Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/80

§ 43 in the interpretation of the curve the linear and velocity quantities alternatively represented by abscissae are interchangeable, and the scale value of the axis of $$x$$ is proportional to the magnitude of the kinematic viscosity, and the scale value of the axis of $$y$$ to the square of the kinematic viscosity.

§ 44. Form of Characteristic Curve.—The form of the characteristic curve of resistance for different forms of body can, in all probability, only be determined experimentally. There are three ways by which the curve could be plotted, (a) by experimentally determining $$R$$ for different values of $$V$$ (or vice versa), for any given body; (b) by the determination of the resistances of a number of bodies of geometrically similar form but of different scale dimensions, at any standard velocity; and, (c) by employing fluids of different viscosity and plotting indirectly, using a standard body at a standard velocity. The same curve should result in every case.

Of the three methods the last (c) may be dismissed as impracticable; the two former, (a) and (b), are, however, well suited to experimental conditions, and would furnish a complete check on the foregoing investigation. At present the experimental data are fragmentary and the evidence inconclusive.

The general properties of the curve, common to all forms of body, may be gathered from the circumstances of the problem. For very small values of $$V$$ we allow that quantities varying as $$V^{1.5}$$ and $$V^2$$ become negligible, and the curve will be of the form $$R \propto V$$ and leave the origin as an inclined straight line. When the velocity is very great resistances that vary as the lower powers of the velocity will be negligible in comparison to those that vary as $$V^2 ,$$ and consequently the curve will approach asymptotically to the form $$R \propto V^2 .$$ It is questionable whether the $$R \propto V$$ stage can exist when the viscous reaction of the fluid is due wholly to its own inertia; in the demonstration of the "normal law of skin-friction" it was shown that this condition results in the "1.5 power" law, and it would appear probable that