W oodward—Air-Ship Propeller Problems. 3 
It is‘ assumed that the propeller is correctly designed for the veloc- 
ity v of the air current. For discussion of the design of the pro- 
peller see § 10. 
Instead of a motor driving a horizontal shaft, one may use 
an electric motor and a vertical shaft, with arrangements for 
measuring the lifting or depressing effect of the propeller when 
in motion. 
2. WHaT IS THE HoRSE-POWER REQUIRED TO DRIVE AN AIR- 
Sure In Stizt Arr AGAINST A KNOWN RESISTANCE P at 
THE Rats or V MILES PER Hour? 
If all the air acted upon by the propeller be given an absolute 
velocity of v ft. per second, it is evident that the volume of air 
acted upon per second is now A (v+v’) in which v’ is the velocity 
of the ship in feet per second. 
To make this truth still more evident, it may be added that if 
we assume that the air-ship is drawn or towed thru the air 
by some other ship or motor, at the rate of v’ ft. per second, our 
propeller standing still, the air would pass thru it, at the rate 
v feet per second, or it would appear to do so, though really 
standing still. Now if the propeller be started and turned fast 
enough to press 7p Ibs. per sq. ft. upon all the air passing, so as to 
give it an absolute velocity of v feet: per second, then the rela- 
tive or apparent velocity of the air passing thru the propeller 
would be v+v' ft. per second, so that the volume of air acted 
upon every second would be A (v+v’). 
A speed of V miles per hour is sue feet per second, 
22 
Hence v' = 15° OBE DEP BEG cue ei woee [VI] 
The mass of the volume actually acted upon per second is 
A (v+v') —, and since the velocity imparted to this mass is 2, 
the kinetic energy generated in the air-current per second is 
