Cricket Ball Physics

The Two Effects Considered, the swerve of the ball — dependent on the spin — and the swing of a fast ball — dependent on the seam — arise from the presence of a very thin layer of air, about a hundredth of an inch thick, which adheres to the surface of a moving ball. This layer is known as the 'boundary layer'.

The swerve of a spinning ball is described by the Magnus effect. Only the spin component about an axis perpendicular to the direction of motion of the ball is important here. Since the ball moves forward whilst spinning, the air in the boundary layer on one side of the ball has a speed relative to still air greater than that of the ball itself, that of the other side a speed less than that of the ball itself. Bernouilli's equation tells us that there is exerted on the ball a smaller air pressure on that side at which the speed is greater, so that there is a net transverse thrust on the ball.

Now for the swing. Consider firstly what would happen if the ball had a uniform surface (no seam). The thin boundary layer of air would be retarded at the surface by friction but would be dragged round the ball (and finally be swept away as a turbulent wake at the rear) by viscous forces arising from still air further away. The motion would be affected also by the pressure gradient along the surface, which would tend to place the line of reformation of the boundary layer away from the rear, while the viscosity would tend to place it near the rear of the ball. As the viscosity varies as the speed of the ball, and the pressure gradient as its square, the line of reformation (near the rear for a slow ball) moves towards the front as the ball's speed increases, until at the so-called critical speed it is at about eighty degrees from the front of the ball.

At this speed the motion of the boundary layer suddenly becomes turbulent, and this causes mixing of the surrounding still air (which is moving quickly with respect to the ball) with the air of small relative speed near the surface. The consequent increase in momentum transfer increases the effective viscosity, subordinating the pressure gradient effect and so causing the line of reformation to move back again towards the rear. Surface roughness, especially if it is near the front of the ball where the boundary layer is extremely thin, assists the transition to turbulence, so lowering the critical speed.

The seam consists of a band of six parallel lines of stitches round an equator of the ball. The zone is about three-quarters of an inch wide and the four outermost lines page 15 stand out about a fiftieth of an inch. This roughness causes negligible turbulence for a slow ball but for a faster one (still below the critical speed) the boundary layer becomes thinner, and, if the seam of an otherwise smooth ball is inclined to its direction, turbulence is produced on only one side of the ball. On this side the reformation of the boundary layer is delayed and the resulting asymmetrical pressure distribution makes the ball swing sideways. This effect would be lost if the ball were rough all over, as the boundary layer would then be everywhere fully extended.

The side affected by the seam should be left rough, the other side polished and the ball given a slight rotation about an axis perpendicular to the plane of the seam for maximum swing. The reason for the rotation is that without it the greater friction on the turbulent side of the ball would cause the plane of the seam to rotate, increasing the effective area of roughness and giving a symmetrical turbulent flow and so a symmetrical flight to the ball. If, however, the plane of the seam rotates very slowly the ball may swing to one side and then to the other.

'Late swing' may occur with fast bowling because the ball is initially travelling above the critical speed so that turbulent flow exists on either side of the ball. Resistance to the ball's motion finally reduces the speed to less than the critical value and swing occurs.

Swinging is more marked in sultry weather because eddies in the air form more frequently and the boundary layer is thicker and so less affected by surface roughness — except that of the seam, which, in the humid conditions, swells and increases its effect. In this sort of weather shine on the ball is of less importance and even old balls can be made to swing.

(The above is a résumé of a talk given to the Mathematics and Physics Society by Dr Burns, Senior Lecturer in Applied Mathematics.)

Charles Pearse