Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/292

§ 186

For the aeroplane we know that the weight supported per unit area is (for small angles) given by the expression—$$c\ \beta \times C\ \rho\ V^2 ,$$ which is $$= P_3 .$$

We therefore have $$\frac{P_3}{V^2} = \rho\ c\ C\ \beta_1 .$$

For values of $$\xi$$ respectively .02, .015, .0125, and .01, and taking $$\rho$$ as before = .078, the values of $$\frac{P_3}{V^2}$$ for least resistance are given in Table XI.

In Table XII. the foregoing results have been interpreted as pounds per square foot for different values of $$V$$ ranging from 5 to 80 feet per second, and for values of $$\xi =$$ .02, .015, and .01.

It is scarcely necessary to remark that the values given in the preceding Tables are not based on sufficiently reliable data to justify their being carried to so many places of decimals; the figures as tabulated have a probable error of 10 per cent, or even 20 per cent, one way or the other, and the employment of the third significant figure is only justified as a means of showing the relation of any one value to those adjacent to it in the Table.

It has not been thought necessary to re-tabulate in metric