240 SYMPOSIUM ON AERONAUTICS. 



2>^.7Dp + 314^ = - 314^(1 - e-'-O, 



^/J = _ I + ,-8.055. + ^ ^-^55 ^_, _ 8.055 



.055 - r 8.055 - '' 



This means that for any ordinary sharp gust p rapidly acquires the 

 value — /, and (^ the value — Jt (radians). It must therefore be 

 expected that unless / is very small indeed, the motion will be much 

 disturbed. There will be developed a component of the weight in- 

 ducing side-slipping, and yawing will rapidly develop — the machine 

 apparently goes off on a spiral dive. 



We may make the calculations in detail when r=i. Here 

 V/ = — 3.14— .114^-*, /,o=r:_3.25/, 



/^// = 40.4—1.1^-*, /_^, = 39.3/, 



/r//=io.58 — .234^-S 7,^=: 10.35/. 



Coi=: — 39.1/, Con=^.oo2yJ, €"23 = — .219/, C24 = — .163/. 



The equations of motion become 

 </>// = — 39.i^0'^2'^* + .oo3g-^-5"f ^40_4_ J j^-f 



_|_ ^-.3268t(- — 219 COS 1. 215; — .163 sin 1.215O, 

 V / J = 2,2^e-^'^^^^ + .0103^'^-^*"' — 3.14 — .114^"' 



_j_ ^-.3268f(- — 220 COS 1.215^-1-49.2 sin 1.2150, 

 r// = — io^°2436* _|_ jQ_rg — .234(?-' 



_|_^-.3268f(__23 COS 1.215^-1-3.35 sin 1.215O. 

 In the equation for (/> the effective terms are 



and there is a steady divergence in <^ to the approximate amount 

 — Jt as foreseen. The side- ways velocity v develops more slowly, 

 perhaps, but after one second amounts to something like 300/. It 

 is clear that / must be very small or the motion becomes disastrous. 

 It would be of especial interest to know what sorts of magnitudes 



