104 



Dr. G. H. Bryan and Mr. W. E. Williams. [Jan. 7, 



depend on the form and dimensions of the machine and the angle of 

 gliding. 



We shall now show how the nine coefficients X« . . . Qe can be 

 calculated for a system of aeroplanes if the laws of variation of the 

 resultant pressures and of the positions of the centres of pressure are 

 known. We shall assume that .the resultant pressure on a plane 

 lamina varies as the square of the velocity, and acts in a direction 

 normal to the lamina. 



We may therefore write 



R = KSVy(a), 



where S is the area of the lamina, V the velocity, and a the angle 

 between the plane of the lamina and the direction of' motion, K a 

 constant depending on the units employed. 



The function / (a) has been determined by Langley* for certain 

 rectangular planes. 



Also, let the distance of the centre of pressure from the centre 

 of figure be a<j> (cc), 2a being the breadth of the lamina. 



Experiments to determine (f> (a) for square planes have been made 

 by Joesel,f Kummer,J and Langley,§ and Kummer has also experi- 

 mented on oblong planes, with their longer side in the direction of 

 motion. 



Their results show a certain amount of discrepancy, and there 

 appears to be considerable difficulty in obtaining consistent results 

 at small inclinations. 



Further experiments are very necessary, and it is to be hoped that 

 more attention will be given to determinations of («), when their 

 importance, as affecting the stability, has been recognised. 



Experiments show that / (a), <f> (a) are, to a first approximation, 

 independent of the translational velocity of the lamina, but the effects 

 of a rotational angular velocity, 6, have never been considered. 

 It would not be difficult to determine these effects by experiments 

 with a whirling table, making 6 the angular velocity of the table. 

 Failing such experiments, these effects must be neglected, and, as 6 is 

 zero in the steady motion, and only small oscillations are considered, 

 they are probably small. When the system consists of a number of 

 planes rigidly connected together, we may now write the component 

 forces and couple in the form 



mX = EKSiV i 2 /(a 1 - ft) cos ft ^ 



mY = SKSiYi 2 /^! - ft) sin ft L (7), 



mG = SKSiVx 2 /^ - ft) { Pl + atf (a x - ft)} J 



* ' Experiments in Aerodynamics,' p. 62. 

 f Joesel, ' Memorial dn Genie Maritime,' 1870. 

 X ' Berlin Akad. Abhandlungen,' 1875, 1876. 

 § Loc ext., p. 90. 



