WILSON— AEROPLANE ENCOUNTERING GUSTS. 227 



ii, = A+B, 



w,= — 4.04A + 34.5C— .1058Z) + .002587Z), 



= — -132 A — .0946C + .0024785 + .oo=,/ggD, 

 q^ = .yo^A -\- .205C — .001246Z) + .000084Z}. 



(9) 



Analytically the effect of the impulsive gust upon the equations 

 for determining the constants of integration is merely to replace the 

 initial values of the particular solutions luo, Iwo, ho> I'e^> obtained 

 on the hypothesis of finite gusts, by the respective values — Mq, 

 — Wq, o, — q,-j. The effect of the disturbance may therefore be 

 calculated at once from my equations (23), (24), (25), (26), as 

 soon as the values u^, ■cCy, q,^ have been determined. 



26. In the calculation of iia, Wo, Qo the same doubt arises as in 

 the theory of any very sharp gust, namely, the effect of the partial 

 immersion of the machine. Is the effect of a blow traveling along a 

 mechanism the same as that of the blow applied instantaneously at 

 all points of the mechanism? The possibility of a difference be- 

 tween the instantaneous immersion and the immersion distributed in 

 time would arise only if, 1°, the machine had time enough to change 

 its orientation appreciably or, 2°, the acquired velocities were suffi- 

 cient to change the relative wind and thus affect considerably the 

 impulsive pressure. 



Even if we assume that no material difference in effect is to be 

 expected, it is difficult to make the proper assumptions to lead to 

 reasonably satisfactory values for u^,, zi\„ q^ for any actual machine 

 whose characteristics are expressed in terms of the mechanical 

 coefficients m, k^~, U, and the aerodynamical coefficients Xu, Xiv, Xq, 

 Zu, Zxc, Zq, Mu, Mw, Mq. It is by no means certain that for a con- 

 siderable aerial disturbance the finite instantaneous changes in u, w, 

 q can be calculated from the equations (8) by replacing D by the 

 sign A for the increment and taking /„, Jic, Jq as the intensities of 

 the impulsive gusts ; for the nine coefficients Xu, etc., vary with the 

 intensity of the relative wind. 



It is for this reason that I have used finite gusts of various 

 degrees of sharpness instead of impulsive gusts. Moreover, it is 



