Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/176

§ 116 along and conserved just as is the case in wave motion. The motion round about the plane may thus be considered as a supporting wave. When the amplitude of motion becomes sensible, there is no doubt that the streamlines react on one another in a manner not accounted for by the form of field contemplated, i.e., that of the quiescent state. Under these conditions the method of investigation is not strictly applicable, but there would appear no reason to doubt the validity of the main inference. This conclusion is confirmed by a subsequent investigation conducted on different lines.

Considered in the light of wave motion, the peripteroid system must be regarded as a forced wave, the aerofoil supplying a force acting from without.

§ 117. Departure from Hypothesis.—Before proceeding to the further investigation, it is of interest to note briefly the consequences of a departure from the initial hypothesis.

If we suppose the aerofoil to be of finite lateral extent, it is immediately obvious that neither the lines of force nor the lines of flow can be represented by a single section through the field. The former, being no longer constrained to lie in parallel planes, diverge laterally, some portion of them escaping, as it were, and passing round the ends of the aerofoil through the regions marked o, o, o, (Fig. 67), in which R and L are the right and left-hand extremities of an aerofoil whose direction of motion is perpendicular to the paper. The fluid traversing the regions o, o, o, will have upward momentum communicated to it during the whole time that it is in those regions, and will be finally left in a state of upward motion.

Now, owing to this lateral spread of the ascending field forward of the aerofoil, the upward velocity imparted to particles in that region is less than the downward velocity imparted in the corresponding portion of the descending field, and the fluid crossing the medial line P Q (Fig. 64) will have, on the whole, a downward velocity. Similarly the downward momentum imparted