222 SYMPOSIUM ON AERONAUTICS. 



and as against the natural motion, we should reasonably expect to 

 require, i°, that the resonant frequency p be large (for if it be small 

 the pilot will have ample time to take care of it), and that, 2°, it be 

 reasonably different from any natural frequency which is only 

 slightly damped (for in the latter case the initial conditions will 

 probably be such as to cause the natural and forced effects to clash 

 for a considerable interval of time). 



This problem in its generality is so complicated that I have as yet 

 been unable to determine whether there may be practically serious 

 effects due to resonaiace, but from the cases I have here treated, from 

 the general considerations which I have advanced, with due regard 

 to the restrictions on p which appear to be reasonable, and from cases 

 which I have examined without mentioning them here, I should 

 judge that resonance is not a practically serious matter in longi- 

 tudinal motion, and that we may safely confine our attention to gusts 

 of the form /(i — e~^^). 



20. One type of resonance which deserves consideration is that 

 of the damped harmonic gust /^~"* sin pt. It would be conjectured 

 that if — n ± pi were nearly equal to a pair of roots of A^o, there 

 might arise a considerable disturbance. It is not likely that a gust 

 of this type would exist in reality, but the commencement of any 

 gust might resemble very closely the commencement of such a gust 

 and if the effect of this type were very marked as compared to that 

 of the types already considered, it would be necessary, for the sake 

 of foreseeing the worst that could happen, to discuss this type. 



I have not time to take the matter up here. Moreover, I imagine 

 that it would be found that the constants of integration turned out 

 to have such values that the gust, though tuned in damping and in 

 frequency to the natural motion of the machine, did not have very 

 large eft'ects except in cases where n and p were small enough to 

 allow the pilot easily to correct for the disturbance. 



The damped periodic gust has been treated by Brodetsky,^ who 

 finds the amplitude of the particular solution is a maximum (for the 

 machine I am dealing with) when ?=i6 sec. and is then a tolerably 

 large quantity, — but the pilot has a quarter of a minute in which to 

 react to his environment. It is, however, by no means certain that 



'^Aeronautical Journal, London, 20, 1916, p. 154. 



