Page:Aerial Flight - Volume 1 - Aerodynamics - Frederick Lanchester - 1906.djvu/351

Rh value of “n,” being chiefly dependent upon the relative length of the blade as compared to the diameter; the number of blades thus depends upon the discard percentage. For a 90 per cent, discard four blades are the appropriate number; if the discard be 95 per cent, six blades may be employed. In general the following rough-and-ready rule may be employed: Let $$r_1$$ and $$r_2$$ be the radii of the inner and outer extremities of the blades, then the number of blades permissible will be $$= 2.5\ \frac{r_2 + r_1}{r_2 - r_1} ,$$ fractions being neglected.

(8) All that remains to be done is now to give a scale to the design that will render the propeller suitable for the intended load. To this end any convenient scale should first be assumed and the load calculated, for the actual value of $$V$$ (the velocity of flight), which it is intended to employ. The linear dimension will then be in the ratio to the dimension required as the square root of the calculated thrust is to the square root of the thrust required. That is to say, the scale unit will be in the inverse ratio.

An example of the design of an aerial propeller on the foregoing principles is given in Figs. 136, 137, 138, 139; the supposed data being as follows:—Velocity 70 feet per second; thrust = 100 lbs.; discard 90 per cent.; n = 6 ; $$\gamma$$ taken = 10 degrees.

§ 219. Power Expended in Flight.—The principles governing the expenditure of power in flight have, in this and the preceding chapters, been fully expounded, and it now only remains to draw certain elementary deductions.

The power essential to flight or thrust horse-power may be defined as that represented by the thrust multiplied by the velocity of flight, that is to say, the equivalent of the tow-rope expenditure. The actual power required will then be a thrust or essential power divided by the efficiency of the propulsion.

We have seen (§ 200) that the efficiency of propulsion may theoretically be greater than unity, so that the term essential must not be construed as meaning the minimum theoretically necessary on the Newtonian basis.