1、NASA TECHNICAL NOTE NASA TW D-6946 LATERAL-DIRECTIONAL AERODYNAMIC CHARACTERISTICS OF LIGHT, TWIN-ENGINE, PROPELLER-DRIVEN AIRPLANES by Chester fi Wolowicz and Roxunah B. Yuncey I i i Flight Research Center I EdwardsI Calif: 33523 Provided by IHSNot for ResaleNo reproduction or networking permitted
2、without license from IHS-,-,-This report documents representative state-of-the-art analytical procedures and design data for predicting the lateral-directional static and dynamic stability and control characteristics of light, twin-engine, propeller-driven airplanes for propeller-off and power-on co
3、nditions. Although the consideration of power effects is limited to twin-engine airplanes, the propeller-off considerations are applicable to single-engine airplanes as well. The procedures are applied to a twin-engine, propeller- driven, semi-low-wing airplane in the clean-confi-eration through the
4、 linear lift range. The calculated derivative characteristics are compared with wind-tunnel and flight data. Included in the calculated characteristics are the spiral mode, roll mode, and Dutch roll mode over the speed range of the airplane. All calculations are documented. *For sale by the National
5、 Technical Information Service, Springfield, Virginia 22151 TERISTICS OF LIGHT, Light airplane Aerodynamic characteristics - prediction Unclassified - Unlimited 22. Price* $6.00 A 21. No. of Pages 2 93 19. Security Classif. (of this report) Unclassified 20. Security Classif. (of this page) Unclassif
6、ied Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CONTENTS TABLES RELATED TO THE SIWJE CT AIRPLANE vii FIGURES COMPARING CALCULATED CHARACTERISTICS .
7、WITH EL AND FLIGHT DATA ix SUMMARY . 1 1 . 0 INTRODUCTION 2 2.0 SCOPE OF TSEE STUDY 3 3.0 THE AIRPLANE 4 3.1 Center-of-Gravity Positions Used in the Analysis . 7 3.2 Pertinent Geometric Parameters 8 3.2.1 Symbols 8 4. 0 PBEDICTION OF PROPELLER-OFF AERODYNAMIC CHAMCTEIUSTICS. 19 4.1 Side-Force Deriva
8、tive. CyR 17 I- . 4.1.1 Wing Contribution. + (“dl- 17 4.1.2 FuselageContributionto Cy 18 P 4.1.3 Nacelles Contribution to Cy 19 P 4.1.4 Vertical-Tail Contribution to C 20 y 4.1.5 C of the Complete Airplane 23 Yi? 4.1.6 Symbols 24 4.2 Weathercock Stability. C . 41 4.2.1 Wing Contribution to CnB . 41
9、. 42 4.2.2 Fuselage Contribution t6 4.2.3 Nacelles Contribution to C nB.eeeeeeeee.e 44 4.2.4 Vertical-Tail Contribution to Cq 44 . 4.2.5 Weathercock Stability of the Complete Airplane 44 4.2.6 Symbols 45 4. 3 Effective Dihedral. C . 57 ZB 4.3.1 Wing Contributionto C . 57 b 4.3.2 Effect of Fuselage o
10、n Wing Contribution to C . 59 L 4.3.3 Vertical- Tail Contribution to C 60 lP 4.3.4 C of the Complete Airplane . 61 lP 4.3.5 Symbols 61 4.4 Rolling and Pawing Moments Due to Aileron.Deflection 77 . 4.4.1 Rolling Moment 13ue to Aileron Deflection. C 71 Provided by IHSNot for ResaleNo reproduction or n
11、etworking permitted without license from IHS-,-,-CONTENTS . Continued Page 4.4.2 Yawing Moment Due to Aileron IEeflection. C 79 qa 4.4.3 Symbols . 81 4.5 Yawing and Rolling Moments Due to Rudder Deflection 97 4.5.1 Side Force Due to Rudder Deflection. C 97 %r . 4.5.2 Yawing and Rolling Moments Due t
12、o Rudder Deflection 98 4.5.3 Symbols . 99 5.0 PI33 DICTION OF POWER-ON STATIC STABILITY AND CONTROL CHARACTEXISTICS 108 5.1 Power-On Static Stability Characteristics 109 5.1.1 Power Effects on C 109 y 5.1.2 Power Effects on CnB 112 5.1. 3 Power Effects on C 113 b 5.1.4 Symbols . 115 5.2 Power-On Con
13、trol Characteristics 132 5.2.1 Aileron Parameters . 132 5.2.2 Rudder Parameters . 132 5.2.3 Symbols . 132 5. 3 Comparison of Predicted Static Stability and Control Characteristics With Flight Data 136 5.3.1 Flight-Test Conditions and Maneuvers . 136 5.3.2 Analysis of the Dutch-Roll Maneuver Flight D
14、ata 136 5.3.3 Analysis of the Increasing-Sideslip-Maneuver Flight Data . 140 5,3.4 Comparison of Predicted Stability and Control . Characteristics With Flight Data 140 5.3.5 Symbols . 142 6.0 DYNAMIC DEWATWE CHARACTERISTICS 150 6.1 Damping-in-Roll Derivative. 6 . 151 “p 6.1.1 Wing-Body Contribution
15、to C . 151 43 6.1.2 Horizontal- Tail Contribution 6 C 152 113 6.1.3 Vertical-Tail Contribution to C 153 ZP 6.1. 4 Nacelles Contribution to 6. 154 6.1 . 6 Summary of Contributions to C 158 EP 6.1.7 Symbols . 158 . 6.2 Damping-in- Yaw Derivative. C, 179 6.2.1 Wing Contribution to Cn 179 r 6.2.2 Fusela
16、ge Contribution to Cnr 181 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CONTENTS . Continued Page 6.2.3 Vertical- Tail Contribution to Cnr 181 . 6.2.4 Power Contributions to Cnr and Summary 182 6.2.5 Symbols 183 . 6.3 Roll-Due- to- Yawing Derivati
17、ve. Czr 195 . 6.3. 1 WingContributionto C 195 z r 6.3. 2 Vertical-Tail Contribution to C 197 r . 6.3. 3 Power Contributions to C 197 r 6.3.4 Summary of Contributions to Cz 198 r 6.3.5 Symbols 199 . 6.4 Yaw-Due-to-Rolling Derivative. C 208 n 6.4.1 Wing Contribution to Cnp 208 6.4.2 Vertical-Tail Cont
18、ribution to Cn 210 P . 6.4.3 Power Contributions to C 210 n 6.4.4 Summary of Contributions to Cnp 6.4.5 Symbols 6.5 The Derivatives C nb and 6.5.1 Symbols 6.6 Comparison of Predicted Dynamic Derivatives With Flight Data . 6.6.1 Analysis of Flight Data 6.6.2 Comparison of Predicted and Flight-Determi
19、ned Dynamic l?e rivative s 6.6.3 Symbols . 7. 0 DYNAMIC STABILITY CHAMCTER,I STIGS 7-1 Equations of Motion 7.1,1 Symbols 7.2 Determination of Roots of Characteristic Equation Men Spiral Divergence. Roll Subsidence. and Dutch Roll Modes Exist . 7.2. P Spiral Divergence Root 9.2.2 Roll absidence Root
20、. . 7.2. 3 Roots of the Dutch Roll Mode 7.2.4 Symbols 7.3 Ratio of Roll to Sideslip in the Dutch MlP Mode 7.3.1 Roll-to-Sideslip Ratio 7.3.2 Roll-to-Sideslip Phase Angle . 7.3.3 Comparison of Predicted Characteristics With Flight Data 7.3.4 Symbols . 7. 4 Roll Performance 7.4. P Derivation of the Ro
21、ll Equation . 7.4. 2 Steady- State Roll Rate Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-CONTENTS . Concluded Page 7.4.3 Apparent Roll Mode Constant . 265 7.4.4 Roll and Dutch Roll Mode Coupling 266 7.4.5 Symbols 269 8.0 REFERENCES 281 Provided b
22、y IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-TABLES RELATED TO SUBJECT AIRPLANE Page 3-1 MANUFACTURER S PHYSICAL CHARACTERISTICS OF THE SUBJECT AIRPLANE . . . . . . . . . . . . . . . . . * 5 PREDICTION OF PROPE LLER-OFF AERODYNAMIC CHARACTERISTICS 4.1.1-1 W
23、INGCONTRIBUTIONTO C . . . . . . . . . . . . . . . . , * 28 Yp 4.1.2-1 FUSELAGE CONTRIBUTION TO Cyp . . . . . . . . . . . . . . . . . 28 4.1.4-1 VERTICAL-TAIL CONTRIBUTION TO C . . . . . . . . . . . . . . 30 y 4.2.1-1 WINGCONTIUBUTIONTO Cn e.e.e.e. 48 P 4.2,2-1 FUSELAGE CONTRIBUTION TO Cn . . . . . .
24、 . . . . . . . . . . , 49 P 4.2.3-1 NACELLE CONTRIBUTION TO CnP . e . a e . e m e . e e a e e e e 50 4.2.4-1 VERTICAL-TAILCONTRIBUTIONTO Cn . . . . . . . . . . . . . . 51 P 4.2,5-1 WEATHERCOCK STABILITY OF THE AIRPLANE. . . . . . . . . . . 52 4.3.1-1 WING CONTRIBUTION TO C . . . . . . . . . . . . .
25、. . . . . . . 64 lP 4.3.2-1 EFFECTOFFUSELAGE ONWINGCONTIUBUTIONTO C . . . . . 65 lP 4.3.3-1 VERTICAL-TAIL CONTRIBUTION TO C . . . . . . . . . . . . . , 66 lp 4.3.4-1 C OFTHECOMPLETEAIRPLANE . 67 lp 4,4.1-1 ROLLINGMOMENTSDUETOAILERONS, C . . . . . . 84 6a 4.4.2-1 YAWINGMOMENTSDUE TOAILERONS, Cq . . .
26、 . . . . . . . . 86 a 4.5.1-1 SIDEFORCE DUETORUDDERDEFLECTION, C . . . + . . . 0. 103 Y6r 4.5.2-1 G AND ROLLING MOMENTS DUE TO RUDDER DEFLECTION. . . . . . . . . . . . . . . . . . . * . 104 PREDICTION OF POWE R-ON STABILITY AND CONTROL CHARACTERISTICS 5.1.1-1 EFFECTOFPOWERON C . 119 vii Provided by
27、IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-.TABLES - Concluded Page 5.11.2-1 EFFECT OF POSIIIERON Cn . . . . . . . . . . . . . . . . . . . . 122 P 5,1,3-1 EFFECTOFPOWERON C . . . . . . . . , . . . . . . . . 124 lP 5.3-1 TRANSFORMATION OF DERIVATIVES FROM ST
28、ABILITY TO BODY AXIS . . . . . . . . . . . . . . . . . . , . . . . . . . . 146 DYNAMIC DERNATIW CHARACTERISTICS 6.1,l-1 WING-FUSELAGE CONTRIBUTION TO C . . . . . . . . . . , , I63 ZP 6,1.4-1 CONTIXIBUTION OF NACELLES TO PROPELLER-OFF C . . . . 166 ZP 6.1.5-1 EFFECT OF POWER ON WING CONTRIBUTION TO C
29、 . . . . . . 167 ZP 6.1.5-2 CONTRIBUTION OF PROPELLER NORMAL FORCES TO C . . . . 168 lp 6.1.5-3 POWER-INDUCED CHANGE I?X NACELLE CONTRIBUTIOPJ TOCb ee.aeeeeee*eeeeeeeooeeee 169 6.1.6-1 SUMMARY OF CONTRIBUTIONS TO C . . . . . . . . . . . . . . 170 ZP 6.2,l-1 WING CONTRIBUTION TO C, . . . . . . . . .
30、. . . . . . . . . , . 187 6.2.3-1 VERTICAL-TAIL CONTRIBUTION TO en,. . . . . . . , . . , . . . 188 6.2.4-1 SUMMARY OF CONTRIBUTIONS TO Cnr INCLUDING POWER. . . 189 6.3.1-1 WINGCONTRIBUTIONTO Clr e e a . . . . . . . . . . . . . . . 202 6.3,2-1 VERTICAL-TAIL CONTR3BUTION TO C . . . . . . . . . . . . .
31、 , 203 2, 6,3,3-1 EFFECT OF POWER ON WING CONTNBUTION TO C . . . . . . 205 1, 6,3,4-1 SUMMARY OF CONTR3IBUTIONS TO C . . . . . . . . . . . . . . . 205 1, 6.4.2-1 VERTICAL-TAIL CONTRIBUTION TO . . . . . . . . . . . . . . 217 P 6.4.4-1 SUMMARY OF CONTRIBUTIONS TO Cnpe e e e * e 0 e e e a e 0 218 viii
32、Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-FIGURES COMPAHNG CALCULATED CHARPICTERISTICS WITH WNDrTUPJNEk AND FLIGHT DATA PROPELLE R-OFF CHPaRBCTERITICS 4,P, 5-1 Comparison of calculated C with wind-tunnel data. P Propellers off. 4 0 4,2.5-1 Comp
33、arison of calculated C with wind-tunnel data. nP Propellers off, 56 4.3.4-1 Comparison of calculated C with wind-tunnel data. lP Propellers off, 7 6 4.4.1-6 Comparison of calculated rolling-moment effectiveness of ailerons of subject airplane with wind-tunnel data. . 94 4.4.2-2 Comparison of calcula
34、ted yawing moment due to ailerons of subject airplane with wind-tunnel data, 96 4,5.2-1 Comparison of calculated and wind-tunnel values of rudder side force and yawing- and rolling-moment effectiveness. 107 POWER-ON CHAIEaACTEHSTIeS 5.1.1-4 Comparison of calculated G with wind-tunnel data as a funct
35、ion of angle of attack and thrust coefficient. 129 5.1.2-1 Comparisonofcalculated C withwind-tunneldataasa nP function of angle of attack and thrust coefficient. 130 5.1.3-1 Comparison of calculated C with wind-tunnel data as a 20 function of angle of attack and thrust coefficient, 131 5.2-1-1 Compa
36、rison of calculated aileron characteristics with wind-tunnel data, . 134 5-2.2-1 Comparison of calculated rudder characteristics with wind-tunnel data. . 135 5.3,4-P Comparison of predicted static stability characteristics with flight data relative to body axes. . ,. 148 5.3.4-2 Comparison of predic
37、ted control characteristics with flight data relative to body axes. 149 6.6.2-1 Comparison of flight-determined and calculated dynamic stability derivatives relative to the body axes as a function of angle of attack, 233 7.2,3-2 Predicted period and damping characteristics of the subject airplane co
38、mpared with flight data. . 253 Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-FIGURES - Concluded Page 7.3.3-1 Predicted amplitude ratio and phase angle characteristics of the subject airplane for trim level-flight conditions compared with several f
39、light-determined values, . . . . . . . . 260 7.4.2-1 Time histories of roll rate response to aileron input and bw - , shown as a function the wing-tip helix angle, pss 2V Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IHS-,-,-LATERAL-DIRECTIONAL AERODYNAMIC
40、 CHARACTERISTICS OF LIGHT, TWIN-ENGINE, PROPELLER-DRIVEN AIR PLANES Chester H. Wolowicz and Roxanah B. Pancey Flight Research Center Representative state-of-the-art analytical procedures and design data for predicting the lateral-directional static and dynamic stability and control characteristics o
41、f light, twin-engine, propeller-driven airplanes for propeller-off and power-on conditions are documented. Although the consideration of power effects is limited to twin-engine airplanes, the propeller-off considerations are applicable to single-engine airplanes as well. The procedures are applied t
42、o a twin-engine, propeller-driven, semi-low-wing airplane in the clean configuration to determine the lateral and directional control deriv- atives as well as the static and dynamic stability derivatives as functions of angle of attack and power condition through the linear lift range of the airplan
43、e. Also determined are the spiral mode, roll mode, and Dutch roll characteristics for level-flight conditions over the speed range of the airplane. All calculations are documented. Attempts to calculate the weathercock stability characteristics indicated a need to account for wing-body interference
44、effects on the body contribution as a function of angle of attack and vertical position of the wing relative to the body. Vertical-tail-off wind- tunnel data of a single-engine version of the subject airplane are used to expand the design nomograph from which the body-plus -wing-body contribution to
45、 weathercock stability was determined in order to obtain the contribution for a semi-low-wing airplane as a function of angle of attack. Application of the expanded nomograph to the subject airplane resulted in improved correlation of calculated weathercock stability character- istics with wind-tunn
46、el and flight data at low angles of attack. For additional improve- ment,in correlation, there is a need for design data to account for the effects of angle of attack on the sidewash acting on the vertical tail. The correlation of the calculated effective dihedral with wind-tunnel data was excel- le
47、nt through the linear lift range for all power conditions considered, However, flight- determined values were approximately 40 percent to 50 percent smaller than wind-tunnel values, Within the scope of this study, it was not possible to identify in-flight phenomena which altered the contribution of
48、the wing or the wing-fuselage interference to the varia- tion of rolling-moment coefficient with sideslip and which were not accounted for in the full-scale wind-tunnel tests of the airplane. The effect of the discrepancy on several response characteristics is noted at the end of this summary. The calculated directional control derivatives correlated well with wind-tunnel and flight data throughout the linear lift range and all power conditions investigated. Provided by IHSNot for ResaleNo reproduction or networking permitted without license from IH
