initial sizing estimation of design gross weight
TRANSCRIPT
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
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
67
Cruise 1
Cruise 2
LoiterWeapon 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 7Cruise 1
Cruise 2
Loiter
Weapon Drop
8 9Approach
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 45 6
7 8
Cruise 1
Cruise 3
Weapon Drop
910
1211
* 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
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
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
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
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
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
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:
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
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
AE-332M / 714 Aircraft Design Capsule-3
ESTIMATION OF MAX L/DMostly using historical data !