aircraft preliminary weight estimate
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Aircraft Preliminary Takeoff Weight
Estimation
05A_Aircraft-sizing.ppt
Copyright Don Edberg 2006-present
Courtesy Pointwise Gridgen
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Required Requirements Must have specific, hard numbers to begin an aircraft layout:
Payload weight, dimensions, & peculiar needs
Avionics weight, dimensions, & peculiar needs
Range and/or endurance
Speeds - max., approach, stall,...
Takeoff/landing
Turn rate
Rate of climb orPs
Structural load factor
Target stability
Dimensional constraints
If you dont have them, get them or make them up
Initial values of requirements will be refined by trade studies using first
layout as an analytical tool
Need for Wo& Wf
Solve for T/W & W/S
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Sizing determines takeoff weight and fuel weight
(range & payload specified)
Range & payload are independent variables, aircraft
size and weight are the answer
Have to work backwards
Aircraft Sizing
sizing
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Begin With The Takeoff WeightW0= Wempty+ Wfuel+ Wpayload+ Wcrew (R3.1)
W0= Maximum takeoff weight
Wempty= operating weight empty (OWE) of basic
aircraft
Wfuel= Fuel to do mission
Wpayload
= Payload weight (passengers, cargo, bombs,
missiles, crop dusting chemicals, etc.)
Wcrew= Weight of all crew members: includes pilot(s),
crewmembers such as flight attendants
(quantity specified by FARs), and their
baggage
)
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A Little Algebra Yields:
(R3.2, R3.4)
W0=
Wcrew+
Wpayload+
Wf
W0
"
#$
%
&'
W0+
We
W0
"
#$
%
&'
W0
W0 =Wcrew +Wpayload
1( Wf W0( )( We W0( )Here Wf W0 = Fuel Weight fraction and
We W0 = Empty Weight fraction
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Statistics: Empty Weight Fraction vs W0
(Raymer fig. 3.1)*
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Empty Weight Fraction vs. Takeoff Weight
(from Mattingly et al, Aircraft Engine Design)
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Typical Mission Profiles(Raymer fig. 3.2)
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Heres a Nice Mission Profile Diagram
211
10Takeoff1
Cli
mb1
Cruise1
Descent1
AttempttoLand
Cruise2
Land
Loiter2
3
4
1 5
67
8 9
12
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Definition of Mission Segment Weight
Fractions(2nd Case, 2 Slides Previous)
W1/W0 Warmup and takeoff
W2/W1 Climb 1
W3/W2 Cruise 1
W4/W3 Loiter 1
W5/W4 Climb 2W6/W5 Cruise 2
W7/W6 Loiter 2
W8/W7 Land
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Historical Mission Segment Weight Fractions
(Wi/Wi-1 )Phase Nicolai &
Carichner 5.4RaymerTable 3.2
Warmup &Takeoff
0.970 0.975 0.970
Climb Depends oncruise Mach no.
Refer to Table 5.2
0.975
Descent Not given 1.0(consider part of
range)
Landing Not given 0.995
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CRUISE WEIGHT FRACTIONCruise Breguet Range Equation
(N&C 5.2 or 5.3; R 3.5)
or
R = rangec = SFC = specific fuel consumption
= cpV/!p= cbhpV/(550!p) for props
!p = TV/P= TV/(550 HP) prop efficiency
V = velocity
L/D = lift-to-drag ratio Be careful with Units!!!
Wi
Wi"1
= e
"Rc
V L D( )
R =V
c
L
DlnW
i"1
Wi
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L/DEstimation, Method 1 (N&C)
CD0from N&C Table 5.2, p. 129
K= 1/("eAR)
L /D( )max
=
1
2 CD0K
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L/DEstimation,
Method 2
(Raymer)
Guess or
extractfrom
Raymer,
Fig. 3.6
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c(SFC) Estimation
Use references or Raymers Tables 3.3, 3.4 below:
JET Specific Fuel Consumption, c
Typical jet SFCs: lbm/hr/lbf{mg/Ns} Cruise Loiter
Pure turbojet 0.9 {25.5} 0.8 {22.7}
Low-bypass turbofan 0.8 {22.7} 0.7 {19.8}
High-bypass turbofan 0.5 {14.1} 0.4 {11.3}
Prop: c= cpowerV/!p= cBHPV/(550 !p),
use !p= 0.8 0.85
SFC units: lbm/hr/BHP {mg/Ws}
Cruise
Loiter
Piston-prop (fixed pitch) 0.4 {0.068} 0.5 {0.085}
Piston-prop (variable pitch) 0.4 {0.068} 0.5 {0.085}
Turboprop 0.5 {0.085} 0.6 {0.101}
Propeller Specific Fuel Consumption, cBHP
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Example: Cruise Weight Fraction CalculationFor Cruise 1 and 2 (military jet cargo bomber)
R= 500 NM = 3,038,065 ft
c= 0.7 lbm/h/lbf= 0.000194 lbm/s/lbf
V= 400 kt = 675.1 ft/s
h= 30,000 ft
L/D= 15 !0.866 = 12.99
W3/W2= W6/W5= 0.935
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Loiter Weight Fractions(Nicolai & Carichner 5.6, 5.7; Raymer 3.7, 3.8)
Endurance
or
whereE = endurance or loiter timeBE SURE to use consistent units,
either (ft, lbf, s) or (m, kg, s)
E=
L D
c ln
Wi"1
Wi
Wi"1
Wi
= e
"Ec
L D
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Loiter Weight Fraction ExampleFor Loiter 1
E= 4 h = 14,400 s
c= 0.000167 lbf/s/lbm
L/D= 15
W4/W3= 0.852
Wi"1
Wi
= e
"Ec
L D
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General Fuel Fraction Calculation
Mission Segment Weight Fractions
Total Mission Weight Fraction
Mission Fuel Fraction
Total Fuel Fraction
Wi
Wi!1
Wx
W0
=
W1
W0
!
"# $
%& W2
W1
!
"# $
%& W3
W2
!
"# $
%&. ..etc
1 !W
x
W0
Note: 6% extra added for reserve and trapped fuel
Wf
W0
=1.06 1 !Wx
W0
"
#$ %
&'
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Weight Estimation Calculations ExampleNow multiply all mission segment weight fractions: the
result is
W8/W0= 0.687
Then get the fuel weight fraction
Wf/W0= 1 W8/W0= 0.332
The empty weight fraction is obtained from RaymerTable 3.1 (military cargo bomber):
We/W0= 0.93 W00.07
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Weight Estimation Calcs. (cont.)
Make a table using a guessed W0, We/W0, and the
calculated W0 using
Plot the calculated versus the guessed W0 and find the
intercept.
This is the MTOGW to use.
W0=
Wcrew +Wpayload
1" Wf W0( )" We W0( )
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Calculated Weight Values (Example)W
0Guess W
e/W
0W
0Calculated
40000 0.4429 67466
45000 0.4393 66394
50000 0.4361 65471
55000 0.4332 64664
60000 0.4305 63948
65000 0.4281 63307
70000 0.4259 62729
75000 0.4239 62202
80000 0.4220 61719
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Plot of Weight Numbers
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Another Way to Find MTOGW
Courtesy Dr. Mark Anderson, UCSD')
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2nd Weight Estimation ExampleMission Segment Weight Fractions
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Weight Estimation Calculations (2nd Example)
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Sizing Graph
0.0
500.0
1000.0
1500.0
2000.0
2500.0
3000.0
0 500 1000 1500 2000 2500 3000
Wo Guess
WoCalculated
Alternate Weight Estimation Method
Wo guess We/Wo We Wo calculated
1000 0.6680 668.0 2403.2
1500 0.6440 966.0 2087.3
2000 0.6276 1255.1 1914.2
2500 0.6151 1537.7 1801.0
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Trade Studies
Courtesy Dr. Mark Anderson, UCSD',
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Spreadsheet Data
Courtesy Dr. Mark Anderson, UCSD'-
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Final Spreadsheet
Courtesy Dr. Mark Anderson, UCSD(!
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Final Carpet Plot
Courtesy Dr. Mark Anderson, UCSD(&
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Takeoff Gross Weight Carpet Plot
Courtesy VPI Casper Team
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References
Fundamentals of Aircraft & Airship Design, Nicolai
& Carichner, Ch. 5
AircraftDesign, Raymer, Ch. 3
Aircraft Engine Design, Mattingly, Heiser, and Daley,
Chs. 2 & 3
The Elements of Aircraft Preliminary Design,
Schaufele (alternate sizing method)
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Direct Operating Costs vs. Wing Area and Aspect Ratio
www.mh-aerotools.de/company/paper_9/global_transport_aircraft.htm ()
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Fuel Mass (kg) vs. Wing Area & AR
www.mh-aerotools.de/company/paper_9/global_transport_aircraft.htm ("