Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/333

Rh with the Newtonian principle) to operate on a given cross-sectional area of fluid. Then this area is represented by an annulus whose inner and outer boundaries are of the radii of the blade limits.

Let us, firstly, assume the straight line thrust grading curve of Fig. 129, so that the whole of the fluid within the annular area will be uniformly accelerated; and let us regard the thrust grading curve as representing the useful work of propulsion over one unit distance, and let the curve $$a\ a\ a\ a$$ (Fig. 132) represent the work expended in the same time. Let $$E$$ represent the efficiency as a variable, i.e., the ordinate of the efficiency curve, and let $$w$$ represent the useful work per unit length of the blade, i.e., the thrust grading ordinate (Fig. 132); then the ordinate $$y$$ of the curve $$a\ a\ a\ a$$ will be $$y = \frac{w}{E} .$$

Now, if we suppose the limits of the blade length be moved from place to place, so that, however, the annular disc area of