226 SYMPOSIUM ON AERONAUTICS. 



With an infinitely sharp gust ii^, w^, q^ may be considered as not 

 vanishing but as starting at finite values, /„, /,„, Jq. The derivatives 

 are then at the initial instant 



Dtl = XuJu -\- Xu-Jxc -f- XqJq, 

 DZV = ZtJu + ZyJiv + ZqJq, 



(8) 



kj,~Dq = Mufu ^MJ^ + MqJq, 



D6 = o. 



The first two equations give the X and Z accelerations of the ma- 

 chine which determine the stresses as the accelerations times the 

 mass. 



We have, for numerical values, 



Du = — .i28/„H- .162/,,, + o/q, if ^5 = 0, 



Z)w = — .557/„ — 3.95/,, + 0/.,, if Zq = o, 



ZADq = oJu + I ■74Jw — i S^Jq, i f M,, = o. 



The last equation determines the couple tending to break the ma- 

 chine, by bending in the .i--.:r-plane, on multiplication by the mass m. 



25. That which I have called an infinitely sharp gust is not an 

 impulsive gust. The implusive gust is both infinitely sharp and 

 infinitely intense, but endures for only an infinitesimal time. The 

 effect of an impulsive gust is to produce instantaneous changes in 

 u, zv, q. Such an impulse, like the impulses of ordinary mechanics, 

 puts an infinite strain on the machine for an infinitesimal time, and 

 the only way to tell whether the machine will stand the strain is to 

 take the yielding of the framework into account — it is a problem 

 in elasticity. For the purpose of calculating the stresses produced 

 by gusts on the machine I therefore prefer the sharp gust to the 

 impulsive gust. 



For the purpose of treating the motion of the machine after the 

 gust strikes it — the gust being now a sudden fierce squall in other- 

 wise still air — we have merely to determine the constants of integra- 

 tion from the initial condition «„, zv,„ q^, and 6 = 0, wdiere «,,, zi'q, go 

 are the impulsively generated velocities. These eqviations are 

 (p. 61): 



