AIR PERFORMANCE 39 



Now in practice the angle will be round about 7 or less, so 

 that cos will be about '993, or even nearer to unity. 



Therefore we do not lose much in accuracy by dropping cos 

 from the above equation, leading to 



W = L + T tan 0. 



Substituting for L and T from equations (L) and (T) we 

 have 



tan 0\ R tan 

 W = -005 IX 



T> 



Now 



tan 6> 



- I 

 l 



tan /w ,s 





Now the rate of descent = V' sin 9 and the rate of horizontal 

 travel relative to the ground = V cos - v, therefore we have 

 the equation 



V sin 6 tan d 



tan 6 = ^r, -- 4 -- / 

 V cos - v 



I - 



v cos e 



Remembering that cos is approximately equal to unity we 

 can write 



tan d 

 tan </> = - j . (tan <) 



<- v 



It will be noticed that <r has not dropped out, so that the 

 " best gliding angle against a given wind " (and the value of X 

 corresponding to it) is not independent of altitude. 



Equations (tan 0), (a), (V), and (tan </>) are in a form amen- 

 able to tabular treatment for values of X from -i to ro (see 

 Chapter XII., page 118). 



Such a table can be drawn up and then, by plotting, the 

 minimum value of tan $ can be found : this is the tangent of the 

 " best gliding angle against the given wind at the given altitude ". 



It is of interest to note that for a given value of X, tan 6 is 

 constant and V'^/0- is constant. 



Hence we see that if v and a both vary, but in such a manner 



