Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/277

Rh given plotted for different values of aspect ratio in Figs. 105 and 106, and, tabulated, are as follows:—

§ 178. On the Constants $$\kappa$$ and $$\epsilon$$.—Of the constant $$\kappa$$ we know but little with certainty. Langley's experiments with two pairs of planes four inches by fifteen inches superposed (Fig. 102) suggest that for planes whose aspect ratio is about 4 or 5 $$\kappa$$ has a value of somewhat less than 1. For reasons given in § 161 the actual value is probably somewhat greater than that ascertained experimentally for pairs of superposed planes.

On the value of $$\epsilon$$ we are entirely without information so far as direct experiment is concerned. If the value of $$\kappa$$ were known for an aerofoil of given aspect ratio, the value of $$\epsilon$$ can be obtained from the equation given in the preceding article, i.e., $$\epsilon = \frac{c\ C}{\kappa} - 1 .$$

We may provisionally assume that $$\kappa$$ is a function of $$n$$ and constant in respect of other variables. It is true that we have taken no account of the influence of plan-form, but we may legalise our position in this respect by specifying some standard form such as a rectangle, and leave the onus of drawing up tables of equivalent proportions in any other form to future experimenters.

At present the quantitative data are in so unsatisfactory a A.F.