WILSON— AEROPLANE ENCOUNTERING GUSTS. 237 



For this calculation v and y\i may be simplified to 



v^ — J A^ ] e--^"^^^^ {cos 1.215? — .2 sin 1.215?), 



100./. = — .378/ — .4/r"2«c« _|_/^-. 3208^(^8^2 COS 1.215O; 

 and 



3' = — .56/f + i8.5/(^«-^2*'* — I ) — -146/ 



_|_ j^-.326Si(^_j^5 COS 1. 215? -|- .066 sin 1.215?). 



From this it will be seen that the oscillatory motion is, so far as 

 concerns the lateral displacement, of very small amplitude. The 

 first two terms which are progressive, are the ones which count. 

 Moreover, the displacement is of the same sign as J although the 

 side-slip v is of the opposite sign. This apparent contradiction is 

 due to the change in orientation \\j — the machine moves away from 

 the gust owing to the lateral excess wind-pressure, but turns into the 

 gust owing to the moment of the pressures, and by virtue of the 

 great forward velocity, this turning more than makes up, in the dis- 

 placement, for the side-slipping. 



38. Case 2. — Side-gust — mild. v^^J{i — ^"•^*). 



/r = /(— I + 1. 0205^--*), /t.o = .0205/, 



l^ =/(.ooo4O43^--0, 7^0= -0004043/, 



r^=j{ — .0000809^--' )> i'^[i= — .0000809/, 



Ir = J{— .001514^--*), /ro =— .001514/, 



Coi= .000331/, Coo = .00000738/, C23 = .0000807/, 



Co4 = . 0001055/. 



It is again seen that there is practically no rolling motion pro- 

 duced by the side-gust. For v and r, 



z///=.0027e-°-^^'^* — I + 1.0205^--* 



_j_^-.326si(^ — .0244 cos 1. 215? + .1554 sin 1.215O, 



ioor// = — .0085^°'*^''* — .I5i4e'--' 



+ ^-•■■'-'^^'(.1628 cos 1.215? -f- .0672 sin 1.215?). 



(The check v^=o, r = o, when t = o, shows that the accuracy has 

 been reduced so that the third place is not sure.) The effects of 



