Why? The Science of Athletics

SOME MATHEMATICS IN ATHLETICS 259 put into modern dress. All the same there are times when temperament and tactics enter into a race to such an extent that any thought of uniformity of pace at a distance of less than a mile would seem like athletic suicide. In I 866 the first English Open Pole Calculations Vault Championship was won at ro ft., a Concerning Jumping height which most first-class Public School boys can clear to-day; in I932 Wm. Graber, U.S.A., set the world's record mark at I4 ft. 4 3/4 ins. What were the factors that allowed him to clear a height that would have carried him through the first floor window of most residences ? I think the dicovery that bamboo poles are light to carry, allow a man to run at greater speed and yet are strong enough to bear his weight when vaulting to height, together with the introduction of the slide-way, which affords a fulcrum to the pole-point, are factors which account largely for the circumstance that the record has improved nearly 4 I/2 ft. in the last 70 years; but science has contributed to the dynamics of the event by teaching the athlete how a delayed swing, a strong pull and a quick push-up, following a very fast approach run, may enable him to propel his body over a lath set as much as 18 ins. above the height at which his hands grip the pole wherewith he makes his vault. Here is how the mechanics of the vault may be worked out. To determine the effect of approach speed upon the height the athlete is able to clear, or should be capable of clearing, it is first necessary to find the height to which a body will rise against gravity when its horizontal velocity is converted into vertical velocity. We will assume, therefore, that the athlete approaches his take-off at a rate of 25 ft . per second, i.e. 100 yards in 12 secs. The symbols to be employed in our calcula~on are v = velocity, h = height obtained, g = acceleration due to gravity, and t =the time taken for a body with velocity v to reach a given height.