If made too small then the propeller will not be so efficient, or, at any rate, such is the conclusion come to in marine propulsion, where it is found for the most economical results to be obtained that the slip should be from 10 to 20 per cent.
In the case of aerial propellers a slip of 25 per cent. is quite good, 40 per cent. bad; and there are certain reasons for assuming that possibly about 15 per cent. may be the best.
§ 7. It is true that slip represents energy lost; but some slip is essential, because without slip there could be no "thrust," this same thrust being derived from the reaction of the volume of air driven backwards.
The thrust is equal to—
Weight of mass of air acted on per second × slip velocity in feet per second.
In the case of an aeroplane advancing through the air it might be thought that the thrust would be less. Sir Hiram Maxim found, however, as the result of his experiments that the thrust with a propeller travelling through the air at a velocity of 40 miles an hour was the same as when stationary, the r.p.m. remaining constant throughout. The explanation is that when travelling the propeller is continually advancing on to "undisturbed" air, the "slip" velocity is reduced, but the undisturbed air is equivalent to acting upon a greater mass of air.
§ 8. Pitch Coefficient or Pitch Ratio.—If we divide the pitch of a screw by its diameter we obtain what is known as pitch coefficient or ratio.
The mean value of eighteen pitch coefficients of well-known full-sized machines works out at 0·62, which, as it so happens, is exactly the same as the case of the Farman machine propeller considered alone, this ratio varying from 0·4 to 1·2; in the case of the Wright's machine it is (probably) 1. The efficiency of their propeller is admitted on all hands. Their propeller is, of course, a slow-speed propeller, 450 r.p.m. The one on the Blériot monoplane (Blériot XI.) pitch ratio 0·4, r.p.m. 1350.
In marine propulsion the pitch ratio is generally 1·3 for a slow-speed propeller, decreasing to 0·9 for a high-speed one. In the case of rubber-driven model aeroplanes the pitch ratio is often carried much higher, even to over 3.
Mr. T.W.K. Clarke recommends a pitch angle of 45°, or less, at the tips, and a pitch ratio of 3-1/7 (with an angle of 45°). Within limits the higher the pitch ratio the better the efficiency. The higher the pitch ratio the slower may be the rate of revolution. Now in a rubber motor we do not want the rubber to untwist (run out) too quickly; with too fine a pitch the propeller "races," or does something remarkably like it. It certainly revolves with an abnormally high percentage of slip. And for efficiency it is certainly desirable to push this ratio to its limit; but there is also the question of the