The Science of Soccer pdf

[...]... accuracy of the ball’s direction these two effects combine to give a requirement on the accuracy of the foot’s direction more like 158 The geometry of this example is illustrated in figure 2.9 The accuracy of the slower side-foot kick is much better than that of the fast kick struck with the top of the foot Because of the flatness of the side of the foot the error from Figure 2.9 When there is an error in the. .. the distance faced by a penalty taker Figure 2.7 gives a graph of the distance by which the target would be missed for a range of errors in the angle of the kick There are two sources of inaccuracy in the kick, both arising from the error in the force applied by the foot The first contribution comes from the error in the direction of the applied force and the second from misplacement of the 26 The science. .. kick the upper leg is driven forward and the lower leg whips through for the foot to transfer maximum momentum to the ball the ball would follow simply from two conservation laws The first is the conservation of energy and the second is the conservation of angular momentum These laws determine the fall in speed of the foot during the impact, and the resulting speed of the ball If, further, the mass of the. .. to the contact area, as illustrated in figure 1.3(b) These two descriptions are equally valid Because the force on the ball is proportional to the area of contact with the ground and the area of contact is itself determined by the distance of the centre of the ball from the ground, it is possible to calculate the motion of the ball The result is illustrated in the graph of figure 1.4 which plots the. .. and the resulting reduction in vertical velocity after the bounce has lowered the angle of the trajectory slightly In the more general case the ball slides at the start of the bounce, and the sliding produces friction between the ball and 12 The science of soccer Figure 1.6 Bounce on a slippy surface the ground There are then two effects Firstly the friction causes the ball to slow, and secondly the. .. figure 1.7 The friction slows the bottom surface of the ball, and the larger forward velocity of the upper surface then gives the ball a rotation If the surface is sufficiently rough, friction brings the bottom surface of the ball to rest This slows the forward motion of the ball but, of course, does not stop it The ball then rolls about the contact with the ground as shown in figure 1.8 Since the rotation... positions on the underside of a circular crossbar For the highest the top of the ball is 1 inch above the centre of the crossbar and the other positions of the ball are successively 1 inch lower Figure 1.11(b) gives the corresponding bounce directions, taking the initial direction of the ball to be horizontal and the coefficient of restitution to be 0.7 It is seen that over the 3 inch range in heights the direction... direction of the applied kick the error in the direction of the ball is much less 28 The science of soccer placement of the foot on the ball is virtually eliminated, leaving only the error arising from the direction of the foot This makes the side-foot kick the preferred choice when accuracy is more important than speed How fast? The fastest kicks are normally unhindered drives at goal, the obvious... negligible compared with the effective mass of the leg, the speed of the foot would be unchanged on impact In this idealised case, the ball would then ‘bounce’ off the foot and take a speed equal to twice that of the foot In reality the leg and the foot are slowed on impact and this reduces the speed of the ball Frictional losses due to the deformation of the ball cause a further reduction in speed This... 2.3 The lower rod is pulled around by the upper rod and is thrown outward by the centrifugal force, accelerating the foot of the rod 22 The science of soccer does so As the upper rod moves round, the lower rod ‘whips’ around at an increasing rate and in the final stage illustrated the two rods form a straight line The whipping action gives the foot of the lower rod a speed about three times that of the . of the centre of the ball from the ground, it is possible to calculate the motion of the ball. The result is illustrated in the graph of figure 1.4 which plots the height of the centre of the. with the ground the air press- ure is uniform throughout the ball. When contact occurs and Figure 1.1. Sequence of states of the ball during the bounce. 6 The science of soccer the bottom of the. results, what is the best time of year for them to be born? Further subjects include analysis of the laws, various theoretical aspects of the play, and the economics of the professional game. In the first