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 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 (illegible text) by the Aerodynamic Balance.
  • 247. Author's Experiments. Summary.

Glossary.

Appendices.

Index.