MATHS AND PHYSICS OF CRICKET, ESPECIALLY SWING BOWLING Tickey de Jager January 2002

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1 Page 1 of 6 MATHS AND PHYSICS OF CRICKET, ESPECIALLY SWING BOWLING Tickey de Jager January 2002 H K F G $ The ball lands at A and moves along AFGHK, rising about a metre. It may also change direction because of spin (legbreak or off- break) and swing. But this change of direction is much less than the rise. The figures below show the situation as seen from the bowler's end, bowling to a righthand batsman. Fig 2 Offbreak and inswinger S R Fig 3 Legbreak and outswinger R S A B C Between A and DH, the ball moves a distance PS vertically and a distance SR horizontally. So it moves along PR. For maximum safety, the bat should therefore be parallel to PR. D E P Q Q P Players are coached to play with a vertical bat. A slope as in fig 3 is physically almost impossible. That is why legbreaks are more difficult to play. Returning to Fig 1: Between A and DH the ball is rising and it is very dangerous to play with a horizontal bat. * Apart from getting bowled, you can get a top edge and get caught. Because the ball is rising, it is also likely to go up off even a vertical bat and lead to a catch. In fact, the danger zone for batsmen is between A an CG, and the batsman tries to avoid playing a ball in that zone by playing forward or back. Between DH and EK the ball is going horizontally and should be played with a horizontal bat. This is the time to hook or square cut, not when the ball is rising. *(Exception: The sweep shot which depends on hitting the ball immediately after it lands.) $ Spin bowling Consider a right-hand offspin bowler as seen from the bowler's end. The spin is clockwise. If the axis of rotation is directly forward and horizontal, the ball will change direction a lot. If the axis of spin is vertical, the ball will not change direction when it lands. So the off-spin bowler can change the amount of change in direction (or in the language of cricket, the amount of spin he gets) by changing the direction of the axis of rotation. So can an orthodox left-hand legspin bowler. This seems to be little known, although righthand legbreak bowlers know it and use it to change from legbreak to topspin to

2 Page 2 of 6 googly. $ An elementary treatment of the physics of swing bowling Preliminary experiments: Force a) The change of the force of the air on a smooth sphere as the speed of the air increases. A smooth sphere is suspended from a balance in a wind tunnel so that we can measure the force of the air on it. If we increase the speed of the wind, the force increases, but at a certain speed, which we call the critical speed, the force suddenly becomes erratic. At higher speeds he force increases again. The graph shows all that. $ Why do we get this odd behaviour? In laminar flow the air is in contact with the ball all the way and there is friction between the air and the sphere. In turbulent flow less of the air is in contact with the sphere and so there is less friction. Once the air is turbulent, the friction between the air and the sphere naturally increases and that explains the last part of the graph. $ The difference of the force of the air on a smooth sphere and on a rough sphere If from the arms of a balance we suspend a smooth sphere and a similar one that has been roughened, place the apparatus in a wind tunnel with rising air, and observe what happens as we increase the speed of the air, this is what we will find: At low speeds the roughened sphere rises because the air resistance is greater, but at a certain speed, called the critical speed, the smooth sphere rises because the air flowing over the roughened ball is turbulent so the air is not in contact with the sphere and so the air resistance on the roughened sphere is less. Now we can try to deal with swing bowling. Speed At low speeds the flow of air over the sphere is laminar. That is, the molecules of air flow in a regular, steady way and their paths do not cross. At the critical speed, the flow becomes turbulent. That is, the flow is irregular and the molecules follow sinuous paths that may cross one another. You can see the change from laminar flow to turbulent flow in water running slowly from a tap. Near the tap it is laminar; further down it is turbulent.

3 Page 3 of 6 $ Swing bowling When a top is spinning it keeps standing on its point. That is why a swing bowler bowls the ball with backspin with the seam vertical and pointing more or less forward. The spin keeps the seam pointing in more or less that direction during flight. Let us consider a ball that is smooth on one side and rough on the other At very high speeds the flow is turbulent on both sides, so the air pressure is the same on both sides and the ball does not swing. When the ball slows to below the critical speed, the flow is turbulent on the rough side and laminar on the smooth side. Where the flow is turbulent, the air is not in such intimate contact with the ball, so the air pressure is less on the rough side than on the smooth side. So the ball swings towards the rough side. That is why a very fast bowler does not swing the ball while a slightly slower bowler can, and also why for many bowlers the ball swings late - as the ball comes below the critical speed. The ball often starts swinging when it hits the pitch because it then loses speed and so moves below the critical speed. If a bowler bowls below the critical speed, the flow is turbulent on the rough side and laminar on the smooth side all the way, so the air pressure is more on the smooth side than on the rough side and the ball swings towards the rough side all the way, which makes it easier to play. What matters is speed relative to the air, and so a fast bowler has even more trouble swinging the ball when bowling into the wind than usual. At low speeds the ball does not swing, perhaps because the flow is laminar on both sides, or perhaps because there is just not enough force to make the ball change direction. Let us consider a new ball that is still smooth on both sides, bowled with the seam pointing to the left. At very high speeds the flow is turbulent on both sides, so the air pressure is the same on both sides and the ball does not swing. When the ball slows to below the critical speed, the seam will make the flow turbulent on the left side and the ball will swing to the left. The ball often starts swinging when it hits the pitch because it then loses speed and so moves below the critical speed. The ball often starts swinging when it hits the pitch because it then loses speed and so moves below the critical speed. It is probably not only the seam acting as a rudder. This question can be settled by using overhead cameras. If the seam acting as a rudder causes the change in direction, the ball will travel like this: That is, it will change direction sharply and travel in a go straight after that..

4 Page 4 of 6 If the difference in pressure between laminar flow and turbulent flow causes the change in direction, the ball will travel like this: That is, it will change direction gradually and travel in a curve after that. $ 7 Some remarks on bowling 1. If a team has two opening bowlers, which one should bowl down the wind? Whether a ball will swing or not depends on its speed relative to the air. If a very fast bowler bowls into the wind, this speed will be above the critical speed all the way and the ball will not swing. If he bowls down the wind he will not only bowl faster, but at the end the speed of the ball relative to the air will be below the critical speed and the ball will swing. In South Africa's second innings in the Melbourne test of 2001, Steve Waugh correctly opened with the slower Glen McGrath into the wind and the faster Brett Lee down the wind. The late swing with which Lee induced Gary Kirsten to give a catch in the slips was a perfect example of how going below the critical speed lets the ball swing. 2. No-balls Longjumpers run about 30 metres flat out, and if they step 1 cm too far back, they lose 1 cm off their jump, and this may lose them the event. So they establish an exact run-up and practise running from it, always with exactly the same strides. Bowlers run a much shorter distance and more slowly, and if they step 10 cms too far back, it can surely make little difference. So why this passion for stepping close to a no-ball? Most bowlers mark out their run-up and seldom start precisely from it. There can be no reason for ever bowling a no-ball. It is not bad luck. 3. Bowling at the right speed for swing If the ball goes through the air too fast is will not swing because the air is turbulent on both sides of the ball. That is why a really fast bowler should bowl down wind. The secret of late swing is to bowl just above the critical speed. Then the ball will swing as it gets below the critical speed. Also, as the ball hits the ground, it is slowed down and so it then swings. When once a bowler understands the principles clearly, he will be able to work out the speed to bowl at to bowl at to swing the ball under the given conditions, and how to vary the amount the amount of swing. 4. Keeping the seam steady If the seam wobbles at all the airflow is slightly turbulent on the side where it should be streamlined and so the swing is less. So it is vital for the seam to be steady. A way to practise this is to paint one side of a ball white. Then it is easy to see whether the seam is steady. If it is not, one plan is to hold the ball with the index and middle fingers slight wider apart. The more backspin you put on the ball, the steadier the seam will be. It is also an effective and deceptive way to change pace. 5. Bounce The height that the ball will bounce depends on the downward speed at the moment of impact. A fast bowler bowls at an angle below the horizontal, so his

5 Page 5 of 6 speed has a downward component, and the faster he bowls, the greater the downward component and the steeper the bounce. A slow bowler bowls at an angle above the horizontal, so his speed has a upward component. The higher the ball is at the top of its flight, the steeper the bounce. 6. The effect of the dampness in the air The ball swings more when the air is damp. This is partly because a damp grassed pitch slows the ball down more. It may also be because dampness in the air changes the critical speed or because it increases the difference in pressure on the ball between laminar flow and turbulent flow. Side spin In tennis or table tennis, if the ball spins clockwise as seen from the top, it will swerve to the right. Shane Warne also seems to do this with a cricket ball. With topspin one can also get the ball to dip and drift in the direction in which the seam is pointing. Specific comments about the bowling of Kallis and Boje When Kallis temporarily lost the ability to swing the ball, it was probably because he was bowling too fast. He should bowl most of the time just above the critical speed so that the ball will swing late. That is, as it goes below the critical speed, which will usually happen at or just before it hits the pitch. He must also learn how to bowl, as a variation,. an extremely fast ball with no apparent extra effort.. With his natural skill, balance and control, he could become one of the best bowlers in the world. Nicky Boje Bounce The height that the ball will bounce depends on the downward speed at the moment of impact. Nicky bowls most balls almost horizontal. He will get more bounce if he bowls some slower balls as below as a variation. His spin will then also bite more. Spin If Nicky spins the ball so that the axis of rotation is horizontal and straight forward (if that is possible) he will get a lot of turn.

6 Page 6 of 6 If the axis of rotation points in some other direction, he will get less turn. If the axis of rotation points straight up, he will get no turn. If the axis of rotation points up diagonally to the left the ball may swerve to the right and break to the left as it lands. So Nicky can change the amount of turn he gets. Doing it that way makes him hard to read. Another device he can use is to bowl from A, B, C, E, F, G or even H. A B C E F G H