Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/303

Rh relation to its width at each point, the mass dealt with per unit length will be everywhere as the width. But for a given height of the arched section the values of $$\alpha$$ and $$\beta$$ will be inversely as the width, and consequently the load sustained for any particular element of the length will be constant in respect of width; that is to say, the sustaining power of the aerofoil for a given midsection and a given grading is constant, no matter what the plan-form, both as to total and as to each element of length.

This is a very convenient rule to remember, but one which, from the nature of the assumptions made, is more or less approximate; it can be applied legitimately to all ordinary modifications of plan-form.

When an aerofoil is designed according to the foregoing specification, whether as a solid as in the case in point, or as a lamina of the same mean section, the equivalent area for uniform values of $$\alpha$$ and $$\beta$$ will evidently be that of a plane whose plan ordinates are those of a segment, that is, proportional to the thickness ordinates. Such a form may be taken as having two-thirds the area of the circumscribed rectangle; that is, if $$L$$ be the length of the aerofoil the equivalent area will be:—

$$\frac{2}{3} \times \frac{L^2}{n} .$$

By adopting and adhering to some standard such as that above defined, the experimental information obtainable becomes of greater value than when a variety of forms are employed. It