Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/214

§ 140 By similarly fitting a lip or a projection to the edge of the normal plane, opposed to the relative direction of the wind, its pressure constant can be considerably increased. If the lip be of sufficient height to render motions of the fluid adjacent to the plane itself very small, so that the square of such velocity as it may possess may be everywhere negligible, then the pressure on the face of the plane will, on the hydrodynamic principle already cited (§ 138), be everywhere that due to the Torricellian head, and the pressure constant will be .5; it would appear to be impossible for it to rise above this value.

In viscous fluids there would be doubtless some departure from strict theory, owing to the fact that the fluid in advance of the plane has rotation impressed upon it by viscous stress, and the hydrodynamic principle assumes irrotation; in ordinary fluids the error due to this cause should not be great. Beyond this there is the separate phenomenon of the suction on the back of the plane, which may be regarded as supplying an added constant, the sum of this and the pressure constant making the $$C$$ of the equation.

§ 141. The auantitative Effect of a Projecting Lip.—For planes of compact outhne. Dines obtained the following results:—

Plane 1 foot diameter, circular.

We have stated that the probable value of the pressure constant on the Helmholtz basis for a plane of compact outline is about .40 or somewhat less; this would give a possible augmentation of 25 per cent, or somewhat more (the limit being .5 according to the preceding article); but Dines' result is the percentage on the whole constant and requires to be multiplied by 66/40, so that his figure for a 5/8 inch rim becomes 23 per cent. This result is in harmony with the theory, but would seem to