Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/320

§ 204 usage. The term slip, in its application to a screw propeller, is one that leads to confusion of thought; it is unscientific in its present usage, and would be better abolished.

Let us estimate the possible efficiency in the case of the maximum conditions of the preceding section. Employing equation, $$E\ (\mbox{efficiency}) = \frac{\tan \theta}{\tan (\theta + \gamma)}$$ we have—

Now these efficiencies are only obtainable at the particular section of the blade where the angle $$\theta$$ is correct for maximum efficiency, and at all other points the efficiency must be less. A section of the blade here discussed is the section on a cylindrical surface which may be fully defined by its radius $$r .$$

In Figs. 126 and 127 we have plotted the calculated efficiency for different values of $$r$$ on the basis of the $$\gamma$$ values assumed for water and air. Abscissae represent radius in terms of pitch, the ordinates give corresponding efficiency values. The abscissae are also figured for values of $$\theta .$$ The efficiency falls to zero when $$\theta = 0 ,$$ and again when $$\theta + \gamma = 90$$ degrees, for in the first place $$\tan \theta = 0 ,$$ and in the second $$\tan (\theta + \gamma)$$ becomes infinite.

§ 205. The Propeller Blade Considered as the Sum of its Elements.—Much of the faulty work of early writers on hydrodynamic problems has been due to the treatment of a body or surface as the equivalent of the sum of elements into which it may be arbitrarily divided, and this form of error is one against which it is important to be on guard.

We have already adopted in substance the principle of regarding an aerofoil as the sum of its sectional elements in the sense now contemplated in respect to the propeller blade (§ 192), but we do not suppose, in assessing the individual elements, that they are removed from their environment.