WILSON— AEROPLANE ENCOUNTERLNG GUSTS. 243 



46. It would be a relatively easy matter to discuss the effect of 

 gusts of various types on the aeroplane constrained in various ways ; 

 two equations are much easier to handle than three. Until some 

 definite problem is proposed as important, until some particular con- 

 straining device is indicated as likely to be adopted, it may be as well 

 not to go into the calculations, which are quite straightforward. 



That a constraint against rolling might be worth while, and 

 would indeed be very valuable if rolling gusts were a common thing, 

 is suggested by the work done on the free machine (§42) where 

 gustiness was seen not to be very serious except for the rolling gust. 



Discussion of Method. 



47. I pointed out in my earlier paper that there were several 

 outs about my method of treating gusts. First the gusts must be 

 small. If they are not tolerably small, flying would be too difficult — 

 so that assumption is not wholly unjustifiable. Second, the calcula- 

 tions for determining the individual equations of motion and for 

 determining formulas for the constants of integration are very 

 tedious. Third, the numbers are of such various magnitudes that 

 the arithmetical operations which must be carried out cut down the 

 accuracy of the work a good deal and indeed, unless great care is 

 taken, will lead to illusory or incorrect results. This does not ap- 

 pear to be due to any very rapid variation of the true results cal- 

 culated from varying data, but to the mode of computing. 



To offset these inconveniences we have the satisfactory result 

 that once the preliminary calculations are made, many and varied 

 types of gusts may easily be treated, and the further valuable result 

 that the actual motion for each case is known so that not only the 

 initial motion is determined, but the whole extent of the motion. 

 This last is necessary for any just appreciation of the eft'ects of 

 periodic gusts and resonance, as has been shown. 



48. For another method of treating gusts reference may be made 

 to a recent paper by Brodetsky and Bryan, " The Longitudinal Initial 

 Motion and Forced Oscillations of a Disturbed Aeroplane," Aero- 

 nautical Journal, London, 20, 1916, 139-156, which has already 

 been cited in the text. 



