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 Capsule-3 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 Loiter 5 Approach 1 2 6 7 Warm up, Taxi-out, Landing, Taxi-in Take Off AE-332M / 714 Aircraft Design Capsule-3 Mission Profile: Air Superiority Aircraft Cruise 2 7 Cruise 1 6 4 3 Combat Loiter 5 5 Approach Loiter 1 2 Weapon Drop 8 9 Warm up, Taxi-out, Take Landing, Taxi-in Off AE-332M / 714 Aircraft Design Capsule-3 Mission Profile: Ground Attack Fighter Cruise 2 7 Loiter Cruise 1 6 4 3 Loiter Combat Approach 1 2 5 5 8 9 Warm up, Taxi-out, Weapon Drop Landing, Take Off Taxi-in AE-332M / 714 Aircraft Design Capsule-3 Mission Profile: Strategic Bomber Cruise 3 10 Loiter Cruise 1 9 3 4 5 6 Combat Approach 1 2 7 8 11 12 Warm up, Taxi-out, Weapon Drop Landing, Take Off Taxi-in * R: Re-Fuelling 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 AE-332M / 714 Aircraft Design Capsule-3 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 20 25 5 50 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 +Wpay +W fuel +Wempty W +W W = crew pay o W W 1− empty + fuel Wo Wo Wcrew +Wpay Wo = 1−{wˆ e + wˆ f } wwˆˆef& are the two unknowns to be determined Estimation of empty weight fraction ώe C ώe = A Wo * 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 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 Note: Wo in kg 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 120000 BAE 146-200 y = 0.5598x F100 110000 BAE 146-300 100000 DC-9-30 737-200 90000 DC-9-40 Empty Weight (lbs) Weight Empty 80000 DC-9-50 - 717-200 70000 empty 737-300 W 737-400 60000 MD-81 50000 737-600 737-700 40000 80000 100000 120000 140000 160000 180000 200000 220000 240000 WTO - Maximum Takeoff Weight (lbs) AE-332M / 714 Aircraft Design Capsule-3 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 th Mission segment weight fraction for i 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 W W W W W W W 6 = 6 ⋅ 5 ⋅ 4 ⋅ 3 ⋅ 2 ⋅ 1 W0 W5 W4 W3 W2 W1 W0 W W W 6 = 0.995⋅ 5 ⋅1.0⋅ 3 ⋅0.985⋅0.97 W0 W4 W2 W W W 6 = 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 Capsule-3 Breguet Range Equation Fuel Consumption: dW = −tsfc×T × dt V∞dW Range for dW fuel ds = V∞dt = − (tsfc)T During Cruise T = D, W = L Drag changes due to changing lift: assume L/D is constant, V∞ L dW Hence: ds = − tsfc D W Assuming L/D, tsfc and V∞ (= aM) are constant: AE-332M / 714 Aircraft Design Capsule-3 Breguet Range Equation a L W R = M ln initial tsfc D W final Engine efficiency Aerodynamic Structural (fuel consumption) efficiency 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 Capsule-3 Fuel Fraction in Cruise segment Cruise segment mission weight fraction can be estimated using the Breguet Range Equation VWcruise L i−1 R =⋅⋅ ln cDcruise cruise Wi 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 L Wi−1 E =⋅⋅ ln cDloiter loiter Wi 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 Mostly using historical data ! ESTIMATION OF MAX L/D AE-332M / 714 Aircraft Design Capsule-3.