Science of Cricket 

part 2 - Balling

1. Force on a cricket ball

Drop a cricket ball on a cricket pitch and the ball bounces up off the pitch. How long does the ball remain in contact with the pitch and how big is the force on the ball? Cricket balls are relatively stiff compared to say a tennis ball, and the contact time is shorter. A tennis ball spends 0.005 seconds in contact with the court or the strings of a racquet. A cricket ball spends about 0.001 seconds in contact with the pitch or in contact with a bat. 

The force on the ball has to slow it down to a complete stop and then accelerate it back in the other direction, all in the space of 0.001 seconds. Suppose that a 0.16 kg cricket ball hits a bat at 100 km/hr and then comes off the bat at 100 km/hr in the reverse direction. Imagine a car accelerating from 0 to 100 km/hr in 0.001 seconds. That's a lot of acceleration. A Porshe can do it in 5 seconds, but a cricket ball does it 10,000 times faster. The average force on the ball is 8,800 N,  enough to lift a mass of 880 kg off the ground. The peak force on the ball is about double that, enough to lift a 1.76 tonne car off the ground. That's why it hurts to get struck on the head or anywhere else with a cricket ball.

2. Air resistance

Air plays an important role in cricket. Apart from allowing players to breathe, it causes the ball slow down through the air and it can cause a ball to curve or swing away from the path it would otherwise follow. Air is heavier than you might expect. One cubic metre of air at ground level weighs 1210 gm. A cricket ball weighs 160 gm. A room full of air weighs more than most cricket players.

If you drop a cricket ball out of a helicopter hovering 300 m above the ground, it will accelerate up to 123 km/hr in about 5 seconds, having fallen through a distance of about 100 m. It will then fall the remaining 200 m to the ground at 123 km/hr, without gaining any additional speed. At 123 km/hr, the force of gravity pulling the ball down is equal to the drag force of the air pushing it upwards. The total force on the cricket ball is then zero so it falls at constant speed after the first 100 m. A more dramatic effect would be seen if you dropped a cricket ball into a swimming pool. Air has the same basic effect as water in slowing the ball, but it is a smaller effect.

A ball bowled horizontally at 123 km/hr experiences a backwards horizontal drag force that is equal to the weight of the ball. At world record bowling speeds around 160 km/hr, the drag force is 1.7 times greater than the weight of the ball. Regardless of the speed of the ball when it leaves the bowler's hand, air resistance causes the ball to slow down by about 12% by the time it lands on the pitch. It slows down by another 30% or 40% when it hits the pitch, depending on the speed of the pitch and the angle of incidence. A ball bowled at 150 km/hr will arrive 0.46 s later at the batter's end, travelling at about 85 km/hr.

3. Collision between bat and ball

What happens to a ball when it hits a bat? It comes in at around 100 km/hr, reverses direction, and bounces off the bat 0.001 seconds later. But what happens during that 0.001 second it is on the bat? Assuming that the ball is hit in the middle of the bat and heads off straight back to the bowler, all that happens is that the ball squashes, comes to a complete stop, expands back to its original shape and then leaves the bat. If the ball comes off at some other angle, then it hits the bat at an angle and starts to slide across the bat. As it does so, it slows down in a direction perpendicular to the face of the bat and it slows down in a direction across the bat. In addition it will start to rotate if it had no rotation to start with, otherwise the rate of rotation will either decrease or increase depending on the original direction of rotation. The part of the ball in contact with the bat will then grip the bat without any further sliding or rolling, while the rest of the ball continues to rotate. The ball therefore gets twisted out of shape as well as getting severely squashed. As the ball starts to come off the bat it expands back towards its original shape, it releases its grip on the bat, there is a sudden change in the rate of rotation, and the ball slides backwards off the bat. Most likely, the ball will come off the bat spinning much faster than it was before it hit the bat.

4. Wicket keeping

Suppose that a wicket keeper needs to move as fast as possible to the right to catch a ball. Which foot should move first, and in what direction? It seems obvious that his left foot should stay on the ground and his right foot should move to the right while pushing as hard as possible to the left with the left foot. That way, his whole body and every part of it moves rapidly to the right. But suppose he pushes to the left with his left foot and moves his right foot to the left. That way, he will tend to fall over to the right and his upper body moves even faster to the right. Such a step is called a gravity-step and it is counter-intuitive.

The same situation arises when a tennis player is facing a 200 km/hr serve and needs to move as fast as possible to the right.  High speed film shows that players who move their right foot to the left, before moving it to the right,  get their racquet to the ball faster. The physics explanation is that keeping the feet together reduces the moment of inertia and the upper body will therefore rotate faster. The same sort of thing happens when a diver wants to do a double or triple somersault. Tucking the arms and legs in reduces the moment of inertia and the diver spins faster.

5. World's fastest bowler

The cricket equivalent of a 4 minute mile is to bowl a ball at 100 mph (161 km/hr). Akhtar and Lee have come close, but noone knows for sure if they have actually done it yet. The newspapers said that Akhtar did it in 2002, but how do we know that the radar gun was correct? I know for a fact that it wasn't correct because they never are. That's because (a) the ball doesn't travel straight at the gun and (b) the ball slows down down through the air by 0.6 mph after it travels the first 1.0 m. If a 100 mph ball travels 5 degrees away from the gun the speed will be recorded as 99.6 mph. Balls are bowled about 5 degrees down from the horizontal and anything up to 5 degrees horizontally away from the middle stump. That can give an error of around 1 mph in the recorded speed.

In order to get the speed to the nearest 0.1 mph, the gun would need to point almost exactly in line with the ball and it would need to capture the speed before the ball travels 160 mm out of the bowler's hand. That means the gun has to be located near the stumps. Also, the ball can't rotate because it might gain an extra 1 mm if the seam comes into view, so it could gain an extra 0.6 mph.

If someone ever bowls a ball at 101 mph then there will be a good chance that it was actually 100 mph or more. Until then Akhtar's 161 km/h (100.04 mph) should be taken with a grain of salt. All recorded speeds should be quoted as plus or minus 1 mph or whatever the appropriate margin of error happens to be.

6. Ball spin

Spin bowlers have lots of tricks up their sleeve since a ball can be spun in many different ways. A cricket ball, like anything else, has three main axes about which it can spin. Each spin axis has a different effect on the flight of the ball through the air and a different effect on the way the ball bounces. The three axes are perpendicular to each other. The first axis is vertical, pointing to the sky, and the other two are horizontal. The second axis points along the pitch towards the batter. The third axis points across the pitch. A ball can also be spun about an axis that is inclined at an angle to the three main ones, in which case it will have a component of spin about each of the main axes.

A ball that spins about a vertical axis will swerve to the left or right through the air (like a golfer's hook or slice shot) depending on the spin direction. There is no kick when it bounces since there is no preferred direction in which it can kick.

A ball that spins about the second axis does not swerve at all through the air. However it will kick sharply to the left or right when it bounces, depending on the amount and direction of spin. The ball kicks in the same direction of motion as the top of the ball. Drop a spinning ball vertically onto the pitch and you will see why.

Topspin or backspin results when the ball spins about the third axis. A topspin ball dives down towards the pitch faster than a ball without spin, and it bounces at a reduced angle since it kicks forwards when it bounces. A backspin ball tends to float through the air and kicks up when it bounces since it tends to kick backwards, causing the ball to slow down more than a ball without spin. The actual result depends on both the amount of spin and the angle of incidence. If a non-spinning ball is incident at an angle of about 20 degrees to the horizontal, then it will slide along the pitch until it bounces,  at about 22 degrees to the horizontal. If the ball has backspin then the trajectory will probably be different. It depends on the ball speed and launch angle or on where the ball lands. In general,  a ball with backspin landing at the same spot will be incident at a lower angle, say 18 degrees, and it will bounce up at about 20 degrees. But if the bowler sends down a slower backspin ball and if it lands at an angle of incidence of say 40 degrees, then the ball will start to slide along the pitch for a while and then grip the pitch before it bounces. This will cause the ball to slow down a lot during the bounce, so it will bounce up quite steeply, say at 50 degrees. The formula for the bounce angle is: 

Slope of bounce angle = (vertical bounce speed) / (horizontal bounce speed)

where slope means the same thing as tangent in trigonometry. So, the effect of backspin or topspin depends on whether the ball slides throughout the bounce (as it does at low incident angles) or whether it gets a chance to grip the pitch, as it does at high angles of incidence.

7. Swing bowling

A cricket ball can swerve to the left or the right as it moves through the air, either because it spins about a vertical axis or because it spins about an axis perpendicular to the seam. Vertical axis spin is commonly used by spin bowlers by not by fast bowlers. Fast bowlers prefer to swing the ball by making sure the seam is inclined at an angle of about 20 degrees to the direction that the ball is headed, in such a way that about 3/4 of the front of the ball is smooth. That way, the air flows smoothly around the smooth half but it becomes turbulent on the other side since it has to flow past the seam. Turbulent air is at a lower pressure than smooth flowing air, so the ball gets pushed sideways. It is almost impossible to eliminate backspin as the ball leaves the bowler's hand, but if the spin axis is perpendicular to the seam then it will help to keep the seam aligned at a fixed angle.

The sideways force on the ball peaks at about 110 km/hr, drops to zero at about 120 km/hr and then reverses direction. Reverse swing arises because the air flow on the smooth side becomes turbulent at sufficiently high ball speeds. The smooth side then becomes the low pressure side so the ball swings in the opposite direction. Normally, this effect is significant only at speeds above about 140 km/hr. However, the effect can occur at lower speeds if the ball has a roughened side and if the roughened side faces forward. Conventional swing bowlers polish the ball so one side is as smooth as possible. Reverse swingers like to make sure the other side is as rough as possible. The best ball to swing is therefore one that stays smooth on one side and roughens up during normal play on the other side.

Details of the aerodynamics involved are described on my home page under the heading Ball Trajectories where you can find several pdf files to download on the subject, including one called Sports Balls.pdf and one called Fluidflow Photos.pdf. The secret behind swing bowling lies in the way that the thin boundary layer of air near the ball surface can separate from the ball either early or late depending on whether the air flows smoothly over the surface or is tripped into turbulence by the seam or by roughness of the surface, or both. Those boundary layers were revealed many years ago by the marvelous smoke tunnel photos shown in the Photo early. Here is one taken by the late Professor F. Brown from University of Notre Dame showing how air flows around a sphere when part of the bottom half is covered in a rough grit. Air separates early over the smooth portion, becomes turbulent over the rough portion and separates later, so the air is deflected upward, resulting in an equal and opposite downward force on the ball. That is the secret that lies behind almost all aerodynamic flows, and it is what determines both the lift and drag coefficients acting on an object. Note how air backflows into the low pressure  “hole” left behind the ball, forming a turbulent wake

gostarmax thanks