Methods for measuring the coefficient of restitution and the spin of a ball

Abstract

F our m ethods for measuring the coefficient of restitution of a ball are discussed and employed experimentally. These methods are : 1. The two-pendulum ballistic method of Thomas, in which the ball is struck by a flat-nosed projectile driven from an airgun. 2. A method based on spark photograp h y, b y m eans of which the ratio of the speed of the ball to that of the projectile is det ermined. 3. The measuremen t of the vertical rebound of a ball from a m assive horizon tal plate , when dropped from a known height, correction being made for air resistance. 4. The measurem en t of the angle of reflection of a ball rebounding from a smooth inclined plate, the angle of incidence being k nown. A correction for spin is necessary in method 4 if the plate is not ideally smooth. Methods are described for m ea suring the spin velocity, a nd an app roximate method for computing t he spin is given, provided the coeffi cient of restitution is known. The variation of the coeffi cient of restitut ion of golf balls with impact sp eed an d with t empera ture is experimen t ally det ermined, a nd a m ethod for determining t he time interva l during which the ball remains in contact with the club is described. The coefficient of restit ution of a golf ba ll wh en hit ha rd is roughly 0.7; the corresponding value for a baseball of p rewar construction is abo ut 0.45. CONTENTS Page I. In trod uction _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ , 2 II. Coefficient of restitution_ _______________________________ __ ______ 2 III. Ballistic method _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 3 IV. Spark photography as a m eans of determining the coefficient of restit ution ________ ____ __ ______ ____ _____ __________________ _. _ 5 V. Perpendicular rebound from a flat plate_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 7 VI. Rebound from an inclined plate__ __ _____ __ ____ ___________________ 10 VII. Measurement of spin _____ ~ ____ " _____ ________ __ _____ _____ , _______ 11 1. Measurement of spin by spark photography _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 12 2. Measurement of spin from residual turns_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 12 3. Computation of spin ___ __ ~_ ___ ___ ______ _____ _ ___ __ __ _ ____ 13 VIII. Correction for spin_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 15 IX. Effect of impact speed on the coefficient of restitution _ _ _ _ __ _ _ _ _ _ _ _ _ 16 X. Contact area of a deformed balL _____________ __ __ __ :, _ _ _ _ _ _ _ _ _ _ _ _ 17 XI. Duration of contact between ball and projectile_ _______________ ____ _ 18 XII. Influence of temperature on the coefficient of restitution _ _ _ _ _ _ _ _ _ _ _ _ 19 X III. Variation in the coefficient of restitution of golf balls_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 20 XIV. Coefficient of restitution of baseballs _ _______ ____________ _______ __ 21 1 .,