Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/253

importance of the matter warrants its premature introduction as touching the aerodynamic aspect of the subject.

Let us suppose that the position of the centre of gravity be such as will coincide with the centre of pressure when the plane makes an angle $=\beta _{1}$ with its direction of motion. Now we know (§ 184) that the position of the centre of pressure varies as a function of $\beta$ and that its distance from the front edge of the plane diminishes the less the angle; if then the angle from any accidental cause becomes less than $\beta _{1}$ the centre of pressure will move forward in advance of the centre of gravity so that the forces acting on the plane will form a couple tending to increase the angle and so restore the condition of equilibrium. Likewise if the angle become too great the centre of pressure will recede and the resulting couple will tend to diminish the angle, and again the equilibrium is restored; thus the conditions are those of stable equilibrium, the plane tends to maintain its proper inclination to its line of flight.

There is not only equilibrium between the angle of the plane and its direction of motion as above demonstrated, but also between the gliding angle and the velocity of flight; thus if the velocity is deficient, so that the weight is insufficiently sustained, the gliding angle and the component of gravity in the line of flight automatically increase and the aerodrome undergoes acceleration. Conversely, if the velocity is excessive, the gliding angle (and so the propulsive component) diminishes, and the velocity is thereby reduced.^[1]

1. The above explanation of the automatic stability of an aerodrome is, in a condensed form, that given by the author in his paper to the Birmingham Natural History and Philosophical Society in 1894.

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