Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/321

Rh Let us examine our former procedure. We have an aerofoil whose aspect ratio is of considerable magnitude, and whose grading is specified, and we prove that the reaction due to each increment of length is proportional to the grading ordinate proper to that increment, irrespectively of the fore-and-aft dimension. The proof involves the tacit assumption that for the smooth curve form of grading specified, a geometrical similarity of section at all points involves a uniform pressure distribution.

Now, so long as the aspect ratio is great and the grading a smooth curve, there can be little question as to the propriety of this assumption; if, however, the aspect ratio be small, or the changes in the grading curve sudden, then the grading curve and the relative reaction curve ma}^ cease to coincide. Our assumption may therefore be considered as an approximation—a close approximation when the value of $$n$$ is great (say upwards of 4 or 5), and a rough approximation when the aspect ratio is small.

§ 206. Efficiency Computed over the Whole Blade.—On the basis of the efficiency curve (Figs. 126 and 127) and a knowledge of the radial distribution of the thrust reaction (the F of § 202), the computation of the efficiency for the whole blade is merely a matter of integration.

We have first to settle how much of the efficiency curve we propose to employ i.e., the radial limits of the blade length. If we make the blades too long, the efficiency at the extremities would be so low as to involve an extravagant expenditure of power; if, on the other hand, we confine the length of the blade to the region where the efficiency is about its maximum, in order to reap the benefit of the full value (as given in § 204), we encounter practical disadvantages in the increased propeller diameter required to deal with a given quantity of fluid (the proportion of the “disc” area utilised becoming small), and in the length (and consequent resistance) of the arm necessary to attach the blade to its boss.

In Figs. 126 and 127 we have taken the blade length,