Aircraft Preliminary Weight Estimate

7/27/2019 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 ("

Aircraft Preliminary Weight Estimate

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