62 AEROPLANE PERFORMANCE CALCULATIONS 



very nearly constant. We will assume it to be constant and 

 equal to T poundals. The method of finding T will be given later 

 on page 67. 



Let KV 2 be the total resistance of the machine (wings and 

 body) at V feet per second relative to the air in poundals, includ- 

 ing the effect of slip stream action on the wings and body. The 

 method of finding K will be given later on page 67. 



Let M be the total mass of the machine impounds (then M is 

 represented by the same number as ordinarily represents W, the 

 weight of the machine in pounds, in other calculations). 



Let / be the time in seconds, reckoned from the starting of the 

 run. 



Let v s be the forward velocity of the ship in feet per second, 

 relative to fixed axes. 



Let v w be the velocity in feet per second of the wind as read 

 by an anemometer on the ship. Then the forward velocity of 

 the wind relative to the fixed axes is v s - v w . 



Let X be the linear co-ordinate in feet of the ship relative to 

 the fixed axes. 



Let X + x be the linear co-ordinate of the machine in feet 

 relative to the fixed axes. Then x is the co-ordinate of the 

 machine relative to the ship. 



Let / be the length of run in feet relative to the ship which is 

 required before the machine reaches its minimum flying speed 

 v m relative to the wind. 



Then M = T - KV 2 . (i) 



ar 



Now 



x) 



dv, 



and s = o, since v s is constant, 



dt L dt 



x) = #x ^dx_ ^dx_dx ^ .dx , , 



d? = W 1 ~ ~dt " ~dtdx " *dx 



Also the speed of the machine relative to the air equals the 

 absolute forward velocity of the machine minus the absolute 

 forward velocity of the air. 



- ^ 



.: V = v w + x ........ (3) 



.;. V - ' - (v s - v w ) = X + x - v s + v w = v s +x - v s 



