ae332 initial sizing

INITIAL SIZINGEstimation of Design Gross Weight

Prof. Rajkumar S. PantAerospace Engineering Department

IIT Bombay

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

What is Initial Sizing ?

AE-332M / 714 Aircraft Design Capsule-3

MISSION PROFILEVary with the purpose of the aircraft

Mission ProfilesMission profile purpose of the aircraftGeneral Aviation Aircraft Simple Cruise + Hold

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


Mission Profile: Simple Cruise

Warm up, Taxi-out, Take Off

Cruise

Loiter

1 2

3 4

5

5

6 7

Landing, Taxi-in

Approach


Mission Profile: Air Superiority Aircraft

Warm up, Taxi-out, Take Off

Combat

Landing, Taxi-in

Loiter

1 2

3 4

5 5

67

Cruise 1

Cruise 2

LoiterWeapon Drop 8 9

Approach


Mission Profile: Ground Attack Fighter

Warm up, Taxi-out,Take Off

Combat

Landing, Taxi-in

Loiter

1 2

3 4

5 5

6 7Cruise 1

Cruise 2

Loiter

Weapon Drop

8 9Approach


Mission Profile: Strategic Bomber

Warm up, Taxi-out,Take Off

Combat

Landing,Taxi-in

Loiter

1 2

3 45 6

7 8

Cruise 1

Cruise 3

Weapon Drop

910

1211

* R: Re-Fuelling

Approach


Mission Profile: UAV

Predator (Tier II) Mission Profile

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)

Issues in Initial Sizing

50

25

205

25

Empty weight Payload Usable Fuel Trapped Fuel

Typical Take-off weight break-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

Take-off weight build-up

Equation for Initial Sizing

emptyfuelpaycrewo WWWWW +++=

+−

+=

o

fuel

o

empty

paycrewo

WW

WW

WWW

1

{ }fe

paycrewo ww

WWW

ˆˆ1 +−

+=

are the two unknowns to be determinedˆ ˆ&e fw w


ESTIMATION OF EMPTY WEIGHT FRACTION

Mostly using historical data !

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

Estimation of empty weight fraction ώe

A/C type A C Sailplane (unpowered) 0.83 -0.05 Sailplane (powered) 0.88 -0.05 Homebuilt-metal/wood 1.11 -0.09 Home-built composite 1.07 -0.09 General Aviation-1 Engine 2.05 -0.18 General Aviation-2 Engine 1.40 -0.10 Agricultural a/c 0.72 -0.03 Twin turboprop 0.92 -0.05 Flying Boat 1.05 -0.05 Jet trainer 1.47 -0.10 Jet fighter 2.11 -0.13 Military cargo 0.88 -0.07 Jet transport 0.97 -0.06

“A” and “C” for various a/c types

Note: Wo in kg


TYPE A CUAV- Recce and UCAV 1.53 -0.16UAV- High Altitude 2.48 -0.18UAV- Small 0.86 -0.06

ώe = A WoC * Kvs

UAV Weight Fractions

Source: Table 3.1, pg. 31, Raymer, 5th edition

Empty Weight Fraction Trends


y = 0.5598x

40000

50000

60000

70000

80000

90000

100000

110000

120000

130000

140000

80000 100000 120000 140000 160000 180000 200000 220000 240000

Wem

pty

-Em

pty

Wei

ght (

lbs)

WTO - Maximum Takeoff Weight (lbs)

Weight Trend Data - Single Aisle Jet TransportFrom The Elements of Airplane Design, Schaufele.

Bae 146-100

DC-9-10

BAC-111

BAE 146-200

F100

BAE 146-300

DC-9-30

737-200

DC-9-40

DC-9-50

717-200

737-300

737-400

MD-81

737-600

737-700

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 fuel fraction ώf

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

0

1

1

2

2

3

3

4

4

5

5

6

0

6

WW

WW

WW

WW

WW

WW

WW

⋅⋅⋅⋅⋅=

97.0985.00.1995.02

3

4

5

0

6 ⋅⋅⋅⋅⋅=WW

WW

WW

2

3

4

5

0

6 95067.0WW

WW

WW

⋅⋅=

Mission Profile


ESTIMATION OF FUEL WEIGHT FRACTION

Using mission profile and historical data for engines !


Breguet Range Equation

dtTtsfcdW ××−=Fuel Consumption:

( )TtsfcdWVdtVds ∞

∞ −==Range for dW fuel

LWDT == ,During Cruise

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

WdW

DL

tsfcVds

−= ∞Hence:

Assuming L/D, tsfc and V∞ (= aM) are constant:


Breguet Range Equation

Source: Jet Sense; The Philosophy and the Art of Aircraft Design, Zarir D. Pastakia

final

initial

WW

DLM

tsfcaR ln

=

a is sound speed

Engine efficiency (fuel consumption)

Aerodynamic efficiency

Structural efficiency

Winitial = MTOW (Maximum Takeoff Weight)Wfinal = OEW + Pax + reserve fuelOEW = Operational Empty Weight = Empty Weight + Crew + trapped fuel & Oil

Fuel Fraction in Cruise segmentCruise segment mission weight fraction can be

estimated using the Breguet Range Equation

1lncruise i

cruisecruise i

V WLRc D W

− = ⋅ ⋅ R = Cruise Range (m)ccruise = Specific Fuel consumption in cruise (per sec) Vcruise = Cruise Velocity (m/s)[L/D]cruise = 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 segmentLoiter segment mission weight fraction can be

estimated using the Breguet Endurance Equation

11 ln i

loiterloiter i

WLEc D W

− = ⋅ ⋅ E = Endurance (sec)cloiter = Specific Fuel consumption in Loiter (per sec) [L/D]loiter = 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


ESTIMATION OF MAX L/DMostly using historical data !

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

configuration is not yet finalized !!

Thumb RuleFor 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/cCessna 310 13.0Beech Bonanza 13.8Cessna Cardinal 14.2

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

Drivers of subsonic L/D

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

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

20


ESTIMATION OF ENGINE PARAMETERS

Again using historical data !

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

SFC trends for various engine types

Typical SFC values (SI system)


For a 2020 Airplane consider TSFC ~ 0.47-0.5

y = -0.00428x + 9.099R² = 0.835

0.5

0.52

0.54

0.56

0.58

0.6

0.62

0.64

0.66

1970 1975 1980 1985 1990 1995 2000

Cru

ise

TSFC

lb/

(lbf·h

)

Year

Historical TSFC Trend for Turbofan Engines

Series1Linear (Series1)


0

0.2

0.4

0.6

0.8

1

1.2

0 4 8 12 16

Inst

alle

d sf

c (lb

/hr/l

b)

Bypass Ratio

Trend Data for Cruise sfc: Jet Aircraft

HeavierBigger Landing Gear

ηp and SFC for Propeller Driven a/c

Aircraft Type ηp c lb/(SHP-hr)

Personal / Utility 0.80 0.60

Commuter 0.82 0.55Regional Turboprop 0.85 0.50

Concept of Equivalent Jet SFCBreguet Range & Endurance equations for

Turbo/Pistonprop a/c are very messy !!Equivalent jet SFC for Turbo/Pistonprop enginesCpower = 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 !

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 RFF = Reserve Fuel Fraction

o = 0.06 to 0.1 for commercial transport aircraft

Estimation of mission fuel fraction

Design Gross Weight Estimation

( )

−++⋅−

+=

0

111WWRFFWA

WWW

xCo

paycrewo

{ }fe

paycrewo ww

WWW

ˆˆ1 +−

+=

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


EXAMPLE OF SIZINGMedium Range Jet Transport Aircraft


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

Requirements


Mission Profile


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

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

Reserve Fuel Fraction = 10%

Assumptions


S O L V E !!

ae332 initial sizing

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