Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/337

Rh Referring to § 181, we have the angle $$\beta$$ given by the expression $$\sqrt{\frac{2\ \xi\ C}{\kappa\ (1 - \epsilon^2)}} .$$ Taking $$\xi$$ for water as = .01 and density = 64 lbs. per cubic foot we obtain, $$\beta$$ = .132 (radians) or, = 7.6°, and the theoretical minimum gliding angle is 3.95°, which in practice becomes 6° about. The $$P_2 / V^2$$ relation (given for air in Table IX.) will become $$\rho\ \kappa\ (\epsilon + 1)\ \beta =$$ 12.5.

The above are the data on the pterygoid basis; similarly on the plane basis, that is, for blades of perfect helical form, we have, taking $$\xi =$$ .005, on the principle explained in § 182, $$\beta =$$ .048, or, $$\beta$$° 2.75°, that is $$\gamma$$ (least value) = .096, or $$\gamma$$° = 5.5°. The $$P_3 / V^2$$ relation is given by the expression—

$$\frac{P_3}{V^2} = c\ \beta\ C\ \rho$$ (§ 186) = 4.55.

The above results may be tabulated as follows:—

The $$P / V^2$$ values given above are in absolute units. The pressure value is extended in Table XIV. as pounds per square foot for values of $$V$$ in feet per second.

§ 215. The Marine Propeller (continued).—Cavitation.—It is very questionable to what extent the plane basis of operation is applicable in the case of a screw propeller. There seems to be a grave theoretical objection that does not exist when the motion is rectilinear, as in the analogous case of a weight supported by an aeroplane.

When we have to deal with the propeller blade on the