22 l\.AVLl-:i(;ii, The Mechanical Principles of Flight. 



su|)i)()rting; himself in this way by his own muscular 

 power, we take in C.c;.s. measure 



/F^68ooox98i, ^7=15, p = ^^, 

 thus fniding 



.S'' ^ 6'o X lo^ s(]. cm. 



This re[)resents the cross-section of the descending 

 column of air. If we ecjuate S' to \-Kd'\ d will be the 

 diameter of the screw required, and we get d=^(^Q metres. 

 It is to be observed that this assumed value of 6^" corres- 

 ponds to the power which a man may exercise when 

 working for eight hours a day. But even if he could do ten 

 times as much for a few minutes, d would still amount to 

 9 metres ; and in this estimate nothing has been allowed 

 for the weight of the mechanism, or for frictional losses. 

 It seems safe to conclude that a man will never support 

 himself in this manner by his own muscular power. 



A screw works to better advantage when it has a 

 forward motion through the fluid, for then a larger mass 

 comes under its influence. Let us suppose that a screw, 

 now rotating about a horizontal axis, is advancing through 

 still air with horizontal velocity V. Also let v be the 

 actual velocity with which the column of air leaves it. 

 The volume acted on per second is S\ V +v). If i^ be the 

 prc:)pulsive force 



F=S\^{V^v)v {i^). 



Again, the work per second required to generate the 

 kinetic energy (jf the ccjlunin is 



\S\.{V^v)v^ (34). 



The whole work expended per second (//') is 

 accordingly 



H'=^FV^\S'^.{V^v)v' = F{V-,\v) . . (35). 

 When l^is great compared with z^, the right hand member 



