weight estimation of airplanes

2

Content

3

Guidance

4

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.

Glossary

5

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

Some Tasks in the Conceptual Design

6

Preliminary

sizing

(We,Wto,Wf)

Sensitivity study (Wto to Wpl,

We, R, S.F.C(Cj), and L/D)

Estimating

T/W, W/S

Configuration

selection

Design of cockpit and

the fuselage

Design of the

wing

Landing gear design

Cost prediction

Selection Integration

of the Propulsion

system

Design of stabilizers

and control

surfaces

Estimation of cg

variation and

airplane inertias

This course material is concerned with

7

Preliminary

sizing

(We,Wto,Wf)

Sensitivity study (Wto to Wpl,

We, R, S.F.C(Cj), and L/D)

Estimating

T/W, W/S

Configuration

selection

Design of cockpit and

the fuselage

Design of the

wing

Landing gear design

Cost prediction

Selection Integration

of the Propulsion

system

Design of stabilizers

and control

surfaces

Estimation of cg

variation and

airplane inertias

8

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

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.

11

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.

• 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

Operating empty weight = basic empty weight + operational items

(From an equipment standpoint, the airplane is ready for operation.)

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

15

Weight Definitions

Take-off weight (WTO) – (Roskam method)

WTO = WOE + WF + WPL

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.

(1)

16

Weight Definitions

Operating weight empty may be further broken down

into:

WOE = WE + Wtfo + Wcrew

where:

WE = empty weight

Wtfo = trapped (unusable) fuel weight

Wcrew = crew weight

(2)

17

Weight Definitions

• Empty weight sometimes further broken down

into:

WE = WME + WFEQ

where:

WME = manufacturer’s empty weight

WFEQ = fixed equipment weight

(includes avionics, radar, air- conditioning, APU, etc.)

(3)

18

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) twin-

engine 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.

22

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).

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Roskam’s Empty Weight Estimation Method

Category 7 Category 8

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Raymer’s Empty Weight Fraction Estimation Equation

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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)

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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.

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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.

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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.

Prof. Bento S. de Mattos

30

Mission Fuel Weight • This is the sum of the fuel used and the reserve

fuel.

WF = WF(used) + WF(res)

• 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.

(5)


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1. Start & warm-up 2. Taxi 3. Take off 4. Climb 5. Cruise 6. Loiter 7. Descend 8. 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.

civil jet transport

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

34

For piston-prop a/c:

For jet a/c:

where:

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.

3

4

1lncl

clj cl

WLE

c D W

3

4

1375 ln

p

cl

clcl p cl

WLE

V c D W

(6a)

(6b)


35

• 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).


36

Phase 5 (cruise)

• Weight fraction calculated using Breguet range

equations.

• For prop a/c:

• For jet a/c:

• These give the range in miles.

(7a)

(7b)

4

5

1375 ln

p

cr

clcl p cr

L WR

V c D W

4

5

lncr

clj cr

V L WR

c D W

37

• For jet a/c, range maximised by flying at 1.32 x

minimum drag speed and minimising sfc.

– 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.

38

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

• Using Roskam (Table 2.2 – selected values):

cruise loiter

Homebuilt & single-engine 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

Military patrol, bombers & transports 13 – 15 14 – 18

Supersonic cruise 4 - 6 7 – 9

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Jet Airplane Airplane fitted with propeller

1ln i

fj

L WR

Wc D

ln i

fj

V L WE

Wc D

ln i

fj

V L WR

Wc D

1ln i

fj

L WE

Wc D

In order to obtain a better estimation for the L/D ratio we shall

consider the Breguet equations for range (R) and endurance (E):

(6b) (6a)

(7a) (7b)

40

2

0D D LC C kC

Considering that he TSFC does not vary with speed and that the

drag polar can be written as

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:

max range 0

1 3

4 D

L A e

D C

max endurance 0

1

2 D

L A e

D C

with 1

kAe

(8a) (8b)

(9a) (9b)

41

with

42

Specific Fuel Consumption Jet aircraft - Initial estimates of cj (lb/hr/lb)

• Using Raymer (Table 3.3):

• Roskam Vol.1 Table 2.2 (p.14) gives a/c

category-specific values (see next slide).

cruise loiter

Turbojet 0.9 0.8

Low-bypass turbofan 0.8 0.7

High-bypass turbofan 0.5 0.4

43

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

44

Specific Fuel Consumption

• Using Raymer (Table 3.4):

• Take propeller efficiency (p) as 0.8 or 0.7 for

fixed-pitch piston-prop in loiter.

cruise loiter

Piston-prop (fixed pitch) 0.4 0.5

Piston-prop (variable

pitch)

0.4 0.5

turboprop 0.5 0.6

45


• 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


Better estimation for

Engine Thrust and

fuel flow

Java code and applet can be obtained @

http://www.grc.nasa.gov/WWW/K-12/airplane/ngnsim.html


47

• 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

48

• Mission fuel used (WF(used))

8 7 6 5 34 2 1

7 6 5 4 3 2 1

ff

TO

W W W W WW W WM

W W W W W W W W (10)

(11) ( ) 1F used ff TOW M W

49

• 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.

50

• Two other possible mission phases may need

to be considered for certain aircraft:

– manoeuvring

– payload drop

51

• 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).

• For manoeuvre under load factor of n:

turn turn turnR N P

2

22

1turn

VP

g n

(12a)

(12b)

52

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: 5 34 2 1

5

4 3 2 1

TO

TO

W WW W WW W

W W W W W (13a)

(13b) 6 5 PLW W W

53

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.

54

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.

55

Jet Transport Example

• WPL = 150 x (175 + 30) = 30,750 lbs

• Wcrew = 1,025 lbs

• Initial guess of WTO required, so compare with

similar aircraft:

– Boeing 737-300 has range of 1620 nm for payload

mass of 35,000 lbs – WTO = 135,000 lbs.

– Initial guess of 127,000 lbs seems reasonable.

• Now need to determine a value for WF, using

the fuel fraction method outlined above.

56


As in earlier example, for a transport jet:

W1/WTO = 0.99

W2/W1 = 0.99

W3/W2 = 0.995

57


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.

58


• 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:

W5/W4 = 0.909

4

5

lncr

clj cr

V L WR

c D W

59

Phase 6 (loiter)

• 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

3

4

1lncl

clj cl

WLE

c D W

60

Simple Cruise Mission Example

• 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

61


• 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

62


• 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.


63

• Specification / design requirements often re-

evaluated 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.

64

• 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:

• Regression constants used in equations are relevant

to particular a/c category.

TOW

y


Estimating Cruise Fuel Consumption

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

IPET7 Airliner

67

Estimating Cruise Fuel Consumption

41000 ft

0,150

0,170

0,190

0,210

0,230

0,250

0,270

0,290

0,40 0,50 0,60 0,70 0,80 0,90

Mach

SR

[n

m/k

g]

MTOW 90% MTOW 80% MTOW

Long Range MMO

SR vs. Mach number 41000 ft

0,00

2,00

4,00

6,00

8,00

10,00

12,00

14,00

0,40 0,50 0,60 0,70 0,80 0,90

Mach

M*L

/D

MTOW 90% MTOW 80% MTOW

Mach*L/D vs. Mach number

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 IPET7

TASSR

Fuel flow

weight estimation of airplanes

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