Copyright ©1996, American Institute of Aeronautics and Astronautics, Inc.

AIAA Meeting Papers on Disc, 1996, pp. 469-481A9638748, AIAA Paper 96-4191

Procedure to match experimental and analytical aerodynamic data for acommercial aircraft

Surya SurampudiRaytheon Aircraft Co., Wichita, KS

Mark RichardsonRaytheon Aircraft Co., Wichita, KS

Dayton HartleyRaytheon Aircraft Co., Wichita, KS

AIAA, NASA, and ISSMO, Symposium on Multidisciplinary Analysis and Optimization,

6th, Bellevue, WA, Sept. 4-6, 1996, Technical Papers. Pt. 1 (A96-38701 10-31), Reston,

VA, American Institute of Aeronautics and Astronautics, 1996, p. 469-481

A general method of matching theoretical steady-state doublet lattice aerodynamic loads to experimental(wind-tunnel) results, based on a force and moment equivalent system philosophy, is presented. The practicalapplication of this method involves the use of a DMAP alter and DMI cards in a MSC/NASTRAN bulk data deckto modify the aerodynamic force matrices (WKK in a static aerodynamic solution, and WTFACT in a dynamicsolution). Results of the matching procedure are given for a commercial swept-wing, cruciform tail business jetaircraft, indicating that the method matches theoretical aerodynamic coefficients and the shapes of theaerodynamic distributed loads. (Author)

Page 1

96-4191

A96-38748

AIAA-96-4191-CP

Procedure to Match Experimental and Analytical AerodynamicData for a Commercial Aircraft.

Surya Surampudi*, Mark Richardson* and Dayton Hartley*.

Raytheon Aircraft Company, Wichita, Kansas.

Abstract

A general method of matching theoretical steady-state doublet lattice aerodynamic loads to experimental(wind-tunnel) results, based on a force and moment equivalent system philosophy, is presented. Thepractical application of this method involves the use of a DMAP alter and DMI cards in a MSC/NASTRANbulk data deck to modify the aerodynamic force matrices (WKK in a static aerodynamic solution andWTFACT in a dynamic solution). Results of the matching procedure are given for a commercial swept-wing, cruciform tail business jet aircraft indicating that the method matches theoretical aerodynamiccoefficients (e.g. dCL/dot) and the shapes of the aerodynamic distributed loads.

Nomenclature

a = Angle of incidence.a, b = Constants used in the linear weighting

function.C = Local chord length.C = Standard mean chord (SMC).CL = Local lift coefficient.CL = Wing/fuselage/nacelle lift coefficient.a I = Wing/fuselage/nacelle lift curve slope.a i TT = Total tail lift curve slope.h0 = Wing/fuselage/nacelle aerodynamic

center.Lwi = Total wind tunnel lift between section

boundaries.LJ = Theoretical lift on element.q = Dynamic pressure.W = Width of lifting surface or slender body

element.

Wi = Element lift weighting coefficients.Xt — Location of lift with respect to leading

edge.Xac = Aerodynamic center location from

leading edge,de/dcc = Steady state downwash derivative.

Introduction

This paper describes a methodology to matchsteady aerodynamic forces obtained by analyticalmethods with wind tunnel results. Thismethodology plays an important role during thedesign and certification phases of new aircraftprograms. This procedure is crucial to bothaerodynamics engineers working on loads andstructural dynamics engineers developingaeroelastic models. The purpose of this study is toestablish a procedure, for the Raytheon Aircraft

* Senior Engineer, Structural Dynamics group. Associate Fellow AIAA.f Engineer, Aero/Loads group. Member AIAA.* Group Engineer, Structural Dynamics. Senior Member AIAA.Copyright © 1996 by Raytheon Aircraft Company, WichitaPublished by the American Institute of Aeronautics and Astronautics, Inc., with permission

469American Institute of Aeronautics and Astronautics

company, to modify analytical aerodynamic forcesto be consistent with wind tunnel results.

A survey of existing methods used by variousresearchers was conducted to select a suitablematching procedure for this study. Giesing,Kalman and Hodden1 developed a correction factormethod to modify doublet lattice aerodynamics bymatching total experimental force data. Pitt2

developed a correction factor technique whichmodified strip aerodynamic influence coefficientsusing data generated by a transonic full potentialfluid dynamics program. Pitt used the correctionfactors derived from the steady state data to modifyunsteady doublet lattice calculations. Wieseman3

identified three correction factor methodologieswhich use steady experimental or analyticalpressure or force data to correct steady andunsteady aerodynamic calculations.

A commercial business jet aircraft, a Hawker 1000is considered for the current study using a methodsimilar to Giesing et al. This paper describes themethods developed for the matching ofaerodynamic forces for an aircraft responding to avertical gust, although the general principles can beapplied to many loading conditions both static anddynamic.

Approach

Static Aeroelastic AnalysisStatic aeroelastic analysis deals with the interactionof aerodynamic and structural forces on a flexibleaircraft that results in redistribution ofaerodynamic loading as a function of speed. Theaerodynamic load distribution and consequentinternal load and stress distributions are of concernto both aerodynamicists and structural analysts.The static aeroelastic capability inMSC/NASTRAN addresses these needs bycomputation of aircraft trim conditions, withsubsequent recovery of structural responses,aeroelastic stability derivatives and staticaeroelastic divergence dynamic pressure. TheMSC/NASTRAN user guide4 describes themethodology and equations used in this analysis.However, for the purposes of this study, the staticaeroelastic solution (module 144) was used as aconvenient tool for obtaining a rigid aircraft unitload distribution due to incidence. The output ofthe static aeroelastic analysis contains the elementaerodynamic forces and aircraft aerodynamiccoefficients (e.g. CLa and CM(X) for the analysisflight condition. Using these results and therequired wind tunnel data, correction factors forthe theoretical aerodynamic forces on the wing,fuselage and horizontal stabilizer were calculatedusing the procedure described below :-

Aerodynamic Model

Wing

11060 11001

Figure 2. Wing lifting surface (LS) elements.Figure 2 shows the aerodynamic model for thehalf wing. The model consists of 15 spanwisestrips and 4 chordwise strips to create 60 boxes.The wing spanwise grid boundaries were chosen

to coincide with the existing loads model for theHawker 1000. The planform is flat (i.e. nodihedral) and extends to the aircraft center-line.

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Fuselage

Fuselage length (I) = 565.992 ins.

Fuselage Interference elements.

* s 7 a a M ii

Fuselage slender body elements.

Figure 3. Fuselage slender body (ZSB) and interference elements.Figure 3 shows the aerodynamic model for thefuselage. 25 slender body elements and 7interference elements were used to model thefuselage. The fuselage slender body elementboundaries were chosen to coincide with theexisting loads model for the Hawker 1000. Theinterference element boundaries at eta = 0.4380

and eta = 0.6854 have been chosen to coincidewith the intersection of the wing leading edgeand trailing edge with the center-line of theaircraft, while those at eta = 0.7078 and eta =0.8986 coincide with the leading edge andtrailing edge of the engine pylon.

Horizontal stabilizer

Figure 4. Horizontal stabilizer lifting surface (LS) elements.

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The aerodynamic model for the horizontalstabilizer is shown in Figure 4. It consists of 7spanwise strips and 4 chordwise strips to make28 boxes. The horizontal stabilizer spanwise gridboundaries were chosen to coincide with theexisting loads model for the Hawker 1000. Itwas found that the stated MSC/NASTRANmodeling requirement for box boundariesdownstream of the main lifting surface to be atthe same spanwise position had little influenceon the results.

Nacelles and pylonsFor the existing loads model of the Hawker1000, the longitudinal aerodynamiccharacteristics of the engine nacelles and pylons(i.e. lift and pitching moment) were modeled aspoint loads on the structure of the rear fuselage.This method was also used for theMSC/NASTRAN analysis.

Vertical stabilizerFor symmetric loading conditions, the verticalstabilizer is not important and was notconsidered as an aerodynamic surface.

Control surfaces

The control surfaces such as elevators, rudder,ailerons and flaps are considered to be fixed inan undeflected position.

Experimental Aerodynamic Data

The experimental aerodynamic data used forstructural load calculations for the Hawker 1000is published in the form of aerodynamic datasheets5, which give the tail-off lift curve slope(dCL/dcc) variation with Mach no., the tail-offaerodynamic center (h0) variation with Mach no.and the wing and fuselage lift distributions dueto incidence which are also functions of Machno. Horizontal stabilizer aerodynamic data used

for this procedure is the isolated tail lift curveslope (dCL/doOTT variation with Mach no., thesteady state downwash derivative (ds/da)variation with Mach no. and the spanwise liftdistribution due to incidence variation withMach no. Note that all wind-tunnel incidencedistributions used for this matching procedureare for the aircraft structure undistorted from itsjig shape. Also, the matching proceduredescribed here is dependent on the continuouswind tunnel distributions being idealized into adiscrete 'strip load' form.

Methodology to Match Analytical andExperimental Aerodynamic Data

A static aeroelastic analysis was conducted forthe aircraft flying at an angle of incidence of0.172 degrees (0.003 radians) and a Machnumber of 0.795. The MSC/NASTRANsolution was used to generate a theoreticalaerodynamic load distribution, due to incidence,for two rigid body aircraft configurations. Therigid aircraft solutions were achieved by usinglarge values of Young's modulus (E) and shearmodulus (G) in the MAT1 material propertiescard. The first configuration (case 1) is for thewing, fuselage & nacelles (no horizontalstabilizer). The second configuration (case 2) isfor the complete aircraft. The wind tunnellongitudinal balance out data, specificallydCL/da and h0, are for the aircraft withouthorizontal stabilizer. Therefore the wing,fuselage & nacelle (case 1) aerodynamics werematched using these quantities in conjunctionwith the wing, fuselage and nacelle liftdistributions due to incidence. The horizontalstabilizer aerodynamics were matched using acombination of isolated tail lift curve slope,steady state downwash derivative (de/doc) andspanwise lift distribution due to incidence.

Figure 6 shows the positions of the theoreticallift forces acting at the lifting surface element1/4 chord points for a 4 chordwise elementsection.

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LS\ element 1

LSelement 2

LSelement 3

LSelement 4

U-x-—•

Section chord = cL,

X, =0.06250-

leadingedge

.chordJlne..

t~"X,= a5825c

•X.= O.B125.

Figure 6. Aerodynamic forces along chord.

In order to adjust the theoretical lifts a linearweighting function was used. Note that in thefollowing equations the aerodynamic grid liftsare acting at the grid 1/4 chord points rather thanthe grid box centers.

The linear weighting function is defined as :-

.(1)Equating wind tunnel loads and moments withtheoretical loads and moments, for a liftingsurface section gives :-

(2)

.(3)

Substituting equation 1 into equations 2 and 3gives :-

(4)

Lwi.(Xac)ie = L.(a. Xi + b). Xi ..(5)

Where :-

Lwt is the total wind tunnel lift at a particularwing section (derived by integrating the

spanwise CI.C/CL.C between cross-sectionboundaries).Li is the lift calculated by MSC/NASTRAN atthe lifting surface element 1/4 chord point for thesame wing section considered for wind tunneldata (ref. figure 6).

(Xac)ie is the wind tunnel aerodynamic centerlocation from the leading edge for the same wingsection.

Xi is the location of the lifting surface element1/4 chord point from the leading edge. ( ref.Figure 6).

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Equations (4) and (5) are solved simultaneouslyto yield expressions for ' a ' and ' b ' which are

Results

-(4)

a - ,(5)

The values obtained for 'a' and 'b' can then besubstituted back into equation (1) to yieldweighting values ' Wi' for each aerodynamicelement lift.A similar procedure was applied to the fuselagelift distribution due to incidence. The lift isacting at the center-line of each slender bodyelement and the weighting factor' W>'' is simplythe ratio of the wind tunnel 'strip' load (i.e. theincidence grading Lwij q. w. CL integratedbetween element boundaries) and the slenderbody element theoretical lift.

W, = L*/L .(6)

In practice the weighting factors are applied toboth the MSC/NASTRAN lifts and momentsusing a combination of DM AP instructions andDMI cards.

a i (/rad)ho (%C)a i TT (/rad)

MSC/NASTRANUNMATCH-

ED5.846619.84

3.1994

MSC/NASTRANMATCHED

6.878025.71

2.1475

WINDTUNNEL

6.878025.50

2.0197

Table 3. Longitudinal balanceparameters.

A comparative study of analytical results usingMSC/NASTRAN and wind tunnel data wasconducted for the following two cases :-

Case 1 : Aircraft with wing, fuselage andnacelle, (horizontal stabilizer was not included).Case 2 : Complete aircraft model (horizontalstabilizer results with downwash effects).

Table 3 presents the values of lift curve slope forcases 1 and 2 and the location of theaerodynamic center for case 1. This tablepresents a good comparison of MSC/NASTRANresults with wind tunnel data. Figures 7, 8 and 9show the results for case 1. Figure 7. shows thespanwise variation of non-dimensional liftcoefficient (CL.c/ CL . c) for the aircraft wing.This plot shows close agreement ofMSC/NASTRAN matched results with windtunnel data. Figure 8 shows the variation ofaerodynamic center locations at various cross-sections of the wing. This plot clearly indicatesthat the aerodynamic moments calculated byMSC/NASTRAN closely matches with theaerodynamic moment obtained by wind tunnelexperiments. Figure 9. shows the variation ofnon-dimensional lift coefficient Lwt/q. w. CL atvarious fuselage locations. The opposing windtunnel load and the theoretical load in the regionof the wing center-section results from the windtunnel wing center-section load beingredistributed onto the fuselage. The wing center-section lift has been removed from theMSC/NASTRAN matched aerodynamics by theapplication of zero factors. TheMSC/NASTRAN matched results for fuselagecompare well with wind tunnel aerodynamicdata. Figures 10 and 11 show the results for case2. The downwash is due to the rigid aircraftderivative (ds/doc) with no aeroelastic alleviation

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or spanwise variation. Figure 10 shows thevariation of non-dimensional lift coefficientwith wind tunnel data. Figure 11 shows thevariation of aerodynamic centers at varioushorizontal stabilizer cross-sections. As for case1, both the aerodynamic lift and momentcalculated by MSC/NASTRAN compare wellwith wind tunnel aerodynamic data.

Concluding Remarks

Based on the results presented in this paper, thematching procedure developed during this studyis an acceptable method for modifying theMSC/NASTRAN doublet lattice theoreticalaerodynamics to wind-tunnel values. Eventhough the results were presented for theHAWKER 1000, this procedure can be adaptedto other commercial and military aircraft.

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Hawker 1000.Wing spanwise lift distribution due to incidence.

M=0.795

S3u

o"55

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Spanwise position (eta)

x WIND TUNNEL RESULTS

_ -e_ NASTRAN RESULTS WITH CORRECTION FACTORS

A NASTRAN RESULTS WITHOUT CORRECTION FACTORS

Figure 7.

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Hawker 1000.Wing spanwise aerodynamic centre distribution due to incidence.

M=0.7950.35

0.3

0.25 ...

0.2 - - - - -

0.15

0.1 -

0.05

00.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Spanwise position (eta)

—e,— WIND TUNNEL RESULTS

_ -x _ NASTRAN RESULTS WITH CORRECTION FACTORS j

—e— NASTRAN RESULTS WITHOUT CORRECTION FACTORS I

Figure 8.

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Hawker 1000.Fuselage lift distribution due to incidence.

M=0.795

0.100 0.200 0.300 0.

Fuselage station (eta)

-*— WIND TUNNEL RESULTS

-e- NASTRAN RESULTS WITH CORRECTION FACTORS

-A_ NASTRAN RESULTS WITHOUT CORRECTION FACTORS

Figure 9.

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Hawker 1000.Horizontal stabilizer spanwise lift distribution due to incidence.

M=0.795

(0.au

.a1O

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Spanwise position (eta)

—*—WIND TUNNEL RESULTS

_ .Q_ NASTRAN RESULTS WITH CORRECTION FACTORS

—A—NASTRAN RESULTS WITHOUT CORRECTION FACTORS

Figure 10.

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Hawker 1000.Horizontal stabilizer aerodynamic centre distribution due to Incidence.

M=0.7950.3

0.25

0 . 2 - - - -

o 0.15tox

0.1

0.05

0.000 0.100 0.200 0.300 0.400 0.500 0.600 0.700 0.800 0.900 1.000

Spanwise position (eta)

! a~ WIND TUNNEL RESULTS |

_ -x- NASTRAN RESULTS WITH CORRECTION FACTORS

—e—NASTRAN RESULTS WITHOUT CORRECTION FACTORS

Figure 11.

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References

1. Giesing, J.P., Kalman, T.P., Rodden, W.P.,"Correction Factor Techniques for improvingaerodynamic prediction methods", NASA CR.144967, 1976

2. Pitt, D.M. and Goodman, C.E., "Fluttercalculations using Double Lattice Aerodynamicsmodified by the Full Potential Equations", AIAApaper 87-0882, 1988

3. Wieseman, C.D., "Methodology for matchingexperimental and analytical aerodynamic data",AIAA paper 88-2392, 1988.

4. Rodden, W.P. and Johnson, E.H., "AeroelasticAnalysis ", MSC/NASTRAN User GuideVersion 68

5. British Aerospace Hawker 1000Aerodynamics Data Sheets.

ADS 125/1/8001 iss. 2 - Balance out data(zero flap).ADS 125/2/8001 iss. 1 - Downwash,downwash factor and tailplane liftslope flaps 0,dive brakes closed.

ADS 125/4G/800I iss. 1 - Wing spanwise loadgradings flaps 0.ADS 125/11/8001 iss. 1 - Fuselage verticalload distributions - clean wing.ADS 125/30/8001 Iss. 1 - Loads on enginenacelles and pylons - flaps up.ADS 125/31T/800 Iss. 1 - Tailplane spanwiseload grading.ADS 125/2/800 Iss. 2 - Tailplane lift curveslope.

Acknowledgments

Authors would like to express sincereappreciation to Dr. Erwin Johnson of MacNealSchwendler Corporation and Colin Burgess ofRaytheon Corporate Jets (U.K) for thesuggestions and advise given to them throughoutthis study. The encouragement and supportgiven by Larry Young, Jim Megrail, KevinMarks and Stan Lemke of Raytheon AircraftCompany for this study are gratefullyacknowledged.

481American Institute of Aeronautics and Astronautics