Aerodynamics (Lanchester)

by Frederick William Lanchester

 

AERODYNAMICS

Photograph Showing Flow of Air Round a Cylinder in Motion.

[Frontispiece.

Aerodynamics

 

Constituting the First

Volume of a Complete

Work On Aerial Flight

 

BY

 

F. W. Lanchester

 

With Appendices on the Velocity and Momentum of Sound Waves, on the Theory of Soaring Flight, etc

 

London
Archibald Constable & Co. Ltd.
Orange Street Leicester Square

 

1907

Chapters (not listed in original)

• Preface

CONTENTS.

CHAPTER I.

Fluid Resistance and its Associated Phenomena.

• § 1. Introductory.
• 2. Two Methods.
• 3. The Newtonian Method.
• 4. Application of the Newtonian Method in the Case of the Normal Plane.
• 5. Deficiency of the Newtonian Method. (The Principle of No Momentum.)
• 6. Illustrations of the Principle of No Momentum.
• 7. Transmission of Force. Comparison of Fluid and Solid.
• 8. When the Newtonian Method is Applicable.
• 9. On Stream-line Form.
• 10. Froude's Demonstration.
• 11. The Transference of Energy by a Body.
• 12. Need for Hydrostatic Pressure. Cayitation.
• 13. The Motion of the Fluid.
• 14. A Question of Relative Motion.
• 15. Displacement of the Fluid.
• 16. Orbital Motion of the Fluid Particles.
• 17. Orbital Motion and Displacement. Experimental Demonstration.
• 18. Orbital Motion. Eankine's Investigation.
• 19. Bodies of Imperfect Stream-line Form.
• 20. The Doctrine of Kinetic Discontinuity.
• 21. Experimental Demonstration of Kinetic Discontinuity.
• 22. Wake and Counterwake Currents.
• 23. Stream-line Motion in the Light of the Theory of Discontinuity.
• 24. Stream-line Foiin in Practice.
• 25. Stream-line Fonn. Theory and Practice Compared.
• 26. Mutilation of the Stream-line Form.
• 27. Mutilation of the Stream-line Form—continued.
• 28. Stream-line Flow General.
• 29. Displacement due to Fluid in Motion.
• 30. Examples Illustrating Effects of Discontinuous Motion.

 

CHAPTER II.

Viscosity and Skin Friction.

• § 31. Viscosity. Definition.
• 32. Viscosity in Relation to Shear.
• 33. Skin Friction.
• 34. Skin Friction. Basis of Investigation.
• 35. Law of Skin Friction.
• 36. Kinematical Relations.
• 37. Turbulence.
• 38. General Expression. Homomorphous Motion.
• 39. Corresponding Speed.
• 40. Energy Relation.
• 41. Resistance-Velocity Curve.
• 42. Resistance-Linear Curve.
• 43. Other Relations.
• 44. Form of Characteristic Curve.
• 45. Consequences of Interchangeability of V and l.
• 46. Comparison of Theory with Experiment.
• 47. Froude's Experiments.
• 48. Froude's Experiments—continued. Roughened Surfaces.
• 49. Dines' Experiments.
• 50. Allen's Experiments.
• 51. Characteristic Curve, Spherical Body.
• 52. Physical Meaning of Change of Index.
• 53. Changes in Index Value—continued.
• 54. The Transition Stages of the Characteristic Curve.
• 55. Some Difficulties of Theory.
• 56. General Conclusions.

 

CHAPTER III.

The Hydrodynamics of Analytical Theory.

• § 57. Introductory.
• 58. Properties of a Fluid.
• 59. Basis of Mathematical Investigation.
• 60. Velocity Potential, φ Function.
• 61. Flux. ψ Function. φ and ψ interchangeable.
• 62. Sources and Sinks.
• 63. Connectivity.
• 64. Cyclic Motion.
• 65. Fluid Rotation.—Conservation of Rotation.
• 66. Boundary Circulation, the Measure of Rotation.
• 67. Boundary Circulation. Positive and Negative.
• 68. Rotation, Irregular Distribution. Irrotation, Definition.
• 69. Rotation, Mechanical Illustration.
• 70. Irrotational Motion in its Relation to Velocity Potential.
• 71. Physical Interpretation of Lagrange's φ Proposition.
• 72. A Case of Vortex Motion.
• 73. Irrotational Motion. Fundamental or Elementary Forms. Compounding by Superposition.
• 74. The Method of Superposed Systems of Flow.
• 75. ψ, φ, Lines for Source and Sink System.
• 76. Source and Sink, Superposed Translation.
• 77. Rankine's Water-lines.
• 78. Solids Equivalent to Source and Sink Distribution.
• 79. Typical Cases constituting Solutions to the Equations of Motion.
• 80. Consequences of inverting ψ, φ Functions in Special Cases. Force at right angles to Motion.
• 81. Kinetic Energy.
• 82. Pressure Distribution. Fluid Tension as Hypothesis.
• 83. Application of the Theorem of Energy.
• 84. Energy of Superposed Systems.
• 85. Example: Cyclic Superposition.
• 86. Two opposite Cyclic Motions on Translation.
• 87. Numerical Illustration.
• 88. Fluid Pressure on a Body in Motion.
• 89. Cases fall into Three Categories.
• 90. Transverse Force Dependent on Cyclic Motion. Proof.
• 91. Difficulty in the case of the Perfect Fluid.
• 92. Superposed Rotation.
• 93. Vortex Motion.
• 94. Discontinuous Flow.
• 95. Efflux of Liquids.
• 96. The Borda Nozzle.
• 97. Discontinuous Flow. Pressure on a Normal Plane.
• 98. Deficiencies of the Eulerian Theory of the Perfect Fluid.
• 99. Deficiencies of the Theory—continued. Stokes, Helmholtz.
• 100. The Doctrine of Discontinuity attacked by Kelvin.
• 101. Kelvin's Objections Discussed.
• 102. Discussion on Controversy—continued.
• 103. The Position Summarised.
• 104. The Author's View.
• 105. Discontinuity in a Viscous Fluid.
• 106. Conclusions from Dimensional Theory.

 

CHAPTER IV.

Wing Form and Motion in the Periptery.

• § 107. Wing Form. Arched Section.
• 108. Historical.
• 109. Dynamic Support.
• 110. In the Region of a Falling Plane. Up-current.
• 111. Dynamic Support Reconsidered.
• 112. Aerodynamic Support.
• 113. Aerodynamic Support—continued. Field of Force.
• 114. Flight with an Evanescant Load.
• 115. Aeroplane of Infinite Lateral Extent.
• 116. Interpretation of Theory of Aeroplane of Infinite Lateral Extent.
• 117. Departure from Hypothesis.
• 118. On the Sectional Form of the Aerofoil.
• 119. On the Plan-form of the Aerofoil: Aspect Ratio.
• 120. On Plan-form—continued. Form of Extremities.
• 121. Hydrodynamic Interpretation and Development.
• 122. Peripteroid Motion.
• 123. Energy in the Periptery.
• 124. Modified Systems.
• 125. Peripteroid Motion in a Simply-connected Region.
• 126. Peripteral Motion in a Real Fluid.
• 127. Peripteral Motion in a Real Fluid—continued.

 

CHAPTER V.

The Aeroplane. The Normal Plane.

• § 128. Introductory.
• 129. Historical.
• 130. The Normal Plane. Law of Pressure.
• 131. Wind Pressure Determinations.
• 132. Still Air Determinations.
• 133. Quantitative Data of the Normal Plane.
• 134. Resistance a Function of Density.
• 135. Fluids other than Air.
• 136. Normal Plane Theory Summarised.
• 137. Deductions from Comparison of Theory and Experiment.
• 138. The Nature of the Pressure Reaction.
• 139. Theoretical Considerations relating to the Shape of the Plane.
• 140. Comparison with Effiux Phenomena.
• 141. The Quantitative Effect of a Projecting Lip.
• 142. Planes of Intermediate Proportion.
• 143. Perforated Plates.

 

CHAPTER VI.

The Inclined Aeroplane.

• § 144. Introductory. Present State of Knowledge.
• 145. The Sine² Law of Newton.
• 146. The Sine² Law not in Harmony with Experience.
• 147. The Square Plane.
• 148. The Square Plane: Centre of Pressure.
• 149. Plausibility of the Sine² Law.
• 150. The Sine Law Applicable in a Particular Case.
• 151. Planes in Apteroid Aspect (Experimental).
• 152. The Infinite Lamina in Pterygoid Aspect.
• 153. Planes in Pterygoid Aspect (Experimental).
• 154. Superposed Planes.
• 155. The Centre of Pressure as affected by Aspect.
• 156. Resolution of Forces.
• 157. The Coefficient of Skin Friction.
• 158. Edge Resistance in its Relation to Skin Friction.
• 159. Planes at Small Angles.
• 160. The Newtonian Theory Modified. The Hypothesis of Constant "Sweep."
• 161. Extension of Hypothesis.
• 162. The Ballasted Aeroplane.

 

CHAPTER VII.

The Economics of Flight.

• § 163. Energy Expended in Flight.
• 164. Minimum Energy. Two Propositions.
• 165. Examination of Hypothesis.
• 166. Velocity and Area both Variable.
• 167. The Gliding Angle as affected by Body Resistance.
• 168. Relation of Velocity of Design to Velocity of Least Energy.
• 169. Influence of Viscosity.
• 170. The Weight as a Function of the "Sail Area."
• 171. The Complete Equation of Least Resistance.

 

CHAPTER VIII.

The Aerofoil.

• § 172. Introductory.
• 173. The Pterygoid Aerofoil. Best Value of β.
• 174. Gliding Angle.
• 175. Taking Account of Body Resistance.
• 176. Values of β and γ for Least Horse Power.
• 177. The Values of the Constants.
• 178. On the Constants κ and ε.
• 179. An Auxiliary Hypothesis.
• 180. κ and ε Plausible Values.
• 181. Best Values of β. Least Values of γ.
• 182. The Aeroplane. Anomalous Value of ξ.
• 183. Aeroplane Skin Friction. Further Investigation.
• 184. Some Consequences of the Foregoing Aeroplane Theory.
• 185. The Weight per Unit Area as related to the Best Value of β.
• 186. Aeroplane Loads for Least Resistance.
• 187. Comparison with Actual Measurements.
• 188. Considerations relating to the Form of the Aerofoil.
• 189. The Hydrodynamic Standpoint.
• 190. Discontinuous Motion in the Periptery.
• 191. Sectional Form.
• 192. A Standard of Form.
• 193. On the Measurement of "Sail Area."
• 194. The Weight of the Aerofoil as influencing the Conditions of Least Resistance.
• 195. A Numerical Example.
• 196. The Relative Importance of Aerofoil Weight.

 

CHAPTER IX.

On Propulsion, the Screw Propeller, and the Power Expended in Flight.

• § 197. Introductory.
• 198. The Newtonian Method as applied by Rankine and Froude.
• 199. Propulsion in its Relation to the Body Propelled.
• 200. A Hypothetical Study in Propulsion.
• 201. Propulsion under Actual Conditions.
• 202. The Screw Propeller.
• 203. Conditions of Maximum Efficiency.
• 204. Efficiency of the Screw Propeller. General Solution.
• 205. The Propeller Blade Considered as the Sum of its Elements.
• 206. Efficiency Computed over the Whole Blade.
• 207. Pressure Distribution.

• 208. Load Grading.
• 209. Linear Grading and Blade Plan Form.
• 210. The Peripteral Zone.
• 211. Number of Blades.
• 212. Blade Length. Conjugate Limits.
• 213. The Thrust Grading Curve.
• 214. On the Marine Propeller.
• 215. The Marine Propeller—continued. Cavitation.
• 216. The Influence of the Frictional Wake.
• 217. The Hydrodynamic Standpoint. Superposed Cyclic Systems.
• 218. On the Design of an Aerial Propeller.
• 219. Power Expended in Flight.
• 220. Power Expended in Flight—continued.

 

CHAPTER X.

Experimental Aerodynamics.

• § 221. Introductory.
• 222. Early Investigations—Hutton, Vince.
• 223. Dines' Experiments. Method.
• 224. Dines' Method. Mathematical Expression.
• 225. Dines' Method—continued.
• 226. Dines' Results. Direct Resistance.
• 227. Dines' Experiments—continued. Aeroplane Investigations.
• 228. Dines' Aeroplane Experiments—continued.
• 229. Dines' Experiments Discussed.
• 230. Langley's Experiments. Method.
• 231. Langley's Experiments. "The Suspended Plane."
• 232. Langley's Experiments. "The Resultant Pressure Recorder."
• 233. Langley's Experiments. "The Plane Dropper."
• 234. Langley's Experiments. "The Component Pressure Recorder."
• 235. Langley's Experiments. "The Dynamometer Chronograph."
• 236. Langley's Experiments. "The Counterpoised Eccentric Plane."
• 237. Langley's Experiments. "The Rolling Carriage."
• 238. Langley's Experiments. Summary.
• 239. The Author's Experiments. Introductory.
• 240. Scope of Experiments.
• 241. Author's Experiments. Method.
• 242. Author's Experiments. Method—continued.
• 243. Method of Added Surface.
• 244. Method of Total Surface.
• 245. Method of the Ballasted Aeroplane.
• 246. Determination of ξ by the Aerodynamic Balance.
• 247. Author's Experiments. Summary.

Glossary.

Appendices.

Index.

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