AIR PERFORMANCE 45 



problem is doomed to lead to equations only soluble by trial 

 and error. This process, though most useful when none other is 

 available, is terribly laborious, and we should not, therefore, be 

 justified in employing it merely for the purpose of getting a 

 closer approximation than we have yet got. 



We will therefore employ a flank attack, making use of the 

 principle that corrections on corrections are unimportant* 



We will start with the machine performance curve obtained 

 by the First Method and with our pair of propeller performance 

 curves. 



Now we have to correct this machine performance curve for 

 the full power slip stream : we shall do so on the assumption that 

 the extra lift and the extra resistance can be added (causing the 

 speed to drop and the value of P to be modified, and thus giving 

 us a point on the corrected curve for horizontal flight) without 

 altering the value of\ and thus invalidating the work : this, as- 

 sumption is untrue, but the error involved, being an error on a 

 correction, need not trouble us. 



Well then we have our propeller curves, which give us the 

 value of P p for any derived value of V, and we have our original 

 curve giving P in terms of V. 



First choose a value of X and then obtain from the table the 

 corresponding value of V and call it X V ; also get from the table 

 jP, the corresponding value of P, and from the curve, ^Pp, the cor- 

 responding value of P p . 



Then the full power thrust T is given by the equation 



Hence the slip stream velocity (i + ^V is given by the 

 equation 



T = l -^-d^B 



where B = (i + bj - I, 



as we see by referring to page 26, for instance. 



Now the total lift under slip stream conditions is 



oo5i L (S + ^SOiV 2 

 (see page 26), whereas under conditions of no slip stream it is 



Therefore, assuming as we do that the value of X is unaltered, 



* This principle, so valuable to the computer, is a bold generalisation to finite 

 differences of the mathematician's principle of neglecting infinitesimals of the second 

 order. 



