Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/95

Rh For large birds and flying machines the "$$R$$ varies as $$V^2$$" law is probably accurate enough for ordinary computations of resistance, whether frictional or direct. The $$V^2$$ law is generally assumed in the present work as sufficiently near the truth; the assumption of one law for both classes of resistance results in a simplification of method which fully justifies its employment, even at the expense of some small degree of accuracy.

The meaning of the statement (§ 36) that viscosity gives a scale to the fluid, may be illustrated by supposing a "blue-bottle" to find itself transformed into a common fly (supposing the two to be strictly proportional in their parts): it would find that the apparent viscosity of the air had increased; in other words, the air would appear to be more "sticky" than usual. The same fact is familiar in other cases—for example, the difference in character of a large and a small flame, etc. Other physical properties are capable of giving a scale to a fluid: thus elasticity as demonstrated by the length traversed by a wave in unit time; surface tension as demonstrated by the velocity of slowest surface wave.

One of the least satisfactory results of dimensional theory, so far as revealed by a comparison with conclusions that would be naturally formed from experience, is the inverse relation that exists for homomorphous motion between $$V$$ and $$l .$$ It would appear that for bodies of similar form any state of motion—say the state when discontinuity sets in—is reached when their respective velocities are in the inverse ratio of the linear dimension. Thus, if a salmon and a herring were geometrically proportional, the herring would be capable of a higher velocity, without ceasing to be of streamline form (by definition), than the salmon in the inverse proportion of their respective lengths. Now this seems very unsatisfactory, for a whale would be scarcely capable of locomotion without carrying a dead water region in its wake—a most improbable conclusion. Certain explanations are possible, but the author has been unable up to the present to find any conclusive solution to the difficulty.