230 SYMPOSIUM ON AERONAUTICS. 



deliver a constant thrust or a constant power is not very important 

 to the theory either of stability or of gusts. It is not unlikely that 

 the actual behavior of the screw lies within the limits set by these 

 two assumptions or sufficiently near to one of the limits to validate 

 the use of either hypothesis. 



The Aeronautical Journal, London, 20, 1916, p. 142, quotes 

 Bairstow and Fage as giving the formula 



dH ^ — .oiiHdV, V in miles per hour, 



which is dH^= — .ooy 7,HdV, V in feet per second. 



With [/= 115.5 numerically we would have for constant power 



dH = — .oo866HdV, V in feet per second; 



and, if I understand correctly the use of the signs -\- and — in the 

 quotation, the results are in as good agreement as could be expected 

 in view of the fact that I have no knowledge of the value of U 

 for which the data quoted are given. (If the motor and screw were 

 exactly designed to give a maximum efficiency at a standard speed 

 U, we could not expect the efficiency to be the same at relative air 

 speeds either higher or lower, and this would slightly influence the 

 result.) 



Equations for Lateral Motion. 



30. The dififerential equations for the lateral motion of a machine 

 in a gust may be written as (p. 54) : 



dv/dt + g4> -\-Ur— Y^v — Ypp — F^r = Y,z\ + Ypp, + Yrr„ 



A/m. dp/dt — L^v — Lpp — Lrr = LvZ\-\-Lpp-^-\- Lrr^, (12) 



C/m. dr/dt — N^v — N.p — Nrr = N,v, + Npp^ + Nrr^, 



where the terms involving the small unknown product of inertia E 

 have been neglected and gusts of the type v-^, p^, r^ have been 

 allowed. 



The gust z\ corresponds to a side wind. A change in the direc- 

 tion of the wind by a small angle would produce such a gust even 

 in absence of any change in the wind velocity. The gust p^ is a 

 rotary gust tending to produce a bank ; as a disturbance in the air 

 it would correspond to a horizontal roller run into end-on (axially). 



