Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/166

§ 110 If now we impress upon the plane a simultaneous horizontal motion, it is evident that the air encountered by its leading edge will be in a state of upward motion, and it would appear probable that this up-current, in front of the advancing plane, would only cease to exist when the horizontal velocity of the plane becomes equal to the velocity of sound.

But if an up-current is encountered, impinging on the advancing edge of a loaded aeroplane, the downward momentum communicated to the air will be augmented, and may be regarded as consisting of two parts, to the sum of which the sustaining force is due, i.e., the part communicated in bringing the up-current to a state of rest and the part communicated to the air as velocity downwards.

It is evident that the problem as above presented is in effect identical with that of an inclined plane moving horizontally—that is to say, the relative direction of the horizon is not of importance. The force of gravity in the one case can be substituted by the resultant of the force of gravity and an applied force of propulsion in the other.

§ 111. Dynamic Support Reconsidered.—When we consider part of the support of a body as derived from an up-current, it is necessary to examine the origin of the up-current, for it is evident that the generation of such a current must give rise to a downward reaction, and everything depends upon whether such reaction is borne by the body itself or by the deeper layers of the air, and eventually by the earth's surface.

Reverting to the case of a body supported by the communication of momentum to a number of independent material particles, it is evident that the particles projected downwards eventually give up their momentum on striking the surface of the earth. We may follow the subsequent history of the particles in two extreme cases:—

Case 1.—If the particles or the earth's surface are supposed quite inelastic, the impact is accompanied by a continual loss of