Development of Aerodynamic Prediction Methods for Irregular Planform Wings

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NASA Contractor Report 3664

Development of AerodynamicPrediction Methods forIrregular Planform Wings

David B. Benepe, Sr.

CONTRACT NASl-15073FEBRUARY 198 3

. .

Nnsn

LOAN OPY:RETUR?AFWLTECliNICALIBiiKJRTIANDAFB,M.



TECH LfBFtARY KAFB, N

NASA Contractor Report 3664

Development of AerodynamicPrediction Methods forIrregular Planform Wings

David B. Benepe, Sr.General Dynamics

Fort Worth, Texas

Prepared forLangley Research Center

under Contract NAS l- 15 0 7 3

NASANational Aeronautics

and Space Administration

Scientific and Technical

Information Branch

1983

OOb2467





TABLE OF CONTENTS

LIST OF TABLES

LIST OF FIGURES

SUMMARY

INTRODUCTION

LIST OF SYMBOLS & NOMENCLATURE

SCOPE OF THE INVESTIGATION

EXPERIMENTAL DATA BASE

GEOMETRIC TERMS AND EQUATIONS USED IN ANALYSES AND PREDIC-TION METHODS

Wing Description

Geometric Equations

Body Description

EVALUATION OF EXISTING METHODS

WINSTAN Empirical Method for Nonlinear Lift ofDouble-Delta Planforms

The Peckham Method for Low-Aspect-Ratio IrregularPlanform Wings with Sharp Leading Edges

The Peckham Method as Modified by Ericcson forSlender Delta-Planform Wings

The Polhamus Leading-Edge Suction Analogy as Modi-fied by Benepe for Round-Leading-Edge Airfoils

Pagevi

viii

xxxv

1

4

16

18

37

37

37

45

48

50

52

53

53

. . .111



TABLE OF CONTENTS (Cont'd.)

Aeromodule Computer ProcedurePage

60

Lifting Surface Theory of Mendenhall, et al, IncludingEffect of Leading-Edge Suction Analogy

The Crossflow Drag Method

DATA CORRELATIONS

Nonlinear Lift

Drag Due to Lift

Aerodynamic Center Location

High Angle of Attack Pitching-Moment Characteristics

PREDICTION METHOD DEVELOPMENT

Lift Characteristics Prediction

Drag Characteristics Prediction

Minimum Drag

Friction, Form and Interference Drag

Friction Drag

Form Factors

Interference Factors

Base Drag

Miscellaneous Drag Items

64

65

94

94

98

104

105

198

199

201

202

202

203

205

207

208

208

iv



-

TABLE OF CONTENTS (Cont'd.)

Drag Due to Lift

Pitching-Moment Characteristics Predictions

Aerodynamic Center.in Primary Slope Region

Pitch-Up/Pitch-Down Tendencies

Pitching-Moment Variation with Angle of Attack

REVISIONS TO BASIC METHODS

Addirional Testing and Analysis

Revised Lift Prediction Method

Revised Drag Prediction Method

Revised Pitching-Moment Prediction Method

COMPARISONS WITH TEST DATA

CONCLUDING REMARKS

APPENDIX

REYNOLDS NUMBER EFFECT ON LIFT OF SHIPS WINGS

REFERENCES

Page209

214

214

216

217

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258

262

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268

322

408

409

440

V



LIST OF TABLES

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

PageGeometric Characteristics of Basic Wings 23

Geometric Characteristics of Irregular Planforms 26

Mini-matrix of Aeromodule Prediction Comparisons with Test 60

Key to Lift Correlation Charts 263

Angle-of-Attack Boundaries for Drag Due to Lift and Pitching-Moment Segments - NACA OOxx Airfoils, RNmin 272

Angle-of-Attack Boundaries for Drag Due to Lift and Pitching-Moment Segments - NACA 00xX Airfoils, RNstd

273

Angle-of-Attack Boundaries for Drag Due to Lift and Pitching-Moment Segments - NACA OOXX Airfoils, RN 274

max

Angle-of-Attack Boundaries for Drag Due to Lift and Pitching-Moment Segments - NACA 65A012 and NACA 651412 Airfoils 275

Plateau Values of Suction Ratio and Slopes o f Suction-Ratio

Segments - NACA OOXX Airfoils, RNmin276

Plateau Values of Suction-Ratio and Slopes of Suction-RatioSegments - NACA OOXX Airfoils, hstd 277

Plateau Values of Suction-Ratio and Slopes of Suction-RatioSegments - NACA OOXX Airfoils, RN 278

max

Plateau Values of Suction-Ratio and Slopes of Suction-RatioSegments - NACA 65A012 and 651412 Airfoils 279

Pitching-Moment Intercepts and Segment Slopes for NACA 00xXAirfoils, RNmin 280

vi



LIST OF TABLES (Cont'd.)

Page14. Pitching-Moment Intercepts and Segment Slopes for NACA 00xX

Airfoils, &.J 281std

15. Pitching-Moment Intercepts and Segment Slopes for NACA 00xXAirfoils, BN 282

max

16. Pitching-Moment Intercepts and Segment Slopes for NACA 65AO12

and 651412 Airfoils 283

17. Key to Comparisons Made Using the,"Basic" SHIPS PredictionMethod. 322

18. Key to Additional Comparisons of Predictions Made With theSHIPS Prediction Methods. 325

19. Numerical Values of Elements in Lift Correlation Parameter. 411

vii



LIST OF FIGURES

Figure 1.

(a>

(b)

cc>

Cd>

(e>

Figure 2.

Figure 3.

Figure 4.

Figure 5.

Figure 6.

Figure 7.

Figure 8.

Figure 9.

Figure 10.

Figure 11.

PageSketch of models used in investigation 31

Wing I; LE = 25 , TE : 25' 31

Wing II; LE = 35', TE = 20' 32

Wing III; LE = 45', TE = 15' 33

Wing IV; LE = 53', TE = 7O34

Wing V; LE = 60°, TE = 0' 35

Sketch showing general arrangement of model usedin investigation 36

Wing Planform Geometry Definitions 38

Body Geometry 46

Early Analysis Approach 66

Recent Potential Flow (Lifting Surface Theory)Analysis 66

Analysis Including Effect of Vortex Flow 66

Calculation Chart for Prediction of Nonlinear Liftof Double-Delta Planforms at Subsonic Speeds 67

Comparison of Spencer CLaPrediction With TestData 67

Effect of Outboard-Panel Sweep on Lift 68

Effect of Outboard-Panel Sweep on Lift ata= 16O 68

. . .VIII



Figure 12.

Figure 13.

Figure 14.

Figure 15.

Figure 16.

Figure 17.

Figure 18.

Figure 19.

Figure 20.

Figure 21.

Figure 22.

Figure 23.

LIST OF FIGURES (Cont'd.)

PageWINSTAN Nonlinear Predictions for Wing I Planforms(Sharp Thin Airfoils)

Effect of Fillet Sweep on Lift of Wing I Planformsata= 16O

Effect of Round Leading Edges on Vortex Lift ata = 16’

Correlation of Lift Curves of Gothic and Ogee Plan-forms

Effect of Outbogrd Panel on Peckham-Type CL Corre-lation (AF = 80 )

Effect of Outbogrd Panel on Peckham-Type CL Corre-lation (hF = 75 )

Effect of Inbgard Panel on Peckham-Type CL Correla-tion a, = 25 )

Modified Peckham Correlation for SHIPS Wing I Plan-forms

Ericsson Version of Peckham Method - Area-Weighted

'Osine ALEeff

Analysis Method for Round Leading Edges

Variations of Suction Ratio With Angle of Attackfor Various Reynolds Numbers

Variations of Suction Ratio With Angle of Attackfor Various Planforms at Unit Reynolds Number of4.0x106/Ft

69

69

70

70

71

71

72

72

73

74

74

74

ix




Figure 24.

Figure 25.

Figure 26.

Figure 27.

Figure 28.

Figure 29.

Figure 30.

Figure 31.

Figure 32.

Figure 33.

Figure 34.

Figure 35.

Variations of Suction Ratio With Angle of AttackShowing Effect of Fillet

Prediction of Nonlinear Lift Using Test Values ofSuction Ratio for Various Reynolds Numbers

Prediction of Nonlinear Lift Using Test Values ofSuction Ratio for Wing I With 60' Fillet

Prediction of Nonlinear Lift Using Test Values ofSuction Ratio for Wing I With 80° Fillet

Prediction of Nonlinear Lift Using Test Values ofSuction Ratio for Wing V With 80° Fillet

Variation of Leading-Edge-Suction Ratio With Angleof Attack - Wing I With 80° Fillet

Variation of Leading-Edge-Suction Ratio With Angleof Attack - Wing I with 65' Fillet

Variation of Leading-Edge-Suction Ratio With Angle

of Attack - Delta and Cropped Delta Wings

Leading-Edge-Suction Values Calculated From TestData - Wing III With 70' Fillet

Comparisons of Predicted and Test Lift Curves -Wing III With 70' Fillet

Modified Variations of Leading-Edge-Suction Ratio -Wing III With 70' Fillet

Comparisons of Aeromodule Predictions With TestData - Configuration 25 25.0008

X

Page

74

75

75

75

75

76

77

78

79

80

81

82



LIST OF FIGURES (Cont"d.)

Figure 36. Comparisons of Aeromodule Predictions With TestPage

Data - Configuration 45 45.0008 83

Figure 37. Comparisons of Aeromodule Predictions With TestData - Configuration 60 60.0008 84





Figure 42. Comparisons of Aeromodule Predictions With 'lestData - Configuration 55 45.0008 : 89


Figure 44. Comparison of Aeromodule Longitudinal StabilityDerivative With Test Data for Wing I With VariousFillets 91

Figure 45. Minimum Drag Test-To-Theory Comparisons 92

Figure 46. Results of Analysis Using Mendenhall LiftingSurface Plus Suction Analogy Computer Procedureand WINSTAN Methods 93

Figure 47. Scatter Plot Showing Spread of Lift Data for all35 SHIPS Planforms 109

xi




Page

Plot Showing Spread of Lift Data for Constant FilletSweep 110

Example of Lift Data Collapse Using CL/CLQ,Parameterfor 80' Fillet Sweep 111

Example of Lift Data Collapse Using CL/CLcrParameterfor Basic SHIPS Planforms 112

Figure 48.

Figure 49.

Figure 50.

Figure 51.

Figure 52.

Figure 53.

Figure 54.

Figure 55.

Figure 56.

Figure 57.

Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings with 80' Fillet Sweep

Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 75' Sweep Fillets


Correlation of SHIPS Test Data Using WINSTAN Corre-

lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 65' Sweep Fillets


113

114

115

116

117

Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings with 55' Sweep Fillets and Basic Wing IV 118

Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 45' Sweep Fillets 119

xii



Figure 58.

Figure 59.

Figure 60.

Figure 61.

Figure 62.

Figure 63.

Figure 64.

Figure 65.

Figure 66.

Figure 67.

Figure 68.


PageCorrelation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 35' Sweep Fillets and Basic Wing I

SHIPS Lift Data Correlation Using WINSTAN Methodfor Double-Delta Wings (Preliminary)

Scatter Plot for Modified Peckham Lift Correlation

Parameter for All 35 SHIPS Planforms

Modified Peckham Correlation of Lift Data - BasicWings

Modified Peckham Correlation of Lift Data - AF = 65'

Modified Peckham Correlation of Lift Data - AF = 80°

Data Collapse With Further Modification of PeckhamLift Correlation Parameter - Basic Wings

Data Collapse With Further Modification of PeckhamLift Correlation Parameter - AF = 80

Data Collapse With Further Modificat&on of PeckhamLift Correlation Parameter - AF = 75

Data Collapse With Further Modificathon of PeckhamLift Correlation Parameter - AF = 70

Data Collapse With Further ModificatAon of PeckhamLift Correlation Parameter - AF = 65

120

121

122

123

124

125

126

127

128

129

130

. . .XIII






Figure 79.

Figure 80.

Figure 81.

Figure 82.

Figure 83.

Figure 84.

Figure 85.

Figure 86.

Figure 87.

Figure 88.

Figure 89.

Ratio of Test Lift to Predicted Linear Lift of SHIPSPage

Planforms with NACA 0008 Airfoils - AF = 55'and 53' 141

Ratio of Test Lift to Predicted Linear Liftoof SHIPSPlanforms with NACA 0008 Airfoils - AF = 45 142

Ratio of Test Lift to Predicted Linear Liftoof SHIPSPlanforms with NACA 0008 Airfoils - AF = 35 143

Ratio of Test Lift to Nonlinear Potential Flow Esti-mate for Basic SHIPS Planforms 144

Ratio of Test Lift to Nonlinear Po&ential Flow Esti-mate for SHIPS Planforms Having 80 Fillets 145

Variations of Leading-Edge-Suction Ratio pith Angleof Attack for Irregular Planforms with 75 FilletSweep 146

Example of Angle-of-Attack Boundary Variations withFillet Sweep for Wing I Planforms 147

Correlation of Suction Ratio "R" Using EffectiveLeading Edge Radius Reynolds Number 148

Correlation of Suction Ratio Using WINSTAN 0 Para-meter 149

Comparison of Correlation Curve Values of SuctionRatio with SHIPS Basic Wing Test Data

Comparison of Simple Prediction Approach withSuction Ratio Data

150

151

xv




Figure 90.

Figure 91.

Figure 92.

Figure 93.

Figure 94.

Figure 95.

Figure 96.

Figure 97.

Figure 98.

Figure 99.

Figure 100.

Figure 101.

Figure 102.

Page

Calculation Chart for Incrementa l Effect of FilletSweep on Suction Ratio in Plateau Regio BetweenCY= 0' and a2 152

Upper Angle-of-Attack Boundaries for Region 1 153

Incremental Angle of Attack for Region 2 154



Effect of Reynolds Number on a3 157

Correlation of Reynolds Number Effects on "2 forBasic Wings Using Chappell's Correlation Parameter 158

Correlation of Reynolds Number Effects on cx2 forBasic Wings Using Q Function Based on Leading-Edge Radius at Tip 159

Envelope Correlation Curve for Change in "2 ofBasic Wings Due to Change in Reynolds Number 160

Envelope Correlation Curve for Change in a3 ofBasic Wings Due to Change in Reynolds Number 161

Envelope Correlation Curve For Change in a4 ofBasic Wings Due to Change in Reynolds Number 162

Envelope Correlation Curve for Change in "5 ofBasic Wings Due to Change in Reynolds Number 163

Correction Term for Effect of Fillet Sweep on aBoundaries 164

xvi



Figure 103.

Figure 104.

Figure 105.

Figure 106.

Figure 107.

Figure 108.

Figure 109.

Figure 1lJ.

Figure 111.

Figure 112.

Figure 113.


PageAerodynamic Center Locations of SHIPS Wing I Plan-forms for Various Lift Regions 166

Aerodynamic Center Locations of SHIPS Wing II Plan-forms for Various Lift Regions 167

Aerodynamic Center Locations of SHIPS Wing III Plan-forms-for Various Lift Regions

Aerodynamic Center Locations of SHIPS Wing IV Plan-forms for Various Lift Regions

Aerodynamic Center Locations of SHIPS Wing V Plan-forms for Various Lift Regions

Angle-of-Attack Envelope for Primary AerodynamicCenter Location

Lift Coefficient Envelope for Primary AerodynamicCenter Location

Aerodynamic Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing I Planfonns

Aerodynamic Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing II Planforms

Aerodynamic Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing III Planforms

Aerodynamic Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing IV Planforms

168

169

170

171

172

173

174

175

176

xvii



Figure 114.

Figure 115.

Figure 116.

Figure 117.

Figure 118.

Figure 119.

Figure 120.

Figure 121.

Figure 122.

Figure 123.


PageAerodynamic Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InobardPlanforms - Wing V Planforms

Aerodynamic Center Location Referenced to MeanGeometric Chord of Each Irregular Planform

Aerodynamic Center Referenced to Mean GeometricChord of Each Basic Wing

Aerodynamic Center Location Referenced to Apex of80' Fillet for Each Planform Family

Aerodynamic Center Location Referenced to Apex of80°/25' Planform with Common Location of QuarterChord of MGC of each Basic Wing

Aerodynamic Center Location as a Percentage ofRoot Chord of Each Irregular Planform

Variation of Aerodynamic Center Location Referencedto Mean Geometric Chord of Each Irregular Planformwith Outer Panel Leading-Edge Sweep

Variation of Aerodynamic Center Location as a Per-centage of Root Chord of Each Irregular Planformwith Outer Panel Leading-Edge Sweep

Effect of Reynolds Number on Aerodynamic CenterLocation for Various Lift Regions - Wing I Plan-forms

Effect of Reynolds Number on Aerodynamic CenterLocation for Various Lift Regions - Wing II Plan-forms

177

178

179

180

181

182

183

184

185

186

. . .xv111



Figure 124.

Figure 125.

Figure 126.

Figure 127.

Figure 128.

Figure 129.

Figure 130.

Figure 131.

Figure 132.

Figure 133.


Effect of Reynolds Number on Aerodynamic CenterLocation for Various Lift Reigons - Wing III Plan-forms

Effect of Reynolds Number on Aerodynamic CenterLocation for Various Lift Regions - Wing IV Plan-forms

Effect of Reynolds Number on Aerodynamic CenterLocation for Various Lift Regions - Wing V Plan-forms

cM - CL Curve Shape Schematics

Pitch-Up/Pitch-Down Tendencies. as Functions ofWing and Fillet Sweep

Correlation of Data Related to Shift of AerodynamicCenter in Region Above Primary Slope

Correlation of Lift Coefficients for Upper Limitof Primary Slope Region

Correlation of Lift Coefficients for Upper Limitof Primary Slope Region Based on Smoothed Wind-Tunnel Data

Example of Variation of Pitching Moment with Angleof Attack Approximated by Linear Segments BetweenAngle-of-Attack Boundaries Defined by Suction-RatioAnalysis - Irregular Planform with Low Fillet Sweep

Example of Variation of Pitching Moment with Angleof Attack Approximated by Linear Segments BetweenAngle-of-Attack Boundaries Defined by Suction-Ratio

Page

187

188

189

190

191

192

193

194

195

Analysis - Irregular Planform with High Fillet Sweep 196

Xix




Figure 134. Pitch-Up/Pitch-Down Design Guide Based on Low Angleof Attack Aerodynamic Center Location

Figure 135. Basic Lift Curve Correlation Parameter

Figure 136. High CYLift Adjustment for Outboard Panel SweepEffects to be Applied Abovea = 16O Only

Figure 137. High a Stall Progression Factor

Figure 138. Turbulent Skin-Friction Coefficient on an AdiabaticFlat Plate (White-Christoph)

Figure 139. Skin Friction on an Adiabatic Flat Plate, X, = 0.1

Figure 140. Skin Friction on an Adiabatic Flat Plate, ~ = 0.2



Figure 143. Skin Friction on an Adiabatic Flat Plate, Xr = 0.5

Figure 144. Supercritical Wing Compressibility Factor

Figure 145. Wing-Body Correlation Factor for Subsonic MinimumDrag

Figure 146. Lifting Surface Correlation Factor for SubsonicMinimum Drag

Figure 147. Schematic Variation of Suction Ratio with Angle ofAttack

Figure 148. Correlation Curve for Suction Ratio of Basic WingPlanforms in Region 1

Page

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220

221

221

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223

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226

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xx




Figure 149.

Figure 150.

Figure 151.

Figure 152.

Figure 153.

Figure 154.

Figure 155.

Figure 156.

Figure 157.

Figure 158.

Figure 159.

Figure 160.

Figure 161.

Figure 162.

Figure 163.

Figure 164.

Calculation Chart for Incrementa l Effect of FilletSweep on Suction Ratio in Region 1

Upper Angle-of-Attack Boundaries for Region 1

Incremental Angle of Attack for Region 2

Incrementa l Angle of Attack for Region 3

Incrementa l Angle of Attack for Region 4

Calculation Chart for Change in a'Boundaries ofBasic Wings Due to Change in Reynolds Number

Correction Term for Effect of Fillet Sweep onBoundaries

Slope of Suction-Ratio Curve in Region 2

Slopes of Suction-Ratio Curves in Region 3

Slopes of Suction-Rat io Curves in Region 4

Slopes of Suction-Ratio Curves in Region 5

Aerodynamic Center Test-to-Theory Comparison

Aerodynamic Center as Percent MGC

Pitch-Up/Pitch-Down Tendencies as Functions ofWing and Fillet

Pitch-Up/Pitch-Down Design Guide Based on LowaAerodynamic Center

Lower Angle-of-Attack Boundary for Region 1

Page

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237

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249

Xxi



III I

Figure 165.

Figure 166.

Figure 167.

Figure 168.

Figure 169.

Figure 170.

Figure 171.

Figure 172.

Figure 173.

Figure 174.

Figure 175.

Figure 176.

Figure 177.

Figure 178.


Upper Angle-of-Attack Boundary for Region 5Pane

230

Pitching-Moment Coefficient at Zero Angle ofAttack

Pitching-Moment Coefficient Derivative for Region 0

Pitching-Moment Coefficient Derivatives for

Regions 1 and 2





Comparison of Pitching-Moment Data From DifferentTests

Comparison of Lift-Correlation Parameter for Ir-

regular Planform

Comparison of Lift-Correlation Parameter for BasicPlanform

Effect of Airfoil-Thickness Ratio for IrregularPlanform From LTPT Facility

Effect of Airfoil-Thickness Ratio for IrregularPlanform From ARC 12-Ft Facility

Effect of Airfoil-Thickness Ratio for Basic Plan-form From LTPT Facility

251

252

253

254

255

256

257

284

285

286

287

288

289

xxii



LIST dF FIGURES (Cont'd.)

Figure 179.

Figure 180.

Figure 181.

Figure 182.

Figure 183.

Figure 184.

Figure 185.

Figure 186.

Figure 187.

Figure 188.

Figure 189.

Figure 190.

Figure 191.

Figure 192.

PageEffect of Airfoil-Thickness Ratio for Basic PlanformFrom ARC 12-Ft Facility 290

Effects of Airfoil-Thickness Distribution and Camberfor 80-45 Irregular Planform 291



Effect of Reynolds Number for NACA 0012 Airfoil 294

Effect of Reynolds Number for NACA 65A012 Airfoil 295

Effect of Reynolds Number for NACA 651412 Airfoil 296

Effect of Fillet Sweep on Lift-Parameter Incrementfor Thin Airfoil With Sharp Leading Edge 297

Effect of Fillet Sweep on Lift-Parameter Incrementfor NACA 0012 Airfoil 298

Effect of Fillet Sweep on Lift-Parameter Incrementfor NACA 0015 Airfoil 299

Effect of Fillet Sweep on Lift-Parameter Incrementfor NACA 65A012 Airfoil 300

Effect of Fillet Sweep on Lift-Parameter Incrementfor Cambered Airfoil

Effects of Reynolds Number Confuse the Situation

Lift Correlation for NACA 0004 Airfoils

301

302

303




Figure 193.

Figure 194.

Figure 195.

Figure 196.

Figure 197.

Figure 198.

Figure 199.

Figure 200.

Figure 201.

Figure 202.

Figure 203.

Figure 204.

Lift Correlation for NACA 0008 Airfoils at StandardReynolds Number

Incremental Values of Lift-Correlation Parameterfor NACA 0008 Airfoils at Minimum Reynolds Number

Incremental Values of Lift-Correlation Parameterfor NACA 0008 Airfoils at Maximum Reynolds Number


Incremental Values of Lift Parameter for NACA 0012Airfoils at Minimum Reynolds Number

Incremental Values of Lift Parameter for NACA 0012Airfoils at Maximum Reynolds Number


Incremental Values of Lift Parameter for NACA 0015

Airfoils at Minimum Reynolds Number

Incremental Values of Lift Parameter for NACA 0015Airfoils at Maximum Reynolds Number

Lift Correlation for NACA 65A012 Airfoil at StandardReynolds Number

Incremental Values of Lift Parameter for NACA 65A012Airfoils at Minimum Reynolds Number

Incremental Values of Lift Parameter for NACA 65A012Airfoils at Maximum Reynolds Number

Page

304

305

306

307

308

309

310

311

312

313

314

315

xxiv




Page

Figure 205. Lift Correlation for NACA 651412 Airfoils at StandardReynolds Number 316

Figure 206. Incremental Values of Lift Parameter for NACA 651412Airfoils at Minimum Reynolds Number 317

Figure 207. Incremental Values of Lift Parameter for NACA 651412Airfoils at Maximum Reynolds Number 318

Figure 208. Lift Correla tions for Thin Airfoils 319

Figure 209. Lift Correlation of Wing III Planforms with NACA0008 Airfoils at Standard Reynolds Number fromTest ARC 12-086 320

Figure 210. Schematic of Typical Variation of Suction RatioWith Angle of Attack Used in Revised PredictionMethod 321

Figure 211. Comparisons Between Basic SHIPS Prediction and Testfor Basic W ing I

(a) Lift Curve 328

(b) Drag Polar 329

(c) Pitching-Moment Variation with Angle of Attack 330

(d) Pitching-Moment Variation with Lift 331

Figure 212. Comparisons Between Basic SHIPS Prediction and Testfor Basic Wing III

(a) Lift Curve

(b) Drag Polar

(c) Pitching-Moment Variation with Angle of Attack

(d) Pitching-Moment Variation with Lift

332

333

334

335

XXV




PageComparisons Between Basic SHIPS Prediction and Testfor Basic Wing V

Lift Curve 336

Drag Polar 337

Pitching-Moment Variation with Angle of Attack 338

Pitching-Moment Variation with Lift 339

Figure 213.

(a>

(b)

Cc)

Cd)

Figure 214.

(a>

(b)

cc>

Cd)

Figure 215.

(a)

(b)

cc>

Cd)

Figure 216.

Comparisons Between Basic SHIPS Prediction and TestWing I with 80° Fillet

Lift Curve 340

Drag Polar 341



Comparisons Between Basic SHIPS Prediction and

Test Wing III with 80' Fillet

Lift Curve 344

Drag Polar 345



Comparisons Between Basic SHIPS Prediction and Testfor Wing V with 80° Fillet

xxvi



(a>

(b)

cc>

Cd)

Figure 217.

(a>

(b)

cc>

Cd)

Figure 218.

(a>

6)

cc>

Cd)

Figure 219.

(a>


Lift Curve

Drag Polar


Pitching-Moment Variation with Lift

Comparisons of Basic SHIgS Prediction and Test

for Basic Wing I with 35 Fillet

Lift Curve

Drag Polar



Comparisons of Basic SHIPS Prediction and Testfor Wing III with 55' Fillet

Lift Curve

Drag Polar



Comparisons of Basioc SHIPS Prediction and Testfor Wing V with 65 Fillet

Lift Curve

Page348

349

350

351

352

353

354

355

356

357

358

359

360

(b) Drag Polar 361

xxvii




Page(c) Pitching-Moment Variation with Angle of Attack 362


Figure 220. COmPariSOnS of Basic SHIPS Prediction for A = 75'andAw = 40' for Configurations AF = 75', Aw =F350 and 45'

(a) Lift Curve 364

(b) Suction-Ratio Variation with Angle of Attack 365

(c) Drag Polar 366

(d) Pitching-Moment Variation with Angle of Attack 367

(e) Pitching-Moment Variations with Lift 368

Figure 221. Comparisons of Basic SHIPS Prediction and Testfor Wing I with 60' Fillet

(a) Lift Curve 369


(c) Drag Polar 371

.(d) Pitching-Moment Variation with Angle of Attack 372

(e) Pitching-Moment Variation with Lift 373

Figure 222. Comparisons of Basic and Reviged SHIPS Predictionsand Test for Wing III with 65 F illet for Two Dif-ferent Test Facilities

(a) Lift Curve 374

(b) Drag Polar 375

Xxviii




(c) Pitching-Moment Variation with Angle of AttackPage

376


Figure 223. Comparisons of Revised SHIPS Prediction and Testfor Wing III with NACA 0004 Airfoil

(a) Lift Curve 378


(c) Drag Polars 380

(d) Pitching-Moment Variation with Angle of Attack 381

(e) Pitching-Moment Variation with Lift 382

Figure 224. Comparisons of Basic and Revised SHIPS Predictionsand Test for Basic Wing III with NACA 0008 AirfoilsFor Two Different Test Facilities

(a) Lift Curve 383

(b) Drag Polar 384


(d) Pitching-Moment Variation with Lift Coefficient 386

Figure 225. Comparisons of Revised SHIPS Prediction and Testfor Wing III with NACA 0012 Airfoils

(a) Lift Curve 387

(b) Drag Polar 388

(c) P itching-Moment Variation with Angle of Attack 389

XXiX




(d) Pitching-Moment Variation with LiftPage

390

Figure 226. Comparisons of Revised SHIPS Prediction and Test forWing III with 75' Fillet and NACA 0004 Airfoils

(a) Lift Curve 391

(b) Drag Polar 392



Figure 227. Comparisons of Revised SHIPS Predictions and Test forWing III with 75' Fillet and NACA 0012 Airfoils ShowEffects of Reynolds Number

(a) Lift Curve 395

(b) Drag Polar 396



Figure 228. Comparisons of Revised SHIPS Prediction and Test forWing III with 75' Fillet and Cambered NACA 651412Airfoil

(a) Lift Curve

(b) Drag Polar


399

400

401

402d) Pitching-Moment Variation with Lift

XXX




PageFigure 229.

(4

(b)

cc>

(d)

(e)

Figure 230.

(a)

(b)

cc>

Cd)

(e)

(f)

w

Comparisons of Basic and Revised SHIPS Predictionsand Test for Wing III with 80' Fillet and NACA0008 Airfoils For Two Different Test Facilities

Lift Curve

Suction-Ratio Variation with Angle of Attack

Drag Polar



Incremental Values of Lift-Correlation Parameterat Unit Reynolds Numbers of 13.13 and 19.67 MillionPer Meter From Test ARC 12-086 for SHIPS PlanformsHaving Constant Values of Fillet Sweep

*F= 25O

AF = 35O

*F = 45O

AF= 55O

hF= 60'

/IF = 65'

hF = 7o"

403

404

405

406

407

412

413

414

415

416

417

418




(h) AF = 75'

(i) AF = 80'

Page

419

420

Figure 231. Incremental Values of Lift-Correlation Parameterat Unit Reynolds Numbers of 13.13 and 19.67 MillionPer Meter from Test ARC 12-086 Showing Effect ofThickness Ratio for Wing I With Various Fillet

Sweeps

(a) AF = 25’ 421

(b) AF = 60' 422

(c) AF = 80’ 423

Figure 232. Incremental Va lues of Lift-Correlation Parameterat Unit Reynolds Numbers of 13.13 and 19.67 MillionPer Meter from Various Langley LTPT Tests ShowingEffect of Thickness Ratio for Wing III with VariousFillet Sweeps

(a) AF = 45'

(b) AF = 65O

(c) hF = 7o”

(d) AF = 75'

(e) AF = 80°

424

425

426

427

428

xxxii




PageFigure 233. Incremental Values of Lift-Correlation Parameter

at Unit Reynolds Numbers of 32.81, 39.37 and 45.93Million Per Meter from Various Langley LTPT TestsShowing Effects of Thickness Ratio for Wing IIIwith Various Fillets

(a) AF = 45' 429

(b) AF = 65O 430

(c) AF = 70° 431

(d) AF = 75' 432

(e) AF = ao" 433

Figure 234. Incremental Values of Lift-Correlation Parameter atUnit Reynolds Numbers of 13.13 and 19.67 MillionPer Meter from Langley LRPT Test 262 Showing Effectsof Airfoil Section and Camber for Wing III withVarious Fillet Sweeps

(a) AF = 70' 434

(b) AF = 75O 435

(c) AF = 80' 436

Figure 235. Incremental Values of Lift-Correlation Parameter atUnit Reynolds Numbers of 32.81, 39.37 and 45.93Million Per Meter from Langley LTPT Test 262 Show-ing Effects of Airfoil Section and Camber for WingIII with Various Fillet Sweeps



LIST OF FIGURES (Concluded)

(a) AF = 70'

(b) AF = 75O

(c) AF = 80'

Page

437

438

439

xxxiv



INTRODUCTION

In the early 1970's,the Langley Research Center of The National Aeronautics and Space Administration initiated a combineexperimental and analytical investigation to study the aerodyna-mic characteristics of irregular planform wings (also sometimesreferred to as cranked wings (ref. 1) or double-delta wings(ref. 2). For this study, the planforms were referred to as wfillet combinations with the inboard more highly swept portion

the planform being defined as a fillet.

The early phase of the study was directed toward improvingthe aerodynamics of the space shuttle orbiter (e.g., ref. 3),

though the general long-range goals are applicable toward improdesign of aircraft as well as certain advanced aerospace vehicleThe benefits to be derived from the use of fillets with selectedplanforms include linearization of the subsonic lift-curve slopto high angles of attack. With regard to the space shuttle orter design, the improved lift at the angle of attack specified landing allowed for either reduced landing speed or reduced winplanform area for specified mission return weight. In addition,proper tailoring of the wing-fillet combination allows lineariza-tion of the curve of pitching moment against angle of attack tangles for high lift; thus, trim penalties on both lift and pe

formance are reduced. Although these subsonic benefits might favorable, the question arose as to what effect a near-optimum sign would have on the desired hypersonic trim angle and stabilityrequirements (dictated by cross-range or heating constraints).Since both subsonic and hypersonic conditions were the two priareas of concern in the application of wing-fillet combinations,the overall study was designated the Subsonic-Hypersonic Irregu-lar Planform Study (SHIPS).

With regard to the overall SHIPS program, the objectives the study are to generate an experimental data base from low ssonic to hypersonic speeds accounting for secondary effects ofReynolds number, airfoil section, leading-edge radius and sweeas well as planform geometry; to provide an aerodynamic predic-tion technique for irregular planform wings based on these extesive wind-tunnel results;,and to provide empirically determined



boundaries to serve as design guides regarding linearized lift,pitch,and realistic longitudinal center-of-pressure locations

as functions of Mach number.

The present report is an element of the overall SHIPS pro-

gram and presents the results of an investigation to develop aprediction technique for the low-speed static 'aerodynamic charac-teristics in pitch of a class of low-aspect ratio irregular plan-form wings for application in preliminary design studies of ad-vanced aerospace vehicles.

The presentation is organized in the following manner.

*The scope of the investigation is discussed firstto provide a basis for understanding the goals andthe technical approaches used.

@The experimental data base is described in enoughdetail to support certain judgments that were madeduring the course of the investigation.

.A presentation of the many geometric parametersused in the investigation and the equations usedto generate them is provided.

*The results of an evaluation of previously exist-ing prediction methods are presented and discussed.

*Efforts made to develop additional correlations oftest data to help formulate new prediction methodsare described and results presented.

l The development of the basic set of predictionmethods for lift, drag, and pitching moment ofirregular planforms having NACA 0008 airfoils isdescribed.

l The analyses accomplished to account for the secon-dary effects of Reynolds number, airfoil thickness,

airfoil thickness distribution and airfoil camberare illustrated and modifications made to the predic-tion methods are presented.

2



@Comparisons between predicted lift, drag and pitch-ing moments and test data are presented.

Woncluding remarks are presented.

@The effects of Reynolds number on the lift-correla-tion parameter are described in an Appendix.

3



LIST OF SYMBOLS AND NOMENCLATURE

A=PR - Aspect ratio

ABASIC = AW -Aspect ratio of basic w ing

ATRUE- Aspect ratio of irregular planform wing

Al

A2

- Aspect ratio of inboard wing panel

- Aspect ratio of outboard wing panel

a.c. - Aerodynamic center

a.c.,/,

c1

- Aerodynamic-center location,in percent

of root chord of irregular planform

asc% -Aerodynamic center location, in percent of meangeometric chord of irregular planform

b

C

cR

cT

cl

c2

cD

- Wing span, meters (ft)

- Wing chord, meters (ft)

- Root chord of basic wing, meters (ft)

- Tip chord of basic wing, meters (ft)

- Root Chord of inboard wing panel, meters (ft)

- Root Chord of outboard wing panel, meters (ft)

- Drag coefficient



cDBASE

cDC

cDFRICT

CDFORM

cDINTER

cDL

CDmin

cDMIsccF

cf

cfi

cfTURB

LIST,OF SYMBOLS AND NOMENCLATLW (Cont'd.)

Base-drag coefficient

Cross-flow drag coefficient

Friction-drag coefficient

Form-dr'ag coefficierit

Interference-drag coefficient

Drag due to lift

Minimum-drag coefficient

Miscellaneous-drag coefficient

Friction-drag coefficient

Flat-plate skin-friction coefficient

Incompressible flat-plate skin-frictioncoefficient

Turbulent skin-friction coefficient



cL

cL,= 0

cLBREAK

CLmax

cLP

- Lift Coefficient

- Lift coefficient atCY = 0

- Lift coefficient at upper limit of primaryslope region of pitching moment

- Maximum-lift coefficient

- Potential flow lift coefficient from nonlinearpotential flow (lifting surface) theory

CT - Lift coefficient produced by Spencer's empiri-

LIST OF SYMBOLS AND NOMENCLATURE (Cont'd.)

cal method for irregular planformsSPENCER

CLw

- Lift coefficient produced by WINSTAN empiricalINSTANSLE method for sharp leading edge double delta

planforms

%!- Lift-curve slope evaluated near zero lift,

l/radians or l/degrees

- Lift-curve slope in low-lift region

9 - Design lift coefficient for two-dimensionald airfoil

cm - Pitching-moment coefficient

Cma= 0

- Pitching-moment coefficient at zero angle ofattack

6




h25E = -CM-.25CBAR

(62

%0,1,2,3, -

4,5,6,7

E=MGC= CBAR -

Eeff = EWF -

Eref

Fl' F2

FF

FR

F.S -a.c.

f

fl

HB

Pitching-moment referenced to quarter chordlocation of mean geometric chord

Slope of pitching-moment variation with angleof attack evaluated near zero angle of attack

Slopes of linear segment in pitching-momentprediction method

Mean geometric chord, meters (ft)

Mean geometric chord of irregular planform,meters (ft)

Value of mean geometric chord used as referencelength for pitching-moment coefficient

Functions in White-Christoph skin-frictionanalysis

Form factor in minimum-drag prediction

Body fineness ratio for arbitrary crossectionbody

Fuselage station location of aerodynamiccenter, inches

Function in skin-friction analysis

Stall progression factor used in lift predic-tion

Height of rectangular part of body cross sectionmeters (ft)

7



LIST,OFjSYMBOLS AND NOMENCLATURE (Cont'd.)

Hf

IF

K

Kl

L

LB

LERcw

LERCT

LN

LREF

I

M

MGC = MAC =CC CBAR

RB

Control surface hinge factor used in minimum-drag analysis and prediction

Interference factor used in minimum-draganalysis

Admissible surface roughness (equivalent sand-grain roughness) diameter, cm (inches)

Function in admissible roughness prediction

Characteristic length for calculation of Rey-nolds number in skin-friction analysis, m (ft)

Overall body length, meters (ft)

Leading-edge radius at mean geometric chordof basic-wing planform, meters (ft)

Leading-edge radius of tip chord, meters (ft)

Forebody length, meters (ft)

Reference length for pitching-moment coefficient

Overall length of irregular planform, meters (ft)

Mach number

Mean geometric (aerodynamic) chord length,

meters (ft)

Radius of semicircular portion of body cross-

section, meters (ft)



n

%.S.

RN

RNL

RNLERT

RNmin

RNmaxRNstd

"IW-"l

"R"

"%W

"Rl"

"R(a) "

LIST OF SYMBOLS-AN? NOMENCLATURE (Cont'd.)

Reynolds,number based on leading edge radiusand velocity evaluated normal to leading edge

Lifting surface interference factor used inminimum-drag prediction

Reynolds number

Reynolds number basedof aircraft component

Unit Reynolds number,

Reynolds number based

on characteristic length

l/meter (l/ft)

on leading-edge radiusof mean geometric chord of basic wing

Reynolds number based on leading-edgetip

minimum Reynolds numberi defined in

Maximum Reynolds number 1 -.or use intextpre-

Standard Reynolds number diction method

radius at

Wing-body-interference factor used in minimum-drag calculation

Leading-edge-suction ratio

Plateau value of leading-edge-suction ratiofrom correlation of basic wing data

Plateau value of leading-edge-suction ratio forirregular planforms

Leading-edge-suction ratio as function of angleof attack

9




"R@Yl 2 39 9 , -

4,5,6,7

r

r/c

r

'BASE

%EF

'TRUE

sW

%ETB

%ETwl

%ET

w2

S

Value of leading-edge-suction ratio in variousregions of linear segmented representation

Leading-edge radius of airfoil, meters (ft)

Leading-edge radius as decimal fraction ofairfoil chord

Recovery factor used in skin friction analy-sis only

Base area contributing to base drag in mini-mum drag prediction, Sq.meters (Sq.ft)

Reference area for aerodynamic coefficients(prediction methods Use -SmF = STRUE.# sq-

meters (Sq. ft))

Total planform area of irregular planforms,

Sq meters (Sq ft)

Wing area of basic wings, Sq.meters (Sqft)

Wetted area of body, Sq.meters (Sq.ft)

Wetted area of inboard wing panels, Sq.meters

(Sq- ft>

Wetted area of outboard wing panels, Sq meters

WI* ft>

Wing semispan, meters (ft)

Slenderness ratio = s/..

10



Taw

T

t

t

t/c

W

wl

w2

wB

X

Xc*g

'i

'1:

.

LIST OF SYMBOLS AND NOMENCLATURE (Cont'd~.)

- Adiabatic wall temperature

- Free-stream temperature

- Function, in skin-friction equation

- Airfoil thickness - meters (ft)

- Airfoil thickness as fraction of chord

- Basic-wing planform

- Inboard wing panel of irregular planform

- Outboard wing panel of irregular planform

- Body width, meters (ft)

- Longitudinal distance from apex of planform,

meters (ft)

- X location of pitching-moment reference point,meters (ft)

- X distance from apex to break in leading-edgesweep

- Longitudinal distance from body nose or wingleading edge to point of transition to tur-bulent flow, meters (ft)

(x/c) a.c. - Chordwise location of aerodynamic center asdecimal fraction of wing chord

11




wc>t,cmax

r

a

aBREAK

%

%TALL

aL2,3,4,

5,6,7

P

Sauw,3,

495

%LvoRSLE

Chordwise location of airfoil maximum thick-ness as fraction of chord

X distance from apex of planform or panel toleading edge of mean geometric chord

Spanwise distance from root chord of planformor wing panel to mean geometric chord

Angle of attack, degrees or radians

Angle of attack for upper limit of primaryslope region of pitching moment, degrees

Angle of attack for initial flow separationused in Chappel's wing flow separation analysis,

degrees

Limit of linear lift in WINSTAN cranked wing

analysis, degrees

Angle-of-attack boundaries in suction ratioand pitching-moment predictions, degrees

Angle-of-attack boundaries for reference Reynoldsnumber condition in suction-ratio prediction, de-grees

Prandtl Glauert factor:

Incremental value of angle-of-attack boundary

due to a change in Reynolds number, degrees

Incremental value of lift coefficient causedby vortex flow from sharp wing leading edge

12




A a.c.BREAK -

ACL

AC,RLE

AcLSLE -

Ax

Aa(3-2> -

Aq4-3) -

q5-4) -

Change in aerodynamic center location at angleof attack for upper limit of primary slope re-gion of pitching moment

Increment of lift coefficient above lineartheory

Increment of lift coefficient for round leadingedge

Increment of lift coefficient for sharp leadingedge

Fictitious distance ahead of transition in mixedlaminar-turbulent flow prediction for skin fric-tion, meters (ft)

Incremental value of change in angle-of-attackboundary function due to a change in Reynoldsnumber, degrees

Incremental value of lift correlation parameter(note three different types of increments arediscussed in the text)

Incremental value of angle of attack betweenboundaries cY3 and(Y2, degrees

Incremental value of angle of attack betweenboundaries a; and cY3, 'degrees

Incremental value of angle of attack betweenboundaries a5 and cu4, degrees

, 13



7)B= ETAB

0 LE

A

n,

*LE = *W

'TE

AC/2

AC/4

At/cmax

AW

Q

*T


Nondimensional spanwise location of break inleading-edge sweep

Compliment of leading-edge-sweep angle, degree

Sweep angle, degrees

Leading-edge-sweep angle of fillet, degrees

Leading-edge-sweep angle of basic wing andoutboard wing panel, degrees

Trailing-edge-sweep angle, degrees

Sweep angle of half chord line, degrees

Sweep angle of quarter chord line, degrees

Sweep angle of maximum thickness line, degrees

Taper ratio of basic wing planform

Correlation function for suction ratio inplateau region

Correlation function for effect of Reynoldsnumber on angle-of-attack boundaries defining

regions of linear variation of suction ratiowith angle of attack

Longitudinal stability derivative evaluatednear zero angle of attack

14



LIST OF SYMBOLS AND NOMENCLATURE (Concluded)

(W,i

Slope of suction-ratio curve in each region

5,6,7

CODES

Configuration code used in many figures

AF AW .AirfoilExample 80 45 .0008

Computer Procedure Code

RlT - Air Force version of Aeromodule Computer Proce-dure (Ref. 8)

X61 - SHIPS Aerodynamic Prediction Procedure for Ir-regular Planform Wings

Note: Quantities are presented in the International System ofUnits (U.S. customary units in parenthesis). The workwas performed using U.S. customary units.

15



SCOPE OF THE INVESTIGATION

The scope of this investigation as originally conceived wasbased on the analysis of wind-tunnel test data from a single para-metric experimental investigation of 35 planforms having NACA0008 airfoils plus a few configurations having NACA 0012 airfoilsor sharp leading-edge double-wedge airfoils. The nominal unit

Reynolds number range of the test data was from 6.56 million permeter (2 million per foot) to 26.25 million/meter (8 million perfoot). The test data base consisted of 131 pitch runs.

Additional tests were tentatively scheduled to provide data

to higher Reynolds numbers on a limited series of planforms in-cluding variations of airfoil sections. Data from the additional

tests were to be considered when and if they became available.

The basic objectives of the investigation were:

(1) To evolve empirical methods from the SHIPSexperimental data base for the predictionof first and second order subsonic lift,drag,and pitching-moment characteristics of ir-regular planform wings of moderate to high

thickness ratios having application on pos-sible advanced aerospace vehicles.

(2) To provide correlating parameters and simplepredesign charts as well as a rapid and ef-ficient computer program for quick evalua-tion of new configurational concepts.

The proposed technical approach to meet these objectives hadfour basic elements.

(1) Existing prediction methods would be examinedfirst to evaluate their applicability.

(2) Where needed,correlations of the SHIPS ex-perimental data would be accomplished toformulate improved methods.

16



(3) The basic prediction methods would be de-veloped from the data available from theinitial test at the maximum unit Reynoldsnumber for the configurations having

NACA 0008 airfoils.

(4) Modifications to the basic methods to ac-count for Reynolds number effects and air-foil section effects would be sought de-pending on the scope of data availableduring the course of the investigation.

In fact, five additional tests were accomplished by NASAwhich increased the test data base to 452 pitch runs as de-scribed in the next section. The additional tests were essen-tial to meet the objectives of the investigation.

Prediction methods were sought for the following elementsof the static aerodynamic characteristics in pitch.

@Lift-curve slope near zero lift

*Nonlinear lift increment AC ( >

CLa

0L

dCmGLOW angle-of-attack stability derivative -

( >CL 0

l Aerodynamic center location - (x/c). c. .

@Angle of attack for stall -aSTAIL

*Pitch-up/pitch-down boundaries

*Drag due to lift - CDL

@Variation of leading-edge-suction ratio with angleof attack - "R (a)"

It was assumed from previous experience that existingmethods of predicting the minimum-drag coefficient were suf-ficiently accurate to meet the objectives of the investigation

if properly applied to the irregular planforms.

The magnitude of the analysis task is illustrated by thefact that more than 4000 curves were plotted during the courseof the investigation. Small programmable calculators and desktop computers were beneficial in manipulating and plotting thelarge mass of data.

17



EXPERIMENTALDATA BASE

The scope of the experimental data base is described in thissection. The planform study (ref. 4) consisted of 35 planformsillustrated in Figure 1 in which the geometry is shown normalizedwith respect to the root chord of the basic wings. The detailed

geometric characteristics of these planforms are presented inTables 1 and 2 for the initial series of models. In essence,the

planform families started with five basic tapered planforms havingleading-edge sweeps of 25, 35, 45, 53 and 60 degrees. The irregu-

lar planforms were generated by adding various fillets of increasedleading edge sweeps up to a maximum of 80 degrees. The wing area

(SW) and aspect ratio (ABA ICconstant,and the spanwise ?

= 2.265) of the basic planforms wereocation of the intersection of the fil-

let leading edge and the basic wing leading edges was constant

(qB=0.41157). The airfoil chordwise thickness distribution was

constant across the span.

The models were constructed such that each planform was aseparate model which was attached under a minimum cross sectionbalance housing as shown in Figure 2. Nose fairings and constantcross sectionaftextensionswere fitted to the balance housing to

produce a "minimum body" for each wing-fillet combination.

Data were supplied from six tests as described below.

(1) Test ARC 086-12-l. Ames Research Center 12-foot pres-sure tunnel. Planform Study - small models.

Complete planform matrix (35 planforms) withNACA 0008 airfoils

3 planforms with NACA 0012 airfoilsA, = 25'; 'F = 25', 60°, 80'

4 planforms with 8 percent thick modified doublewedge airfoils$J = 35°,AF= 35O, 80°

Aw = 60°, AF = 60°, 80°

18



(2)

Boundary-layer transition strips on wings and bodynose for most runs.

Mach number = 0.30

Nominal unit Reynolds numbers = 6.56, 13.12, 19.69,26.25 million per meter (2, 4, 6, 8 million per foot)

NOTE: some planforms were tested at only the twoor three highest unit Reynolds numbers.

CVRange from -2O to 26O

SRFF = total planform area - STRLJELREF = MGC of total planform =EWF

%G =0.25 MGC

Test 8-ft TPT-780 Langley Research Center Eight-Foot

Transonic Pressure Tunnel. Inboard Panel Alone Tests -small models. Zero suction wing test.

AIRFOILAF

= 65O, 70°, 75', 80'NACA 0012 (xlNACA 0008 X X

THIN MODIFIED DOUBLE WEDGE; =x45o A = 7o"UNIT REYNOLDS NUMBER 9.84 (Yl.48) ilg.4) x 1061meter

3.0 (3.5) (5.0) x 106/foot

MAC3 NUMBER 0.3 (.6) C.8)

NOTE: Conditions in ( )orun only for NACA 0012model with AF = 80

Boundary-layer transition strips on body nose andwing surfaces

CYRange: -2O to 21.5O

%EF= Total planform area of irregular planform'k

LREF

= Mean geometric chord of irregular planform*

X CG = 0.25mean geometric chord of irregular planform

*For fillet-alone tests,planform area was that ofWing II plus fillets.

19



(3) Test LTPT-255. Langley Research Center Low-TurbulencePressure Tunnel. Airfoil Thickness Study to High Rey-nolds Nmbers.

Limited Matrix of Planforms - small models

AIRFOIL SECTION A, = 45'; AF = 45O, 65O, 70°, 75O, 80'NACA 0008 X X X X

NACA 0012 X X X X X

NACA 0015 X X X X

THIN MODIFIED DOUBLE WEDGE X X X

UNIT REYNOLDSNUMBERS 13.12, 19.67, 26.25, 32.81, 39.37, 45.93 x 106/M

4, 6, 8, 10, 12, 14 x 106/FT

MACH NUMBER .30 .30 .30 .28 .26 .21

Boundary-layer transition strips on wings and body nosefor most runs. Complete range of unit Reynolds numbersfor each configuration.

CrRange from -2' to 26OSLREF

= basic wing area - SW

REF= Root chord of irregular planforms -Cl

%G = 70 percent of rOOt chord

(4) Test LTPT-262. Langley Research Center Low-TurbulencePressure Tunnel. Additional airfoil section studies tohigh Reynolds numbers.

Limited Planform Matrix - small models

SECTION A, = 45'; A, = 65O, 70°, 75O, 80°

X

X

X

X X X

X X X

20



UNIT REYNOLDSNUMBERS 13.12;19.67, 26.25, 32.81, 39.37, 45.93 x 106/M

4 6 8 10 12 14 x 106/FtMACH NUMBER .30 .30 .30 .28 .24 .21

Free transition for all runs.

cvRange from.-2' to 36'+

%EF= SW

LREF= Root chord of irregular planforms -Cl

'CG = 70 percent of Root chord -Cl

(5) Test LTPT-266. Langley Research Center Low-TurbulencePressure Tunnel. More additional Airfoil SectionStudies to High Reynolds Numbers.

Limited Planform Matrix - small models

AIRFOIL SECTION Aw = 45'; AF = 60°, 65', 70°, 75', 80°

NACA 0008 X

NACA 0012 X

NACA 0015 X

NACA 0004 X X X X X X

UNIT REYNOLDS

NUMBERS 13.12, 19.69, 22.97, 26.25, 32.81, 39.37 x 106/meter4 6

A8 10 12 x 106/Ft

MACH NUMBERS .2(.3)

:23 .2

(.3)

NOTE: Conditions in ( ) only for NACA 0008, 0012, 0015

Boundary-layer transition strips on wings and body nosefor all runs.

CYRange from -2O to 36O+

S%EF= W

LREF = Root chord of irregular planform -Cl

XCG

= 70 percent of Root chord -Cl

21



(6) Test ARC-12-257. Ames Research Center 12-Foot PressureTunnel. Airfoil Section Study at High Reynolds Num-bers and constant Mach Numbers. Limited Planform Ma-trix - large models (twice size of small models).

AIRFOIL SECTION A, = 45O; AiF = 60°, 70'. 75', 80'

NACA 0008 X X X X

NACA 0012 X X X X

NACA 0015 X X X X

NACA 658012 X X X

NACA 651412 X X X

UNIT REYNOLDSNUMBERS 6.56, 13.12, 16.40, 19.69, 22.97, 26.25 X 106/Ft

2* 4* 5, (6) 7, 8*MACH NUMBER .3 .3

.3,(.3) .3, .3*

NOTES: (1) NACA 658012 and.NACA 651412 configurationsrun only for conditions in ( ).

(2) Conditions noted by * run for only one con-figuration.

Free transition for all runs.

CYRange - 2' to 200

SREF= SW

LREF= Root Chord of irregular planform -Cl

XCG = 70 percent of Root Chord

The fact that three different test facilities and two dif-ferent test techniques as well as two different size modelswere used during the experimental program was considered in theanalysis. As a consequence, there are uncertainties in the ex-perimental data which are reflected in the prediction methods.

The use of different sets of reference quantities in thedata reduction for the additional tests from those used in thebasic planform series test required that pertinent data fromthe additional test be recalculated to be put on the same basisas data from the basic test.

22



TABLE 1

GEOMETRIC CRARACTERISTICS OF RASIC WIRGS

UIi;G I

Leading-edge svccp, dcg ........................ 25Trollinvdge s~ccp, deg ............ T .......... 25Quarter-chord sweep. deg ....................... 13.12k27Half-chord s~ccp, deg ......................... 0.00000Aspect ratio ............................. 2.26500Taperratio ....Planformarea,ft2 (m2).

............................................. .30882.52724 f.04898)

spfm, rt (a) ......................... 1.09279 t.333071Root chord, ft (m) ...................... .73726 f.22471)

Tip chord. ft (m) ....................... .22768 l.06939)Mean acrcdynsmic chord, ft (n) .52733 t.16973)Longitudinal location of mean ae;o&kkii ch&i ixi,'fi imj 1 : .lOh97 (.03199)Spanvise location of mesn aerodynamic chord (y), ft (m) .... .22511 (-06861)Airfoil sections ........................ HACA 0008, 0012

WIJG II

Leadingedge svecp, deg ....................Trailing-edge svccp, deg ...................

Quarter-chord svcep, deg ...................Ha..f-char d svecp, deg ....................Aspect ratio .........................Taperratio ..........................Planfoxmarea,ft2 (m2) ....................spsn.ft (m)Root chord, ft.(i)

.

Tip chord, ft (m)........

: :.......................................................

Mean aerodynamic chord, ft (m)Longitudinal location of mean ae;o&k&i lhiri ixj,'& irni 1 1Spanvise location of mean aerodynamic chord (y). ft (m) ....Airfoil sections ........................

. . . . 35

. . . .

. . . . 23.468;:

. . . .iz::::

124798.52724 t.04898)

1.09279 t.333071.77320 l.23567).19174 t.05844).54088 t.16486).15287 l.04659).21832 t.06654)NACA 0008, Double

Wedge

23



TABLE 1

CEOt-lEl'RIC hARACTERISTICS F BASIC WIIlGS

WING III

Leadingedge weep. dec ........................ 45Trailing-c&e sveep, deg ....................... 15Quarter-chord svcep, deg ....................... 34.33357Half-chord sveep. dcg ......................... 20.10485Aspect ratio ............................. 2.26500Taperratio ..............................Planform uea, ft2 (m2)

-16416.................... -52724 f.04898)

span, ft (ID) .......................... 1.09279 (-33307)Root chord, ft.(m)Tip chord, ft (m)

...................... -82887 (.25263)....................... -13607 (.04147)

Mean aerodynamic chord, it (n) ................ .56538 (-17232)Longitudinal location of mean aerodynamic chord (x). ft (m) . . -20782 (-06334)Spsnvise location of meanerodynsmichord (y), ft (m) .... -35351 (-06334)Airfoil sections ........................ NACA 0008

Leading-d&e sveep, deg ....................Trailing-edge sveep, deg ...................Quarter-chord sveep. deg ...................Half-chord sveep, deg ......................Aspect ratio ..........................Taperratio .. ..Planform area, it2 (m2)

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

Span,ft(m) .........................Root chord, ft (m) ......................Tip chord, It (m) .......................Mean aerodynemic chord, ft (m) ................Longitudinal location of mean aerodynamic chord (x), ft (m) . .Spanvisc location of mcsn aerodynamic chord (y)* ft (m) ....Airfoil sections ........................

. . . . 53

. . . .

. . . .

. . . .;pj

. . . . 2:26500

..j2;2; (.o:g"1.09279 (.33307)

.87856 (.26778)

.0863g (.02633)-59086 ( .18oog ).263x9 (.08026).I9844 (-06048)

NACA 0008

24



TABLE 1

GEGKETRIC CHARACT~ISTICS OF BASIC HIllcS

UING V

Leadinecdge sveep, deu ....................Trailing-edge weep, deg ...................Quarter-chord svecp, deg ...................Bali-chord sveep, de6 .....................Aspect ratio .........................Taperratlo ...........................Planform l rea,ft2 (m2). ...................Span, ft (ml

oot chord, it'(;)' : : : : : : : : : : : : : : : : : : : : : :Tip chord, ft (m) .......................Mean aerodynamichord, ft (m) ................Longitudinal location of mean aerodynamic chord (x). ft (a) . .Spanvise location of mean aerodynamic chord (y), ft (I) ....

Airfoil sections ........................

60

52.4109:40.89615

2.26500.oog6g

.52724 (.048g8)1.09279 (.33307)

-95566 (.29x8).oog26 (.00282)-63717 ( .lg4a)-31850 (.09708)-18389 t.05605)

HACA 0008, DoubleUedge

25



TABLE

GEtMETRICHNWTERISTICS F WING-FILLET OMBINATIOIfG

UI?iG Ate = 25' he - 25O srci = .04898 d scf - 2.26500

A,, dw 80 75 70 65 60 55 45 15

II,/~,~~~, dwx 57.970 6 49.7656 44.0165 39.0915 34.7258 30.7894 23.9277 18.1252

A,/2,cff. *g 56.242 4 46.3857 38.0010 30.8123 24.6805 lg.4625 11.1867 4.9436

1.51076 1.72474 1.85838 I.95096 2.01978 2.07369 2.15470 2.21530

.07343 .06432 l 05969 .05686 .05493 .05350 .05149 .05008

. 58147 .44855 .38107 .33974 .3l147 .29064 .26wg .2407u

.32187 .25502 .22362 .20549 .19363 .18522 .17390 .16636

.23471 .16664 .12929 .10523 .08816 .07523 .05644 .04286

.05337 .0577u .06040 .06227 ~6366 .06475 ~16639 ~6761

.41157 .41157 .41157 .41157 .41157 .41157 .41157 .41157



.

TABLE2

Ar, deg

Ac/lr,cff~ d=g

GEOM!n'RICHARACTERISTICSF WIGG-FILLETOMBINATIONSESTED

WINGI Ale - 35' A,, = 20' %er = .a4898 in2 set - 2.26500

I 80 75 70 65 60 55 45 35

I 60.6042 ( 53.8730 1 48.4308 1 43.7321 I 39.5459 I 35.7570 I 29.1199 I I-

57.1494 47.6537 39.6649 32.8715 27.ll29 22.2486 14.7040

1.53370 1.75471 1.89323 1.98940 2.06101 2.11717 2.20169

.07233 .06322 .05860 l 05577 I .05383 .05240 a5039

I .57640I

.44348I .37599 I

.33466I .30639 I

.28556I

.25622I I

.32144 .25415 .22254 .20426 .19233 .10385 A7245

.23588 .I6869 .13186 .10812 . ogl28 .07853 A5999

.05244 a5670 .05937 .06123 A6261 A6369 .06532

.41157 .41157!

.411571

.41157 .41157 1 .41157 .41157I



TABLE 2

GEOMEl'RIC HARACTERISTICSF WING-FILLETOMl3I?IATIONSESTED

WING II Allc = 45O 4. - 150 %ef - .048g8 a2 A ret - 2.26500

Ai, dw - 80 75

A,/4,&f, d&s 6404756I I

58.2148

%'RUE* m2 .07093 .06182

cR,TRuE* I .57282I .43990

I.41157 .41157

70 I 65 I 60 I 55 I 45 35 I

53.0556 48.5494 44.5046 40.8236

42.4106 36.1350 30.8972 26.5621

1.93985 2.04095 2.11639 2.17565

.05719 .05436 .05242 A5099 I

.37241 .33108 I .30281 I .28198 I I

.22326 .20470 .19256 .I8394 1 I

.13374 .11048 .09399 .08150 I

.o5753 .05933 .06068 .06174 , I

.41157 1.411571 .41157 1 .41157 I II



Q4,cw d=g

ATUE

%UE' Ill2

'R,TRUE'n

5, eff, m

Y, es, PI

7, efl, m

'y/b/2

TABLE 2

GEIMETRICRARACTRRISTICSF UIHG-FILLEi' OMRIIVATIORSESTID

WIIG IV A& = 53O Ate = 7" sref . .04898m2 hei * 2.26500

80 75 70

( 1.59876 ( 1.84039 ( 1.99335

I ;o6g3g 1 .06028 1 a05565 .05282 1 .05088 I

I .56554 1 .43262 1 .36514

I .32354 1 .25490 l-.22256-

65 Ii 60 55 45 35 ’

52.6950 48.8291

40.6503 36.0796

2.10025 ( 2.18023 ( 1 I

.32381 .29554

.20384 .19159

.11289 ] .o9669 1

.05775 1 .05907 1

.41157 .41157



Note: ~11 Dimensions Normalized by Root Chord of Basic Wing

Wing II; LE = 35', TE = 20'

Figure 1. - Continued



~---+iAF,7-0.75034

1.5083.-j

Wing

Figure

Note: All Dimensions Normalized by Root Chord of Basic Wing

III; LE = 45', TE = 15'

1. - Continued



0.0983 p-f

r==+ ,.3636---l


W Wing IV; LE = 53', TE = 7'

Figure l.- Continued



wl

243332

b" 4 8-0.6667

-F--.

70.1924


(4 Wing V; LE = 60°, TE = 0'

Figure l.- Concluded



/---0.2247--4

LONC Bow SW21 ooov

Note: All dimensions in meters

Figure 2. - Sketch showing general arrangement of model usedin investigation



GEOMETRIC TERMS AND EQUATIONS USED INANALYSES AND PREDICTION METHODS

Many geometric quantities were used in the analysis and indevelopment of the various prediction methods. The terminologyand equations needed to compute specific values are presented this section.

Wing Description ,

Figure 3 illustrates a typical irregular planform. Togenerate the families of irregular planforms used in this study,the irregular planforms were considered to be made up of a basitapered planform, W, to which various fillets were added. Thefollowing seven geometric parameters provide sufficient informa-tion to allow all other planform parameters to be calculated:

*LE’ +E’ A,’ ‘w’ ‘w’ ‘B and

The analyses and prediction methods consider the irregularplanforms to be made up of an inboard panel, W , and an outboard

panel, W2. The inboard ,panel consists of the, s illet and thatportion of the basic wing inboard of the intersection of the filet leading edge and the basic wing leading edge. The outboardpanel consists of the portion of the basic wing outboard of theintersection of the leading edges.

Geometric Equations

Taper ratio of basic wing

xW z CT/CR (1)

37



I-- S =g .-&J

la

69uul-

wl

w2

W

Figure 3. - Wing Planform Geometry Definitions





Chordwise distance from fillet apex to intersection of

fillet leading edge with basic wing leading edge

‘i = CF = (dyl) tan A, (9)

Chordwise distance .from apex of basic wing to leadingedge of basic wing at the intersection with the fillet lead-ing edge

c3 = dyl, tan ALE (W

Chordwise distance from trailing edge of basic wing to

trailing edge of root chord of outboard panel

c4

= dyl tan ATE (11)

Root chord of inboard panel

e= Cl = CR + CF - c3 (12)

Root chord of outboard panel

c2 = CR - cc3 + c4> (13)

Chordwise distance of half chord sweep of inboard panelacross inboard panel

cg = clT-

(14)

Chordwise distance of half chord sweep of basic wingacross inboard panel

‘6 = 'R _

2

(15)

Chordwise distance of quarter chord sweep of inboard

panel across inboard panel

c7 = .75c1 - (. 75c2 + c4) (16)

40



Chordwise distance of quarter chord sweep.of basic wingacross inboard panel ,,

C8 = .75CR - (.75C2 +. C4) (17)

Chordwise distance of maximum thickness sweep of in-

board panel across inboard panel

'9' ~-~~~t,c~a~c~- [~-i~)t/cmax]c2+c~(18)"

Chordwise distance of maximum thickness sweep ofsic

wing across inboard panel

Sweep angle of quarter-char'1

W,) = tan-l1

(C71dyl) (20)

Sweep angle of quarter-chord of basic wing or outboardpanel

@C/4) = tan-' (C8/dyl) (21)

2

Sweep angle of half-chord of inboard panel

@C/,), = tan -' (C5/dyl) (22)

Sweep angle of half-chord of basic wing or outboardpanel

(Ac/2)2

= =-’C6/dy1)23)

41



Sweep angle of maximum thickness line of inboard panel

(At / cmax) = tan1

-’ (Cg/dyl) (24)

Sweep of maximum thickness line of basic wing or out-

board panel

et / cmax> = tan -’ (CIO/dyl) (2%3L

Average chord of inboard

'AVl = $ (Cl + c2>

panel

(26)

Average chord of outboard panel

'AV2 =i (5 + cT> (27)

Effective quarter chord sweep of irregular planform

cAc14) 1 (‘AV > Wl) + (Ac/4)2

AV &)

ccAV2

> WY21

(*weff =(28)

(c

+1 (‘AV )W2)2

Cosine of effective half chord sweep of irregular plan-

form

(Cos W),ff =

. rcos (*c/2> l KAVdyl)O443/2)2 (‘AV

2>Wy2)

a('AV

1,(&,) + ('AV

2> WY21 (29)

Total planform area of irregular planform

'TRUE = 21

> Wl) + ('AV 2) W2) 1 (30)

42



Aspect ratio of irregular planform

AT RUE = b2 ' 'TRUE(31)

Aspect ratio of basic wing

Aw = b2 /SW (32)

Aspect ratio of inboard planform

Al ti(2dylj2 2dYl

2(cAV

1) Wl) 'AVl

(33)

Mean geometric chord of basic wing

Ew=$ CR( J13”l+A,

(34)

Mean geometric chord of inboard panel

(35)

Ewl = $ Cl

Mean geometric chord of outboard panel

(36)

Mean geometric chord of irregular planform

GF (%~~AVIKYl) + ('w2) (cAV2)(dy2)=

('AV l) WY11 + ('AV2

) W2)

(37)

43



Spanwise location of mean geometric chord of basic wing

I 1(hW),=$+A$b/2)Spanwise location of mean geometric chord of inboardpanel

Spanwise location of mean geometric chord of outboardpanel from root of outboard panel

(40)

Spanwise location of mean geometric chord of irregularplanform

ywF = (;Wl)(cAVl) ("'L) {(dyl) +e2,]p2) ("'4 (41)

(%Vlpl) + (cAV2) (dy2)

Chordwise location of leading edge of mean geometricchord of basic wing from apex of basic wing

xw = yw tanI&

44

(42)



Chordwise distance of leading edge of mean geometricchord of irregular planform from apex of fillet

i?wF = (-'Wl)(tanhE) (CAVl) (dyl) + $'I) (tan*,) +pW2)(tanALE)]('AV2)(2)--y

(cAVl)(v% ("AV2) (dy2)

(43)'

Leading-edgewing

radius of mean geometric chord of basic

LER- =cw

c

(100 r/C') i$( >

Leading edge radius of wing tip chord

LERC =T

(100 /C> m6( >

cT

Chordwise location of moment reference point

c

‘CG = %F + F

Body Description

(44)

(45)

(46)

The models had a "minimum body" on the upper wing surface tohouse a strain-gage balance. The body consisted of a nose fair-

ing, the balance housing and a constant crosssection aft exten-sion which reached to the wing trailiig edge at the centerline.Body geometric parameters are shown in Figure 4. The nose fair-ing contour lines consisted of circular arcs in the longitudinal

direction in both the vertical and horizontal planes. The cross-sections of the balance housing and aft extension consisted offlat vertical sides plus a half circle. The nose fairing cross-sections matched the balance housing at the point of tangency.

45



er

-.., ___ - _._.-- __-LI.--. _ . _. -..--..- -r

I 1

!‘t

Figure 4. Body Geometry

46



The geometric data needed for the analyses are the surfacewetted area and the effective fineness ratio of the bodies.

The body wetted area can be approximated by:

%ETB +F,>, fB- LN)(2HB+ "R$ (47)

Note:

The effective fineness ratio is defined by:

(48)

Wing Wetted Area

Inboard Panels

GET1 = 4 ('AVl) (dyl) - LN f$ 'B) - (LB - LN) @) (49)

Outboard Panels

SWET2 = 4 (cAV2) (dy2) I (50)

47



EVALUATION OF EXISTING METHODS

The initial task in this investigation was to evaluate exist-ing methods of predicting the aerodynamic characteristics of wingsat low speed. Most of the existing aerodynamic prediction meth-ods were developed for thin sharp-edged wings of slender planform,for moderately thick wings of variable-sweep planform, or for mod-erately thick to thick wings of conventional planform. None ofthese methods was expected to apply directly to the configura-tions tested in the SHIPS program without additional correlationeffort. Thus, the objective of the study of existing methods wasto define the limits of applicability when applied to moderately

thick to thick wings of slender irregular planform.

While methods were sought for predicting all of the steady-state forces and moments in pitch, the fundamental requirementwas to accurately predict the lift and pitching-moment behaviorin the region of angle of attack pertinent to approach and land-ing of an advanced aerospace vehicle. Previous NASA studies indi-cated this region to be between 15 and 25 degrees of angle of at-tack. For that region, a significant amount of nonlinear or vor-tex lift occurs with many of the planforms tested. Therefore, em-phasis was placed on examining the ability of existing methods to

predict nonlinear lift characteristics.

Early theoretical analyses of the lift produced by "thin"wings were based on linearized potential-flow theory. These a-nalyses produced estimates of the slope of the lift curve (CL=)evaluated near zero lift which compared well with test data overa limited range of angle of attack. Deviations from the linearextension of the lift-curve slope at higher angles of attack wereattributed to airfoil-thickness effects and flow-separation ef-fects (Figure 5). In recent years, lifting-surface analyses ac-counting for the true surface boundary conditions have been de-

veloped. These analyses show that the potential-flow lift (CLp)is actually nonlinear with angle of attack such that the curvefalls below the linear estimate at all angles of attack above thevalue for zero lift (Figure 6). In addition, many wings, and par-ticularly those with sharp leading edges, generate leading-edge

48



flow separation in the form of bubbles (low-sweep planforms) orvortices (swept planforms) and tip vortices which produce liftabove that predicted by potential-flow analyses (Figure 7). Asthe angle of attack is increased, a point is reached at which thbubbles or vortices burst and the lift increases at a lower rate

and finally decreases. The angle of attack at which bursting ocurs varies with wing planform and airfoil-section geometry.

The preceding discussion indicates that a lift curve is primarily nonlinear. If a particular set of test data shows alinear variation over a significant range of angle of attack, itis apparent now that opposing nonlinear effects compensate eachother over that range.

The following existing prediction methods were examined:

1. The WINSTAN nonlinear lift method for slender double-delta wings with sharp leading edges (AFFDL TR-66-73,ref. 5).

2. The Peckham method (WINSTAN) for low-aspect-ratioirregular-planformwings with sharpleadingedges (ref. 5

3. The Peckham method as modified by Ericsson for slenderdelta-planform wings (AIAA Paper 76-19, ref. 6).

4. The Polhamus leading-edge suction analogy for slender

delta wings as modified by Benepe for round-leading-edge airfoils (GDFW ERR-FW 799, ref. 7).

5. The empirically based Aeromodule computer procedure asmodified by Schemensky (AFFDL-TR-73-144, ref. 8).

6. The vortex lattice lifting-surface theory computer pro-cedure (including effects of leading-edge suction anal-ogy) developed by Mendenhall et al. (NASA CR 2473, ref

9).

7. The crossflow drag method for predicting nonlinear lift(NASA TN D-1374, ref. 10).

The different methods were applied either to predict the lcurves for a series of planforms for comparison with test data

49



to attempt correlation of the test data. The results for eachmethod are presented in the order listed.

WINSTAN Empirical Method for

Nonlinear Lift of Double-Delta Planforms

This method is based on an empirical correlation of wind

tunnel-test data accomplishedduringtheWINSTANproject in 1965(ref. 5). The method also appears in the USAF Stability and Con-trol DATCOM (ref. 11). The calculation chart is presented in Fig-

ure 8. Note that the method requires a value of the linear lift-

curve slope as an input.

As a preliminary effort, the Spencer method (ref. 12 ) was

used to estimate CLQl for all 35 SHIPS planforms and compared withtest data for a unit Reynolds number of 8 million per foot (eval-uated near zero lift). The results are presented in Figure 9. TheSpencer method produces a satisfactory preliminary design esti-mate for .C+ but additional improvement is possible by applyinga simple correction factor. The deviations of predicted values

test data are attributed to interference effects of the mini-bodies of the wind-tunnel models as noted by displacement of

amd Cm near zerocu, especially for the lower fineness ratio

It was anticipated that the WINSTAN nonlinear method wouldlift coefficients higher than the test values, since it is

that wings with round-leading-edge airfoils produce lesslift than do wings with sharp-leading-edge airfoils.

THE WINSTAN nonlinear lift predictionmethod was applied toseries of SHIPS planforms. One series consisted of the 80-

leading-edge-sweep fillet and outboard-panel sweeps of

o 60 degrees. The other series consisted of an outboard-

sweep of 25 degrees with various fillet sweeps from 80 to

Figure 10 presents predicted nonlinear and linear lift

with angle of attack for the 80-degree-sweep-filletof planforms. Also shown is the range of experimental

for this series of planforms at 16 degrees of angle of at-The experimental data falls between the linear and non-estimates for all the outboard-panel sweeps.

50



All of these planforms have true aspect ratios which are lthan 1.65. It is apparent that the basic flow field is dominatedby the leading-edge vortices generated by the highly swept filletsthus, one must expect only a small variation of lift with outboapanel sweep at a constant angle of attack. Figure 11 illustratesthis -fact. Note that the round-leading-edge airfoils produceabout 50 to 55% of the vortex lift that is estimated by the WINSTAN method for sharp leading edges.

The second series in which the fillet sweep is varied pro-duces considerably larger variations in the lift curves. Figure12 presents estimates for this series of planforms. The resultsof the WINSTAN nonlinear method are shown for all the planforms.Note that the planforms with fillet sweeps of 35, 45, and 55 degrees are outside the bounds of the data base for the WINSTAN nlinear correlation, but the estimates appear quite reasonable.Also shown are linear estimates of lift and the nonlinear

potential-flowliftforthethreeoftheplanforms. The ranges of SHtest data are indicated for 12 and 16 degrees of angle of attack.For fillet sweeps from 35 to 70 degrees, the test data fall belothe linear estimates but above the CL estimates. Figure 13shows the variation of lift coefficie R t with fillet sweep for aconstant angle of attack of 16 degrees to illustrate this re-

c sult more clearly. It is apparent that little vortex lift isproduced for fillet sweeps of 60 degrees or less with the 25-degree-sweep outboard panel, which suggests a boundary conditionexists with respect to the fillet contribution to nonlinear lift.

It is of interest to plot the ratio of vortex lift producedby the SHIPS wings to the vortex lift predicted by the WINSTANnonlinear method for sharp-leading-edge wings. Figure 14 showsthat when a strong vortex is produced by a high-sweep fillet,there is little variation in the vortex lift at 16 degrees ofangle of attack with sweep of the outboard panel. The variationof the vortex-lift ratio with fillet sweep clearly shows that tvortex lift is small up to 60 degrees of fillet sweep and thenincreases rapidly as fillet sweep is increased to 75 degrees.There is apparently a plateau slightly above 75 degrees.

As expected, the WINSTAN lift prediction method for sharp-

leading-edge wings significantly overpredicts the lift generatedby the SHIPS models. However there are two possible ways to usthe method as a basis for a new method. One way is to derivefamilies of plots similar to those of Figure 14 for various

51



I I I I II

angles of attack, fillet sweep angles, outboard-panel sweep an-

gles, and Reynolds numbers and then to seek analytical expres-sions to curve-fit the data. A second way would be to use theWINSTAN nonlinear-method correlation parameters to define a cor-relation of the SHIPS data for irregular planforms with round-leading-edge airfoils. Reynolds number effects would require aseparate correlation chart.

The Peckham Method for Low-Aspect-RatioIrregular-Planform Wings with Sharp Leading Edges

The Peckham method as applied to irregular-planform wingsas also investigated during the WINSTAN program (ref. 5). Thisethod, which is most appropriate for slender wings, consists of

a plot of the correlation parameter CL/(s//)k against angle ofattack, as shown in Figure 15. The parameter s is the wingsemispan and e is the overall length parallel to the plane ofsymmetry.

The Peckham method was applied to correlate SHIPS test datafor three series of planforms, as shown in Figures 16, 17, and 18.

spread of data in these curves is systematic with eitherinboard- or outboard-panel sweep. It is apparent that the term(s/e)% is too powerful for the round-leading-edge wings.

As an alternate, a weaker relationship, (s/e) 4 , was at-tempted. Figure 1,9 presents the correlation achieved with the

CL/(s/e)<. Note that belowa = 15', data for all thefillet sweeps from 35 to 80 degrees can be represented by a singlecurve, whereas abovea = 15O there is still a systematic spreadn the data. This spread is obviously caused by the variation in

breakdown effects with sweep angle;and, thus, it should beto gain some insight about correlating the effects from

body of literature covering vortex breakdown. The modifiedmethod was thus considered a candidate for additional

52



The Peckham Method as Modified by Ericssonfor Slender Delta-Planform Wings

Ericsson 's version of the Peckham correlation method forslender delta wings (ref. 6) uses the parameters

cL/(A/4)"* = f (a&L,)

where A is the aspect ratio, CY the angle of attack, and eLE is

the complement of the leading-edge sweep angle. Note that for aA/4 = s/e = taneLE. By making the assumption that

for slender wings,

Peckham c?!rrelation byeLE.

Ericsson divides each side of the

Several attempts were made to define an effective 8LE for iregular planforms that would correlate the test data using Eric-sson's approach. None were successful. The best of the severalthat were tried used area-weighted cosine ALE to define the 8,Eeffective. The results are presented in Figure 20 for six of theSHIPS planforms. It is apparent that dividing the angle of at-tack by the effective 8LE causes the data to spread rather thancollapse because the outboard-panel-sweep contribution variesrapidly as the sweep changes. This approach was dropped from

further consideration.

The Polhamus Leading-Edge Suction Analogyas Modified by Benepe for Round-Leading-Edge Airfoils

This method, which was originally developed for round-leading-edge delta wings, is summarized in Figure 21. The method makesuse of the leading-edge suction parameter "R," which is definedby the equation:

"R" -CL tan u + cDmin - CD

CL tanu - cL27TA

53



The numerator in this definition represents the equivalent amountof suction actually present while the denominator represents theamount of suction theoretically possible for a wing of the sameaspect ratio but having an elliptic loading. In the past, "R"hasbeen successfully used in analyzing and predicting drag-due-to-lift in the lift coefficient range up to polar break.

In the present investigation, it had been proposed to utilizethe suction ratio concept to define the nonlinear lift of roundleading-edge wings by combining the "R" concept with Polhamusleading-edge suction analogy concept (ref. 12) which is applicableto sharp leading-edge wings. This has successfully been done forlow to moderate aspect ratio delta wings (ref. 7).

The lift prediction approach is represented by the followingequations:

cL = CLp+6

cL Il- "R (a)"]

"RSLE

where C is the nonlinear potential flow lift which is de-

fined by:LP

CLp = cLa2

sin Cy cos cy

and 6

CL

is the vortex lift produced by an equivalent plan-

'ORSLEform having an infinitely thin sharp leading-edge airfoil. Ac-cording to Polhamus leading-edge suction analogy concept, theleading-edge suction calculated by potential flow theory actuallyproduces a normal force on a sharp thin highly swept wing.

In the present evaluation of existing methods, thebC

term is obtained by subtracting CLLvo~s E

Pfrom values of CL predicte if

from a correlation of lift of sharp-edged double delta irregularplanforms developed prior to the revelation of Polhamus leading-edge suction analogy concept of vortex lift during the WINSTANproject studies (ref. 5). Thus,

bC=

LVORSLEcL

WINSTANSLE cLP

54



For convenience, the C term in the nonlinear potential lift i

evaluated by Spencer's method (ref. 12) for irregular planforms:

57.3 per degree

For wings having round leading-edge airfoils, it is assumedthat the difference between full leading-edge suction and the atual leading-edge suction is converted to vortex lift.term

C 1 8CThus, t

1-"R (aj" is applied to

LVoRSLE

to obtain the vortex

lift increments.

This method was applied to analyze data for several SHIPS

planforms. The variations of "R" with angle of attack calculatedfrom the test data are presented in Figures 22-24. These varia-tions are typical of the results that can be expected from theSHIPS data. Figure 22 presents data for Basic Wing V at four dferent unit Reynolds numbers; it illustrates the fact that a sig-nificant Reynolds number effect occurs throughout the angle-of-attack range. Figure 23 presents data for two basic planformsand two irregular planforms -- all obtained at the same unitReynolds number, 3.98 x lo6 per foot. Note the significant dif-ference in the shape of the variation of "R" with CY for BasicWings I and V. The variation shown for Wing I is representative

of upper-surface flow separation developing on a low-sweep wingand the loss of lift associated with the flow separation. The

variation shown for Wing V, on the other hand, is representativeof the generation of a vortex-type flow separation, which gener-ates additional lift above that for potential flow. The varia-tion for the combinations of Wing I with a 60-degree fillet shothe general characteristics of that for Basic Wing I;and, thus,one should expect little vortex lift to be generated at highangle of attack. The variation shown for Wing I with the 80-degree fillet,also exhibits the dominant effect of the low-sweepoutboard panel;but, since a lower level of "R" exists at low tomoderate angles of attack, some vortex lift should be presenton that wing.

Figure 24 presents the variations of "R" with CY for the BaWing V and Wing V with an 80-degree fillet. The more rapid de-

55



crease in "R" at low to moderate angle of attack is indicative ofa stronger vortex flow than that occurring on the Basic Wing V,and one would expect a large nonlinear lift contribution for thisirregular planform.

The test variations of "R" with 01 were then used to predictthe lift curves for four of the planforms. The linear lift-curveslope was predicted by Spencer's method. The nonlinearpotential-flowcurves were generated byuseofthelinearlift-curveslope and the appropriate geometric equation for correcting thelinear lift to nonlinear lift. Sharp-edged vortex-lift incre-ments were obtained by estimating the total nonlinear lift for anequivalent sharp-edged thin wing by use of the WINSTAN method andsubtracting the nonlinear potential-flow values. The effects ofthe round leading edges were thus computed by applying l-"R(a)"values to the sharp-edged vortex-lift increments. The results

are presented in Figures 25-28.

Figure 25 is for Basic Wing V. Predictions are comparedwith test resu lts for two values of unit Reynolds number. Bothpredictions are slightly higher than test values; however, thecorrelation of Spencer's C,

aprediction with test data shown in

Figure9 indicate.d the predicted value to be about 6% high. A 6%reduction in the estimates for 20 degrees of angle of attack in-dicates good correlation between ,the test data and the estimates.Figures 26 and 27 show the predictions for Wing I with 60- and

80-degree fillets. The predictions are obviously poor above theangle of attack for stall of the low-sweep outboard wing panel.It thus would be necessary to modify the analysis/correlationmethod to account for the fact that loss of leading-edge suctionon the low-sweep outboard panels does not necessarily contributeadditional lift.

Figure 28 presents the result for Wing V with an 80-degreefillet. In this case, the prediction compares well with test.

While there were some difficulties associated with this

method, it was attractive from the standpoint that defining thevariations of "R" with 01 with the planform geometry parameters,and with leading-edge-radius Reynolds number was also consideredthe best approach for predicting the drag-due-to-lift.

56



At this point, several of the SHIPS models were altered toobtain force and moment data with the outborad wing panelsremovedso that the leading-edge suction parameter variations wither coube determined for use in estimating the fillet contributions. T

results of Test 8TPT-780 (inboard panel alone) were initiallyreferenced to the total planform area of the irregular planformsfrom which they were made. The presentanalysis required that tlift and drag values be re-referenced to the actual planformareas.

Figures- 29 and 30 show typical results for two differentfillet sweep angles. Figure 20 presents variations oftheleading-edge suction Ratio - "R" for the inboard panel alone, the basicwing and the combined irregular planform for the 80-degree filletand Wing I with the NACA 0008 airfoil section. On the basis ofprevious analyses for delta wings, the variation for the inboardpanel was expected to have a generally similar shape to that ofthe irregular planform, but lower values of "R" at each angle oattack. The actual variation was entirely different from whatwas expected, starting with a low value at low angle of attackand increasing with angle of attack. Figure 30 presents a similacomparison for the 65-degree fillet and Wing I, and the resultsshow the same type of effects. After considerable contemplationof these results, it was concluded that the tip vortex formedalong the side edge of the inboard panel models interacts favor-ably with the leading-edge vortex to enhance the leading-edgesuction as angle of attack is increased.

This concept was verified by analyzing test data for deltaand cropped delta wings having thin, biconvex airfoils with sharleading edges (ref. 14). The results are presented in Figure 3Note that for the cropped wing, the values of leading-edge suctioratio are initially higher than those for the delta wing andincrease at higher angles of attack while values for the deltawing decrease throughout the angle-of-attack range.

Further examples of the leading-edge suction ratio dataand lift prediction comparisons are presented in Figures 32and 33, respectively, for the irregular planform consisting of

Wing III with 70-degree sweep fillet. Results are shown forboth the NACA 0008 airfoil section and the thin modified doublewedge airfoil section models.

57



Figure 32 shows that the variation of "R" with 01 is signifi-cantly different for the wings having an NACA 0008 airfoil and ashiarp leading-edge modified double wedge airfoil. Note that theforward facing slopes of the sharp leading-edge airfoil produce

significant suction values at low angle of attack. The value of"R" decreases rapidly with increasing cy forthe sharp wings. At

a = 14.3 degrees a kink was also noted from the basic data (notpresented). The naviation for the round-leading-edge airfoil ismuch different. "R" remains at relatively high values up to 11.4degreescu. Above that ar, a distinct change occurs in the slopeof the curve. These changes, noted for either airfoil, areimportant clues to a change in flow field which causes theamount

ofsuctiontobeless than the value 1 - ["R(a)"] .

Figure 33 presents the buildup of lift predictions and com-

parisons with test data for the two wings previously discussed.The curves labeled WINSTAN S.L.E., SPENCER LINEAR and C

LPrepre-

sent elements of the prediction method that are dependent onlyon the planform and-vach number. The curves labeled SLE and RLEhave the term

Iapplied to determine the vortex lift as

explained earlier.

For the sharp-edged airfoil, the agreement between prediction

and test is good up to 14.3 degrees when a change in the flowfield apparently occurs (probably an outboard panel stall). Forthe round-leading-edge airfoil, the agreement between predictionand test is good up to 11.4 degrees where again a change in flowfield occurs although the effect on the experimental lift curveis not as apparent as it is for the sharp-leading-edge airfoil.

Working the method in reverse order, the suction ratio val-ues required to make the predicted lift match the test data werecalculated for these two cases and the results are shown in Fig-ure 34. In essence, the difference between the dashed curves

and the test data curves of "R" represents the amount of "lost

suction" that is not converted to vortex lift.

In general, the nonlinear method based on the leading-edgesuction analogy overpredicted the lift at high angles of attackfor the round-leading-edge airfoil irregular planform wings.There is a trend toward better agreement over a larger range ofangles of attack as the fillet sweep and outboard panel sweep

58



increase. The best agreement occurs, as expected, for Wing Vwith the 80-degree sweep fillet (Fig. 40).

Reynolds number effects were evaluated for the irregularplanform consisting of Wing I with 80 degree fillet. Both the

NACA 0008 and NACA 0012 airfoil data were analyzed. For the

NACA 0008 airfoil, the agreement between prediction and testdata improved with decreasing Reynolds number because the testvortex lift increased faster than the predicted vortex lift.For the NACA 0012 airfoil, the agreement between prediction andtest improved as the Reynolds number increased because the pre-dicted vortex lift decreased faster than the test vortex lift.(The specific data substantiating these statements are not pre-sented, however the reader is referred to the appendix where thincremental effects of Reynolds number on the finalized liftcorreiation parameter are presented. The effects are highly

configuration dependent.)

It is apparent that for this irregular planform, the effectsof Reynolds number are threefold. First, the angle of attack f"stall" of the outboard wing panel is increased as the leading-edge-radius Reynolds number is increased. Second, the strengthof the leading-edge vortex flow produced on the inboard panelis reduced substantially as the leading-edge radius Reynoldsnumber is increased. Third, the interaction between the inboardand outboard wing panel flow changes drastically between the twoextremes of leading-edge-radius Reynolds number tested.

The obvious difference in inboard panel/outboard panel flow

interactions is that at low Reynolds number, the outboard panelhaving the NACA 0008 airfoil produces a leading-edge flowseuaration, while at high Reynolds number, the outboard panelhaving the NACA 0012 airfoil produces a trailing-edge flow separtion. It is likely that the wing having NACA 0008 airfoils pro-duces leading-edge flow separation on the outboard panel at allunit Reynolds numbers tested, whereas it is possible that mixedleading-edge and trailing-edge flow separation occurs for theNACA 0012 airfoil at the lowest unit Reynolds number tested.

From this evaluation of applying the leading-edge suction

analogy to predict nonlinear lift of the SHIPS planforms, itwas concluded that a significant amount of resources and timewould be required to make the approach a useful preliminary de-sign tool.

59



Aeromodule Computer Procedure

The Aeromodule computer procedure was developed to provide arapid means of assessing the lift, drag and pitching moment char-acteristics of aircraft configurations, from low speed to super-sonic speeds. The basis for the calculations is an extensiveset of empirical and semi-empirical methods developed from a database encompassing fixed wing and variable sweep wing configura-tions. The computer program has been revised and updated severaltimes since the initial development in 1969 as the data base ex-panded and imprpved prediction methods were developed. A versionof the program (General Dynamics Procedure Code RlT) developedfor the U.S. Air Force (ref. 8) was used in the present investi-

gation.

Aeromodule predictions were obtained for most of the SHIPSplanforms during this evaluation. Comparisons between Aeromodulepredictions of lift,drag,and pitching moments with the SHIPSwind-tunnel data obtained at 26.25 million per meter unit Rey-nolds number are presented for a mini-matrix of 9 configurationsshown in Table 3. These results adequately illustrate some ma-jor points to be made from the Aeromodule prediction evaluationstudy.

TABLE 3 MINI-MATRIX OF CONFIGURATIONS PRESENTED

Fillet Sweep 1 Win Leadin IEd-e Swee - De . I

Deg ; 60I I -----!

1I

None Figure 35 ! Figure 36 Figure 37 ]

80I

Figure 38 1 Figure 39 Figure 40 :k 1

I I II

i65

1

I I Figure 43

iII

55 ; Figure 42

35

60



The overall evaluation for the Aeromodule prediction methodindicated that,while there were sometimes significant differencesbetween predicted and test values, the methodologies containedthe basic elements that were needed to provide more accurate predictions and could be adapted through data correlations to a-

chieve the necessary accuracy. In general, the discrepanciescould be explained by the fact that the SHIPS wings and test conditions fall outside the data base that was available when theempirical methods were developed.

Comparisons for basic Wings I, III,and V are presented inFigures 35, 36,and 37, respectively. These results were infor-mative for they showed that the empirical factors inherent inthe computer procedure were not completely sati%factory for thebasic planforms. This is not surprising, since the SHIPS basicwings are generally lower in aspect ratio or have thicker air-

foils than wings which supplied the data base. In addition, the26.25 million per meter unit Reynolds number was higher than previously available in any significant parametric study.

The differences between the predicted lift curves and dragcurves and the test data were not distressing from a methodologydevelopment standpoint. The SHIPS data base could provide ade-quate information to define new empirical factors. The pitching-moment predictions were actually encouraging even though the discrepancies are quite large.

The fact that the general nonlinear characterofthepitching-moment curves also occurred in the predictions was a signifi-cant point. Obviously, some alteration to the methodology wasrequired, but again, it could only be a matter of changing theempirical factors to better account for stall progression on thewings with angle of attack. This assumption is borne out bythe results shown (Fig. 38, 38, and 40).

Figures 38, 39,and 40 present the comparisons between pre-diction and test for Wings I, III and V with 80-degree fillets.For all of these irregular SHIPS planforms, the Aeromodule com-puter program logic selected the WINSTAN nonlinear lift predic-

tion method for sharp leading-edge wings, which does not in-clude the effects of round leading edges or Reynolds number. Thepredicted lift curves tend toward better agreement with testdata as the outer wing panel sweep increases to 60 degrees be-cause the round-leading-edge and Reynolds number effects decrease

61



There is an improvement in the agreement between the pitch-ing moments and test data corresponding to the improvement inagreement of the lift predictions.

The drag-polar predictions for the wings with 80-degree

sweep fillets all produced higher drag values than test at mod-erate lift coefficients. These results were also due to the lackof accounting for round-leading-edge and Reynolds number effects.

The third set of 3 configurations for which comparisons arepresented between Aeromodule predictions and SHIPS test data con-sists of Wing Iwith the 35-degree sweep fillet, Wing III with 55-

degree sweep fillet, and Wing V with the 65-degree sweep fillet.The comparisons are shown in Figures 41, 42 and 43, respectively.For the first two cases, the computer program logic initiallyselected the WINSTAN nonlinear lift method for double-delta plan-

forms, but then attempted to match the USAF DATCOM low-aspect-ratio CLmax method results and determined that the CLmax value

predicted by that method was lower than the lift predicted by po-tential flow. The program flow then shifted to the WINSTAN non-linear lift method for cranked wings and the DATCOM high-aspect-ratio CLmax method despite the fact that the configuration is a

low-aspect-ratio wing. In this case, the procedure computed a

'Lmax but did not attempt to fair from the computed lift curve

to 'Lmax' The user must do that by hand.

The corresponding moment curves in Figures 41 and 42 reflect

the use of the CLmax

values above the angle of attack at which

the computed lift values exceed CLmax'

The pitching-moment pre-

diction methodology assumes a center ofpressurelocationforafullyseparated ilow at lift values above Cb,,. A better prediction

of the angle of attack at which CL,,, occurs could improve the

calculated pitching moments.

It was not at all obvious from the comparisons shown inFigure 43 (for Wing V with 65-degree sweep fillet) what computa-tional path was used by the computer procedure, but it appeared

to be the same one as occurred for the configurations presentedin Figures 41 and 42. Unfortunately, the specified CL range forthe series of predictions only extended to a value of 1.0, so thepitching-moment curve does not give a ciue.

62



The comparisons between predicted and test drag polars pre-sented in Figures 41, 42 and 43 again show that the predicteddrag is too high in the moderate CL range and too low in thehigher CL range. Improved accounting of Reynolds number effectson the lift coefficient for initial flow separation and the liftcoefficient -for drag break could lead to significant improvementin both these areas.

The longitudinal stability derivative dCm/dCL is compared

in Figure 44 with data evaluated in the low lift coefficientrange for Wing I combined with several different fillets. Themethodology is that of Paniszczyn from the WINSTAN study (ref. 5)which also appears in the USAF Stability and Control DATCOM (ref.11) in the section on wing-body pitching-moment predictions fordouble-delta, cranked and curved planforms. The discrepancieswhich occur are attributable in part to discrepanc ies in pre-dicting the lift curve slope. The only drawback to the methodis the fact that it requires generation of geometry for a ficti-

tious outboard panel.

Comparisons between predicted and test values of the minimumdrag coefficient, ~~~~~ are presented in Figure 45. In generalthe discrepancies between predicted values and test values weremuch larger than was anticipated from previous experience. Thevariations of the experimental data with fillet sweep show somesignificant deviations from smooth curves. Some of this type ofdiscrepancy was found to be attributable to the effects of the dif-ferent forebody shapes on the measured base pressures. In addition,the inherent lack of sensitivity at low angle of attack of a wind-tunnel balance when designed to measure large forces at high angleof attack contributed to the "scatter." Investigation as to whythe predicted values were so much higher than expected revealedthat the geometry calculations contained in the Aeromodule programcould not properly account for the fact that the body existed onlyon the upper surface,so the calculated wetted areas for the bodycontributions to minimum drag were too large. When the predictedvalues were corrected to account for the actual wetted areas, theagreement between prediction and test values was much better andwithin the expected accuracy.

In summary, an extensive evaluation of the Aeromodule pre-

diction methods was completed, and the conclusion was that themethods contain most of the necessary elements to produce accu-rate predictions for the SHIPS planforms. The discrepanc iesthat did occur are primarily due to an inadequate data basewhich the SHIPS test data could remedy. The Aeromodule methodswere used as guidelines during the data correlation efforts.

63



Lifting-Surface Theory of Mendenhall, et al.,Including Effect of Leading-Edge Suction Analogy

This method (ref. 9) was included in a preliminary study be-cause it offers a convenient way to obtain theoretical values ofthe nonlinear lift contribution for sharp leading edges and alsobecause the amount of leading-edge suction converted to lift canbe arbitrarily applied for eachwingpanelofatwo-panelirregular-planform wing. Analysis of Wing I with a 60-degree fillet

was tried, first, by using full-leading-edge suction analogy and,then, by arbitrarily assigning various amounts of leading-edgesuction to the inboard and outboard panels at each angle of at-tack. Guidance in selecting the applied amounts was obtained

from the plot of R(a) for the configuration. The results arepresented in Figure 46.

The plot shows the variation of CL , the WINSTAN sharp-leading-edgeprediction, theMendenhallp?edictions for full and ar-bitrary amounts of suction assigned, and the test data. The Men-

denhall result for full suction conversion to vortex lift agreeswith the WINSTAN prediction. The result with partial suctionconversion agrees better than when the test value of suction wasapplied to the WINSTAN increment. The reason is that at CL = 15'

and above the outboard-panel suction ratio was set to zero since

lift data for Basic Wing I indicated wing stall at about CY= 15'.

The next step was to apply the same technique as had beendone in the WINSTAN study for cranked wings of moderate thickness,that is, to assume that at 15 degrees of angle of attack thepotential-flow contributionhadceasedtogrowandthe only addi-

tional lift was that caused by the vortex flow on the inboardpanel. This result is shown by the symbol x in Figure 46. The

agreement with test data is excellent. .The choice of 15 degrees

was arbitrary,in this case; what is needed is a valid correlation

of cy for CL as a function of planform parameters, airfoilBRE K

suction parame e ers, and Reynolds number. The basis for such cor-relations is contained in the Aeromodule methods, but data perti-nent to the SHIPS planforms would be helpful to refine theapproach.

64



The Crossflow Drag Method

The crossflow drag method for predicting nonlinear lift(ref.10) assum es that the total lift is obtained by a relationof the form

2CL = CL

04Y

(u) + CDC ( )7.3

where'the term CDC

is the planform drag coefficient evaluated

u= 90' at high Reynolds number and a units are degrees.

Althoughthismethodis useful forverypreliminary estimatesof the nonlinear lift, the CD term is relatively insensitive

Cto wide differences in planform shape for low-aspect-ratio wingValues in the literature vary from about 1.15 to 1.30 for wingswith round-leading-edge airfoils. In addition, the availabledata are not systematic with planform shape, so it would be dicult to apply the method with sufficient accuracy to differen-tiate between the effects for the various SHIPS planforms.



/

Linear Prediction

. . . . . ..'

-.*: Test Data

::

Ja

Figure 5. Early Analysis Approach

Li:-&earPrediction

Potential Flow

a

Figure 6. Recent Potential Flow (Lifting-Surface Theory) Analysis

t Data

Noniinear IncrementDue to Vor 'tex Flow

Figure

-a

7. Analysis Including Effect of Vortex Flow

66



, .2

.:

.I

.I

0

1 .I I I I I I II

a

I I I I I I2 4 6 8 IO

bTm A,,

.I2

.050

,045

.@40

.035

.@30

.0?5

(MACH - 0.3)

Mx106JFt

WING AW

0 IV 53Ot V 6C"

Pilled SymbolsF.re Basic Wings

Figure 8. Calculation Chart for Prediction of Nonlinear Liftof Double-Delta Platforms at Subsonic Speeds

Figure 9. Comparison of Spencer r

With Test DataLq Prediction

u"



.8

.6

cL

WINSTAN Nonlinear Sharp L.E.

Range of Test Data for NACA 0008Pirfoils at a- 16’

Spencer Linear

0 4 8 12 16 20 24 28

cr-Deg.

Figure 10. Effect of Outboard-Panel Sweep on Lift

.7OJ

.60-

cLa = 16'-

.50-

.4oi

0

AF= 80° OWINSTAN Nonlinear Sharp L.E

D Spencer Linear

0

0 0 Nonlinear CLAEATest Data 00080 Airfoils0

0 0 00

0 0 00

O 0

I I I I 1 1 I I 1

20 30 40 50 60

AW-Deg.

Figure 11. Effect of Outboard-Panel Sweep on Lift at (Y= 16'

68



.6

.4

.2

0

80' 25' 1.51175O I 1.724 /f// 65

i0”I

1.858 /65') 1.95160°550 I

,,2.020'2.074

WINSTANNonlinear Sharp L.

/(Xl Teat Data @ a I 16'

/ (x) Teat Data @ a- 12'

L Spencer Linear CLcr Estimate

Id

&if@.’.l

-___L.... - .A ----.-- -- - -.7.d

.50

0 4 2 12 10 LO 24 2b

a-Deg.

Figure 12. WINSTAN Nonlinear Predictions Wing I Planforms(Sharp Thin Airfoils)

.90 -

.80-

.70-

.60-

0 0 00

0

OWINSTAN Nonlinear-Sharp L. E.

OSpencer Linear

0 Nonlinear CLp

Iest Data - NACA 0008 Airfoils 0

..40 I 1 I

35 45 55 60 65 70 75 -8C

hF -Deg

Figure 13. Effect of Fillet Sweep 0:: Lift ofWing Planforms at a= 16

6



.8-

AC .6-LRLE

AcLSLE

.4-

1.2.

l.O-

.8.

cL

(sip

.6 -

.4 -

.2 -

%=I 80'

NOTE:

AcLi

RLE

AcL ISLE

AW= 25'

CLTEST - cLP

r I , > I 1 I 420 40 60 25 35 45 55 65 75

AW-Deg AF-Deg

Figure 14. Effect ofoRound Leading Edges on Vortex Liftnt a= 16

8 10

w-kg.

0 Ogee

O Gothic

hRS2.0

?I<0 . s

i2 14-7

16 18 20

Figure 15. Ccrrelation of Lift Curves of Gothic andOgee Planforms

70



1.8

1.6 AF iz vRCX AIRF3IL- - --

380'c, 1.4 0 I

WINSTAN Curve

Sharp L.

Thin Curved L. E.

I ,

24 28

o-Deg

Figure 16. Effect of Cutboard Pane; on Peckham-TypeCL Correlation (I\F = 80 >

1.81

-2 \&v-__+ -- w-- -- ----

-- ---. -

8

4 8 12 16 2: 24"

JCz-Deg

42Figure 17. Effect of Outboard Pane& on Peckham-Type

CL Correlation (IF = 75 >

2

71



1.8

1.6

cL1.i

wl)~l 2.

1.0

.8

.6

-IAE *W RUN AIRFOIL-.- RN/FT l4P .--

0 80'

b 7s”0 7o"

0 6S"

h 60'

0 55O

0 45O

3 3s"b &SO

'20

40

43

48

:51

56

59

6215

NACA

r’ I

I-. -u -ueg

l.O-

.8-

.6-

I I I

16 20 24

Figure 18. Effect of Inboard Paneloon Peckham-TypecL Correlation.(AW = 25 >

'F 'W RUN AIRFOIL RN/FT N- _-

0 80'

n 75O

0 7o"

0 65'

h 60'

a 5s"

0 4s"

0 3s"

0 25'

2,

20

40

43

48

51

56

5962

16

)008 4.0x106 0.30

2'8

i8

Figure 19. Eodified Peckham Correlation for SRIPS King I Planforms

72



cL

7-T

!!i%4

*‘F ‘h RUN0x6 23 18o 65 25 46

0 o

0

0

t

d0

00

0

0

0

cL

7-T!?E%4

4-.‘F ‘W RUN

0% m 830 65

045 91

0

3-

0

00000

2- - 00

l-*

0Q

eQ

00

0 4

3

2

1

00

.i, .'W RUN

WWiE‘b5 60 117

t

’8 1.2 1:b ‘4 l.b “” ’.2 0 .4 .a 1.2 1.6

“ceff air tff ale tff

.4

Figure 20. Ericsson Version of Peckharn Method - Area- Weighted Cosine ALEeff



VORTEX LIFT- _

Wing V (No Fillet)

,'" = 60' NACA 0008

EXPERIMENTAL SHARP-LEADING-

fi -( yRTE;,‘:‘:;,“,:,“’. ““r.--. I- / ROUND-LEADING-EDGE VORTEX

/‘-A--- T-.. __ ..--.._ ._SUCTION ANALOGY APPLICATION

“R”

a

Figure 21. Analysis Method for Round Leading Edges

I WING I

1.0 -I

.8 -

.6 -

.4 -

.2 -

RUN AF:\A 0-X zz

'W RNx106/FtE 3.911.--

20 80 25A 16 25 25

-- 36 60 60 I

\

0 10 4 8 12 16 20 24 28

a-kg

Figure 23. Variations of Suction Ratio with Angle of Attackfor Various Planforms at Unit Reynolds Number of4.0x106/Ft

n/1 8 12 16 20 24 28

a-Deg

Figure 22. Variations of Suction Ratio With Angle of Attackfor Various Reynolds Numbers

Wing V

NACA 0008

00. I0 4 8 12 16 20 24 28

a-Deg

Figure 24. Variations of Suctim Ratio With Angle of AttackShowing Effect of Fillet



1.0

cL

.8

.6

WING V "F - .'W - 60'

0 4 8 12 16 20 24 28&-Dee

Figure 25. Prediction of Nonlinear Lift Using Test Values ofSuction Ratio for Various Reynolds Numbers

1.2 IWING I AF = 80' Aw - 25'

1.0

CL

.8

PRED TEST RUN RN/Ft---

- cl 20 3.98xlO'IFtJ

-Nonlinear Method for R.L.E. 0

Based on Test R Valuess

///II

0

0

.b

i., I. 3

0

/ /’/--

: 0

/

,f-' CLF/

///

//

//,

0 10 20 30a-Deg'

Figne 27. Prediction of Nonlinear Lift Using Test Values

of Suction Ratio for Wing I with 80' Fillet

1.2

1.0

cL

.8

.6

WING I AF - 60’ Ay - 25;ING I AF - 60’ Ay - 25;

Prcdictlon -rcdictlon -

Round L.E.ound L.E.MY cY c

/''Lpp

0 ccTest Dataest Data

ilm 51lm 51

4 8 122 '66 200 2478478

a'-Deg'-DegFigure 26. Prediction of Nonlinear Lift Using xest Valuer

of Suction Ratio for Wing I With 60 Fillet

1.0

cL

0.8

WING v AF - 80' Aw - 60'

PRE3 TEST RUN---v-- 0

- Nonlinear Method for R.L.E.

,4 8 12 16 20 24 28 32

a-Deg

Figure 28. Prediction of Nonlinear Lift Using zest Values

of Suction Ratio for Wing V with 80 Fillet



1.0

.4

.2

0

TEST RUN M_ RNxlO+FT *F *W AIRFOILI

I0 TPT 780 9 .3 1.9 80 -- .0008 Inboard Panel /

0 12-086 21 1.9 80-25 -0008 Planform17 1.97 25-25

Irregular.0008

rl Basic Wing I!,/

0 5 10 15 20

tudeg

Figure 29. Variation of Leading-Edge-Suction Ratio With Angleof Attack - Wing I With 80° Fillet



1.2

1.0

II 11R

.8

.6

.4

.2

0

1

0

TEST RUN M- - RNx106/Ft *F *W AIRFOIL

Inboard Panel.,

0 TPT 780 15 .3 1.9 65 -- .0008

4.0 65-25 .0008 Irregular Planform /'1 25-25 .0008 Basic Wing I 4'

/P

5 10 15 20aDeg

Figure 30. Variation of Leading-Edge-zuction Ratio With Angleof Attack - Wing I with 65 Fillet



1.0 -

.8 -

.6 -

.4 -

.2 -

Ref R & M 3714

0 ,ALE = 68.198 Aso A51.60 Delta Wing

0 A= .3333 A= 0.8 Cropped Delta Wing

t/c = .04 Biconvex Sharp L.E.

V = 200 Ft/Sec RN = 1.27x106/Ft.

Cropped Delta Wing

0 ( 1 I0 5

10 15 20U Deg

Figure 31. Variation of Leading-Edge-Suction Ratio With Angleof Attack - Delta and Cropped Delta Wings



AF AW AIRFOIL TEST RUN RN/1.-

--

--

1.0 0 7045

Wedge780 17 1.97s:06

0 70 45 NACA 0008 086 89 7.57.:' !I6

115

I20

adeg

Figure 32.eading-Edge-Suction Values Calculated From Test

Data - Wing III With 70' Fillet



WINSTAN SLE

l.Gl *F *W AIRFOIL

;lo

TEST RUN-- RN/FT-

0 45 Wedge 780 17 1.97x106

0 70 45 NACA 0008 086 89 7.97~10~ /

CL

----- __.I-‘-

5 10 15 2baDeg

,- - ..-

Figure 33. Comparisons of Predicted and Test Lift Curves -

Wing III With 70' Fillet



oac

M- .3

1.0

1

*F *W AIRFOIL RN LE

0 70-45 .0008 7.97x106/Ft Round0 70-45 .0008 1.9x106 /Ft Sharp

.2 1,OI.

0 5 10; ;o

.6-

-91 ,

15 20adeg

;5 2.0adeg

Figure 34. Modified Variations of Leading-Edge-Suction Ratio -Wing III With 70' Fillet



I’

/

WI..I ! .j’:

I I

TESTIRUN CONFIG. %x.I. .A_

1

.I,!, 0 086 14 25 25.0008 .0445 :

Figure 35. Comparisons of Aeromodule Predictions With TestData - Configuration 25 25.0008



-.- .-‘.

.I.:.j,, I,

. .:

i.‘I:

.. !!TEST/RUN CONFIG. CLa

0 086 26 45 45.0008 .0446- Aeromodule .05038

_ ..- -1:. . 1

_.‘.! 1.:.:..! .,

’ II;/: ,:

‘i” , l;-T

,i i,k

i.. .:1.:/.

_:

.i .j:.’1:’ I’.:. :;:1:I... .::_‘...I../ 11: ..!..):j

,I. 1., ‘.

ii I,.-k,J’ ” I.-

:‘[ ‘-1

I[ :.i

1 11.II

1 :..I.I.. -..

1 :.I

.I .!

.!

t 4/ .I.i.1. i

! ]7




1.

ri..

.I-

i.1,_II!

I1..I”,I_..

G CL-L -2.EST/RUN CONF

086 34 60 60.0008 .0416'Aeromodule .04651!

II ,,16_. .20 1 i4 : 28 !

I 1

v

I

.I: .,.

.I;. “’i.:i ._ .

,:

‘d

. ..._-.1’. ‘.:

-.

Comparisons of Aeromodule Predictions With Test

Data - Configuration 60 60.0008Figure



" i

I

_..._

:._

:j,“’ ::j;;

11. .

{;; ,Yj

,.:

.:.:

( :

;i.,, j:::I.. . ./..:.._!_,./ I

&j I 1

y-‘i

.-I .I_.;.I-. i._/ ._ ../.. :.

..i. ..i.j

__p.

-A:,:1

!.YI. .,1 I

.I, _i

I I :

‘- 7 :i

:.I;

._I

..I

-i--

:.

.‘I

‘I

I,-kI

.---i. ,; .._ii ‘.;_.

.I_!:

j:;; -

/. ‘f.i_ .!

i !1.

b/i

T/.

-I:I.:

2i

i

I!

TEST/RUN CONFIG. CLa':..i: 0 086 18 80 25.0008 .0300I - Aeromodule .03182'I 1 'I I I I

1.6: i I I .8

,-; r.;, ’.!. /

1,/. 1.jyi

Figure 38. Comparisons of Aeromodule Predictions With Test

Data - Configuration 80 25.0008



086 83 80 45.0008 .0316:

_. . ., _ __

.II e ‘. -

!

i i :.’.I: -‘”

~ 1. ._( (.

j

.:I’ .I’

.I: 1::‘.

I i 1/

I

I/.

..I jl

1, ijI,

118 I .!

._. - . _:[, I... i. i.11 I 1,....i_: j.

’1

I-..1 I

+;.‘.‘.Iki .:.I:, 1:I.

1 :Ii I

-’1/:;:; ;.:I.::I:.,

i:.l j.‘jj I/ ;

:.. ;.j!

I ’ i. : .acient:- !\

j I4 I,:: .'i

;A..: .I: i .1




- -_I

‘I- i: I j:- .,

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-./

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Ii

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.

_.

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I

I

III

I

4

II

80 60.0008 .0306.02995




[,’I’.,

1:

i,

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:

7

,!.i

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I

‘...,_

1II.

.!

:.

-,.I

1(I

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1

r0

/I

‘I- ,

ogle of Attack - Deg \' 20 1 24 j 2~ ;

i!! I j ! iI. .,

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t

j /: ::.

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i.,.

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.L. .

TEST/ RUN CONFIG. cL,

0 oa6 95 55 45.0008 .0436.04829

112, i6l i 'io i 2'4 28

! Angle of A ttack iII.‘L.

Figure 42. Comparisons of Aeromodule Predictions With Tc'stData - Configuration 55 45.0008





0

-.05

-.lO

-.15

-.2c

-.25

I-

Test Data

Prediction

Wing I

NOTE:

All moments referenced to individual

wing planform area and quarter-chord mat

\

0

I I I 1 I I I

25 35 45 55 65 75 85

Figure 44. Comparison of Aeromodule Longitudinal StabilityDerivative With Test Data for Wing I With VariousFillets

91



ma-0 Test Data RE= 26 25x106/m (8.0x106/ft>

- RlT

---El RlT Corrected for Actual Wetted Areas

z . 0120~--.~-..--‘-~.-..--...--- .--.- ..- __--. .-..- -

.CDmin.. _ _. t- -- - - ._ _- .-: .-.1_.-.~35b-

., .-

----- +,..* -_--- _----_. - -\- -__..I-.- .-- - --- - -..-..---- --.

-.... -. ---.0080+ .___-_~.binb '- .--.L..-L.... .-- .-. _

CDmi*---. .-.- ..__ _--.. ..-.--_--

-.

.- _ .-: .-- . ~ .__ - ____,..___.-.OOSOi

.- - .-.-- .- ._... .-... . -.- .._ -...

-.0120: '-

CDmin ..--... .~; -___._-:n_:_ 53O .._

--.::A.- -^- ._-.-.---.-. --<--__ -

Figure 45. Minimm Drag Test-to-Theory Comparisons

92



1.2

1.0

.a

cL

.6

.4

.2

1

0

Mendenhall Sharp L. E.

-h

hw Aw0025 60 WINSTAN Sharp L.E. d

Mendenhall Assigned Suction Ratios

RNN = 4.0x106/Ft4.0x106/Ft

RU1?51U1?51

/ CLCLP

Test Dataest Data

Arbitrary Baseline for 6VORrbitrary Baseline for 'VORRLELE

Combined Kendenhall & WINSTAN Methodsombined Kendenhall & WINSTAN Methods

1

4 8 12 16 20 24 28

a-Deg

Figure 46. Results of Analysis Using Mendenhall LiitingSurface Plus Suction Analogy Computer Proce-dure and KtNSTAN Methods



DATA CORRELATIONS

The goals of the data correlation efforts were twofold:

(1) to provide a means of removing the deficienciesand limitations of existing prediction methodsor developing new empirical methods, and (2) togenerate simplified design guides for evaluatingnew configuration concepts.

The specific objective of the task was to obtain combina-

tions of planform geometric parameters, airfoil section param-eters and flow parameters that would correlate the SHIPS lift,

drag, and moment data.

The evaluations of existing prediction methods indicatedthat new or revised correlations were needed for the followingelements of the aerodynamic characteristics:

(1) Second order (nonlinear) lift

(2) Drag due to lift

(3) Aerodynamic-center location

(4) High angle-of-attack pitching moment characteristics(pitch-up boundaries).

The approach used was to obtain the basic effects of plan-form parameters from the test data obtained at 26.25 million permeter unit Reynolds number with the NACA 0008 airfoils and thenexamine the effects of Reynolds number and airfoil section para-meters. The efforts will be described in the order listed above.

Nonlinear Lift

The analysis of existing methods indicated that accurate pre-diction of nonlinear lift was perhaps the most essential ingre-dient in the development of an improved prediction methodology.

94



Therefore, a considerable amount of effort was devoted to investi-gating different correlation approaches for lift.

A plot showing the spread of the lift coefficient data

for all 35 SHIPS planforms with NACA 0008 airfoils is pre--

sented in Figure 4'. The coefficients are referenced to the to-tal planform area. What is desired is to find correlation para-meters that will coalesce these data into either a single line a family of lines. From previous work it was known that plottingdata for constant values of fillet sweep would reduce scatter cosiderably. Figure 48 which presents the data for SHIPS planformswith 80 degree fillets illustrates this fact. Note that the re-maining scatter is systematic with outboard panel sweep. A fur-

ther reduction in scatter for angles of attack below 20 degreeswas obtained by dividing the test lift coefficient (CL) by thelift curve slope per degree angle of attack CL~ (estimated bv th

Spencer method) as illustrated in Figure 49. Figure 50 presentsthe same correlation parameter applied to the lift data for theBasic Wings. The reduction in scatter is excellent below 16 de-grees angle of attack.

The WINSTAN correlation parameter for lift of double deltaplanforms was examined next. The parameter combines C~/C~~with

two irregular planform geometric parameters: (1) Al the aspect

ratio of the inboard panel and (2)qB, the spanwise location ofthe break in leading-edge sweep as a fraction of semispan. The

parameter is

In this case,the lift-curve slope is per radian.

Figures 51 through 58 present correlations of SHIPS liftdata for each of the fillet sweeps starting with the 80-degreesweep fillet wing combinations. In each case,the correlation

produces a satisfactory collapse of the data up to 16 degreesangle of attack and a reasonably systematic spread of the data

above that angle,which is dependent on outboard panel sweep.

The data were then further correlated using the second cor-relation parameter from the WINSTAN double-delta lift-prediction

95



method.

lished at f attack as shown in Figure 59. Thecurves for anglesof attack from 0 to 16 degrees. apply to all

outer panel sweeps. The curves above 16 degrees apply onlyfor A, = 45 degrees.

Further effort to account for other outboard panel sweepswas held in abeyance until other correlations of lift were a-chieved. It was obvious, however, that the WINSTAN double-deltamethod was a prime candidate for developing a SHIPS lift predic-tion technique.

The next lift correlation technique investigated was themodified Peckham method in which the parameter CL/(s//)% is

plotted against angle of attack. Figure 60 is a plotshowing the spread of data for all 35 SHIPS planforms. The col-

lapse of data below 16 degrees angle of attack is remarkable con-sidering the simplic ity of this correlation. The spread of data

above 16 degrees reflects, of course, the differences in stallprogression among the many wing planforms. Figures 61, 62 and 63

present individual correlations for the basic wings and for thefillet wing combinations with 65-degree and 80-degree fillets.

The data collapse up to 16 degrees angle of attack is notsignificantly better than that of the overall correlation.The data above 16 degrees do indicate definite families of

curves for the various outboard panel sweeps.

A further modification of the Peckham method was also evalu-ated. The previously described correlation parameter was dividedby the lift-curve slope,per degree,as predicted by the Spencermethod. The new parameter

is plotted against angle of attack in Figures 64 through 72 forthe basic wings and then for wing fillet combinations for constant'values of fillet sweep. The data collapse for angles of attack

below 16 degrees is much improved compared to using only cL

except for fillet sweeps of 65 and 70 degrees where the <s/e 1%improvement is less significant. In addition, correlation curves

96



representing these results have different initial slopes. A plotsimilar to the WINSTAN double-delta method presented earlier woulbe needed to have a viable prediction technique. Althoughthe correlations do not appear to be quite as good as those of the WIN-STAN method, this approach did offer an alternative to the WIN-

STAN method.

The many different approaches presented thus far were aimedspecifically at trying to develop correlations that could evolveinto a prediction method. The next two analyses were intendedprimarily to evolve design guidelines.

First, the SHIPS lift data were plotted using the para-meter

CL

cLSPENCER

in which CLSPENCER

is the linear estimate of lift variation with

angle of attack. Figures 73 through 81 present the plotted cal-culations for the basic wings first and then the fillet-wing com-binations for constant fillet sweeps. The primary use of thesecurves would be to establish the upper limit of angle of attackfor quasi-linear lift for each configuration. Rather than pro-vide arbitrary boundaries, it was decided to allow the designer

to exercise some judgment as to how much nonlinearity would beacceptable for a given situation. The design guide would con-sist of faired curves grouped like the test data plots.

The final correlation parameter examined is the ratio oftest lift coefficient to the nonlinear potential flow lift co-efficient, CL/CL

Pwhere

CLp = cLcw.

'cosCYsin2

aand CLa, is the Spencer value

97



per degree. Typical variations of'this parameter with angle ofattack are shown in Figures 82 and 83. The results for 80 de-gree sweep fillets (Figure 83) show large contributions due tovortex lift,whereas the results for the basic wings exhibit lit-

tle vortex lift except on the 60-degree sweep wing.

Drag Due to Lift

The basic approach to developing correlations for drag dueto lift was the analysis of the leading-edge-suction ratio, "R",as a function of angle of attack, planform parameters, airfoil'section parameters, and Reynolds number. The basis of the ap-proach was the fact that for low to moderate angles of attack,correlation of leading-edge-suction ratio with planform para-meters and the effective leading-edge radius Reynolds number hadbeen achieved and verified for both swept and irregular planformsduring the WINSTAN investigation (Ref. 5).

As an initialstepintheanalysis,. values of the suction ra-tio were calculated for all runs of test ARC 12-086-l and plottedversus angle of attack. Figure 84 presents a typical family ofsuction ratio data for the SHIPS planforms with 75 degree filletsweeps obtained at unit Reynolds number of 26.25 million permeter (8 million per foot) and illustrates a fact noted in mostof the plotted data. There are six distinct regions to the varia-tions with angle of attack. At low angles of attack the varia-tions are erratic because the analysis is extremely sensitive tothe value selected for C

%-band the test values of lift and drag

coefficients are not sufficiently accurate to define specific

data trends. At angles above about 4 degrees, a plateau

value is apparent which has been used in previous work to definethe basic drag polar shape for attached flow. For analysis pur-poses,the lower limit of the plateau region was defined as a'1

and the upper limit as ar2. Next there is a slight decrease in

the slope of the variations which is apparently caused by theinitial develbpment of flow separation on the wing. While this

region is probably a curve, for analysis purposes it is con-sidered to be linear, the upper limit of this region is defined

as ar3'

The flow separation then develops more rapidly causing

a marked decrease in the value of the suction ratio with angle of

98



attack,which again appears to be nearly linear. The upper limitof this region is defined as ar4. Next, there is a reduction in

the rate of decrease of the suction ratio with angle of attack athe spread of flow separation slows. The upper limit of this re-gion, which also apparently marks the beginning of a region in

which the upper surface flow is fully separated, is defined as (r5

As an initial step in the analysis the values of the anglesof attack bounding each of the regions were determined from thetest data obtained on all the planforms at unit Reynolds numberof 26:25/million per meter. Typical results are presented inFigure 85 which shows th.e variations of al, a2, cu3,cy4, anda

with fillet sweep angle for the Wing I planforms.

Further examination of the variations of suction ratio withangle of attack for the wings with NACA 0008 airfoils suggested

that for prediction purposes the slopes of the variations in agiven region could be considered to be the same at each of theReynolds numbers for a particular planform. Thus it might bepossible to establish a prediction method which could accountfor Reynolds number effects on the angle-of-attack boundaries.

It was first necessary to establish a correlation of theplateau values with planform geometry and Reynolds number. Fur-

ther consideration of the plotted data led to the followingapproach:

(1) A correlation of suction ratio would be obtainedfor the basic wing planforms.

(2) The effect of fillet sweep would be accounted forby a correction term.

Two correlations of the basic wing data were achieved.The first correlation uses the effective leading-edge radiusReynolds number in which the velocity and radius are both takennormal to the,swept leading edge. The results are compared inFigure 86 with the band of data presented by W. P. Henderson inNASA TN D-3584 (Ref. 15) for wings of 4 to 6 percent thickness

ratio and boundary-layer transition fixed by the Braslow tech-nique (Ref.16). The SHIPS data agree quite well with the earlierdata, but there-is slightly more scatter. The reason for the

99



scatter is most likely the fact that the balance axial-force sen-sitivity is lower than those used for the data presented inTN D-3584,because the balance had to be capable of handling loadsat high angles of attack,cross the speed range.

high values of dynamic pressure and a-

The second correlation used the WINSTAN correlation para-meter (Ref 5).

0 - %ER COTALE 1-M2 2

Cos ALE

where:% ER

is the leading-edge radius Reynolds number based on

the streamwise velocity and radius measured at the mean geometricchord. The other two terms provide an empirical fit for sweepand Mach number effects. The original WINSTAN correlation also

used another parameter A)c to further account for planformeffects. COSA

LE

The results of applying this approach to the SHIPS basicwing test data are presented in Figure 87 along with the originalWINSTAN correlation curves for Ah values of 0 and 1 which

cosnbound the SHIPS planform values. Tkz SHIPS data which were ob-tained with fixed transition form a different correlation bandthan the original WINSTAN data which were obtained with freetransition. In addition, the planform correlation does not ap-

pear to be appropriate for the SHIPS data.

Figure 88 presents a comparison of correlated values of suc-tion ratio with test data assuming the long dash short dash linein Figure 87 represents a correlation curve for the effects ofReynolds number and leading-edge sweep, "R"BW, for the basic wings.

Using the premise that the data correlation curve, "R"

shown in Figure 87 should form the basis for evaluation of B! ;!effects of Reynolds number on the leading-edge suction ratio atlow lift coefficients for the irregular planforms, it was possible

to establish families of straight line "curves" (shown in Figure89) with fillet sweep angle and unit Reynolds number as the para-meters.

100



The families of curves presented in Figure 89.can be repre-sented by another family of curves shown in Figure 90 which presenthe curve slopes A"R"

$3

as functions of outer panel-leading-edge

sweep angle, Aw, for parametric values of leading-edge radiusReynolds number based on streamwise velocity and radius measuredat the mean geometric chord of the basic wing. Thus, the lead-ing-edge suction ratio at low lift coefficients &an be predictedusing a relatively simple equation:

“R’ll = “R”o<a<a A”R”

2

= “RttBW + i 1A, -A,>(A, -12,)

L J

where "R"B

!!Iis obtained from Figure 87 and the term in brackets

is obtaine from Figure 90. For simplicity the "plateau value"of "R" is assumed to apply from zero angle of attack to the boun-

dary a2.

With a satisfactory methodology .in hand for predicting thesuction ratio in the plateau region, attention was then turnedto refining the evaluation of the angle-of-attack boundaries andslopes for the other regions. Despite several iterations between

selections of the boundaries and slopes,no satisfactory correla-tion could be achieved when using the boundaries directly,exceptfora2. The curves defining cW2 are presented in Figure 91. How-

ever, it was finally noted that incremental values of angle of

attack between each boundary formed reasonable sets of curvesfor regions 2 and 3 as shown in Figure 92 and 93. The incre-mental values for region 4 were somewhat erratic but definableas shown in Figure 94.

It therefore appeared that a workable prediction methodfor the variation of suction ratio with angle-of-attack wasachievable if a suitable correlation could be found for the ef-fect of Reynolds number on the angle-of-attack boundaries. Thataspect of the,methodology was completed in the following way.

First, plots were made of the values of thear boundariesas functions of fillet sweep with parametric variations of unit

101



Reynolds number. Figure 95 is a typical example. After muchthought, it was decided to attempt to correlate the boundariesfor the basic wings as functions of Reynolds number and then ap-ply a- ratio term to the increment inarfor the basic wings to ac-

count for the effect of fillet planforms.

A clue to a possible method of correlating the data for thebasic wings was obtained from a paper by Chappell of the RoyalAero Society's Engineering Services Data Unit (Ref. 17). Hehad correlated the angle of attack for initial separation, a,,of swept, tapered wings by plotting CY,COS/\LE against the leading-edge radius Reynolds number evaluated normal to the wing at thetip. Figure 96 shows a2 for each of the basic wings correlatedusing Chappell's approach and comparisons of his results for air-foil thickness ratios of .08 and .lO. The results were encourag-

ing:

Then a form of the 52 function was tried in which the stream-wise leading-edge radius Reynolds number at the tip was substi-tuted for the value based on the mean geometric chord. The re-sults are presented in Figure 97. This approach was tried withall the CY boundaries. There was enough consistency to the re-sulting plots to attempt to pursue this approach.

Since a correction term was sought rather than the absolutevalues, the individual values for each basic wing sweep were

shifted along the ordinate axis to form a reasonably smooth en-velope curve encompassing the data obtained at the maximum unitReynolds number of 26.25 million per meter (8.0 million perfoot). Figures 98 through 101 show the results for each angle-of-attack boundary. The correction terms A@,( )cosAw) due toReynolds number effects are obtained from Figures 98 through 101by first calculating values ofnT at a reference Reynolds numberand the Reynolds number appropriate to the conditions to beevaluated, then subtracting the value of @a( )cosAw) ref fromthe value @a( )cosAw) as illustrated in Figure 98.

The reference value of Reynolds number is evaluated assuminga unit Reynolds number of 26.25 million per meter (8.0 millionper foot) and a tip leading-edge radius corresponding to a wingspan of 0.33307 meters (1.09279 feet). If the reference value of$2, is less than the value ofJ2T for the condition to be evaluated,then A@@( )cosAw) will have a positive value.

102



The next step was to obtain the effect of the irregularplanforms by forming ratios of the increments in angle of attack-due to Reynolds number at the various values of fillet sweep tothe increments measured for each basic w ing planform. The re-

sults are shown in Figure 102. These ratios are applied to the

increments produced by the previous step to obtain the final,re-sult for the effect of Reynolds number on the, angle-of-attackboundaries for each region.

103



Aerodynamic-Center Location

The initial step in the pitching-moment analysis was to sur-vey the $ - CL-curves for each configuration for the data ob-

tained from test 12-086 at unit Reynolds number of 26.247 millionper meter (8.0 million per foot). In this initial survey, 3 dis-tinct quasilinear regions were observed for many of the wings:A small region near zero lift, a "primary-slope" region generallyfalling between lift coefficients of 0.1 and 0.5,and a region athigh lift coefficients.

The aerodynamic-center locations (referenced to the meangeometric chord of each planform) for each region are presentedin Figures 103 through 107. The angle of attack and lift coeffi-cient envelopes for the primary slope region are shown in Figures108 and 109. In general,the variations of a.c. location withfillet sweep in the low-lift and "primary-slope" regions aresmooth curves, whereas the variations forthehigh-liftregionare

irregular for fillet sweeps in the neighborhood of 60 to 70 de-grees. The envelope curves for the upper and lower limits ofthe "primary-slope" region also-shows distinct irregularities in

the region of fillet sweep from 60 to 70 degrees. It is apparentthat when a significant amount of vortex flow is present on thefillet there is a definite reduction in the shift of a.~. loca-tion between the primary-slope region and the high angle-of-at-tack region. In a few cases, the shift in a.c. location is

actually destabilizing at higher lift coefficients.

Emphasis was then placed on attempting to correlate the a.c.location in the "primary-slope" region. One approach was tomodify the Panisczcyn method of predicting the a.c. location (de-veloped in the WINSTAN investigation, Ref. 5) by applying a mul-

tiplying factor k to the lift prediction for the inboard panel.A parametric evaluation was conducted for a range of k valuesfrom 0 to 2. The results are presented in Figures 110 through

114. The comparisons with test data indicated that weighting

104



factors (k) in the range from .9 to 1.1 would give good correla-tion.

In seeking an alternative to the Panisczcyn method whichmight be more simple to apply, the a.c. locations in the "pri-

mary-slope" region were analyzed and plotted in several differentformats as presented in Figures 115 through 121. None of theseformats provided a significant collapse of the data, but in eachcase the data form families of curves for parametric values ofeither fillet sweep or outboard panel sweep. Eventually, Figures120 and 121 were curve fitted to produce simple and useful pre-diction techniques.

The effects of Reynolds number on the a.~. location in thelow and high-lift-coefficient regions and the "primary-slope"regions are shown in Figures 122 through 126. The effects were

small in both the low-lift and "primary-slope" regions for allconfigurations, but are quite pronounced for some of the confi-gurations athigh lift coefficients. In general, an increase inunit Reynolds number produces an aft shift in a.c. location.Figure 125 for example shows that for Wing IV with 65 degreefillet an increase in unit Reynolds number from 19.67 millionper meter (6.0 million per foot) to 26.25 million per million(8.0million per foot) changes a pitch-up trend to a pitch-down trend.

As a consequence,efforts to analyze pitch-up/pitch-downcharacteristics were initially concentrated on the data obtainedat 26.25 million per meter unit Reynolds number.

High Angle-of-Attack Pitching-Moment Characteristics

As an aid to describing the pitching-moment characterisitcs,the CM - CL curves were reduced in size and assembled on one page

for all 35 planforms (Figure 127). At low angles of attack, thechange in the static stability derivative dCm/dCL is in the nega-

tive direction with increasing values of either fillet sweep or

outboard panel sweep. At high angles of attack,the changes indCm/dCLare in the opposite direction. All of the planforms with



fillet sweep of 60 degrees or less and outboard panel sweep of53 degrees or less exhibit a definite pitch-downtendency at highangles of attack.sweep is increased,

As the fillet sweep or the outboard panelthe trend at high angle of attack is toward

less stability until eventually a definite pitch-up tendency oc-curs. The moment reference pointis 0.25+ in Figure 127.

The pitch-up/pitch-down tendencies are SummarizedinFigure128 which is a matrix chart having the same arrangement as Figure127 in terms of the placement of the data for each combinationof fillet sweep and outboard panel sweep. Superimposed on thechart are arbitrary boundaries which separate the regions of de-finite pitch-down and definite pitch-up fromtheother configura-tions. In the region between these boundaries,the data does notdefine whether pitch-up or pitch-down exists.

Some attempts were made to quantify and correlate the shiftin a-c. location from the "primary slope" CL region to higher

lift coefficients and the angle of attack and lift coefficientfor the break point (upper limit of the primary slope region) ofthe pitching moment curves. A typical example is shown in Figure129 in which A~.c.~~~, mBREAK' and CLBREAK are plotted against

the variable Btan CA, -Aw >. This approach produced groupings of

the &BREAKand CL data which showed some promise, so effort

BREAKwas concentrated on the CL analysis and several correlation

BREAKparameters were tried and the most promising results (shown inFigure 130) used the parameters CL

BREAKIATRUE

and tan (A, -,dw >.

Figure 131 presents the same correlation approach after the

cLpoints had been reviewed and considerable smoothing was

BREAKapplied to the raw results. The smoothed data show two distinct-ly different trends. Planforms having either Wing I or Wing IIouter panels,show a decreasing value of CL

BREAK'ATRUE as

tan (A, - Aw ) increases, whereas planforms having Wing IV and

Wing V outer panels show an increasing value of CLBREAK'ATRUE.

106



Planforms having Wing III outer panels apparently are on theborderline between the two trends.

Although this correlation was informative, it didnotappearto be easily translated into a prediction method. Shortlythereafter it was noted that the angle-of-attack boundaries ob-tained in the suction-ratio analysis corresponded closely the

.break points occurring the plots of pitching-moment variationwith angle of attack for many of the planforms. Figures 132and 133 show typical examples of fitting the experimental pitch-ing moment curves with linear segments between the an.gle-of-attack boundaries established from the suction-ratio analysis.

This approach was adopted and it was found that two addi-tional angle-of-attack bo,undaries were needed for the pitching-moment analysis: QI which corresponded to the lower limit of

the plateau region'of the suction-ratio analysis and a6 whichoccurred at high angle of attack for a few configurations. Thusit appeared possible to produce prediction methods for lift,drag,and pitching-moment variations with angle of attack which wouldproduce consistent results.

The analysis of pitching-moment variations with angle ofattack also brought to mind an alternate approach to developinga design guide for the high angle-of-attack pitching behavior.The author remembered a comment in a British paper on the useof irregular planforms to minimize the aerodynamic-center travel

which occurs between subsonic and supersonic flight. The commewarned that along with the favorable reduction in a.c. travel

came a tendency toward pitch-upathigh angles of attack at lowspeed.

This author interpreted that comment to mean that a corre-lation between a.c. location at low lift coefficients and highangle-of-attack pitchup might exist. Such a correlation was at-tempted,and the results presented in Figure 134 show that it ispossible to define a boundary between pitch-upandpitch-down be-havior as a function of outboard panel sweep and aerodynamic-center location in terms of percent mean geometric chord of theirregular planforms.

107



One of the goals of the overall SHIPS program is to providea guide for using irregular planforms yielding desired improved

CL, reduced transonic a.c. shift, while avoiding pitch-up. Figures128 and 134 provide one element of the overall design guide appro-

priate to the landing condition. Note that the design guides donot rule out any configuration, they merely point out that cer-tain configurations must be evaluated in more detail than others.

108



Figure 47. Scatter Plot Showing Spread of Lift Data for all35 SHIPS Planforms



; ::“j, ; ; !.!

.:.i.:.

.’ ,::a

:i ;i

, :(. ::: ,, :: j i,,

/__.jj.,:,;...: :....: ,.__ 1,... j :..! ., ~.; :’

80 2580 3580 4580 5380 60

Figure 48. Plot Showing Spread of Lift Data for Constant FilletSweep



80 25 .0008

80 35

80 4580 5380 60 I

Figure 49. Example of Lift Data Collapse Using CL/CLcrParameter

for 80' Fillet Sweep



Figure 50. Example of Lift Data Collapse Using CL/CLa!Parameterfor Basic SHIPS Planforms



/. i I !

.s’ i I

1

JESj/R;LJN

; 0 086 18638397

80 25.000880 3580 4580 5380 60

I

I/

2: ,

,/’

-,

1

I

/i .I,A’

Figure 51. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings with 80' Fillet Sweep



i

fIII.iiI.

iii

,iI.

/

1

.

1

i 10 086 38

Figure 52.

1

I

I

a;,a

:

68

86100

112

IIt

t

75 25.000875 3575 4575 53

75 60

I II !I i I

1

i.

I

I

!

4

!

I

I

OF

Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaCJings - Wings With 75 '-Sweep Fillets



/ ‘:cL&~,,,,,,” ‘-’ i i7d i5.00088: 086 49/ iti 69

89

103115

70 3570 45

70 5370 60

II I

4!

$:

I

I II !I

’I’

t

/H’

,d$4JA

iL

iii;

RTTFI *

i19la

Figure 53. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 704Sweep Fillets



.i

i

I. i

III

j

j

t.

I

I

Ii: :j ’

086 46 65 25.000865 3565 4565 53 ,i

7291

105117

’ :

II

I_t__ei

.I

I

1

b/

i

I

2

I

I

.

ir

:

,

. I

i -0.

I

I :1

I

1

:--I

.’

j ’

I

Correlation of SHIPS Test Data- Using WINSTAN Corre-lation Parameter for gonlinear Lift of Double-Delta

Figure 54.

Wings - Wings With 65"-Sweep Fillets





cc00

jQiE

3; '086 54 55 25.0008

3 i 78 55 35 Icm1.1 950 553 453 I/

I ! ,.L4d

L

I

I

I1I

!

I

1 L

Figure 56. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-Delta

Wings - Wings with 55'- Sweep Fillets and Basic W ing IV



:

II

II

----I--.

?+I!?

I

!!

I

j

j

:

,

I

I

/:

/

.

I

I-

?

I

I1 I

-.!

3g

,/

II

I

45 25'.000878126

!

B'

I

c

c

4

I

45 3545 45

I

I ,//

c1I

II

1EL

I

.I

/F r

III

/ ;

:

IIz

I!

I

(

IL

Figure 57. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 45:Sweep Fillets



1 : : /

IES~-/RMJ!I ! ;

CbNFl I EURRi I I086 60 35 25.0008

22 35 3514 25 25 1..4

N

!gks

*-

1

I !. - , .

i

I

: j

I

)

,

I

i

!

I; I

, II

/ /

I I

I

Figure 58. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift o f Double-Delta

Wings - Wings With 35' Sweep Fillets and Basic Wing I



._-

/’ ;.j 1

.:.1 II .k

CL Al--

cLaqB

.3

,; .2

I.l

; ;; +i ,i

i 0

. .

/ /

:-- ‘..i I i I

These curves are gnlyfor wings with 45 sweepon outboard panel

j i.; 1I

Applies to allSHIPS Planforms '/in region below I

CY= 16' 1

I

) ;Ij I

L

Figure 59. SHIPS Lift Data Correlation Using WINSTAN Methodfor Double-Delta Wings (Preliminary)



Figure 60. Scatter Plot for Modified Peckham Lift CorrelationParameter for All 35 SHIPS Planforms



.

8

I

II

I /\W RUNi c> j

25 14 !I :@ ; '- c

Figure 61. Modified Peckham Correlation of Lift Data - Basic

Wings



;o'F*W RUN

65 25 46I

45 9153 105

I I

I i.I

II I

I

I.! ..

I.‘8

.

;$

:

+ 60 117

.

i@

1.0

CL

(s/e>* 1

1 ! ’

I

;2 : ; ;6I III i :

Figure 62. Modified Peckham Correlation of Lift Data - AF = 65'



I

I I I ) 1 : - *F *W RUN

,.!

/ _

80 25 18

I 35 63

I.I

..;I

I

._;

‘.

1 45 83

1I

5360

.; I :

I

8

I

:

Ii..

B.i

.

‘II

2

1

A

; 1.5 i

. . :

: :i

,:

/

:;i

.!

IIII

Figure 63. Modified Peckham Correlation of Lift Data -AF

= 80'



,‘, ::I

‘.:: :\,: ;:!’ ::’ 1’,!“,,‘:.; ,.’ ., : :I,: ::::‘: i.;; 1; /;)l/I:);, I::; 1, ::I ~I,!:,I;!i.I::l iI:. ‘1 1 ” ) ).., ;:,., ,..,..,.,::..:.

‘-

; ;:;’.,,,.. 2::: /:!j lAl;i;il’il ;l.“l,’ ;: .I..

,. ..I, .,I

, ,,. .: IL:’ / :,;. 1 ::’ 1 A, 1 i,::,,, 53.: I A li/:;I.II.I .: I.: :I :,:I..I,I~I::I:/;. rn

Figure 64. Data Collapse With Further Modification of PeckhamLift C orrelation Parameter - Basic Wings



:

:.:_. . . .;.. . _... 8.

;

$-.

.’

t

:‘: ‘...:. ..,. .:.. ,._. ._.. :.,. ,.

if--L-,

imr.; ._,.._. Jlj.jL:.I .:..

,+---y:;:,.:.I,.. ‘I: ,.

. . ..!....‘~.g;:‘--

‘.

! ,,’

Figure 65. Data Collapse With Further Mod.ification of PeckhamLift Correlation Parameter - AF = 80



I I I. I I ’ I :.I I. I I. :. : I I : ‘::: :I:I I I. I ,I I : I : I .:. I :: I ‘I.,: I.:: .:

Figure 66. Data Collapse With Further Modificathon of PeckhamLift Correlation Parameter - AF = 75



..l..::l.~l.. i..: I:...! Iv LJ -“Vu0

.,..,..

r-.,. .’il..ll~.l_..,.:..lAl.l.: ( / ;i.,‘i/..i.i-li.;.d.1..: .I...:i ._.. I.: /:.l.I.::./.:..I .,.(.:_.I

.l..:.::i;.l:.. i I / I..:.i:...l.:..l.:...I:iiii.i:.I.i:ilili:

Figure 67. Data Collapse With Further Modification of PeckhamLift Correlation Parameter - AF = 70



Figure 68. Data Collapse With Further ModificatAon of PeckhamLift Correlation Parameter - AF = 65



4 ,. .,,. ..I .I b

BI I I:;, ::., ii: :I;: ::,: I::I I

.,.I ..;, I.:;:’ /:! ,! .’

/ j: j




: I

...:_~ . . .- 1. u i;j:.:. ‘.: :..:.: ,: ‘i:;;i(..:I:. ,:,. ..I

A 2:. L::. .:.. . :::. :.:. L!. ,;+i !::. ::i..:.:: .:._ ..:: ..i .A.. .;_. ii..

::,.: 3,: j.; I’ I?$ ,;xj ::i:..In .. :/,;;I :/:./i,/j: 1

,.I: i’1:::: l::;I::,I:,: ii, I ’.: i ‘1, ::::;I:; ‘;~ ::;:\::~ .I.,: l:, 1,: I.:/: 1;




E

:. I. Il :.:I~:.I:.I :I I~‘ :I::::I,:~.~~1,,~1~:~l I:. I :A.: I:.;,l::.I~ ..I, I ,:.I: I,~:vi!l:,I I!:

Figure 71. Data Collapse With Further Modificatioon of PeckhamLift Correlation Parameter - AF = 45



E




Figure 73.

E

. .': 60

.> ,j, :'I: .i.,

,II.. , -I.

::. j., ,!i:. .:. :

'!; : i. .:.,' ..,

Ratio of Actual Lift to Predicted Linear Lift of SHIPSPlan,forms With NACA 0008 Airfoils - Basic Wings



Figure 74. Ratio of Test Lift to Predicted Linear Lift ofSHIPS Planforms with NACA 0008 Airfoils - ,iF = 80'



.-L!l.i. h

1.’:1.- ..__‘; :! ,I;j; jlj: :m;

‘I!.

I: $’ j]:i._-__- .L

,:.:a. ,/:

. ::’ii, ,’

I:; I :. :- .-.

.i!,7: :‘,I ::,, ..

” I” :::

:,I :.:; ::-- _-. i__.

‘I, i ”.;,.;,! .:: ‘.

.!. .I __:

‘2b

ilE1 I

Figure 75. Ratio of Test Lift to Predicted Linear Lift ofSHIPS Planform with NACA 0008 Airfoils - AF = 75'

---r-:. ,

:::.j::-:

Y-1

r: ;::.

:: ::_.: .

_l-z,

.,:;.,

:: 1.:.

1

!.. :.. . . .

-.-.. .-!: :!.. :1”:’

,.I .:.-.-...A

“I ‘.

-.I 1:

? .: i.I. :

..::

,.I :::-. .: .__...^

1;;;

1 ‘1.L-L;1



I

/.,I:./,I

(1,...P

.A...1,;:.;.I...::/_.:

I !

1’..,. :

ii;: 2.I: :

..:: ;:I; I:.., 2..,, I./. 8,’

:,..:

I.‘.:,._: ,

. ,,..

:

E

Figure 76. Ratio of Test Lift to Predicted Lineal Lift ofSHIPS Planforms with NACA 0008 Airfoils - '4, = 70'



$

I.,..:i

I ../

j:::.j

Figure 77. Ratio of Test Lift to Predicted Linear Lift ofSHIPS Planforms with NACA 0008 Airfoils - ,dF = 65'



Figure 78. Ratio of Test Lift to Predicted Linear Lift-of SHIPS

j:.. vI...1 I I~i:.I.:..I,~ .,/‘.j:I ./::.I 1 :I II ._I_ iI:’

I:i

Planforms with NACA 0008 Airfoils - AF = 60"



E

Figure 79. Ratio of Test Lift to Predicted Linear Lift of SHIPSPlanforms with NACA 0008 Airfoils - AF = 55' and 53'



I.I-j:L.I’j:

_:

.

7:

-

i.

1:

_:

7

. .:.:.

,A.

,Y

--

.

I

:_ _,:.

--

::

Figure 80. Ratio of Test Lift to Predicted Linear Liftoof SHIPSPlanforms with NACA 0008 Airfoils - AF = 45





I/,/ j‘CbN6 fEtllRR/T I

25 25 .000835 35 .0008 _

45 45 .000853 53 .000860 60 .0008

I ;/

i

I

I

Figure 82. Ratio of Test Lift to Nonlinear Potential Flow Esti-mate for Basic SHIPS Planforms



I

i

i .:

,I

!

_i

I

I

i

. _

II I I ;6;

TE~T/R;uN086 18

a: I 63

I

I II

1 II

I

I

I

I

CjINFj Ei.JRR,TtiN80 25 .006880 35 .0008

I

j i i )

I

I

.i

I

I

11,I

Figure 83. Ratio of Test Lift to Nonlinear Potential Flow Esti-mate for SHIPS Planforms Having 80' Fillets'

.



75 3575 4575 5375 60 w

Figure 84. Variations of Leading-Edge-Suction Ratio with Angleof Attack for Irregular Planforms with 75' Fillet

Sweep



SR

28-

24-

20-

CTDeg

16-

12-

8-

4-

a25' Wing

Region 5

1

'\

,: / a5, / \ /

-----+. \ ,"\/

.A-

v

\ Reeion 3 N->’

//

j////p - /M--3

Region 1,' .I ' '/ ,I \ ' ./ /RZgion 2

/ /

'Plateau'Value 'of SR

Region 00 ’ *

25 35 45 55 65 75

.I\

Fillet

- Deg

Figure 85. Example of Angle-of-Attack Botidary Variations withFillet Sweep for Wing I Planforms



.8

.6

.2

0

Band of Data from NASA TND 3584

for 4 to 6% Thick Wings

0 250 35

h 53d 60

._.-. :..I Open Symbols NACA 0008 Airfoils j

ISolid Symbols NACA 0012 Airfoils.Unflagged Fixed Transition

! / I ' Flagged Free Transition

1 2 4 6 8 10 Rle 20 40 60 80 10

Figure 86. Correlation of Suction Ratio "R" Using EffectiveLeading-Edge Radius Reynolds Number

0 x lo3



.8

11 11R

.6

.4

.2

0

Ah

n

AAco "ALE

.,:II:’Y..;.!...,I!.,.li_ ..,iI’.../,I!

NACA 0012 Airfoi

Fixed TransitionI I Flageed Free Transition

-L :. ‘.’'=R

,eLER ,

1 2 4 6 10 40 60 100

Figure 87. Correlation of Suction Ratio Using WINSTAN Q Parameter



Figure 88. Comparison of Correlation Curve Values of SuctionRatio with SHIPS Basic Wing Test Data



SHIPS TEST DATA,. I

Figure 89 Comparison of Simple Prediction Approach withSuction Ratio Data



i..:.::. .1::: .--- ;.! . . . . . . . . ..- i::

.‘::fi:.:::~:f.:.::::::

::... __.:“. ”

Note "R", = "R"nTa, +

k-.0005;1- i- .I..: :.. .i.::.f :,.!:.-:i.:..!L : --I ---.----! -"I

l-.ri _-:: i i.:i.::ii

I-::-j::il:

I.. I

Figure 90. Calculation Chart for Incremental Effect of FillSweep on Suction Ratio in Plateau Region Between

cY= 0' and cU2

.et

152



,

Figure 91. Upper Angle-of-Attack Boundaries for Region 1

E



: .... . . . . . . . . : ::::::::.rr..... ..... ........

W2

aeg :.:;:;:::.I- :.I:-:f-::-::.:rI:.:-~--..i...- . . . (.. .._ .

.( ,. ..,.... f _. i ,.r--:- : , -.::.. -!4 - 1

Li,.‘/ :-:::.: ‘i

:,.- .: :.:i ..:::,::.f ~::li::..; -: .1./ -:: : .: ,.:: .:

L: - - 33 -J..iI;,::.]:.::1-,:ii-:--: :J:

Figure 92. Incrementa l Angle of Attack- for Region 2

154



Unit Reynolds Number

“w, deg

2535

.._ - i .::: _,.. i . . . . ._,_ .__. .. .L:.:!:.. !:. .;_:.,__... a_..:.._: 111:.1:..: _. :--1: 1: .”_..... ..-. ,..,~ . . . .-+-... _:TT-~.l.l.-. .._.: -ii+;;;;.i:.

~:::.lL:r-::.1_. .-

.i j .._. :.::!: !I:

.r.. .-..._- ._.. ._... . .._-_. .-. I.. . ,.:::::::. :~~l:l:-:t..:::-:l.‘-.:.; .: .._--+^-. ...‘-.--t.-.‘.-. _--_ _._. --+___._._ _.._--.- . .-_-_. -..- . ..-. _.--

. _. --w

Figure 93. Incremental Angle of Attack for Region 3

155



,:.:.i.. ;. :. .,:_:_. ._._: .I. .:.i:.-: :.::!:::. :_ /j::j :: :i::,: ._:.;::. . . . . . . : .’ ‘:,,:.:T:.‘. _.._:.. . : ___...._ .._.,._. .::...:.!I..:‘::::: :.i’-.. :..:If :,.: i:I .I::. i:. 1 :. : i ,:.: .!:liril!:: ;:.;’ y 1 ;l.;:l:l11::11’:: ::::::.:: ,..... ::..i.. .:...

.-..~ll.:::..::::::.~.: . . . . .

I..:.: :: .::ii:::: .:..i:i:i :. ::: :k::::I-. :I.:.:;:: .:..:.,.:

::::: :i::i::i-ri,-:::~..-: Xrii::I:t ~i:~~.I:i~. ii : ‘:‘fti:‘:’

:..: . . ..ix.. -:.L1.:.: . . . . :.:.! .: ,:..;::I. :-:-iI::.I.:.T.y..!-:.I :. :- .::. p: -.:;:.i.I. i :::_ J .,: $ z;::;l.: :_: !:: :: :I:l:.: :.,. . . . . . . . . . . :rr:;7~1: :-. .

:I.. ; : _: ::: ::.I-:. .-::,--Ii :... ! :.;I.:-! : :.:- :.

I...... -.:..- ,, . . . ...! . . . . . . . . . . / .,. + . ...; . . . . _‘. .I.~ A, , ..:.. .;.

!i:::i:: .I... :.-..I. :;:::;I

j:. ;..:.I: L.,/.: .ii:i::,j:j.,;;i.(i,l:. ..:I ,::i.:::_

Figure 94. Incremental Angle of Attack for Region 4

156



: :.:: ..,.. .._. .., .._ ,_. _._.,.,_ .,::ii:::1..:.‘-::‘;::: l:ii:iii{i ii:-ii:ii{ :i::iliii t.l

., _,...

!.‘.’I---- .--.$--

: ” _. . . .i... ._.+ .__. . ,- ,,__ .::!::::,....:.:.:i .::::::~ .:i;;i+i; i;i;xmy.

..\.:::i;;;r~:::;-I:; -yiri,~ .-.I....,.‘. “:‘::i....: :..,..::!:::: .::::. ,.

‘I;li,;;;,I;;iL;; ::...( . . .._.... .._ _,.._ ,.. ._.. 2

:..::,:::.t.:: ::::.j:::,i:::$-:li:::.l..::~~~~.~~~.~~~:~.::: .:::;::.. ::::!::;1 _:.. .1:: .I::‘.::: .:.:..: I::::.::._ 1i:.;:i _... i.. .i.;::i.:i:;::;: ;;“i.‘:; ;:;j;;:i

i--ri-l-,l.:lfii’ti~l::, . . . . . . . ../__.:::_::I::_ ‘:ljijil.,iiii.j_:,,.::.. ,_,,,,._ .._ .._ ,_, _. _, .._. ..:j::iiiilili:ii:‘iI::l~~~,~~~,l::...::::,:. ..! . . . .._._._. I.. .I . ...! ._._ 1..:.::....:::..:I::::::::: .x:zx: .::i.::: .::::::I: :.::I:::: ::21.:::. :::.::..:.:I :.:

_; i :.:::. :.:I .._ i .:.t :::_:::.: !.:.:i‘;!:::.I::. : .:,I . ..!.::.!-:.::i::..l::::i:~i:l

. ..: -1.‘::::‘:‘..:‘:.: ..::::::. .::.I:::: I.::.:.:l:I:1:.::.::1 -:!‘:.:,..:::::I:

1 .:

:.-:,:.:.i.i.i:::i:,:-:::. -.I.-_....

I

! ::. .:-

..~. : t.. : :.,: r.!::r.{ :..

rd61++74 c

1 1'. : i-: I.. .: .;:i~:~:jlly :!; T

.:..:. ..... i

I : ++-8.0x10w/iL, . .(. ... . .... /_ .. , .... .:. ... . ... .

157



8

6

. .

--

-.!-

L .._ , -I! o

.-- .I;

L1- -__-

.I

_t3

-_.

,II-

hW.-

25.^2535

4553-- 60

.08

.08

. 10

.08

Figure 96. Correlation of Reynolds Number Effects onCY2 for

Basic Wings Using Chappell's Correlation Parameter



---sg+

8

6

1” --

I

-. - ;---I

I..-..,i

I

---c--.I

~-t --t---.1-- -I---i .._. )_ --I. 1. .!. _/. !.-I- .- j _... i

.I_i .’I

I

I_.,._I

.’I..i-t-.’....

.l

Figure

Aw

0 250 25

0 35A 45

D" '6;

.08.12

.08

.08

.08

.08

I

_/ i

I

.I

1*T

97. Correlation of Reynolds Number Effects oncv2 forBasic Wings Using $2 Function Based on Leading-Edge Radius at Tip



8---

8 - 35O, A----- - -

I

REF

-4

+2

0

-2

-4

-6

-8

Figure 98. Envelope Correlation Curve for Change ina ofBasic Wings Due to Change in Reynolds Number



+6

+4

+2

0

-2

-4

1 c

sa3cos.$J

L

.-.-l

t/c - Aw *

I

I12-25' :;.

Figure 99. Envelope Correlation Curve for Change in cw3 of

Basic Wings Due to Change in Reynolds Number

-‘-

. .

.

T

t-6

+4

+2

0

-2

-6



-2

-4

-6

-8

e--

-1c. 1

t/c - Aw

.r,’

.’

12 - 2 5.;/

-6

-8

Figure 100. Envelope Correlation Curve For Change ina ofBasic Wings Due to Change in Reynolds Number



0

-2

-4

-6

-8

---

-1c

.l

8 - 35;

t/c - Aw j

12 - 25’ /

i

Figure 101. Envelope Correlation Curve for Change inar5 ofBasic Wings Due to Change in Reynolds Number



L2t I .-_ -.__..- - -

6a3cd4F) -

- L.. : .- . . . . ._... i ..-

! I 1 I 4 f

! ---.- --..---.- . .._ - ..-. ..-._- -l.- - . _I ..: :.. : : :. :

1. ;--L

i n~+~-,-lkG2b_.+-3~ ;. 4b__.jo .'( .: . , ..;

._: j : ! .. !..:.; F w .! ..; : ; :.;: ; :.] _: -----.-L-_ _ -.-.-!-l.- !--.--..i-.-A-- .-.L---i-.__.A -.L-! ___ .i.- !

Figure 102. Correction Term for Effect of FilletSweep on aBoundaries

164



Ii-j . . . . . ..i

:-.---...:-I--.,i ,.:. :: _‘._:. .-. 11-L.: lj. ;..

--L ._..: .__ -1;--:--i I.:_ .,. :.:.-c .,__.. .._,. _I-, ~::Yj7:::::.:: .:.. _:

1 : i..’ 7 .y. , .. --

I :: ! , : .- (A, - A,.) 1 i j :.i,-- .7--r-.‘--

,

t+.e-. :__I.-+ _..... r -w’

L-. -. Figure 102. Concluded

i

j---j-

-___-.” : i _.: .I. :

:I

_.-.. . i.- .---... -.._ ,__.. - -. . ..-..--.-.1- -.--..-.. -

+-- ;

:

---._-- .- _._...._.. ._..--- __- -: :.

-:-.i-- ; --: : -’

_... .-- i. _....

: ;

,.__ j.. -. _--. .,--.-:--__-: !

y--:-.-.

: --_....-. __: ! ~------.-?I.’ -_. _ --_.--.-_-. -~

+ -----

:.. : i . 4 I I.. ..:

1.. i.., 1t-+ ._.___ -~I _. a. _-. --: _.______ --_-._- __.__ L--_-_-_-:. -...

i:

I:-

‘.’ i .. i : .i.:.:. I. ; ;. . . . . .: :.:.: .__I ; /

! .: 1. /: : I

; ; ::

.--__.---_. .-._- --..----.:-.--, :. , ! ! ; i : ! / / i ’ -i .j. -f . . I

I!

:./

I-::= : : *

:j ;. / : j,:.; ; -j-- -..i..---A ..__. -_...-..

i : j ] :I-:. j i i:- I j j

! 1.; j.:- ;..-. -.-__-. / ____.. -i -.;---:---;- .-..._.- &

.: i ‘i I:. r-7. .;. ,. j

165



SHIPS WinddTunnel Data

M= -3, RN '= 8.0x106/Ft

AW = 25O 4 4 a

,.\,\\\\\ 0 Primary SlopeI\

4

c.1 to .5 CL)

I 0 Slope at Low CL\

\I A Slope at High CLI

ac

%Ere

60

50

40

f 30

20

10

020. 30 40 50 60 70 80 90

AF

Figure 103. Aerodynamic-Center Locations of SHIPS Wing I Pian-forms for Various Lift Regions

166



-

40ac%iZ

ref30

SHIPS Wind-Tunnel Data

M= .3, RN = 8.0x106/Ft

Aw - 35O

0 Primary Slope.

(.l to .5 CL)

Slope at Low CL

Slope at High CL

20 --

10 -*

0 I I

20. 30 40 50 60 70 80 90

Figure 104. Aerodynamic-Center Locations of. SHIPS Wing II Planforms for Various Lift Regions

167



50

50

40ac

%Cref

SHIPS Wind-Tunnel Data.

M= .3, RN = 8.0x106/Ft

AW = 45O

0 Primary Sldpe

(.l to .5 CL)

Cl S lope at Low CL

A Slope at High CLt

30 --

20 --

10 --

0 I I

20 ' 30 40 50 60 70 80 90

Figure 105. Aerodynamic-Center Locations of SHIPS Wing III Plan-forms for Various Lift Regions

168




M- .3, RN = 8.0x106/Ft

$J = 53O

0 Primary Slope-t

(.l to .5 CL)

Cl Slope at Low CL

A Slope at High CL

20’ 30 40 50 60 70 80 90

Figure 106. Aerodynamic-Center Locations of SHIPS Wing IV Plan-forms for Various Lift Regions

169



60

n Slope at High CL

P

50

40ac

%Eref

30

20

10

0 I

20 c 30 40 50 60 70 80 go

*F


M = .3, RN = 8.0x106/Ft

"W = 60'

0 Primary Slope

(.l to .5 CL)El Slope at Low CL

Figure 107. Aerodynamic-Center Locations of SHIPS Wing V Plan-forms for Various Lift Regions

170




28

24

20

16a

12

i1w = 25OUpper Limitof PrimarySlope

8

4

0

-4

i

Lower Limitof Primary

I lope

20 30 40 50 60 70 80 90

AF

M=. 3, RN = 8. OxlO%Ft

Figure 108. Angle-of-Attack-Envelope for Primary Aerodynamic-Center Location

171



1.2

1.0

.8

CL

.6

.4

.2

1


M = .?, RN = 8.0x106/Ft

Figure 109.

J

Upper Limitof PrimarySlope

Lower Limitof PrimarySlope

30 40 50 60 70 80 90

.AF

Lift-Coefficient Envelope for Primary Aerodynamic-Center Location

172



701 O- SHIPS Wind-Tunnel Data-I\W = 25'

60 --

50 -.

Eref

40-.

30--

20*

M = -3, RN =8.0x106/Ft

Figure 110. Aerodynamic-Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing I Planforms

173



701 q - SHIPS Wind-Tunnel Data-AW = 35'

60 -.

50 --

%Yref

40 --

30--

20 -*

M = .3, RN = 8.0x106/Ft

/

K=O

0.5

1.0

1.5

2.0

10

t0 I I I f

'0 30 40 50 60 70 80 90

Figure 111. Aerodynamic-Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing II Planforms

174



70

TO

SHIPS Wind-Tunnel Data-AW = 45'

60

t

ac 50-%E

ref40 -.

30 .

20 -*

M = .3, RN = 8.0x106/Ft

/

K=O

0.5

Il.0

1.5

2.0

I I20 30 500 60 70

*F

80 90

Figure 112. Aerodynamic-Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing III Planforms

175



70

60

A- SHIPS Wind-Tunnel Data-AW =53'

/

K=O

M = -3, RN = 8.0x106/Ft

0.5

50ac

%Cref

40 .-

30 '-

20 --

10 --

1.0

1.5

2.0

0' I I20 30 40 50 60 70 80 90

AF

Figure 113. Aerodynamic Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InboardPanel - Wing IV Planforms

176



70-

60 -.50

%:zef40 I.

30

A-20 1.10 *.

0- SHIPS Wind-Tunnel Data+AW =600K = o

M = -3, RN = 8.0x106/Ft

/0.5

1.0

1.5

2.0

c

O/20 30 40 50 60 70 80 90

*F

Figure 114. Aerodynamic-Center Prediction - Paniszczyn MethodModified by K Factor Applied to Lift of InobardPlanforms - Wing V Planforms

177




M = .3, Rx = 8.0x106/Ft

Primary Slope

(CLLY . 1 t&.5)

20 30 40 50 60 70 80 go

AF

Figure 115. Aerodynamic-Center Location Referenced to MeanGeometric Chord of Each Irregular Planform

178



60

ac %E 40

of EachBasic Wing

30

20

10

0

cs


M= -3, R~J =8.0x106/Ft

Primary Slope

(CL%. 1 to .5)

-101

20 30 40 50 60 70 80 90AF

Figure 116. Aerodynamic Center Referenced to Mean GeometricChord of Each Basic Wing

179



FS ac

from 80' apexof each wing

17.8


M= -3, RN = 8.0x10%Primary Slope

(CL z.1 to .5)

17.4

17.0

16.6

16.2

15.8

15.4

15.0 I.-

14.6- : I

20 30 40 50 60 70 80 90

AF

Figure 117. Aerodynamic-Center Location Referenced to Apex of80° Fillet for Each Planform Family

180



_~.._ ---SHIPS WindLTEnnel Data-

M = -3, RN

Primary Slope(CL e. 1 to .5)

FSE/4 = 16.887 For all Basic Wings17.8.-

17.4..

17.0-sFS ac

comnik

16.6,-

16.2-v

15.8.-

14.61 -++- 4. I I20 30 40 %I 60 70 80 90

*F

Figure 118. Aerodynamic-Center Location Referenced to Apex of80°/25' Planform with Common Location of QuarterChord of MGC of each Basic Wing

181



80SYM

T 0

7c

6C

ac %c,

50

40

30

2c

10

0

1 -

I--

l --

_

I --

80”


M= .3, RN = 8(10)6Primary Slope(CL z. 1 to .5)

AW

60°53O45O

35O25'

20 30 40 50 60 70 80 go

/\F

Figure 119. Aerodynamic-Center Location as a Percentage ofRoot Chord of Each Irregular Planform

182



60-

50-n

40..ac

%Sref

30 -.

20 -.


M= .3, RN = 8.0x106/Ft

SYMI hFPrimarv SloDe

0” 80"75O7o"65'

60'55O

(CL%. i to 15)

'25'

10

t0 1

0 8 10 20 30AW

40 50 60 7b

Figure 120. Variation of Aerodynamic-Center Location Referencedto Mean Geometric Chord of Each Irregular Planformwith Outer Panel Leading-Edge Sweep

183




80

70

60

5c

4c

ac "/,c.

30.

20

10

0

IT

I __

t -_

L

SYM

0

;a

0”A0Q

M = .3, RN = 8.0 x 106/Ft= .3, RN = 8.0 x 106/Ft

Primary Slope (CL=.1 to .5)rimary Slope (CL=.1 to .5)

AFF

t

0 10 20 30 40 50 60 70

AW

Figure 121. Variation of Aerodynamic-Center Location as a Per-centage of Root Chord of Each Irregular Planformwith Outer Panel Leading-Edge Sweep

184



SHIPS Wind-The1 Data

60

50

40t

30

20

I

M= .3

25O Wing

3 0\

kc:\\ 2\

Primary Slope

10 --

0 4

20 30 40 50 60 70 80 90

AF

Figure 122. Effect of Reynolds Number on Aerodynamic-CenterLocation for Various Lift Regions - Wing I Plan-forms

185




60

M= .3

35O Wing

Slope

0 1 I20 , 30 40 50 60 70 80 90

*F

Figure 123. Effect of Reynolds Number on Aerodynamic-CenterLocation for Various Lift Regions - Wing II Plan-

forms

186




M= .3

45' Wing

RN /FtYM i

0 j 8 (lO)6

0 j 6 (I(+

60, 0 4 (lop

A 2 (lop

/

50 -.

40 ._

ac %Eref

30 -*

Slope

20 --

0 I i

20 , 30 40 50 60 70 80 90

*F

Figure 124. Effect of Reynolds Number on Aerodynamic-CenterLocation for Various Lift Reigonk - Wing III Plan-forms

187




M= .3

53' Wing

SYM 1 RN /Ft

0 i 8 (1Of

o i 6 (lO)6

ac 40 -.o _"'ref

30 **Low CL

10

I0’ I I

20 30 40 50 60 70 80 go

Slope

Figure 125. Effect of Reynolds Number on Aero-dynamic-center Location for Various

Lift Regions - Wing IV Planforms

18%




60-

50--

40 --

ac %Cre f

SYM RN/Ft

0 8 (1Of

6 (lO)6

: 4 (10>6A 2 (10)6

M= .3

60' Wing

30 --

20 --

lO-

0-20 30 40 50 60 70 80 9b

Figure 126. Effect of Reynolds Number on Aero-dynamic-center Location for VariousLift Regions - Wing V Planforms

lope

189



'rn.2

-flw

*F +80

+

25 35 45 53 60

75 i-+;I

70 1"

+ I 0 1

25I"'" RN = 26.247 x 106/mI

0 1 Airfoil = NACA 0008

MRJ? = .25EW,F

Figure 127. CM - CL Curve Shape Schematics

190



-: / .I. i . . .i. -J- _..: 1::--.-. .._.---

: ,_’ : :. ; . . . f j . ,I : ‘: :::- t:

: ; .L 1. j .;----7 ,-A---.1 -1_..:-A-L- --....-- - --~ -.

j. i.--l-i !: j : i ; -! : j : .i .j i I j I

_: : : :.. .:.-.:

: AfPitchi I.._ ; : ..:_ ; -:, ;

_..-: : Up/Pitch Down Design Guide;-:--;- :_.. _ _ . __ ._ -.- -..y:: : :jt--Y--.:--- : !: -i.-.i .. NACA 0008 Airfoils :.-:....I : i-r:: j ~--.--.-..---.:I .-f--Y; ~___-

_::.:.: I : .: {'. :

. _: :

: : : ! 9-I _...L..- ..,. _ i.. . 1-- : ._-. _.-__ :.L-.. Probably will Pitch

- ‘80

70:

+%-I--(deg)-66-

Figure 128. Pitch Up/Pitch Down Tendencies asFunctions of Wing and Fillet Sweep

191



30

20

iac

Break

10

20

16

CYBreak

R/I ’

d ‘,\\\\\i\


I -

M=. 3, RN = 8.0x106/Ft

8

.8

.6

'LBreak

.4

.2 I AI

0 .2 .4

&an(*i8- Aij"

1.2 1.4

Figure 129. Correlation of Data Related to Shift of AerodynamicCenter in Region Above Primary Slope

192



CLBK

A

SHIPS

Wind-Tunnel Data

M= -3, RI1 = 8.0x106/Ft

.4

. 3

.2

“O-I I

.2 .4 .6 .8 1.0. ,1.2 1.4Tan(AF - A,>

Figure 130. Correlation of Lift Coefficients for Upper Limitof Primary Slope Region

193



I., .

SHIPS Pitch-Up/DownSmoothed Wind-Tunnel Data

M=. 3, RN = 8.0x106/Ft

.4

CLBK

A. 3

. 1

I0 ’

0 l .2 .4 6 1.2 1.4

T'an(AF.8 1.0- hW 1

Figure 131. Correlation of Lift Coefficients for Upper Limitof Primary Slope Region Based on Smoothed Wind-Tunnel Data

194



Figure 132. Example of Variation of Pitching Moment with Angle

of Attack Approximated by Linear Segments BetweenAngle-of-Attack Boundaries Defined by Suction-RatioAnalysis - Irregular Planform with Low Fillet Sweep



Figure 133. Example of Variation of Pitching Moment with Angleof Attack Approximated by Linear Segments BetweenAngle-of-Attack Boundaries Defined by Suction-Ratio

Analysis - Irregular Planform with High Fillet Sweep



0008 Airfoils :::::T.:: ::::.T::~..:: .z:~..:i::iFrFll::-z. _qz:I ::

, . . , ..I’.. ; ..-, -.... ,.,--.- _1.-. ..... . ... . .. . . ,..- -; _._. I. .. . _. ... L _ .-...., -.-. --+-A .-..+. .... ... .

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

. ..li.~::1:.::i.:.i :r:i ._.. I::-i:-:I.:.-:.I..:.:-:. :..... - . . .. . .. . . .. . . . .. - . - . . . -

... ....... _ ... ..... _. ........

I :_.. I..::.::.

.: : ., .:::‘:‘: . ..::i..i., .l..i ,_,: ..i’: ,:,.:: :‘:.i :. :i:itiii’ __,____ .:iiii:i:

. . . . . ..: L:. ,:.._.._ . . . . . . . -.. .,

%F!. ! _..,_. _: . .i...Stability at '-: '!::.Y ! ._. ._ !a.c. .-- 1.. I, i ..: Higha -

.: .,. . . ..-I..-.. .- .,.... . .. , ,

DUnstable Break at Higha i i iI

reak at Higha ' 1

Figure 134. Pitch-Up/Pitch-Down Design Guide Based on LoAngle of Attack Aerodynamic-Center Location

197



PREDICTION METHOD DEVELOPMENT

The previously described efforts produced several approachesfor developing a set of prediction methods forlift, drag, andpitching-moment characteristics, but additionalwork remained.As discussed earlier, it was intended to devise a basic set ofmethods from the data obtained at unit Reynolds number of 26.25million per meter (8.0 million per foot). This section describes _how selected approaches for lift, drag, and pitching moment (inthat order) were developed into the "basic" prediction technique.

One guideline-in the method development process was the fact

that eventually prediction methods would be required for tran-sonic and supersonic speeds and compatibility among the methodswould be desirable. A second guideline was the desire to comput-erize the final methods. A third guideline quite obviously wasthe need to obtain sufficient accuracy from the predictions to beable to represent the differences in the aerodynamic characteris-tics that occurred between changes in the irregular planforms.

The methods selected for development or modification were:

(1) The WINSTAN nonlinear lift correlation

(2) The Aeromodule prediction method for minimum drag

(3) The leading-edge suction ratio correlation approach

for drag due to lift

(4) The quasilinear variation of pitching moment with-

in regions of angle of attack defined from thedrag-due-to-lift prediction

The development efforts related to predicting the liftcharacteristics are presented first, followed in order by thosefor the drag characteristics and the pitching-moment characteris-tics.

198



Lift Characteristics Prediction

While many approaches for correlating the lift characteris-tics of the SHIPS planforms were examined and several showed prmise, the WINSTAN lift correlation approach shown previously inFigure 59 was selected for further development because it hadproduced the best collapse of data at angles of attack up to 16degrees and contained parameters which would allow extension tohigher Mach numbers. In addition, it was apparent the spreadof

data above 16 degrees angle of attack was sufficiently syste-matic in terms of the values of outboard panel leading-edgesweep for each value of fillet sweep that the chances of finding

a means of accounting for the effects were good.

The approach taken was to redefine the basic correlationfor angles of attack above 16 degrees on the basis of data forthe outboard panel sweep equal to 25 degrees. These incremen-tal values of the lift correlation parameterdetermined for each value of outboard panel

A cL A1

sweep. ( 1

were- -%a ?'B

Plots were made of the incremental values as fclnctionsof the parameter @tatiF for various fixed angles of attackfrom 16 degrees to 26 degrees. The results were somewhat ir-regular for fillet sweeps below 65 degrees and angles of at-tack above 20 degrees, but it proved possible to smooth thebaseline curves in a way (Figure 135) which also producedsmoother variations of the incremental values with OtatiF.It was also noted that,if the smoothed incremental values at22 degrees angle of attack (Figure 136) were used as a basis,the variations of the incremental values with angle of attackat fixed values of BtandF could be reproduced to good accuracyby a correlation curve, fl, (Figure 137) which represents thestall progression of the family of 35 wing planforms.

The final results provided the following prediction equa-tion:

CL= B [(k. 2L1+ ,*(k ‘-.i)]

199



where the terms in the brackets are read from correlation chartsas follows:

AcL *1--

( J

CLa r)B

from Figure 135

from Figure 136

flfrom Figure 137

Al is the aspect ratio of the inboard panel

7Bis the non-dimensional spanwise location of thebreak in the leading-edge sweep.

is a function of the parameters Pt=+

The term A is a function

of BtanAF andAW that is applied only for angles of attack

greater than 16 degrees and accounts for the effects of outboardpanel sweep. The factor fl varies with angle of attack above 16

degrees to reproduce the incremental effect on stall progressionwhen applied with the incremental effects caused by variationswith outboard panel sweep.

The lift curve slope, CL,&

is the incompress%ble value cal-

culated using' Spencer's semi-empirical expression:

200





Minimum *Drag

The minimum drag of the irregular planform wings is com-

posed of drag items that are "assumed" to be independent of liftsuch as friction, form, interference, base, roughness and protu-berance drag contributions. The methods used to determine eachof the minimum drag contributions are discussed in the followingsubsections.

Friction, Form, and Interference Drag

A large part of the subsonic minimum drag is comprised ofthe sum of friction, form, and interference drag of all the con-figuration components. The drag of each component is computedas

- FF . 1F (3-l)

where Cf is the compressible flat-plate skin-friction coefficient,S

wetis the component wetted area, and FF and IF are the compo-

nent form and interference factors.

For emphasis ,the specific configuration components con-sidered are illustrated in the sketch below. The pertinent geo-metric equations are presented in an earlier section

Hidden areanot used inwetted area

calculation(Body sideand wingupper surfaceonly)

/Forebody Nose

-BalanceHousing

202



Friction Drag

The flat-plate, compress ible, turbulent, skin-friction coef-

ficient is determined from the general equation give,n in Refer-ence 18

Cf = $ Cf1 i ('L ' F2)

(3-z)

where Fl and F2 are functions of the free-stream Mach number and

wall temperature. The incompressible skin-friction coefficient,

cf 'is evaluated at the equivalent Reynolds number, s F .

i L 2

White and Christoph (Reference 18) developed expressions for thetransformation functions Fl and F2 along with a more accurate

explicit equation, based on Prandtl/Sch lichting type relations,

for computing the incompressible, turbulent, flat-plate frictioncoefficient (Cf ) with the following results:

i

Fl = t-1 f-1

F2 = t l+nf

For an adiabatic wall condition, t and f are given by

t ='TOO/Taw = l+ry Mz -'1f = 1+ 0.044 r & t

203



Using a recovery factor r = 0.89 and a viscosity power-law expo-nent n = 0.67, recommended in Reference 18, results in the follow-ing expression for Cf:

cf= t f2 --.- 0.430

(

loglo(sL . P7 . f 2*56

,)

(3-3)

where

11

t 1 +0.178 M,2

f = 1 + 0.03916 M,2 . t

The Reynolds number, s , is based either on component length orL

an admissible surface roughness, whichever produces a smallervalue of Reynolds number, as follows:

(RN/ft) L%I = minimum (3-4)

L5

. (L/K) l. 048g

where

RN’t is determined from standard atmospheric tables

or is input.

L is the characteristic length of the component.

K is the admissible surface roughness and is an

input quantity.

Kl = 37.;87 + 4.615M + 2.949M2 + 4.132M3



For mixed laminar-turbulent flow, transition location isspecified for the upper and lower surfaces of the wing. Forthe laminar portion of the flow, the Blasius skin-friction rela-tion

cf = 1.328$/T @JLainar (3-5)

where cf'cfi= (1 + 0.1256M2)-'12, is used up to the transition

point. At the transition point, Xr, the laminar momentum thick-

ness is matched by an-interative process to a turbulent momentumthickness, which begins some fictitious distance, AX, ahead oftransition. The skin-friction coefficient for the turbulent part

of the flow is calculated from Equation 3-3, where the Reynoldsnumber is calculated from

%L= AX- Xr> . (s/ft)

The value of Cf with transition is finally given by

cf = (: + ?) CfTurb.

(3-e)

(3-7)Calculated values of Cf versus s are presented in Figures 138

L

through 143 for mixed laminar-turbulent flow.

Form Factors

The component form factors, FF, account for the increased

skin friction caused by the supervelocities of the flow,overthe body or s&face and the boundary-layer separation at the

trailing edge. The form factor for the "body" component iscomputed as

FF = l+ 60/FR3 + 0.0025 - FR (3-B)

20



whereComponent Length

FR =Width x Height

For "nacelle" components, the form factor is given by

FF = l+ 0.35/FR O-9)

Equations 3-8 and 3-9 were obtained from the Convair AerospaceHandbook (Reference 19) and also appear in the DATCOM (Refer-ence 11).

The airfoil form factors depend upon airfoil type and stream-wise thickness ratio. For 6-series airfoils, the form factor is

given by

FF = l+ 1.44(t/c) + 2(t/c)2 (3-10)

For 4-digit airfoils, the form factor is given by

FF = l+ 1,68(t/c) + 3(t/c)2 (3-11)

For biconvex airfoils, the form factor is given by

FF = 1 + 1.2(t/c) + 100(t/c)4 (3-12)

And for supercritica l airfoils, the form factor is given by

FF = 1 + KICld + 1.44(t/c) + 2(t/c)2 (3-13)

The factor K$Cld in Equation 3-13 is an empirical relationship

which shifts he 6-series form-factor equation to account for

the increased supervelocities caused by the supercritical-sectiondesign camber Cld. The factor Kl (d erived from experimental

data) is shown plotted in Figure 144 as a function of the Machnumber relative to the wing Mach critical. Equations 3-10 and

3-11 were obtained from informal discussions with NASA/LRC per-sonnel; Equation 3-12 appears in both the DATCOM and the ConvairHandbook.

206



Interference Factors

The component interference factors, IF, account for the mu-tual interference between components. For the fuselage, the in-

terference factor is given by

IF = S-B (3-14)

whereRw-B

is shown plotted in Figure 145 as a function of fuse-

lage Reynolds number and Mach. For other bodies such as stores,canopies, landing-gear fairings, and engine nacelles, the inter-ference factor would be an input factor based on experimentalexperiences with similar configurations. The Convair AerospaceHandbook (Reference 19) recommends using

IF = 1.0 for nacelles and stores mounted out ofthe local velocity field of the wing.

IF = 1.25 for stores mounted symmetrically onthe wing tip.

IF = 1.3 for nacelles and stores if mounted inmoderate proximity of the wing.

IF = 1.5 for nacelles and stores mounted flushto the wing or fuselage.

The interference factor for the main wing is computed as

IF = %S - S-B (3-15)

whereRW-B

is the wing-body interference factor presented in

Equation 3-14, and RI,, is the lifting surface interference

factor presented in Figure 146. For supercritical wings thewing interference factor is set equal to one. Other airfoil

surfaces such as horizontal or vertical tails use an interfer-

ence factor determined by

IF = RIs . Hf (3-16)

207



where H is the hinge factor obtained from input (use Hf = 1.0

for an al-1 movable surface, 1.1 if the surface has a flap for

control). The factors%

s are plotted in Reference 5and also appear in the

Base Drag

Data presented in Reference 20 were used to establish equa-tions from which the base drag of bodies could be determined.The trends of these data show three different phases: (1) agradual rise of CD at transonic speeds up to M = 1, (2) a

Baserelatively constant drag level supersonically up to about M =1.8, and (3) a steadily decreasing value of drag above M = 1.8.The resulting empirical equations are given as

(0.1 + 0.1222M8) 'Base, MI1S

Ref

CDBase=0.2222SBase/SRef, 1.05 MS1.8

1'42SBase'SRef)/(3.15 + M2), M B1.8

(3-19)

Miscellaneous Drag Items

In the preliminary design stage of aircraft drag estimation,the drag due to surface irregularities such as gaps and mis-matches, fasteners, small protuberances, and leakage due topressurization are estimated by adding a miscellaneous drag in-crement which is some percentage of the total friction, form,and interference drags. The miscellaneous drag varies between5 and 20 percent of the total friction, form, and interferencedrags for typical aircraft.

208



Drag Due To Lift.

- The approach selected for development of a drag-due-to-liftprediction method is based on the concept of the leading-edgesuction ratio. The various correlations developed have alreadybeen discussed in some detail. The task that remained was toformalize a calculation procedure using forms of the correla-tions suitable for calculation and define the specific equa-tions to be used. As a consequence, some of the charts pre-sented with the following summary of the prediction method arerepeats of previous figures.

The basic equation for drag due-to-lift,

'DL = 'L

where:

CL tana

cL2

?TA

"R(a) "

A

[2

tana - "R(a)" CL tana - cLTA

3L

C, , is:

is the drag due-to-lift with zero leading edgesuction

is the drag due-to-lift with full leading edgesuction

is the ratio of leading-edge suction derivedfrom the test data to the full leading-edgesuction value as a function of angle of attack.

is the "true" aspect ratio of the irregularplanform.

The variation of "R(a)" with a typically consists of 5

distinct quasi-linear regions as illustrated in Figure 147..

Region 1 is the plateau region for which "R(a)" is a con-

stant for a specific aircraftgeometry and test condition, butis a function of leading-edge radius Reynolds number, Mach

209



number, and leading-edge sweep of both the basic wing planformand the fillet planform.

The value of ."R1" is obtained from the equation:

“Rl”Rgw”where: cAF,)"RBW" is obtained from the correlation curve of "R

BW"

vs Q in Figure 148 for

SEER

eLER

COT Aw dm

?L is the leading-edge radius Reynolds number based oneLER streamwise values of velocity and radius determined

at theof the

spanwise location of the mean geometric chordbasic wing.

andA"R~"

[ 1F - *Wis obtained from Figure 149.

The upper bound of Region 1 is defined as a2, which is a func-tion of planform geometry and Reynolds number. The planformeffect for 26.25 million per meter (8.0 million per foot) unitReynolds number on the small-scale models (the "referencevalues") is presented in Figure 150.

The methodology for determining the other angle-of-attackboundaries and the Reynolds number effect on all the angle-of-attack boundaries requires that "reference values" of cY2, a3,

ah, and a5 corresponding to 26.25 million per meter (8.0million per foot) unit Reynolds number on the small-scale

models be computed first. Then the Reynolds number correctionscan be applied to the "reference values".

220



Thus,

a2is obtained from Figure 150.

ref

a3 = a2 + Acr(3-2)from Figure 151.

ref ref

a4=a3 +

Aa(4-3)from Figure 152.

ref ref

a5=a4 +

Aa(5-4)from Figure 153.

ref ref

The incremental effect due to Reynolds number requires useof two figures (154 and 155) in which an incremental effect of

Reynolds number is first evaluated for the basic wing planformand the effect of irregular planform is applied as a factor.Note that in Figure 154 the Reynolds number parameter eT isbased on the leading-edge radius at the wing tip.

The effect of Reynolds number is applied to the Cy boundaryvalues obtained for 26.25 million per meter (8.0 million perfoot) and model scale, i.e.,

where

A (ECU, cos Aw) = ( Sa, cos A,>QT

-(6a2 cosAw) R,ref

Thus, for a particular design,52 T must be evaluated at modelref

scale and at a unit Reynolds number of 26.25 million per meter

(8.0 millionper foot), and Q, is evaluated at full scale orother desired conditions.

The other angle-of-attack boundaries cY3, a4, and a5 arethen calculated in the same way.

211



a3=a3 +

ref[

a4=a4 +

ref [

a5=a5 +

ref [

A (6a3

&$a4

cos A w>

I

cos Aw>I

A(6a5 cos A w>1

1cos Aw

1--cos 12 w

1

cos n w

The variation of "R(a)" with CY is then constructed by

sequentially applying the slope functions shown in Figures 156through 159 in each appropriate angle-of-attack region as

follows:

llR( a)ltl = "Rll' ; 05a-cx2

dR"R(a)"2 = “R(a)“l + da (a - a21 ;

0 2a25 asa

1'R(a)113 = "R(a)"l +2

a3sasa4

"R(a)"4 = "R(a)"l +(a4-a31

dR+ da (a - a4) ;

0 4a4sa<a5

"R((Y)"5 = "R(a)"l +(a;-a3)

dR+ da (a,-a4) + pa (a - a5>

0 4 0 5

; a5<-a I26 degrees

212



In practice,one computes corresponding values of,C~ from thelift prediction method and "R(a)" from the above listed equa-tions for a series of angles of attack and solves the basic drag-due-to-lift equation.

213

-



Pitching-Moment Characteristics Predictions

The prediction methodology with respect to pitching moments

provides three types of information. First, the aerodynamic-center location at low angles of attack can be calculated interms of percent root chord or in terms of the mean geometricchord from relatively simple curve fits of data obtained at unitReynolds number of 26.25 million per meter (8.0 million perfoot).

Second, the pitch-up/pitch-down tendencies of the irregular

planforms at high angles of attack can be assessed on the basisof the a.c. location at low angles of attack calculated in termsof percent effective mean geometric chord.

Third, the complete variation of pitching moment (relativeto 25 percent of the effective mean geometric chord) with angleof attack can be constructed.

Aerodynamic Center In Primary Slope Region (0.1 < CL < .5)

The prediction method for aerodynamic center in terms ofpercent root chord is based on curve fits of the experimentaldata for unitReynolds number of 26.25 million per meter (8.0million per foot). The plot used (Figure 160) presents the

variations of a.c. location with basic wing leading-edge sweepand parametric values of fillet leading-edge sweep.

A cross-plot of the a.c. location variation with fillet

leading-edge sweep for a basic wing leading-edge sweep of 45degrees was fitted with a 4th degree Legendre polynomial. Theeffects of wing sweep -are accounted for by different linearfunctions in four regions represented by combinations of wingand fillet sweep.

The base'line polynomial for variation of a.~. %Cl.with *F

for *W = 45O is:

214



l (a.c. %C1)B = 30.10775858 + 0.1524242511 AF

+ 0.007543290783 AF2 - 0.0001686738033 AF3

+ 0.000001609816225 AF4

aTo account for other AW

l AW < 45O; AF from 25' to 65'

a.c.%Cl = (a.c.%Cl)B-+ $--t (Aw - 45')

= (a.c.%Cl)B + (Aw - 45o)(.5700-0.004307692308AF)

..Aw < 45O;

AF

from 65O to 80°

a.c.%Cl = (a.c.%Cl)B+(hW-450) .2900-.007733333333 (AF-65') 1..A w > 45O; AF from 45' to 65O

a.c.%Cl=(a.c.%Cl)B+(Aw -45') [2380 + .01035 (AF-450) 1&eAiy > 45'; AF'from 65' to 80'

a.c.%C1=(a.c.%Cl)B+(AW-450) .4450 - 0.017 (A,-65O)]

A comparison of the predicted and test values of aerodyna-mic ten-ter location is presented in Figure 160. A similarapproach was used to establish a prediction of the aerodynamiccenter in terms of the percent of mean geometricchord of theirregular planform.

The baseline polynomial for variation of a.c. %ceff with~~ for Aw = 45' is:

( a.c. % k eff)Basic = 28.61247819 - .9174258792 A,

Aw=450 +.04500815340 "f - .000803241088A;

+.000005350951339 A;

215



To account for other A,

0 n, < 45O ; AF FROM 25O.to 600

a.c. % c eff = (a.c. % c eff)RASIC+(Aw -45°>(.275-.00041666666AF)

. Aw < 45’ ; A; FROM 60° to 80°

a.c. % c eff = (a.~.% c eff)RASIC +(AW-45') .250-.0024(AF-60)3

l Aw> 45O ; AF FROM 45' to 72.5O

a.c. % c eff = (a.c.% c eff)RASIC+(AW-45O)

+ .0078181818 (A F - 45)

1. nw >45O ; AF FROM 72.5O to 80°

a.c. % c eff = (a.c.% E eff)BASIC+(AW-450)

.340 - .0286666666(AF - 72.5) 1Predicted and test values are compared in Figure 161.

Pitch-Up/Pitch-Down Tendencies

Two forms of design guides are presented. The first,

Figure 162, is a simple matrix presentation showing the tenden-cies for each combination of wing sweep and fillet sweep. Whilethis guide is useful for interpreting the SHIPS data base, itis not necessarily appropriate for analyzing data for otherconfigurations. The second guide, Figure 163, makes use of theaerodynamic-center location in the primary slope region in termsof percent mean geometric chord. For the SHIPS data base it canbe used with Figure 161 to assess any pitch-up/pitch-down ten-dencies. The chart is in the form of a.c. as a percentage ofeffective mean geometric chord rather than percent root chord,because the MFC is a more descriptive property of the planform

than is the root chord.

216





= CmQ!=O

+cm cwl+c

ab.mal

(a2ref

- a,)

+ cm )+c

cu2

(a3

ref-a2

ref

"Q;

!LY-qref) '

a3ref

Q) Sa4ref

= C +c a +cma=O ma0 J ma1

(a2ref

- a$

+c

"Q;

(a3 -02ref ref

>+cm 'Q;c

?3ref

-a3 )ref

+c

ma4

(a-a4

ref

) ; a4

refsa_< 5

ref

= C +cma=O TV.,

a1 + cm

%

(a2ref

- a,>

+cma

‘cy3 >+c

2ref

- a2

refma3

!a4 -9 >ref ref

+ cma4

(cy5ref

- a4 >+c ) ;ref ma

(cu-a5

5ref

= C +cma=O So

9 + %al

(F2ref - al)

+cma (Qiref- a3ref)+cm

2 a;(a4ref-a3ref)

+ c -a4 >+c

ref ref

(ar6- a5 )

ref+c

ma(a- a6> ; a6-<as26

6

218



where:

a l and e6 are obtained from Figures 164 and 165, and the

values of C Cma=O’ "cy,

#Cm, ,c SC #Cm #Cm4 %t2 w3 a4

, anda5

C

“73

are obtained from Figures 166 through 172.

The variation of pitching moment at zero angle of attackpresented in Figure 167 represents smoothed average values forall outboard panel sweeps. The maximum deviation from the curvewas + 0.004 at AF =65, which is well within the desired accuracy.

Note that for the NACA 0008 airfoils the values of Cm

5

and Cma

are identical, but provision has been made in the

2methodology to account for the fact that for thicker airfoilsC and C

m? ma2

may have different values.

Since the intent of the pitching-moment calculation is pri-marily to define the stability characteristics of the configura-tion, the basic prediction method does not account for Reynoldsnumber effects on either the angle-of-attack boundaries or onthe pitching-moment slopes because the lift prediction does not

include such effects. The effect of Reynolds number on thepitching-moment slopes is small for the NACA 0008 airfoils, butsome effect was noted for the thicker airfoils from the basicdata plots. These effects were to be accounted for in the finalmethodology.

219



;.,::: ‘Ii:’‘jj: ;: .:. ,,: j.

.: .:: .

t--k::, : ,:..L..,.:_..:: .. :

.

Figure 135. Basic Lift Curve Correlation Parameter-t--- 7j. .)..:

I 1t

‘ _._L__.



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

ii:trlLl~iiiiiil:.:irij::jjji/ili~j.i:if_1:.~:iji

i.

... I .... 7. ...... ..... ._ .. ,........., .. .. .._.......( ., .: ,j_,: :.-::::::‘I:-iiI:il:j:i:.j :__: IIIIit,._....._.

,_.- -I-_. I...:; I:.. : . !.:..:...:I

...A .._

, . . . ,, t.. : .:i::..:

PLanIF

Figure 136.

g-y 1-y '.j : .j j ; : : i' .:; :;/

High Cy Lift Adjustment for Outboard Panel SweEfTects to be Applied Above a= 16" only

::,:-r7;::.,,. .,, ., 1. / a - aeg ;- . ..; ,.,../ 11.. e..l.:..: I : _,I

Figure 137. High Cy Stall Progression Factor

eP

cL a>169 = cL:lvB [($jq + q&2)]

221



+..q+jq: I”-;.i~~~~~~~~~~~~~~~~CrCI.~ii:.!I~’.~IFigure 138.1 '

Turbulent. Skin-Friction Coefficient on an Adiabatic Flat.Plate ' ,I

(White-Christoph)

.OO’

.OOC

.OO!

Cf

. 001

.oo:

.002

.OOl

0

A-- 1.-I.. -.

’ I 1.-j j-r__,._!/ Ii-i __.....

1 .2 6 60 80 100

I ikyn~lda Number X 10e6'. ..__' .

.4.6 *& '; . . :..I

/

i

200 400 600 1000



.l .2 .4 .6 .8 1 2 4 6 8 10 20 40 60 80 100 200 400 600 1000



*Figure 140. Skin Friction on an Adiabatic Flat Plate,

Xr = 0.2

., 0 I Ll..1--l-J-LiJ-L

.4 .6 .8 1 2 4 6



Skin Friction on an Adiabatic Flat Plate,

400 600 1000



I Fiaure 142. Skin Friction on an Adiabatic Flat Plate,

.1 .2 .4 .6 .8 1 2 4 6 1 400 600 1000



jji;

I Figure 143. Skin Friction on an Adiabatic Flat Plate,

".l .2 .4 .6 .8 1 2 4 6 8 10 20

----.-,I..:.:-....^i; .‘.

:

.- -i1#i

.

$I_..I! 1

40 60 80 LOO 200 400 600 1000



0.5

0.4

0.3

Kl

0.2

0.1

0 I II

-. 2 -.16 -.12 -.08 -.04 0 .04 .08

AM - M - McR0

Figure 144. Supercritical Wing Compressibility Factor



1.1

RW-B

1.0

.9

.8

3 5 10 30 50 100

FUSELAGE REYNOLDS NUMBER - ReFUS (MILLIONS)

Figure 145. Wing-Body Correlation Factor for Subsonic Minimum

Drag



-6 iI L

I I L 84 A 4

.s .7 .8 .9 1.0

Figure 146. Lifting Surface Correlation Factor for SubsonicMinimum Drag

230



“R

Figure 147. Schematic Variation of Suction Ratio with Angle ofAttack

231

- _--



-,.8

"R'lBW

-.---.I :. 6

I

I-

10= lOa.1

R = ReLER COTdLE 1-M2 2

cos ALE

"R"BW

1.0

,955

.8

.6

Figure 148. Correlation Curve for Suction Ratio of Basic WingPlanforms in Region 1



’

Figur

-_

i .j :I i.--.:-: Ii.:’ i-

I. ..: ._._.-...

..! .._....... . . . . ..I , ,.. ‘t.jl.... :::::.‘.::I1 ::::::.: --:.:;-::: _.., ..,-..:.-.. .._....._. - _.. _:_,

, _ ,. 7 _ 1.--l. . . -_ . . .

. .,. : : ~~!.::.i:::.i~rr.::l:.l..:.:I:1 I.:..::::.I

,,,: :,... .,:::,:.. . .-., ‘: :::,:::. ..ys:~::.r . :. ..- . . . . .- . _.-_ .L_-. : ~.. . .__-,; ,.,,- +‘;:Y:-, y::::.

I I ,

-:-:::,!:::ytrr-y + i;ri;;~. iiiiii”i tiiiiii: “)iiii,i Ii YX;~X ;~ 7iii:;j,/:ii.;:;i : ;_i;*;{:: +L!lj-

1.- : . . . _,__ _,,, -:l::r:_.I’: .::;: ll.: :::.. ::::i: :.‘:...a .,.. ITT... .I ._..,_._. -. ; _._.. . .._. L.... !.-..:.:&::.1:..1

1. ._: _.._

,:: I”:;: I..,.:.! ,:.: :::1:~::7.- . . ::.:~::.I/:::~:~:.t:::!~::.t::..~~~~.(.~~~~:~~~)~~~.j~‘~~~~~~-’:~~: :

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

.:. 1 . I . . . . . . . . . , . . . . . . . . . . . . . . . . . . .. I I I . . . . . . . . .“.F’ii,l'e 149. Calculation Chart for Incremental Effect of

Sweep on Suction Ratio in Region 1

__---...-. I ~.,...,.,:lr:::,::::i::,::..~,i~::~~-... ._. ,... ’_.,_. i I::::.:..llr~::::.:tr:~~.-=~

et

233



_..

Upper Angle-of-Attack Boundaries for Region 1,. :,. ,, .:,,,,, I I,,*,., I





f....-.- i...:.::::LY.!

-.-- j:::j.. .i:yy’i

]...:I:.+iiL..j .:iI -. --’ --I..:. t--y:.:: :.:...._. _.:::. : .!

B

. .-.... .- -..-.-.. ,I... _.-. .(-..1:.,. : .:. .T: I:!..A..-_

-4W, deg

0 25

q 350 45A 53d 60

:::I j.:.:. . .- ..-- :

I[ ::.i”‘ti--

: . . ..a .

--4--^---i.:i::‘-::,I,:I:T::..

/Figure 152. Incremental Angle of

236



AW, deg

0 25

0 350 45A 53A 60

J-q ._: 1 -.:.. _- . . . . . .

/Figure 153. Incremental Angle of Attack for Region 4'

237



-6

-8

T

.--.-II. _.,

-2- _-._..-i j I

--7-- ----.I!

Figure 154. Calculation Chart for Change in Cy Boundaries ofBasic Wings Due to Change in Reynolds Number

($?T Based on Leading-Edge Radius at Wing Tip)



:.1:1li -.-._-..- -,h-:.. .:.1:.:,11-r::

Figure 155. Correction Term for Effect of Fillet Sweep onBoundaries

239



_.. _..._ . ..(. . . . . I:“.“’( : ‘:

.:y.r~rll., ::: Unit Reynolds Number. ..:..:. :: '!:

: :- :~I....__...:_ ..._. ..: _:.._-.... .,: -..._._. ‘I:.riI:.rlLr_r:l______I.. . __-7_- ._.. L

.'W, degJ!!-iiii~~‘~-----. . .

_ .._ ..,..... . . . . . . . . ,-. f. ..:....,...-:..- :. ., . . . . . . . . : .,I -_ . , . .,‘. jr ;;:j

- . . .Ilj;Itrr:: iilitli:: ::1 :::: I --_!::r: ::.. irl: x;;:‘” :::::::: ::::rl::. i-;j 1 !._-

.__. _ + ..^._. . . .._..__.. I‘.:: -Y:::TI--z.!...:“.1”.’._...._. .-.‘I-:::.I: .lr -0 1. -:-;:::+yii:: :f:-l.i... .:..;...:’ yi:j: :jj’;‘:j -.::::i:.: l~,::i:-.:.iii:i:::.t. j I:,,-; :.:/::I :I::.

--!.::. ..:ri::.: .:::‘LL ::::I:. : :::::r::: ::::iI:: .:-::I:::: .:::!:::I 7:::::: i.:-:.r::i:i:_;-.I:i-.~-,

. :... .. . . _. ..T:L-Tf._I._..,. i5 }ij:/:;i{i: j5 $:ii.‘-.:li 45 yj 1: .; -;5 :j+;i:. ..:i:.

.- ., ,.. . ._. ._-_- :_.-.., .Q5 “‘::j:Y::‘.-j\ ; ,,:-‘I

..- .. .-... , ..-:;:..I: . . . ..I. ..::*:::I ~~,.~ .~:

I :::: ’ . ..-I.:.. -.-,:x. . .*.l. . ..jr-I.,:...:

. ._-,.. .-__ , "F. deg :.i:::.I:..::-. k I... 1. ::..: Il:ilI~.: :;r:.l::: ::::;::~: :I ::,:...,..:

:..::,‘.‘:.. j

:.:. :.:::. . ...::.:. :::21.. ...‘. ‘..---__ k..,.. ..-_. .:.::I...‘:-::.,::i:::.l: ::::::Yj rryf:::.1~.. : i ‘..Y 1

Figure 157. Slopes of Suction-Ratio Curves in Region 3

242



;r : .: !,:..:,.:.i::.::,:::~

-unit Reynolds Number = 8.0 x lO"/Ft

.

Il.:..:.:.i.~~:. 1 - -- vuI. .-- .1 . ..~ ..__... , .r.

(

d”R”\ -a

:.:.

;r

. .

t-g

\ dQfI

..‘I..: ..!:-I )_ :. ::..

1 . .I... 1.1j,.. j i .: i:: :j::::i:II._._. ._.. ...

‘,, . .! , , ::, _ j . . : :!.:. :. ..I... .::i:.:.i:.r L

Figure 158. Slopes of Suction-Ratio Curves-in Region 4

243



..... .., ........ r , .... .... (.-. _. (. ... ...

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

Figure 159. Slopes of Suction Ratio Curves in Region 5

244



-.L--t--. .: .+ : . -: -. -.---.. ----.

--_ . ..-... _ iyM .iF -... _ ..__--.i.. __.. .-.- _- . -.

470 A--,a/-& ‘. :

+rr--- - ..--- ---L-.. 0 80.- *-0’- ._.. .-.. . .-- _. ._.

q 75+--+.-. g.-,

P---0 .._ __.--.. . ..__

----1--- . . . -. . . . _.-.. -....--.-... ~ . - --j : :

- 20 _ ...~._._~... : - L ~. ; .-_, ..- ..-._ _ _- -...- .._-.-. --___..-

7 --i..- . ------A...-.

-_ -.,-.-I_

/ ! : ! ;_- -

-Si:r..; __, j ._ .I- j ~.:--.;_.,

-t-.i.--r--f _-....: -... - . . . . . . .-.-. ---. -.

&io . i---A-- -...,

Le... i.--.. i j j : : : :- ._. ..+y.-- _^_. l:---;. .-._---A.. + . -.L. .._... ..- _ .- ._ __.~ - . .

! I i I+y-

i-----.t --. i.I : ; : : :

L-- .-.- -..

m" +

/-I+

K-y 1-y 2--- .i-!-A2-.l-.L.l_1_!.L I ._... .---.I ___,_ e. i.. ..-i __. : :. - : --i

Figure 160. Aerodynamic Center Test-to-Theory Comparison

w 600 55

Unit Reynolds Number = 8.0 x 106/Ft

245



--+6C ---. -.:---

_- _

.__-

-40.-.. _ .-

a.c.-.%E

ref

--30!

-&O ! : _ ._- --.-.--2.

-.-;.---7.. -7.-. ~~-.... ILr_ ..i -.I.--..: . ._ i--.-l- :2525 j -- ’ __...._... ---.r -- -.. _....-! : :

,: : ; ;

.^ _ ..__ .--.--L ..-..- f 1 i 1 ! 1 --_. - -..I$

I--; ; WING WING WING WING WINGI

--.:.-.- j---q:._, I II III IV v -- _. .- -... . .;I I ! !.: ! i :

I -7

. ,’/ I : : I : ; , :

__. : __._. ;.--+.7..; _.__ .~.--.‘i--. . . -.:.-.; ._. -z-.--i...-...+. --..i... . .-. . --.: : : ! :

-l-10

--__ -;

i

Figure 161. Aerodynamic Center as Percent MCG

246



..-. :...: :

: _. :. .: : :i.. !

.-..j.::.:.. ;:.Y i f-I?: :.. i.: .;. ..;.. .; j-A--

---.-I :.’ ! 0’ ,; .- - Probably will Pitch-

/. .

:_:.

:.-.-: ~.- : :.i=:..L

?*F-'. i_ +. May Pitch Up or Down

-(deg)-,6O 1____ -/---- -.--.-__-.

.: :: :

- II : CIY Y

.--L, . ,.i-------.-.- Stable Break __. , .-

I e: ,-.i : .-: .I’,’ : ..::.: : ::

ti .-..

--L----: i 1 !

_’ ..i.: ,: iTi..‘-..1--..-.-- ..-- -

: : .I , .: : :.:’;!Aw ~(Deg);.-.~--~~-.------.---

. .; : ,. ; :: .i. :..;,‘.I -;-:.A- - :... : :

,----.-i-L ‘. j .I’ i... ..!.. : j ._.. :.: : .! :.j.,..-- .- --_- _A-.-’ __-. - -.:I I.i. r.I. ::. j i : .i .: j : ,!. 1 j :

I ,

! . :L-=-

: I? : ..i .I.-1-i: I’: j,_ ! (._ , : i : T-. l: i ..; j .,,;-:.k,-i:: ;,,,.:I .-:i ‘:! ; ’

: ,! .I: : I::.; __ i .._. . .I ... :.i.._ i,--.:: : ‘--

:. : : :: i :..: :. -, : i : -t

!‘.I i :::::.:

c- “1 ,i,I .-:,i ..‘I ; 1 .;

; : : f . . . . i’- :.-,ii,.ri,--j::,i--,:i: .i... I .i f ;-; .I i’ ; :. j .-y

.i i” i : ‘. i _i -.!..I: ..i f.. ;-..:.. ,.-.::..i.z-::-.i

I -i-- .--I ! , :. :.:. ..:... : I..: ;._. ..i .._. .i .I:.! ,_.. :..!...::: ” : ::.. : i

Figure 162. Pitch Up/Pitch Down Tendencies asFunctions of Wing and Fillet Sweep

247



0 0 Test DataFor Use'in Prediction Method

‘-.--- ------

: :

__ -- -..

:

Figure 165. Upper Angle of Attack Boundary for Region 5

250



--L25

.i j .i.++irrj : ,,. :i .,,. ..i. / i j

_’ I i j i i., j .:I.. ! . .I 1 .I. 1, : 1 i i : i

Fiiure 166.

/ ; i 7 j i ; -1 j i.: i : 1

Pitching-Moment Coefficient at Zero Angle ofAttack

251



Fixed Fillet Sweep--- Boundary for Basic Wings

I : L’!.‘I..:.‘..I. ..: ..:.

1..,. :! .: .I.

.AF

2535455560

6570758053

‘. “. :..I..i -41 : ,:..: .., i 1 : ; j ,

i __..~:’ .,:

:3%

.’ :- .!.-IL..:- ,..

‘. ::.. .;:.; I ..; :. j

Figure 167. Pitching-Moment Coefficient Derivative for

Region 0

252



Fixed Fillet Sweep--- Boundary for Basic Wings

.,I: 14

: __:. .j... :..,.... ..:. : / 0 6Om

i ! .-i :,.I!:::! . i AI

.I. :.!. :,:I’., ..,-.:, I’: , i , , ! ,; :A:-:..:A..‘: ..7..:’

( ,. , ,I- ;. ,I j’ 1 . ..i. /: +:./.: i

:::..i: I

j:: .::. I:.. ..:.I.’ ’_ _ , . .- :.

7

:. ..::.. :l.::I. I I.... _-. :::. ..I

lij=$.ii- .. i ,:I-. ,;.:-., :.,-..j i -. ..-i..i..Figure 168. Pitching-Moment C

Regions 1 and 2

Zoefficient Derivatives for

253



,_- _.

Fixed Fillet Sweep

--- Boundary for Basic Wings

I-. i :j ‘. [

Figure 169. Pitching-Moment Coefficient Derivative for

Region 3

254



Fixed Fillet Sweep


j~.i::j.l:lj::j::il:::ij

.,-! .,.: I:.I 1:. ., .i

r\

Fj :j;i:;l- ::.:i..: :. i .:

m--I2535

.

,::.: : :!-. ;.:;I

t

‘.--c.:Y’. ‘-I

. .y7

Figure 170. Pitching Moment Coefficient Derivative for

Region 4

255



Fixed Fillet Sweep


:::. !:.:, 0

V

0

D:q0

: : : ! : : ! , .!/, ; , :

_.,.. , . ., ( ! ..,. .:. .I- .:

Region 5

256



Fixed Fillet Sweep

--,:, :..:- ‘.:

EE

,I ::.. :.

-.OlOO_

_:,.. ./

:_.:. :

. . . .

:.:‘I :

~

-. -

.: :.: j..

‘-‘:.’ :

:.:

: . . : . : .

. ----.-.i

Figure 172. Pitching Moment Coefficient Der.ivative for

. Region 6

257



REVISIONS TO "BASIC" METHODS

The basic prediction methods presentedinthe previous sectionpartially achieved the objectives of the investigation. OngoingNASA configuration definition studies of an advanced aerospacevehicle indicated the need for data on configurations with otherairfoils than the NACA 0008 airfoil. The very limited data ob-tained with three configurations having NACA 0012 airfoils indi-cated that Reynolds number effects might be significant to muchlarger Reynolds numbers than had been obtained in test ARC 12-086.In addition, limitations on the angles of attack obtained in thefirst test had left some questions as to the pitching-moment be-

havior for some configurations. Thus,it was apparent even beforethe "basic" prediction method task was completed that additionaltesting would be required to provide data to resolve these is-

sues.

Additional Testing and Analysis

The Vehicle Analysis Branch of the NASA Langley Research Cen-ter planned the additional tests of a limited series of plan-

forms (described earlier in the Test Data Base section of thisreport) to define the effects of different airfoil sections andhigher Reynolds numbers,and eventually data were obtained athigher angles of attack. The tests were accomplished in the NASALangley Research Center Low Turbulence Pressure tunnel with thesmall models and the NASA Ames Research Center 12-foot tunnel withthe large (twice-size) models.

Analysis of the additional data was performed using the same

approaches that were used for the "basic" prediction method de-velopment. This required that the reference quantities of wing

area, moment reference length,and moment reference point be onthe same basis,whereas the test data for the additional tests hadbeen reduced originally using different quantities. The neces-

258



sary revisions to the data were made by altering a few equationsin the analys is procedures which had been programmed for solutionon a Hewlett Packard 9820 desktop- computer.

One of the first steps in the analysis was to make compari-

sons of data obtained in the different facilities to determineif significant differences occurred. An example comparison ofthe variations of pitching moment with angle of attack is pre-sented in Figure 173. It is apparent that the data for the65A012 airfoil configuration obtained in LTPT test 262 is signi-ficantly different from that for all of the other configurations.In contrast, data from test ARC 12-257 shows only small differencesbetween the pitching-moment curves for 0012 and 65AO12 airfoilconfigurations. It later became apparent that erroneous momenttransfer distances had been used in reducing data for four con-figurations in test LTPT 262,including the 70 and 75 degree fil-

let configuration with 65A012 and 651412 airfoils. It becamenecessary later to adjust the moment-transfer distances forthese configurations in order to complete the pitching-moment pre-dictions. The adjustments were made such that the slopes at lowangle of attack agreed with the data from ARC test 12-257.

An overall survey of Reynolds number effects indicated thatabove a unit Reynolds number of 26.25 million per meter the ef-fects are small in comparison to the effects noted between 13.13million per meter and 26.25 million per meter for the small mo-dels. The configurations with 12 percent thick airfoils showthe most sensitivity to Reynolds number. It is apparent that the

major effects occur as a result of relatively low leading-edgesweep of the outboard wing panel or of the fillet-outboard panelcombination.

A brief look at the suction-ratio data showed that, in gen-eral,the values in region 1 are higher than those measured inARC test 12-086. The reason for this fact is not iumediatelyobvious. It was therefore decided to concentrate first on thelift correlation to see if significant differences occurred bet-ween the tests in the different facilities and with the differ-ent size models and to look at the effects of airfoil thickness

ratio, thickness distribution,and camber.

259



Some example comarisons are presented in Figures 174through 179. Figures 174 and 175 illustrate the magnitudes ofthe differences in the,variation of the lift-correlationparameter with angle of attack for three of the 4 tests in whichthe same configurations were run. Also'shown are the predicted

values obtained from the overall correlation procedure. It isapparent that measurements made in the Low Turbulence PressureTunnel on the small models and in the ARC 12-ft tunnel on thelarge models produced higher lift coefficients at a given angleof attack than did the original measurements in the ARC 12-foottunnel on the small models. The differences are of the order of4 to 7 percent in the regions where the curves are reasonablysmooth. It is not at all obvious that any one set of data ismore correct than the others.

Figure 176 and 177 present the effects of airfoil-thickness

ratio variations as measured in the LTPT and AKC 12-ft facilitieson the small'and large models of,Wing III with the 80 degree fil-let. Although there are differences in details of the curves, thegeneral trends of the effects are similar. The same comment ap-plies to the data for the effects of airfoil-thickness ratiospresented in Figures 178 and 179 for Wing III with no fillet.

Figures 180, 181 and 182 show the effects of airfoil thick-ness distribution and camber for the three planforms havingWing III with 80, 75 and 70 degree fillets, respectively . Thetrends with fillet sweep are consistent. The camber effect de-creases with increasing fillet sweep. The large model data pro-duces similar trends.

Figures 183, 184 and 185 show the effect of Reynolds numberfor Wing III with 70 degree fillet and the three 12-percent thickairfoil sections. Note that the effects are primarily in thestall progression region and,therefore,would affect the stallprogression factor and the incremental lift charts.

One approach considered for modifying or revising the pre-diction methods was to obtain incremental lift curve parametervalues from the data obtained on the NACA 0008 airfoil configura-tions at unit Reynolds number of 26.25 million per meter (8.0million per foot). Figures 186-190 present the effect of fillet

260



sweep on the lift curve, parameter increments as functions ofangle of attack for the different airfoil sections as tested inthe LTPT facility. For each airfoil, a reasonably consistenttrend exists for the effects of fiTlet sweep...However, when th

effects of Reynolds number are included as in Figure 191 the picture becomes confused.

The approach of trying to use the NACA 0008 airfoil data a baseline for the airfoil effects and obtain increments kor thairfoil effects and other increments for the Reynolds number effects was not successful. There were too many conflictingtrends in the data to evolve simple correlations. As a conse-quence, it was decided to use a more direct approach.

The plots of Reynolds number effects on lift, suction ratio,and pitching moment were reviewed:.,one more time and it was notedthat the key results could be represented by defining the characteristics for three values of unit Reynolds number: (1) theminimum value tested (13.13 million per meter or 4.0 million pefoot), (2) a "standard" value corresponding to the maximum valuetested in the original planform series (26.25 million per meteror 8.0 million per foot), and (3) the maximum value tested in thadditional test series (Usually 45.93 million per meter or 14.0million per foot).

A prediction using the minimum Reynolds number data couldbe used to help define loads for wind-tunnel models to be tested

in facilities having only relatively low unit Reynolds numbercapabilities.

The use of the "standard" Reynolds number data would allowa tie-in between the airfoil effects and the planform effectsobtained from the "basic" prediction method. For practical purposes the maximum unit Reynolds number data might be consideredrepresentative of what could be expected for full-scale flight.

This approach was taken and a set of revised predictionmethods were developed. The revised methods use slightly dif-

ferent chart formats and equations for two reasons:

261



(1) The maximum angle of attack was extended from 26 de-grees to as high as 32 degrees.

(2) The limited series of planforms tested consisted

only of Basic'Wing III with various fillets. Thusthe effect of outer panel sweep could not be con-sidered in the revised methods.

Revised Lift prediction Method

The revised prediction method for the lift characteristicsuses the same correlation parameter as the basic prediction meth-od, but in a slightly different way. The revised lift prediction

equation is:

The terms in this equation are the sameas for the basic predictionmethod with the following exceptions:

(1) The terms in brackets are defined by sets of chartsappropriate to a specific airfoil section.

(2) The first term in brackets is obtained from a correla-tion chart which has the lift parameter

against the parameter @tanAF forangle of attack.

The values obtained from this term represent data ob-tained at the Standard unit Reynolds number of 26.25million per meter (8.0 million per foot).

(3) The second term in brackets represents the incrementaleffect of Reynolds number and is obtained from charts

262



which show the incremental value for

either KN . or KN

angles ofmi?tack. max

in carpet plot form for various

Table 4 presents a key to the Figures which containthe sets of charts for each airfoil.

TABLE 4 KEY TO REVISED LIFT PREDICTION CHARTS

AIRFOILSECTION

NACA 0004 Fig 192 N.A. N.A.NACA 0008 Fig 193 Fig 194 Fig 195NACA 0012 Fig 196 Fig 197 Fig 198NACA 00.15 Fig 199 Fig 200 Fig 201

NACA 65A012 Fig 202 Fig 203 Fig 204NACA 651412 Fig 205 Fig 206 Fig 207

THIN HEXAGON Fig 208N.A.

N.A.WITH SHARP L.E.

Figures 192, 193, 196,and 199 present the lift correlationcurves for the NACA 0004, 0008, 0012 and 0015 airfoils,respect-ively. The NACA 6541012, 651412,and thin hexagon airfoils wereonly tested for a few configurations, Figures 202 and 205 showcomparisons of the lift correlation curves of the 65A012 and65 412 airfoils tested with the corresponding curves for theNAEA 0012 airfoil, and Figure 208 shows comparison of the liftcorrelation curves of the 4 percent thick hexagon airfoils

with corresponding curves for the NACA 0004 airfoils. If forsome reason it were necessary to estimate the lift curve of aconfiguration having the 65A012 or 651412 airfoils with a filletsweep less than 70 degrees,, the appropriate correlation curvescould be extended to lower values of@tanAF using the NACA 0012curves as a guide.

With respect to the incremental values due to Reynoldsnumber,it was found that for the 4-percent thick airfoils

263



the effects of Reynolds number were not significant.

The prediction method consists of calculating CL values forseveral values of angle of attack using the appropriate set ofcharts for the desired configuration and airfoil section. Thecharts are set up to produce lift curves for any thickness ratiobetween .04 andt.15.

In order to provide a tie-in to the "basic" predictionmethod, data for the Wing III series of planforms with NACA0008 airfoils from test ARC 12-086 were plotted in the formatused for the revised prediction method. The resulting chartis presented in Figure 209.

Figure 209 can be of value in two ways. First,it can be

used to establish the uncertainties in lift predictions forthe family of irregular planforms having Wing III as the basicplanform, by comparing results obtained using Figure 209 andFigure 193. Second,it provides a means of applying the incre-mental effects of airfoil thickness ratio, airfoil shape,andReynolds number determined from the revised prediction methodto a broader range of planforms. It is likely-that reasonableestimates of the lift curves could be made for irregular plan-forms having basic planforms in the range from Wing II toWing IV, by applying the increments to results obtained fromthe "basic" prediction method.for the desired planform.

264



Revised Drag-Prediction Method

Revisions to the drag prediction methodol,ogy affected onlythe drag-due-to-lift part of the method. Revisions were re-quired for three reasons:

(1) The plateau values of suction ratio for the basicwings of different thickness ratios,as tested inthe LTPT facility,were significantly higher andformed a different correlation curve as a functionof the R parameter from the curve developed for thebasic prediction method. '

(2) The slopes of the suction-ratio curves in the var-ious regions varied significantly with Reynolds num-ber for the thicker airfoils for some of the plan-forms.

(3) The approach used to predict the effects of Reynoldsnumber on lift was not compatible with the methodused to account for Reynolds number effects on dragdue to lift in the original formulation used in thebasic prediction method.

The revised method still makes use of the suction-ratioconcept and the representation of the variation of suction ratiowith angle of attack by a series of linear segments as illu-strated in Figure 210. The angle-of-attack boundaries definingthe segments also apply to the pitching-moment prediction andin fact some iteration between values appropriate to the suc-tion-ratio curves and those appropriate for the pitching-momentcurves was required to produce compatible results.

265



As many as 7 linear segments were required to produce rea-sonable fits to the experimental 'suction ratio and/or pitch-ing moment data because the angle-of-attack range for the pre-

diction was extended. from 26 to 32 degrees. Some of the con-figurations did not require 7 segments. In those cases,ficti-tious boundaries were defined to allow a single generalizedequation to represent all the configurations.

The basic drag-due-to-lift equation is the same as usedfor the "basic" prediction method.

cDLCLtanCG "R&X)"

but for the revised method

[

C2CLtana! - L

-1A

"R(,)" = Rl

=R1 +

= Rl +

= Rl +

; osa<ar2(a-a2 > ; a21aw3

car-q

3

(a3-a2) + (a4-T>

(a-cu,)

4

; a4sa<a5

266



“R(tY) ” (cU,-a$ +

2

(a5 -a4) + (a-a5 1

5

@x4-a3

+ (a5-a41 +

(a-a )

a66

w4-a3 >

(a, -a41 + ca6-as >

267



6

(a-a7 >

7

The values of the aboundaries, the plateau value of the suc-tion ratio, Rl, and the values of the slopes of the suction ra-

d"R"tio curves in each region, d

c >

were determined for each con-

figuration for each of the three Reynolds number conditionsused in the revised lift prediction method. The Cy boundariesare tabulated in Tables 5 through 8,and the plateau values ofsuction ratio and the slopes of the various segments of thesuction ratio variations with angle of attack are tabulated inTables 9 through 12.

To use the prediction method,the calculations are made fora series of angles of attack using compatible values for thevarious terms, i.e., the planform, airfoil section,and Reynoldsnumber condition must be the same for both lift and the drag-dueto-lift conditions. If the user wishes to predict full-scale

flight characteristics, the lift and drag-due-to-lift terms for

RNconditions should be used. The minimum-drag term should

max

be calculated for the actual flight Reynolds number condition.

Revised Pitching-Moment Prediction Method

The only revisions to the pitching-moment prediction meth-

od are those required to extend the angle-of-attack range from26 to 32 degrees and to make the method consistent with the re-vised lift and drag-due-to-lift predictions.



The. equation for the variation of pitching moment withangle of attack is:

cm = cm +c.25; a=0 n?cw (a-0) ; Osa<al0

= C +cma=o “h;

(ar,-0) + cm

cy1fwal> ; a,salor,

='rn + 'rn

(al-O> + Cma

<a2T)

a=0 ao 1

+ ‘rnQi

(a -y i a2sas a3

='rn + 'rn

(al-o) + c ‘cy2-q)

a=0 ab “cyl

+%Y2a3-a2) + cm

73

(a-a;) ;a35 asQt

='rn + 'm (ap) + cm

(a2 -5)

a=0 aO ?l

+c

“OlO

Ca3-a2 + Cma3

<a4-a31

+c

“OL4

(a-a4 1 ; ~4-f-95

269



Cm. 25:

(al-o) + c

"h;

(a2 .-al)

+c%2

‘Q’3-a~> + cm (a4 -a313

+c

“014

(a5 -aA) + assa<a6

+c= cmcY,O mao

(al-o> + c“bi

(a2 -al >

+c

“cy2

(a, -a2) + C

%3

‘cy4-%)

+cma <cus-a4) +

ca6-a5 >

4

+cma

WcLi;16

='rn + 'rn

(al-o) + c 02 -5 >

a=0 cyo "cy1

+cma2

(cy3-q + cma3

(a4-a31

+c

ma4(a5-a4) + %

ca6-5)

5

; a6-< asa

l+ c

“O(6

(al-a61 + cm

ai

(cu-cw7) ;a7sas32

270



The angle-of-attack boundaries used for this equation are iden-tical to those used for the suction-ratio calculation whichwere presented in Tables 5 through 8.

The values of Cmiyi0

and the slopes of the various seg-

ments of pitching-moment variations with angle of attack arepresented in Tables 13 through 16 for the various combinationsofplanforms, airfoil section,and Reynolds number condition.Obviously, the pitching-moment prediction requires use of thesame planform, airfoil section,and Reynolds number conditionsas are used for the lift and drag-due-to-lift calculations.

The "revised" prediction methods are strictly applicableonly to the Wing III series of irregular planforms with fillet

sweeps between 45 degrees and 80 degrees, whereas the "basic"prediction methods are applicable to a wide range of irregularplanforms having NACA 0008 airfoils but only at the standardReynolds number condition.

It is considered feasible to apply judicious combinationsof the two sets-of prediction methods to obtain the lift,drag,-and pitching-moment variations with angle of attack for configu-rations which have planforms which are not of the Wing IIIseries but have airfoils other than the NACA 0008 airfoil sec-tion.

271



TABLE 5

Angle-of-Attack Boundaries for Drag Due to Lift andPitching-Moment Segments - NACA OOXX Airfoils, F$

min

CONFIGURATION

AF %I45 45

60 45

65 45

70 45

75 45

80 45

AIRFOIL

00040008

00120015

0004

2.4 2.4 7.2 13.4 22.7 26.6 30.54.4 4.4 7.5 15.4 20.6 27.8 31.2

6.0 6.0 10.8 10.9 17.5 22.0 26.07.0 7.0 12.0 17.7 19.8 25.8 30.0

3.0 3.0 6.35 15.6 19.3 23.5 30.6

0004 3.0 3.00008 5.6 5.60012 7.4 7.40015 6.0 6.0

0004 3.6 3.60008 6.6 6.60012 7.0 7.00015 5.6 5.6

0004000800120015

0004000800120015

3.0 3.04.5 4.56.0 6.04.4 4.4

2.6 2.64.8 4.86.4 4.87.0 7.0

7.010.213.512.2

6.810.013.514.0

7.17.18.68.0

7.957.5

11.112.0

a7

15.6 19.3 23.5 30.614.2 17.0 22.4 27.015.6 18.0 22.6 29.013.3 20.0 24.0 28.0

11.5 is.8 la.8 28.314.2 20.2 24.6 28.518.0 22.5 26.6 30.517.2 20.6 27.2 30.0

12.111.313.213.8

la.417.117.517.9

17.318.1la.720.0

25.6 29.020.8 26.421.1 25.020.8 30.0

14.512.515.715.7

25.5 29.323.9 29.325.6 30.023.0 28.0

272



TABLE 6

Angle-of-Attack Boundaries for Drag Due to Lift andPitching-Moment Segments - NACA 00xX Airfoils, Qstd

CONFIGURATION

'F 'W AIRFOIL

45 45

60 45

65 45

70 45

75 45

a0 45

0004 2.4 2.4 a.4 13.8 22.7 26.6 30.50008 4.4 4.4 9.6 16.9 23.0 27.8 31.20012 6.0 6.0 10.8 14.4 21.0 25.6 31.10015 7.0 7.0 12.0 19.1 21.0 24.2 28.0

0004 3.0 3.0 6.6 11.7 14.8 19.2 31.2

0004 3.0 3.0 7.0 15.6 19.3 23.5 30.60008 5.6 5.6 11.2 16.0 19.6 24.4 28.00012 7.4 7.4 11.7 16.0 20.0 25.2 32.00015 6.0 6.0 12.2 16.0 19.8 24.0 26.4

0004 3.6 3.6 7.2 12.7 15.8 18.8 28.30008 6.6 6.6 11.0 17.0 21.8 24.6 29.60012 7.0 7.0 13.9 17.5 21.5 25.6 30.00015 5.6 5.6 14.0 18.0 21.0 25.6 30.4

0004 3.0 3.0 9.4 12.1 la.4 25.6 29.00008 4.5 4.5 a.1 13.8 19.8 23.7 28.0

0012 6.0 6.0 a.1 14.1 17.8 22.0 28.00015 4.4 4.4 8.0 13.8 17.9 20.8 30.4

0004 2.6 2.6 8.8 14.5 17.3 25.5 29.30008 4.8 4.8 9.5 12.6 17.4 23.9 28.80012 6.4 6.4 10.8 12.2 17.3 24.0 31.20015 7.0 7.0 lo.8 12.0 20.0 27.2 33.0

273



TABLE 7

Angle-of-Attack Boundaries for Drag Due to Lift andPitching-Moment Segments - NACA OOXX Airfoils, Nax

CONFIGURATION

AF Aw

45 45

60 45

65 45

70 45

75 45

80 45

AIRFOIL

000400080012

00150004

0004000800120015

000400080012

0015

0004000800120015

2.4 2.4 9.2 13.8 22.7 26.6 30.54.4 4.4 12.2 16.0 la.4 23.0 27.86.0 6.0 12.6 20.6 22.2 23.5 27.5

7.0 7.0 12.0 18.2 22.2 23.5 29.53.0 3.0 7.6 11.7 14.8 19.2 31.2

3.0 3.0 7.0 15.6 19.3 23.5 30.65.6 5.6 11.15 16.0 19.6 24.4 28.07.4 7.4 13.0 17.9 20.8 28.6 32.06.0 6.0 12.2 14.2 18.0 20.3 25.2

3.66.67.0

63::7.0

5.6 5.6 14.8 17.6 19.3 27.0 31.0

3.0 3.04.5 4.56.0 6.04.4 4.4

0004 2.6 2.60008 4.8 4.80012 6.4 6.40015 7.0 7.0

7.65 12.7 15.8 18.8 28.311.65 16.7 21.0 23.6 27.0

14.7 17.7 21.8 25.3 30.0

9.88.0a.1

12.0

9.1

X:i10.8

12.1 la.4 25.6 29.012.45 19.8 24.0 29.0

16.6 20.5 24.5 28.616.9 20.1 25.6 29.6

14.5 17.3 25.5 29.313.1 16.9 22.5 29.116.0 la.9 25.0 28.012.0 20.0 24.4 29.0

274



TABLE 8

Angle-of-Attack Boundaries for Drag Due to Lift anr'Pitching-Moment Segments, NACA 65A012 end 651412

CONFIGURATION

'F A W A IRFOIL

70 45 65A01275 45 65A01280 45 65A012

70 45 65A012

75 45 65801280 45 65A012

70 45 65AO1275 45 65A01280 45 65A012

70 45 65141275 45 65141280 45 651412

70 45 65141275 45 65141280 45 651412

70 45 65141275 45 65141280 45 651412

45 45 OOSLE75 45 OOSLE80 45 OOSLE

RNa2 a3 a4 a6 a7

Min. 7.4 7.4 9.6 15.7 20.3 24.8 27.5Min. 5.4 5.4 9.1 11.1 16.9 22.0 26.1Min. 7.1 7.1 12.2 15.4 20.2 26.0 31.4

Std. 7.4 7.4 10.2 14.8 20.4 24.6 30.8

Std. 4.6 4.6 9.6 17.0 20.8 24.6 27.8Std. 5.8 5.8 10.8 15.1 20.0 27.2 31.0

Max.Max.Max.

7.4 7.4 10.2 15.8 20.1 25.0 28.64.8 4.8 10.0 16.2 la.4 21.6 28.26.0 6.0 12.0 15.8 21.2 27.7 32.0

Min.Min.Min.

7.4 7.4 10.7 13.8 17.7 22.8 27.26.9 6.9 14.4 la.2 20.7 27.3 32.05.6 5.6 13.0 la.9 23.5 28.0 30.5

Std. 7.6 7.6 10.3 14.1 19.1 25.6 32.4Std. 6.9 6.9 15.3 17.8 22.4 28.4 31.0Std. 5.5 5.5 10.8 15.4 20.6 25.7 30.1

Max. 7.4 7.4 11.0 15.4 19.2 22.6 28.6Max. 6.9 6.9 13.6 16.2 19.2 24.0 29.0Max. 5.6 5.6 13.0 16.0 22.8 28.0 32.0

Std.Std.Std.

2.4 2.4 7.2 15.8 20.0 22.9 26.92.0 2.0 7.0 13.0 la.2 23.4 31.62.0 2.0 7.9 11.6 17.2 23.8 28.0

275



TABLE 9

Plateau Values of Suction Ratio and Slopes ofSuction-Ratio Segments - NACA OOXX Airfoils, RN,i,

dR dRz6 dCY7R1

dR dRFa, da5

ONFIGURATION

'F 'W

45 45

60 45

65 45

70 45

75 45

a0 45

AIRFOIL

000400080012

0015

0004

0004000800120015

0004000800120015

0004000800120015

0004000800120015

-.0727 y.0355 -.0197 -.0102 -.0070 -.0031-.0032 -.0705 -.0443 -.0075 -.0028 -.0028-.0040 -.0040 -.0874 -.0488 0 0

-.0037 -.0037 -.1960 -.0260 -.0238 -.0238

Min. a85:967.9ao

,985

Min. .a38 -.0893 -.0414 -.0290 -.olsa -.ooaa -.0036

Min. ,835

I

860: 905.940

-.1175 -.0229 -.0103 -.0126 -.0077 -.0048-.0048 -.0844 -.0417 -.0215 -.0215 -.0060-.OOlO -.1484 -.0812 -. 0292 -.0012 -.0222-.0039 -. 0039 -.0470 -.0817 -.ooia -.oola

Hin. .a40

I

.950

.955

.,990

-.1254 -.0315 -.0142 -.0142-.0498 -. 0846 -.0102 -.0245-.0067 -.0865 -.04ia -.OlOl-.ooaz -.0082 -.0930 -.0300

-.0092 -.0048-.0168 -.0087-.0122 -.0114-.0140 -.0140

Min. .a10

I

.910

.955

. 965

-.0943 -.0310 -.0137 -.0068 -.0030 -.0047-.0087 -.0931 -.0338 -.0055 -.0166 -.0056-.0022 -.0186 -.0638 -.0475 -.0092 -.0182-.0120 -.G142 -.0342 -.0906 -.0125 -.0048

M'n.

I

a82:915.912.915

-.1070 -.0161 -.0096 -.0063 -.0038 -.0078-.0337 -.0707 -.0392 -.0055 -.0079 -.0130-.0327 -.0327 -. 0593 -.0016 -.0016 -.0016-.0220 ,-.0127 ;.037a -.0683 -.ooao -.ooao

276



TABLE 10

Plateau Values of Suction Ratio and Slopes ofSuction-Ratio Segments - NACA OOXX Airfoils, RN

std

CONFIGURATION

‘F *W

45 45

60 45

65 45

70 45

75 45

80 45

AIRFOIL

R1dR dRzi2 35,

000400080012

0015

Std

1

.940 -.0727 -.0355 -.0197 -.0102

.980 -.0032 -.0705 -.0443 -.0075

.990 -.0040 -.0040 -.0721 -.0512

.965 -.0037 -.0037 -.1560 -.1032

0004 Std .882 -.0893 -.0414

0004000800120015

Std

I

-. 0229-.0844-.OOlO-.0039

0004000800120015

Std

I

: 90040 -.0048.1175

.925 - .OOlO

.940 -. 0039

.905 -.1254

.975 -.0198

:98060 -.0067.0082

-.0315 -.0142 -.0142 -.0092 -.0048-.0924 0 -.0204 -.0167 -.0167-.0833 -.0429 -.0244 -.0163 -.0118-.0118 -. 0609 -.0431 -.0150 -.0218

0004000800120015

Std

I

.930 -.0943 -.0310 -.0137 -.0008 -.0030 -.0047

.945 -.0087 -.0708 -.0465 -.0091 -.0112 -.0180

.955 -.0022 -.0172 -.0771 -.0473 -.0093 -.0184

.965 -.0120 -.0142 -.0342 -.0906 -.0125 -.0048

0004000800120015

Std

I

.960 -.1070940

:912-.0337-.0262

.915 -.0220

-.0161 -.0096 -.0063-.0408 -.0755 -.0057-.0262 -.0304 -.0427-.0220 -.0127 -.0345

sdR dR dR dR-5 3

4aTi

5 6ZE

7

-.0290

-.0103-.0417-. 0932-.0145

-.0158

-.0126 -.007+ -.0048-.0153 -.0153 -.0060-.0451 -.0163 -.0310-.0817 -.0436 -.0146

-.0070 -.0031-.0028 -.0028-.0055 -.0061

-.0229 -.OOlO

-.0088 -.0036

-.0038 -.0078-.0067 -.0067-.0027 -.0027-.0138 -.0072

277



TABLE 11

Plateau Values of Suction Ratio and Slopes ofSuction-Ratio Segments - NACA 00X.X Airfoils, RN

Illax

CONFIGURATION

'F 'W

45 45

60 45

65 45

70 45

75 45

80 45

AIRFOIL% R1

dR dR dR dRzi, zi3 xi4 zi%,

000400080012

0015

Max. .970 -.0727 -.0355 -.0197

I :98298580 -.0032.0040.0037 -.1048.0040.0037 -.2470.0623.1385

-.0102-.0443-.2470

-.1385

0004 Max. .925 -.0893 -.0414 -.0290 -.0158

0004000800120015

Max. .962 -.1175 -. 0229 -.0103

J .925956 -.OOlO.0048 -.0055.0844 -.0417.1144.940 -.0039 0.0039 -.OllO

-.0126 -.0077 -.0048-.0153 -.0153 -.0150-.0225 -.0150 -.0150-.2000 -.OlOl -.0141

0004000800120015

Max. .945 -.1254 -.0315 -.0142

I : 9826590 -.0048.0080.0070 -.1073.0829.0160 -.0167.0587.1060

-.0142 -.0092 -.0048.0197 -.0242 -.0108

-.0233 -.0150 -.0218-.0366 -.0148 -.0148

0004000800120015

Max. .972 -. 0943 -.0310 -.0137

I .97055980 -.0087.0070.0120 -.0422.0165.0120 -.0685.0895.0178

-.0068 -.0030 -.0047-.0020 -.0167 -.0167-.0255 -.0087 -.0087-.0925 -.0214 -.0022

0004000800120015

Max. 1.000 -.1070 -.0161 -.0096.940 -.0322 -.0322 -.0965.912 -.0262 -.0175 -. 0990.914 -.0220 -. 0220 -.0127

-.0063 -.0038 -.0078-.0062 -.0076 -.0076-.0320 -.0076 -.0076-.0687 -.OlOO -.0020

dR dRzi6 zE7

-.0070 -.0031-.0075 -.0028-.0160 0

-.0090 -.OOlO

-.0088 -.0036

278



TABLE 12

Plateau Values of Suction Ratio and Slopes ofSuction-Ratio Segments - NACA 658012 and 65,412

%I R1dR dR dR dR dR dRZZ, Z3 TE, Zi5 Xi6 G7

ONFIGURATION

AF A W AIRFOIL

70 45 65AO1275 45 65A01280 45 65A012

70 45 65A01275 45 65A01280 45 65A012

70 45 65A01275 45 65A01280 45 65A012

70 45 65141275 45 65141280 45 651412

70 45 65141275 4580 45

651412651412

70 45 65141275 4580 45

651412651412


Min. 880

I:s50.841

0 -.0575 -.0765 -.0325-.0135 -.0967 -.0495 -.0022-.0775 -.0392 -.0123 -.0004

-.OlOO -.0205+.0004 0.0160-.0050 -.0138

-.0167 -.0058-.00X! -.0180-.00054 -.bO54

-.0240 -.0240-.OOlO -.0170--0062 -.0062

-.0255 -.0124-.0184 -.0184-.0032 -.0120

-.0098 -.0168-.0153 -.0153-.0098 -.0054

-.0220 -.0220-.0178 -.0202-.0036 -.0036

-.0060 -.0031-.0031 -.0048-.0027 -.0027

Std. .905

I900

:860

0 -.0352 -.0577 -.0167-.0033 -.0452 -.0613 -.00,12-.0254 -. 0492 -. 0492 -.0024

.920 0890

:880-.0042-.0222

-.0202 -.0545 -.0290-.0243 -.0635 -.0575-.0222 -.0677 -.Ob22

Min. .930.900.925

-.0047 -.0322 -.lllO -.0020-.0080 -.0965 -.0376 -.0070-.0156 -.0745 -.0123 -.0080

-.0047 -.0027 -.0372 -.0527-.0074 -.0618 -.0537 -.0218-.0174 -.0174 -.0508 -.0270

Std. .930

I910

: 895

M x.

t

.910890

: 895

0 -.0050 -.0282 -.0828-.0085 -.0203 -.0328 -.0638-.0174 -.0174 -.0572 -.0081

.968 -.1003 -.0301 -.0267 -.0123

.870 -.1170 -.0208 -.0050 -.0084-890 -.0988 -.0330 -.0092 -.0048

279



TABLE 13 PITCHING-MOMENT INTERCEPTS AYI SLOPES OF PITCHING MONENT-SEGMENTS

NACA OOXX AIRFOILS, RNMIN

CONFIGURATION Cma=0

AF Au AIRFOIL

45 45 00040008

0012

0015

-.ooa-.005

-.003+.001

-.0019 -.0030 -.0013 -.0042 -.OOlO -.0037 -.OOlO-.0021 -.0036 -.0043 -.0044 +.0012 -.0005 -.0020-.0014 -.0030 -.c)o30 -.0047 -.002a +.0002 +.0006-.0013 -.0025 -.0040 -.0056 +.0003 -.0023 -.0016

60 45 0004 -.007 -.0034 -.0050 -.0026 -.0035 -.OOlO -.0017 -.0024

65 45 0004 -.0065 -.004a -.oosa -.003a +. 0001 +.0001 -.0021 -.00210008 -.005 -.0043 -.0062 -.0057 -.0045 -.0013 +.0012 -.00120912 -.002 -.0039 -.0059 -.0082 -.0054 +.0020 -.0002 -.oooa

0015 +.001 -.0030 -.0052 -.0052 -.0072 +.0016 -.OOOl -.OOOl

70 45 0004 -.003 -.0056 -.0073 -.0056 -.0056 +.0037 -. 0029 +.00400008 -.002 -.005a -.ooa2 -.0067 -.0065 +.0039 -.0009 +.00100012 -.002 -.0050 -.0068 -.007a -.0019 +.0017 -.OOlO +.00100015 +.00 2 -.0047 -.0062 -.ooaa -.ooaa +.0010 +.0010 +. 0010

75 45 00040008

00120015

-.006 -.0070 -.ooa4 -.0076 -.oila +.0062 +.0007 +.0007+.002 -.0073 -.0092 -.0092 -.007a -.0132 +.0062 -. 0010

+.005 -.0065 -.ooa4 -.0084 -.0106 -.0043 -.oloa +.0076

+. 005 -.0062 -.0069 -.ooa2 -.0106 -.0029 -.0065 +. 0090

80 45 00040008

0012

0015

+.001

-.002

+.001+.004

-.ooa7

-.ooaa

-.0083

-.0077

-.009a-.0103

-.oloa-.0103

-.oioa

-.0103

-.oloa-.0103

-.0109 -.0126 +.0106 +.0106

-.OlOO -.0136 -.0092 +.022a

-.007a -.0132 -.0096 +.0137

-.0105 -.0068 -.0114 -.OOSl

280



TABLE i4 PITCHING-MOMENT INTERCEPTS AND SLOPES OF PITCHING-MOMENT SEGMENTSNACA OOXX AIRFOILS, RNSTD

_. _-- --~.-CONFIGURATION C*F*W AIRFOIL LO

cm

%1__-

45 45 0004000800120015

-.ooa-.005-.003-.OOl

-.0019 -.0030-.0021 -.0036-.0014 -.0033-.0013 -.0031

-.0034 -.0050

-.004a -.005a-.0043 -.0062-.0039 -.0059-.0033 -.0052

-.0056 -.0073-.005a -.ooa2-.0050 -.0068-.0047 -.0064

-.0070 -.ooa4-.0073 -.0077-.0065 -.ooa4

-.0062 -.0069

-.ooa7 -.009a-.ooaa -.0103-.ooa3 -.0103-.0077 -.0103

-.0013 -.0042 -.OOlO-.0043 -.0044 +.oooa-.0033 -.0054 -.oooa-.0043 -.0058 +.oola

-.0037+. 0019+.0007+.0002

-.OOlO-.0002+.0004

0

60 45 0004 -.007 -.0034 -.0017 -.0034 -.0014 -.0029

-.0043 +.0005-.0077 +.0010-.0059 -.0078-.0064 -.0064

-.0004-.0009+.0028+.0049

-.0033+.0005

00

65 45 0004 -.00650008 -.0050012 -.0020015 +.001

-.003-.002-.002+.002

-.0056 -.0090 +.005a -.0027 +.ooos-.0070 -.0054 -.0077 0 0-.ooaa -.0022 -.0043 +.ooao 0

-.ooa7 -.ooa7 -.0019 -.0015 +.ooaa

70 45 0004000800120015

75 45 0004 -.0060008 .0020012 .005

0015 .005

-.0077 -.0114 +.0062 +.0007 +.0007-.0095 -.0063 -.oi2a +.0120 +.0012-.ooa4 -.0106 -.OOlO -.0106 +.0126

-.ooa2 -.0106 -.0029 -.0065 +.0063

a0 45 0004000800120015

.OOl

-.002.OOl,004

-.oloa -.oloa -.0126 +.0106 +.0106

-.0103 -.OlOO -.0141 -.0117 -.03oa-.0103 -.0117 -.ooa2 -.0123 +.oia5-.0103 -.OllO -.0075 -.0102 -.0132

281



TABLE 15 PITCHING-MOMENT INTERCEPTS AND SLOPES FOR PITCHING-MOMENT SEGMENTSNACA 00xX AIRFOILS, RN

CONFIGURATION C C C

AF h&=o

‘ma

W AIRFOILmao

I 4‘ma7

45 45 0004 -.ooa -.0019 -.0030 -.0013 -.0042 -.OOlO -.0037 -.OOlO0008 -.005 -.0021 -.0036 -.0049 -.0049 -.003a +.0006 +.00150012 -.003 -.0014 -.0030 -.0053 -.0045 +.0019 +.oooa +.00020015 -.OOl -.0013 -.0031 -.0043 -.0053 +.0065 +. 0010 -.oooa

60 45 0004 -.007 -.0034 -.0050 -.0034 -.0017 -.0034 -.0014 -.0029

65 45 0004 -.0065 -.004a -.005a -.0043 +.0005 -.0034 -.0002 -.00330008 -.005 -.0043 -.0062 -.0041 -.0023 -.0002 -.0017 00012 -.002 -.0039 -.0059 -.0067 -.0064 -.0059 +.oooa +.ooia0015 +.001 -.0036 -. 0049 -.0049 -.0060 -.0036 -.OOll +.ooia

70 45 0004 -.003 -.0056 -.0073 -.0057 -.0104 +.0073 -.0027 +.0005or)08 -.002 -.oosa -.0053 -.0053 -.0051 +.0030 +.0030 -.00050012 -.002 -.0050 -.0068 -.0099 -.0032 -.0048 +.0045 00015 +.002 -.0047 -.0064 -.0092 -.0155 -.0022 +.0050 +.oola

75 45 0004 -.006 -.0070 -.ooa4 -.0077 -.0114 +.0062 -.0070 -.0070

0008 +.002 -.0073 -.0077 -.0086 -.007a -.0133 +.0113 +.0005

0012 +.005 -.0065 -.ooa4 -.0093 -.0054 -.0054 -.OlOO +.00770015 +.005 -.0062 -.0073 -.0097 -.0054 -.0065 -.0065 +.0072

a0 45 0004 +.001 -.0087 -.009a -.oioa -.oloa -.0126 +.0106 +.0106

0008 -.002 -.ooaa -.0103 -.0103 -.OlOO -.0136 -.0120 +.0220

0012 +.001 -.ooa3 -.0105 -.0102 -.0106 -.0132 -.009a -.00400015 +.004 -.0077 -.0103 -.0103 -.0113 -.0045 -.oioa -.0078

282



TABLE 16 PITCHING-MOM?XT INTERCEPTS AND SLOPES OF PITCH-ING-MOMENT SEGMENTS NACA 65A012 AND 6S1412

CONFIGURATION

‘F A W AIRFOIL 6 7

+.005 -.0049 -.0063 -.004a +.0025 +.0062 +.0005 +.0023+. 003 -.005a -.0070 -.ooa7 -.0059 -.0072 -.0037 +.0115+.004 -. 0079 -.OlOO -.ooao -.oioa -.0115 -.0042 +.0153

70 45 65AO1275 45 65AO1280 45 65A012

MIN.

I

70 45 65AO12

75 45 65AO12a0 45 65AO12

S D.

I

+.005 -.004a -.0063 -.0072 -.0056 -.oola +.0065 0

+.006 -.0058 -.0076 -.ooao -.0025 -.0076 -.0025 +.0123+.004 -.0079 -.OlOO -.OlOO -.0077 -.012a -.0055 +.0156

70 4575 45a0 45

65601265601265A012

MAXI

+.005 -.004a -.0063 -.0060 -.0093 -.0039 +.0069 +. 0069

+.006 -.005a -.0072 -.0070 -.ooaa 0 -.0074 +.0175+.004 -.0078 -.OlOO -.OlOO -.0067 -.0134 -.0067 +.0150

70 45

75 45

a0 45

651412

651412

651412

70 45 651412

75 45 6S1412

a0 45 651412

70 45

75 45

a0 45


MIN.

I

-.054 -.0057 -.0074 -.0075 -.0036 -.0036 +.0042 +.0042

-.050 -.0068 -SO072 -.0063 -.0051 -.0034 .0145 +.ooai

-.045 -.0087 -. 0096 -.0102 -.OlOO -.OllO -.0066 +.0123

STD.

I

-.053 -.0053 -SO072 -.0072 -.ooa35 -.OOll -.0057 0

-.04a -.0066 -.0076 -. 0092 -.0064 0 +.0156 +.0077

-.045 -.0057 -. 0096 -.0096 -.OllO -.0082 -.0115 +.0057

-.053 -.0053 -.0072 -.0074 -.0056 -.0056 +.004a +.0048

-.04a -.0066 -.0076 -.0066 -.0092 -.005a -.0004 +.0162

-.045 -.ooa7 -.0096 -. 0096 -.0106 -.ooas -.0079 +. 0095

STD.

I

+.003 -.OOlO -.0025 -.0012 -.004a +.0003 +.0016 -.0032+.004 -.0068 -.0080 -.0088 +.0113 +.ooa2 +.0005 -.002a-.004 -.0080 -.0105 -.0097 -.0109 -.0136 -.oooa +.0124

283



Unit Reynolds Number

Model Size ConfigurationSmall 70 45.0012Small 70 45.5012Small 70 45.0008Small 70 45.0008Large 70 45.0008

V ARC 12-257 Large 70 45.0012 :L+,'.,,ALLI.

,.,, /‘i j, : :

:!:,iI .:: Figure 173. Comparison of Pitching Moment Data Prom Ditterent,,,, :.:.:I, .,.. : Testsit'; 2+ :.:: :,:. :::. ::.; :::: .::. :. :... -::: :,. :,:,I::~;;;:.:;,.',:!'.::,,, I.......,. i:,:.,:,::j.::.!Ij:. ,,,. ,.,, :j jjj,.:.::,:.,,I ,..,:: !i:, ,.,:.:,: :;-/:.,f,. .:. ,,:: ,.:.: ;. , ,,, ;,:.... ::I :I;: :y., .: ,jj:,, '.



.6

Test Model Configuration_. _80

-- _-'- ARC 12-086 Small 45 .0008

i ------ LTPT 255 Small- ARC 12-257 Large 1

- - Prediction

Figure 174. Comparison of Lift Co rrelation Parameter for Ir-regular Planform





.6

.5

4

.3

.2

.l

Test Configuration- - LTPT 255 80 45.00 - SLE

80 45.0008------ 80 45.0012-- 80 45.0015

Figure 176. Effect of Airfoil-Thickness Ratio for Irregular

Planform From LTPT Facility



.6

.5

.4

.3

.2

.l

Test Configuration

- ARC 12-257 80 45.0008--es--

180 45.0012

-- 80 45.0015

RN = 16.40x106/m (5x106/Ft)

I

/I I * 8 4

-4

I

4 8 12 16 20 24 28

CT deg

Figure 177. Effect of Airfoil-Thickness Ratio for IrregularPlanform From ARC 12-Ft Facility



.6 -I

.5go+.4

.3

.2

.l

TestConfiguration

- LTPT 255.-v

----mm

1--

45 45.000845 45.00 - su45 45.001245 45.0015

4 8 12 16c- 24 28 32

a!de&i

Figure 178. Effect of Airfoil-Thickness Ratio for Basic Plan-form From LTPT Facility



.6

Test Configuration

- ARC 12-257 --__ - ------ L .\ --a-

24 28a deg

Figure 179. Effect of Airfoil-Thickness Ratio for Basic Planform

From ARC 12-Ft Facility



.6

1

.5I Test Configuration

- LTPT 255 80 45.0012-- - LTPT 262 80 45.5012- - LTPT 262 80 45.5412

Figure 180. Effects of Airfoil Thickness Distribution and Camber

for 80-45 Irregular Planform



.6

.5

.4

.3

.2

.1

/.

*

L 0,

/

/ 0,I 0

//

*/ /’

/ /

//

/ ’ 0’

.

16.

20 24I a

28 3;a deg

Figure 181. Effects of Airfoil Thickness Distribution and Camber

for 75-45 Irregular Planform

Test Configuration- LTPT 255 75 45.0012-.--- LTPT 262 75 45.5012--.-- LTPT 262 75 45.541-

/



.6

/ - 4

.3

.2

.l

II

----

Test ConfigurationLTPT 255 70 45.0012LTPT 262 70 45.5012LTPT 262 70 45.5412

1 I

4 8 12.

16I

20I

24b D

28 32.

a.deg

182. Effects of Airfoil Thickness Distribution and Camberfor 70-45 Irregular Planform



.6 Test LTPT 255

.5

&*$

.4

.3

0unit RN W16/W

6 13.139.676.25

% 45.932.819.37

4 8 12 16 20 24 28 a 32deg

Figure 183. Effect of Reynolds Number for NACA CO12 Airfoil



.6

.5

CL Al5' q-ii

.4

.3

.2

.l

- 0.0

Unit RN (106/W

0 13.130 19.672 26.25

it 32.819.3745.93

Configuration

70 45.5012

CPg,

#4 8 12 16 20 24 28 32

Q! deg

-4 .'

4‘

IQ Figure 184. Effect of Reynolds Number for NACA 65A012 Airfoil

Test LTPT 262



.5

$a+

.4

.3

.2

.l

H

d0.C-P

Test LTPT 262

Unit RN (106/M)

$.3.13

19.67

2 26.252.81

39.37

45.93

Configurationd*O~O 0

70 45.5412

!

4g

Jp

$a

4 8 12 16

--. .-- _.- -. II----20 24 28 32

a deg

Figure 185. Effect of Reynolds Number for NACA 651412 Airfoil



XX45.OOSLE

.2

I

Note: Reference Configurations haveNACA0008 Air oils

d

Iat

RN - 26.25~10 /mI

-.I J I

1

eg

Figure 186. Effect of Fillet Sweep on Lift-Parameter Incrementfor Thin Airfoil With Sharp Leading Edge



xX45.0012

RN = 26.25X106/m (8x106/Ft)

.21

Note: Referenc e Configurations haveNACA 0008 Airfoils

Figure 187. Effect of Fillet Sweep on Lift-Parameter Incrementfor NACA 0012 Airfoil



Xx45.0015 RN = 26.25X106/m

Note: Reference Configurations haveNACA0008 Airfoils

.2 T

-. 1T

Figure 188. Effect of Fillet Sweep on Lift-Parameter Incrementfor NACA 0015 Airfoil



xX45.5012

RN =: 26.25X10%

Note: Reference Configurations haveNACA 0008 Airfoils

16

Figure 189. Effect of Fillet Sweep on Lift-Parameter Increment

for NACA 65A012 Airfoil



.2

A k--G(.)

..l

-I

xX45.5412

RN = 26.25X1061m (8.0X106/Ft)

Note : Reference Configurations haveNACA0008 Airfoils

Figure 190. Effect of Fillet Sweep on Lift-Parameter Incrementfor Cambered Airfoil



- 70 45 .5412- - 75 45 .5412

.- - 80 45 .5412

Note: Reference Configurations haveNACA 0008 Airfoils at ReferenceUnit Reynolds Number = 26.25X106 /m

RNx~O-~/FT1

-. 1' I0 4

b ;2 ;6 2: 2: ;e 132

a deg

Figure 191. Effects of Reynolds Number Confuse the Situation



45O 60' 65' 70' 75O ROO



Reynolds Number



- .-._ --J.--.--LI

I i j j.j 1

I

! I : : i:! ; ! j:i

! -. -...I. ---I-.L _-. L---i

!I-?. I i : I i : i-1 j / : (1

: ! : ! : I i.i i ! ! I

Figure 194. Incremental Values of LiftCorrelation Parameter for NACA0008 Airfoils at Minim-m ReynoldsNumber

0 for 30°

0 for 28'

0 for 26O

0 for 24O

0 for 22'

0 for 20°

0 for 18O

0 for 16'

0 for 14'

0 for 12'

305



----. -0i

L-

I

.._

,_-- -. _....

1 ! :

:

0 for 30'

0 for 28O

0 for 26'

0 for 24'

-..~-___- .._.

_--

for

Figure 195. Incremental Values of Lift CorrelationParameter for NACA 0008 Airfoils atMaximurn Reynolds Number

306





I I. I I --,,.m I . I. .---. - - . . - .__... - -_~--

/... _. .-.__-

----.

;.

i

1..

i. _. :

! .._

r---------.j__...f_-

: I

--L i !

-----f-f L-..--

j : : ;

/ t*

/

_ ..-..i.---_.----. ..I------ . .._ L.--. ..*!

..-. -.-.- ..--. -_./

: : j I

: I I--. ..- .._... +-..- : ..- --- ..-..---.....-.. ~ ;--.+ ..-

: j I i: : !: !: :: : I

: ii i jj..- ++ j---.- ++ j---’

I I ! :.i:.i

i : : ’: : :.-__ i...A.---- ._-.

j :

-7 ji

.- - . --;---‘---.t.. --+-‘_...... +i j j :__ : : 1 1-?-

.-.__ _ i. ..--. ; ;.-.L- 1..--...._-i.-._.. _-1. _.’ !!

;--...I.__._.--...I . .__._ .:

.--; .._i-.-.-..;-L...---I .._ +.i- . i...-I ! /! /

j j

: :: :--_i..---L.-l--.-_i..---L.-l--. :--+-j---+-j-: ,’ e-i...-i...+f

-... ;.-.-..I. . . -..;---....-.-..j.-_j_.--I !L- ; 3 .- I ..--._ j- ..___ ..-i : i

k. ..:-I .____.._.. ..; .__.. Jj/ ; I

0 for 32'

0 for 30'

0 for 28'

0 for 26'

0 for 24O

0 for 22'

0 for 20'

0 for 18O

0 for 16O

0 for 14'

Figure 197. Incremental Values of Lift Parameter

for NACA 0012 Airfoils at Miriimum

Reynolds Number

308







-

:-- -7-05i --7 .-‘-

- ---3

-.-A-;-05,

-.--.

1_.--.-Ii--

i-. --’~..L . - - .- - -

t7I ._._.1.!

: i.1 i : I : j i 1_... I.-.-.i-.. _- i ._. _. i_.. l.l_...-c--r--

: :..i.-j ....: _i- : 1. : .. /,,

! :J-Ld: ! :, I_... i 1 i ,j :

; i I.-.-. -..-...-..-1i.. .A _.A..-i..-J-11

Figure 200. Incremental Values of Lift Parameterfor NACA 0015 Airfoils at MinimumReynolds Number

0 for 32'

0 for 30°

0 for 28O

0 fQ?F6O

0 for 24'

0 for 22O

0 for 20°

0 for 18'

0 for 16'

0 for 14'

311



A --

0 for 32'

0 for 30°

0 for 28'

0 for 26'

0 for 24O

0 for 22O

0 for 20'

0 for 18O

0 for 16O

0 for 14O

Figure 201. Incremental Values of Lift Parameterfor NACA 0015 Airfoils at MaximumReynolds Number

312



;qy - - A NACA65A0127

LLI i1;;; . Figure 202. Lift Correlation for NACA 65AO12 and 0012 Airfoils,.i :' ___,_ at Standard Reynolds Number I. I

;j.j.I -.:



CLA-( .

:- :. _ : -.-i-- _. : -.. -:I8: I ; -... + ..--. ;-- .-I.____- - ..- -.-.. _. L-.-

____ -.-. -..A_--.---. --.__j_- _ .-. 1 . -.-- -- .I.

: :

. .-

____..- ..--..- --.. - .

i

___-..-~ -L--.-.- -_ - --.- -,.- - .- -

:. . . - --. .-

__~

~-

! .!

l.-_-.- . . . -i

i-_--I.’

; , 1 r

i ,.__ L. ._ . .! I j

. .-.. -L.-------e

0 for 32'

0 for 30'

0 for 28'

0 for 26'

0 for 24'

0 for 22'

0 for 20'

0 for 18'

0 for 16'

0 for 14"

0 for 12O

0 for 10'

0 for 8'

0 for 6'

Figure 203. Incremental Values of Lift Parameter

for NACA 65A012 Airfoils at MinimumReynolds Number

314



; ._._. +. .f . .,.I .f i--i

,

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: : : . .1---I-..,-L-i-.-I f., : , : / : eq4..;.-:i-jI’

0 for 32'

0 for 30'

0 for 28O

O-for 26'

0 for 16O

0 for 14O

0

for 24'

for 22O

for 2o"

for 18O

for 12O

Figure 204. Incremental Values of Lift Parameterfor NACA 65A012 Airfoils at MaximumReynolds Number

315



,I’:-.I.. if:::.:![:

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Standift' Correlation for NACA 651415 Airfoils at

Reynolds Number



: : j .._ .--.-..L-..-1--1 .--.-‘--.-; 1 -r-L-

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0 for 32'

0 for 30'

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0 for 18'

0 for 16'

0 for 14'

0 for 12'

0 for 10'

Figure 206. Incremental Values of Lift Parameterfor NACA 651412 Airfoils at MinimumReynolds Number

317



j./ i j

0

0

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for

for

for

for

for

for

for

for

for

for

32'

3o"

28'

26'

24'

22O

2o"

18'

16'

14O

Figure 207. Incremental Values of Lift Parameterfor NACA 651412 Airfoils at MaximumReynolds Number

318



I I I j4f: I

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: 0 NACA 0004. "; d 4% Hexagon

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wr40





COMl'AI$ISONS WITH TEST DATA

The only evaluation that could be made of the predictionmethods described in the previous sections was to compare-predic-tions with test data from which the methods had been derived. Inthe comparisons which are presented in this section, the predic-tions were obtained using a computer program written for a CYBER172 computing system. The computer procedure utilizes simplelinear interpolation between tabular data representations of manyof the charts and graphs presented in this report. Therefore,one of the objectives of the comparisons of predictions with testdata was to evaluate the accuracy of the computer procedure. A

second objective was to evaluate what improvements had beenachieved over the capabilities to predict the lift, drag, andpitching moment that had existed prior to this work.

The first set of comparisons used the "basic" predictionmethod applied to the 9 configurations which were presentedearlier in Figures 35 through 43 of this report as representativeof the evaluation of the aeromodule prediction methods. Table 17identifies the specific figures which present these comparisons.

Table 17 Key to Comparisons Made using the"Basic" SHIPS Prediction Method

CONFIGURATION ! FIGURE NUMBER

'F ' W Airfoil CL VSQ! CL VS CD &., VSa! / c, vs CL

25 25 0008 211a 211b 211c 211d45 45 0008 212a 212b 212c 212d

; 60 60 0008 . 213a 213b 213~ 213d1 80 25 0008 214a 214b 214c 214d

I 80 45 0008 215a 215b 215~ 215dj 80 60 0008 216a 216b 216~ 216di 35 25 0008 217a 217b 217~ 217d, 55 45 0008 218a 218b 218~ 218d1 65 45 Ooo8 219a 219b -219c 219d

322



Figures 211, 212 and 213'present comparisons of predictions

with test-data from test ARC 12-086 for th,e basic Wing configura-tions WI, WIII, and WV,respectively. The comparable comparisons

with Aeromodule methods were shown in Figures 35, 36,and 37. For

each of these configurations, the basic SHIPS prediction methodproduces much better agreement with test data than the Aeromodulemethods for lift and pitching-moment variations with angle of at-tack and for drag variations with lift coefficient. Also shown

for the SHIPS method are comparisons of predicted and test varia-tions of pitching moment with lift coefficient. Despite the fact

that some discrepancies occur in the pitching-moment curves, thegeneral character of the variations is well represented.

Figures 214, 215 and 216 present similar comparisons for theirregular planforms consisting of Wings 1,III;and V with 80 de-gree fillets. Corresponding comparisons with Aeromodule predic-tions were shown in Figures 38, 39 and 40. For these configura-tions the agreement of the SHIPS predictions with test data isvery good for all of the characteristics and again is betterthan the Aeromodule methods.

Figures 217, 218, and 219 present comparisons for irregularplanforms consisting of Wings I, II and III with fillet sweepsof 35, 55,and 65 degrees,respectively. Corresponding comparisonsof Aeromodule predictions with test data were presented in Fig-ures 41, 42,and 43. Again,the SHIPS prediction method produces

good agreement with the test data and much better agreement thanthe Aeromodule method for all of the characteristics.

In general, the "basic" SHIPS prediction method produces goodagreement with test data and represents a significant improvementover the Aeromodule method from which some of the components ofthe SHIPS method were adapted. There is one disturbing trendthat should be noted in the SHIPS predictions. At the high an-gles of attack,there is a tendency to predict the lift coefficientslightly lower*or slightly higher than the test data. Theseslight discrepancies are reflected in the pitching-moment varia-

tions with angle of attack and sometimes produce an exaggeratedor even erroneous change in slope. This situation occurs becausethe stall progression function used in the lift prediction-does not completely account for all of the variations

323



,..

which occur due to outboard panel sweep variations. As a conse-quence, the user should pay attention'to the pitch-up/pitch-downdesign guides when evaluating a specific configuration.

Ten additional comparisons of predictions with test data-arepresented,some of which use only the "basic" method, some ofwhich use both the "basic" and the "revised" methods, and some ofwhich use only the "revised" method. Table 18 presents a key tothese additional comparisons with test data.

Figure 220 presents comparisons of predictions for an ir-regular planform having a fillet sweep of 75 degrees, an outboardpanel sweep of 40 degrees,and an NACA 0008 airfoil. The outboardpanel sweep is intermediate between two of the test configura-tions,and the basic wing planform fits this SHIPS planform familyin terms of half-chord sweep, taper ratio,and aspect ratio. Thetest data show that,except for the variation of suction ratiowith angle of attack, the test data bracket the predictions.

The discrepancy for the suction-ratio curve represents one of thecompromisesthat had to be made during prediction method develop-ment to achieve smooth variations of the angle-of-attack bound-aries and slopes in the quasi-linear representation.

Figure 221 presents comparisons of prediction with test forthe irregular planform configuration 60 25.0008 using the basicSHIPS prediction methods. The comparison for lift, suction ratio,and drag are very good. The variations of pitching moment with

angle of attack and lift coefficient both show some discrepan-cies. The discrepancies for the irregular planforms with rela-tively low values of fillet sweep and outboard panel sweep _occur because the linear segment representations ofthe pitching-moment variation with angle of attack requires anadditional segment which is not reflected in the suction-ratiovariation with angle of attack. The "basic" SHIPS method utilized

the angle-of-attack boundaries determined from the suction ratio

analysis,and provisions were made for use of fictitious values toaccommodate the pitching-moment curves only at low and very highangles of attaik.

Figure 222 presents comparisons of predictions made with

both the "basic" and "revised" SHIPS methods and test data from

324



Table 18

Key to Additional Comparisons ofPredictions Made With the SHIPS PredictionMethods

CONFIGURATION METHOD FIGURE NUMBERS

*F 'WAIRFOIL B R CL -a "R(@" VSQ' CL vs CD Cm VSCY c, vs CL

75 '45 0008 J 220a 220b 22oc 220d- 220e

60 25 0008 J 221a 221b 221c 221d . 221e

65 45 0008 4 J 222a 222b ,222~ 222d

45 45 0004 4 223a 223b 223~ 223d. 223e

45 45 0008 4 J 224a 224b 224~ 224d

45 45 0012 J 225a 225b 225~ 225d

75 45 0004. J 226a 226b 226~ 226d

75 45 0012 J 227a 227b 227~ 2nd

75 45 651412 J 228a 228b 228~ 228d

80 45 0008 4 J 229a 229b 229c 229d' 229e



two different facilities but obtained at the same Reynoldsnumber (26.25 million per meter). The predictions made usingthe "basic" method slightly undershoot the lift curve at highangles of attack which is reflected in the drag polar and

pitching-moment variation with lift coefficient for theirregular planform 65 45.0008. The "revised" prediction methodvery accurately predicts all three characteristic.s. Thedifferences between the sets of test data are representativeof the magnitudes which occurred for all of the configurationswhich were tested in both facilities. This is a representationof the uncertainties in wind-tunnel test data historicallynoted for configurations tested in several facilities.

Figures 223, 224 and 225 present data comparisons withpredictions for Basic wing III with NACA 0004, NACA 0008 andNACA 0012 airfoil sections, respectively. The "revised"prediction methods produce accurate. representations of thetest data for all three airfoil thickness ratios with theexception of the drag at low coefficients for the NACA 0004airfoil configuration. The measured minimum drag for thatconfiguration appeared to be unusually low at the test Machnumber of 0.20, probably due to balance accuracy.

Figure 226 shows the comparisons of predictions using the"revised" prediction method with test data for the irregularplanform configuration 75 45.0004. For this case, the methodpredicts the test data quite accurately even though the pre-diction was inadvertently made for Mach 0.30 and the data wereobtained at M = 0.20. Note that the test minimum drag valueis the same for this configuration as it was for the 45 45.0004configuration which is further evidence that the test value forthe 45 45.0004 configuration is unusually low. Of particularimportance is the fact that the pitch-up at high angle ofattack is accurately .predicted.

Figure 227 presents comparisons of predictions with testdata for irr,egular planform 75 45.0012 for the standard andmaximum Reynolds number conditions. The revised prediction

methods produce good agreement for both Reynolds number con-ditions and, in particular, reflect the increase in angle ofattack for maximum lift coefficient and subsequent pitch-up.

326



The next comparison of predictions with test data is for theirregular planform consisting of ,Basic Wing III with 75 degreesweep fillet and having the cambered NACA 65 412 airfoil-and ispresented in Figure 228. In this case the e * feet of camber on

the lift, drag, and pitching mt curves are well predicted'with the ex-ception of a slight undersho,ot on ,the lift curve at the highestangles of attack which is reflected in the drag polar and pitch-ing moment curves. Again the shape of the predicted pitchingmoment curve. reflects thepitch-up characteristic which occursin the test data.

The last comparisons between predictions and test datapresented in Figure 229 use both the "basic" and "revised" pre-diction methods and are for the irregular planform consistingof Wing111 with the 80 degree fillethaving the NACA 0008 airfoil.These comparisons show that the "revised" method more accurately

predicts the lift curve than does the "basic" method. Thisimprovement is also shown to correct an erroneous occurrence inthe pitching-moment variation with lift coefficient in which the"basic" method showsspitch-down whereas the "revised" methodaccurate ly predicts apitch-up. In retrospect it appears thatthe simplified representation of the lift curve in the "basic"prediction method using a single curve for the stall progressionfunction should be modified 'to better account for the effectsof outer pane l planform effects. The "revised',' method is limitedin the scope of planforms to which it can be applied, but pro-duces very accurate results and is more applicable when predict-

ing full-scale conditions of airfoils having higher thicknessratios.

The fact that the test results obtained in different facili-ties are somewhat different reflects the fact that even at lowspeed there are still uncertainties inherent in the availabletest techniques.

327



(a) Lift CurveFigure 211. Comparisons Between Basic SHIPS Prediction and Test

for Basic W ing I



w

s: (b) Drag PolarFigure 211. Continued



(c) Pitching-Moment Variation with Angle of AttackFigure 211. Continued



Figure 211. Concluded.



(a) Lift Curve

Figure 212. Comparisons Between Basic SHIPS Prediction and Testfor Basic Wing III



(b) -Drag Polar

Figure 212. Continued











(a) Lift Curve

Figure 213. Comparisons Between Basic SHIPS Prediction and Testfor Basic Wing V



2 (b) Drag Polar





Figure 213. Continued.



ti (d) Pitching-Moment Variation with Lift\D




(a) Lift CurveFigure 214. Comparisons Begween Basic SHIPS Prediction and Test

Wing I with 80 Fillet



(b) Drag Polar





Figure 214. Continued.




Figure 214. Concluded



-mAirfoOn08

.,(a) Lift Curve

Figure 215. Comparisons Between Basic SHIPS Prediction andWing III with 80' Fillet



-_-_d_L.,

!. !.:I 1 ; ,,,.; !

I7:--,-- yjy.iji’?:.,. I i 1. ..:j::::;:j;...~:p.,::!~,~~~:

(b) Drag PolarFigure 215. Continued



: ‘.”

:,..

-t-‘;.j:..:.!..:

‘r..-. _..i j

_....: .

(c) Pitching-Moment Variation with Angle of AttackFigure 215. Continued



I I _-I ..- ...’ 1. -c--J---.!--- l-.-i--!-~~~..‘-~ -..i-~irfoil ..I 1. 1. 1. j:., 1. .I. I. j...'.:..~:.: (::I ..;I.:../... .1l.j1..

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IM

: ,’__._- L _( . : :::..: .,. :., 1..: ‘Y.





(a) Lift Curve

Figure 216. Comparisons Between Basic SHIPS Prediction and Testfor Wing V with 80' Fillet



(b) Drag Polar

Figure 216. -Continued







(cl) Pitching-Moment Variation with Lift




(a) Lift Curve

Figure 217. Comparisons of Basic SHIPS Prediction and Test

for Basic Wing I with 35' Fillet



(b) Drag Polar










(a) Lift Curve

Figure 218. Comparisons of Basic SHIPS Prediction and Testfor Wing III with 55' Fillet



(b) Drag Polar












(a) Lift Curve

Figure 219. Comparisons of Basic SHIPS Prediction and Testfor Wing V with 65' Fillet



(b) Drag Polar










w% *F $J Airfoil

075 35 0008 Test 086-68-75 40 0008 Prediction X61075 45 0008 Test 086-86

I !j: ,,,ij/j!::l/j/i/jj:, !: I.:. ;:, .,I, :,I: !I!, :,,

:. ,., ,.,. I’ CL:’

(a) Lift Curve

Figure 220. Comparisons of basic SHIPS Prediction for

Configuration A = 75', /\ = 40' and Test

Data for AF = 73', hW = 3!!' and 45'



075 35 0008 Test 086-68

-75 40 0008 Prediction X61 Procedure075 45 0008 Test 086-86

:: “: J!l::(!!I:II:I:!;; ‘.‘. i”,. ,.I, ..,. il i I: :::,,,,!

&Jeg w

(bl Suction-Ratio Variation with Angle of Attack




xedure

(c) Drag Polars






!dure

(e) Pitching-Moment Variations with Lift




w (a) Lift Curve

3 Figure 221. Comparisons of Basic SHIPS Prediction and Testfor W ing I with 60 Fillet



(b) Suction-Ratio Variation with Angle of Attack




Yc

(c) Drag Polar




(d) Pitching-Moment Variation with Angle of Attack




(e) Pitching-Moment Variation with Lift




(a) Lift Curve

Figure 222. Comparisons of Basic and Revised SHIPS Predictionsand Test for Wing III with 65’ Fillet for TwoDifferent Test Facilities





Airfoil 1 j. 1 .i ( I... I. j ..I j . .I.....!..../ .i....l....l_._.l...S._. 1........: .l

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'rn t25 ;:

..I....... I.. _I.,:.( .I.. 65 45 0008 .I .I I i I I. i- X61 Basic OTest

-A.___._...._..-.1.,-i&- X61 Revised OTesl 262-5 ._

., . .I.4 ..,.. a’.. .: .12 . ..16 ,.., i.20

:L-l-l-r.- ---L..086-91









(a) Lift Curve

Figure 223. Comparisons of Revised SHIPS Prediction and Testfor Wing III with NACA 0004 Airfoil



(b) Suction-Ratio Variation with Angle of Attacks Figure 223. Continued



(c) Drag Polar




/ I I, I I I I I I i I I I I I I : ,,.., :‘:’ j;; “”

(d) Pitching-Moment Variation with Angle of Attack




(e) Pitching Moment Variation with Lift




(a) Lift Curve

Figure 224. Comparisons of Basic and Revised SHIPS Predictionsand Test for Basic Wing III with NACA 0008 Airfoils for

Two Different Facilities



(b) Drag Polars




/I’.:i,:. 1 ‘1 (:,:.I.:

61 - - - - -----X61 Revised q Tes

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(d) Pitching-Moment Variations with Lift






(b) Drag Polar




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I. .I I... 1 I TI[J----/ ;. ,I I,... ,I, :I::.~::li,::l:..:l:,:;ji/ ii:,.. :, !:. : ::.,,A--- .--L .LxL:.L,-:::::.:. :: :: :: :::;:....:‘::, “..,..: ...I.._.:.

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,









(a) Lift Curve

Figure 226. Comparisons of Revised SHIPS Prediction and Testfor Wing III with 75' Fillet and NACA 0004 Airfoils



(b) Drag Polar




;. ..;. 1 : .:. ;:. ::'

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1 12. 16 I... 2'.I

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(c) Pitching-Moment Variation with Angle of Attack-




(d) Pitching Moment Variation with lift




(a) Lift Curve

Figure 227. Comparisons of Revisgd SHIPS Predictions and Testfor Wing III with 75 Fillet and NACA 0012 AirfoilsShow Effects of Reynolds Number



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-X61 Revised OZ23-bU

: ,,,;::. : ,..t,,!.,, /:’ -- 0255-63

RN26.25 x lO'/m

45.96 x 106/m

(b) Drag Polar




1::::1.::.1:..:1 .:..1....1..:.1. ...1....l. ..i..:.I.. .I.:../... I.

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--- -

X61 Revised 0255-60 26.25 x 106/m

5-63 45.96 x lO'/m

]:iill.li;iili llr::ii;ii.l jjj; I,, pi;. j;‘.:;” : i :I J’ !’ /:j ,/’ 1’ j:, j lj, 11: ij: iI:.:l;il;:. ,/ 1’: II ,I’: ::ji,! 1.ij.i .i,/

(d) Pitching-Moment Variations with Lift




(a) Lift Curve

Figure 228. Comparisons of Revisgd SHIPS Prediction and Test

for Wing III with 75 Fillet and Cambered NACA

651412 Airfoil



00

(b) Drag Polar




4 .'$

;I:!!

“i-ii: .'.._ ._

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-X61 Basic

(a) Lift Curve

Figure 229. Comparisons of Basic and REvised SHIPS Predictionsand Test for Wing III with 80' Fillet and NACA 0008Airfoils for TWO Different Facilities



(b) Suction-Ratio Variations with Angle of Attack




30

(c) Drag Polar





3



cs

---*",. Revised OTest 255

-I-- .i!:!‘::!:I::Ls/ ;:.,i,,1,,: . 3 .:jj;/;j/i/:j,.,,,,;,;,!:I, 1 :!: + .,!, “’ ! ,:,.!i,:!‘:;!,/!:: ,., ,.. 1 I.ilifj:: !,,!, ,I:!:I:,,‘,‘.’ :,. . ..., j:(;/:/;,/;!jljl;ki! I. I, ,,I,,f 7

‘: ,. .,.. : ,I, ,I.,

I:: I:,:,I:,,,I ,I: I;, ,I: I, :, :,i

(e) Pitching-Moment Variations with Lift




CONCLUDING REMARKS

The objectives of this investigation were to develop predic-tion methods for low speed lift, drag,and pitching moment of ir-regular planform wings and design guidelines appropriate for pre-liminary design of advanced aerospace vehicles.

At the outset of the investigation it was hoped that quitesimple empirical methods could be evolved that would be suitablefor solution with nothing more than a hand calculator. As theinvestigation progressed, it became apparent that the flow fields

produced by the component panels of irregular planform wings havecomplicated interactions that are affected by differences in Rey-nolds number in different ways depending on the fillet/wing com-bination and on the airfoil thickness. As a consequence themethods as finally devised are more complex than originally en-visioned and require a computer procedure for efficient solution.

The methods provide a significant improvement in capabilityto accurate ly predict variations of lift, drag,and pitching-mo-ment with ang le of attack for a wide range of irregular planforms,and for a more limited range of planforms can account for effects

of airfoil-thickness ratio and Reynolds number.

The investigation also showed that there are differences intest results obtained in different test facilities that introduceinherent uncertainties in the low speed aerodynamic characteris-tics of any given configuration. The magnitude of the uncertain-ties can be evaluated for the limited range of irregular plan-forms by making predictions using both the "Basic" and "Revised"prediction methods.

408



APPENDIX A

REYNOLDS NUMBER'EFFECT ON LIFT OF SHIPS WINGS

During the investigation described in the main body of this

report, a concerted effort was made to derive some simple methodto obtain corrections to the lift curves for the effects of Rey-nolds number. No successful method was found that could ade-quately describe the effects as a general function of Reynoldsnumber for the complete range of SHIPS planforms.

In order to facilitate extrapolation of test results froma test performed at relatively low Reynolds numbers to flightconditions at low speed, data on the effects of Reynolds numberon the lift correlation parameter are presented in this appendixfor all configurations having airfoils with thickness ratios of0.08 or larger. There were no significant effects for the

NACA 0004 or thin hexagonal airfoils.

The dataarepresented in the form of the variation of the

incremental value of the lift correlation parameter,

with angle of attack for various values of unitThe baseline for the incremental value is the value of the liftcorrelation parameter obtained at the standard unit Reynolds num-ber of 26.25 million per meter at each angle of attack for eachconfiguration.

For the reader's convenience the plots are sorted into twomajor categories:

1. Corrections that were obtained from data for testARC 12-086. These data should only be applied topredictions made using the "basic" predictionmethod (Figures 230, 231).

409



2. Corrections that were obtained from Langley LTPT Tests255, 262 and 266. These data apply only to predic-

. tions made using the "revised" prediction method for

the "standard" Reynolds' number (Figures 232-235).

The appropriate values of CLcu, Al and qB are listed inTable 19.

410



TABLE 19 NUMERICAL ALUESOF ELEMENTSN LIFT CORRELATIONARAMETER

80°

75O

7o"

65'

60'

55O

53O

45O

35O.

25'

*W

250 350 450 I,, 530 1 600%/RAD' A1 k/RAD Al A1dRAD 1; A1 j %.r/RAD ; A1 1 %Y/RAD

1.76586 .36937 1.76374 .37098 i' 1.74586 I .37123 /' 1.70925 .37355 1.65654 .37512/I'1 I I

2.08310 .45377 2.08631 .45228 ' 2.07674 1 .45271 ;, 2.04603 .45617 2.00300 '.460801

2.29286 .50598 2.30071 .50893 j 2.29871 ; .50948 2.27424 .51386 2.24118 .51975

I;2.43851 .54776 2.45071 .55122 1, 2.45518 ! .55186 2.43673 .55222 2.41261 .56393

I

2.54296 .58140 2.55923 .58444 2.56920 .58517 2.55642 .59096 2.54004 .59489

2.61996 .60735 2.64002 .61160 2.65469 .61239

2.67726 .62857

2.72350 .64957 2.74997 .65443 2.77214 .65534

2.78881 .68281 2.82083 .68819

2.83379 .71120A L L

NOTE: TB = .41157 for all wings



hW t/c-25 .08

RN = 19.67 x 106/m

(6 x 106/ft).OS

0

-P5 -' i -.05

0

I

4 8

I

12 16 20 24adeg

28

(a) hF = 25'

Figure 230. Incremen tal Values of Lift Correlation Param eterat U nit Reynolds N umbers of 13.13 and 19.67 MillionPer Meter From Test ARC 12-086 for SHIPS PlanformsHaving Constant Values of Fillet Sweep



AW t/c

-35 .08--25

ki - 19.67 x 106/m

(6 x 106/ft)-

RN - 13.13 x6106/m .05(4 x 10 /ft)

. -%-- 0/\\

\--- --- -05

I I I I I I 1

0 4 8 12 16 20 24 28adeg

(b) ~~ = 35'




hd t/c

-60 .08---53--45---35---25

RN A 19.67 x lO$n(6 x 106/ft) .05

0

0 4 8 12 16 20 24 28adeg

(e) hF = 60’




AU t/c

-60 .08---55--45

---35----25

RN = 19.67 x lO$

(6 x 106/ft).05

L705

RN = 13.13 106/m(4 x 206/ft) .05

c----- --

-->md=e - --- -- --Z

i

0

-05

4 8 16 20

(0 AF = 65'




*w t/c

-60 .08---53--45----35---25

RN = 19.67 x lo'/,

(6 x 106/ft)

- -P5

L

0 4 8 12 16

(g) $ = 7oo


1

20

I

24 28adeg







AF AW t/c

-25 25 .08--25 25 .12

.;5

cL *1Ayi

( >

0

a Ba.05

i

.OS

0

7.05

tf0

',.05

0

-P5

--.lO-.lO -\\\ ’

-.15 :_/--

I 1 I I I t-.lS

RN - 19.67 x6106/m(6 x 10 /ft)

RN - 13.13 x 106 /m(4 x 10%ft)

. ---,v\

0 4 8 12 16 20 24 28

(a) AF 25'adeg

Figure 231. Incremental Values of Lift Correlation Parameterat Unit Reynolds N umbers of 13.13 and 19.67 MillionPer Meter from Test ARC 12-086 Showing Effect ofThickness Ratio for W ing I With Various FilletSweeps





.05

A cL *1--

.( >

'L 'B0

a

-D5

-.lO

t

0

AF AW t/c-80 25 .08--80 25 .12

RN = 19.67 x6106/m(6 x 10 /ft)

.05

r. A-----

t

0---_

RN = 13.13 x 106/m(4 x 106/ft)

-- ------------_ ._- --.

4 8 12 16

(cl AF = 80'


20 24adeg

!

.OS

0

-.05

-.lO

28



"F *W t/c

-45 45 .08---45 45 .12--45 45 .15

.057

.os,

CL A1&TX O-( >

-D5

i

-.10-j 0

RN - 19.67 x6106/m(6 x 10 /ft)

-- -.-4.-- .05

o.-A ,/--‘4 -. 05

REI - 13.13 x61061m .05

(4 x 10 /rtj

.,/--

.

\ /\

i

0'

-.os

I 14 8 1 I 112 16 20

I -.lO

I24 28adeg.

(a) hF = 45'

Figure 232. Incremen tal Values of Lift C orrelation Param eterat Unit Reynolds Numb ers of 1 3.13 and 19.67 MillionPer Meter from Various Langley LTPT Tests ShowingEffect of Thickness R atio for Wing III with VariousFillet Sweeps



'F *W t/c

-65 45 .08--65 45 .12--65 45 .15

.05

(11

RN - 13.13 x6106/m

CL %(4 x 10 /ft)

*XT0 .---

a B * -105

-4

T - 3 -- -- 0

705 J

.05

3 0nB>

-.lO

I--.95

a RN = 19.67 x6106/m '-

(6 x 10 /ft).

.05

--a.0

I I I I0 4 8 12 16 20 24

adeg28

(b) AF = 65'




-70 45 .08--70. 45 .12--70 45 .15

RN i 19.67 x 106/m

(6 x 106/ft)

'OS 1 RN - 13.13 x 106/m(4 x 106/ft)

b.05

'. - 0

-DS --\ \

'. --PS

I I I I .0 4 8 12 16 20 24 28

adeg

(cl AF - 7o"


“-u.



hF 'W t/c

-75 45 .08--75 45 .12--75 45 .15

.05 -1

Act-;;- 0(L Al

a B) t5 •I

RN - 19.67 x 106/m

(6 x lO'/ft)

.

RN = 13.13 x 106/m

(4 x 106/ft).

0 4

. . .

8 12 16 20 24 28

Cd) AF = 75'adeg




*F AW t/c

-80 45 .08--80 45 .12--80 45 .15

RN = 19.67 x 106/m

(6 x 106/ft)

x6106/m- .05

- 13.13(4 x 10 /ft) /----- -

- -2--- -CT- _/'c 0

-05 - - -.05

0

I

4

I I I I .

8 12 16 20 24 28adeg

(e) AF = 80'




'F *W t/c

-45 45 .08

--45 45 .12

--45 45 .15

RN - 45.93 x 1 06/m(14 x 106/ft)

.

RN 9 39 .37 x lob/m

(12 x lO%ft) ,-i---

RN - 32.81 x 1 06/m

(10 x 106/ft)

. --l-SL'

105

0

-.05

t

.05

0

-.05

1

.05

0

-.os

c

s1

0I 1 I

4 8' 1; lb 20 24adeg

28

(a) AF - 45'

Figure 233. Incremental Values of Lift Correlation Parameterat Unit Reynolds Num bers of 32.81 , 39.37 and 45.93Million Per Meter from Various Langley L TPT TestsShowing Effects of Thickness Ratio for Wing IIIwith Various Fillets



-65 45 .08

--65 45 .12--65 45 .'15

45.93 x 106/m

(14 x 10b/ft)

.os., RiJ - 39.37 x 106/m

x12 x 106fft)_-- -

_cr11

\-- -- /'----__

.05&j I 32.81 x 106/m

cL A1A- -

(.)

i

(10 x 106/ft)

'L, 'IB0. -

-.05

I

.05

0

-.05

I I I I I

OI-

4 8 12 16 20 24 adeg28

(b) AF - 65'




.05 t

cL AlA-()IL,

'Ig O-

-D5 1

.05t

cL *1A-C )L ng0

a

-.05

1

RN = 45.93 x 106/In

(14 x 10Vft)

RN = 39.37 x 106/m

(12 x 106Ift)a ----n-T, _ --- ,Y_/ -

m = 32.81 x l&n

(10 x 106/fO

--L-- ---b/T--------=--

.05

t

0

.05

t

.05

0

-D5

1

.05

0

-.05

-t

O 4

I I I-

8 12 16 20 24 28adeg

(cl AF * 7o"




*F 'W t/c

-75 45 .08--75 45 .12--75 45 .15

f&Z 45.93 x 106/ln RN - 39.37 x d/m RN - 32.81 x 106/m

(14 x 10G/ft) (12 x 109ft) .05

0

. .

0 4 8

1

12 16 20 24 adeg '8

(d) AF - 75O


-“.wb&.



RN = 45.93 x 106/m(14 x 106/w

AF hW t/c

-80 45 .08--80 45 .12--80 45 .15

.05 RI = 39.37 x 106/ln

(

(12 x 106lft)

cL *1A CL -ii

) t

0 . . .

a B-.05 '

.05/-c--

/-- -,e-

0

+ -.05

- -.05

0

I I I 1 1 1

4 8 12 16 20 24Czdeg

28

(e) AF = 80'




AF 'W Airfoil-70 45 0012--70 45 5012--70 45 5412

RN = 19.67 x 106/m

(6 x 106/ft)

RN - 13.13 x 106/m(4 x 106/ft)

,scs-~

I

I I 1 t-

0 4 8 12 16 20 24 28

(a) AP - 70'adeg

Figure 234. Incremental Values of Lift Correlation Parameter atUnit Reynolds Numbers of 13.13 and 19.67 MillionPer Meter from Langley LTPT Test 262 Showing Effectsof Airfoil Section and Camber for Wing III withVarious Fillet Sweeps

t

.O!i

0

-. 05

F .05

- 0

- 45



RN - 19.67 x 10%

(6 x lO'/fc)

“F 'W Airfoil-75 45 0012--75 45 5012--75 45 5412

.05-.RN = 13.13

(4 x

x6106/m

10 /ft)

0

I

4

1 I I I

8 12 16 20

I

..4 28adeg

(b) ,iF - 75'




AF Aw Airfoil-80 45 0012--80 45 5012--80 45 5412

I I I .1-----I

0 4 8 12 16 20 24 28adeg

(c) AF - 80'




.OSi

'F 'W-70 45

--70 45

--70 45

RN = 45.93 X 106/m(14 x lO%ft)

RN = 39.37 x 106/m

(12 x 106/Ct)

RN = 32.81 x 106/m

(10 x lo6/ft)-

Airfoil001250125412

I I I I I I I

- .05

f

0

-..O!i

_ .o!i

f

0

-AI5

r

05

0

-p5

0 4 8 12 16 20 24 28

(a) AF = 70°

adeg

Figure 235. Incremental V alues of Lift Correlation Parameter atUnit Reynolds Numbers of 32.81, 39.37 and 45.93Million Per Meter from Langley LTPT Test 26 2 Show-,ing Effects of Airfoil Section an d Camber for WingIII with Various Fillet Sweeps



f

*F .'W

-75 45--75 45--75 45

RN - 45.93 x 106/m

(14 x 106/ft)

RN * 39.37 x 106/m

(12 x 106/ft).-

RN - 32.81 x iD6/m

(10 x lab/ft)-

Airfoil

001250125412

-4.05

.'----' -, 0

L-.05

.05

0

I I .4 8 ;2 1;- .0 2;adeg

2'i3

(b) hF - 75'




A

.057

cL *1A-

C )La x0

-.05

I

'F 'W Airfoil

-80 45 0012--80 45 5012--80 45 5412

T

RN = 45.93 x l&m(14 x UP/ft)

RN - 39.37 x lOGI.;

(12 x 106/ft)

BN = 32.81 x 106/m

(10 x 106/ft)

r -05

.---------\.y---I

------L--L -.05

i

-D5

. . I I I I I

0 4 8 12 16 20 24 28adeg

(cl ~~ = 80'




REFERENCES

1. Hopkins, Edward J.; Hick-s, Raymond M.; and Carmichael,Ralph L.: Aerodynamic Characteristics of Several CrankedLeading-Edge Wing-Body Combinations at Mach Numbers from0.4 to 2.94. NASA TN D-4211, 1967.

2. Corsiglia, Victor R.; Koenig, David G.; and Morelli,Joseph P.: Large-Scale Tests of an Airplane Model Witha Double Delta Wing, Including Longitudinal and LateralCharacteristics and Ground Effects. NASA TN D-5102, 1969.

3. Stone, David R.; and Spencer, Bernard, Jr.: Aerodynamic

and Flow Visualization Studies of Variations in the Geometryof Irregular Planform Wings at a Mach Number of 20.3.NASA TN D-7650, 1974.

4. Kruse, Robert L.; Lovette, George H.; and Spencer, Bernard,Jr.: Reynolds Number Effects on the Aerodynamic Character-istics of Irregular Planform Wings at Mach Number 0.3.NASA TM X-73132, July 1977.

5. Reference deleted. Information referred to is also

presented in either Reference 8 or Reference 11.

6. Ericsson, L. E.; and Reding, J. P.; "Nonlinear Slender WingAerodynamics." AIAA Paper No. 76-19, 26 January 1976.

7. Benepe, D. B.: Analysis of Nonlinear Lift of Sharp- andRound-Leading-Edge Delta Wings. General Dynamics Fort WorthDivision Report ERR-FW-799, 20 December 1968.

8. Schemensky, R. T.: Development of an Empirically Based Compu-ter Program to Predict the Aerodynamic Characteristics of

Aircraft, Volume I, Empirica l Methods. AFFDL-TR-73-144,Volume I, November 1973.

440



9.

10.

11.

12.

13.

14.

15.

16.

Mendenhall, M. R.; and Nielson, J. N.: Effect of Symmetri-cal Vortex Shedding on the Longitudinal Aerodynamic Charac-teristics of Wing-Body-Tail Combinations. NASA CR-2473,

January 1975.

Spencer, B., Jr.; and Hammond, A. D.: Low-Speed Longi-tudinal Aerodynamic Characteristics Associated with aSeries of Low-Aspect-Ratio Wings Having Variations inLeading-Edge Contour. NASA TN D-1374, September 1962.

USAF Stability and Control DATCOM. Air Force Flight Dyna-

mics Laboratory, October 1960 (Revised August 1968).

Spencer, B., Jr.: A Simplified Method for Estimating Sub-sonic Lift-Curve Slope at Low Angles of Attack for Irre-gular Planform Wings. NASA TM X-525, 1961.

Polhamus, E. C.: A Concept of the Vortex Lift of Sharp-.Edge Delta Wings Based on a Leading-Edge-Suction Analogy.NASA TN D-3767, December 1966.

Kirby, D. A.: Low-Speed Wind-Tunnel Measurements of the

Lift, Drag and Pitching Moment of a Series of CroppedDelta Wings. Aeronautical Research Council (Great Britain)Report R&M 3744, November, 1972.

Henderson, W. P.: Studies of Various Factors AffectingDrag Due to Lift at Subsonic Speeds, NASA TN D-3584,

September 1966.

Braslow, Albert L:; Hicks,. Raymond M.f and Harris, Roy .V..Jr.: Use of Grit-Type Boundary-Layer-Transition Trips onWind-Tunnel Models. NASA TN D-3579, 1966. (Also included

in NASA SP-124).

44



17. Chappell, P. D.: "Flow Separation and Stall Characteristicsof Plane, Constant-Section Wings in Subcritical Flow." TheAeronautical Journal of the Royal Aeronautical Society,Vol 72, January 1968, pp 82-90.

18. White, F. M.; and Christoph, G. H.: A Simple New Analysisof Compressible Turbulent Two-Dimensional Skin FrictionUnder Arbitrary Conditions. AFFDL TR-70-133, February 1971.

19. Aerospace Handbook, Second Edition (C. W. Smith, Ed.)General Dynamics' Convair Aerospace Division Report FZA-

381-11, October 1972.

20. Hoerner, S. F.: Fluid-Dynamic Drag. Hoerner Fluid Dynamics,Brick Town, N.J., c.1965.

a

Documents

Development of Aerodynamic Prediction Methods for Irregular Planform Wings