AE332 Initial Sizing

INITIAL SIZING Estimation of Design Gross Weight

Prof. Rajkumar S. Pant Aerospace Engineering Department IIT Bombay

What is Initial Sizing ? 

Estimation of its design take-off gross weight Wo  Weight at the start of the design mission profile



Mission Profile specified by the user



Additional Requirements by Regulatory Bodies



Objectives  Identify requirements that are likely to drive the design  First estimate of the size of the aircraft, through Wo

Vary with the purpose of the aircraft

MISSION PROFILE

AE-332M / 714 Aircraft Design

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Mission Profiles  Mission profile  purpose of the aircraft  General Aviation Aircraft  Simple Cruise + Hold

 Commercial Transport Aircraft  Main Profile + Missed Approach + Diversion + Hold

Mission Profile: Simple Cruise Cruise 3

4 5

1

2

Warm up, Taxi-out, Take Off


Loiter 5 Approach 6

7

Landing, Taxi-in

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Mission Profile: Air Superiority Aircraft Cruise 2

7 Cruise 1

4

3 5 1

2



6 Combat

Loiter

5

Loiter Weapon Drop

Approach

8

9

Landing, Taxi-in

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Mission Profile: Ground Attack Fighter Cruise 2

6

Cruise 1

3

4

7

Loiter

Loiter Combat Approach

1

2



5

5 Weapon Drop

8

9

Landing, Taxi-in

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Mission Profile: Strategic Bomber Cruise 3

9

Cruise 1

3

Loiter

4 5

6 Combat

1

10

2


7

Approach

8 Weapon Drop

11

12

Landing, Taxi-in

* R: Re-Fuelling AE-332M / 714 Aircraft Design

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Mission Profile: UAV

Predator (Tier II) Mission Profile AE-332M / 714 Aircraft Design

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Issues in Initial Sizing 

Very little known about a/c configuration



Most methods are deeply rooted in past  Statistical inference of parameters  Similar aircraft designed earlier

 

Most procedures empirical / semi-empirical Various methodologies / approaches, e.g.,  Loftin’s method  Raymer’s approach (explained here)

Typical Take-off weight break-up Empty weight

Payload

Usable Fuel

Trapped Fuel

25

25

50

20 5

Take-off weight build-up  

Wo = Wcrew + Wpay + Wfuel + Wempty Wempty  Weight of structure, engines, landing gear, fixed

equipment, avionics, etc. 

Wcrew and Wpay are both known  User-specified requirements



Wfuel & Wempty are unknowns to be determined

Equation for Initial Sizing

Wo = Wcrew + W pay + W fuel + Wempty Wcrew + W pay Wo = Wempty W fuel  + 1−   Wo   Wo

Wcrew + W pay Wo = 1 − {wˆ e + wˆ f } wˆ e & wˆ f

are the two unknowns to be determined

Mostly using historical data !

ESTIMATION OF EMPTY WEIGHT FRACTION AE-332M / 714 Aircraft Design

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Estimation of empty weight fraction ώe ώe = A WoC * Kvs 

Where “A” and “C” are constants



Their values for various aircraft types are obtained from statistical curve-fits



Kvs is a factor depending on the a/c sweep  Kvs = 1.00 for conventional, fixed-wing  Kvs = 1.04 for wing with variable sweep

“A” and “C” for various a/c types             

A/C type

A

Sailplane (unpowered) Sailplane (powered) Homebuilt-metal/wood Home-built composite General Aviation-1 Engine General Aviation-2 Engine Agricultural a/c Twin turboprop Flying Boat Jet trainer Jet fighter Military cargo Jet transport

0.83 0.88 1.11 1.07 2.05 1.40 0.72 0.92 1.05 1.47 2.11 0.88 0.97

Note: Wo in kg

C -0.05 -0.05 -0.09 -0.09 -0.18 -0.10 -0.03 -0.05 -0.05 -0.10 -0.13 -0.07 -0.06

UAV Weight Fractions TYPE UAV- Recce and UCAV UAV- High Altitude UAV- Small

A 1.53 2.48 0.86

C -0.16 -0.18 -0.06

ώe = A WoC * Kvs Source: Table 3.1, pg. 31, Raymer, 5th edition AE-332M / 714 Aircraft Design

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Empty Weight Fraction Trends

Empty Weight Fraction Trends

Weight Trend Data - Single Aisle Jet Transport From The Elements of Airplane Design, Schaufele. 140000

Bae 146-100 DC-9-10

130000

BAC-111

Wempty - Empty Weight (lbs)

120000

BAE 146-200 y = 0.5598x F100

110000 BAE 146-300 DC-9-30

100000

737-200 90000

DC-9-40 DC-9-50

80000

717-200 70000

737-300 737-400

60000

MD-81 50000 40000 80000

737-600 737-700 100000

120000

140000

160000

180000

200000

220000

240000

WTO - Maximum Takeoff Weight (lbs) AE-332M / 714 Aircraft Design

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Estimation of mission fuel fraction ώf  

Wfuel = Wmission fuel + W reserve fuel Wmission fuel depends on  Type of mission  Aircraft aerodynamics  Engine SFC



Wreserve is required for  Missed Approach, Diversion & Hold  Navigational errors and Route weather effects  Trapped Fuel (nearly 0.5% to 1 % of total fuel)



Assumption  Fuel used in each mission segment is proportional to a/c weight

during mission segment  Hence

ώf is independent of the aircraft weight

Estimation of Mission Segment Weights  Various segments or legs are numbered, with ‘0’ denoting the

mission start  Mission segment weight fraction for ith segment = Wi/Wi-1  Total fuel weight fraction (W6/W0) obtained by multiplying the weight fractions of each mission segments

Estimation of Mission Segment Weights  The warm-up, take-off, and landing weight

fraction estimated by historical trends  Fuel consumed (and distance traveled) during

all descent segments ignored

Weight fractions in Climb and Acceleration

Effect of using historical data Mission Profile

W6 W6 W5 W4 W3 W2 W1 = ⋅ ⋅ ⋅ ⋅ ⋅ W0 W5 W4 W3 W2 W1 W0

W6 W5 W3 = 0.995 ⋅ ⋅1.0 ⋅ ⋅ 0.985 ⋅ 0.97 W0 W4 W2

W6 W W = 0.95067 ⋅ 5 ⋅ 3 W0 W4 W2

Using mission profile and historical data for engines !

ESTIMATION OF FUEL WEIGHT FRACTION AE-332M / 714 Aircraft Design

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Breguet Range Equation Fuel Consumption:

dW = −tsfc × T × dt

Range for dW fuel

V∞ dW ds = V∞ dt = − (tsfc )T

During Cruise

T = D, W = L

Drag changes due to changing lift: assume L/D is constant,

Hence:

 V∞  L  dW   ds = −  tsfc  D  W

Assuming L/D, tsfc and V∞ (= aM) are constant: AE-332M / 714 Aircraft Design

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Breguet Range Equation

a  L  Winitial R=  M  ln tsfc  D  W final Engine efficiency (fuel consumption)

Aerodynamic efficiency

Structural efficiency

a is sound speed Winitial = MTOW (Maximum Takeoff Weight) Wfinal = OEW + Pax + reserve fuel OEW = Operational Empty Weight = Empty Weight + Crew + trapped fuel & Oil Source: Jet Sense; The Philosophy and the Art of Aircraft Design, Zarir D. Pastakia AE-332M / 714 Aircraft Design

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Fuel Fraction in Cruise segment  Cruise segment mission weight fraction can be

estimated using the Breguet Range Equation

Vcruise R= ccruise R ccruise Vcruise [L/D]cruise

Wi −1  L ⋅  ⋅ ln    D  cruise  Wi 

= Cruise Range (m) = Specific Fuel consumption in cruise (per sec) = Cruise Velocity (m/s) = Optimum lift to drag ratio during cruise = [L/D]max for Propeller driven a/c = 0.866*[L/D]max for Jet engined a/c

Fuel Fraction in Loiter segment  Loiter segment mission weight fraction can be

estimated using the Breguet Endurance Equation

1 E= cloiter E cloiter [L/D]loiter

Wi −1  L ⋅  ⋅ ln    D  loiter  Wi 

= Endurance (sec) = Specific Fuel consumption in Loiter (per sec) = Optimum lift to drag ratio during loiter = 0.866 [L/D]max for Propeller driven a/c = [L/D]max for Jet engined a/c

WE WERE HERE ON 26 AUG


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Mostly using historical data !

ESTIMATION OF MAX L/D


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Estimation of [L/D]max  Accurate value is not available since the aircraft

configuration is not yet finalized !!  Thumb Rule For 7 ≤ ARwing ≤ 11, [L/D]max = 2 * ARwing

Approx. values of Cruise L/D max

[L/D]max values for 4-6 seater Piston/Turboprop a/c Cessna 310 13.0 Beech Bonanza 13.8 Cessna Cardinal 14.2

Drivers of subsonic L/D   

Configuration dependent In level flight, L = W; L/D depends on D Two main components of subsonic D  Parasite or “Zero Lift”  f(wetted area)  Induced or “lift dependent”:  f(wing span)



Concept of wetted aspect ratio  ARwet = b2/Swet  ARwet is a better indicator of max. L/D



Proof: B-47 v/s Vulcan

Different shapes, same Max. L/D

Source: Raymer,D., Aircraft Design, A Conceptual Approach, 2nd ed., pp 20 , AIAA Education Series, 1989

Wetted area ratios for some configurations

Source: Raymer,D., Aircraft Design, A Conceptual Approach, 2nd ed., pp 21, AIAA Education Series, 1989

Max. L/D v/s ARwet

Source: Raymer,D., Aircraft Design, A Conceptual Approach, 2nd ed., pp 22, AIAA Education Series, 1989

Historical Trends in Max L/D 20

From: The Historical Fuel Efficiency Characteristics of Regional Aircraft from Technological, Operational, and Cost Perspectives, R. Babikian, S. Lukachko and I. Waitz, http://web.mit.edu/aeroastro/people/waitz/publications/Babikian.pdf


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Again using historical data !

ESTIMATION OF ENGINE PARAMETERS AE-332M / 714 Aircraft Design

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SFC trends for various engine types 

Jet Engine TSFC = fuel mass flow rate per unit thrust  units = mg/N-s or lb/lb-hr



Propeller engine PSFC = fuel mass flow rate per unit power  units = mg/W-s or lb/SHP-hr

Typical SFC values (SI system)

Historical TSFC Trend for Turbofan Engines 0.66 y = -0.00428x + 9.099 R² = 0.835

Cruise TSFC lb/(lbf·h)

0.64 0.62 0.6 0.58

Series1 Linear (Series1)

0.56 0.54 0.52 0.5 1970

1975

1980

1985

1990

1995

2000

Year

For a 2020 Airplane consider TSFC ~ 0.47-0.5 AE-332M / 714 Aircraft Design

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Trend Data for Cruise sfc: Jet Aircraft

1.2

Installed sfc (lb/hr/lb)

1

0.8 Heavier Bigger Landing Gear

0.6

0.4

0.2

0 0

4

8

12

16

Bypass Ratio AE-332M / 714 Aircraft Design

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ηp and SFC for Propeller Driven a/c Aircraft Type

ηp

c lb/(SHP-hr)

Personal / Utility

0.80

0.60

Commuter Regional Turboprop

0.82 0.85

0.55 0.50

Concept of Equivalent Jet SFC  Breguet Range & Endurance equations for

Turbo/Pistonprop a/c are very messy !!  Equivalent jet SFC for Turbo/Pistonprop engines  Cpower = Fuel Flow rate/Power  = Fuel Flow rate/{TV/ηp }  = [Fuel Flow rate/T] {ηp/V}  = [Cjet]. ηp/V  Thus, Cjet = CpowerV/ηp  Thus by using Cjet in Brequet Equations, we can use them also for Turbo/Pistonprop a/c also !

Estimation of mission fuel fraction 

Segment Weight fractions estimated using the Brequet equations for Cruise and Loiter segments, and historical values for others



Total fuel fraction estimated as  Wf/Wo= ώf = (1 + RFF)*(1 - Wx/Wo) o o

RFF = Reserve Fuel Fraction = 0.06 to 0.1 for commercial transport aircraft

Design Gross Weight Estimation

Wcrew + W pay Wo = 1 − {wˆ e + wˆ f } Wo =

Wcrew + W pay   Wx   C 1 −  A ⋅ Wo + (1 + RFF )1 −    W0   

Steps in Wo estimation  Assume starting value of Wo (say, 4 times Wpay)  Estimate ώe = A WoC * Kvs  Estimate segment weight fractions, using  Historical Data  Breguet Range and Endurance formulae

 Estimate ώf = (1 + RFF)*(1 - Wx/Wo)  Calculate Wo = {Wcrew + Wpay}/{1- ώe – ώf}  Iterate till convergence

Medium Range Jet Transport Aircraft

EXAMPLE OF SIZING


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Requirements  



     

Payload: 150 pax at 175 lb & 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 Climb: direct climb to 35,000 ft at max WTO Climb rate of 2500 ft/min at a speed at 275 kt Take-off & landing: FAR 25 field-length of 5,000 ft Assume ISA deg oC atmosphere


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Mission Profile


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Assumptions

   

ώe = 0.97 Wo-0.06 (W0 in kg) ώe = 1.02 Wo-0.06 (W0 in lb) Max(L/D) = 16 Cruise:  cj = 0.5 lb/hr/lb



Loiter  cj = 0.55 lb/hr/lb

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Diversion  Cruise speed of 250 kts (FAR 25)  L/D of 10 and cj = 0.9 lb/hr/lb

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Reserve Fuel Fraction = 10%


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S O L V E !!


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AE332 Initial Sizing

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