INITIAL SIZING Estimation of Design Gross Weight Prof. Rajkumar S. - - PowerPoint PPT Presentation

INITIAL SIZING Estimation of Design Gross Weight

• Prof. Rajkumar S. Pant

Aerospace 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 PROFILE

Vary with the purpose of the aircraft

Mission Profiles

Mission profile  purpose of the aircraft General Aviation Aircraft

• Simple Cruise + Hold

Commercial Transport Aircraft

• Main Profile + Missed Approach + Diversion + Hold

AE-332M / 714 Aircraft Design Capsule-3

Mission Profile: Simple Cruise

Warm up, Taxi-out, Take Off Cruise Loiter 1 2 3 4 5 5 6 7 Landing, Taxi-in Approach

AE-332M / 714 Aircraft Design Capsule-3

Mission Profile: Air Superiority Aircraft

Warm up, Taxi-out, Take Off Combat Landing, Taxi-in Loiter

1 2 3 4 5 5 6 7

Cruise 1 Cruise 2 Loiter Weapon Drop

8 9

Approach

AE-332M / 714 Aircraft Design Capsule-3

Mission Profile: Ground Attack Fighter

Warm up, Taxi-out, Take Off Combat Landing, Taxi-in Loiter

1 2 3 4 5 5 6 7

Cruise 1 Cruise 2

Loiter

Weapon Drop

8 9

Approach

AE-332M / 714 Aircraft Design Capsule-3

Mission Profile: Strategic Bomber

Warm up, Taxi-out, Take Off Combat Landing, Taxi-in Loiter

1 2 3 4 5 6 7 8

Cruise 1 Cruise 3 Weapon Drop

9 10 12 11 * R: Re-Fuelling

Approach

AE-332M / 714 Aircraft Design Capsule-3

Mission Profile: UAV

Predator (Tier II) Mission Profile

AE-332M / 714 Aircraft Design Capsule-3

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 20 5 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

empty fuel pay crew

• W

W W W W + + + =

      + − + =

• fuel
• empty

pay crew

• W

W W W W W W 1

{ }

f e pay crew

• w

w W W W ˆ ˆ 1 + − + =

are the two unknowns to be determined

ˆ ˆ &

e f

w w

ώe = A Wo

C * Kvs

 Where “A” and “C” are constants  Their values for various aircraft types are

• btained 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

Empty Weight Fraction Trends

Empty Weight Fraction Trends

AE-332M / 714 Aircraft Design Capsule-3

y = 0.5598x 40000 50000 60000 70000 80000 90000 100000 110000 120000 130000 140000 80000 100000 120000 140000 160000 180000 200000 220000 240000

Wempty - Empty Weight (lbs) WTO - Maximum Takeoff Weight (lbs)

Weight Trend Data - Single Aisle Jet Transport From 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

1 1 2 2 3 3 4 4 5 5 6 6

W W W W W W W W W W W W W W ⋅ ⋅ ⋅ ⋅ ⋅ =

97 . 985 . . 1 995 .

2 3 4 5 6

⋅ ⋅ ⋅ ⋅ ⋅ = W W W W W W

2 3 4 5 6

95067 . W W W W W W ⋅ ⋅ =

Mission Profile

AE-332M / 714 Aircraft Design Capsule-3

ESTIMATION OF FUEL WEIGHT FRACTION

Using mission profile and historical data for engines !

AE-332M / 714 Aircraft Design Capsule-3

Breguet Range Equation

dt T tsfc dW × × − =

Fuel Consumption:

( )T

tsfc dW V dt V ds

∞ ∞

− = =

Range for dW fuel

L W D T = = ,

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

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

∞

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

AE-332M / 714 Aircraft Design Capsule-3

Breguet Range Equation

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

final initial

W W D L M tsfc a R ln       =

a is sound speed Engine efficiency (fuel consumption) Aerodynamic efficiency Structural efficiency Winitial = MTOW (Maximum Takeoff Weight) Wfinal = OEW + Pax + reserve fuel OEW = Operational Empty Weight = Empty Weight + Crew + trapped fuel & Oil

Fuel Fraction in Cruise segment

 Cruise segment mission weight fraction can be

estimated using the Breguet Range Equation

1

ln

cruise i cruise cruise i

V W L R c 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 segment

 Loiter segment mission weight fraction can be

estimated using the Breguet Endurance Equation

1

1 ln

i loiter loiter i

W L E c 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

AE-332M / 714 Aircraft Design Capsule-3

ESTIMATION OF MAX L/D

Mostly using historical data !