Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/298

§188 the adjustment has been carried to its limits will behave in a most capricious manner, sometimes gliding perfectly and at others dropping suddenly in the midst of a flight like a bird when shot.

§ 189. The Hydrodynamic Standpoint.—Let us revert to the Hydrodynamic aspect of the subject as expounded in Chap. IV. We have seen that the supporting reaction is due to a cyclic motion in the fluid which is maintained by, and is in equilibrium with, the load on the aerofoil; it is of course understood that there is a superposed motion of translation, i.e., the motion of flight. Now in the case of an aerofoil of infinite lateral breadth we have seen that this equilibrium is permanent, and we have in

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several instances plotted the resulting field of flow. When we have to deal with a case of finite lateral extent we have seen that there must be a continual dissipation of the cyclic motion, which vanishes in the manufacture of the trailing vortex filaments which the aerofoil is continually shedding on either hand.

In the Eulerian fluid there is no reaction on the aerofoil possible except that due to the cyclic motion, but in a real fluid this is not the case; a reaction may always be generated and always is generated when the motion gives rise to discontinuity, whether kinetic or physical.

Now the cyclic motion is in equilibrium with the reaction to which it gives rise, so that if we suppose an aerofoil supported entirely by the cyclic reaction and in equilibrium at any instant with the cyclic reaction, then if, firstly, it be supposed of infinite extent it will be in equilibrium at every other instant of time;