# Aerodynamics (Lanchester)/Index

INDEX.
A.
* Added surface, method of, for the determination of ξ, § 243
* Aerial tourbillion the, § 30
* Aerodone; definition, glossary; trajectories of, § 176; ballasted aeroplane, § 162; experiments with, § 241 et seq.
* Aerodonetics, definition, glossary.
* Aerodrome, aerodromics, definition, glossary.
* Aerodynamic balance, construction of, § 242; employment of, § 246
* Aerodynamic support, theory of, § 112; field of force, § 113
* Aerofoil, definition, § 128, glossary; the, § 172 et seq.; plane and pterygoid, § 128; angles, table of, § 181; best value of β, § 173; form of, §§ 118, 119, 120, 188, 191; a standard of form, § 192; equivalent area, § 192; generation of vortices by, 117; grading of, § 192; pressure on, § 185; best pressure values, § 185; weight of, as affecting least resistance, §§ 169, 194; relative importance of weight, §§ 195, 196, App. IV.; hydrodynamic standpoint, § 189; discontinuity in peripteral system, § 189; angles of leading and trailing edges, § 188
* Aeroplane, the, § 128 et seq.; infinite lateral extent, case of, § 115; in Eulerian fluid, peripteroid motion, typical cases of, § 122; thickness, edge resistance, §§ 128, 158; considered as medium of experiment, § 128; resolution of forces, §§ 128, 156; history of experimental study, § 29; inclined, present state of knowledge, § 144; the sine-squared law of Newton, § 145; the sine-squared law at variance with experience, § 146; the falling plane, the experimentum crucis of the sine-squared law, §§ 145, 233; the aeroplane a problem distinct from the surface in presentation of a solid body, § 144; inclined planes of square proportion, Dines and Langley compared, § 147; centre of pressure, Joessel, Kummer, Langley, § 148; planes in apteroid aspect, §§ 150, 151; planes in pterigoid aspect, §§ 152, 153; superposed planes, § 154; the law of the small angle, § 159; the ballasted aeroplane, § 162; best angle of, § 172; aspect ratio influence on best angle, § 172; tables of pressure values, § 186; flow of Rayleigh-Kirchhoff type, §§ 152, 182, 183; compared to pterygoid form as organ of sustentation, § 184
* Albatros, wing pressure and velocity of flight, § 187; soaring energy available, App. V. ​
* Allen's experiments, fluid resistance, §§ 50, 51
* Allen's law, f. n. § 35
* Apteroid aspect, planes in, §§ 150, 151
* Arched section, §§ 107, 108, 118, 188
* Area, aerofoil area proper to least resistance, § 165; as a factor affecting total load, § 170
* Aspect, meaning of, glossary; apteroid and pterygoid, §§ 151, 153; as affecting pressure reaction, § 144 et seq.; as affecting position of centre of pressure, § 155
* Aspect ratio, meaning, § 150; influence of, on pressure reaction, § 159; employed by experimenters in fight, § 119
* Author's experiments, § 239 et seq.; on discontinuous flow, § 21; on orbital motion of fluid particles, § 17; on attendant vortices, § 125
В.
* Ballasted aeroplane, the, 162; stability of, § 162; determination of aerodynamic constants by means of, §§ 241, 245; launching device for, § 245
* Beaufoy, pressure on normal plane (water), §§ 135, 136
* Best values of β, tables of, § 181
* Body resistance, effect of, § 175
* Borda nozzle, theory of, § 96
* Boundary circulation, positive and negative, § 67; the measure of rotation, § 66
* Bounding flight, theory of, App. IV.
C.
* Cavitation, §§ 12, 82; in connection with screw propeller, § 215
* Centre of pressure, square plane, § 148; theoretical, for infinite lamina, § 155; changes with change of angle, § 148; determined by the ballasted aeroplane, § 245
* Changes of index value, in curve of resistance, § 52
* Compressibility, relative, of air and water, § 1; influence of, on power expended in flight, App. I.
* Conjugate property, of φ and ψ, § 61
* Connectivity, §§ 62, 63
* Conservative system, in periptery, proof of, §§ 115, 116
* Constant sweep, as basis of quantitative theory, § 172 et seq.
* Constants, the aerodynamic, C table of, § 177; c, table of, § 177; κ and ε, § 178; κ and ε, auxiliary hypothesis, § 179; κ and ε, plausible values, table of, § 180
* Continuity of motion, provisional assumption of, § 173
* Contraction, efflux coefficients, §§ 95, 96
* Corresponding speed, law of, § 39
* Counterwake current, the, § 22 ​
* Cyclic motion, simple case, § 62; irrotational, § 64; a cyclic function, § 64; nature of, § 64; two opposite cyclic motions, superposed on translation, § 86; on translation, force at right angles, §§ 89, 90; superpositions plotted, § 122; in simply connected region, § 125; in different planes, compounding of, § 127; in propeller race, § 217
* Cylinder, streamlines of, §§ 21, 79; energy in fluid, § 83
D.
* Dead-water, meaning of term, § 19; negative pressure in the, § 139
* Design of propeller, § 218
* Density, relative, of air and water, § 1; as related to pressure, § 58
* Dimensional investigation, law of fluid resistance, § 36
* Dimensional method, application to phenomenon of discontinuity, § 105
* Dines' experiments, § 223 et seq.; reference to publications, § 223; basis of method, § 224; centrifugal balance, §§ 223, 225; results of resistance experiments, § 226; aeroplane investigations, S§ 227, 228; currents on back of plane, § 228; pressure on normal plane, §§ 133, 136; perforated plates, § 143; curve for square plane, § 147; comparison of results, Dines, Langley, § 153; on law of fluid resistance, § 49
* Dipping front edge, see Arched section; rudimentary development in the ornithoptera, § 184
* Discontinuity, physical and kinetic, §§ 12, 19, 94 et seq.; resistance due to, 19; surface of, due to corners or sharp curves, §§ 18, 20; doctrine of kinetic, §§ 20, 94 et seq.; surface of discontinuity a stratum in viscous fluids, § 20; experimental demonstration of, § 21; consequences and examples of, §§ 21, 30; surface of kinetic discontinuity unstable, § 101, App. III.; kinetic, doctrine of, Kelvin's objections, §§ 100, 101, 102; case of normal plane, § 97; explanation of anomalous case of fluid resistance by doctrine of kinetic discontinuity, § 55
* Discontinuous flow. See Discontinuity.
* Displacement of fluid due to body in motion, § 15; its orbital character, § 16; demonstrated by smoke experiments, § 17; Rankine's investigation, § 18; due to fluid in motion, § 29
* Dissipation of supporting wave, § 117
* Dragon-fly, wing pressure and velocity, § 187
* Duchemin, formula and curve plotted, § 147
* Dynamical equations, § 59
* Dynamic support, Newtonian basis, § 109; broadly considered, § 111; without expenditure of energy, § 111
E.
* Economics of flight, § 163 et seq.
* Efficiency, of propulsion, § 198; of screw propeller, § 206
* Efflux theory, § 95 et seq.; in its relation to pressure on a normal plane, § 140 ​
* Elasticity, influence of, on resistance, § 55; as defining pressure-density relation, § 58; influence of, on power expended in flight. App. I.
* Electro-magnetic analogy, App. VI.
* Energy, expended in fluid resistance, § 40; kinetic, in system of flow, § 81; kinetic, in ψ, φ, squares equal, § 81; of the fluid surrounding a cylinder in motion, § 83; of superposed systems, §§ 84, 85; of vortex pair, § 86; numerical illustration of energy theorem, § 87; conditions of minimum expenditure in flight, §§ 163, 164; in the periptery, § 123
* Entrance and run, § 11
* Equation of continuity, § 59
* Equations of motion, § 59
* Equilibrium, of ballasted aeroplane, § 162
* Eulerian theory, the, § 59 et seq.; deficiencies of, §§ 98, 99
* Evanescent load, special case considered, §§ 104, 115
* Experimental confirmation of dimensional theory of resistance, Froude's experiments, §§ 47, 48; Dines, §§ 49; Allen, § 50
* Extremities, form of, §§ 120, 191
F.
* Field of force, §§ 60, 113
* Finite lateral extent, conditions considered, § 117
* Flight, power expended in, §§ 219, 220; estimated extreme range of, § 220; of golf ball, § 30; bounding or leaping, App. IV.
* Flow, lines of, § 79
* Fluids, properties of, §§ 1, 31, 58
* Fluid prismatic column, as defining application of Newtonian method, § 112
* Flux (ψ function), § 61
* Force, lines of, field of, §§ 60, 113
* Frictional wake, due to viscosity, § 17; its influence on propulsion, §§ 200, 216
* Froude, theory of propulsion, §§ 8, 198, 200, 216; negative slip of propeller, § 200; pressure on normal plane, §§ 135, 136
G.
* Gliding angle, conditions governing, §§ 166, 167; least value, § 174; equation for, § 174; for least horse power, § 176; in excess of theoretical value, § 181
* Grading, of aerofoil, 192; of propeller blade, §§ 208, 209
* Gull (Larus argentatus), wing pressure and velocity of flight, § 187; wing section, § 107
* Gyration surface (Helmholtz), § 99, also App. III.
H.
* Height of aeroplane above earth's surface, as affecting load sustained, § 112 ​
* Helmholtz, on discontinuous motion, §§ 99, 104; Helmholtz-Kirchhoff, pressure on infinite lamina, §§ 97, 136; surface of gyration, § 99, App. III.; surface of discontinuity unstable, App. III.
* Homomorphous motion, in fluid system, general expression for,§ 38
* Horse-power in flight, tables of, § 220
* Hutton, pressure on normal plane, § 136; experiments in resistance, 221, 222
* Hydrodynamic theory, general treatment, Chs. I. and II.; analytical theory of inviscid fluid, § 57 et seq.; applied to conservative system of sustentation, § 121 et seq.
I.
* Impulsive forces, in fluid dynamics, § 60
* Infinite lateral extent, special case of, § 115; aeroplane in pterygoid aspect, case of, § 152
* Infinitesimal load, special case of, § 115
* Interchangeability, of velocity and linear quantities in the dimensional equation of resistance, §§ 43, 45; of φ and ψ in hydrodynamic plotting, § 61
* Inviscid, definition of, § 58
* Irrotation, definition of, § 68; in its relation to velocity potential, § 70
* Irrotational motion, fundamental forms, § 73; compounding by super-position, §§ 73, 74
J.
K.
* Kinematic relations, kinematic-viscosity and kinematic-resistance, § 36
* Kinetic discontinuity. See Discontinuity.
* Kinetic energy. See Energy.
* Kirchhoff-Rayleigh, equation for inclined infinite lamina, §§ 97, 152; plotting, § 152; position of centre of pressure and magnitude of pressure reaction, table, § 97
* Kummer, centre of pressure, § 148
L.
* Lagrange's theorem, an interpretation of, § 71
* Lanchester, form of aerofoil used in 1894, § 108; experiments by, see Author's experiments.
* Langley, pressure on normal plane, §§ 133, 136; experiments with falling plane, a direct disproof of sine-squared law, § 146; curve for plane in apteroid aspect, § 161; curve for plane in pterygoid aspect, § 153; form ​of aeroplane employed, § 153; superposed planes, §§ 154, 233; pressure-velocity and pressure-angle laws, § 232; influence of aspect, § 233; critical angle, or angle of reversal, §§ 233, 234; on the efficiency of an aerial propeller, § 235; misquotes Newton, §§ 232, 238
* Langley's experiments, § 230 et seq.; suspended plane, § 231; resultant pressure recorder, § 232; plane dropper, § 233; component pressure recorder, § 234; dynamometer chronograph. § 235; counterpoised eccentric plane, § 236; rolling carriage, § 237; summary, § 238
* Larmor's theorem, sound momentum, discussion of, App. II. B.
* Leaping or bounding flight, theory of, App. IV.
* Least energy, conditions of, § 164
* Least horse power, values of β and γ, § 176
* Least resistance, equation of, § 171
* Least value of γ, table of, § 181
* Length of blade (screw propeller), conjugate limits, § 212
* Lilienthal, arched section, § 108
* Linear grading, of propeller blades, § 209
* Lines of force (see Force), §§ 60, 113
* Load grading, of propeller blades, § 208
M.
* Mathematical treatment, hydrodynamics, § 59
* Maxwell, definition of viscosity, § 31; method of hydrodynamic plotting due to, § 74
* Moilliard, the ballasted aeroplane mentioned by, § 162; supposed change in position of centre of gravity, § 162
* Momentum, continuous communication of, § 3; principle of no momentum, §§ 5, 6, App. II.; in theory of propulsion, communication of, § 197 et seq.; transference of, from different standpoints, § 7; communication of, as source of sustentation in fight, §§ 109, 111, 112, 160, 161, 174; apparent momentum, § 81; of sound waves, App. II.
* Motion of fluid, in vicinity of streamline body, § 13; relative motion, stream lines, § 14; in vicinity of wing or aerofoil, § 107 et seq.; hypothetical in theory of flight, §§ 160, 161; discontinuous in vicinity of aerofoil, §§ 188, 189, 190, see also Discontinuity; round about propeller and in race, § 217; in wake of a loaded aerofoil, §§ 126, 127
* Multiple connectivity, meaning of, §§ 62, 63
* Mutilation of streamline form, §§ 26, 27
N
* Negative slip, in propulsion, Froude's explanation, § 200
* "Neoids," Rankine's water lines, § 177
* Newton, definition of viscosity, § 31; medium of, its nature, § 2; medium of, essentially discontinuous, § 23; method of, founded on third law of motion, § 2; method of the Newtonian medium, demonstration, § 3 ​
* Newtonian method, application to normal plane, §§ 4, 136; deficiency of the, § 5; application by Rankine and Froude to theory of propulsion, §§ 8, 198; results in the sine-squared law, § 145; sine-squared law plotted, § 147; Newtonian law subjected to experimental investigation, § 222. See also Momentum.
* Newtonian theory modified, the hypothesis of constant sweep, §§ 160, 161, 172, et seq.
* Normal plane, stream lines and lines of flow, for inviscid fluid, § 79; theory and data of the, § 130 et seq.; law of pressure, § 130; pressure due to wind on, § 131; still air pressure determination, § 132; quantitative data, §§ 133, 134; in fluids other than air, § 135; theory summarised, § 136; theory and experiment compared, §§ 136, 137; influence of shape of plane, § 139; in the light of efflux theory, § 140; effect of projecting lip, §§ 140, 141; planes of varying proportions, pressure on, § 142; influence of perforations, § 143
O.
* Orbital motion, of fluid particles, §§ 16, 17; Rankine's curve, § 18
* Osborne Reynolds, on turbulence, § 37
P.
* Parachutist, weight borne by earth's surface, § 6
* Peripteral area, meaning of, § 210; expression for, § 210; in relation to the soaring mode of Hight, App. V.
* Peripteral zone. See Peripteral area.
* Peripteral motion, §§ 126, 127; alternative theories relating to, § 190
* Peripteral system, considered as wave motion, § 116
* Peripteroid motion, types of, § 122; plotting of the field of flow, § 122; energy in the periptery, § 123; modified systems of, § 124; in a simply connected region, § 125
* Periptery, the, f. n. § 107; motion in the, § 107 et seq.
* Phillips, H. F., on arched section of aerofoil, § 108; superposed supporting members, § 154
* Plan-form of aerofoil, aspect ratio, § 119; a standard of form, § 192
* Plausible values, employment of, §§ 177, 178
* Power, conditions of least h.p., § 164; expended in flight, §§ 219, 220
* Poynting, momentum of sound waves, App. II. B. and II. D.
* Pressure, as related to density, 58; lines of equal, §§ 60, 113; distribution in a field of How, § 82; system compounded of accelerative system and steady motion system, § 88; on normal plane, §§ 130, 138; on pterygoid aerofoil, best value of, § 185; on aeroplane, best value of, 186; tables of best values, §§ 185, 186; actual examples, § 187
* Propulsion, theory of, § 197 et seq.; in relation to body propelled, § 199; hypothetical study in, negative slip, § 200; Newtonian method vindicated, jet propulsion fundamentally deficient, § 201; variety of methods of, § 201; the screw propeller, § 202 et seq. ​
* Proximity to earth's surface, influence on load sustained, § 112
* Pterygoid aspect, planes in, §§ 152, 153
* Pterygoid aerofoil, best values of β, least gliding angle, § 173, 174, 181
R.
* Rankine, theory of propulsion, §§ 8, 198; plotting stream lines, § 78; "water lines" derived from source and sink system, § 77
* Rayleigh, momentum of sound waves, App. II.; see also Kirchhoff-Rayleigh.
* Resistance, nature of fluid resistance, § 1 et seq.; as a function of velocity, § 41 ; as a function of size, 42; characteristic curve of, § 43; least resistance, conditions of, § 163 et seq.; complete equation, § 171; of aerodone in flight, plotting, § 176; load for least resistance, §§ 186, 187; of a new kind of hypothetical medium, App. VII.
* Resolution of forces, in case of inclined aeroplane, §§ 128, 156, 167
* Reversal, of relative pressure reaction, critical angle of, § 153
* "Rift," Stokes', § 99
* Robins, inventor of the whirling table, an early experimenter in aerodynamics, § 221
* Robinson, enunciation of pressure law for inclined aeroplane, § 146
* Rotation, in fluid dynamics, conservation of, § 65; measured by boundary circulation, § 66; of fluid, mechanical illustration, § 69
* "Run." See Entrance.
S.
* Sail area (or wing area), measurement of, § 193
* Sailing vessel, peripteral theory applied to the, App. VIII.
* "Scale" of fluid, as due to the viscosity, §§ 36, 56
* Screw propeller, theory of, § 202 et seq. ; peripteral theory, blade treated as analogue of aerofoil, § 202; efficiency of, §§ 203, 204, 235; blade equivalent to sum of its elements, § 205; efficiency computed over whole blade, § 206; thrust grading, § 206; load grading, distribution of pressure on blade, §§ 207, 208; linear grading, § 209; peripteral zone and area, § 210 ; number of blades, § 211; conjugate blade limits, § 212; marine propeller, §§ 214, 215; cavitation, § 215; relative reaction borne by back and face of blade, § 215; marine propeller, limiting blade velocity, § 215
* Sectional form, of aerofoil, §§ 107, 108, 118, 188; of aeroplanes used by Langley and Dines. § 153
* Simply connected, meaning, §§ 62, 63
* Sine-squared law, curve representing, §§ 147, 151; plausibility of the, § 149; applicable in particular case, § 150. See also Newtonian method.
* Skin-friction, no slipping of fluid at surface, § 33; investigation and law of, 34, 35; Froude's experiments in sea water, §§ 47, 48; roughened surfaces, §§ 48, 246; magnitude of, coefficient of, § 157; in its relation ​to edge resistance, § 158; Langley on, § 232; supposed negligibility, Dines in agreement with Langley and Maxim, § 229; anomalous value of, §§ 182, 183; primâ facie evidence of, § 240; determination of coefficient of, § 240 et seq.; as deduced from loss of pressure in pneumatic transmission, § 247
* Small angles, planes at, the laws for, § 159
* Soaring, rationale of, energy derived from wind fluctuation, App. V.
* Sound waves, momentum of, due to displacement of matter, App. II.; velocity of, calculated from communication of momentum, App. II.A.; negative momentum, App. II.A.; Larmor's theorem defective in respect of, App. II.B.; sound pressure experiments discussed, App. II.B.
* Source and sink, definition, § 62; φ, ψ lines of, § 75; superposed on translation, § 76; system the equivalent of a solid, § 78
* Speed of flight, of greatest range and least power, § 164; of birds computed from pressure, § 187
* Sphere, stream lines, § 79
* Stability of flow set up by impulse, § 60
* Stability of aerodone, statement as to, § 239
* Stokes' law, in the curve of resistance, confirmed by Allen, §§ 50, 51
* Stokes, on discontinuous motion, § 99
* Streamline body, Newtonian method not applicable, §§ 8, 9; resistance absent, Froude's demonstration, § 10; transference of energy by, § 11; imperfect form of, § 19; as interpreted by nature and art, fish forms, torpedo forms, § 24; conclusions as to, § 25; mutilations of the, truncated forms, §§ 26, 27; dictum of Froude, limitations of, § 27; definition of, § 23; streamline form not based on analytical theory, § 78; universal character of streamline motion, § 28; all bodies of streamline form in Eulerian fluid, §§ 23, 78, 79
* Stream lines, definition of, as distinct from lines of flow, § 79; examples, plotted from hydrodynamic equation, §§ 79, 122
* Streamline motion. See Streamline body.
* Superposed planes, §§ 122, 154; thickness of layer acted upon by, §§ 160, 161
* Superposed rotation, impossibility of, § 92
* Superposition, of fundamental irrotational forms of motion, §§ 73, 74
* Sweep, meaning of term, § 109, glossary; hypothesis of constant sweep, §§ 109, 160, 131
* "Swish" of stick in motion, explanation of pitch note, § 106; "swish" or "whirring" of bird's wing an evidence of discontinuous motion in periptery, § 190
T.
* Tables, constants C and c, § 177; plausible values κ and ε, § 180 ; β and γ values, § 181; aerofoil pressures appropriate to least resistance, §§ 185, 186
* Tension, fluid tension as hypothesis, § 82 ​
* Thrust grading, of propeller blade, §§ 206, 213
* Torricellian principle, in its application to the field of flow, §§ 82, 138
* Total surface, method for determination of coefficient of skin friction, § 244
* Transverse force, consequent on cyclic motion, §§ 89, 90
* Tree on cliff, as evidence of kinetic discontinuity, § 30
* Turbulence, § 37
U.
V.
* Velocity gradient, in viscous motion, § 31; in skin friction, § 33
* Velocity of flight, of greatest range and least power, § 164; of birds computed from pressure, § 187
* Velocity of design, in its relation to velocity of least resistance, § 168
* Velocity potential, § 60; in cyclic system, § 64; in its relation to irrotational motion, §§ 70, 71
* Vince, experiments with normal and inclined aeroplanes, §§ 146, 222; demonstrates fallacy of sine-squared law, § 222
* Viscosity, as a factor in causing resistance, § 1; definition of, § 31; in its relation to shear, §§ 32, 58; action of, in giving rise to turbulence, § 55; the nearly inviscid fluid, § 104; its influence as modifying the equation of least resistance, § 169; viscous resistance due to distortion of fluid in its passage through a tube of flow, § 32
* Vortex atom theory, § 93, App. II.
* Vortex filaments, trailing from extremities of aerofoil, §§ 125, 126, 127; attached to blade of screw propeller, § 217; generation of, by aerofoil, §§ 117, 126, 189, 190
* Vortex hoop, sustaining a load in flight, § 125
* Vortex motion, a case of, § 72; brief exposition of, § 93; filaments and rings, § 93; compound systems, § 93
W.
* Wake and counterwake, momenta equal and opposite, § 22
* Weight, as affected by aerofoil area, § 170; relative importance of wing or aerofoil weight, § 196, App. IV.; of aerofoil as affecting conditions of least resistance, §§ 171, 194, 195
* Whirling table, the, § 221; invented by Robins, §§ 129, 221; used by Langley, § 230
* Wing area, or sail area, equivalent area, measurement of, §§ 192, 193
* Wing form, arched section, §§ 107, 108, 118; section deduced from theory, § 124; plan form, §§ 119, 120
BRADBURY, AGNEW, & CO. LD., PRINTERS, LONDON AND TONBRIDGE.