Spin-bowling in cricket re-visited: model trajectories for various spin-vector angles

In this paper we investigate, via the calculation of model trajectories appropriate to slow bowling in cricket, the effects on the flight path of the ball before pitching due to changes in the angle of the spin-vector. This was accomplished by allowing the spin-vector to vary in three ways. Firstly, from off-spin, where the spin-vector points horizontally and directly down the pitch, to top-spin where it points horizontally towards the off-side of the pitch. Secondly, from off-spin to side-spin where, for side-spin, the spin-vector points vertically upwards. Thirdly, where the spin-vector points horizontally and at 45 degrees to the pitch (in the general direction of 'point', as viewed by the bowler), and is varied towards the vertical, while maintaining the 45 degrees angle in the horizontal plane. It is found that, as is well known, top-spin causes the ball to dip in flight, side-spin causes the ball to move side-ways in flight and, perhaps most importantly, off-spin can cause the ball to drift to the off-side of the pitch late in its flight as it begins to fall. At a more subtle level it is found that, if the total spin is kept constant and a small amount of top-spin is added to the ball at the expense of some off-spin, there is little change in the side-ways drift. However, a considerable reduction in the length at which the ball pitches occurs, similar to 25. cm, an amount that batsmen can ignore at their peril. On the other hand, a small amount of side-spin introduced to a top-spin delivery does not alter the point of pitching significantly, but produces a considerable amount of side-ways drift, similar to 10. cm or more. For pure side-spin the side-ways drift is up to similar to 30. cm. When a side-spin component is added to the spin of a ball bowled with a mixture of off-spin and top-spin in equal proportions, significant movement occurs in both the side-ways direction and in the point of pitching, of the order of a few tens of centimetres.