Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/362

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§ 224

AERODYNAMICS.

But—

F={\frac {M\ V^{2}}{r}},

and

R=c_{2}\ F

∴

A\ C\ \rho \ c_{1}^{2}\ V^{2}={\frac {c_{2}\ M\ V^{2}}{r}}

or

C={\frac {c_{2}\ M}{A\ \rho \ c_{1}^{2}\ r}}

^[1]

all of which are known quantities; consequently the value of the constant $C$ is determined.

§ 225. Dines' Method (continued).—Of the practical working of the foregoing apparatus, which may not inaptly be termed a centrifugal balance, Mr. Dines says:—“It had been assumed in the above that the wind pressure varies as the square of the velocity. The experiments have proved this to be the case, for when upon a calm day equilibrium for any plate is once attained, it has been found impossible to disturb it by any alteration of the velocity of rotation, and since the centrifugal force varies as the square of the velocity the wind pressure must do so also. For the smaller planes the maximum velocity of which the machine is capable is about seventy miles per hour.”

We may consequently infer that the $V^{2}$ law of resistance holds good as a very close approximation over a very considerable range of speed, certainly as great a range as concerns the problem of flight. This is a result previously considered in doubt.

The arrangement of the centrifugal balance figured is not one altogether suited to planes of large size, owing to the fact that the different portions of the plane are situated at different distances from the centre of the whirler, and the position of the centre of pressure becomes uncertain. In such cases a modified design is adopted (Fig. 142), of which the description is given in § 227.

The obvious difficulty of observing the position of the plate

↑ This expression differs somewhat in form from that given by Dines, the difference being due firstly to the introduction of the area (A) of the plane, and the restriction of the use of the term pressure as being of the dimensions force divided area, and secondly to the difference in the units employed, the use of absolute units eliminating the gravitation constant.

340

[1] This expression differs somewhat in form from that given by Dines, the difference being due firstly to the introduction of the area (A) of the plane, and the restriction of the use of the term pressure as being of the dimensions force divided area, and secondly to the difference in the units employed, the use of absolute units eliminating the gravitation constant.

[1]