Mr. G. T. Walker. On Boomerangs. 



239 



<4 On Boomerangs." By G. T. Walker, M.A., B.Sc, Fellow of 

 Trinity College, Cambridge. Communicated by Professor 

 J. J. Thomson, F.R.S. Received March 15, — Read 

 April 8, 1897. 



(Abstract.) 



A typical returning boomerang resembles in general outline a 

 symmetrical arc of a hyperbola, and is about 80 cm. in length 

 measured along the curve. At the centre, where the dimensions of 

 the cross section are greatest, the width is about 7 cm., and the thick- 

 ness 1 cm. 



Of the two faces, one is distinctly more rounded than the other ; 

 in addition the arms are twisted through about 4°, in the same manner 

 as the blades of a right-handed screw propeller. 



Such an implement, if thrown with its plane vertical, will describe a 

 circular path of 40 or 50 metres in diameter, rising to a height of 

 from 7 to 12 metres, and falling to the ground with its plane of rota- 

 tion horizontal at a point somewhere near the thrower's feet. 



The flight may be regarded as a case of steady motion, of which 

 the circumstances gradually vary. In the more complicated, as well 

 as the simpler, paths, observation makes it clear that everything 

 depends on the changes in direction and inclination of the plane of 

 the boomerang, and that the character of these changes is always the 

 same ; if they can be explained theoretically, the peculiarities of the 

 motion may be accounted for. 



Since the effects of the different forces at work are conflicting, it 

 is necessary to adopt quantitative methods, even if the degree of 

 accuracy attainable is not high ; accordingly ratios comparable with 

 a tenth are treated as small, and their squares neglected. 



If we regard the boomerang as a thin, slightly distorted lamina, 

 and integrate over it the forces indicated in S. P. Langley's paper on 

 " Experiments in Aerodynamics,"* we can obtain equations of motion. 

 From these, treating the motion as steady (to the first approxima- 

 tion), we may deduce the values of the angular velocities on which the 

 direction of the axis of rotation depends. Five cases are worked out 

 numerically, and the various effects of the "rounding " and " twisting " 

 agree in character with the experimental facts ; the discrepancies in 

 actual magnitude are not larger than might, from the nature of the 

 case, have been anticipated. 



The theoretical results may be further tested by applying them to 

 determine the conditions favourable to the production of other 

 flights in which, after the first circle, a loop is described, either in 



* ' Smithsonian Contributions to Knowledge,' 1891. 



