THEORETICAL AND :\IEASURED PUMPING POWER OF WINDMILLS. 



95 



or accelerating force is equal to the mass A,M of air flowing over 



/\,s in time /\t multiplied by the acceleration in the direction of 



/\P. This acceleration is equal to the difference in velocity of 



l\M in the direction of /^P before and after impact, and equals 



c sin X — w, cos z^ at B, and c sin x — w^ cos z^ at A. 



From Fig. 3 w^ cosZj=W2 cos Zg^=v cos x. Hence 



/\M 

 A P== (c sin X — V cos x) (i) 



If M is the mass of air deviated per second by /\s, then AM = 

 M/\^t. The volume deviated per second is equal to the relative 



Fig. 3 



velocity v^ multiplied by the area of the projection of As on a 



plane perpendicular to the relative velocity. Hence 



. r 

 /^^P=:K — v^ ^s sin(x — 3' )(c sin x — v cos x") .... (2) 

 S 

 From Fig. 3 v, sin (x~y ) = H B=rN M=NG— G M=c sin x— 



v cos X. Hence 



/2^P=rK — /\,s{c sin X — V cos x)- 



(3) 



Resolving A,P into two components, one perpendicular to the 



plane of the wheel and the other parallel to it, we have for the 



latter, which causes the wheel to revolve 



r 

 ^P cos x:=K l\^{c sin x — v cos x)^ cos x. . . (4) 

 S 

 The other component 



r 



/\P sm x^K — /\s(c sm x — v cos x)sin x (5) 



causes friction, and will be considered later. 



