WILSON— AEROPLANE ENCOUNTERING GUSTS. 239 



taking place about every if seconds. A slower oscillation, i. e., a 

 longer periodic time, would diminish n and p, — an oscillation at one 

 spot every half minute corresponds to a value p^i.2 on the basis 

 of the assumptions made above. 



In considering the values of p which make the amplitude of r 

 large, the only hope is to make the term 34610/' — 23780/?^ tolerably 

 small. This means p^ must be about 1.5. For this value, the 

 modulus of r is about .03/ and the modulus of the yawing oscillation 

 corresponding will be about .025/. If a wind of 20 ft./sec. is 

 whipping through an angle of 45°, the side-gust will be only of 

 about 7 ft./sec. semi-amplitude and the angle of yaw will be in the 

 neighborhood of .175 radians or 10°. There is nothing to indicate 

 that this would be fatal, though it would surely be a nuisance. 



Owing to the fact that the coefficients of i in both numerator and 

 denominator are relatively small, the angular velocity Ir would be 

 about in phase with the gust v^, and hence the angle I ^ would be 

 about quartered in phase. If there were periodically an angle of 

 10° or 12° between the direction of flight and the relative wind, we 

 should find that we were getting into a region where considerable 

 rolling and pitching might be induced — for as Hunsaker has shown 

 (loc. cit., p. 62) the lateral and longitudinal motions are not strictly 

 independent; but as the machine makes the major part of the rela- 

 tive wind, the directions of flight and of the relative wind never 

 differ greatly — only some three degrees at most in the case under 

 consideration. 



It seems hardly necessary at this time to go into the calculation 

 of the actual motion ; enough has perhaps been accomplished in 

 showing that the oscillation of the direction of the wind induces at 

 most a moderate yawing of the machine. The semi-amplitude of 

 115.51// ^vould be, if 7 = 7 ft./sec, about 20 ft. ; the center of gravity 

 of the machine would sway back and forth across the line of flight 

 with a total amplitude of 40 ft., until the divergent term became 

 effective. 



40. Case 4. — Rolling gust. p^^J(i — c~''^). If there were no 

 interaction between v, p, r, the efifect on rolling of a rolling gust 

 would be figured from the equation 



