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.
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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
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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
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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
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65
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-
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
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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
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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
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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
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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
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LIST OF FIGURES (Cont'd.)
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
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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 38. Comparisons of Aeromodule Predictions With TestData - Configuration 80 25.0008 85
Figure 39. Comparisons of Aeromodule Predictions With TestData - Configuration 80 45.0008 86
Figure 40. Comparisons of Aeromodule Predictions With TestData - Configuration 80 60.0008 87
Figure 41. Comparisons of Aeromodule Predictions With TestData - Configuration 35 25.0008 88
Figure 42. Comparisons of Aeromodule Predictions With 'lestData - Configuration 55 45.0008 : 89
Figure 43. Comparisons of Aeromodule Predictions With TestData - Configuration 65 60.0008 90
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
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LIST OF FIGURES (Cont'd.)
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 70' Sweep Fillets
Correlation of SHIPS Test Data Using WINSTAN Corre-
lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 65' Sweep Fillets
Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 60' 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
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Figure 58.
Figure 59.
Figure 60.
Figure 61.
Figure 62.
Figure 63.
Figure 64.
Figure 65.
Figure 66.
Figure 67.
Figure 68.
LIST OF FIGURES (Cont'd.)
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
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LIST OF FIGURES (Cont'd.)
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
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LIST OF FIGURES (Cont'd.)
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
Incremental Angle of Attack for Region 3 155
Incremental Angle of Attack for Region 4 156
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
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Figure 103.
Figure 104.
Figure 105.
Figure 106.
Figure 107.
Figure 108.
Figure 109.
Figure 1lJ.
Figure 111.
Figure 112.
Figure 113.
LIST OF FIGURES (Cont'd.)
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
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Figure 114.
Figure 115.
Figure 116.
Figure 117.
Figure 118.
Figure 119.
Figure 120.
Figure 121.
Figure 122.
Figure 123.
LIST OF FIGURES (Cont'd.)
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
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Figure 124.
Figure 125.
Figure 126.
Figure 127.
Figure 128.
Figure 129.
Figure 130.
Figure 131.
Figure 132.
Figure 133.
LIST OF FIGURES (Cont'd.)
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
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192
193
194
195
Analysis - Irregular Planform with High Fillet Sweep 196
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LIST OF FIGURES (Cont'd.)
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 141. Skin Friction on an Adiabatic Flat Plate, X, = 0.3
Figure 142. Skin Friction on an Adiabatic Flat Plate, X, = 0.4
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
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LIST OF FIGURES (Cont'd.)
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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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.
LIST OF FIGURES (Cont'd.)
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
Pitching-Moment Coefficient Derivative for Region 3
Pitching-Moment Coefficient Derivative for Region 4
Pitching-Moment Coefficient Derivative for Region 5
Pitching-Moment Coefficient Derivative for Region 6
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
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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
Effects of Airfoil-Thickness Distribution and Camberfor 75-45 Irregular Planform 292
Effects of Airfoil-Thickness Distribution and Camberfor 70-45 Irregular Planform 293
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
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LIST OF FIGURES (Cont'd.)
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
Lift Correlation for NACA 0012 Airfoils at StandardReynolds 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
Lift Correlation for NACA 0015 Airfoils at StandardReynolds 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
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LIST OF FIGURES (Cont'd.)
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
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LIST OF FIGURES (Cont'd.)
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
Pitching-Moment Variation with Angle of Attack 342
Pitching-Moment Variation with Lift 343
Comparisons Between Basic SHIPS Prediction and
Test Wing III with 80' Fillet
Lift Curve 344
Drag Polar 345
Pitching-Moment Variation with Angle of Attack 346
Pitching-Moment Variation with Lift 347
Comparisons Between Basic SHIPS Prediction and Testfor Wing V with 80° Fillet
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(a>
(b)
cc>
Cd)
Figure 217.
(a>
(b)
cc>
Cd)
Figure 218.
(a>
6)
cc>
Cd)
Figure 219.
(a>
LIST OF FIGURES (Cont'd.)
Lift Curve
Drag Polar
Pitching-Moment Variation with Angle of Attack
Pitching-Moment Variation with Lift
Comparisons of Basic SHIgS Prediction and Test
for Basic Wing I with 35 Fillet
Lift Curve
Drag Polar
Pitching-Moment Variation with Angle of Attack
Pitching-Moment Variation with Lift
Comparisons of Basic SHIPS Prediction and Testfor Wing III with 55' Fillet
Lift Curve
Drag Polar
Pitching-Moment Variation with Angle of Attack
Pitching-Moment Variation with Lift
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
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LIST OF FIGURES (Cont'd.)
Page(c) Pitching-Moment Variation with Angle of Attack 362
(d) Pitching-Moment Variation with Lift 363
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
(b) Suction-Ratio Variation with Angle of Attack 370
(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
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LIST OF FIGURES (Cont'd.)
(c) Pitching-Moment Variation with Angle of AttackPage
376
(d) Pitching-Moment Variation with Lift 377
Figure 223. Comparisons of Revised SHIPS Prediction and Testfor Wing III with NACA 0004 Airfoil
(a) Lift Curve 378
(b) Suction-Ratio Variation with Angle of Attack 379
(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
(c) Pitching-Moment Variation with Angle of Attack 385
(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
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LIST OF FIGURES (Cont'd.)
(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
(c) Pitching-Moment Variation with Angle of Attack 393
(d) Pitching-Moment Variation with Lift 394
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
(c) Pitching-Moment Variation with Angle of Attack 397
(d) Pitching-Moment Variation with Lift 398
Figure 228. Comparisons of Revised SHIPS Prediction and Test forWing III with 75' Fillet and Cambered NACA 651412Airfoil
(a) Lift Curve
(b) Drag Polar
(c) Pitching-Moment Variation with Angle of Attack
399
400
401
402d) Pitching-Moment Variation with Lift
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LIST OF FIGURES (Cont'd.)
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
Pitching-Moment Variation with Angle of Attack
Pitching-Moment Variation with Lift
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
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LIST OF FIGURES (Cont'd.)
(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
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LIST OF FIGURES (Cont'd.)
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
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LIST OF FIGURES (Concluded)
(a) AF = 70'
(b) AF = 75O
(c) AF = 80'
Page
437
438
439
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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
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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.
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@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.
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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
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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
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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
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LIST OF SYMBOLS AND NOMENCLATURE (Cont'd.)
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)
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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)
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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
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LIST OF SYMBOLS AND NOMENCLATURE (Cont'd.)
"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/..
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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
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LIST OF SYMBOLS AND NOMENCLATURE (Cont'd.)
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
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LIST OF SYMBOLS AND NOMENCLATURE (Cont'd.)
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
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7)B= ETAB
0 LE
A
n,
*LE = *W
'TE
AC/2
AC/4
At/cmax
AW
Q
*T
LIST OF SYMBOLS AND NOMENCLATURE (Cont'd.)
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
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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.
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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.
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(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.
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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°
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(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.
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(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
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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
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(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.
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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
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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
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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
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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
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.
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
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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
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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
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Note: ~11 Dimensions Normalized by Root Chord of Basic Wing
Wing II; LE = 35', TE = 20'
Figure 1. - Continued
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~---+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
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0.0983 p-f
r==+ ,.3636---l
Note: All Dimensions Normalized by Root Chord of Basic Wing
W Wing IV; LE = 53', TE = 7'
Figure l.- Continued
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wl
243332
b" 4 8-0.6667
-F--.
70.1924
Note: All Dimensions Normalized by Root Chord of Basic Wing
(4 Wing V; LE = 60°, TE = 0'
Figure l.- Concluded
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/---0.2247--4
LONC Bow SW21 ooov
Note: All dimensions in meters
Figure 2. - Sketch showing general arrangement of model usedin investigation
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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)
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I-- S =g .-&J
la
69uul-
wl
w2
W
Figure 3. - Wing Planform Geometry Definitions
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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)
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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)
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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)
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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)
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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&
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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.
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er
-.., ___ - _._.-- __-LI.--. _ . _. -..--..- -r
I 1
!‘t
Figure 4. Body Geometry
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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)
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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
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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
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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.
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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
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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
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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
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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
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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-
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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.
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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.
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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
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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.
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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
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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
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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.
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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.
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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.
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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.
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/
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
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, .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"
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.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'
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.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
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.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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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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
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-.- .-‘.
.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., ‘.
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Data - Configuration 80 25.0008
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086 83 80 45.0008 .0316:
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Figure 42. Comparisons of Aeromodule Predictions With Tc'stData - Configuration 55 45.0008
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0
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NOTE:
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wing planform area and quarter-chord mat
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Figure 44. Comparison of Aeromodule Longitudinal StabilityDerivative With Test Data for Wing I With VariousFillets
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ma-0 Test Data RE= 26 25x106/m (8.0x106/ft>
- RlT
---El RlT Corrected for Actual Wetted Areas
z . 0120~--.~-..--‘-~.-..--...--- .--.- ..- __--. .-..- -
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1.2
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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
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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.
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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
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method.
lished at f attack as shown in Figure 59. Thecurves for angles- of 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
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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
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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
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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
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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.
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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
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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.
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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.
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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
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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
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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
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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
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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
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Figure 47. Scatter Plot Showing Spread of Lift Data for all35 SHIPS Planforms
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; ::“j, ; ; !.!
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/__.jj.,:,;...: :....: ,.__ 1,... j :..! ., ~.; :’
80 2580 3580 4580 5380 60
Figure 48. Plot Showing Spread of Lift Data for Constant FilletSweep
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80 25 .0008
80 35
80 4580 5380 60 I
Figure 49. Example of Lift Data Collapse Using CL/CLcrParameter
for 80' Fillet Sweep
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Figure 50. Example of Lift Data Collapse Using CL/CLa!Parameterfor Basic SHIPS Planforms
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/. i I !
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Figure 51. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings with 80' Fillet Sweep
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Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaCJings - Wings With 75 '-Sweep Fillets
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/ ‘:cL&~,,,,,,” ‘-’ i i7d i5.00088: 086 49/ iti 69
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Figure 53. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 704Sweep Fillets
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Figure 54.
Wings - Wings With 65"-Sweep Fillets
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cc00
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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
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Figure 57. Correlation of SHIPS Test Data Using WINSTAN Corre-lation Parameter for Nonlinear Lift of Double-DeltaWings - Wings With 45:Sweep Fillets
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Wings - Wings With 35' Sweep Fillets and Basic Wing I
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j i.; 1I
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Figure 59. SHIPS Lift Data Correlation Using WINSTAN Methodfor Double-Delta Wings (Preliminary)
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Figure 60. Scatter Plot for Modified Peckham Lift CorrelationParameter for All 35 SHIPS Planforms
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.
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Figure 61. Modified Peckham Correlation of Lift Data - Basic
Wings
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;o'F*W RUN
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Figure 62. Modified Peckham Correlation of Lift Data - AF = 65'
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Figure 63. Modified Peckham Correlation of Lift Data -AF
= 80'
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Figure 64. Data Collapse With Further Modification of PeckhamLift C orrelation Parameter - Basic Wings
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Figure 65. Data Collapse With Further Mod.ification of PeckhamLift Correlation Parameter - AF = 80
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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
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Figure 67. Data Collapse With Further Modification of PeckhamLift Correlation Parameter - AF = 70
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Figure 68. Data Collapse With Further ModificatAon of PeckhamLift Correlation Parameter - AF = 65
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4 ,. .,,. ..I .I b
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Figure 69. Data Collapse With Further Modification of PeckhamLift Correlation Parameter - AF = 60
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Figure 70. Data Collapse With Further Modification of PeckhamLift Correlation Parameter - AF = 55
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E
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Figure 71. Data Collapse With Further Modificatioon of PeckhamLift Correlation Parameter - AF = 45
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E
Figure 72. Data Collapse With Further Modification of PeckhamLift Correlation Parameter - AF = 35
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Figure 73.
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Ratio of Actual Lift to Predicted Linear Lift of SHIPSPlan,forms With NACA 0008 Airfoils - Basic Wings
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Figure 74. Ratio of Test Lift to Predicted Linear Lift ofSHIPS Planforms with NACA 0008 Airfoils - ,iF = 80'
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Figure 75. Ratio of Test Lift to Predicted Linear Lift ofSHIPS Planform with NACA 0008 Airfoils - AF = 75'
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Figure 76. Ratio of Test Lift to Predicted Lineal Lift ofSHIPS Planforms with NACA 0008 Airfoils - '4, = 70'
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Figure 77. Ratio of Test Lift to Predicted Linear Lift ofSHIPS Planforms with NACA 0008 Airfoils - ,dF = 65'
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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"
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E
Figure 79. Ratio of Test Lift to Predicted Linear Lift of SHIPSPlanforms with NACA 0008 Airfoils - AF = 55' and 53'
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Figure 80. Ratio of Test Lift to Predicted Linear Liftoof SHIPSPlanforms with NACA 0008 Airfoils - AF = 45
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Figure 82. Ratio of Test Lift to Nonlinear Potential Flow Esti-mate for Basic SHIPS Planforms
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Figure 83. Ratio of Test Lift to Nonlinear Potential Flow Esti-mate for SHIPS Planforms Having 80' Fillets'
.
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75 3575 4575 5375 60 w
Figure 84. Variations of Leading-Edge-Suction Ratio with Angleof Attack for Irregular Planforms with 75' Fillet
Sweep
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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
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.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
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.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
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Figure 88. Comparison of Correlation Curve Values of SuctionRatio with SHIPS Basic Wing Test Data
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SHIPS TEST DATA,. I
Figure 89 Comparison of Simple Prediction Approach withSuction Ratio Data
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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
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,
Figure 91. Upper Angle-of-Attack Boundaries for Region 1
E
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: .... . . . . . . . . : ::::::::.rr..... ..... ........
W2
aeg :.:;:;:::.I- :.I:-:f-::-::.:rI:.:-~--..i...- . . . (.. .._ .
.( ,. ..,.... f _. i ,.r--:- : , -.::.. -!4 - 1
Li,.‘/ :-:::.: ‘i
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L: - - 33 -J..iI;,::.]:.::1-,:ii-:--: :J:
Figure 92. Incrementa l Angle of Attack- for Region 2
154
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Unit Reynolds Number
“w, deg
2535
.._ - i .::: _,.. i . . . . ._,_ .__. .. .L:.:!:.. !:. .;_:.,__... a_..:.._: 111:.1:..: _. :--1: 1: .”_..... ..-. ,..,~ . . . .-+-... _:TT-~.l.l.-. .._.: -ii+;;;;.i:.
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. _. --w
Figure 93. Incremental Angle of Attack for Region 3
155
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!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
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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
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---sg+
8
6
1” --
I
-. - ;---I
I..-..,i
I
---c--.I
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.I_i .’I
I
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.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 $2 Function Based on Leading-Edge Radius at Tip
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8---
8 - 35O, A----- - -
I
REF
-4
+2
0
-2
-4
-6
-8
Figure 98. Envelope Correlation Curve for Change ina ofBasic Wings Due to Change in Reynolds Number
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+6
+4
+2
0
-2
-4
1 c
sa3cos.$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
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-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
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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
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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
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Ii-j . . . . . ..i
:-.---...:-I--.,i ,.:. :: _‘._:. .-. 11-L.: lj. ;..
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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- -.--..-.. -
+-- ;
:
---._-- .- _._...._.. ._..--- __- -: :.
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_... .-- i. _....
: ;
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: --_....-. __: ! ~------.-?I.’ -_. _ --_.--.-_-. -~
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! .: 1. /: : I
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.--__.---_. .-._- --..----.:-.--, :. , ! ! ; 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
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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
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-
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
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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
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SHIPS Wind-Tunnel Data
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
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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
SHIPS Wind-Tunnel Data
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
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SHIPS Wind-Tunnel Data
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
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1.2
1.0
.8
CL
.6
.4
.2
1
SHIPS Wind-Tunnel Data
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
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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
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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
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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
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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
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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
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SHIPS Wind-Tunnel Data
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
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60
ac %E 40
of EachBasic Wing
30
20
10
0
cs
SHIPS Wind-Tunnel Data
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
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FS ac
from 80' apexof each wing
17.8
SHIPS Wind-Tunnel Data
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
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_~.._ ---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
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80SYM
T 0
7c
6C
ac %c,
50
40
30
2c
10
0
1 -
I--
l --
_
I --
80”
SHIPS Wind-Tunnel Data
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
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60-
50-n
40..ac
%Sref
30 -.
20 -.
SHIPS Wind-Tunnel Data
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
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SHIPS Wind-Tunnel Data
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
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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
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SHIPS Wind-Tunnel Data
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
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SHIPS Wind-Tunnel Data
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
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SHIPS Wind-Tunnel Data
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
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SHIPS Wind-Tunnel Data
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
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'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
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-: / .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
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30
20
iac
Break
10
20
16
CYBreak
R/I ’
d ‘,\\\\\i\
SHIPS Wind-Tunnel Data
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
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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
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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
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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
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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
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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
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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.
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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)]
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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:
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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
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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
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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
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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$/T @JLainar (3-5)
where cf'cfi= (1 + 0.1256M2)-'12, is used up to the transition
point. At the transition point, Xr, the laminar momentum thick-
ness is matched by an-interative process to a turbulent momentumthickness, which begins some fictitious distance, AX, ahead oftransition. The skin-friction coefficient for the turbulent part
of the flow is calculated from Equation 3-3, where the Reynoldsnumber is calculated from
%L= AX- Xr> . (s/ft)
The value of Cf with transition is finally given by
cf = (: + ?) CfTurb.
(3-e)
(3-7)Calculated values of Cf versus s are presented in Figures 138
L
through 143 for mixed laminar-turbulent flow.
Form Factors
The component form factors, FF, account for the increased
skin friction caused by the supervelocities of the flow,overthe body or s&face and the boundary-layer separation at the
trailing edge. The form factor for the "body" component iscomputed as
FF = l+ 60/FR3 + 0.0025 - FR (3-B)
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whereComponent Length
FR =Width x Height
For "nacelle" components, the form factor is given by
FF = l+ 0.35/FR O-9)
Equations 3-8 and 3-9 were obtained from the Convair AerospaceHandbook (Reference 19) and also appear in the DATCOM (Refer-ence 11).
The airfoil form factors depend upon airfoil type and stream-wise thickness ratio. For 6-series airfoils, the form factor is
given by
FF = l+ 1.44(t/c) + 2(t/c)2 (3-10)
For 4-digit airfoils, the form factor is given by
FF = l+ 1,68(t/c) + 3(t/c)2 (3-11)
For biconvex airfoils, the form factor is given by
FF = 1 + 1.2(t/c) + 100(t/c)4 (3-12)
And for supercritica l airfoils, the form factor is given by
FF = 1 + KICld + 1.44(t/c) + 2(t/c)2 (3-13)
The factor K$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.
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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)
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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.
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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
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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".
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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.
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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
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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
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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:
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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;
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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.
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= 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
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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.
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;.,::: ‘Ii:’‘jj: ;: .:. ,,: j.
.: .:: .
t--k::, : ,:..L..,.:_..:: .. :
.
Figure 135. Basic Lift Curve Correlation Parameter-t--- 7j. .)..:
I 1t
‘ _._L__.
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....... .......... ......
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)]
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+..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
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.l .2 .4 .6 .8 1 2 4 6 8 10 20 40 60 80 100 200 400 600 1000
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*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
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Skin Friction on an Adiabatic Flat Plate,
400 600 1000
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I Fiaure 142. Skin Friction on an Adiabatic Flat Plate,
.1 .2 .4 .6 .8 1 2 4 6 1 400 600 1000
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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
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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
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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
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-6 iI L
I I L 84 A 4
.s .7 .8 .9 1.0
Figure 146. Lifting Surface Correlation Factor for SubsonicMinimum Drag
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“R
Figure 147. Schematic Variation of Suction Ratio with Angle ofAttack
231
- _--
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-,.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
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’
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
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_..
Upper Angle-of-Attack Boundaries for Region 1,. :,. ,, .:,,,,, I I,,*,., I
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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
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AW, deg
0 25
0 350 45A 53A 60
J-q ._: 1 -.:.. _- . . . . . .
/Figure 153. Incremental Angle of Attack for Region 4'
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-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)
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:.1:1li -.-._-..- -,h-:.. .:.1:.:,11-r::
Figure 155. Correction Term for Effect of Fillet Sweep onBoundaries
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_.. _..._ . ..(. . . . . 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
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;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
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..... .., ........ r , .... .... (.-. _. (. ... ...
........... ......... ....... ...
Figure 159. Slopes of Suction Ratio Curves in Region 5
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-.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
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--+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
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..-. :...: :
: _. :. .: : :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
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0 0 Test DataFor Use'in Prediction Method
‘-.--- ------
: :
__ -- -..
:
Figure 165. Upper Angle of Attack Boundary for Region 5
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--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
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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
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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
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,_- _.
Fixed Fillet Sweep
--- Boundary for Basic Wings
I-. i :j ‘. [
Figure 169. Pitching-Moment Coefficient Derivative for
Region 3
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Fixed Fillet Sweep
--- Boundary for Basic Wings
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
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Fixed Fillet Sweep
--- Boundary for Basic Wings
:::. !:.:, 0
V
0
D:q0
: : : ! : : ! , .!/, ; , :
_.,.. , . ., ( ! ..,. .:. .I- .:
Region 5
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Fixed Fillet Sweep
--,:, :..:- ‘.:
EE
,I ::.. :.
-.OlOO_
_:,.. ./
:_.:. :
. . . .
:.:‘I :
~
-. -
.: :.: j..
‘-‘:.’ :
:.:
: . . : . : .
. ----.-.i
Figure 172. Pitching Moment Coefficient Der.ivative for
. Region 6
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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-
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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.
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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
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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:
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(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
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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
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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.
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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.
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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
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“R(tY) ” (cU,-a$ +
2
(a5 -a4) + (a-a5 1
5
@x4-a3
+ (a5-a41 +
(a-a )
a66
w4-a3 >
(a, -a41 + ca6-as >
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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.
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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
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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
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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.
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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
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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
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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
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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
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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
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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
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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
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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
45 45 OOSLE75 45 OOSLE80 45 OOSLE
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
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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
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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
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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
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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
45 45 OOSLE75 45 OOSLE80 45 OOSLE
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
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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:,, '.
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.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
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.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
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.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
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.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
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.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
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.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
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.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-
/
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.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
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.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
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.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
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.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
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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
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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
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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
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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
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.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
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- 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
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45O 60' 65' 70' 75O ROO
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Reynolds Number
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- .-._ --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
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----. -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
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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
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-
:-- -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
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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
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;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 -.:
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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
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; ._._. +. .f . .,.I .f i--i
,
. . .:-- -; ,_. i.;-;_cx.t&& ’ :.,I :
I:,:. .!.,:I.1
L ._.. --_
A-
i
!
I
I
-. -. .:-.A.
i .. ! __-_- ._.-.-
I i/
i
r-7
--‘-.T---‘.
I
-- 1 -.’I :
--:---t-Y-
I : i...1..1..-.-..L-..-...i.. ..;- . ..1..- -1
: : :/ : j :
I-.1..--.
j,: 1 1 I.-l_--+-: -.L---c--L .!...: !.- . ._. ----._. __..-..:
I,; :I
I
r-.-- ! ;: :---+-..--: - _,_, .;. ;;“-+ ! :22 j : i ’
I ;- ; ---- ~ ----. i2*.T. i
__ ..i.--+--L.. .i-...-i . ..- i-.-i.-...l----. .. j: :! : ;
-18 &-L-l
..- .-.--L I
: : : . .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
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,I’:-.I.. if:::.:![:
m
._,:. -- -‘-
1
5-. ,..- .,....: - ..-__ _,.,I:,' :jij "
:: .,:
1.4
:
.-
r_-
:
-_.
:
._
-7
:..
i :
1
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WV
.j
:
L
;i:
I!:a..
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.L.:_.:..
-_--127.-.-.1 I.s4_._.:.4-.,::’, ’7r.::;!J”2”,.:_..:,::’.-.-.::,,,.:iI:j---CL-r:
--.
.
_:
T
.-.
: .:’
. .-.
1.
i.
,_
L .
1. :.
:
-; _.,
,:
I’
;:
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0 NACAq NACA
-.
.-. . . .
‘.
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: “;
,:. I.:
I
‘:: .T’,. .:,
,,,
: ‘.
.:. !..
.:, :I
:: ”
--” 7-:.,
‘.a:.I
:..., . .
‘.,, ; .:. .::,. , . - -. ..,. ‘.’ ‘I”,, . ,. ,..I, , , ,. .;.;. .LL lil. 1;L;, ““,,,8: ,. ..,
.,. .
.I I’.:. . __ ._.l:‘,:I: I;,,: I!.. :.j
.,,I!I ”_, -..:a .,i: .-’
,. :._ .;. :..
7 .i '.
; .:..
Standift' Correlation for NACA 651415 Airfoils at
Reynolds Number
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: : j .._ .--.-..L-..-1--1 .--.-‘--.-; 1 -r-L-
___.i--... 1.. ..,...:- --- 1 i
:I() / !: I4
0 for 32'
0 for 30'
0 for 28'
0 for 26O
0 for 22O
0 for 20°
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
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j./ i j
0
0
I
I-., -- :. ._ :. .L. -.-
: : ; : : : II
:------ -.-
---i -- .-b
.---t.--.-I-.- ..‘--.+.-.. . -. I
: ! : :
..1- .L..i.. -.i... -.L-.. .i-.-. L--i .- .A_ -A-. .i .._.. ._^._: : : : : I
. . _
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
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I I I j4f: I
.:Airfoil
: 0 NACA 0004. "; d 4% Hexagon
: with Sharp . .
.;I:: Leading Edge 1
T&
jpjj;
-.,..,.,:.:.:.j::::77.:I.::’ ., --:.:,.;L::::.:.aI.jj::.. :;
,1i: I!:;
,I!. .j:,
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.‘: ‘:i
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‘:.’ ::;
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wr40
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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
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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
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,..
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
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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
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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.
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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.
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(a) Lift CurveFigure 211. Comparisons Between Basic SHIPS Prediction and Test
for Basic W ing I
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w
s: (b) Drag PolarFigure 211. Continued
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(c) Pitching-Moment Variation with Angle of AttackFigure 211. Continued
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Figure 211. Concluded.
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(a) Lift Curve
Figure 212. Comparisons Between Basic SHIPS Prediction and Testfor Basic Wing III
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(b) -Drag Polar
Figure 212. Continued
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(c) Pitching-Moment Variation with Angle of Attack
Figure 212. Continued
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(d) Pitching-Moment Variation with Lift
Figure 212. Concluded.
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(a) Lift Curve
Figure 213. Comparisons Between Basic SHIPS Prediction and Testfor Basic Wing V
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2 (b) Drag Polar
Figure 213. Continued
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(c) Pitching-Moment Variation with Angle of Attack
Figure 213. Continued.
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ti (d) Pitching-Moment Variation with Lift\D
Figure 213. Concluded.
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(a) Lift CurveFigure 214. Comparisons Begween Basic SHIPS Prediction and Test
Wing I with 80 Fillet
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(b) Drag Polar
Figure 214. Continued
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(c) Pitching-Moment Variation with Angle of Attack
Figure 214. Continued.
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(d) Pitching-Moment Variation with Lift
Figure 214. Concluded
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-mAirfoOn08
.,(a) Lift Curve
Figure 215. Comparisons Between Basic SHIPS Prediction andWing III with 80' Fillet
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-_-_d_L.,
!. !.:I 1 ; ,,,.; !
I7:--,-- yjy.iji’?:.,. I i 1. ..:j::::;:j;...~:p.,::!~,~~~:
(b) Drag PolarFigure 215. Continued
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: ‘.”
:,..
-t-‘;.j:..:.!..:
‘r..-. _..i j
_....: .
(c) Pitching-Moment Variation with Angle of AttackFigure 215. Continued
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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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CL.,!.’ : ..;j :.:
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(d) Pitching-Moment Variation with Lift
Figure 215. Concluded.
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(a) Lift Curve
Figure 216. Comparisons Between Basic SHIPS Prediction and Testfor Wing V with 80' Fillet
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(b) Drag Polar
Figure 216. -Continued
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(c) Pitching-Moment Variation with Angle of Attack
Figure 216. Continued
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(cl) Pitching-Moment Variation with Lift
Figure 216. Concluded.
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(a) Lift Curve
Figure 217. Comparisons of Basic SHIPS Prediction and Test
for Basic Wing I with 35' Fillet
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(b) Drag Polar
Figure 217. Continued
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(c) Pitching-Moment Variation with Angle of Attack
Figure 217. Continued
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(a) Lift Curve
Figure 218. Comparisons of Basic SHIPS Prediction and Testfor Wing III with 55' Fillet
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(b) Drag Polar
Figure 218. Continued
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(c) Pitching-Moment Variation with Angle of Attack
Figure 218. Continued
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(d) Pitching-Moment Variation with Lift
Figure 218. Concluded.
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(a) Lift Curve
Figure 219. Comparisons of Basic SHIPS Prediction and Testfor Wing V with 65' Fillet
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(b) Drag Polar
Figure 219. Continued
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(d) Pitching-Moment Variation with Lift
Figure 219. Concluded
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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'
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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
Figure 220. Continued
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xedure
(c) Drag Polars
Figure 220. Continued
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!dure
(e) Pitching-Moment Variations with Lift
Figure 220. Concluded.
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w (a) Lift Curve
3 Figure 221. Comparisons of Basic SHIPS Prediction and Testfor W ing I with 60 Fillet
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(b) Suction-Ratio Variation with Angle of Attack
Figure 221. Continued
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Yc
(c) Drag Polar
Figure 221. Continued
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(d) Pitching-Moment Variation with Angle of Attack
Figure 221. Continued
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(e) Pitching-Moment Variation with Lift
Figure 221. Concluded
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(a) Lift Curve
Figure 222. Comparisons of Basic and Revised SHIPS Predictionsand Test for Wing III with 65’ Fillet for TwoDifferent Test Facilities
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Airfoil 1 j. 1 .i ( I... I. j ..I j . .I.....!..../ .i....l....l_._.l...S._. 1........: .l
.::. :.:_ .
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'rn t25 ;:
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., . .I.4 ..,.. a’.. .: .12 . ..16 ,.., i.20
:L-l-l-r.- ---L..086-91
(c) Pitching-Moment Variation with Angle of Attack
Figure 222. Continued
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(d) Pitching-Moment Variation with Lift
Figure 222. Concluded
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(a) Lift Curve
Figure 223. Comparisons of Revised SHIPS Prediction and Testfor Wing III with NACA 0004 Airfoil
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(b) Suction-Ratio Variation with Angle of Attacks Figure 223. Continued
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(c) Drag Polar
Figure 223. Continued
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/ I I, I I I I I I i I I I I I I : ,,.., :‘:’ j;; “”
(d) Pitching-Moment Variation with Angle of Attack
Figure 223. Continued
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(e) Pitching Moment Variation with Lift
Figure 223. Concluded
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(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
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(b) Drag Polars
Figure 224. Continued
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/I’.:i,:. 1 ‘1 (:,:.I.:
61 - - - - -----X61 Revised q Tes
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I
!
,:‘,: j:jj:. ,I..,,,.,... II.I.,,I, ,::I I:‘: :::I iii: /iij,... ,,., ,,,. A,., ,I,. I,,._,. ..__ ..A_ .,a. ..a, 4l. . .a.., ..,, I. ,,:, I, ,,I:
‘. : ,,:’ ,, ,. :i:i ::!I ‘,/I
-.1. ‘_:,,, :;i: :,:: s :,:. I,,. I,,.
1 .‘ -:t:-
./ ,,: ‘. ‘., ::::..: :::: .::,:’ ““’: ,,. ,,.. 1,:. :.: .:.. :..: .,.. :.:: ::::
:. .I, ”
1. i
.‘. ., ,,
, :,:. ‘:
.I I I I .I. .I- l....L., L~LiA .Aof Attackc) Pitching-Moment Variation with Angle
Figure 224. Continued
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(d) Pitching-Moment Variations with Lift
Figure 224. Concluded
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(b) Drag Polar
Figure 225. Continued
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,:,.._:..._.:_:_i
I. .I I... 1 I TI[J----/ ;. ,I I,... ,I, :I::.~::li,::l:..:l:,:;ji/ ii:,.. :, !:. : ::.,,A--- .--L .LxL:.L,-:::::.:. :: :: :: :::;:....:‘::, “..,..: ...I.._.:.
f!I... . ... I..... .i.j_
,
(c) Pitching-Moment Variation with Angle of Attack
Figure 225. Continued
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(d) Pitching-Moment Variation with Lift
Figure 225. Concluded
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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
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(b) Drag Polar
Figure 226. Continued
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;. ..;. 1 : .:. ;:. ::'
:: ":,:.. ,.:. . ,.,. .,.. :,,: ,...
: : :' ::,' :': :
.---L -LL . . ..e..
.: ,...
' :I' :' ' ." " ' .'. ..I. , I.,:., ! .:; .,:.
j / 1 1.. 1. 1. (:...I / / /.
1 12. 16 I... 2'.I
/ .: /..
(c) Pitching-Moment Variation with Angle of Attack-
Figure 226. Continued
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(d) Pitching Moment Variation with lift
Figure 226. Concluded
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(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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::I:,‘I,. !
.‘. ‘:: : ,,,.,
I;:~l,.i,j~~ l, 1:: /j..,]:-1
:_: .:,. _:_. . :I:. :..:
(jj:j/II .Iy.vI’:. ji,;/~:!:!:ji /jjf ,f/,Tect
i,,
l.-,L.:
II:: :,,,; ,,:, /,,
.!lil.L.. .I-.::;
-X61 Revised OZ23-bU
: ,,,;::. : ,..t,,!.,, /:’ -- 0255-63
RN26.25 x lO'/m
45.96 x 106/m
(b) Drag Polar
Figure 227. Continued
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1::::1.::.1:..:1 .:..1....1..:.1. ...1....l. ..i..:.I.. .I.:../... I.
:,, ::“., ‘: .,.;:. :,: .:. ::.:
.I J::,; :.. ,. :.L=’ -’ - -.. -- ..-. -._. _. . _-
.I ,I,i .,
j_..._.... .i...
f i
~ . II. .~.. ~i..i.:,___.-- 1
(c) Pitching-Moment Variation with Angle of Attack
Figure 227. Continued
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I 8.1 I _I
--- -
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
Figure 227. Concluded
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(a) Lift Curve
Figure 228. Comparisons of Revisgd SHIPS Prediction and Test
for Wing III with 75 Fillet and Cambered NACA
651412 Airfoil
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00
(b) Drag Polar
Figure 228. Continued
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4 .'$
;I:!!
“i-ii: .'.._ ._
:. :
-1_I. :. I:: :1.
:..:;.. 2.:::. .:j
.,...,:. :. :;,.,
4-4-4-H::
::; ‘:: ‘.,,._.. ._ .._I -... .
(c) Pitching-Moment Variation with Angle of Attack
Figure 228. Continued
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(d) Pitching-Moment Variation with Lift
Figure 228. Concluded
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,tll:: !!:;/:::;:::::.:,;, .: : ., .,;; ;:.; ,‘;’,I. 1” ,j’ ‘i’,‘:Yi: 1;. !vji;: ./: :::: ‘:I: ( ! I, : :::: .:,I ,j;;;;jy
-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
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(b) Suction-Ratio Variations with Angle of Attack
Figure 229. Continued
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30
(c) Drag Polar
Figure 229. Continued
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Figure 229. Continued
3
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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
Figure 229. Concluded
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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
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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
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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
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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
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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
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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'
Figure 230. Continued
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hd t/c
-60 .08---53--45---35---25
RN A 19.67 x lO$n(6 x 106/ft) .05
0
0 4 8 12 16 20 24 28adeg
(e) hF = 60’
Figure 230. Continued
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AU t/c
-60 .08---55--45
---35----25
RN = 19.67 x lO$
(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'
Figure 230. Continued
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*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
Figure 230. Continued
1
20
I
24 28adeg
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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
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.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'
Figure 231. Concluded
20 24adeg
!
.OS
0
-.05
-.lO
28
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"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
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'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'
Figure 232. Continued
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-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"
Figure 232. Continued
“-u.
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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
Figure 232. Continued
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*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'
Figure 232. Concluded
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'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
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-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'
Figure 233. Continued
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.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"
Figure 233. Continued
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*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
Figure 233. Continued
-“.wb&.
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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'
Figure 233. Concluded
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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
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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'
Figure 234. Continued
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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'
Figure 234. Concluded
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.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
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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'
Figure 235. Continued
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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'
Figure 235. Concluded
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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
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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
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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