Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/245

Fig. 106.

Fig. 105 illustrates the manner in which $c$ may be plotted as a function of the aspect ratio $n$. The values of $c$ are at present not known with any pretence to accuracy; $c$ is probably different in the case of an aeroplane from what it is in the case of a pterygoid aerofoil.^[1] For the former Langley found that variations in $n$ gave rise to very considerable variations in $c$ (Fig. 99); Dines failed to discover any variation at all (Fig. 101).

The values given in Fig. 105 are “plausible values” (see Chap. VIII.) for a pterygoid aerofoil. The same data have been laid out in Fig. 106, where abscissae give angle and ordinates pressure reaction.

In addition to the equation,

we may also formulate as a direct consequence of the small angle hypothesis,

and from the resolution of forces we have,

where $y=$ aerodynamic resistance.

Consequently,

${\frac {W}{A}}=c\ \beta \quad P_{90}=c\ C\ \rho \ \beta \ V^{2}$

1. See foot-note, § 172.