Science of Cricket  

part 1- Batting

 Cricket is a subtle game requiring a great amount of patience as well as skill. It takes 5 days to complete a Test match so the grass needs to be mown and the pitch needs to be rolled as the game progresses.  It is not something that is easy to learn and appreciate as an adult, especially by North Americans.

1. Heavy vs Light Bats

The crowd loves a batter who can hit sixes. If you want to hit the ball as fast and far as possible, should you use a light or heavy bat? That's an age old question with plenty of answers, but which is the correct answer? Light bats can be swung faster than heavy bats, but only about 10% faster (for the usual range of bat weights). Imagine hypothetically that the bat weighs 10 grams - light as a feather. If you swing it as fast as possible, you might get the tip to travel at say 160 km/hr. Now double the weight to 20 gm. This time the tip travels at about 159 km/hr. The problem here is that your arms weigh about 8 kg all up, so the extra 0.01 kg is hardly noticeable. Most of the effort needed to swing a bat goes into swinging the arms. That's why light bats can be swung only about 10% faster than heavy bats.

If a light bat was swung at the same speed as a heavy bat and both hit the same ball, the heavy bat would pack more power since it has more energy and more momentum. But light bats can be swung 10% faster. If a bat is swung 10% faster, the ball comes off the bat about 7.5% faster. That almost makes up for the fact that light bats are basically less powerful when swung at the same speed as heavy bats. The end result is that heavy bats are about 1% more powerful than light bats. Having a heavy bat is a definite advantage if you swing all bats at the same medium speed, but if you need to move the bat quickly into position to strike the ball, a light bat will get there faster. Heavy for a 10 year old might be light for a 100 kg cricketer, so the real answer for raw bat power is to use a bat that is as heavy as feels comfortable to swing.

2. The Sweet Spot

Every batter knows that there is a special spot on a bat where the shot feels best. It sometimes feels so good that there is almost no sensation at all that the bat hit the ball. It's the same with a baseball bat or a tennis racquet or a golf club, so there is nothing special in this respect about cricket bats. Two special points on a bat are good candidates for the sweet spot. Technically, they are known as the fundamental vibration node and the centre of percussion. The node point is concerned with bat vibrations. Most impact points on a bat will cause the whole bat to vibrate, including the handle. Those vibrations persist well after the ball has left the bat, and they tell you whether you hit the ball cleanly. The biggest vibrations result when the ball strikes the tip of the bat. However, there is a spot about 150 mm from the tip where an impact causes no vibrations at all. That is the node point. As the impact point moves closer to the node point, bat vibrations get weaker and the shot feels nicer.

An impact near the tip of a bat will generate bad vibrations and it will also cause the handle to jerk forwards (towards the bowler), pulling your hand and arm with it. An impact higher up, near the handle, will push the handle backwards towards the body. In both cases there is a certain amount of jarring that feels unpleasant. The result is a sudden shock to the arm in one direction rather than a back and forth vibration. There is an impact point between the tip and the handle where there is no sudden motion of the handle at all. That point is called the centre of percussion. However, recent measurements show that it is too close to the handle to qualify as the sweet spot that batters talk about.

3. Vertical bounce of a cricket ball

Almost every type of ball used in a sporting event must bounce according to the rules of the game. If the ball bounces too high or too low, the players will complain that something is wrong with it. The standard test for bounce is to drop a ball from a certain height onto a hard surface such as a slab of concrete and then measure how high it bounces. When a tennis ball is dropped from a height of 100 inches (2.54 m) it must bounce to a height between 53 inches (1.35 m) and 58 inches (1.47 m). For official use in major tournaments, tennis balls must be properly tested and approved, for a moderately large fee, but the fee is only a small fraction of the total value of balls sold. Tennis courts themselves vary in hardness, which affects bounce height, so a standard surface such as concrete is used for these tests.

There is no such official rule for a cricket ball. There is simply a tradition that is monitored by umpires, and one that is an industry standard. When a cricket ball is dropped from a height of 2.0 m onto a heavy steel plate, it bounces to a height somewhere between 0.56 m and 0.76 m. Cricket balls are a lot less bouncy that tennis balls and the permitted range of possible bounce heights is larger. A useful way of specifying the bounce is to take the ratio of the bounce speed to the incident speed. When a ball is dropped from a height of 2.0 m it lands at a speed of 6.26 m/s, regardless of the type or weight of the ball. A cricket ball bounces to about one third of that height (0.67 m), in which case it rebounds at a speed of 3.61 m/s. The ratio of these two speeds is 3.61/6.26 = 0.58 and is called the coefficient of restitution (COR). The COR of a tennis ball is about 0.75. The COR determines not only the bounce height but also the speed at which a ball comes off the bat. The batted ball speed also depends on the speed of the bat.

4. Batted ball speed

Suppose that a cricket ball is bowled at 100 km/hr, the  batter swings the bat at 60 km/hr, and hits the ball straight back over the bowler's head. How fast does the ball come off the bat? This is a simple question but the answer is not so simple since it depends on which part of the bat is moving at 60 km/hr and it depends on where the ball makes contact with the bat. Suppose that the ball strikes the middle of the bat rather than near an edge and suppose that 60 km/hr is the speed of the impact point on the bat rather than the speed of the tip or the handle. We also need to know the mass of the bat, or better still we need to know how fast the ball comes off the bat when the bat is not swung at all. Suppose that the bat is used just to block the ball and the ball bounces off the bat at 20 km/hr. If E = ratio of bounce speed to incident speed = 20/100 = 0.2 then the speed of the ball when the bat is swung at speed V is 20 + (1 + E)V = 20 + 1.2 x 60 = 20 + 72 = 92 km/hr. For most bats, E varies from about 0.1 near the tip to about 0.3 half way up the bat. E is smallest near the tip of the bat but V is biggest there when the batter takes a huge swing at the ball.

5. Grip firmness

The effectiveness or the power of any given bat can be tested without swinging the bat at all. If the bat is held in a fixed position and a ball is fired at the bat at say 100 km/hr, the ball will bounce off the bat at a speed of about 20 km/hr. That speed gets added to the bat speed when the bat is swung. A surprising result is that the bounce speed off a fixed bat does not depend on how firmly the handle is held. It can be gripped in a vice or it can be dangled on the end of a piece of string and the ball will bounce at exactly the same speed. For that reason, the speed of a struck ball does not depend on how firmly the handle is gripped in the hands.

There is a simple reason for this strange result. When the ball strikes the bat, it causes the bat to bend slightly at the impact point. That bend then propagates along the bat up to the handle, reflects off the end of the handle and then travels back down to the impact point. The bend takes about 0.002 seconds to travel up to the handle and back again. But the ball is on the bat for only 0.001 seconds, and it bounces off before the reflection gets back to the impact point. The ball has no way of knowing how the handle was held so it bounces off the bat at the same speed regardless of how the handle is gripped. The handle could be attached by a hinge and the ball would still come off the bat at the same speed.