Tatiana Quercia_presentazione

AIRPLANE DESIGNPRELIMINARY SIZING OF AN AIRPLANE

“Pilots make it work,engineers make it possible”.

To a pilot

By

Tatiana Quercia

Aerospace EngineeringSapienza University of Rome

2012

1Tatiana Quercia – Airplane Design

MarketSurvey

Mission specification

WeightsEstimation

SensitivityStudies

W/S, W/P & CL,max

EstimationWing shapeEstimation

Conclusions

CONTENTS

Tatiana Quercia – Airplane Design 2

MISSION SPECIFICATION

Payload(passengers)

Cruise speed

(km/h)

Range(km)

Loiter(h)

Service ceiling(m)

4 250 1300 0.5 4000


MARKET SURVEY

Airplane Seats(passengers

+ pilots)

Cruise speed

(km/h)

Range(km)

Service ceiling

(m)

Maximum Take-off Weight

(kg)Piper PA-32R-301

Saratoga II HP

4+2 307 1590 5029 1633

Cirrus SR203+1 289 1357 5335 1360

Cessna 182 Skylane 3+1 269 1505 5515 1406

Cessna 206 Stationair 4+2 263 1352 4785 1632


MARKET SURVEY

CATEGORY

SINGLE ENGINE PROPELLER DRIVEN AIRPLANES

WEIGHTS ESTIMATION


Payload weight (W

PL)

&Crew weight

(Wcrew

)

Missionfuel

Weight(W

F)

EmptyWeight

(WE)

+ + =Take-offWeight(W

TO)

PAYLOAD WEIGHT &

CREW WEIGHT


WEIGHTS

ESTIMATION

Passengers and crew: 80 kg each

Baggage: 15 kg each

For 4 passengers + 1 pilot:

WPL

=380 kg

Wcrew

=95 kg

MISSION FUEL WEIGHT

WEIGHTS

ESTIMATION


Fuel-fraction Method

Division of the airplane mission into phases.

Fuel fractions are defined as the ratio of end weight to begin weight for each phase.

Figure 1.1: Mission profile and phases

MISSION FUEL WEIGHT

WEIGHTS

ESTIMATION


W1/WTO 0.995

W2/W1 0.997

W3/W2 0.998

W4/W3 0.992

W7/W6 0.993

W8/W7 0.993

From Roskam's: From Breguet's Range equation:

R=375(ηp/cp)(L/D)ln(W4/W5)

W5/W4=0.836

R 808 miηp 0.8

cp 0.6 lbs/hp/h

L/D 9

From Breguet's Endurance equation:

E=375(1/V)(ηp/cp)(L/D)ln(W5/W6)

W6/W5=0.984

E 0.5 hV 155 mphηp 0.7

cp 0.6 lbs/hp/h

L/D 11η

p: propeller efficiency

cp: specific fuel consumption

L/D : lift-to-drag ratio

WEIGHTS

ESTIMATION


EMPTY WEIGHTMISSION FUEL WEIGHT

Mission fuel fraction:

Mff=(W1/WTO)Пk(Wk+1/Wk) k=1,2,...,7

Mff=0.796

With 6% of fuel reserves:

WF/WTO=(1-Mff)*1.06

WF/WTO=0.216

WEIGHTS

ESTIMATION


EMPTY WEIGHT&

TAKE-OFF WEIGHT

log10WTO=A+B log10WE

Process of iteration

Select a value of WTO

Find a new value of WTO

Find a value of WE

Estime the error or start again

From market survey, as medium value: WTO guess=1508 kg

A=-0.144B=1.1162

WTO

=WPL+W

crew+(W

F/W

TO)WTO+W

E

|WTO-WTOguess| ≤ 0.005

WTO

=2108 kgWE=1178 kg

SENSITIVITY STUDIES

Regression line method

Record of new results after modifying each parameter of +/-5% and +/-10%.Making of a regression line for each parameter.The sensitivity coefficients are the regression line constants.

Sensitivity of WTO to parameters used in weights estimation.

Analytical method

Starting from eq. of WTO

, it results:

∂WTO/∂y=(BWTO 2 ∂C/∂y-BWTO ∂D/∂y)/[C(1-B)WTO-D]

where y can be each parameter of interest.

C=1-1.06*(1-Mff)=0.784D= WPL+Wcrew=475 kg

B=1.1162 as in weights estimation


9,5 10 10,5 11 11,5 12 12,52085

2090

2095

2100

2105

2110

2115

2120

2125

f(x) = -9.27x + 2210.60

Figure 2.1: Regression line for lift-to-drag (L/D) in conditions of loiter

Lift-to-drag (L/D)

Max

imum

tak

e-of

f w

eigh

t (k

g)


REGRESSION LINE METHODSENSITIVITY STUDIES

L/D|loiter

WTO (kg)

9,9 211910,45 2114

11 210811,55 210312,1 2099

Ex.

∂WTO/∂(L/D)|loiter=-9.27 kg

ANALYTICAL METHOD&

COMPARISONSENSITIVITY STUDIES


Sensitivity coefficient Regression line method

Analytical method

Unit

∂WTO/∂WPL 3,53 3,53 -

∂WTO/∂R 3,09 3,07 lbs/mi

∂WTO/∂E 440,8 445,37 lbs/h

∂WTO/∂V 1,42 1,44 lbs/mph

∂WTO/∂cp|loiter 376,67 371,14 hp/h

∂WTO/∂cp|cruise 4150 4138,18 hp/h

∂WTO/∂ηp|cruise -3157,23 -3103,63 lbs

∂WTO/∂ηp|loiter -321,14 -318,12 lbs

∂WTO/∂(L/D)|loiter -20,43 -20,24 lbs

∂WTO/∂(L/D)|cruise -280,64 -275,88 lbs


WING LOADING, TAKE-OFF POWER LOADING AND MAXIMUM

LIFT COEFFICIENT

FAR 23 REQUIREMENTS

Stallspeed

Take-offdistance Climb Landing

distanceCruisespeed

Sizing to

Assumption:

Take-off and land in any Cuban International Airport

Shortest field lenght: 1295 m; almost all at sea level.

SIZING TO STALL SPEED


FAR 23 REQUIREMENTS

VS ≤61 kts=103 ft/s

(W/S)TO=1/2ρVS2CL,MAX

ρ (0 ft) 0.07595 lbs/ft3

CL,MAX 1.6 (medium value)

(W/S)TO≤20 psf

SIZING TO TAKE-OFFDISTANCE


FAR 23 REQUIREMENTS

Figure 3.1: Definition of FAR 23 take-off distance

sTO=1.66 sTOG

sTO=8.134 TOP23+0.0149 TOP232

TOP23:=(W/S)TO(W/P)TO/(σ*(CL,MAX)TO)=130.9 lbs2/ft2hp

sTOG≤242 m=795 ft(As minimum value from market survey)

σ:=ρ/ρ0≈1

5 10 15 20 25 30 35 40 45 50 550

5

10

15

20

25

30

FIGURE 3.2: Effect of Take-off Wing Loading andMaximum Take-off Lift Coefficient

on Take-off Power Loading

1,31,51,61,71,9

Take-off Wing Loading (psf)

Take

-off

Pow

er L

oadi

ng (

lbs/

hp) C

L,MAX,TO


FAR 23 REQUIREMENTS

SIZING TO TAKE-OFFDISTANCE

The region where take-off distance requirement is satisfied is underneath each curve.

SIZING TO CLIMB


FAR 23 REQUIREMENTS

FAR 23.65 (AEO) Far 23.77 (AEO)

RC≥300 fpm;

CGR≥1/12 rad

[Configuration: gear up, take-off flaps, maximum continuous power]

CGR≥1/30 rad

[Configuration: gear down, landing flaps, take-off power]

SIZING TO RC SIZING TO CGR

AEO: All Engines Operating; RC: Rate of Climb; CGR: Climb Gradient.

DRAG POLARS DETERMINATION

DRAG POLARSDETERMINATION


SIZING

TO CLIMB

CD=CD0+CL2/(πAe)

CD0=f/S

log10 f =a+b*log10 Swet

log10 Swet=c+d*log10WTO

Configuration ΔCD0 e

Clean 0 0,82

Take-off flaps 0,015 0,78

Landing flaps 0,060 0,72

Landing gear 0,020 No effect

f: equivalent parasite areaA: aspect ratioe: Oswald efficiency numberSwet: wetted areaS: wing areacf: equivalent skin friction coefficient

Cf 0.0070

a -2.1549

b 1

c 1.0892

d 0.5147

A 7.4

S 16.3 m2

Swet

=948 ft

f=6.64 ft2

CD0

=0.0378

Configuration Drag polar

Low speed, clean CD=0.0378+0.0525 CL2

Take-off, gear up CD=0.0528+0.0551 CL2

Take-off, gear down CD=0.0728+0.0551 CL2

Landing, gear up CD=0.0978+0.0597 CL2

Landing, gear down CD=0.1178+0.0597 CL2

SIZING

TO CLIMB


SIZING TO RATE OF CLIMB

RC:=dh/dt=33000 RCP

RCP:=ηp/(W/P)-(W/S)1/2/[19(CL3/2/CD)σ1/2]

RCP≥0.0091 hp/lbs

Respective polar: CD=0.0528+0.0551 CL2

(CL3/2/CD)max=1.345(Ae)3/4/CD01/4=10.4

ηp=0.8 as in cruise and σ≈1

SIZING

TO CLIMB


SIZING TO CLIMB GRADIENT

CGRP=[CGR+(L/D)-1]/CL1/2

CGRP=18.97ηpσ1/2/[(W/P)(W/S)1/2]

FAR 23.65 FAR 23.77

CGR≥0.0833 rad

Respective polar: CD=0.0528+0.0551 CL

2

C

L,CGR max=1.4 (C

L,max-0.2)

(L/D)CGR max

=8.7

CGRP=0.1675

CGR≥0.0333 rad

Respective polar:CD=0.1178+0.0597 CL

2

CL,CGR max=1.8 (CL,max,L-0.2)

(L/D)CGR max=5.8

CGRP=0.1533

15 20 25 30 35 40 45 50 550

5

10

15

20

25

30

Figure 3.3: Effect of FAR 23 climb requirements on the allowable values ofTake-off Power Loading and Take-off Wing Loading

FAR 23.65 (AEO-RC)FAR 23.65 (AEO-CGR)FAR 23.77 (AEO-CGR)

Take-off Wing Loading (W/S) - psf

Take

-off

Pow

er L

oadi

ng (

W/P

) -

lbs/

hp

WTO

=4646 lbs

A=7.4

ηp=0.8

σ≈1

SUMMARY OF CLIMBREQUIREMENTS

SIZING

TO CLIMB


The region where the requirement is met is underneath each curve.

Most critical requirement: FAR 23.65 (AEO-CGR)

SIZING TO LANDINGDISTANCE


Figure 3.4: Definition of FAR 23 landing distance

sLG=180 m=590 ft(As minimum value from market survey)

sL=1.938sLG

sL=0.5136VSL2

WL=0.997WTO

(W/S)L=1/2ρV2SLCL,max,L

(W/S)TO

=7.9 CL,max L

FAR 23 REQUIREMENTS

12 13 14 15 16 17 180

1

2

3

4

5

6

7

Figure 3.5: Allowable Wing Loadings to meetthe landing distance requirement

1,61,822,2


Take

-off

Pow

er L

oadi

ng -

lbs/

hpC

Lmax L

SIZING TO LANDINGDISTANCEF

AR 23 REQUIREMENTS

The region where the landing requirement is met is to the left of each curve.


SIZING TO LANDINGDISTANCE

FAR 23 REQUIREMENTS

SIZING TO LANDINGDISTANCESIZING TO CRUISE SPEED

Tatiana Quercia – Airplane Design

0 20 40 60 80 100 1200

10

20

30

40

50

60

Figure 3.6: Allowable values of Wing Loading and Power Loading to meet a given Cruise Speed

Wing Loading W/S - psf

Pow

er

Load

ing

W/P

- lb

s/hp


Ip:={(W/S)/[σ(W/P)]}1/3

For Vcr=250 km/h=155 mph: Ip=0.9

Service ceiling

4000 m

ρ(4000 m) 0.0819 kg/m3

σ 0.6686

(W/S)=0.49(W/P)

Power index

0 10 20 30 40 50 600

5

10

15

20

25

30

35

Figure 3.7: Combination of FAR 23 requirements

FAR 23.65 (AEO-CGR)CLmax L=1.6CLmax L=2.2CL, max,TO=1.3CL, max,TO=1.9cruise speedstall speed


Take

-off

Pow

er L

oadi

ng (

W/P

) -

lbs/

hp

FAR 23 REQUIREMENTS


SUMMARY OF FAR 23REQUIREMENTS

Best combination: node between cruise speed requirement (yellow) and maximum landing requirement (light blue)

(W/S)TO=17 psf

(W/P)TO=8.5 lbs/hp

WING SHAPE ESTIMATION


Schrenk's Method

Distribution on the wing of the aerodynamic load (cCl)

c: chord of the airfoil;Cl: lift coefficient of the airfoil;b: wingspan;y: variable standing for the length of the wing;cCl,a: additional aerodynamic load, it describes the effect of the wing plant only;cCl,a1: for CL=1;cCl,b:base aerodynamic load, it describes the effect of the wing twist;Clα=∂Cl/∂α=2π (α: angle of attack) as for the ideal airfoil;ε1(y) is the rotation due to wing twist;ε0 : rotation for zero lift;α0L: angle of attack at leading edge for zero lift.

cCl=cCl,a+cCl,b

cCl=cCl,a1CL+cCl,b

cCl,a1=(c+cell)/2

cell=4S[1-y2/(b/2)2]1/2/(πb)

cCl,b=1/2cClαε1(y)

ε1=α0L+ε0

α0L=- /∫0

b /2

cε0dy ∫0

b /2

cdy

0 1 2 3 4 5 6 70

0,5

1

1,5

2

2,5

3

Figure 4.2: Aerodynamic load distribution on the wingwith and without twist

no wing twistwing twist= - 2°

wing lenght (y)

Aero

dyna

mic

load

(cC

l)

WING SHAPE ESTIMATION


Rectangular wing shape

ε=0°

ε=-2°y/(b/2)

A 7.4

S 25 m2

b 13.6 m

c 1.84 m


CONCLUSIONS

WTO 2108 kg

WE 1178 kg

WF 455 kg

CL,max 1,6

CL,max TO 1,2

CL,max L 2,2

A 7,4(W/S)TO 17 psf

(W/P)TO 8,5 lbs/hp

S 25 m2

PTO 546 hp

Wing shape Rectangular without twist

Critical values in comparison to market survey are marked in bold.

Tatiana Quercia_presentazione

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