Internal Work of the Wind. 



441 



Tig. 2. 



the plane alternates in its aspect to correspond with the 

 changes in the wind. 



It may aid in clearness of conception, if we imagine a set 

 of fixed coordinates X Y Z passing 

 through 0, and a set of movable 

 coordinates x y z, moving with the 

 velocity and the direction of the 

 mean wind. If the moving body 

 is referred to these first only, it 

 is evidently subject to pulsations 

 which take place in the same 

 directions on the axis of X, but it 

 must be also evident that if re- 

 ferred to the second or movable 

 coordinates, these same pulsations 

 may be, and are, in opposite direc- 

 tions. This, then, is the case we 

 have just considered, and if we 

 suppose the plane to change the 

 aspect * of its (constant) inclina- 

 tion as the direction of the pulsa- 

 tions changes, it is evident that 

 there must be a gain in altitude 

 with every pulsation, while the. 

 plane advances horizontally with the velocity of the mean 

 wind. 



During the period of maximum wind velocity, when the 

 wind is moving faster than the plane, the rear edge of the 

 latter must be elevated. During the period of minimum 

 velocity, when the plane, owing to its inertia, is moving faster 

 than the wind, the front edge of the plane must be elevated. 

 Thus the vertical component of the wind pressure, as it strikes 

 the oblique plane, tends in both cases to give it a vertical 

 upward thrust. So long as this thrust is in excess of the 

 weight to be lifted, the plane will rise. The rate of rise will 

 be greatest at the beginning of each period, when the relative 

 velocity is greatest, and will diminish as the resistance pro^ 

 duces " drift;" i. e. diminishes relative velocity. The curved 

 line B in the vignette represents a typical path of the plane 

 under these conditions. 



It follows from the diagram (fig. 1) that, other things being 

 equal, the more frequent the wind's pulsations, the greater 

 will be the rise of the plane; for since during each period of 



* We do not for the moment consider now this change of aspect is to be 

 mechanically effected ; we only at present call attention to the fact that 

 it involves, in theory, no expenditure of energy. 



Phil. Mag. S. 5. Vol. 37. No. 228. May 1894. 2 H 



