# Aerodynamics (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
CONTENTS.
* § 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.
* § 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.
* § 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.
* § 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.
* § 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.
* § 144. Introductory. Present State of Knowledge.
* 145. The Sine$^2$ Law of Newton.
* 146. The Sine$^2$ Law not in Harmony with Experience.
* 147. The Square Plane.
* 148. The Square Plane: Centre of Pressure.
* 149. Plausibility of the Sine$^2$ 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.
* § 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.
* § 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.
* § 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.
* § 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.
This work is in the public domain in the United States because it was published before January 1, 1929.
The longest-living author of this work died in 1946, so this work is in the public domain in countries and areas where the copyright term is the author's life plus 77 years or less. This work may be in the public domain in countries and areas with longer native copyright terms that apply the rule of the shorter term to foreign works.
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