Weight Estimation - Conceptual Design of Airplanes

Content

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Guidance

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Reasoning  Aircraft weight, and its accurate prediction, is critical as it affects all aspects of performance, manufacturing costs, selling price and all other items.  Designer must keep weight to a minimum as far as practically possible.  Preliminary estimates possible for take-off weight, empty weight and fuel weight using basic requirement, specification (assumed mission profile) and initial configuration selection.

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Glossary AFM: Aircraft flight manual MTOW: Maximum takeoff weight MEW: Manufacturer’s empty weight MZFW: Maximum zero-fuel weight MLW: Maximum landing weight BOW: Basic operating weight FAR: Federal Aviation Regulation L/D: Lift-to-drag ratio WTO: Weight at takeoff WPL: Payload weight

Prof. Bento S. de Mattos

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Some Tasks in the Conceptual Design Sensitivity study (Wto to Wpl, We, R, S.F.C(Cj), and L/D)

Preliminary drag and weight estimation (CD0, We,Wto,Wf)

Estimating T/W, W/S

Cost prediction

Configuration selection

Structural layout

Landing gear design

Design of stabilizers and control surfaces Design of cockpit and the fuselage

Estimation of cg variation and airplane inertias Prof. Bento S. de Mattos

Design of the wing

Selection Integration of the Propulsion system 6

This course material is concerned with Preliminary drag and weight estimation (CD0, We,Wto,Wf)

Sensitivity study (Wto to Wpl, We, R, S.F.C(Cj), and L/D)

Estimating T/W, W/S Cost prediction

Configuration selection

Structural layout

Landing gear design

Design of stabilizers and control surfaces Design of cockpit and the fuselage

Estimation of cg variation and airplane inertias Prof. Bento S. de Mattos

Design of the wing

Selection Integration of the Propulsion system 7

Manufacturer’s Empty Weight: Weight of the structure, powerplant, furnishings, systems and other items of equipment that are an integral part of a particular aircraft configuration. It is essentially a “dry” weight, including only those fluids contained in closed systems. Includes: - airframe, systems - closed system fluids - seats, seat belts - seller-furnished emergency equipment - fire extinguishers Does not include: - galley structure, ovens, inserts, etc. - escape slides - life rafts, life vests - portable oxygen bottles - fluids like engine oil, trapped fuel, potable water

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Standard Items: Equipment and system fluids which are not considered an integral part of a particular aircraft configuration, are not included in the MEW, but which do not normally vary for aircraft of the same type. Standard items may include, but are not limited to: - unusable fuel, oil, and engine injection fluids - unusable drinking and washing water - first aid kits, flashlights, megaphone, etc - emergency oxygen equipment - galley/bar structure, inserts, ovens, etc. - electronic equipment required by the operator


Operational Items: Personnel, equipment and supplies necessary for a particular operation but not included in the Basic Empty Weight. These items may vary for a particular aircraft and may include, but are not limited to: - flight and cabin crew plus their baggage - manuals and navigation equipment - removable service equipment: cabin (blankets, pillows, literature, etc.) galley (food, beverages, etc.) - usable drinking and washing water - toilet fluid and chemical - life rafts, life vests, emergency transmitters - cargo containers, pallets, and/or cargo tiedown equipment if used.

Weight Definitions • disposable load = payload + useable fuel (+any necessary ballast) Where Payload = the revenue earning load

Maximum ramp weight: MTOW + start, taxi, and run-up fuel Maximum ramp weight is that approved for ground maneuver Maximum landing weight: maximum weight approved for touchdown

Maximum zero fuel weight: Maximum weight allowed before usable fuel must be loaded in defined sections of the aircraft. Any weight added above the MZFW must be only due to fuel. 11

• APS weight (aircraft prepared for service), which is the same as the basic empty weight, i.e. fully equipped operational, without crew, usable fuel or payload (the load that generates revenue, income). • AUW, Wo The all-up (gross) weight is the maximum weight at which flight requirements must be met. Maximum to take-off weight

= gross (all-up) weight = MTOW = operating empty weight + disposable load

in which operating empty weight and disposable load are built up as follow Basic empty weight = Manufacture’s weight + standard items (From an equipment standpoint, the airplane is ready for operation.)

Operating empty weight = basic empty weight + operational items

The maximum allowable weights that can legally be used by a given airline are listed in the AFM, and Weight and Balance Manual; these are called the airplane’s Certified Weight Limits: • Maximum weights chosen by the airline • Some airlines refer to these as the “purchased weights” • Certified weight limits are often below the structural limits • Airlines may buy a certified weight below structural capability because many of the airport operating fees are based on the airplane's AFM maximum allowable weight value. Typically the purchase price is a function of the certified weight bought


The maximum allowable Operational Takeoff Weight may be limited to a weight which is lower than the Certified Maximum Weight by the most restrictive of the following requirements: • Airplane performance requirements for a given altitude and temperature: - Takeoff field length available - Tire speed and brake energy limits - Minimum climb requirements - Obstacle clearance requirements • Noise requirements • Tire pressure limits • Runway loading requirements • Center of gravity limitations Prof. Bento S. de Mattos

Weight Definitions  Take-off weight (WTO) – (Roskam method) WTO = WOE + WF + WPL

(1)

where: WOE (or WOWE ) = operating weight empty WF = fuel weight WPL = payload weight  Note that other methods (e.g. Raymer) use slightly different terminology but same principles.

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Weight Definitions  Operating weight empty may be further broken down into: WOE = WE + Wtfo + Wcrew

(2)

where: WE

= empty weight

Wtfo = trapped (unusable) fuel weight Wcrew = crew weight 16 Prof. Bento S. de Mattos

Weight Definitions • Empty weight sometimes further broken down into: WE = WME + WFEQ

(3)

where:

WME = manufacturer’s empty weight WFEQ = fixed equipment weight (includes avionics, radar, airconditioning, APU, etc.)

17 Prof. Bento S. de Mattos

Weight Figures for Transport Aircraft Aircraft

MTOW (tones)

MLW(tones)

Basic Operating Weight (tones)

BOW/MTOW

Jet Airliners/Transports Airbus A319

75.5

62.5

40.6

0.537

Airbus A380

560

386

276.8

0.494

ERJ-145LR

22

19.3

12.114

0.550

Embraer 170ER

37.2

32.8

20.94

0.563

Embraer 190LR

50.3

43

27.72

0.551

Boeing 747-400ER

412.769

295.742

180.985

0.438

Boeing 767-400ER

204.117

158.758

103.1

0.505

Boeing 777-200 (HGW, GE Engines)

286.9

206.35

137.05

0.478

Boeing 777-200LR

347.452

223.168

145.15

0.418

Boeing 777-300ER

351.534

251.3

167.83

0.477

Boeing 727-200ADV

95.1

73.1

45.72

0.480

Boeing 757-200

115.65

95.25

62.10

0.537

Boeing 737-900

79.15

66.36

42.56

0.536

Boeing 787-8

219.539

167.829

114.532

0.522

Business Jets Cessna Citation X

16.14

14.425

9.73

0.603

Dassault Falcon 50 EX

18.498

16.2

9.888

0.535

Embraer Legacy 600

22.50

18.5

13.675

0.600

Cessna Encore

7.634

6.895

4.763

0.624

Gulfstream G350

32.160

29.937

19.368

0.602

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Weight Figures for Transport Aircraft (cont.)

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Weight Figures for Fighter Aircraft

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Overview  All textbooks use similar methods whereby comparisons made with existing aircraft.  In Roskam (Vol.1, p.19-30), aircraft classified into one of 12 types and empirical relationship found for log WE against log WTO.  Categories are: – (1) homebuilt props, (2) single-engine props, (3) twinengine props, (4) agricultural, (5) business jets, (6) regional turboprops, (7) transport jets, (8) military trainers, (9) fighters, (10) military patrol, bombers & transports, (11) flying boats, (12) supersonic cruise. 21

Overview (Cont.)

 Most aircraft of reasonably conventional design can be assumed to fit into one of the 12 categories.  New correlations may be made for new categories (e.g. UAVs).  Account may also be made for effects of modern technology (e.g. new materials) – method presented in Roskam Vol.1, p.18.  Raymer method uses Table 3.1 & Fig 3.1 (p.13). 22 Prof. Bento S. de Mattos

Roskam’s Empty Weight Estimation Method

Category 7

Category 8

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Raymer’s Empty Weight Fraction Estimation Equation


This workflow addresses a higher fidelity approach for weight estimation!

 Process begins with guess of take-off weight.  Payload weight determined from specification.  Fuel required to complete specified mission then calculated as fraction of guessed take-off weight.  Tentative value of empty weight then found using: WE(tent) = WTO(guess) – WPL - Wcrew - WF - Wtfo (4)


 Values of WTO and WE compared with appropriate correlation graph.  Improved guesses then made and process iterated until convergence.  Note that convergence will not occur if specification is too demanding.


Initial Guess of Take-off Weight

 Good starting point is to use existing aircraft with similar role and payload-range capability.  An accurate initial guess will accelerate the iteration process. 28

Payload Weight & Crew  WPL is generally given in the specification and will be made up of:  passengers & baggage; cargo; military loads (e.g. ammunition, bombs, missiles, external stores, etc.).

 Typical values given in Roskam Vol.1 p8.  Specific values for some items (e.g. weapons) may be found elsewhere.


Mission Fuel Weight • This is the sum of the fuel used and the reserve fuel. WF = WF(used) + WF(res) (5) • Calculated by ‘fuel fraction’ method. – compares aircraft weights at start and end of particular mission phases. – difference is fuel used during that phase (assuming no payload drop). – overall fraction is product of individual phase fractions. 30 Prof. Bento S. de Mattos

civil jet transport

• •

1. 2. 3. 4. 5. 6. 7. 8.

Start & warm-up Taxi Take off Climb Cruise Loiter Descend Taxi

Fuel fractions for fuel-intensive phases (e.g. 4, 5 & 6 above) calculated analytically. Non fuel-intensive fuel fractions based on experience and obtained from Roskam (Vol I, p12), Raymer, etc. 31


Reference: Roskam Vol. I - Table 2.1 Prof. Bento S. de Mattos

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Using Roskam’s method/data for a transport jet (Vol.I, Table 2.1): W1/WTO = 0.99 W2/W1 = 0.99 W3/W2 = 0.995

For piston-prop a/c: For jet a/c: where:

 1 Ecl  375   Vcl

1 Ecl   c  j

p     cp

 L  W3     ln   cl  D cl  W4 

 L  W3     ln   cl  D cl  W4 

(6a)

(6b)

Ecl = climb time (hrs), L/D = lift/drag ratio, cj is sfc for jet a/c (lb/hr/lb), cp is sfc for prop a/c (lb/hr/hp), Vcl = climb speed (mph), p = prop efficiency, W3 & W4 = a/c weight at start and end of climb phase. 34 Prof. Bento S. de Mattos

•

Initial estimates of L/D, cj or cp, p and Vcl made from Roskam or Raymer databases for appropriate a/c category.

•

Alternatively, use approximations, e.g. from Roskam Vol.1, Table 2.1 (W4/W3=0.98 for jet transport, 0.96 to 0.9 for fighters). 35


Phase 5 (cruise) • Weight fraction calculated using Breguet range equations.  1 p   L   W4  • For prop a/c: Rcr  375  V   c   D  ln  W  (7a) 

V Rcr   c  j

cl



p

cr

 L  W4  ln      D   cl  W5  cr

•

For jet a/c:

•

These give the range in miles.

cl



5



(7b)


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For jet a/c, range maximised by flying at 1.32 x minimum drag speed and minimising sfc. – –

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Wing operates at about 86.7% of maximum L/D value. Cruise-climbing can also extend range.

For prop a/c, range maximised by flying at minimum drag speed and sfc. –

Wing operates at maximum L/D value.


Initial Estimates of Lift/Drag Ratio (L/D) •

Using Roskam (Table 2.2 – selected values): cruise

loiter

8 - 10

10 - 12

Business jets

10 – 12

12 - 14

Regional turboprops

11 – 13

14 – 16

Transport jets

13 – 15

14 - 18

Military trainers

8 – 10

10 - 14

Fighters

4–7

6–9

13 – 15

14 – 18

4-6

7–9

Homebuilt & single-engine

Military patrol, bombers & transports Supersonic cruise


In order to obtain a better estimation for the L/D ratio we shall consider the Breguet equations for range (R) and endurance (E): Jet Airplane V R c  j

  L  W  i ln     W  f   D  

Airplane fitted with propeller  1 R c  j

(7a)

(7b)  1 E  c  j

  L  W     ln  i W  f   D  

(6b)

  L  W     ln  i W  f   D  

V E  c  j

  L  W     ln  i W  f   D  

(6a)

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Considering that he TSFC does not vary with speed and that the drag polar can be written as

CD  CD 0  kC

2 L

(8a)with

1 k  Ae

(8b)

After inserting into the preceding Breguet equations the above drag polar, we obtain the L/D ratio for maximum range and maximum endurance for a jet airplane deriving the resulting equations and equaling them to zero: 1 3  A  e L    CD 0  D max range 4

(9a)

1   Ae L    CD 0  D max endurance 2

(9b)

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Using

CL2 L CL CD  CD 0      Ae D CD

CL CL2 CD 0   Ae

with Differentiating with respect to CL and setting to zero Diff  CL 

d   CD   dCL

CL2  C  CD 0   CL  2 L   Ae   Ae   CL2   CD 0   Ae  

2

 0  CL2  CD 0 Ae

Therefore, the CD for this condition is CD  CD 0 

1  CD 0 Ae   2CD 0  Ae 41

Specific Fuel Consumption Jet aircraft - Initial estimates of cj (lb/hr/lb) • Using Raymer (Table 3.3):

•

cruise

loiter

Turbojet

0.9

0.8

Low-bypass turbofan

0.8

0.7

High-bypass turbofan

0.5

0.4

Roskam Vol.1 Table 2.2 (p.14) gives a/c category-specific values (see next slide). 42

Specific Fuel Consumption Jet aircraft - Initial estimates of cj (lb/hr/lb) • Using Roskam (Table 2.2): cruise

Loiter

Business & transport jets

0.5 - 0.9

0.4 - 0.6

Military trainers

0.5 - 1.0

0.4 - 0.6

Fighters

0.6 - 1.4

0.6 - 0.8

Military patrol, bombers, transports, flying boats

0.5 – 0.9

0.4 - 0.6

Supersonic cruise

0.7 – 1.5

0.6 - 0.8 43

Specific Fuel Consumption •

•

Using Raymer (Table 3.4): cruise

loiter

Piston-prop (fixed pitch)

0.4

0.5

Piston-prop (variable pitch)

0.4

0.5

turboprop

0.5

0.6

Take propeller efficiency (p) as 0.8 or 0.7 for fixed-pitch piston-prop in loiter.

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Specific Fuel Consumption •

Using Roskam (Table 2.2): Cruise

loiter

Single engine

0.5 – 0.7, 0.8

0.5 – 0.7, 0.7

Twin engine

0.5 – 0.7, 0.82

0.5 – 0.7, 0.72

Regional turboprops

0.4 – 0.6, 0.85

0.5 – 0.7, 0.77

Military trainers

0.4 – 0.6, 0.82

0.4 – 0.6, 0.77

Fighters

0.5 – 0.7, 0.82

0.5 – 0.7, 0.77

Military patrol, bombers & transports

0.4 – 0.7, 0.82

0.5 – 0.7, 0.77

Flying boats, amphibious

0.5 – 0.7, 0.82

0.5 – 0.7, 0.77 45

Specific Fuel Consumption Java code and applet can be obtained @ http://www.grc.nasa.gov/WWW/K-12/airplane/ngnsim.html

Better estimation for Engine Thrust and fuel flow


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Fuel fraction (W6/W5) found from appropriate endurance equation as in Phase 4. For jet a/c, best loiter at minimum drag speed (maximum L/D value); for prop a/c at minimum power speed. W7/W6 = 0.99 W8/W7 = 0.992 47


W8 W7 W6 W5 W4 W3 W2 W1 M ff  W7 W6 W5 W4 W3 W2 W1 WTO •

(10)

Mission fuel used (WF(used)) WF (used )  1  M ff WTO 

(11)


• • • •

WF then found from equation (5), by adding reserve fuel (WF,res). This then allows for tentative value for WE(tent) to be found, from eq. (4). This may be plotted with WTO on appropriate a/c category graph to check agreement with fit. If not, then process must be iterated until satisfactory. 49


Two other possible mission phases may need to be considered for certain aircraft: – maneuvering – payload drop


•

Breguet range equation may be used with range covered in turn (Rturn) from perimeter length of a turn (Pturn) multiplied by number of turns (Nturn).

Rturn  Nturn Pturn •

(12a)

For manoeuvre under load factor of n: Pturn

 V2  (12b)  2    g n2  1    51

Payload Drop • •

• •

Treated as separate sortie phase with change in total weight but no fuel change. Fuel fraction taken as 1 but subsequent phases corrected to allow for payload drop weight change. Roskam Vol.1 pp.63-64 gives details. e.g. if W5 and W6 are weights before and after payload drops: W W W W W W5 

5

4

3

2

1

W4 W3 W2 W1 WTO

W6  W5  WPL

WTO

(13a)

(13b) 52


Worked Example – Jet Transport (Roskam Vol.1, p55) Specification • Payload: 150 passengers at 175 lb each & 30 lb baggage each. • Crew: 2 pilots and 3 cabin attendants at 175 lb each and 30 lb baggage each. • Range: 1500 nm, followed by 1 hour loiter, followed by 100 nm flight to alternate and descent. • Altitude: 35,000 ft for design range. • Cruise speed: Mach number = 0.82 @ 35,000 ft. 53 Prof. Bento S. de Mattos

Worked Example – Jet Transport (Roskam Vol.1, p55) Specification (Cont.) • Climb: direct climb to 35,000 ft at max WTO. • Take-off & landing: FAR 25 field-length of 5,000 ft.

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• • •

WPL = 150 x (175 + 30) = 30,750 lb Wcrew = 1,025 lb Initial guess of WTO required, so compare with similar aircraft: –

Boeing 737-300 has range of 1620 nm for payload mass of 35,000 lb – WTO = 135,000 lbs. Initial guess of 127,000 lb seems reasonable.

–

•

Now need to determine a value for WF, using the fuel fraction method outlined above. 55


As in earlier example, for a transport jet:

W1/WTO = 0.99 W2/W1 = 0.99 W3/W2 = 0.995 56

Phase 4 (climb) W4/W3 = 0.98 • The climb phase should also be given credit in the range calculation. • Assuming a typical climb rate of 2500 ft/min at a speed at 275 kts then it takes 14 minutes to climb to 35,000 ft. • Range covered in this time is approximately (14/60) x 275 = 64 nm. 57 Prof. Bento S. de Mattos

•

Cruise Mach number of 0.82 at altitude of 35,000 ft equates to cruise speed of 473 kts.

•

Using eq. (7b):

•

Assumptions of L/D = 16 and cj = 0.5 lb/hr/lb with a range of 1500 – 64 (=1436 nm) yield a value of:

V Rcr   c  j

 L  W4     ln   cr  D cl  W5 

W5/W4 = 0.909 58

1 Ecl   c  j

 L  W3     ln   cl  D cl  W4 

•

Using eq. (6b):

•

Assumptions of L/D = 18 and cj = 0.6 lb/hr/lb.

•

No range credit assumed for loiter phase.

•

Substitution of data into eq. (6b) yields:

W6/W5 = 0.967


•

No credit given for range. W7/W6 = 0.99

• •

May be found using eq. (6b) again. Cruise will now take place at lower speed and altitude than optimum – assume cruise speed of 250 kts (FAR 25), L/D of 10 and cj of 0.9 lb/hr/lb. Gives: W8/W7 = 0.965

•


•

No credit given for range. W9/W8 = 0.992

•

found from eq. (8) (with additional term for W9/W8) = 0.992x0.965x0.99x0.967x0.909x0.98x0.995x0.99x0.99 = 0.796

•

Using eq. (9), WF = 0.204 WTO = 25,908 lb 61


•

Using eq. (4): WE(tent) = WTO(guess) – WPL - Wcrew - WF – Wtfo  WE(tent) = 127,000 – 30,750 – 1,025 – 25,908 - 0 = 69,317 lb

•

By comparing with Roskam Vol. 1, Fig. 2.9, it is seen that there is a good match for these values of WE and WTO, hence a satisfactory solution has been reached. 62


•

Specification / design requirements often reevaluated and refined at this stage, using above method. • Examples include: – Effect of a range increase/decrease on MTO. – Effect of payload mass change on MTO. – Effect of using composite materials instead of aluminium alloys. • More details and examples in Raymer p.28-31 and Ch.19. 63

•

Essentially Roskam’s version (Vol.1, p.68) of Raymer’s trade studies detailed above.

•

Sensitivity of MTO is investigated with changes to the following typical set of parameters: –

• •

Empty weight (WE), payload (WPL), range (R), endurance (E), lift/drag (L/D), specific fuel consumption (cj or cp) and propeller efficiency (ηp).

Sensitivity to general parameter y expressed by: WTO y Regression constants used in equations are relevant to particular a/c category. 64


Estimating Cruise Fuel Consumption IPET7 Airliner

Performance Max operating Mach number

0.83

Max operating altitude

41,000 ft (cabin altitude: 8,000 ft)

Take-off field lenght

6,500 ft (SL / ISA + 15°C / MTOW)

Landing field

5,000 ft (SL / MLW = 90% of MTOW)

Range with max payload

2,200 nm (overall fuel volume for 3,200 nm version)

External noise

FAR 36 Stage IV minus 15 db

Estimating Cruise Fuel Consumption The number of Mach for maximum specific range (SR) is not the same as that for maximum M*L/D because sfc increases with speed

IPET7 Mach*L/D vs. Mach number

IPET7 SR vs. Mach number

41000 ft 14,00

41000 ft

12,00 0,290

10,00 M*L/D

SR [nm/kg]

0,270 0,250 0,230 0,210

8,00 6,00 4,00

0,190

2,00

0,170 0,150 0,40

0,50

0,60

0,70

0,80

0,90

0,00 0,40

0,50

Mach MTOW

90% MTOW

Long Range

MMO

0,60

0,70

0,80

0,90

Mach 80% MTOW

MTOW

90% MTOW

80% MTOW

67

TAS SR  Fuel flow

69

Weight Estimation - Conceptual Design of Airplanes

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