Highway Alignment Principles

BASIC PRINCIPLES OF HIGHWAY ALIGNMENT

Concepts, basic principles a. Horizontal Alignment Fundamentals Horizontal curves Superelevation

b. Vertical Alignment Fundamentals Crest Vertical Curves Sag Vertical Curves Examples

c. Other Stuff - coordination

BASIC PRINCIPLES OF HIGHWAY ALIGNMENT - The alignment of a highway is a three dimensional problem with measurement in

x, y, and z dimensions


DESIGNING STANDARDS Requirements which are involved for highway alignment (generally): MOST IMPORTANT:

LESS IMPORTANT:

- safety, - smoothness and - capacity

comfort predictability esthetic forgiving

FOR DESIGNING WE ARE USING STANDARDS (CZECH – CSN, GERMANY – HBS, POLAND – WPD…)

All of values (curves, superelevation, grades) represent minimum or maximum.


BASIC DESING ELEMENTS •design speed (tool used to determine geometric features of a new road during road design - most important tool) •sight distance (for stopping or overtaking, in curves) •axis of the road (position) •horizontal curves (radius) •transverse slope (cross slope) •drainage gradient (resulting slope) •superelevation (changing the slope between straight and curve) •location of vertical axis (vertical curves, gradients) •lenght of gradient (lenght vs. slope) •coordination of horizontal and vertical alignment •others (depends on used design standard)

DESIGN SPEED Design speed is a selected speed used to determine the various geometric design features of the roadway. USAGE: The selected design speed should be a logical one with respect to the anticipated operating speed, topography, the adjacent land use, and the functional classification of the highway. In selection of design speed, every effort should be made to attain a desired combination of safety, mobility, and efficiency within the constraints of environmental quality and others (aesthetics). Once the design speed is selected, all of the highway features should be related to it to obtain a balanced design. Above-minimum design criteria for specific design elements should be used (on lower speed facilities – urban roads, use of above-minimum design criteria may encourage travel at speeds higher than the design speed).

DESIGN SPEED Some design features, such as curvature, superelevation, and sight distance, are directly related to design speed. Other features, such as widths of lanes and shoulders and clearances to walls and rails, are not directly related to design speed, but they do affect vehicle speeds. Thus, when a change is made in design speed, many elements of the highway design will change accordingly.

DESIGN SPEED – TYPICAL RANGE (DEPENDS ON TYPE OF COMMUNICATION, TERRAIN…)

DESIGN SPEED EXAMPLE – CZECH STANDARD (HIGHWAYS, MOTORWAYS AND ROADS) classification Motorways (highways) Motorwyas (expressways) I.class roads

appropriate technical road category D 33,5/120, 100 a 80; D 27,5/120, 100 a 80 R 33,5/120, 100 a 80; R 27,5/120, 100 a 80; R 25,5/120, 100 a 80

S 24,5/100, 80 a 70; S 20,75/90, 80 a 70 S 11,5/90, 80 a 70 S 9,5/80, 70 a 60*) II.class roads S 9,5/80, 70 a 60 S 7,5/70, 60 a 50 III.class roads S 7,5/70, 60 a 50; S 6,5/60 a 50 S 4,0/40 a 30**) *) can not use for international roads (marked E) **) mostly for reconstruction of III. class roads

S 11,5/70:

S – road, type of communication (D, R – highway, motorway) 11,5 – space among guard rails or marker posts 70 - design speed

DESIGN SPEED EXAMPLE – AASHTO Minimum Design Speeds for Rural Collectors

Rural arterials other than freeways, should be designed for speeds of 60 to 120 km/h [40 to 75 mph] depending on terrain, driver expectancy and, in the case of reconstruction projects, the alignment of the existing facility. - design speeds of 100 to 120 km/h [60 to 75 mph] are normally used in level terrain - design speeds of 80 to 100 km/h [50 to 60 mph] are normally used in rolling terrain, - design speeds of 60 to 80 km/h [40 to 50 mph] are used in mountainous terrain.

DESIGN SPEED EXAMPLE – AASHTO Minimum Design Speeds for Rural Collectors

Rural arterials other than freeways, should be designed for speeds of 60 to 120 km/h [40 to 75 mph] depending on terrain, driver expectancy and, in the case of reconstruction projects, the alignment of the existing facility. - design speeds of 100 to 120 km/h [60 to 75 mph] are normally used in level terrain - design speeds of 80 to 100 km/h [50 to 60 mph] are normally used in rolling terrain, - design speeds of 60 to 80 km/h [40 to 50 mph] are used in mountainous terrain.

DESIGN SPEED EXAMPLE – UK STANDARD Design Speeds for Urban Roads Within the UK the design speed for an urban highway is chosen on the basis of its speed limit. The value chosen will allow a small margin for speeds greater than the posted speed limit. For speed limits of 48, 64, 80 and 96km/hr, design speeds of 60B, 70A, 85A and 100A respectively are employed.

The suffixes A and B indicate the higher and lower categories respectively within each speed band.

DESIGN SPEED Changing the design speed RULE: In the design of a highway segment, it is desirable to select a uniform design speed (for the as longest as possible segment of a highway). However, changes in terrain and other physical controls may dictate a change in design speed on certain sections. If so, the introduction of a lower design speed should not be done abruptly but should be effected over sufficient distance to permit drivers to gradually change speed before reaching the highway section with the lower design speed. Warning: Where it is appropriate to reduce horizontal and vertical alignment features, many drivers may not perceive the lower speed condition ahead, and therefore, it is important that they be warned well in advance - the changing condition should be indicated by such controls as speed-zone and curve-speed signs.

SIGHT DISTANCE Sight distance is defined as the length of carriageway that the driver can see in both the horizontal and vertical planes. Two types of sight distance are detailed: stopping distance and overtaking distance Stopping sight distance - is defined as the minimum sight distance required by the driver in order to be able to stop the car before it hits an object on the highway. It is of primary importance to the safe working of a highway. Overtaking sight distance - is of central importance to the efficient working of a given section of highway. Overtaking sight distance only applies to single carriageways. Full overtaking sight distances are much larger in value than stopping sight distances. Therefore, economic realities dictate that they can only be complied with in relatively flat terrain where alignments, both vertical and horizontal, allow the design of a relatively straight and level highway.

SIGHT DISTANCE

Stopping Sight Distance (SSD) The distance itself can be subdivided into three constituent parts: The perception and reaction distance (l1) – length of highway travelled while driver perceives hazard + length travelled during the period of time taken by the driver to apply the brakes and for the brakes to function The braking distance (l2) – length of highway travelled while the vehicle actually comes to a halt. The safety distance (bv) – distance between stopped vehicle and obstruction (CZ standard) Reaction time: Czech – 1,5 s UK – 2 s US – 2,5 s Notice: - depends on design / standard speed and longitudinal slope - must be ensure on all roadways

SIGHT DISTANCE Stopping Sight Distance (SSD) The perception and reaction distance (l1) calculation:

t r vn (s )

where: vn design speed [km/h], tr reaction time

3,6

The braking distance (l2) calculation: where: vn design speed [km/h], 2 gn normal gravitational acc. 9,81 m/s2, vn ( s ) fv breaking force coefficient (coefficient of 2 2  g n  3,6 f v  0,01  s friction for wet pavement) s longitudinal slope [%].





The safety distance (bv) calculation: Equal to the rounded result to the nearest higher 10 m if vn(s) ≥ 80 km/h and nearest higher 5 m if vn(s) < 80 km/h. This safety distance is calculated in czech standard.

SIGHT DISTANCE Stopping Sight Distance (SSD)

CZECH STANDARD

SIGHT DISTANCE Stopping Sight Distance (SSD) Stopping Sight Distance on Level Roadways

Stopping Sight Distance on Grades

AASHTO - US

SIGHT DISTANCE Stopping Sight Distance (SSD) Stopping sight distances for different design speeds according to UK standard

UK

SIGHT DISTANCE

Overtaking / Passing Sight Distance (OSD / PSD) Full overtaking sight distance is made up of three components: lp, bv2 and l4: lp - distance travelled within the passing manoeuvre (Overtaking Time) – made up from decision lenght l1, overtaking distance (measured separately) l2 and distance travelled within returning to origin lane l3 bv2 - distance between the overtaking and opposing vehicles at the point in time at which the overtaking vehicle returns to its designated lane (Safety Time) l4 - distance travelled by the opposing vehicle within the overtaking time (Closing Time). - have to be ensure only on two lane roads - have to be ensure on as longest as possible part of communication - depends on design/standard speed

SIGHT DISTANCE

Overtaking / Passing Sight Distance (OSD / PSD) Full overtaking sight distance calculation:

DP 

where:

1,112  vn2( s )  32  vn ( s ) v

 bv 2

vn ∆v

design speed [km/h], speed difference between overtaking and overtaken car [km/h]; value is between 15 – 24 km/h.

bv2

equal to the rounded result to the nearest higher 50 m

SIGHT DISTANCE

Overtaking / Passing Sight Distance (OSD / PSD) CZECH STANDARD

UK STANDARD

There is no full overtaking sight distance (OSD) for a highway with a design speed of 100 (CZ) /120 (UK) km/hr since this design speed is not suitable for a single carriageway road (undivided roads). single carriageway road

double carriageway road

SIGHT DISTANCE

Overtaking / Passing Sight Distance (OSD / PSD) CZECH STANDARD Passing Sight Distance for Design of Two-Lane Highways

AASHTO - US

SIGHT DISTANCE Comparison of Design Values for Passing Sight Distance and Stopping Sight Distance

AXIS OF THE ROAD, HORIZONTAL CURVES TWO BASIC ELEMENTS: TANGENTS AND CURVES

Tangents (straights)

Curves

AXIS OF THE ROAD, HORIZONTAL CURVES

HORIZONTAL TANGENT POLYGON CONSISTS OF: - STRAIGHTS - CURVES DUMB DESIGN

Two basic principles should be respected: a)

Lengths of sides of the tangent polygon should be balanced (no short sides followed by long sides)

b)

Central angles should be in proportion to the lengths of the polygon sides


STRAIGHTS Straight - the shortest connection of two points. BUT NOT THE BEST SOLUTION EVERY TIME WHY: - Driving on straight roads is very boring - the driver doesn’t pay so much attention to the situation on a road, increases speed of a vehicle and his driving can be dangerous. - Drivers are dazzled by cars going in the opposite direction at night. - In the spring and autumn mostly at early and late time of the day drivers could be sun glared - There is not many straights in the nature

IF IT IS NECESSARY : MAXIMAL LENGHT OF STRAIGHT SHOULD BE BETWEEN 3 – 5 km (but the lenght is not limited in Czech standards)


CURVES A horizontal curve - is an arc connecting two straight parts (tangents) of the highway.

- The highway engineer must design a horizontal alignment to accommodate (suit to) a variety of vehicles cornering capabilities that range from mini - cars (via Mr.Bean´s minicooper) to long trucks

TYPES OF CURVES: a) Plain circular arcs b) Circular arcs with transition curves c) Transition curves – clothoids d) Compound curves

AXIS OF THE ROAD, HORIZONTAL CURVES Straight

Curve

Tangent to Circular Curve Tangent to Spiral Curve to Circular Curve


CURVES DERIVING THE MINIMUM RADIUS The values for horizontal curvature are derived from the design speed, superelevation rate, and side friction factors. Figure illustrates: - the forces acting on a vehicle of weight

G

as it is

driven in arc of radius R. - the angle of incline of the road (superelevation) is termed as α. -

p denotes the side frictional force between the

vehicle and the highway (p=tg α) - Fo is the centrifugal force acting horizontally on the vehicle and equals:

G v2 Fo = . , g R

where G/g is the mass of the vehicle

As all the forces should be equilibrium, they can be resolved along the angle of inclination of the road: (Centrifugal force resolved parallel to highway) – denoted as Fb= (Weight of vehicle resolved parallel to highway) + (Side friction factor) – as Tb


CURVES DERIVING THE MINIMUM RADIUS As all the forces in should be in equilibrium, they can be resolved along the angle of inclination of the road: (Centrifugal force resolved parallel to highway) – denoted as Fb  (Weight of vehicle resolved parallel to highway) + (Side friction factor) – as Tb

Fb  Tb ,

Fo . cos  G . sin  f b G . cos  Fo . sin  , where:

- fb is side friction factor than:

G v2 G v2 . . cos  G . sin  f b ( G . cos  + . . sin ) . g R g R

and after resolving:

v2 1 - f b . p   g  f b  p . R


CURVES DERIVING THE MINIMUM RADIUS: The basic equation is: Rmin

Where: Rmin p f V

-

v2  , g  f b  p

minimum radius of curve (m) superelevation rate side friction factor vehicle speed (m/s)

or: Rmin Where: Rmin p V

Vn2  0,3 , p

- minimum radius of curve (m) - superelevation rate (in %) - vehicle speed (km/h)

Notice: f is out – it is small value


CURVES - TYPES

PLAIN CIRCULAR CURVES A simple curve has a constant circular radius which achieves the desired deflection without using an entering or exiting transition. This is the most frequently used curve because of their simplicity for design, layout, and construction as shown. Plain circular arc in highway design can be used only if the offset of the circle in the clothoid R  0,25. This condition means that the minimal radius of the plain circle arc must be R  800 2 m or at least R  0,375 V n

NOTICE: For small radii and low design speed (prevailing design conditions for local communications) you can use only circular curves without restrictions above.


CURVES - TYPES TRANSITION CURVES

These curve types are mainly used to connect curved and straight sections of highway. (they can also be used to ease the change between two circular curves where the difference in radius is large). The radius of curvature of a transition curve gradually decreases from infinity at the intersection of the tangent and the transition curve to the designated radius R at the intersection of the transition curve with the circular curve – so the

clothoid is a curve which radius of the osculating circular decreases with length of a curve

USING ???

– WHY IT IS



WHY IT IS USING??? It is difficult for drivers to travel imediately from a tangent section (straight) to a circular arc, because of: CURVATORY OF TANGENT SECTION IS 0, while CURVATORY OF CIRCULAR ARC IS CONSTANT

Than the connecting between tangent and arc is not continuous and could disturb drivers Use of transition curves provides for a number of benefits: -

Provides an easy path for drivers to follow: centrifugal and centripetal forces are increased gradually

-

Provides a desirable arrangement for superelevation runoff

-

Provides a desirable arrangement for pavement widening on curves

-

Enhances highway appearance (travel looks better)



Figure illustrates the situation where transition curves are introduced between the tangents and a circular curve of radius R. Here, the circular curve must be shifted inwards from its initial position by the value S (R) so that the curves can meet tangentially. This is the same as having a circular curve of radius (R + S) joining the tangents replaced by a circular curve (radius R) and two transition curves. The tangent points are, however, not the same. In the case of the circular curve of radius (R + S), the tangent occurs at B, while for the circular/transition curves, it occurs at T .



WHY IT IS USING???

NO TRANSITION

WITH TRANSITION

esthetics


CURVES

OFFTRACKING, WIDENING IN CURVE Offtracking is the characteristic, common to all vehicles, typically to the larger design vehicles, in which the rear wheels do not follow precisely the same path as the front wheels when the vehicle negotiates a horizontal curve or makes a turn. In that cases it is necessary to widen the pavement on sharp curves to accommodate off-tracking of larger vehicles. Widening of the carriageway is done only if the radius of the circular is lower than 250 m.


CURVES

OFFTRACKING, WIDENING IN CURVE The widened portion of the pavement is normally placed on both sides of the curve (according to czech standard).

Where curves are introduced with clothoid transitions, the widening occurs over the length of the clothoid. On alignments without spirals, the widening is developed over the same distance that the superelevation transition occurs. The centerline pavement marking and the center joint (if applicable) should be placed equidistant from the pavement edges.

TRANSVERSE SLOPE (CROSS SLOPE)

1. Gutter; 2. Shoulder; 3. Sub-base; 4. Base course; 5. Asphalt

Cross slope or camber is a geometric feature of pavement surfaces: it is the transverse slope with respect to the horizon.

It is a very important safety factor: Cross slope is designed to provide a drainage gradient so that water will run off the surface to a drainage system such as a street gutter or ditch. Inadequate cross slope will contribute to aquaplaning!!!

TRANSVERSE SLOPE (CROSS SLOPE) On straight sections of normal two-lane roads, the pavement cross section is usually highest in the center and drains to both sides.

In horizontal curves, the cross slope is banked into superelevation to reduce steering effort and lateral force required to go around the curve.

TRANSVERSE SLOPE (CROSS SLOPE) VALUES According to Czech standards: Basic cross slope in straight is 2,5 % (2% extraordinary) for high-type pavements. For low-type pavements in straight 3 % (and more for i.g. gravel).

According to AASHTO: Normally, cross slopes range from 1,5 to 2 % for high-type pavements. A cross slope of 3 to 7 % is desirable for low-type pavements. High-type pavements are those that retain smooth riding qualities and good nonskid properties in all weather under heavy traffic volumes and loadings with little maintenance required. Low-type pavements are those with treated earth surfaces and those with loose aggregate surfaces.

DREINAGE GRADIENT FLOW FIRECTION

Drainage gradient (M) is a term in road design, defined as the combined slope due to road surface cross slope (P) and longitudinal slope (S). (drainage gradient – resulting slope in close czech translation)

Urban roads Rural roads

Most road design manuals require drainage gradient to exceed 0,5% (minimal value), in order to drain water and prevent excessive skid accidents.

DREINAGE GRADIENT Effect of insufficient gradient Due to the normal cross slope and the interaction with grade, road sections with insufficient drainage gradient are few and short (still, they account for an unacceptable number of skid accidents). These hot spots are found at the entrances and exits of banked curves, where the cross slope changes direction in order to create superelevation. As the outside edge of the curve is raised (or superelevated) to create the bank, it passes through a point where the cross slope is absolutely flat. If there is not enough longitudinal grade, water will collect at these spots.

Problem segments may be found at the summits (or sags) of vertical curves, where the longitudinal slope is close to or at zero value.

DREINAGE GRADIENT Minimizing insufficient drainage gradient Roads should be designed so that sections where the cross slope change direction (and sign), are located where the road is going uphill or downhill. Otherwise the pavement will get an area with too little drainage gradient (< 0,5%), resulting in unacceptable skid accident risk. When designing road curves in a flat landscape, it may be necessary to design long wave undulations on purpose. These "synthetic" longitudinal gradients can then be used to reach a sufficient drainage gradient, in sections where the cross slope is close to zero. Another option to minimize crash risk due to low drainage gradient at entrance or exit of banked outercurves, is to move the superelevation further from the curve and out to a straight road section. This results in a banked straight lane. Other option is to – within the superelevation transition section – increase the cross slope "tilt rate" within the zone where the cross slope is between - 0,5 % to + 0,5%.

SUPERELEVATION superelevation = roadway banking It is normal practice for horizontal curves to be superelevated. This allows a component of the vehicle weight to provide some of the centripetal force that is needed for the vehicle to move in a circular path. All the forces should be in equilibrium : (Centrifugal force resolved parallel to highway) – denoted as Fb  (Weight of vehicle resolved parallel to highway) + (Side friction factor) – as Tb

Fb  Tb ,

Fo . cos  G . sin  f b G . cos  Fo . sin  , than:

Rmin Where: Rmin p f V

v2 ,  g  f b  p -

minimum radius of curve (m) superelevation rate side friction factor vehicle speed (m/s)

SUPERELEVATION

Selection of p (superelavation rate) and fb (side friction factor) Practical limits affecting superelevation (p): - Climate - Constructability - Adjacent land use Side friction factor (fb) variations (changes): - Vehicle speed - Pavement texture - Tire condition

SUPERELEVATION

Superelevation rates p Czech stadndard recommends the use of superelevation rates between 2,5 and 7 . Maximum rates across other world standards varies from region to region. Values of superelevation rates are affected by a climate, terrain, development density or frequency of slow moving vehicles.

EXAMPLE: USA restrictions (COMPARE WITH CZECH STANDARDS)

SUPERELEVATION

Side friction factor fb Design values of the side – friction factor (also coefficient of side friction) vary with design speed. Design values represent wet pavements and tires in reasonable but not top condition. Values also represent frictional forces that can be comfortably achieved. They do not represent the maximum side friction that is achieved the instant before skidding.

EXAMPLE: AUSTRALIA

SUPERELEVATION

Side friction factor fb

EXAMPLE: AASHTO

SUPERELEVATION Superelevation rates – using minimal p It is normal practice to superelevate all curves to a value that is at least equal to the normal crossfall on straights (this is normally 2,5% in order to ensure adequate surface drainage). However, there are situations where the application of superelevation can cause pavement drainage problems. In some situations when the grade is nearly flat, water will not run off the road properly at places where the crossfall is also nearly flat (0%). Problems with drainage of the pavement surface may be overcome by modifying the combination of the grading, the superelevation and the application of the superelevation:

If the horizontal curve radius is large enough, there may be scope to leave the curve unsuperelevated (called adverse superelevation). design/ standard speed in km/h

Minimal Radiii with basic transverse slope 2,5% (2%)

30

40

50

60

70

80

90

100

110

120

130

250 450 700 950 1300 1700 2200 2700 3200 3800 4500

SUPERELEVATION Minimum Length of Superelevation on Horizontal Curves The superelevation ramp is mainly designed in the length of the clothoid

p2 - p1 . a´ L s

Or the lenght is given by: Where:

s – slope of superelvation ramp a´ - distance between edge of pavement and the axis of superelevation in m p1 – crossfall of pavement at the beginning of superelevation p2 – crossfall of pavement at the end of superelevation

tab. Max. and min. slope of a superelevation ramp (s) max s (%)

min s (%)

design speed in km/h

a´  4,25 m

a´  4,25 m

 50

1,2

1,4

60 až 70

1,0

1,2

80 až 90

0,7

0,85

100 až 120

0,6

0,7

a´  4,25

a´  4,25 m

0,1 a´

0,07 a´ ( max s)

s

SUPERELEVATION Achieving superelevation Superelevation development length could be defined as the length required to rotate the pavement from the point of normal crossfall to the point where the full superelevation for the curve is achieved. This superelevation development length has two components:

1. Tangent

run - out

This is the length from the point of normal crossfall to the point of zero crossfall.

2. Superelevation

runoff length

This is the length from the point where the pavement has been rotated to zero crossfall to the point where the full curve superelevation has been achieved. Supperelevation runoff

Run-out Tangent

Normal crown

e e edg Insid

4%

8% Runoff

0% e edg e sid out

 Relative gradient

SUPERELEVATION Achieving superelevation - methods 1) Rotate pavement about centerline (b, d, g, h) 2) Rotate about inner edge of pavement (the outer edge of the inner horizontal marking) (a, c, h) 3) Rotate about outside edge of pavement (for dividing roadways – e, g, f)

SUPERELEVATION Achieving superelevation - methods Rotate pavement about centerline Cross section (-1-) is the normal crown section where the transitioning begins (with basic transversal slope 2,5 %) Cross section (-2-) is reached by rotating half the pavement until it is level. Cross section (-3-) is attained by continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section, at a cross slope equal to the normal crown slope. Cross section (-4-) is achieved by further rotation of the planar section, the entire pavement section, to attain the full superelevation at a cross slope.

h0 =

s . p0 200 Lz =

h=

2 . h0 . L h + h0 2

s.p 100

SUPERELEVATION Achieving superelevation - methods Rotate pavement inner edge of the pavement Cross section (-1-) is the normal crown section where the transitioning begins (with basic transversal slope 2,5 %) Cross section (-2-) is reached by rotating half the pavement until it is level. Cross section (-3-) is achievedeby continuing to rotate the same half of pavement until a plane section is attained across the entire pavement section, at a cross slope equal to the normal crown slope. Cross section (-4-) is achieved by further rotation (but by the inner edge) of the pavement to the full value of superelevation.

h0 =

s . p0 200

h=

s.p 100

TANGENT RUN – OUT IS THE SAME FOR BOTH METHODS

SUPERELEVATION Some important factors have to be consider when designing horizontal alignment: -

-

Horizontal alignment should be as smooth and as direct as possible while responsive to the topography. Flatter curvature with shorter tangents is generally preferable to sharp curves connected by long tangents. Angle points should be avoided. Maximum length of straights is not limited, but recommended length of straights is between 3 – 5 km. Also recommended is to have no straights if it is possible. Broken back curvature (a short tangent between two curves in same direction) should be avoided because drivers do not expect to encounter this arrangement on typical highway geometry. If compound circular curves are required in an effort to fit the highway to the terrain or to other constraints, large differences in radius should be avoided. The radius of the largest curve should not be more that 1.5 times the radius of the smaller curve (except for highway ramps). On ramps, the ratio of the larger curve to the smaller curve should not exceed 2:1.

SUPERELEVATION Some important factors have to be consider when designing horizontal alignment: -

-

-

Horizontal curves should be avoided on bridges whenever possible. These cause design, construction, and operational problems. Where a curve is necessary on a bridge, a simple curve should be used on the bridge and any curvature or superelevation transitions placed on the approaching roadway. Plain circular arc can be used if the displacement (shift) of the circular in the clothoid R0,25m. The minimal radius of the plain circular arc must be R  800 m or at least R  0,375 m. Broken back curves should be avoided because they are unsightly and drivers do not expect succeeding curves to be in the same direction. If it is necessary there must be insert straight of minimal length above 2 vn (design speed). If possible, the minimum distance between reverse plain circular arc should be at least 2 x vn (design speed). When it isn't possible to obtain the desired distance between reverse curves, than the transition curves may be placed there. Transition curves should be design as clothoids with parameter (A): Ro  A  Ro 3

notice: using of other curves is also allowed

VERTICAL ALIGNMENT VERTICAL TANGENT POLYGON CONSISTS OF: - STRAIGHTS - CURVES

The design of the vertical alignment is started after completing of the horizontal alignment: The design of vertical alignment consists of: 1.Drawing of terrain into the longitudinal section 2.Design of the vertical alignment by using vertical polygon (according to the same principles as at the horizontal alignment – see „dumb design“) 3.Rounding polygon sides by vertical parabolic curves

VERTICAL ALIGNMENT VERTICAL TANGENT POLYGON

hi s i   100 li Vertical alignment terminology: si Vi li Hi hi

– slope in percent – point of intersection of the two adjacent grade lines V1 – SAG, V2 - SUMMIT – length of segment with same grade (projection onto horizontal surface – corresponds to plan distance) – elevation of each point of intersection and start and end points – elevation difference betwee start and end point of the segment with same grade

VERTICAL ALIGNMENT VERTICAL CURVES A vertical curve - is an arc which provides a gradual change between two adjacent grade lines

CURVE IS PARABOLIC ONLY !!! R  s1  -  s2  T 200

yn

x1 = R 

s1 100

x2 = R 

s2 100

t2 = 2R

x2 yx = 2R

VERTICAL ALIGNMENT Some important factors have to be consider when designing vertical alignment: -

Longitudinal slope is mainly leading by type of terrain and design speed. Minimum value of longitudinal slope is about 0,5 % (exceptionally 0,3 %) Lengths of sides of the tangent polygon should be balanced. The lengths should correspond to the lengths of vertical curves tangents. Avoid vertical straight between two curves in the same direction. Polygon sides breaks must be round by vertical parabolic (second degree) curves. Parabolic curves have to agree with length of sight distance (minimal value of vertical curve radius is derived from minimal sight distance).

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT

Balance curvature and grades -

Use of steep grades to achieve long tangent and flat curves, or excessive curvature to achieve flat grades, are both poor designs.


Balance curvature and grades -

Vertical curvature superimposed (like cascades) on horizontal curvature generally results in a more pleasing facility. Successive changes in profile not in combination with horizontal curvature may result in a series of dips not visible to the driver.

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Curvature in the horizontal plane should be accompanied by comparable length of curvature in the vertical plane.

(horizontal curvature should lead vertical curvature a bit)

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Curvature in the horizontal plane should be accompanied by comparable length of curvature in the vertical plane.

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT No vertical curve overlapping beginning or end of the horizontal curve -

If a vertical crest curve overlaps either the beginning or the end of a horizontal curve, drivers have little time to react to the horizontal curve once it comes into view. This condition can be unsafe, especially at night, if the driver does not recognize the beginning or ending of the horizontal curve. Safety is improved if the horizontal curve leads the vertical curve, that is, the horizontal curve is made longer than the vertical curve in both directions.

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Unexpected combinations of curves and tangents in both the horizontal and vertical planes should be avoided -

i.e., "broken back" curves in vertical or horizontal alignment

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Horizontal curvature should lead vertical curvature -

i.e., the horizontal curve should be longer than the vertical curve and the ZZ/KZ and TK/KT (or TP – with transitions) should not be at the same point.

Horizontal alignment

Vertical alignment

DESIGN PRINCIPLES FOR COORDINATION VERTICAL AND HORIZONTAL ALIGNMENT rounding by the concave parabolic curve is covered with horizontal arc

rounding starts ahead the horizontal arc

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Ideally the vertices of horizontal curves (KK) and vertical curves (VZ) should coincide (same position) or be within 1/4 phase of each other.

Horizontal alignment

Vertical alignment

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT The alignment designs should enhance attractive scenic views of the natural and manmade environment, such as rivers, rock formations, parks, and outstanding man-made structures.

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Fitting the Road to the Terrain

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Fitting the Road to the Terrain


the driver can see before the peak of the parabolic curve to which side the road turns. clothoid is not used

with clothoid

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT In the next two pictures it can be seen the influence of the radius of concave curve in the horizontal straight on the optical deformation. If the radius is small, the road seems to be like broken.

COORDINATION BETWEEN HORIZONTAL AND VERTICAL ALIGNMENT Similarly as in the horizontal alignment the sequence of vertical curves with a short interstraight causes deformation - it can be seen on old roads where the interstraight is designed for a bridge. Sequence of convex and concave curves with small radius in a horizontal straight is also not a good solution – “lost road”.

Direct connection of convex and concave curves (inflex point) also does not look well.


small radius of vertical curves This sequence is sometimes called “flying road” for its big visual deformation.

“Twice lost road”






OTHER MISTAKES

EFFECTS OF ROAD CATEGORY, ALIGNMENT AND GRADIENT ON CAPACITY

EFFECTS OF ROAD CATEGORY NUMBER OF LANES The primary parameter for determining the capacity of a roadway is the number of travel lanes.

COMPARE THE CAPACITY

EFFECTS OF ROAD CATEGORY LANE WIDTH The ideal width for a roadway is about 3,5 m (3,25 – 3,75 m). Narrower lane width = decreasing capacity Wider lane width = increasing capacity Narrower lanes are acceptable only on low – volume and low – speeds. Below a lane width of about 2,5 m capacity deteriorates rapidly.

EFFECTS OF ROAD CATEGORY SHOULDER WIDTH Shoulders

Provides

– portion of the roadway contiguous with the traveled way that accommodates stopped vehicles, emergency use and lateral support of sub – base, base and surface courses. – a refuge for temporarily stopped vehicles, increasing sight distance on horizontal curves, improving capacity and operations, space for snow removal and storage, more space for signs or guardrails, improved drainage on a traveled way

Normal shoulders width is 0,5 m (unpaved) – 1,5 m (paved) - see lecture 1 Shoulders on the roadway= more comfortable operations (sight distances) = increasing capacity

EFFECTS OF ALIGNMENT CURVES A tightly and close curving alignment in rural areas can cause a reduction in free-flow speeds* and decreasing of capacity.

LOWER SPEED = LOWER CAPACITY

HIGHER SPEED = HIGHER CAPACITY

*Free-flow speed: (1) The theoretical speed of traffic, when density is zero, that is, when no vehicles are present; (2) the average speed of vehicles over an urban street segment without signalized intersections, under conditions of low volume; (3) the average speed of passenger cars over a basic freeway or multilane highway segment under conditions of low volume.

EFFECTS OF ALIGNMENT CURVES Tight and close curves causes poor sight lines and forward visibility. This delimits overtaking of slow moving vehicles and reduces overall capacity.

NO OVERTAKING OF SLOW MOVING VEHICLES = LOWER CAPACITY

OVERTAKING IS ALLOWED = HIGHER CAPACITY

EFFECTS OF GRADIENT SLOPES (GRADIENTS) Heavy vehicle speed heavily deteriorates on a combination of gradient and length of gradient.

SPEED

EXAMPLE: Original speed – 80 kph Length of gradient – 1500 m Gradient – 6 

35 kph LENGTH OF GRADIENT

EFFECTS OF GRADIENT SLOPES (GRADIENTS) Additional climbing lanes (for heavy trucks – low speed vehicles) are designed on long steep gradients

Normal traffic lanes

Highway Alignment Principles

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