Wrist-spin Applications #3: The “Square” Leg-Break

Now here’s a tricky one. The seam is vertical and the axis of rotation points straight down the same line as the direction of travel, and as such you’d expect there to be no effect on the ball whatsoever. Indeed, many textbooks will tell you there’s no effect – I’ve seen at least two that say this – but it just ain’t so!

To understand how a square leg-break uses the Magnus effect to generate drift, I’m afraid I’m going to have to teach you a little applied mathematics. Firstly there’s the difficult subject of vectors. Think of it like this: as the ball goes from bowler to pitch it is moving in two different directions at the same time, with two different forces acting on it. Firstly it is travelling horizontally down the wicket, and is held back by wind resistance, and secondly it is travelling vertically, first up into the air and then down onto the pitch as gravity attracts it towards the Earth. Or to put it another way, as you bowl the ball up to get some flight, it leaves your hand at a particular speed diagonally upwards that can be split into two component velocities: towards the batsman so that it reaches him after a certain time, and up into the air so that as it accelerates downwards it travels a certain distance horizontally before pitching, which dictates your length.

Well it turns out that spin – or, to call it by it’s proper scientific name, angular velocity – can also be split into component angular velocities around axies other than the actual axis of rotation. Think of a spinning ball in your mind, first with the axis of spin the same as the direction of travel. At this point the drift is zero. Now imagine turning the ball slightly, and there will be a small amount of drift, increasing gradually until the axis is perpendicular to the direction of travel – this is the point of maximum drift. Between these two points the drift will be some fraction of the maximum.

The diagram above represents the view from the side of a ball bowled by a right-arm wrist-spinner. The black arrows show the direction of travel, the blue line shows an axis at an angle to the direction of travel, the red axis is the axis of zero Magnus effect where the angle is 0, the green line shows the axis of maximum effect where the angle is 90 degrees, and the coloured arrows show the motion of the closer side of the ball as it spins. As the angle increases from zero, the percentage of the maximum drift generated varies as follows:

0 degrees: 0 % drift

15 degrees: 25.9 % drift

30 degrees: 50.0 % drift

45 degrees: 70.7 % drift

60 degrees: 86.6 % drift

75 degrees: 96.6 % drift

90 degrees: 100 % drift

This means the ball can be subject to a portion of the Magnus effect at any point where the axis of rotation is not directly along the line of travel. The reason most textbooks overlook this effect is that they lazily forget that the ball is not travelling in a straight line: it travels in a curved path up and down due to gravity, and hence the Magnus Effect does come into play, since the ball’s axis of rotation changes relative to its direction of motion, despite remaining horizontal at all times relative to the ground.

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