# Aerodynamics (Lanchester)/Contents

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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 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.

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
^{(illegible text)}by the Aerodynamic Balance. - 247. Author's Experiments. Summary.

Glossary.

Appendices.

Index.