216 SYMPOSIUM ON AERONAUTICS. 



w= /^-•0G54f(-_j^5 (,Qg .i87^_.o5i sin .187O 



— /(.164 cos .2f-f .009 sin .2t) — .oi2/^-*-i®* cos 2.43/. 



(The last term is added as a check on the initial condition w = o.) 

 Finally (p. 62), A" = .00007/, B" = .00104/, D"^.oiog/, and 

 Q^jg-.oG:>it(^ — .00104 cos .187^ + .0109 sin .187O 



+ /(.ooo98 cos .2t — .00948 sin .2t) -\- .ooooy/e-^-^^^ cos 2.43^ 



9. Now to find the rise of the machine when the gust strikes it 

 (p. 64). 



w-f ii5.5^ = /^-'06s*'(.o56 cos .187?+ 1.208 sin .187^) 



— /(.051 cos .2f-|- 1.064 sin .2t). 



The cosine terms may be omitted. The integration then gives 



.£: = 5.32/ cos .2/ + 0.44/ — /^-°«5'**(2 sin .187^+5.76 cos .i870- 



A table of values of z may be computed as : 



/ = o, 2, 4, 6, 8, 10, 12, 14, 



2// = 0, O, —.15, —.54, —1. 16, —1.90, —2.60, —2.97. 



This shows the rise or drop, according as / is negative or posi- 

 tive, during the first cjuarter minute. The values of s now fall ofif, 

 pass through o, and only become large as t nears 35. The natural 

 oscillation is then becoming less efifective relative to the forced 

 oscillation which has a double amplitude of about 10.6/, or 202 ft. 

 if / = 20 ft./sec. 



As the existence of a regular periodic gust for any long time is 

 almost unbelievable, the only real interest in the calculation is in 

 showing that during the first 15 seconds the efifect of resonance fails 

 to become so far established that the motion differs appreciably from 

 that due to the simple head-on gust previously studied (p. 74). 



10. In the case of the machine constrained to remain horizontal 

 during flight (by some automatic steering device), the corresponding 

 equations (p. 69) are for u^ = /c^p^ 



n ^ _ .i28/)i+.598 .^^^ 

 / .598 -/>2_|_ 4.078^4^ ' 



"'l ^ -A^lPi ^ipt 



J .598 - p- + 4.07Spi 



