Classical Aircraft Sizing

Note: books on reserve in the Architecture Library: see Schetz or, following Nicolai, With a given TOGW, subtract the fuel and payload... or see Raymer, Torenbeek, Nicolai, Roskam, etc..

Which is 1st

Taken together, the answers to these questions are

known as the Mission Statement, and also

Possible Values

W TO= W fixed

1 − 75

( )= 4 ⋅ W fixed

or: = 1 − W struc

W TO +

W prop

W TO +

W fuel

W TO















 W TO = W fixed

⇒ W TO = W fixed

1 − W struc

W TO +

W prop

W TO +

W fuel

W TO

















TOGW = W TO = W struc + W prop + W fuel + W payload + W systems

W fixed

= W TO W struc

W TO +

W prop

W TO +

W fuel

W TO







 + W fixed

≈ 0.29 ≈ 0.15 ≈ 0.31

fuel + W fixed +W

empty

fixed:

Note: books on reserve in the Architecture Library: see Schetz

or, following Nicolai, With a given TOGW, subtract the fuel and payload Is the weight left enough to

WEmptyReqd = KS x A x TOGW B

10,000 100,000 1,000,000

W empty, lbs

TOGW, lbs

source: Roskam Table 2.14 in Vol 1

€

W empty = 0.500⋅TOGW0.9876

F-111A

B-58 Study Biz Jet

Study Supercruise Fighter

Boeing SST

Concorde B-1B

To Get WEmptyAvail

R R

Mission Phase Definitions

1-2

2-3

3-4

4-5

7-8

• You need detailed propulsion data (and aerodynamics),

R i+1= V

sfc

L D





 



 ln W i

W i+1

E = 1 sfc

L D





 



 ln W i

W i+1

W i+1

W i = e

− R⋅sfc

V ( L/ D)

W i+1

W i = e

−E⋅sfc

( L/ D)

(or see Raymer, Torenbeek, Nicolai, Roskam, etc for

Speed and Altitude: Review of Best Range

(consider specific range, SR)

based on a figure in Shevell, Fundamentals of Flight

0.00

0.10

0.20

0.30

SR

nm/lb

Mach number

40 30

20

Altitude, 1000 ft

0.00 0.10 0.20 0.30

SR at 20K

SR at 40K

SR nm/lb

Mach number

40 30 20 Altitude, 1000 ft

˙

ψ =g n

2

− 1

Time = (no of turns)(360 °) / ˙ ψ ,(in degrees per sec)

and page 582, eqns 19.8 and 19.9

–  where Δ is a relaxation factor to speed

convergence (2 for the examples)

WEmptyReqd − WEmptyAvail < ε

W TO j+1 = W TO j + Δ WEmpty Re qd − WEmptyAvail( )

At 1

W EmptyAvail = W TO − W fuel − W fixed

W final

W final

W TO =

W8

W1 =

W2

W1

W3

W2

W4

W3 ⋅⋅⋅

W8

W7

fuel fraction for each segment (must include a step change

if you drop something)

W fuel = 1 +

W reserve

fuel

W TO +

W trapped

fuel

W TO















 1 −W8

W1







W TO

= 1 +

W reserve

fuel

W TO +

W trapped

fuel

W TO















(W TO − W Landing)

ignores any other weight loss during mission

•  Originally we had an implementation of this scheme in QuickBASIC(still available on the

•  We also have acsweep.QB It computes lines of

WemptyReqd and WemptyAvail

•  Now a REALbasic code (Mac counterpart of

Comparison of Required and Available Weights

6000

7000

8000

9000

10000

11000

12000

10000 11000 12000 13000 14000 15000 16000 17000 18000

WEmpty

TOGW

Radius = 250 nm

Wfixed = 1500 lb.

WemptyReqd

WemptyAvail

Solution for TOGW for the Lightweight Fighter

acsize.QB acsweep.QB makes curves

Sensitivity of TOGW to Change in Payload,

14000

15000

16000

17000

18000

19000

20000

TOGW, lb

Fixed Weight, lb Baseline

Radius = 250 nm

ΔWpay carried out and back

ΔWpay dropped during combat

ΔWpay

Note: TOGW increases by 3.8 pounds for each pound of addtional payload

14000

16000

18000

20000

TOGW, lb

Radius, nm

Wfixed = 1500 lb.

Valid assessment of technology

or multidisciplinary optimization

requires keeping the range fixed

Effect of Range Requirement on Weights

• range = 10,000nm: appears solution would converge

Note: Nicolai, in Fundamentals of Aircraft Design,

2.8 10 5

3.0 10 5

3.2 10 5

3.4 10 5

3.6 10 5

3.8 10 5

4.0 10 5

WEmpty

6.5 10 5 7.0 10 5 7.5 10 5 8.0 10 5 8.5 10 5 9.0 10 5 9.5 10 5

TOGW

WEmptyReqd

WEmptyAvail

100,000 lb payload

Sizing Solution

0.0 100

5.0 105

1.0 106

1.5 106

2.0 106

0.0 100 1.0 106

WEmpty

Sizing Solution

Required and Available Curves slopes start

to be parallel, small errors lead to large

errors in TOGW

note scale!

TOGW

100,000 lb payload

WEmptyReqd

WEmptyAvail

0.0 10 0

5.0 10 5

1.0 10 6

1.5 10 6

2.0 106

WEmpty

WEmptyReqd

WEmptyAvail

Converged solution may occur

at TOGW approaching infinity!

TOGW 100,000 lb payload

0.0 100

5.0 105

1.0 106

1.5 106

2.0 106

WEmpty

WEmptyReqd WEmptyAvail

No solution for this technology level at any size

TOGW 100,000 lb payload

for a specified technology level

the range cannot be increased without limit

1.0 10 6

1.5 10 6

2.0 10 6

2.5 10 6

3.0 10 6

3.5 10 6

4.0 10 6

4.5 10 6

5.0 10 6

Takeoff

Gross

Weight

range, nm

L/D = 21 sfc = 55

KS = 85

M = 77 Payload = 600,000 lb

Using Idealized (Optimistic) Single Segment Analysis

You can investigate how the key technology

–  Ks

•  This method is the 1st cut back of the envelope

•  Note: The example codes available on the software

•  Your skill: Develop confidence by “predicting” the

•  Next sizing class will look at sizing a little more

–  Constraints on takeoff and landing, etc