Woodward — 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- 

 Ship IN Still Air Against a Known Resistance P at 

 the Rate of 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 p lbs. 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). 



22F 

 A speed of V miles per hour is ^p^ feet per second. 



Hence v' = z-^F. feet per sec [VI] 



The mass of the volume actually acted upon per second is 



w 

 A (v + v^) -, and since the velocity imparted to this mass is v, 



9 



the kinetic energy generated in the air-current per second is 



Awv^ , , ,, Aiw^ , AwVh' rVTTl 



2g ^ ^ 2g 2g 



