2 Trans. Acad. Sci. of St. Louis. 



Hence I use the familiar hydraulic formula 



v^ = 2gh 



in which 2g is approximately 64 and h is the " dynamic head" 

 of the current whose value is 



h = p = f [11] 



w Aw 



Hence ^ = "V 1^ ^ 7 ^^^ ^^^^^^ '-^^^-' 



li A = Trr"^, and w = 0.08. 



Substituting for v in the expression for the kinetic energy, 

 we have the Kinetic Energy of the air-current, and hence the 

 work done per second by the motor-driven propeller is 



K.E.^Pi^-^U'-'p^^vP [IV] 



2g V Aw I r •- -■ 



so that we have for the net horse-power actually exerted, 

 dividing by 550, the horse-power-work in one second, 



^ = ^=2€=-«541 m 



approximately. 



This formula gives the horse-power required by means of a 

 propeller of radius r to maintain a steady pull or thrust of P 

 lbs. If there are two or more propellers acting without the least 

 interference, then their combined area is represented by 

 A = 7rr. 



In the formulas [III], [IV], and ["\^] r is the radius of the 

 circle equivalent in area to the combined area of all the propellers. 



The above case may be illustrated by a suspended frame 

 carrying a motor and propellers with horizontal shafts in a yard 

 or a large laboratory. The frame should be anchored by a 

 cable attached to a spring balance, or, passing over a light and 

 easily running pulley be attached to an adjustable weight P. 



