Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/86

§ 49 is indicated by the balanced plane experiment, owing to the smaller plane being unduly affected in each case by its proximity to the larger one. It is conceivable that the smaller plane being situated in the counterwake of the larger, will in effect be surrounded by air moving with above the normal wind velocity, and so show a fictitiously high pressure value. Mr. Dines' elegant method of determining the V2 law, by balancing against centrifugal force, would appear to be quite above suspicion, although it may not be sufficiently sensitive to demonstrate the departure from the law, which for the normal plane is certainly very small indeed. In any case the results, without some such explanation as given, are not altogether consistent, and a repetition of these experiments ought to be made.

'''§ 50. Allen's Experiments. '''—Mr. H. S. Allen, experimenting with bubbles and small solid spheres in liquids, found that for very small velocities the viscous law holds good, whereas for very great velocities the V2 law prevails ; he also shows that there is an intermediate well-defined range, over which the V1.5 law applies. His results are summarised as follows:—

"Three distinct stages have been recognised:

"(1) When the velocity is sufficiently small the motion agrees with that deduced theoretically by Stokes for non-sinuous motion, on the assumption that no slipping occurs at the boundary ; in such motion the resistance is proportional to the velocity.

"(2) When the velocity is greater than a definite critical value, the terminal velocity of small bubbles and solid spheres is proportional to the radius, less a small constant; it may be expressed by the formula given.

"(3) For velocities considerably greater than those just considered, the law of resistance is that which Sir Isaac Newton deduced from his experiments, namely, that the resistance is proportional to the square of the velocity." Of the above three stages, (2) corresponds approximately to the