o 2 h m I 

 BS = CO P [77] 



I + h m - Lh m 

 o o o o o 



2 2 



Incidentally, it may be remarked that if the values of tu and of BS 



given by [76] and [77] are substituted into the v, 6, and 6 equations with 



o 



c = 0, it is found that 



2 



v = ; e = - e^ [I^ + h m^ - Lh^m^]/I 

 ' o o o o o o 



2 2 



If Equations [76] and [77] yield positive values for to and S , then S 



is the critical flutter speed for the system. Even if c =0, any motion 



a 



at a smaller speed will be damped out by the - BSv term in the lift. 



A critical flutter speed will not exist for all values of h^ and L. 



In Equations [76] and [77], only h and L can be negative. Hence to 



2 ? 



make uj and S"^ , as given by these equations, positive, it is necessary 



that : 



I + I + h m - Lh m„ > ; — r_^ - L > 



000 00 ^ ^ 



o o 



(The sign of a fraction is not changed if the fraction is inverted or if 

 numerator and denominator are multiplied or divided by the same number. ) 

 If h > 0, the second inequality requires that: 



I^ 



L < h + 



o h m 

 o o 



and then the first inequality is satisfied also. Here, L may be positive 



or negative. 



If h < 0, substitute h = - |h I . Then 

 o ' o ' o ' 



87 



