WILSON— AEROPLANE ENCOUNTERING GUSTS. 215 



may use p = o.2 in calculating the effect of a periodic gust of 

 maximum resonance on the aeroplane. \\'e shall first note that 

 for p=^o.2 the ratio of the amplitudes of the two fractions in (3) 

 is of the order 400 to i, and the first fraction is therefore entirely 

 negligible in determining the particular integrals. ' 

 For the second fraction we have the complex value 



4.263 - .2,2i (4.275, - 4-3°) /4-275 



A-275 . oA 



2.6i6i — .076 (2.617, 91-6°) 

 where the parentheses contain the polar coordinates of the complex 

 numbers. The expressions into which this is multiplied to determine 

 the coefficients of e'P* are for u/J, zv/J, 9/ J respectively 



— 0.922 — 0.676;'= ( 1. 144, 216.24°), 

 0.0983 -(-0.00456/= (.0984, 2.67°), 



— 0.00572'= (.0057, —90°). 

 Hence the values of n/J, zv/J , 0/J are 



u/J^=.{ — .965-)- 1.65/) (cos .2f-f-t' sin .2t), 

 zv/J={ — .00918 — .164/) (cos. .2f-f-j sin .2t), 

 6/J^{ — .00948 -|- .00098/) (cos .2t-\-i sin .2t), 

 and Iu = J(i-6^ cos .2t — .965 sin .2t), 



I^,, = J{ — .164 cos 2t — .0092 sin .2t). 

 I Q = J(.ooogS cos .2f — .00948 sin .2t), 

 I ' = ]{ — .0019 cos .2t — .0002 sin .21), 

 /„o=i.65/, Aco = — .164/, /go = .00098/, /'go = — .0019/. 



8. On substituting these values to find the constants of integra- 

 tion (p. 61), it is found that A and C, corresponding to the short 

 oscillation in n, are negligible. Also 5 = — 1-65/, D^.'/26J. 

 Hence 

 «==/g-0654f(_j_5- ^Qg .187^ +.726 sin .187O 



-|-/(i.65 cos .2t — .965 sin .2t'). 



In like manner (p. 62), A' and C are small and B'^.i/6J, D' 

 = —.051/. 



