity model, the total trips attracted to each zone is adjusted so that the next iteration of the gravity model will send more or fewer trips to that attraction zone, depending on whether the immediately previous total trips attracted to that zone was lower or higher, respectively, than the trip attractions estimated by the trip generation model. . . . Any unacceptable difference between the generation and distribution model estimates after five iterations of the gravity model usually indicates an inconsistency in the assumptions or functions of the trip distribution model and the growth allocation model. One other consideration in developing a trip distribution model is how to handle unexplained and unacceptable differences between observed and estimated travel patterns. Rather than conduct extensive research to try to find an explanation for all such phenomena, the accepted practical approach is to factor the model estimates to match observed patterns. . . . With the gravity model, and often with other models in this situation, the adjustment factors are called "K" factors. The "K" factors are developed for individual trip interchanges and are assigned values that adjust the estimated trips for the interchanges of concern to match the observed values. 163
8.4.5.
Modal Choice
The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (pp. 114-115).
Mode choice models are usually the most complex of the sequential model structure. Typically these models estimate how many persons will ride public transit and how many will use private vehicles. Further sophistication of these models may include identifying submode choice among different transit services and estimating the number of car pools or van pools of various sizes for high occupancy vehicle facilities. . . . Logit Model
Mode choice models are found in numerous formulations, but the most common are based on the probabilities estimated by some variation or sophistication of the logit function. . . . The common logit mode choice relationship states that the probability of choosing a particular mode for a given trip is based on the relative values of the costs and levels of service on the competing modes for the trip interchange being considered. The level of service provided by a particular mode for a specific trip interchange is usually represented in part by the travel time for that interchange as computed from the transit and roadway networks. The travel time components used to represent level of service include the in-vehicle travel time for each mode and the out-of-vehicle time required to use that mode, such as walking to a transit stop or from a parking lot. The level of service also includes the waiting time likely to be experienced, either to board transit or to transfer. The delay due to roadway traffic congestion is included inherently by using attenuated speeds for congested roadway network links. . . . The travel time and cost of a trip are usually combined using an estimate of the cost of time to convert either cost or time to the terms of the other. The cost of time is usually a variable, based on the economic level of the traveler. Although the mode choice model may be developed using the economic level of individual travelers, forecasts of mode choice are prepared for different economic groups, such as high, medium, and low income travelers. The resulting combination of time and cost is commonly referred to as the "utility" or "generalized cost.". . . . The logit formulation is not a complex mathematical function nor is the utility function it employs. The difficulty in developing a logit model is encountered in estimating the considerable number of parameters for variables in the utility function. The estimation is accomplished using one or another multivariate statistical analysis program to optimize the accuracy of estimates of coefficients of several independent variables.
8.4.6.
Trip Assignment
The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (pp. 115-117).
The traffic assignment process is somewhat different from the mathematical models used for trip distribution and mode choice. Traffic is assigned to available transit or roadway routes using a mathematical algorithm which determines the amount of traffic to allocate to each route. The traffic allocation is usually based on the relative time to travel along each available path, computed from the transit and roadway networks. 164
All or nothing
Historically all trips between two zones were assigned to the route having the minimum travel time, regardless of the available capacity; this is termed an "all-or-nothing" assignment. Such an approach is still used for identifying travel desire corridors as an initial step in locating new and improved transportation facilities. For most transit assignments the all-or-nothing approach is still used since there are rarely closely competing transit routes in an efficiently designed transit system. Similarly the all-or-nothing approach is used for assigning high occupancy vehicle trip assignments. Capacity Restraint
More common today for roadway assignments is the "capacity-restrained" assignment, a strategy which assigns traffic in steps. One option in this approach is "proportional" assignment, which allocates a portion of the trips between every origin-destination zone pair to the network at each step. An alternative is the "incremental" assignment, which allocates all of the trips between a subset of zone pairs at each step. In either case the travel times between all zone pairs are recalculated after each assignment step, considering the traffic already assigned, to adjust the speeds on all network links. The revised speeds on all links are determined by a speed-volume function that indicates the maximum speed likely for a particular volume/capacity ratio. . . . Another assignment step is then computed considering the revised travel times, after which the link speeds are again adjusted as previously. This process is iterated until all trips have been assigned. Additional fully iterated assignments may be necessary to reach an equilibrium in which there is little change in speeds throughout the network at each assignment step.
8.4.7.
Model Calibration and Validation
The following excerpt was taken from the Transportation Planning Handbook published in 1992 by the Institute of Transportation Engineers (p. 116).
(p.116) The process of developing travel models is commonly called "calibration." Given the basic form of a travel forecasting model, such as a gravity model or a logit model, calibration involves estimating the values of various constants and parameters in the model structure. For this reason the model development effort is sometimes termed "estimation." Estimating model coefficients and constants is usually done by solving the model equation for the parameters of interest after supplying observed values of both the dependent and independent variables. The observed values of variables are obtained from the surveys of actual travel patterns. As indicated previously, the estimation process is a trial and error effort that seeks the parameter values which have the greatest probability or maximum likelihood of being accurate within acceptable tolerance of error. Such an effort is commonly accomplished with specialized statistical computer programs designed for just such purposes. . . . Model calibration can also be accomplished by using values of constants and parameters from models estimated for another location that is similar to the area being studied; this strategy is referred to as "importing" model parameters and should be employed only by experienced practitioners. Once satisfactory estimates of the parameters for all models have been obtained, the models must be checked to assure that they adequately perform the functions for which they are intended, that is, to accurately estimate traffic volumes on transit and roadways. Verifying a calibrated model in this manner is commonly called "validation." The validation process establishes the credibility of the model by demonstrating its ability to replicate actual traffic patterns. 165
Validating the models requires comparing traffic estimated by the model to observed traffic on the roadway and transit systems. Initial comparisons are for trip interchanges between quadrants, sectors, or other large areas of interest. . . . The next step is to compare traffic estimated by the models to traffic counts, including transit ridership, crossing contrived barriers in the study area. These are commonly called screenlines, cutlines, and cordon lines and may be imaginary or actual physical barriers. Cordon lines surround particular areas such as the central business district or other major activity centers. . . . Transit ridership estimates are commonly validated by comparing them to actual patronage crossing cordon lines around the central business district. . . . The importance of traffic and transit counts for model validation underscores the need for careful planning, thoroughness and accuracy of a traffic and transit data collection program that has this purpose. As with the travel surveys, the resulting models and forecasts will be no better than the data used for model estimation and validation.
8.5.
Example Problems
It doesn't seem to matter how many times we read about a concept, most of us won't remember it or fully understand it until we have worked with it. To encourage this extra level of comprehension, we have provided an example problem for each of the applicable concepts. The more concerned you are about your understanding of a topic, the more seriously you will want to approach the example problem for that topic.
8.5.1.
Cross Classification
The following cross-classification data have been developed for Beaver Dam Transportation Study Area.
($000)
HH (%)
Autos/HH (%)
Income
High
Med
Low
0
1
2
3
10 20 30 40 50 60
0 0 10 20 50 70
30 50 70 75 50 30
70 50 20 5 0 0
48 4 2 1 0 0
48 72 53 32 19 10
4 24 40 52 56 60
0 0 5 15 25 30
($000)
Trip Rate/Auto
Trips (%)
Income
0
1
2
3+
HBW
HBO
NHB.
10 20 30 40 50 60
2.0 2.5 4.0 5.5 7.5 8.0
6.0 7.5 9.0 10.5 12.0 13.0
11.5 12.5 14.0 15.5 17.0 18.0
17.0 17.5 19.0 20.5 22.0 23.0
38 38 35 27 20 16
34 34 34 35 37 40
28 28 31 38 43 44
Develop the family of cross classification curves and determine the number of trips produced (by purpose) for a traffic zone containing 500 houses with an average household income of $35,000. (Use high = 55,000; medium = 25,000; low = 15,000) 166
Solution The solution to this type of problem is best described through the use of graphs and tables. The graphs and tables used for this problem are shown below.
167
168
Income
Households (%)
HH/Zone
Total HH
Low $under $20,000
13
500
65
Medium $20,000 - 45,000
72
500
360
High $45,000 - $60,000
15
500
75
1 00
5 00
Percentage of HH owning # vehicles Income Auto Ownership Low Medium 0 1 2 3+
26 60 14 0 10 0
3 63 32 2 1 00
High 0 15 58 27 10 0
Trips per HH per Income Level and Auto Ownership Income Auto Ownership Low Medium High 0 1 2 3+
2 7 12 17
3 8 13 18
169
7 13 18 23
Number of HH owning # vehicles Income Auto Ownership Low Medium 0 1 2 3+
17 39 9 0 65
11 2 27 1 15 7 3 60
High 0 11 44 20 75
Trips made by income level Income
Auto Ownership 0 1 2 3+
Low
Medium
High
34 2 73 1 09 0 4 16
32 181 4 149 8 1 30 34 7 4
0 1 46 7 83 4 66 13 95
52 8 5
Trips by Trip Purpose % Income H BW HBO NHB
Low
Medium
High
38 34 28 1 00
37 34 29 1 00
18 38 44 1 00
Number of Trips by Purpose Income Low HBW HBO NHB
Medium
High
12 85 2 51 16 95 11 81 5 30 1 85 3 1007 614 1738 Problem adapted from: Garber, N.J. and Hoel, L.A., Traffic and Highway Engineering, Revised 2nd Edition, PWS, Pacific Grove, CA. 1999. Page 545
8.5.2.
158 14 1 116
Gravity Model
A study area consists of three zones. The data have been determined as shown in the following tables. Assume a K ijij =1.
Zone
Zone Productions and Attractions 1 2 3
Total
Trip Productions
140
330
280
750
Trip Attractions
300
270
180
750
170
Zone
Travel Time between zones (min) 1 2
1 2 3
5 2 3
2 6 6
3 3 6 5
Travel Time versus Friction Factor Time (min) F 1 2 3 4 5 6 7 8
82 52 50 41 39 26 20 12
Determine the number of trips between each zone using the gravity model formula and the data given above. Note that while the Friction Factors are given in this problem, they will normally need to be derived by the calibration process described in the Theory and Concepts section.
Solution First, determine the friction factor for each origin-destination pair by using the travel times and friction factors given in the problem statement.
Fij as Determined from Travel Time Zone 1 2 1 39 52 2 52 26 3 50 26
3 50 26 39
Once you have the friction factors for each potential trip, you can begin solving the gravity model equation as shown below. Solving for the A×F×K term in a tabular form makes this process easier. Study the equation below and the following table.
T P ∑A AFFKK Where: Tij Pi A j Fij K ij
= number of trips that are produced in zone i and attracted to zone j = total number of trips produced in zone i = number of trips attracted to zone j = a value which is an inverse function of travel time = socio economic adjustment factor for interchange ij
171
A jFijK ij
1
2
3
sum
1 2 3
11700 15600 15000
14040 7020 7020
9000 4680 7020
34740 27300 29040
Once the A×F×K terms for each origin-destination are tabulated, you can insert these values into the gravity model equation and determine the number of trips for each origin-destination. The following table illustrates this. Zone to Zone First Iteration: 1 2 3
zone 1 2 3 A given A
47 189 145 380 300
57 85 68 209 270
P
36 57 68 161 180
140 330 280 750 750
Since the total trip attractions for each zone don’t match the attractions that were given in the problem statement, we need to adjust the attraction factors. Calculate the adjusted attraction factors according to the following formula:
A A A C Where: A jk A jk C jk A j j n k
= adjusted attraction factor for attraction zone (column) j iteration k. = A j when k=1 = actual attraction (column) total for zone j, iteration k = desired attraction total to attraction zone (column) j = attraction zone number = number of zones = iteration number
To produce a mathematically correct result, repeat the trip distribution computation using the modified attraction values. For example, for zone 1:
A 300 380 300 237 Zone
1
2
3
A j1
380
209
161
Given A
300
270
180
A j2
237
349
201
172
A jFijK ij
1
2
3
sum
1 2 3
9237 12316 11842
18138 9069 9069
10062 5232 7848
37437 26617 28759
Zone to Zone Second Iteration: 1 2 3
zone 1 2 3 A given A
35 153 115 303 300
68 112 88 269 270
P
38 65 76 179 180
140 330 280 750 750
Upon finishing the second iteration, the calculated attractions are within 5% of the given attractions. This is an acceptable result and the final summary of the trip distribution is shown below. The resulting trip table is: 1 2 35 68 153 112 115 88
zone 1 2 3
8.5.3.
3 38 65 76
Logit Model
Given the utility expression: UK = AK - 0.05 Ta - 0.04Tw - 0.02 Tr - 0.01 C Where: Ta TW Tr C
is the access time is the waiting time is the riding time is the out of pocket cost
a) Apply the logit model to calculate the division of usage between the automobile mode (AK = - 0.005) and a mass transit mode (AK = - 0.05). Use the data given in the table below for your analysis. Mode
Ta
TW
Tr
C
Auto
5
0
30
100
Transit
10
10
45
50
b) Estimate the patronage shift that would result from doubling the bus out-of-pocket cost.
Solution Part ‘A’ is solved by substituting the given values into the utility function and solving the logit model equation. The calculations and results for part ‘A’ are shown in the table below. 173
Part ‘B’ is essentially identical to part ‘A’ except for the change in the out-of-pocket cost for bus travel. The preliminary calculations for part ‘B’ are shown in the table below as well, while the final calculations are located below the table.
Part A
eU
Mode
Ta
TW
Tr
C
Ak
Uk
Auto
5
0
30
100
- 0.0050
- 1.855
0.1565
0.621
Transit
10
10
45
50
- 0.0500
- 2.350
0.0954
0.379
0.2518
1.000
eU
P
Part B
P
Mode
Ta
TW
Tr
C
Ak
Uk
Auto
5
0
30
100
- 0.0050
- 1.855
0.1565
0.730
Transit
10
10
45
100
- 0.0500
- 2.850
0.0578
0.270
0.2143
1.000
A significant number of bus riders are predicted to shift to the automobile.
38 27 100 29% 38 The increase in automobile use will be:
73 62 100 17.7% 62 8.5.4.
Traffic Assignment
Assign the vehicle trips shown in the following O-D trip table to the network, using the all-ornothing assignment technique. To summarize your results, list all of the links in the network and their corresponding traffic volume after loading. Origin-Destination Trip Table: Trips between Zones
From/to
1
2
3
4
5
1 2 3 4 5
400 200 250 200
100 100 150 100
100 200 300 50
200 100 100 350
150 500 150 400 -
174
Highway Network:
Solution The all-or-nothing technique simply assumes that all of the traffic between a particular origin and destination will take the shortest path (with respect to time). For example, all of the 200 vehicles that travel between nodes 1 and 4 will travel via nodes 1-5-4. The tables shown below indicate the routes that were selected for loading as well as the total traffic volume for each link in the system after all of the links were loaded.
Nodes From
1
2
3
4
5
To
Link Path
Travel Time
Volume
2 3 4 5 1 3 4 5 1 2 4 5 1 2 3 5 1 2 3 4
1-2 1-2, 2-3 1-5, 5-4 1-5 2-1 2-3 2-4 2-4 4-5 3-2 2-1 3-2 3-4 3-4, 4-5 4-5 5-1 4-2 4-3 4-5 5-1 5-4 4-2 5-4, 4-3 5-4
8 11 11 5 8 3 5 11 11 3 7 13 11 5 7 6 5 11 13 6
100 100 200 150 400 200 100 500 200 100 100 150 250 150 300 400 200 100 50 350
175
8.6.
Link
Volume
1-2 2-1 1-5 5-1 2-5 5-2 2-3 3-2 2-4 4-2 3-4 4-3 4-5 5-4
200 600 350 450 0 0 300 300 600 250 250 350 1300 700
Glossary
Centroids: Imaginary points within zones from which all departing trips are assumed to originate and at which all arriving trips are assumed to terminate. Cordon Line: An imaginary line that denotes the boundary of the study area. Friction Factor: A mathematical factor that is used to describe the effort that is required to travel between two points. Link: An element of a transportation network that connects two nodes. A section of roadway or a bus route could be modeled as a link. Modal Choice Analysis: The process used to estimate the number of travelers who will use each of the available transportation modes (train, car, bus) to reach their destination. Nodes: Nodes are points at which links terminate. Links may terminate at destinations or at intersections with other links. Routes: Pathways through a network. Routes are composed of links and nodes. Study Area: The region within which estimates of travel demand are desired. Trip: The journey between one point and another. Trip Assignment Analysis: The process used to estimate the routes (for each mode) that will be used to travel from origin to destination. This process yields the total number of vehicles or passengers that a particular route can expect to service. Trip Distribution Analysis: The process used to determine the number of produced trips from each zone that will be attracted by each of the remaining zones. Trip Generation Analysis: A data collection and analysis process that is used to estimate the number of trips that each zone will produce and attract. 176
