1

Appendix 8.1

Notes on Airplane weight estimation

Jasdeep Singh *

1. INTRODUCTION

1.1 Opening remarks

1.1.1 Minimization of the weight of an airplane is a subject of utmost importance in

airplane design. Although reduction in weight is generally obtained only at some initial

cost penalty, its effects on total operating cost are paramount for most high performance

designs. During the initial conceptual design, the choice of the airplane layout, geometry

and detailed configuration influence the weight. Hence accurate prediction of weight is

necessary not only to make an assessment of the design qualities, but also to set a goal for

structural and systems design.

1.1.2 Although considerable information is available on this topic, need has been felt, for

standardized, uni-source set of parametric equations that can correlate the weight data for

existing airplanes to a reasonable degree of accuracy. In terms of teaching aid, the same

set of equations would help in appreciating, the interplay of various parameters on

weight of a component, and the influence of a given weight change on the overall take off

weight, and consequently cost of airplane and its operation.

1.1.3 In the present report the information, has primarily been sought from Airplane

-------------------------------------------------------------------------------------------------------

* M.tech student (2004-2006)

2

Design Part V: Component Weight Estimation by J. Roskam (Ref. 1). A methodology

for estimation of weights of airplane components is presented; it is assumed that the

preliminary weight estimation has already been carried out, and the airplane performance

and structural capabilities have been worked out. Three categories of airplanes are

considered:

1.1.3.1 Twin engine propeller driven airplane

1.1.3.2 Jet transport

1.1.3.3 Fighter

1.2 Aim To present a standard set of parametric equations and the methodology

involved in calculating weights of airplane components.

1.3 Scope The scope of this report is limited to the following aspects.

1.3.1 Overall major groupings of airplane weight

1.3.2 Methodology to calculate component weights using given equations for

the three categories of airplanes mentioned in para 1.1.3

1.3.3 Employment of same set of developed equations for component weight

estimation of B-737-200, and comparison of results obtained with known weight

data of the airplane.

2. Major Groupings of Airplane Weight

2.1 The airplane take-off weight is the sum of fuel load, payload and the empty

weight. While the first two weights may normally be specified in the mission requirement

3

or already known from preliminary sizing process, the empty weight needs to be

evaluated in detail.

2.2 The airplane empty weight can be sub-divided into the following.

2.2.1 Structural weight: It includes weights of the following.

2.2.1.1 Wing

2.2.1.2 Empennage horizontal tail , vertical tail and / or canard

2.2.1.3 Fuselage

2.2.1.4 Nacelles

2.2.1.5 Landing gear nose and main wheels

2.2.1.6 Surface control structure(s)

2.2.2 Power plant weight: It includes the weights of the following.

2.2.2.1 Engine dry weight

2.2.2.2 Air induction system

2.2.2.3 Propeller(s)

2.2.2.4 Engine fuel system

2.2.2.5 Propulsion system

2.2.3 Fixed equipment weight: It includes weights of the following.

2.2.3.1 Flight control system

2.2.3.2 Hydraulic and pneumatic system

2.2.3.3 Electrical system

2.2.3.4 Instrumentation, avionics, electronics

2.2.3.5 Air conditioning, pressurization, anti-icing system

2.2.3.6 Auxiliary power unit (APU)

2.2.3.7 Furnishings

4

2.2.3.8 Baggage and cargo handling equipment

2.2.3.9 Armament (for military airplanes)

2.2.3.10 Paint

Remark: List of symbols is given at the end of the report.

3. Weight equation method Development & procedures for evaluation of

component weights.

3.1. This method accounts for the following factors.

3.1.1 Airplane take-off gross weight

3.1.2 Wing and empennage design parameters, such as, area, taper ratio,

thickness ratio, and sweep.

3.1.3 Load factor

3.1.4 Design cruise and dive speed (from V- n diagram)

3.1.5 Fuselage configuration

3.1.6 Powerplant installation

3.1.7 Landing gear design and disposition

3.1.8 Preliminary structural arrangement

3.2 Pre-Requisites: It is assumed that the following information is available.

3.2.1 Preliminary sizing of various components.

3.2.2 The weights of fuel, payload, trapped fuel and oil, and crew are known.

3.2.3 The limit and ultimate load factors during cruise and dive have been

obtained from respective V-n diagrams.

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3.3 Methodology

3.3.1 Step 1: List all items for which the weights are known (from preliminary sizing, or mission specification).

3.3.2 Step 2: List all airplane components for which weights have to be estimated.

3.3.3 Step 3: Determine the weight estimation category that best represents the airplane being designed.

3.3.4 List out the relevant set of equations for the category of airplane being considered.

3.3.5 List out requisite input data needed for the chosen set of equations.

3.3.6 Compute the component weights, and obtain an estimate for empty weight.

3.4 Types of Methods Four basic methods are generally adopted for estimation of component weights (Ref.1).

3.4.1 Cessna method

3.4.2 USAF Method

3.4.3 GD (General Dynamics) Method

3.4.4 Torenbeek Method

Note: In this report Torenbeek method is mainly used.

4. Twin engine propeller driven airplane Component weight determination

4.1 Known Weight Data

4.1.1. Payload weight (WPL ) = 1250 lbs

4.1.2 Fuel weight (WF ) = 1706 lbs

4.1.3 Weight of trapped fuel and oil ( Wtfo ) = 44 lbs

4.1.4 Weight of engine (We) = 1400 lbs

4.2 Weights to be determined

4.2.1 Structural weight (Wstruct)

6

4.2.1.1 Wing (Ww)

4.2.1.2 Empennage (Wemp)

4.2.1.3 Fuselage (Wf)

4.2.1.4 Nacelles (Wn)

4.2.1.5 Landing gear (Wg)

4.2.2 Powerplant weight (Wpwr)

4.2.2.1 Engine(s) (We)

4.2.2.2 Air induction system (Wai)

4.2.2.3 Propellers (Wprop)

4.2.2.4 Fuel system (Wfs)

4.2.2.5 Propulsion installation (Wprop)

4.2.3 Fixed Equipment Weight (Wfeq)

4.2.3.1 Flight controls (Wfc)

4.2.3.2 Electrical sytem (Wels)

4.2.3.3 Instrumentation, avionics, electronics (Wiae)

4.2.3.4 Air conditioning / De-icing (Wapi)

4.2.3.5 Oxygen (Wox)

4.2.3.6 Furnishings and paint (Wfur and Wpt)

4.3 Airplane weight estimation category: General Awation Airplane

4.4 Set of Equations

4.4.1 Wstruct

4.4.1.1 Ww = 0.00125 1

21

2

12

0.75cos

1 6.3cos

+ TO

bWb

1

2

0.3

0.55( )cos

ult r TOb Sn

t W

7

WT0 = Take-off weight in lbs.

b = wing span; 1/2 = semi chord sweep; S = wing area in ft2

nult = ultimate load factor

tr = maximum thickness at wing root in ft.

4.4.1.2 Wemp = 0.04 { nult (SV + Sh)2 }0.75

Sv= vertical trail area in ft2; Sh = horizontal tail area in ft2 .

4.4.1.3 Wf = 0.021 Kf {(VD lh) / (wf + hf)}1/2 (Sfgs)1.2

where Kf = 1.08, for pressurized fuselage

= 1.07, for main gear attached to fuselage

= 1.10, for cargo airplane with cargo floor

VD = design dive speed (in knots)

lh = tail length i.e. distance from wing c /4 to horizontal tail c h / 4 (in ft)

Sfgs = fuselage gross shell area (in ft2)

4.4.1.4 Wn = 0.14 (PTO) ; PTo= Take-off power in HP

4.4.1.5 Wg = 0.054 (lsm)0.501 (WL nult.l)0.684 ; based on USAF method

Where: nult.l = landing ultimate load factor ( 5.7) lsm = shock strut length for main gear in ft.

WL = Landing weight

4.4.2 Wpwr

4.4.2.1 We (from para 4.1.4)

4.4.2.2 Wai = 1.03 (Ne)0.3 (PTO / Ne)0.7

Ne = Number of engines

4.4.2.3 Wprop = 2propK (NP)0.218 {Dp PTO (Nbl)1/2} 0.782

8

where 2propK = 0.108, for turbo- props

= 0.144, for piston engine

Np = Number of propellers

Dp = Propeller diameter in ft

Nbl = Number of blades per propeller

4.4.2.4 Wfs = 2 (WF / 5.87)0.667

4.4.3 Wfeg

4.4.3.1 Wfc = 0.33 (WTO)2/3

4.4.3.2 Wels = 0.0078 (WE)1.2, also includes weights of hydraulic and pneumatic systems; WE = empty weight in lbs.

4.4.3.3 Wiae = 40 + 0.008 WTO

4.4.3.4 Wapi = 0.018 WE for multi-engined unpressurised airplane.

4.4.3.5 Wox = 7 (Ncr + Npax)0.702 Based on GD method

4.4.3.6 Wfur = 15 Npax + 1.0 Vpax+cargo

Npax = no.of.passengers plus crew

Vpax+cargo = volume of passenger cabin plus cargo compartment in ft3.

4.5 Input Data

WTO = 7900 lbs : nlim = 3.44 : S = 172 ft2

Cruise speed Vc = 248 kts: Dive speed = VD= 310 kts : nult = 5.16

A = 8 : = 0.4 : 1/4 = Oo (t/c)m = 0.17 : b= 37.1 ft : tr = 1.13 ft

(Sh) = 58 ft2 : bh = 14.9 ft : trh = 0.53 ft

lh = 24.3 ft : Sv = 38 ft2 : bv = 6.16 ft

trv = 0.66 ft : lf = 39.3 ft : wf = 4.5 ft

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hf = 5.5 ft : Kf = 1.08 : PTO = 850 hp

lsm = 6 ft : WL = 7505 lbs : nult.l = 4.0

2propK =0.144 : Np = 2 : Nbl = 3

Dp = 7.8 ft

4.6 Weight computation (using paras 4.4 in conjunction with 4.5)

4.6.1 Ww = 410 lbs

4.6.2 Wemp = 155 lbs

4.6.3 Wf = 1130 lbs Wstruct = 2280 lbs ( 28.86 % of WTO) 4.6.4 Wn = 272 lbs

4.6.5 Wg = 313 lbs

4.6.6 We = 1400 lbs

4.6.7 Wai = 88 lbs Wpwr = 1873 lbs ( 23.71% of WTO) 4.6.8 Wprop = 250 lbs

4.6.9 Wfs = 135 lbs

4.6.10 Wfc = 91 lbs

4.6.11 Wels = 209 lbs

4.6.12 Wiae = 103 lbs Wfeq = 901 lbs ( 11.4% of Wro) 4.6.13 Wapi = 88 lbs

4.6.14 Wfur = 410 lbs

Consequently, WE = Wstruct + Wpwr + Wfeq = 5054 lbs ( 63.97%)

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5. Jet Transport Component weight determination

5.1 Known Weight Data

5.1.1 WPL = 30,750 lbs

5.1.2 Wcrew = 1025 lbs

5.1.3 WF = 25,850 lbs

5.1.4 Wtfo = 925 lbs

5.1.5 We = 9224 lbs

5.2 Weights to be determined

5.2.1 Wstruct - Ww , Wemp , Wf , Wn , Wg .

5.2.2 Wpwr - We ,Wfs , Wpc , Wess , ( weight of electrical start system)

5.2.3 Wfeg Wfc ,Wels ,Wiae , Wapi, Wox , Wapu

Wfur , Wbc ( weight of baggage and cargo handling);

Wops (weight of operational items).

5.3 Airplane Weight estimation category : Commercial Transport Airplane

5.4 Set of Equations

5.4.1 Wstruct

5.4.1.1 Ww = 0.0017 WMZF 0.75 1/ 2

1/ 2

1/ 2

cos ( )1 6.3cos

+ b

b

x (nult)0.55 0.3

1/ 2cos r MZW

b St W

where WMZF = Maximum zero fuel weight

= WTO - WF

Note (a) For 2 wing mounted engines reduce Ww by 5%

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(b) For 4 wing mounted engines reduce Ww by 10%

(c) For landing gear net under wing reduce Ww by 5%

(d) For fowler flaps add 2% to Ww

5.4.1.2 Wemp (= Wh + Wv)

5.4.1.2.1 Wh = Kh Sh

( ){ } { }0.2 1/ 21/ 23.81 / 1000 (cos ) 0.287 h DS V where Kh = 1.0 for fixed incidence stabilizers

= 1.1, for variable incidence stabilizer.

5.4.1.2.2 Wv = Kv Sv

( ){ } { }0.2 1/ 21/ 23.81 / 1000 (cos ) 0.287 v DS V where Kv = 1.0 for fuselage mounted horizontal tail

5.4.1.3 Wf = 0.021 Kf {(VD ln / (wf + hf)}1/2 (Sfgs)1.2

Kf = 1.08, for pressurized fuselage

= 1.07, for main gear attached to fuselage

= 1.10, for cargo airplane with cargo floor

Note : Effects of Kf are multiplicative

5.4.1.4 Wn = 0.065 TTO for high bypass ratio turbofans.

5.4.1.5 Wg = Kgr {Ag + Bg (WTO)3/4 + Cg (WTO) + Dg (WTO)3/2

Where Kgr = 1.0, for low wing airplane.

= 1.08, for high wing airplane. Note (a) for Main Wheels

Ag = 40.0 : Bg = 0.16 : Cg = 0.019 : Dg = 1.5 x 10-5

(b) for nose wheels

12

Ag = 20.0 : Bg = 0.10 : Cg = 0.0 : Dg = 2 x 10-6

5.4.2 Wpwr

5.4.2.1 We - from para 5.1.5

5.4.2.2 Wfs = 80 (Ne + Nt 1) + 15 (Nt)0.5 (WF / Kfsp)0.333 , for airplane with integral fuel tank.

5.4.2.3 Wthr.rev = 50.38 (We/1000)0.459

Kfsp = 5.87 lbs / gal for aviation gasoline

= 6.55 lbs/gal for JP-4.

5.4.3 Wfeq

5.4.3.1 Wfc = Kfc (WTO)2/3

Where Kfc = 0.44, for unpowered flight controls

= 0.64 for powered flight controls

5.4.3.2 Wels = 10.8 (Vpax)0.7 {1- 0.018 (Vpax)0.35}

where : Vpax = passenger cabin volume in ft3

5.4.3.3 Wiae = 0.575 (We)0.556 (R)0.25

where R = Maximum range in nm

5.4.3.4 Wox = 30 + 1.2 (Npax) for short flights above 25000 ft.

5.4.3.5 Wapu = (0.004 to 0.013) WTO

5.4.3.6 Wfur = 0.211 (WTO WF)0.91

5.4.3.7 Wbc = Kbc (Npax)1.456

where Kbc = 0.0646, without preload provisions

= 0.316, with preload provisions.

5.5 Input Data

WTO = 1,27,000 lbs ; nlim = 2.5 ; S = 1296 ft2

VC = 295 kts ; VD = 369 Kts ; nult = 3.75

A = 10 ; = 0.32 ; 1/4 = 35o

13

1/2 = 33.5o ; MH = 0.85 ; (t/c)m = 0.13

b = 113.8 ft ; tr = 2.26 ft ; Sh = 254 ft2

bh = 35.6 ; trh = 1.3 ft ; c = 12.5 ft2

lh = 32.5 ft ; Sv = 200 ft2 ; zh / bv = 0

lv = 35.8 ; Sr/Sv = 0.45 ; v = 0.32 Av = 1.8 ; 1/4 = 45o ; lf = 124.3 ft

wf + hf = 26.4 ft ; Dq = 461 psf ; WL = 7505 lbs

nult.l = 4.0 ; Area of inlet= Ainl = 28.3 ft2 ; Diameter of inlet = Dinl = 6.0 ft

5.6 Weight Computation

5.6.1 Ww = 15,973 lbs

5.6.2 Wemp = 1218 + 829 = 2.047 lbs

5.6.3 Wf = 11,140 lbs Wstruct = 37271 lbs ( 29.35%) 5.6.4 Wn = 3120 lbs

5.6.5 Wg = 4208 + 783 = 4994 lbs

5.6.6 We = 9224 lbs

5.6.7 Wfs = 1009 lbs Wpwr = 12853 lbs (10.12%) 5.6.8 Wess = 960 lbs

5.6.9 Wthr. rev = 1660 lbs

14

5.6.10 Wfc = 1617 lbs

5.6.11 Wels = 4063 lbs

5.6.12 Wiae = 1775 lbs

5.6.13 Wapi = 2166 lbs

5.6.14 Wox = 210 lbs Wfeq = 22123 lbs ( 17.42%) 5.6.15 Wapu = 1016 lbs

5.6.16 Wfur = 7565 lbs WE = Wstruct + Wpw + Wfeq 5.6.17 Wbc = 466 lbs = 72247 lbs

5.6.18 Wups = 3245 lbs ( 56.89%)

6. Test Examples: Weight components for B-737-200 (Jet Transport Aircraft)

6.1 Known weight Data

6.1.1 WPL = 34010 lbs

6.1.2 Wcrew = 1057 lbs

6.1.3 WF = 27 395 lbs

6.1.4 Wtfo = 950 lbs

6.1.5 We = 9030 lbs

6.2 Weights to be determined

6.2.1 Wstruct -Ww, Wf, Wg , Wn , Wemp

6.2.2 Wpwr -We, Wfs , Wpc, Wess

6.2.3 Wfeq -Wfc , Wels , Wiae , Wapi , Wox;

Wapu , Wfur , Wbc , Wops

6.3 Airplane weight estimation category : Commercial Transport Airplane

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6.4 Set of Equations: As in Para 5.4

6.5 Input Data

WTO = 100000 lbs ; nult = 3.75; S = 979.59 ft2

VC = 295 kts ; VD = 375 kts ; A = 8.83

= 0.266; 1/4 = 25o 1/2 = 23.5o (t/c)m = 0.1289; b = 93.02 ft; tr = 1.607 ft

MH = 0.85 Sh = 336.9ft2 bh = 41.67 ft

lh = 48.5 ft ; Sv = 204.4 ft2 lv = 39.7 ft

Sr / Sv = 0.45; v = 0.288; Av = 1.74 Ah = 5.15; / 2hc = 30o;

2

c v = 35o

c = 12.47 ft ; trh = 1.18 ft; lf = 96.92 ft

wf + hf = 24.48 sft ; Dq = 460 psf; nult.l = 4.0

diameter of fuselage= df = 12.24 ft ; P2 = 20 psi ; length of nacelle = ln = 22.98 ft

6.6 Weight computation

6.6.1 Ww = 0.0017 WMZF . 12

0.75

1/ 2

1/ 2

6.3 (cos1cos

+ b

b

0.3

0.55

1/ 2

( ) ult r MZF

b Snt W Cos

where WMZF = 43091 Kgf = 94886.4 lbs

Ww = 0.0017 (94886.4) 120.7593.02 6.3 cos 23.51

cos 23.5 93.02

o +

0.3

0.55 93.02 979.59(3.75)1.607 94886.4 cos 23.5 o

16

or Ww = 11718 lbs 11.05 (for 2-eng, wing mounted configuration)

= 11160 lbs

6.6.2 Wemp

6.6.2.1 Wh = Kh Sh [3.81 {(Sh)0.2 VD } / {1000 (cos 1/2 h )1/2 }- 0.287]

where Kh = 1.0, for fixed incidence stabilizers

Wh = (1.0 x 336.9) 12

0.23.81 (336.9) 375 0.2871000 (cos30 )o

or Wh = 1559.81 lbs

6.6.2.2 WV = Kv. Sv . 12

0.2

1/ 2

3.81 ( ) 0.2871000 (cos )

v D

v

S V

where Kv = 1.0 for fuselage mounted horizontal tail

Wv = (1.0 x 204.4 ) 12

0.23.81 (204.4) 375 0.2871000 (cos35 )o

or Wv = 876.42 lbs

6.6.2.3 Wemp = Wh + Wv = 1559.81 + 876.42 = 2436.23 lbs

6.6.3 Wf = 0.021 Kf {(VD lh ) / (wf + hf)}1/2 (Sfgs)1.2

where Kf = 1.08 x 1.07 = 1.1556

Sfgs = df .lf = (12.24) (96.92) = 3726.87 ft2

Wf = 0.02 x 1.1556 12375 48.5

24.48 (3726.87 )

1.2

= 12767.95 lb

6.6.4 Wn = 0.065 TTO

17

since TOTO

TW

= 0.2771 TTO = 0.2771 x 100000 = 27710 lb

Wn = 0.065 x 27710 = 1801.15 lb

6.6.5 Wg :

6.6.5.1 Nose wheel : Wnw = Kgr {Ag + Bg (WTO)3/4 + Cg (WTO) + Dg (WTO)3/2}

where Kgr = 1.0 for low wing airplane

Wnw = 1.0 {20 + 0.1 (100000)3/4 + 0 + 2 x 10-6 (100000)3/2}

= 665.59 lb

6.6.5.2 Main wheels : Wmw = 1.0 {40 + 0.16 (100000)3/2 + 0.019

(100000) + 1.5 x 10-5 (100000)3/2)

= 3314.09 lb

6.6.5.3 Wg = Wnw + Wmw = 665.59 + 3314.09 = 3979.68 lb

6.6.6 We = Ne x weight of one engine

= 2 x 4515

= 9030 lbs

6.6.7 Wfs = 80 [Ne + Nt 1] + 15 (Nt)0.5 (WF / Kfsp).333

where ; Ne = No. of engines = 2

Nt = No. of fuel tanks = 6

Kfsp = 5.87, lbs / gal, for aviation gasoline

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Wfs = 80 (2 + 6-1) + 15 (6)0.5 0.33327395

5.87

= 1172.29 lbs

6.6.8 Wess = 38.93 (We / 1000)0.918 = 38.93 (9030 / 1000)0.918 = 293.5 lb

6.6.9 Wthr.rev = 50.38 (We / 1000)0.459 = 50.38 (9030 / 1000)0.459 = 138.33 lb

6.6.10 Wfc = Kfc (WTO)2/3 ; Kfc=0.64 from para 5.4.3.1

= 0.64 (100000)2/3

= 1378.84 lb

6.6.11 Wels = 10.8 (Vpax)0.7 {1- 0.018 (Vpax)0.35}

where Vpax = volume per passenger x No. of passenger

= 0.19 x 130 x 3.2813

= 872.4 ft3

Wels = 10.8 (872.4)0.7 {1-0.018 (872.4)0.35} = 997.8 lb.

WE / WTO = 0.528 from preliminary weight estimation. Hence

WE = 0.528 x 100000 = 52800 lb,

R = 1900mm

From Para 5.4.3.3 , Wiae = 0.575 (52800)0.556 (1900)0.25

= 1603.76 lb

6.6.13 Wox = 30 + 1.2 (Npax)

= 30 + 1.2 (130) = 186 lb

19

6.6.14 Wapu = 0.0085 WTO

= 0.0085 x 100000 = 850 lb

6.6.15 Wfur = 0.211 (WTO WF)0.91

= 0.211 (100000-27395)0.91 = 5556.63 lb

6.6.16 Wbc = Kbc (Npax)1.456 , Kbc = 0.646 from para 5.4.3.7

= 0.0646 (130)1.456 = 77.29 lb

6.6.17 Wpaint = 0.0045 WTO

= 0.0045 x 100000 = 450 lb

6.7 Summary of Component Weights

6.7.1 Wstruct

6.7.1.1. Ww = 11160 lb

6.7.1.2 Wemp = 2436.23 lb

6.7.1.3 Wf = 12767.95 lb Wstruct = 32145.01 lb

6.7.1.4 Wn = 1801.15 lb

6.7.1.5 Wg = 3979.68 lb

6.7.2 Wpwr

6.7.2.1 We = 9030 lb

6.7.2.2 Wfs = 1172.29 lb

6.7.2.3 Wess = 293.5 lb Wpwr = 10634.12 lb

6.7.2.4 Wthr.rev = 138.33 lb

20

7.3 Wfeq

6.7.3.1 Wfc =- 1378.84 lb

6.7.3.2 Wels = 997.8 lb

6.7.3.3 Wiae = 1603.76 lb

6.7.3.4 Wox = 186 lb Wfeq=11100.32 lb

6.7.3.5 Wapu = 850 lb

6.7.3.6 Wfur = 5556.63 lb

6.7.3.7 Wbc = 77.29 lb

6.7.3.8 Wpaint = 450 lb

6.8 Empty weight (WE)

6.8.1 WE = Wstruct + Wpwr + Wfeq = (32145.01) + (10634.12) + (11100.32)

= 53879.45 lb

6.8.2 The rated ratio of WE / WTO is 0.528, i.e., actual WE is 52800 lb. Hence,

our computation have an error of only 2.04%

7. Fighter Component Weight Computation

7.1 Known Weight Data

7.1.1 WPL = 12,405 lb

7.1.2 Wcrew = 200 lb

7.1.3 WF = 18500 lb

21

7.1.4 Wtfo = 300 lb

7.1.5 We = 6000 lb

7.2 Weights to be determined

7.2.1 Wstruct : Ww ; Wf ; Wtallboom ; Wengine section ; Wg

7.2.2 Wpwr

7.2.2.1 We

7.2.2.2 Wafter-burner

7.2.2.3 Wai

7.2.2.4 Wfs

7.2.2.5 Wp

7.2.3 Wfeg

7.2.3.1 Wfc

7.2.3.2 Wels

7.2.3.3 Wiae

7.2.3.4 Wpi

7.2.3.5 Warm

7.2.3.6 Wfur

7.2.3.7 Wox

7.2.3.8 Waux.gear

7.2.3.9 Wglw

22

7.3 Airplane weight computation category Fighter and Attack Airplane

7.4 Set of Equations

7.4.1 Wstruct

7.4.1.1 Ww =

{ } 0.4642 619.29 ( ) /( / ) {( 2(1 ) / (1 )) 1} 10 + + w ult TO m LEK n W t c Tan A x {(1+)A}0.7 (S)0.58 based on GD method

where : Kw = 1.00, for fixed wing

= 1.175 for variable sweep wing

Note : Check mission specification to use Wgross or WTO in this equation

7.4.1.2 Wemp = Wh + Wv

=

{ }0.9150.813 0.584 0.033 0.280.0034 ( ) ( ) ( ) ( / )TO ult h h rh hW n S x b t c l x 1.0140.5 0.363 1.089 0.60

0.190.726 0.217 0.337 0.363 0.484

1/ 4

(1 / ) ( ) ( ) ( )

( ) (1 / ) ( ) (1 ) (cos ) + + +

h v TO ult v H

v r v v v v

z b W n S Ml S S A

where zh = distance from the vertical tail root to where the horizontal tail

is mounted on the vertical tail (in ft). For fuselage mounted hor.tail zh = 0 ;

Sr rudder area (in ft2)

7.4.1.3 Wf = 10.43 (Kinl)1.42 ( Dq /100)0.283 (WTO/1000)0.95 (lf / hf)0.71

23

where Kinl = 1.25 for inlets on fuselage for buried engine

installation

= 1.0 for inlets located elsewhere

Dq = design dive dynamic pressure (in psf)

7.4.1.4 Wtailboom = 0.021 Kf {(VD lh) / (wf + hf)}1/2 (Sfgs)1.2 ; Kf = 1.0

7.4.1.5 Wg = Same as in para 6.6.5

7.4.2 Wpwr

7.4.2.1 We from para 7.1.5

7.4.2.2 Wai = 0.32 (Ninl) (Ld) (Ainl)0.65 (P2)0.6 +

1.735 {(Ld) + (Ninl) (Ainl)0.5 (P2) Kd) (Km)}0.7331

where Kd = 1.33 for flat section ducts

= 1.0 for curved section ducts

Km = 1.0 for MD < 1.4

= 1.5, for MD > 1.4

Ld = Length of duct (in ft)

P2 = Maximum static pressure at engine compressor

face (in psi) (generally 15 to 50 psi)

7.4.2.3 Wfs = 41.6 {(WF / KfSP) / 100}0.818 + Wsupp

Where Wsupp = Weight of bladder support structure

= 7.91 {(WF / Kfsp) / 100}0.854

24

7.4.3 Wfeq

7.4.3.1 Wfc = 23.38 {(WF / Kfsp)/100}0.442

where WF = mission fuel weight (in lb)

Kfsp= 6.55 lbs / gal, for JP-4

7.4.3.2. Wels = 426 {(Wfs + Wiae ) / 1000 }0.51

7.4.3.3 Wiae = 0.575 (WE)0.556 (R)0.25

7.4.3.4 Wapi = 202 {(Wiae + 200 Ncr) / 1000}0.735

7.4.3.5 Warm : Refer Tables A 9.1 (a) and A 9.2 (a) of Ref.1

7.4.3.6 Wfur = 22.9 (Ncr Dq /100)0.743 + 107 (Ncr WTO / 10000)0.585

7.4.3.7 Wox = 16.9 (Ncr)1.494

7.4.3.8 Wauxgear Refer para 7.4.3.5 above

7.5 Input Data

Wgross =61,660 lbs; nult = 11.0 S =787 ft2

VD = 563 kts; Dq = 1072 psf; nutt = 7.33

A = 6 Kw = 1.0 = 0.5

LE = 3.5o; (t/c)m = 0.1 MH = 0.68

c = 11.9 ft ; Sh = 93 ft2 ; bh = 18.3 ft

trh = 0.51 ft; lh = 32.3 ft ; Sv = 147 ft2

zh / bv = 1.0; lv = 26 ft ; Sr / Sv = 147 ft2

v = 0.55; Av = 1.2 ; 1/4v = 41o

25

Kinl = 1.25 ; for fuselage: lf = 41.3 ft ; hf = 6.83 ft

for tail booms: lf = 33.3 ft ; wf + hf = 3.06 ft; Sfgs = 2 x 30.6 = 61.2 ft2

Nose Gear Ag = 12; Bg = 0.06; Cg = 0; Dg = 0

Main Gear Ag = 33; Bg = 0.04; Cg = 0.01; Dg = 0

Ninl = 2; Ld = 8ft; Ainl = 6.3 ft2

P2 = 30 psi ; Kd = 1.0 ; Km = 1.0 (see para 7.4.2)

7.6 Weight computation

7.6.1 Ww = 9490 lb

7.6.2 Wemp = 720 + 930 = 1658 lb

7.6.3 Wf = 5044 lb Wstruct = 18646 lb

7.6.4 Wtail brom = 458 lb ( 30.24% of Wgrass )

7.6.5 Wg = 1996 lb

7.6.6 We = 4000 lb

7.6.7 Wafter bumer = 2000 lb

7.6.8 Wai = 445 lb WPwr = 7300 lb

7.6.9 Wfs = 777 lb ( 11.84% of Wgrass)

7.6.10 Wp = 78 lb

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7.6.11 Wfc = 1513 lb

7.6.12 Wels = 703 lb

7.6.13 Wapi = 347 lb

7.6.14 Wiae = 1033 lb Wfeq = 5017 lb

7.6.15 Warm = 913 lb ( 8.14 % of Wgrass)

7.6.16 Wfur = 214 lb

7.6.17 Wox = 17 lb

7.6.18 Waux-gear = 277 lb

WE =18646+7300+5017= 30963 ( 50.22% of Wgrass)

Reference:

1. Roskam, J Airplane design Vol. V- component weight estimation Roskam aviation

and Engg. Corp. Ottawa, Kansas 1989.

27

List of symbols

Symbol Definition Dimension

A Wing aspect ratio -----

Ah,v,c Hor.tail, Vert. Tail or Canard aspect ratio ------

Ainl Inlet capture area per inlet ft2

b Wing span ft

bh,v,c Hor.tail,Vert. Tail or Canard span ft

c Wing mean geometric chord ft

c h,v,c Mean geometric chord hor.tail, vert.tail or canard ft

Dp Propeller diameter ft

hf Maximum fuselage height ft

lf Length of fuselage ft

lh,v,c Distance from wing 1/4c to 1/4ch,v,c ft

lsm or n Shock strut length for main gear or for nose gear ft

Ld Inlet duct length ft

M Mach number

N Load factor -------

N Number of (see subscript) -------

28

PTO Required take-off power hp

P2 Maximum static pressure at engine compressor face psi

q Dynamic pressure psf

R Range nm or m

S Wing area ft2

Sfgs Fuselage gross shell area ft2

Sh,v,c Hor, Vert. or canard area ft2

Sr Rudder area ft2

t/c Thickness ratio -------

tr Maximum root thickness ft

T Thrust lbs

VC Design cruise speed KEAS

VD Design dive speed KEAS

VH Maximum level speed at sea level KEAS

Vpax Volume of passenger cabin ft3

Vpax+cargo Volume of .passenger and cargo compartment ft3

wf Maximum fuselage width ft

W Weight lbs

Wi Weight of component i lbs

29

zh Distance from vert.tail root to where h.t. is mounted on

the v.t.

ft

Greek symbols

Wing taper ratio --------

h,v,c Taper ratio for hor. tail, vert. tail or canard --------

n Sweep angle at nth chord station

Subscripts

ai Air induction

api Air conditioning, pressurization, de-icing and anti-icing

system

apu Auxiliary power unit

arm Armament

aux Auxiliary

bc Baggage and cargo handling equipment

bl Blades

c Canard

cc Cabin crew

cg Centre of gravity

crew or cr Crew

30

C Cruise

D Dive

e Engines (all)

ec Engine controls

els Electrical system

emp empennage

ess Engine starting system

E Empty

f Fuselage

fc Flight control system

feq Fixed equipment

fs Fuel system

fur Furnishings

F Mission fuel

g Landing gear

glw Guns, launchers and weapons provisions

h Horizontal tail

hps Hydraulic and pneumatic system

H Maximum level flight at sea level instrumentation

31

i Instrumentation

iae Instrumentation , avionics and electronics

inl Inlet (s)

lim Limit

L Landing (subscript to W)

LE Leading edge

m Maximum

MZF Maximum zero fuel

n Nacelle

ops Operational items

ox Oxygen system

pax Passengers

p Propellers (subscript to N) or Propulsion system

(subscript to W)

prop Propeller controls

pt Paint

pwr Powerplant

PL Payload

struct Structure

32

t Fuel tanks

tfo Trapped fuel and oil

thr.rev Thrust reverser system

TO Take-off

ult Ultimate

ult.l. Ultimate landing

v Vertical tail

w Wing

Acronyms

APU Axillary power unit

C.G., c.g. Centre of gravity

OWE Operating weight empty

SHP shaft horse power

TBP Turboprop

1.Introduction2.Major Groupings of airplane weight3.Weight equation method- Development and procedures for evaluation of component weights4.Twin engine propeller driven airplane-componentweight determination5.Jet transport-Component weight determination6.Test examples: Weight-components for B-737-200 (Jet transport Aircraft)7.Fighte-Component weight computation List of symbols