Page 11 - Aerodynamics for Engineering Students

viii Contents

5.1.3 The bound vortex system 213
5.1.4 The horseshoe vortex 213
5.2 Laws of vortex motion 214
5.2.1 Helmholtz's theorems 215
5.2.2 The Biot-Savart law 216
5.2.3 Variation of velocity in vortex flow 220
5.3 The simplified horseshoe vortex 222
5.3.1 Formation flying effects 223
5.3.2 Influence of the downwash on the tailplane 224
5.3.3 Ground effects 226
5.4 Vortex sheets 227
5.4.1 The use of vortex sheets to model the lifting effects of a wing 229
5.5 Relationship between spanwise loading and trailing vorticity 234
5.5.1 Induced velocity (downwash) 234
5.5.2 The consequences of downwash - trailing vortex drag 237
5.5.3 The characteristics of a simple symmetric
loading - elliptic distribution 240
5.5.4 The general (series) distribution of lift 243
5.5.5 Aerodynamic characteristics for symmetrical general loading 245
5.6 Determination of the load distribution on a given wing 249
5.6.1 The general theory for wings of high aspect ratio 249
5.6.2 General solution of Prandtl's integral equation 25 1
5.6.3 Load distribution for minimum drag 255
5.7 Swept and delta wings 257
5.7.1 Yawed wings of infinite span 257
5.7.2 Swept wings of finite span 259
5.7.3 Wings of small aspect ratio 26 1
5.8 Computational (panel) methods for wings 269
Exercises 270

6 Compressible flow 273
Preamble 273
6.1 Introduction 274
6.2 Isentropic one-dimensional flow 275
6.2.1 Pressure, density and temperature ratios
along a streamline in isentropic flow 278
6.2.2 The ratio of areas at different sections of the stream
tube in isentropic flow 28 1
6.2.3 Velocity along an isentropic stream tube 283
6.2.4 Variation of mass flow with pressure 284
6.3 One-dimensional flow: weak waves 294
6.3.1 The speed of sound (acoustic speed) 29 5
6.4 One-dimensional flow: plane normal shock waves 296
6.4.1 One-dimensional properties of normal shock waves 297
6.4.2 Pressurdensity relations across the shock 298
6.4.3 Static pressure jump across a normal shock 299
6.4.4 Density jump across the normal shock 300
6.4.5 Temperature rise across the normal shock 300
6.4.6 Entropy change across the normal shock 301
6.4.7 Mach number change across the normal shock 301
6.4.8 Velocity change across the normal shock 302