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SMITHSONIAN CONTRIBUTIONS TO KNOWLEDGE 



VOL. 



2. Consider that the renter of pressure is directly over the renter of gravity 

 (<'/',- CGi 0), and in this ease inquire what angle the aerodrome itself may 

 take during horizontal flight. 



First ease. The diagram (Fig. 4) represents the resultants of the separate 

 tern of forces acting on the aerodrome, and these resultants will lie iu a verti- 

 cal medial plane from the symmetry of their disposition. 



Let af represent the resultant of the vertical components of the pressure on 

 the wings; the horizontal component will lie in the line ae. 



Af 



a. \r 



^r 



J- 



Fig. 4. Diagram showing relation under certain conditions of thrust, C. P. and C. G. 



Let the center of gravity be in the line bd, and the resultant thrust of the 

 propellers be represented by cd. 



Let 1L = weight of aerodrome. 



Let T = thrust of propellers. 

 Then if we neglect the horizontal hull resistance, which is small in comparison 

 with the weight, equilibrium obtains when II' ■ ab=Txbd. 



Sec nnl case. The diagram (Fig. ">) represents the same system of forces 

 as Fig. 4, but in this case the point of support is directly over the center of 

 gravity g, when the axis of the aerodrome is horizontal. 



Let W= weight of aerodrome. 



Let T = thrust of the propellers. 



Let R=distance of CG S below CP t =ag. 



Let S^distance of thrust-line below CP~ = ad. 



If now the aerodrome under the action of the propellers be supposed to 

 turn about the CP 2 (or, a) through an angle a, so that g takes the position g', we 



