# Aerodynamics (Lanchester)/Contents

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.