66 AEROPLANE PERFORMANCE CALCULATIONS 



. -. the ground-borne weight = Mg-f i - j 

 . . the equation of motion is 



Now * 



dt dx dt 



.'. from (i) + lax* + 2pg = o . . (2) 



dx 



where a = - . . . . (a) 



M v* 



Now we get different formulae according to whether a does 

 or does not equal zero. First, then, if a = o, we have from (2) 







 O 



/-- ..... (A) 



2/^ 



But if a is not zero, we have 



.'. from (2) 



or 2 + 



X V 



2a \ dx = O 



Ji = o r l 



d log/or 2 + pg) + 2a \ dx = O 

 J*-f 







= O 



tr 



but from (a) azr 2 = z; 2 - 



