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



" The Longitudinal Stability of Aerial Gliders." By G. H. Bryan, 

 Sc.D., F.R.S., and W. E. Williams, B.Sc., University College 

 of North Wales. Beceived June 18, — Bead June 18, 1903, — 

 Received in revised form January 7, 1904. 



1. Introduction. 



The main difficulty connected with the attempt to fly by means of a 

 machine heavier than air is that of longitudinal stability. It is not 

 difficult to construct an aeroplane system which shall be transversely 

 stable. 



But for this difficulty the problem of artificial flight would probably 

 have been solved already. Experiments in gliding under gravity have 

 been always made with machines not too large to be kept balanced 

 by the skill of the experimenter, and the glides, though undoubtedly 

 successful, have been of short duration. Experiments have invariably 

 stopped short of the performance of continuous flight by a mechanically 

 propelled machine. 



The problem of artificial flight is hardly likely to be solved until the 

 conditions of longitudinal stability of an aeroplane system have been 

 reduced to a matter of pure mathematical calculation. 



A theoretical investigation, even if calculated under conditions 

 slightly different to those occurring in nature, will serve as a basis 

 of comparison by which experimental results can be co-ordinated and 

 interpreted in their true light. 



The object of these investigations is (1) to show that the longitudinal 

 stability of aeroplane systems can be made the subject of mathematical 

 calculation; (2) to draw the attention of those interested in the 

 problem of artificial flight to the necessity of acquiring further 

 experimental knowledge concerning the quantities on which this 

 stability is shown to depend. 



2. General Investigation of the Longitudinal Stability of any Symmetrical 

 Aeroplane System. 



Consider any system of aeroplanes, having a plane of symmetry, 

 descending in a vertical plane, in air or in any resisting medium 

 whatever. To specify the motion (which we suppose to be two- 

 dimensional) choose two axes at right angles fixed in the body, having 

 the centre of gravity as origin. 



The motion will be completely determined if at every instant we 

 know — 



(1) the angle 6 which the axis of x makes with the vertical.* 



(2) the velocity components u, v, of the body along the two axes. 



* This angle is supposed measured from the dowmvard drawn vertical in the 

 positive direction. The axis of y must be drawn above the horizontal at an 

 inclination of 0. 



