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The Quarterly Journal of Mechanics and Applied Mathematics 1949 2(1):30-39; doi:10.1093/qjmam/2.1.30
© 1949 by Oxford University Press
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THEORY OF A LOOP REVOLVING IN AIR, WITH OBSERVATIONS ON THE SKIN-FRICTION

C. C. L. GREGORY

( University of London Observatory Mill Hill Park, N.W.7 )

An investigation is made of the dynamics of a flexible loop, driven by a small pulley at a constant speed, for the case when the speed is sufficient to cause the loop to become air-borne. It does this when the air-friction is greater than the weight of the loop. The shape and position of the loop may be calculated for values of the ratio, 2{alpha}, of air-friction to weight and the angle, ø*, that the tangent to the ascending portion of the loop at the pulley makes with the horizontal. This angle may be controlled by means of a second pulley so arranged as to press the loop against the driven pulley. If {alpha} = 1, theory predicts a point of the loop at which its radius of curvature becomes zero. For values of {alpha} between 1/2 and 1 the motion is stable, and the precise value of {alpha} may be found from the photographed shape of the loop. As the result of some trials, values of {alpha} have been obtained which have given a value of the air-friction drag coefficient of the right order of magnitude.


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