Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/305

Rh just as if the wing were continued in the manner shown; also on the improbability that there is any augmentation due to discontinuity, for the body is of a rounded form little likely to produce motion of a discontinuous type, and the tail is essentially a directive organ.

We have seen that the different portions of a bird's wing are of different sectional form and adapted to carry different pressure values at different points. It sometimes happens that, for the purposes of comparison, in place of the actual area the equivalent area is required, as for example when comparing the results of theory, as in § 185, with the proportions adopted by Nature; this area being the area that would be required on an assumption of uniform pressure distribution, or constant values of $$\alpha$$ and $$\beta$$ throughout the length.

In order to rightly assess this equivalent area we require to know the grading of the aerofoil, a knowledge which we do not possess, and which, owing to the flexibility of the wing structure, it is almost impossible to obtain.

The probability is that for birds of similar habits the grading will be found to be similar; that is to say, the distribution of the load along the length of the outstretched wings will be identical. In the absence of more definite knowledge, a rough assumption has been made for the purposes of the present work, i.e., that the grading is substantially that of the standard form adopted by the author, and consequently the effective area is given by the expression $$\frac{2\ L^2}{3\ n} .$$

§ 194. The Weight of the Aerofoil as influencing the Conditions of Least Resistance.—The subject of the influence of aerofoil weight as affecting the conditions of least resistance has been discussed in a previous chapter (§ 171), and a general equation has been deduced from the conditions.