Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/169

Rh thereby on $$C\ D$$ are obviously in equilibrium, and require no consideration.)

When the aerofoil has a horizontal motion through the fluid the conception of the prismatic column will not thereby be altered. Although its contents are constantly passing out on one side and being renewed on the other, the instantaneous condition of the forces acting is not in any way affected; the downward static resultant $$W\ \boldsymbol{-}\ w$$ remains. Consequently the downward momentum imparted per second to the fluid leaving the prism plus the upward momentum received per second from that entering must be equal to $$W\ \boldsymbol{-}\ w .$$

When the height at which the aerofoil is sustained is great in comparison with its own dimensions, the area over which the weight is distributed on the earth's surface is obviously also great, and the quantity $$w$$ becomes negligible. Under ordinary conditions this would usually be the case, so that the weight may be regarded as in no part statically supported. In special cases, however, $$w$$ may become of sensible magnitude, and it is probable that results obtained with a very large aeroplane near the surface of the earth would be found not to hold good for the same aeroplane at any considerable altitude.

§ 113. Aerodynamic Support,—Field of Force.—We have already (§ 60) learnt to regard the lines of flow of hydrodynamic theory in the light of “lines of force” and the region occupied by such lines as a “field of force.” The definition may be given as follows:—

A line of force in a fluid is defined as a line lying everywhere in the direction in which the particles of the fluid are undergoing acceleration, and in the case of a fluid initially at rest at the instant of its being set in motion the lines of force are identical with the lines of flow of mathematical theory. The whole region occupied by the lines of force is termed a field of force whose intensity is everywhere proportional to the acceleration of the particles.