Sanity Check - Data for Aircraf Design Balaji

8/6/2019 Sanity Check - Data for Aircraf Design Balaji

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AD-A270 150@Q IEAEllI|IEEHIE(~) WL-TR-93-3068

, PROCEDURESAND DESIGN DATA FOR THEFORMULATIONOF AIRCRAFTCONFIGURATIONS

THOMAS R. SIERONDUDLEY FIELDSA. WAYNE BALDWINDAVID W. ADAMCZAK

AEROTHERMODYNAMICSAND FLIGHTMECHANICSRESFARCH BRANCH 'JC[,5 3, ,AEROMECHANICSDIVISION

August 1993

FINAL REPORT FOR THE PERIOD JANUARY 1992- JUNE 1993

APPROVEDFOR PUBLIC RELEASE;DISTRIBUTIONUNLMITID

FLIGHT DYNAMICSDIRECTORATEWRIGHT LABORATORYAIR FORCE MATERIEL COMMANDWRIGHT PATTERSON AFB, OHIO 453-7913

93-23106 14.iU IOlNll 0 0 0 0


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NOTICEWHEN GOVERNMENTDRAWINGS,SPECIFICATIONS,OR OTHERDATA ARE

USED FOR ANY PURPOSE OTHER THAN IN CONNECTION WITH A DEFINITELYGOVERNMENT-RELATEDPROCUREMENT,THE UNITED STATES GOVERNMENTINCURS NO RESPONSIBILITYOR ANY OBLIGATION WHATSOEVER, THE FACTTHAT THE GOVERNMENTMAY HAVE FORMULATED OR IN ANY WAY SUPPLIEDTHE SAID DRAWINGS, SPECIFICATIONS, OR OTHER DATA, IS NOT TO BEREGARDEDBY IMPLICATION,OR OTHERWISEIN ANY MANNER CONSTRUED,ASLICENSINGTHE HOLDER, OR ANY OTHER PERSON OR CORPORATION;OR ASCONVEYING ANY RIGHTS ORPERMISSION TO MANUFA'3,TURE, USE, SELL ANYPATENTED INVENTION THAT MAY IN ANY WAY BE RELATED THERETO.

THIS TECHNICALREPORT HAS BEEN REVIEWEDAND IS APPROVED FORPUBLICATION.

THOMAS R. SIER DUDLEY'FIELDSTechnical Manager Senior Aerospace3pecialistFlight Mechanics Research Group AerodynamicsGroup

A. WAYNE BALDWIN DV0ID W. ADAMCZAKSenior Aerospace Engineer Aerospace EngineerAerodynamics Group Flight Mechanics Research Group

VALENTINE DAHLEMChief, Aerothermo& Flight Mechanics BranchAercmechanics Division

IF YOUR ADDRESSHAS CHANGED,IF YOU WISH TO BE REMOVED FROMOUR MAILING LIST, OR IF THE ADDRESSEEIS NO LONGEREMPLOYED BY YOURORGANIZATIONPLEASE NOTIFY WUFIMH,WRIGHT-PATTERSONAFB, OH 45433-1913 TO HELP MAINTAIN A CURRENT MAILING LIST.

COPIES OF THIS REPORT SHOULD NOT BE RETURNED UNLESS RETURNIS REQUIREDBYSECURITYCONSIDERATIONS,CONTRACTUALOBLIGATIONS,OR

NOTICE ONA SPECIFIC DOCUMENT.

0 0 S S 0 0


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FomApprovedREPORT DOCUMENTATION PAGE OMB No . 0?04-0188

fPiic ( frrn. hurdrn for this collectionl of information is estimated Io erqt p t r w O M e . fldtudiii the time' for rpviewinq instructions, weAriholc -- si~tng data sources.a1 therin. rmid tdnwimnqithe data n e e d e .n d Omtrq dd e.'oq h (o0ctot infrma io ndi-om entliria dinga hi butdc-n e.', tim ur iny othinr .spert of this* ollectionotr fnromation.ndkiding sugg3iZornr reduo.n," br den i)Wa ihinqton irtesdiquarteri,`arvi.m I,~feclor..te frt nfomtio nr Oper0ons and Hermfts IMh leferonOavis ltivjwa. Wt~e 1?04. A.-ington. A~11101430), and to thP Office of Maimjin~ement d Midget. P sperwork Fit-duilion Pru t (0?10-1019). Wahinqtin P( 10O'O

4. TITLE AND SUBTITLE S. FUNDING NUMBERS4PROCEDURES AND DESIGN DATA FOR THE F~ORMlULATION OF AI&CRAFT PE : 62201F4

CONFIGURATIONS PR : 2404TA : 240416

6. UTHOR(S) WU : 67THOMAS R. SIERON, DUDLEY-FIELDS, A. WAYNE BALDWIN, DAVID W.ADAIICZAK

7. PERFORMING ORGANIZATION NAME(S)AND ADDAESS(ES) 8. PERFORMING ORGANIZATIONWRIGHT LABORATORY, AFMC REPORT NUMBERFLIGHT DYNAMICS DIRECTORATEAEROMIECHANICS DIVISION, WL/FIIIHWRIGHT-PATTERSON AFB OH 45433-7936 WL-TR-93-3068

9. PONSORING/IMONITORING AGENCY is AI(S) AND ADDRIaS$IS) 10, SPONSORING/I MONITORING

WRIGHT LABORATORY, AFMC AGENCYREPORT NUMBER

FLIGHT DYNAMICS DIRECTORATE WL-TR-93-3068AEROMECHANICS DIVISION, WL/FIMHWRIGHT-PATTERSON AFB OH 4 5 4 3 3 - 7 9 3 6 . - j

11. SUPPLEMENTARY NOTES

O ~Ila- DISTRIBUTION /AVAILARU.ITYSTATEMINT 1lb OISTRA8UTiON CODEl

Approved fo r public release; distribution unlimited.

13 AISTRACT r u m 0 w t f )

This report contains design data and rapid analysis methods to assist in stabl ishing 1an initial aircraft configuration to begin the conceptual design process. It sbased on an array of data acquired over many years for fighter, bomber an d transport

aircraft. Th e data is ompiled to estimate the gross take-off weight aud physicalsize of a representat ive configuration fo r various range, payload and speed require-ments. Other data and procedures are Included to defiat the genrwal dimensions of thifuselage, ving, vertical and horizontal stabilizers. Aerodynamic methods and data ariprovided to rapidly estimate the drag an d lift characteristics at subsonic, transonicand supersonic speeds for the this class of aircraft. Performanc~e data has been as-sembled to show the impact of range, payload, speed, maneuverabi l i ty. take-off da dlanding requirements on the physical and geometric characteristics of t hese coinfigurations. A sample problem is presented to Illustrate the use of this design data informulating an aircraft c,.kfiguration.

AIRCRAPT CONFIGURATIONS, CONCEPTUAL DES$!CNif AEROI)TIWIC pREUlC'lIUNETHOUS, AIRCRAFT U)ESlGN tP%*

SU SCCuRITVCtASWeCATBON 19. SECURITYCLASWICATION 10 . SECURItYCtASW6CAtIONt 10 UMITTIONO ABS~tACTOF 0IPOiAt W TI4S PAGE OF ABSTRACr

1 IiiLa" IFI IIb mu[ k ! t ; I n llft!TWlILVI1IM?1ti 1-i

IV SQ0-W`% S1f0vi 09 0 0' 1


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0 TABLE OF CONTENTS19)

PAGE4D

ID

1. INTRODUCTION 1-12. AIRCRAFT CONCEPTUALDESIGN 2-1

3. IMPACT OF PERFORMANCEREQUIRMENTS 3-1ON CONFIGURATIONSHAPE

4. DESIGN DATA FORINITIAL SIZING AND 4-1SHAPING OF CONFIGURATIONS

5. METHODSAND DATA TO ESTIMATE PRELIMINARY 5-1AERODYNAMICCHARACTERISTICS

* 6. INFLUENCEOF AERODYNAMICAND 6-1CONFIGURATIONPARAMETERS ON PERFORMANCE

7. PROCEDURESFOR THE FORMULATION 7-1AND ANALYSISOF AN AIRCRAFtCONFIGURATION

& CONCLUSIONS 8-1

9. REFERENCES 9-1

APPENDIXA REPRESENTATIVE OPERATIONALAND A-IADVANCEMDCONFIGURATIONS

APPENDIX B VOLUME ANDAREA RELATIONSHIPS B-I S.0...

APPENDIX C WINGS IN SUPERSONIC RLoW C-I

I m -. -.. ,afI

O 4~j O I


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5-15 Parasite Drag Area Correlation at Mach 2 5-24

5-16 Variation of CD0 with Mach Number 5-25

5-17 Subsonic Lift Curve Slope 5-27

5-18 Supersonic Lift Curve Slope 5-28

5-19 Maximum Lift-to-DragRatio 5-30

5-20 Subsonic MaximumL/D Correlation 5-32

5-21 Subsonic Maximum L/D Variation with Aspect Ratio 5-33

5.-22 Variation of Maximum L/D with Mach Number 5-34

5-23 Maximum L/D at SubsonicCruise and MaximumSpeed 5-35

6-1 FLAPSDown CL MA X 6-2

6-2 Stall Velocity Versus Wing Loading 6-3

6-3 Take-Off Velocity 6-4

6-4 Take-Off Distance 6-5

6-5 Cruise Altitude 6-7

6-6 Impact of Cruise Fuel on Transport Range 6-9

6-7 Impact of Cruise Fuel on Fighter Range 6-10

6-8 Impact of Supersonic Speed on Fight-es 6-11

6-9 Specific Excess Power, G = 1.0 6-16

6-10 Specific Excess Power. G = 5.0 6-17

6-11 Maximun Sustaineo "G" CntuurM 1 = 0.6 6-19

6-12 Ntaxuimu Sustained "G" Contours, M = 0.9 6-20

6-13 MaxuinumSustained *G-"CAontos M = 15 6-2)

vi


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6-14 Thrust Variation for a Modem Fighter 6-22

A) 6-15 Aircraft Turn Rate, V = 200 - 800 Knots 6-25

6-16 Aircraft Turn Rate, V = 700 - 1400 Knots 6-26

6-17 Luding Ground Distance 6-28

6-18 Descent Distance Over 50 feet 6-29

A-1 A-7D FighterConfiguration A-2

A-2 F-106 Fighter Configuration A-3A-3 F.-15 Fighter Configuration A-4

A-4 F-16 Fighter Configuration A-5

A-5 Advanced Supersonic FighterConfiguration A-6

A-6 C-141 Transport Configuration A-7

A-7 C-5 Transport Configuration A-8

A-8 AdvancedTransport Configuration A-9

A-9 B-52 Bomber Configuration A-10

C-I Arrowhead Wings with DoubleWedge at ZeroIncidence C-5

vii

0 0 0 0 0 0 0 0


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Alf

Nomenclature

a Acceleration, ft/sec2

Angle of attack, deg

Ax Frontal projected area, ft2

AR Aspect ratio b2 ISf

AWET Wetted area, ft2

b Wing span, ft

I for M>l

= -- 2 for M

"... ...

a ~~ ~. .1 .J .. .. . . . ....

*~ 00,106o

S/I I III

I I I II I I : k I ~I5-I I4


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1 T...............

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00

......................................

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.... .. .. . . . . - - .. . . . .

- . . . . . . . . . . . . . . . . . . . 0

0..... ......t

.. ........ ....................

5-35

S S S


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6. INFLUENCE OF AERODYNAMICAND CONFIGURATION PARAMETERSONPERFORMANCE

The initial designof a configurationis strongly dependenton the performancerequirements.

These requirementsdictate the generalappearance of a configuration,wing loading, thrust-to-

weight, wing sweepback, fuselage fineness ratio and almost every other major feature of an

aircraft. Thus it is important to have an awareness of how eachmission performancesegment

influencesthe selection of key vehicleparameters. A typical fightermission consistsof take-off,

accelerationto speed and altitude,cruise, combat, cruise, and land.

TAKE-OFF

Take-off performanceis dependent primarilyon the weight of the aircraft, the lift generated

by the aircraft wing and the takeoff power available from the engine. The maximum lift

coefficient(Reference 28) is a functionof wing planform (AR,A, X), wing thickness andcamber,

as well as the type of high lift devicesemployed(slot or droopedleading edge flaps, plain hinge

or fowler trailing edge flaps)and the percentageof the wing area that these devices encompass.

In the early preliminarydesign phase, mostof these detailsare not known. However, CL , x can

be estimated based on data from existing aircraft of a similarconfiguration. Figure 6-1 shows

the CL NU, that is availablefor several fighter and transportaircraft. With the estimate of

CL NMx,the stall velocity (ignoring thrust effects) can be detenrined as a function of the wing

loading (WIS) as shown in Figure 6-2. If the stall velocity is a requirement, this curve can be

used to detennine the W/S and thus the wingarea (S) required to meet the stallspeed. The

takeoffvelocity is normallybased onusing only 75% ofCL NW and is shown in Figure 6-3. The

take-offdistance is shown in Figure 6-4 as afunction of thrust loading, wing loading,and CLTO '

This curve is based on data from many aircraft andis presented in tenus of the most importaut

6-1


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6-2


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airplane and engine parameters.

RANGE AND SPECIFIC RANGE

4,) The range of an aircraft is a critical performanceparameter andit stronglyinfluences the

wing design. The primary aerodynamicparameterwhich drives the configuration ismaximum

lift-to-drag ratio, (L/D)Ma. The lift coefficient for (L/D)Max is called theoptimum CL and is

given by: CL O (6-1)

and the requiredCL for one g level cruise flightis:

CL Je = .W162q Sj~ (6-2

then for CLRe=CL Opt - Cq (6-3)

0 Therefore, at maximum LiD, airplanes fly at an altitude andvelocity to satisfy equation (6-2).

Hence for a fixed velocityand wing loading, the cruise altitudeis defined formaximum L)D.

Historical data is pmsentedin Figure 6-5 toevaluate cruise altitude basedon take-"ff wing

loading. The data indicatescruise altitu.c dmcrAscs as wing loadi-g increases, butbegins to

level off at wing loadingsabove M6Wpsf.The crtise raang of an aircraft can be estimated4 uitc

accumatelyby the imguit range equation gin beltw:

R Vv~,.[Jg ,i64

with R in tautic-al milesV in k"sSRK' in lbs of fuel p-r bwor per poundof thrust11) lift to drag ratioWIAFVpinitial cruiuc weightlfinalcmiu.i weight

6-6


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Assumptions used in developing this equation includecruising at constant (LID) (go constant

altitude), constant velocity and constant SFC. Thus an increase in I/D, a reduction in SFC, and

an increase in fuel fraction willlead to increased range.

The impact of lift-to-drag ratio on cruise rangefor transportsis shown in Figure 6-6. Since

fuel fraction for transports (Figure4-7) varies between 35 and 45 percent of the gross take-off-

weight, and typical cruise fuel loads account for 45 to 55 percent of the total fuel load, a

representative range of values for cruise fuel weight to gross take-off weight is 0.15 to 0.25.

Hence, a transportwith an L/D = 16, an initial cruise weightto final cruise weight ratio of 1.25

would have a nominal range of 3800 nautical miles. A similar chart forfighters is presented in

Figure 6-7. Since thenominal fuel fraction for fighters is 27 percent of gross take-offweight

and typic.al internal cruisefuel loads are about 30 to 40 percentof the total fuel load, a nominal

range of values for initial cruise fuel weight to gross take-off weight is 0.075 to 0. C25.

Therefore, a fighter with an LID = 10, an initial cruiseweight to final ciuiaz weight ratio of 1.10,

would have a nowinal range of 500 nautical miles.

The impact of supersonicspeed to fighter range is mradiiy appawvnt in Figore 6-8. Assuming

an UD = 4, at an altitudeof 40.000ft, SFC=2.0 and an initial to finalcruise weight ratio of 1.10.

the fighter range is only 225 naiutical miles. This is over a 55 percent reductionin range

capability. "Tis s optimistic since large quantitiesoil fuel will be coLsumed duringickleratio

from Maclh 0.9 to 2.0. 11T acceleratioi fuel will d& x sc' the fuel avaiiablu for cruise tligjht.

Thus there is a significant penalty for superonic speeds. hiWslarge Xmealtymay be reduced

thmugh theuse of very highfuseae fiteviss ratios, i m a " wing swcepback anzlgi aswd situal

wing thiclatessratios.

6-8

m = = m w =


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Much attention in the 1970's and 80's was given to investigating the technologies which

3maximizethe range parameter M(LID) (References 29-32). A class of vehicles calledSFC

"Osupercruisers"were envisioned where LID at higher Mach numbers was maximized while

keeping engine throttle setting below afterburnerfor low SFC. This was a severe challengeto

the aerodynamicist in trying to maximize supersonic LIDand maintain acceptable transonic

maneuvering characteristics. The design options for increasing high speed LID impact the

available fuel fraction, whilethe thrustrequiredat non-afterburnerengine powersettingsdefines

engine size, which in turn impacts vehiclesize, shape,weight, fuel fraction and LID. These are

the conflicts whichmust be resolved early in the design cycle.

In order to permit rapid estimates involving aircraftrange the following approach can be

used. If a cruise range segment is divided by the fuel consumed for the distance traveled a

parametercalled specific rangeis formed, with units of nautical miles per pound of fuel. This

is an average value of how far a particularaircraft can travel on one pound of fuel. The

instantaneousspecific rangeis found by dividing the flight velocity by the fuel flow

SR V (6-5)FF

where: V - nautical titles pet hourFF - lbs of fuel per hourSR - nautical miles pcr lb of fuel

Equation (6-5) may be expessed as

SR V VR ~3- s''FY~ SF C X 7'

Wand for T=D; L=W; and D -

6-12

O I ... O t


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SF C x W

For a modem aircraft at Mach 0.9 and 30,000 feet:

LID= 10,SF.C = 1.0 lbsihrllbV = 516 knotsWI = 25,000 lbs

SR-- (516)(10)

t el 1.0(25,000) m= 0.206 nm.

1b

Anotheroften used parameteris the range parameterwhich is composedof parametersfromS

the Breguet rangeequation.

R F PSFC *

It is often usedto compareaircraft capabilit-ybasedon aerodynamicsand propulsionefficiencies.

A rapid approximation for the fuel required for a cruise mission segment can be made by

dividing the range required by the specific range. S

SPECIFICEXCESS POWERIMUNEUVERING

Sptifit cxcess power isdefined asS

Ps -I" r- D(6-8)

and is expimseA inthe unitsof fw- per setond. Simpleaircraft forc equilibriumshows thlt Ps

is the rate of climb an aicratq can achieveunder the approximationsof shallowclimb anglesand

,m,acwxrcmted flight (Retcraces 33 io 35). However as cureutly us- Ps is betea

6-13

0S 0 0


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characterizedas the excess power availableto an aircraft for maneuvering or climbing. This

interpretation is based on the fact that PS is calculatedat flight conditionsother than I "g". ForI

example,at a specific altitude, velocity,and weight all terms in thePS equationare fixed except

drag.

Ps

3.5g

1.0 2.0 3.0 4.0 5.0"g's" \

SKETCH A

Sketch A indicates the maximum valueof PS at I *g", the PS 0 point of about 3.5 "g's" and

negative PS beyond 3.5 "g's"

Aircraft perfonrance specificationsare often expressedpartially in terms of Ps. A matrix

of values are used with different levels of PS required at various combinationsof altitude,

velocity, thrust level, maneuver level,and weight. A sample matrix is shown below.

MACH ALTITUDE "g's" THRUST PS (ft/sec)

1.8 0K Ig Max A/B 1000

0.8 10K 7 Max AIB 100

0.9 30K I Max A/B 400

0.9 30K Ig LMil Power 106

0.9 INK 5g _Max A/8

Aeraft designerswillvary iksagn pamimetei such as T1W. WIS.AR and finemws ratio in

6[ 6-14

0 6 0 S~~ S 000


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an attempt to meet these perfornance requirements (aswell as others). Often meeting one

particular requirementsuch as the 5g, M=0.9, h=30,O00ft. point in the example abovewill ensure

that the other requirementsare also met.

Contour plotsof Ps againstaltitude and Mach numberare often generatedto show the global

perfonnancecapability of an aircraft. A typical exampleis shown in Figure 6-9. The Ps = 0

lines indicate on a "lg" chart the flight envelope capability of the vehicle. On charts for

conditions above I "g" (Figure 6-10) the PS = 0 line indicates for each Mach number the

maximum altitude atwhich the aircraft can sustain the "g" evel of the figure.

Anothervaluable use of the PS performanceparameter is in comparing one aircraft against

another. This is typically done in evaluatingvarious aircraftdesign solutions andin evaluatingthe performance advantagesand disadvantagesof threat aircraft. An advantage of 100 feet per

second is generally accepted as significantwhen comparing aircraftperformance, *

SUSTAINED MANEUVERING

Another classic performanceparameterutilized ismaximum sustained "g" capability. As

indicated in the previous discussionPS and maximum *g" capabilityare closely related. When

P. is equal to zero an aircraft is at its maximum sustained"g" level with thrust equal to drag at

the tueuver level. This "g" evel can be detenminedas follow:

When PS= 0;WheuP- P -)

w ~iV

qS

6-15


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0o

Vtr

0- CDfa

r-. G)

C4

(4) pnq.-1


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A C 4

CM J

I

0 I

0 5 0

(4) spnv/


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solving for n results inthe followingrelationship

n = q7t'AR T_ qC-9)WI iV W4

Figures6-11 to 6-13 have plottedthis equationin paiametricform for valuesof AR. "W, nd

CD0 typical of modem aircraft. on e interesting interpretationof Figure 6-12 isto note the

variation of required T/Was WIS varies while keeping the maneuvercapability constant. This

type of chart ,aa identify designchoices for meeting maneuver specificationswith either fixed

or "rubber" engines. Note in Figure 6-12 that the effect of CDOon the required T/W at a

constant WIS is relatively small for this condition. The effectsof wing planfonn (AR) and

design technology("e') can also be estimatedwith equation(6-9). Figure 6-13 indicatessimilardata for supersonic flight conditionsand typical tighteraircraft parameters.

In using equation(6-9) it is important to note that the thrust-to-weight. T/W, parameteris v

specified at the particular flight conditions under consideration. Thrust-to-weightand wing

loading, WIS. are often used to characterize the performance levelsand designemphasis ofI

aircraft, high TIWand low WiS representinghigh performance. Sincethmst varies with altitude

and Mach number andwing loading varieswith payloadand fuel consumption; thrustto weight

values are usually quoted at some refrnce condition suchas sea level statiic maximum thrust

and take-offgross weight. Figure 6-14 pa.sentsthe varia-Jonof T(%Vfor a typical modenifighter

with both M1ch numberand altitude, Cwunt high pefrtfon1ainue ilghtcs have TAV valus around

1.0 or greater at sea level rfkemwo conditionsaid decrcaue to I1 these valutmat mid altitude

and transonic speo.

In awssing the tlatrionshipsbctween pctfrnwmau, veuitenwnts, iypitally 11SAund.susaintdlp

.6-1g

S 5 0 0 0 0 0


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0 I

II

c8 (DIv0 lo ( t C46'

0 -9


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......... ........ c. .... ..*. .. .. ...

. . . . . . . . .

V4 -

6-20


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0

*99

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iv~

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6it21


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.. .... ... .. . ..... .. ..... . .. . .. ....... ... . . .

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ell

"a. 0 0- 0 6 o 6a~dH


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0 0 0 0 .0,' 0

g's, on aircraft design driverssuch as T/W, thefollowing observationsprovide some guidance.

Using the PS equation (6-8) results in

T [ D]

T - If D=O

T Psor For D > 0W V

Givena PS specificationat some altitudeand Mach numberwe can immediatelyestablisha lower

bound on T/W at those conditions. To obtain a betterestimate consider

D I If L= W

if we return to the Ps relationshipwe have

T Ps 1

L L

The minimum value of 1 resultswhen LD (isl -DDD

T Ps Io - +.

At mnueuver lift coefficients where L- nW, (L/D)t.tNa, is less than (I/D)Mr so the final

estimate is

6-23

a

0 0 0 0 0 0 0 0


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T>

)Mau

A typical value for L/D at high speed, subsonic maneuverconditions for current fighters is 3 to

4.

The T/W's estimated by the above procedure can be scaled back to reference conditions

using propulsion data from a candidate engine (see Figure 6-14 for trends) or the following

approximationwhen data is not available.

TATFPJDE =TSpA LEVl - I

TURN RATE

Another performanceparameteroften used is turn rate expressed in degrees per secondand

indicateshow fast the pilot can "point the nose". Turn rate for sustained maneuveringis simply

related to the g capability of the aircraft through the following well-knownexpression

V

Figures6-15 and 6-16 presentparametricdata forquickly convertingbetween sustainedmaneuver

and turn rate.

All of the expressions used or developed in this section relate to sustained maneuvering

which is an idealized steady state condition. Instantaneous maneuvering is also used as a

performance requirementand represents a more dynamiccondition. Instantaneous turn rate or

maneuverlevel is typically characterizedby maneuversat CL &tAXor a structural limit for limited

durationsand drag levels aboveavailablethrust. These maneuvers result in negative Ps and large

6-24

I

* u 0 S Si i0 0w 00


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it)~

SI-.- .b . ...........--- ------

00 00

.. . . .. .

~. , .......

-------------------------------------------------------------------------------------

.. .. . ... .. . .. . . . . .

...................................................

.......--.., k sSe ) a . jj

6-25S


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I - -- -

- , , ,--

*- . . . . . ~ .. ........ .. .... .I.....

---- ---- -I.t-- -- - -

. . . . . .5 .......................... . . . . . . . . . .---

.............. ) S.......---- 4........I. S .

............. ~~~~ ~ ~~~~~~~~~ ..... . .. ... ......................................

.S .......... ...... . . . .. . . . . .. . L . . . . . . S......... A S.

~~~~~~.......... .. I.....~.. .

......... . . . . . . . . . . . . . . v ~

0 ... ...... ............ ....................... ............. . . . . . . . . L....... . . . . . . .....

.........................

6-26


116/153

changes invelocity and/oraltitude,hence the name instantaneousas opposed to sustained.

LANDING

Landing performance is primarily dependent on tile approach speed and thedeceleration

generated from braking (ignoringreverse thrust). The approach speed is normally definedas

20% above thestall velocity for CL MAX,which can be determinedfrom Figure 6-1. A good

breaking systemcan providea mean decelerationrate (-a) of -6 ft/sec2. Figure6-17 providesthe

landing ground distance as a function of approach speed anddecelerationand is based on the

relationship:2

Distance = App-2a

Landing distancecalculationsnormallyincludethe horizontaldistance traveledduring the descent

from a standard 50 foot obstacle. Figure 6-18 presentsthis air distanceas a function of descent

angle or glide slope y, which is defined as the angle whose tangent is the ratio of vertical

distance tohorizontaldistance and is also representedby the reciprocal of the lift to drag ratio,

including power,in the approach configuration(L(D Power Approach), flapsand landing gear

down, and also approximlates the resulting thrust to weight ratio [ - D -

6-27

0 0.. . . .. . 0,0


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4---- -4-I T - r-*

11 -- - 1....i

........ 00

......... . ......

N~ 00

gap - Aajaiy OdOISaP!ID6&29


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7. PROCEDURESFOR THE FORMULATION AND ANALYSIS OF ANAIRCRAFT CONFIGURATION

This section illustrates the procedures to use for sizing and shaping an initialconfiguration,and to determine if it can meet the specified performance requirements.It uses many of the design charts in this report. The problem presented is only forfighters, but the procedure canalso be used for transports andbombers. It is good toremember this is a starting point to defining a configuration. It is assumed the outputfrom this procedurewill be used as inputs to a more elaborateaircraft synthesisprogram(References3 and 4).

Sample Problem

Performance Requirements

Max Speed: Mach= 2Cruise Speed:Mach= 0.9Radius: 325n.m.Payload: 1,8001bsMax Load Factor. 7.33g

Maneuverability:4g's at M= 0.9/h= 30,00Oft5g's at M= 0.6/h= l0,O00ft

, 4g's at M= 1.51h= 40,000ft *Take-Off Distance: 3,000ftLanding Distance: 6,000ft

Step I - Determine the gross take-offweight of this fighter fromFigure 4-2.

Ton -Miles = RangexPayload

2,000650x 1,8002,000

= 585then GTOW 36,000lbs

Step 2 - Detemine length from Figure 4-4a for a 36,0001b fighter.

Lengh = 55 ft

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* S 0


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Step 3 - Determine emptyweight frction from Figure 4-6 fora 36,O0Olbfighter.

WEMPTY 0.68

GTOW

V and WEMrl,- 24,480/bs

Step 4 - Determine fuel fraction and payload fiactionfrom Figure 4-8 for a 36,0001bfighter.

WFUEL .0.7

GTOW

WFUEL + WPL = 0.32 and WpL f 0.05GTOW GTOW

Thus: Fuel Weight = 0.27x36,000= 9,720lbs

Payload = 0.05x36,000

= 1,800lbs

Step 5 - Determinethe wettedarea from Figure 4-10 for a 36,0001b fighter.

Since WEMp,- = 24,480lbs

then SW - 1.920ft2

Step 6 - Estimate the internal volumefrom Figure4-11 for a 36,0001bfighter,or use therelationship:

V 0.0226(SWE"43

Since SWT. = 1,920fi 2

then Vol - 1,332fl3

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w


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Step 7 - Check estimated volume from Figure 4-12 for a 36,0001bfighter.

Since WMp, = 24,480

then PEMPT" = 5.8

where ULF =-1.5xMax Load Factor

= 1.5x7.33311

then pEn~q 5.8(k11hn1%un ,3.75) 5=17.01.lbs

ft3For V 0 = W E M P T Y

PEMPrY

24,48017.01

=1,439ft 3

Step 8- Average the volumefrm steps6 and 7 at thispoint of the design.

Hence V = 1,332 - 1,4392

= 1,385ft3

Step 9 - Re-compute thewetted area from Figure 4-11.

Swu = 1,972fJ

7-3

A .

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tiiim


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Step 10 - Determine fuselage diameter from following relationships:

d-=2 V7IKvL

where Kv - 0.80 (Bombers)= 0.70 (Fighters)S0.75 (Transpons)

Kv is an empirical constantdetermined from many aircraft and is based on thederivation that volume can be representedby the relationship:

V = Kv7,R2 L

This is the volume relationshipfor certain bodiesof revolution and ellipsoids.

For V = l,385ft3

L = 55ftKv = 0.70

I

then d = 2 1 1,385S(3.14)(0.70)(55)

= 6.77ft

Step 11 - Compute the fuselagefineness ratio.

L - 55.f

d -67-7fl

L 55d 6.77

I

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AI

* S SS *


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Step 12 - Check the fuselage fineness ratio from Step 11 with the data contained inFigure 3-3. The computedvalue should be within the bucket of the drag rise

curve at Mach= 1.0. This bucket is located between the values of 8 to 10.5.Hence, the computedvalueof 8.12 is a reasonableestimate. If the computed valuedid not fall within the drag bucket, then an average Lid value shouldbe selectedand the process reversed to estimatevolume and wetted area. The fuselage mayinitially be represented by a sphere, right circular cone nose, a right circularcylinder forthe center-body section,and acone frustrum for theafterbody. Typicallengths of these componentsare:

Fighter TransportNose Section 25%L 10%LCenterBody Section 50%L 70%LAfterbodySection 25%L 20%L

Step 13 - Estimate wing areafrom Figure 4-13 for a 36,0001b fighter. Assume a ratio ofSWET

4.93 for _ . Which is representativeof the F-16.SwSWING

Since SwET = 1,972ft2

SWING - 400ft2

Step 14 - Determinethe wingsweepback angle from Figure 4-16 for a cruise Mach numberof 0.9.

ALE - 490

Step 15 - Determine the wing aspect ratio from Figure 4-15.

AR = 3.0

Step 16 - Estimate the maximum L/D from Figure 5-23 at a cruise speed of Mach= 0.9.Values for fighter. typically vary from 10 to 11. Select L/D= 11 mpresentative

of the F-15 and F- 16. The aspect ratio may then be chocked using figure5-21 fora conventionally shaped fighter.

AR - 3.0

The values foraspect ratio from step 15 and 16 compare favorablyand (oVecanproceed withthe evaluation.

7-5


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0 S S S S 0 O. .

Step 17 - Determinethe wing thickness ratiofrom Figure 4-17 for an AR= 3 wing.

"t 0.055 or 5.5%C

Step 18 - Computethe wing loading at take-off.

GTOW = 36,000lbsSjvjv -=400ft 2

W 9 0 b s

Step 19 - Determine the span loading ftomr Figure 4-14.

AR 3.0

w

W=o30psf

S

b 2

The span loading may also be computed from the relationship:

AR WI

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Step 20 - Determine wingplanform from Figure 4-18 fora 36,0001b fighter.

b GTOW = 36,000 (from span loading equation)4'. W 30b 2

-34.6

CTAssume a wing taper ratio, = 0.2, which is representative for a fighter.

CR = (2S By rearanging equation from Figure 4-18

Ce= 19.30ft

then C7= 3.86ft

A wing planform cannow be generated to reflect awing,A/'= 49, Ci= 19.30ff,C7= 3.86ft, and b= 34.6f.

Step 21 - Determine the size of the horizontal tailusing Figure4-19 and a preliminary3view drawingto estimateIHT for a fighter.

Since C = ( + CT CRCT

=13.3ft

an l Sw = 13.3x400

-= 5,320fl 3

then tosfJ = 1,450ft3

and s/if -1,450

If a value for Ittr can not be 6etermined,assume the horizontal tail area is 20%

of the wing area. This is a non*al value and satisfactoryfor this stage of thedesign cycle.

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Step 22 - Determine the size of the vertical tail using Figure 4-20 anda preliminary 3-viewdrawing to estimate IVT for a fighter.

bSw = 34.6x400

,1 = 13,840ft3

then IVTSVT = 1,070ft 3

an d 8VT=- 1,070

If a value for Iv can not be determined,assume the vertical is 20% of the wingarea. This is a nominal valueand satisfactory for this stageof the design cyclk.

Step 23 - Determine the subsoniczero lift drag, CD0, from figure 5-10. Based on otherfighter aircraft assume an equivalent skin friction coefficient of 0.004.

For SwT = 1,972.ft2

f = CfeSwET = CDOSREFf = O.004x1,972

= 7.89

then Cw f

7.89400

- 0.0197

Step 24 - Determine wing efficiency factorfrom Figure 5-8.

For AR= 3.0, e- 0.85

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* 0 0 0 S 0 0 0


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* 0 0 S 0 O0 .'

Step 28 - Determinethe subsonic lift curve slope from Figure 5-17

0 For ALjE 490, Cie= 19.30ft, C7= 3.86fl,and b= 34.6ftthen Ay,-= 420 and AR= 3.0 and rom Fig 5-17

CLa t = .2 r

= 0.056deg

Step 29 - Determinethe optimum lift coefficientfor cruise flight from the relationshipsonpage 5-29:

CDOCL OPT ~ F where K= 0.125 from step 25

=i0.0197

\0.125

- 0.397

Step 30-Determine the 2T ratio for this postulated fighter from figure 3-4, T

W Wrequired at take-off for a highly agile fighterfor the maneuverabilityspecified will

Wapproach current inventory aircraft. For a -S . 90, assume a minimumST

requirementof T = 1.0. This value may have to be iterated if ou r aircraft doesW

not meet the specifiod maneuverabilitygoals.

Step 31 - Determinethe inaximumlift coefficient from figure 6-1.

For A,,.E 494 ; CLm\,c 1.5

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O O0 0 V 0' '0

Step 32- Determinethe take-off distance fromFigures 6-4.

wFor A =49 0 , CLan1.5 , d 90psfL LMAX =S.5

"VTO= 155knots from figure 6-3

then -=80(T=

T)

w,ere we assume T = 1.0w

and Ca.o = 1.1.5 (CLTO= 75 % CLMAX)

Take -Off Distance = 1,2001f

Step 33 - Determinethe approximatecruise range at Mach 0.9 and 30,000fi from Figure6-7

or the relationship:

R 2.3_V L..-05SF C WFMAL

132oMA)R =LogWINM

SFWF L

Where L GTOW - 3 0%(WFUE1)

whr ZTOW - 7O%(WFUU)

36,000 - (0.3)(9,730)36,000 - (0.7)(9,730)

= 1.133

and SFC = 1.0 at M 0.9; L/D 10.1; IVF, =9,730lbs

then R 651ni.

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* 0 0 O O O 0 O,

Step 34 - Determinethe sustained "g" capabilityfrom Figure6-12 at Mach 0.9 and 30,000ftor the relationship.

n reAR T qCD,

T

Assume: T = 0.52 (from Figure 6-14)WS--77psf (50% Fuel load)

Sq = 360psf

CDO = 0.0197e = 0.85AR = 3.0

then n = 4.0g's

Step 35 - Determinethe sustained"g" capabilityat Mach 0.6 and 10,000ftfrom Figure6-I1.

Assume: T = 0.84; CDo,= 0.0197 w- = 77psfS

q=

367psfthen n = 5.34g's

Step 36 - Determinethe sustained*g"capabilityat Mach 1.5 and 40,00ft from Figure6-13.

A,vume: w . 0.65, CtX=-0.041W-- u77psfSq - 616psf

then n = 4.54g's

7-12

! ml m w .. m m m u l mm , u r ll w m m m m u =w


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S0 0

@Step 7 - Determine the turn rate capability at M= 0.6 and 10,OO0ftfrom Figure 6-15.V = Ma

= 0.6(1,073)

= 644 fA = 383knotssec

0= 15.0deSgi for n = 5.34g'ssec

Step 38 - Determinethe turn rate capabilityat M= 1.5 and 40,000ft from Figure 6-16.

V = 1.5(971)

= 1,4571 = 863knotssec

= 5.6.dg for n = 4.54g'ssee

Step 39 - Determinethe landingdistance from figure 6-2,6-17and 6-18. Assumea landingfuel fractionof 10% (for reserves).

* WLjVD = 36,000 - 0.90(9,720) = 27,252/bs

then W 27,252 = 68 wa CL 1.5 from step 31= 400 L

VsrAU"= 116ksnos from Figure 6-2

VApe = 139 nowts ftom Figure 6-17

Landing Ground Distance = 4500feet

assume a typical glide angle of 30 then

Laiuling descent ovwr 50ft = 950feet

Total Landing Distance - 5450ftet

This completes the preliminary aerodynamic and perfontance characteristics. Thepreliminary perfomance indicates the conceptual aircraft can meet the initial specified goals.The next step is to input the configuration into an aircraft synthesis program and conductparametric trade-off analysis and sensitivity evaluations to arrive at a more optimumconfigumtion.

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* 0 0 0 0 , "

O4,

*. CONCLUSIONS

This reportprovidesdesign data and procedures toinitiallyformulateand analyze an aircraft

configuration. It is based on an array of data from past militaryaircraft. Many convenientcharts

are includedto rapidlydefine pertinentfeatures of a configuration,and to evaluate their impact

on the lift and dragcharacteristics.

The design data and procedurescan be used to perform the followingtasks:

Size and shape initial fighter and transportconfigurations.

Estimate gross-take-offweight, empty weight and fuel weight.

Define fuselage fineness ratio andwing geometry.

* Size horizontal and vertical tails

Estimateaircraft wetted area and volume

Determine pertinent aircraft configurationparameters such as wing loading,

span loadingand thrust loading.

* Predict the drag characteristicsat subsonic, transonic and supersonic speeds

Predict lift curve slopeacross Mach range

Estimate naximum lift-to-drag ratio

* Assess performtncecapabilityof conceptual aircraft

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9. REFERENCES

1. Nicolai,LelandM., "Fundamentalsof AircraftDesign",METS,Inc, SanDiego,CA, 1984.

2. Raymer, Daniel P., "AircraftDesign-A ConceptualApproach" AIAA, Washington D.C.,1989.

3. Rinn, S. "CASPPreliminarySizing ProgramWrightLaboratory, Wright-PattersonAFB,Ohio, 1989.

4. Hollowell, S. et al, "InteractiveDesign and Analysis System", N.A.82-467, RockwellInternational,Los Angeles CA, 1982.

5. Schemensky,R.T., "Developmentof an EmpiricallyBased ComputerProgram to Predict

The Aerodynamic Characteristicsof Aircraft," AFFDL-TR-73-144,Wright- PattersonAFB, Ohio 1973.

6. Ellison, D.E., "USAF Stability and Control Handbook,(DATCOM)", Air Force FlightDynamics Laboratory,Wright-PattersonAFB, Ohio, Revised 1976.

7. Perkins,CourtlandD. and Hage, RobertE., Airplane"Performance,Stabilityand Control,"John Wiley & Sons Inc, September 1954.

8. Wood, K.D., "AircraftDesign", Johnson Publishing Co.,Boulder, Colorado,1966.

9. Roskam, j., "AirplaneDesign", Parts I to VIII, Roskam Aviation & EngineeringCorp.,Ottawa, Kansas, 1989.

10 . Genston,W., "TheEncyclopediaof World Air Power,"Crescent Book, CrownPublishers,Inc., 1986.

II, Taylor, U.W.R., "Janes All The World Aircraft,"Janes PublishingCo, London, England,1984.

12. Aviation Week & SpaceTechnology," 1992 AerospaceForecast,"Vol. 136. No. 11, NewYork, N.Y. March 16, 1992.

13. Coming,Gerald. "AirplaneDesign", Edwards Brothers,Inc, Ann Arbor, Michigan. 1953.

14. Caddell,WKE.,"On the Use of AircraftDensityIn PrelitninaryDesign",SAWE PaperNo.813, 5 May 1969.

15. Abbot, 1.11.,"Theory of Wing Sections,"Dover Publications,hic., 1959.

9-1

LS


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* 16. Abbot, I.W., "Characteristicsof Wing Sections," NACA TR 824, 1945.

17. Jones, R.T., "Propertiesof Low AspectRatio Wings", NACA TR-835, 1946.

18. Johnson, M.E., "Design and Analysisof ManeuverWing Flaps at Supersonic Speeds,"NASA CR-3939,1985.

19. Hoemer, S.F., Fluid DynamicDrag," Midland Park, NewJersey, 1965.

20. Ely, W.E. et el, "Prediction of Aircraft Drag Due to Lift," Air Force Flight DynamicsLaboratory, AFFDL-TR-71-84,Wright-PattersonAFB, Ohio, June 1971.

21. Gollos, W.W., "Transonicand SupersonicPressure Drag fora Family of ParabolicTypeFuselages at Zero Angle of Attack," Rand RM 982, 1952.

22. Morris, D.N., "A Summaryof the SupersonicPressure Drag of Bodies of Revolution",

Journal of AeronauticalSciences, Vol, 28, July 1961.

23. Nelson & Welsh, "Applicationof the Transonic& SupersonicArea Rule to the Predictionof Wave Drag," NASA TN D-446, September 1960.

24. Mirels, H., "Aerodynamicsof SlenderWingsand Wing BodyCombinationsHaving SweptTrailing Edges", NACA TN-3105, 1954.

0 25. Hall, C.F., "Lift, Drag and PitchingMoment of Low Aspect Ratio Wings,"NACA RMA53A30, 1958.

26. Carlson,H.W. and Mann,MJ.. "Survey andAnalysis of Research on SupersonicDrag-

Due-ToLift Minimizationwith Recommendationsfor Wing Design," NASA Tech Paper3202. 1992.

27. Harris, R., "An Analysis and Correlation of Aircraft Wave Drag," NASA TM X-947.1964.

28. May, F. and Widdison,C.A., "STOL High Lift Design Study" AFFDL TR-71-26,WrightPatterson AFB. Ohio, April, 1971.

29. Bonner, E. and Gingrich, P., "Supersonic Cruise.lransonic Maneuver Wing SectionDevelopmentStudy," AFWAL-TR-80-3047,Wright Pa-wum AM, Aiu, Ir.9.

30. Carlson, 11. and Miller, D., "Numerical Methods for the Design and Analysis of Wingsat Supersonic Speeds," NASA "IN D)-7713, 1947.

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* S S 0 0 S "

31. Miller, D., "SupersonicWing Design ConceptsEmployingNon-LinearFlows,' 14th ICASProceedings, 1984. - lt

32. Miller, D. and Schemensky, R., "Design Study Results of a Supersonic CruiseFighterWing", AIAA Paper 79-0062 1979.

33 . Etkins, Bernard, "Dynamicsof AtmosphericFlight," JohnWiley & Sons, 1972.

34. Rutowski,E.S., "EnergyApproachto the GeneralAircraft PerformanceProblem,"Journalof Aeronautical Sciences, March 1954.

35 . Bryson,A.E. and Desai, M.N. "Energy State Approximationin PerformanceOptimizationof Supersonic Aircraft", Journal of Aircraft, Vol. 6, November 1969.

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SS .... 00


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APPENDIX A!P

Representative Operational an d AdvancedConfigurations

This appendixis composed of 3-view drawings of several current and advanced military

aircraft. Each drawingcontains the wing aria, span, length gross take-offweight andmaximum

speed. It is to illustrate the size and shape of aircraft configurations based on specific

performancerequirements.

A-I

* 0 0 0n w0 0 0 J 0 0


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ImI

Si

I' A

rr &Ee

A-2-


138/153

S S S 5 0 O O, "O6

c]

-)v

L.-

4

:: EL 305

A-3C '0

A-C)


139/153

V 0

00

(U) -

00p

A-4A


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141/153

rjr(AinIKcr cm

CA

coi LL

A-6


142/153

II

*4"

00

00

* S

OO

I Sc

CL EC.)

C3 >

A-7

L


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*

!I

0

Ii

C

0

0CQ CL

0

LLC A ~

Il~CD E 4>i

A-81


144/153

O

toN

),-Is

C I C .-

A-9


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0 0 0 O0 '0" . '

0'0

CDM

in4.2

I (U

:1I.

w))

A-IO


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APPENDIXB_ VOLUME AND AREA RELATIONSHIPS

This appendixprovides a numberof mathematicalequationsto compute the volume and wettedarea of several simple shapes. They canbe quickly used tocheckthe volumeand area ofdefinedconfigurations.

1. Sears-Haack Body

V=I X2 R2L

16

SwE= 1.867L"V"=1.27dL

2. Ellipsoid

V=2..J 2L3

3. Von Karman Ogive

0 V-- R2L2

4. Prolate Spheroid

V=1=ab0 where: a- major axis3

b= minor axis

5. Sphere

v i&3Sw4tR 2

S~B-I

,O, e

* .... 0 0mmWm~~wwmme.mwm mS S S~em Semmmmm 0


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6. Right Cone

V=I!R 2L

3

SwEgrT% R'O+L' (Curved Surface)

7. Right Cylinder

V=id?2L

SwET=27xRL (Curved Surface)

8. Cone Frustrum

V=IE R +R R +R 2)

SWET ='[2(RI R4 2 +2(1 -R2)2 (Curved Surface)

Where: RI= Radius of BaseR2= Radius of TopL= Length

9. Formulas for Sears.Haackbody of revolutionshapes, volume and drag

The factor d/L is the fineness ratio, diameter/length.

Case I: Given length, givenvolume

(i~~)

valumme n2LP

T6

CD O 1 d

B-2

o

*ie l mlili lm i m m 4l I i ll l l , .iii m


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149/153


150/153

equationis the profilewave drag due to camberand thickness.The minimumprofile dragoccurs

for a symmetrical wedgeshape, and results in K2= 0 and Kr= (t/c)2 so that

CDWAV" 4l (C-3)

The first term is the wave drag due to lift and is somewhat similarto subsonic induced drag.

The second term is the wave drag due to thicknessand indicates the extreme importance of

keeping wings thin on supersonic aircraft. Th e dependence on Mach number is also indicated

in the equations.

The wave drag due to lift term from equationC-3 can be expressed as

CDw =KC2 where K= 1 . for M>ILAVCL

The above expression is often usedas an asymptoticlimit for wingsat higher Mach numbers.M

Integrationof the pressure in equation C-1 in the lift directionyields4ct

CL= 4 (C4)

or

dC L 4 4

If we ignore friction drag%vecan combine the equation for CL and CD, form CL/CO.

differentiate andestablish the maximunm(LAD)ratio for a 2.D wedge

LMAX 4 j

Whichoaeagain indicates the importanc of thin shapes at supersonic speeds.

C-2

0. . . "0 S" i - - 0-I...'l ii 0.i ' I0[i 1*"i ....


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The wave dragof uncambered anduntwisted trapezoidal wings can be estimated by

CW) t FOR PcotAS > 1

=Ktane FOR IcontA, < 1

withK= 16/3 for biconvex airfoils

K= 4 for double wedge airfoils

Note that the upperexpression is identical to the 2-D wedgeshape in equation C-3.

The above expressions are for ballparkestimates onlyand do not capture manyof the

finerdetails that determinewing wave drag. Leading edgebluntness,aspect ratio, camber and

location of maximumthicknessare all importantparameterswhich can significantly effectwing

wave drag.

Referring to Figure C-1 the followingobservationsare made. Above PcotALE> 1 where

the wing leadingedge is supersonicthe drag is shown to be a strong function of the chordwise

locationof maximum thickness,"b" n Figure C-1, and approachesthe (2-D) symmetric wedge

value given by equation C3 (CL= 0) at higher Mach numbers. The curve is alteredbetween

PcotAtE > I and an abscissavalue that representsthe sweep of line of the maximum thickness.

For example, for b=0.3 this value PcotAL= 0.7 which represents where the sweep angleAO ;

becocues subsonic in an analogous marner to the leading edge. At lower Mach numbers the

location of optimum chordwise thickness reversesand minimum drag is represented by nmre

formwid thickness distributionscharacteristicof subsonic flows.

C-4

0 O O 0-


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4.... .. ......... .. ................. . ... .. .........

...... ..... . . . . . . .

... . . ... . . . -- -- -

.. ..... ~.... .. . . .. .00... .. .. . .

... .. ... .. I....... I .......

.. ........ .... . ....

I IN

Sanity Check - Data for Aircraf Design Balaji

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Transcript of Sanity Check - Data for Aircraf Design Balaji