Page:Aerial Flight - Volume 2 - Aerodonetics - Frederick Lanchester - 1908.djvu/34

§ 7 of motions in the different degrees of freedom (compare § 2) involved in the maintenance of equilibrium as above expounded.

In the longitudinal stability three kinds of motion are involved and interact: (1) rotation about a horizontal axis transverse to the line of flight; (2) motion of translation in a vertical direction, and (8) motion or change of motion in the direction of flight (taken as horizontal for the present purpose). Employing the usual axis symbols, and calling the direction of (mean) flight x, and the axis at right angles thereto in a vertical plane y, the transverse axis will be z; and the three kinds of motion become (1) rotation about z; (2) translation along y, and (3) translation along x. Thus if we were to take away the other three degrees of freedom by arranging the flight model to slide between two parallel vertical planes or walls, we should have the problem of longitudinal stability left in its entirety and nothing else. This is always a convenient supposition to make when the question of longitudinal stability is under discussion.

In the maintenance of lateral stability two degrees of freedom are primarily involved: (4) rotation about the axis of x, i.e., the axis of flight, and (5) translation along the axis of z, i.e., the transverse axis.

The sixth degree of freedom, i.e., rotation about a vertical axis, primarily concerned in direction maintenance, is also closely associated with the question of lateral stability, and it will be subsequently shown that motion of this kind requires to be taken into account when dealing with that subject. There is a peculiar kind of skew instability that is prone to arise if this point is neglected.

§ 8. Other Forms of Aerodone.—The ballasted aeroplane has been chosen for the purpose of initial discussion as being the most elementary form of aerodone known, and as presenting an object lesson in automatic stability of the simplest possible kind. Several experimenters have developed gliding models or aerodones of more elaborate form ; these, though generally inferior to the