Physics of Cricket

T h e P h y s i c s o f C r i c k e t

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The Physics of Cricket

Abstract

A variety of sports such as cricket, baseball, tennis and badminton have benefited from the

scientific analysis of everything from the bat used to the court and even the player’s attire.

Experimental assessment of sports is costly, time consuming and tedious, requiring enormous

patience. However, exploration using basic physics and simple understanding of the laws can

change the way a game is played. Sporting equipment could be modified within the

framework and laws of the game, thus enabling players to leverage their skills to superior

levels. Over time, these sports have increasingly become faster, shorter and more popular.

This paper will provide an overview of the physics behind the game of cricket especially,

mass of the bat, momentum, spin and swing speed, and force on a cricket ball. It also explains

the science behind cricket pitch performance and the physics used by the wicket keeper and

fielders to enhance competence.

1. Introduction

Cricket is a bat and ball game played between two teams of eleven players on an open field,

at the centre of which is a rectangular 22-yard long pitch. Normally, the outer boundaries are

75 metres from the pitch. The team that bats first tries to score runs, which are counted by

running from one end of the pitch to another, and the other team tries to get the batsmen

dismissed and limit their score. A game of cricket could be as short as 20 overs of six

bowling deliveries per team or could stretch to as many as five days in a test match.

First played in England in the 16th century, cricket is particularly a much-loved game in

Austalasia, India, West Indies, South Africa and UK. There is potential viewing audience of

over 1.5 billion in 60 countries of the former British Empire. It could well be the second most

viewed game after football if China commences participating in this game.

Essentials to a game of cricket are an oval-shaped field, a central well-cured and rolled pitch,

a cricket ball made of cork and leather, bats that are wielded by the batsmen and two teams of

11 players each, comprising of batsmen, bowlers, a wicket-keeper and all-rounders.

Physics involved in this sport includes projectile motion, inertia, velocity, momentum and

aerodynamics including slope of bounce.


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2. Performance of a pitch

The central 22-yard rectangular area in a field

is where most of the cricketing action takes

place. Therefore, the physical characteristics

of the pitch may determine the outcome of the

match. When the pitch is hard and dry, the

impact of the reaction makes it more likely to

bounce more. On the other hand, when the

pitch is wet and there is moisture, the bounce

is reduced due to the cushioning effect and

energy absorption caused by the water

molecules. In humid atmosphere, swing

bowlers have an added advantage as the ball tends to swing more due to the increased water

vapour in the air. It is because of this that green top grassy pitches have less bounce and the

ball begins to swing after a few overs, when the sun is out.

3. Aerodynamics of a cricket ball

A cricket ball is made of either 2 pieces or 4 pieces, stitched together to

form a seam. The primary seam has 6 rows of stitches with 70 to 90

stitches in each row. In a 4 piece ball, the hemispheres are stitched

together internally, forming the secondary seam.

Let us first understand the basic flow dynamics of a sphere. When a ball is flying through air,

it forms a boundary layer over the ball’s surface. This layer cannot travel all along with the

ball. So it has to separate at a point. This is called flow separation which determines pressure.

An early flow separation means more pressure and late separation means less pressure.

The boundary layer has two states. One is

laminar flow and other is turbulent flow.

Laminar flow is smooth and does not have

any disturbances or turbulence. When a

cricket ball flies in the air and does not have

any deviation in the position of seam, then


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both sides of the ball may have a laminar air flow pattern. A scientific parameter called

"Reynolds number" is directly related to the dimension and flow speed of the ball. The

transition from laminar to turbulent flow takes place if the Reynolds number exceeds a

critical value.

Reynolds number is: Udv-1 where U is the velocity of the ball; d is the diameter of the ball,

and v the velocity of the medium in which the ball is travelling, i.e. air

The rough side of a cricket ball creates turbulent flow and

thus delays flow separation. This causes the pressure to reduce

on the rough side. This imparts more pressure on the smooth

side. Since the laminar flow exists on the smooth side the flow

separation point is seen early than the rough side. This results in

the ball swinging from high pressure side to low pressure surface

with in-swing or out-swing, depending on the position of the

rough side of the ball.

4. Force on a cricket ball

When you drop a cricket ball on a pitch, does it bounce as much as a tennis ball? What is the

force exerted on the ball? Cricket balls are constructed of cork and leather and are

comparatively stiffer than tennis balls, and their contact time with the pitch or the bat is

shorter. A cricket ball remains in contact with the bat or the pitch for only one- thousandth of

a second. This is in contrast to a tennis ball, which stays in contact with the court or the

strings of a racquet for 0.005 seconds, i.e., five times more than a cricket ball. The force the

bat exerts on the ball causes it to stop and accelerate in the opposite direction, in a short span

of 0.001 seconds! For a constant mass, Force = Mass x Acceleration; F= ma or a = F/m.

Presume 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. Although a Formula 1 racing car can accelerate

to the speed of 100 km/hr in just 1.5 seconds, a cricket ball can do it 1500 times

faster! A cricket ball may not weigh a lot, but its momentum is very large due to the

high velocity and acceleration. The average force on the ball is over 8000 N, enough

to lift a mass of at least 800 kg off the ground!


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This is because force equals the product of mass and acceleration due to gravity.

Hence the mass is 8000 N of force divided by around 10 m/s2. The value is nearly 800

kg. No doubt, the high momentum can cause a lot of pain when a cricket ball hits a

batsman’s body.

5. Air resistance, bowling skills and performance

Air resistance plays an important role in cricket, from making the ball spin, curve and swing

away or towards the batsman. A bowler must bowl overhand with either his right or left hand.

He can deliver the ball by running in from any distance as long as he does not cross the

bowling crease and does not bend his elbow. In most ball sports, the Magnus effect is

responsible for the curved motion of a spinning ball. The Magnus effect is a phenomenon

whereby a spinning object, such as a ball, while flying in a fluid creates a whirlpool of fluid

around itself, experiences a force perpendicular to the line of motion. Given the angular

velocity vector and velocity of the object, the resulting force can be calculated

using the formula where S is dependent on the average of the air

resistance coefficient across the surface of the object.

Skilled bowlers can spin the ball so that it can take advantage of the resistance and make it

difficult for the batsman to hit the ball as he likes. A spin bowler could turn the ball through

the air if he uses the vertical axis or swerve the ball when it pitches when using the second

axis. On using the third axis, a bowler would be able to topspin or backspin. On using a high

angle of incidence the ball grips the pitch causing topspin and on a low incidence angle, the

ball slides through the bounce causing backspin. The formula for the bounce angle is:

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

The following two examples explain how gravity and air resistance will have an impact on

ball speed.

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.


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At world record bowling speeds of around 160 km/hr, the drag force is 1.7 times

greater than the weight of the ball. Notwithstanding the speed of the ball, it arrives

12% slower on the pitch. Depending on the angle of incidence and the speed of the

pitch, the ball slows down by 30 to 40% when it hits the pitch. A ball bowled at 150

km/hr will arrive 0.46 seconds later at the batsman's end, travelling at about 85 km/hr.

6. How fast does the ball come off the bat?

Suppose a cricket ball is bowled at 100 km/hr, the batsman swings the bat at 60 km/hr, and

hits the ball straight back over the bowler's head. So, what could be the batting speed? The

answer to this question depends on which part of the bat is moving at that speed and which

part of the bat the ball hits. 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.

Let us assume the ball strikes the middle of the bat rather than near an edge and suppose that

100 km/hr is the speed of the impact point on the bat rather than the speed of the tip or the

handle. If a defensive dead bat is used then the ball bounces off the bat at 25 km/hr.

The formula E = ratio of bounce speed to incident speed = 25/100 = 0.25.

The speed of the ball when the bat is swung at speed V is 25 + (1 + E) V = 25 + 1.25 x 100 =

25 + 125 = 150 km/hr.

For most bats, E varies from about 0.1 near the tip to about 0.3 half way up the bat. The ratio

E is least near the tip of the bat, but the speed will be highest when the batsman connects bat

to ball. The sweet spot which is a region that lies between 0.12m and 0.18 m from the bottom

of the bat produces the maximum ball velocity.

7. How heavy a bat should the batsman use?

It is obvious that a batsman would like to make as many runs as

possible during his tenure at the crease. While guarding himself

from not getting out, a batsman also performs to the crowd which

always loves a batsman who can hit fours and sixes. The question

in every batsman’s mind is, therefore, “if I want to hit the ball as

fast and far as possible, should I use a light or heavy bat?” An

answer to this question must, in all likelihood, take into account the weight of the bat and the

speed at which it is swung. For the usual range of bat weights a lighter bat can be swung


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faster than a heavier bat - but only about 10% faster. Professional cricket bats must be made

of wood and can have a maximum width of 10.8 cm and a maximum bat length of 96.5 cm.

Interestingly the grip on the bat does not play a role in how the ball bounces off the bat.

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. People of

different ages will feel relaxed with different bats, so the real answer is to choose the heaviest

bat you feel comfortable with and can swing easily.

8. Physics of fielding a ball

When a specially placed fielder like the wicket keeper needs to catch a ball going towards his

right, which foot should he 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. This

is because the body’s movement is partly controlled by gravity and it requires less energy on

his part. This enables him to get to the ball faster.

Take the situation of a fielder taking a catch. Since the retardation of the moving ball is large

and the speed decreases to zero in no time, the fielder has to apply a larger force to stop the


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speeding ball and could get hurt when the ball exerting greater

pressure on his hands. Hence, most fielders prefer taking catches

by moving their arms back so the velocity decreases gradually over

a longer time interval thereby decreasing retardation and the force

exerted by the ball on the hand.

Another aspect of fielding is throwing the ball from the outfield.

How does the fielder know at what angle he must throw the ball? When the cricket ball

travels through the air, it follows a curved, parabolic path, due to the action of gravity. As it

travels up, gravity slows it down until it changes direction and accelerates downwards. This

projectile motion can be controlled by changing velocity, angle of the throw, or rotation of

the cricket ball.

9. Conclusion

The popularity of cricket is fast gaining momentum. A good appreciation of the laws of

Physics has significantly helped teams in skill building. Captains deem it important to inspect

the pitch before commencement of a game. Depending on the type of pitch and moisture on

it, they seek expert opinion on team constitution and a decision to bat or field first. Bowlers

who have the ability to make use of ball and pitch conditions to bowl at varying speeds

simultaneously aided by swing, bounce and spin have been successful at international levels.

Batsmen have realized that it would be wise to have a choice of bats each with different

weight to adapt to the needs of changing game formats. Fielding skills have received a

tremendous boost through better control over throwing angles and velocity. With increased

physics-related technical analysis coaching techniques, cricket gear (including shoes and

attire), physical training and safety equipment have undergone a change for the better.

References:

a) Daniel A. Russell, “Physics and Acoustics of Baseball & Softball Bats”, Kettering University, 2003-2008

b) G. Venkatesh, “Will it bounce”, http://www.scienceinafrica.co.za/2002/december/bounce.htmc) M. Kidger, “The Physics of Cricket”, Nottingham University Press, 978-1-904761-92-1d) “Physics of Cricket”, http://www.physics.usyd.edu.au/~cross/cricket.htmle) Rabindra Mehta, “The Science of Swing Bowling”,

http://www.espncricinfo.com/magazine/content/story/258645.htmlf) Rabindra D. Mehta and Jani Macari Pallis, Sports Ball Aerodynamics: Effects of Velocity, Spin and

Surface Roughness, TMS (The Minerals, Metals & Materials Society), 2001g) V. Hariharan & PSS. Srinivasan, “Inertial and Vibration characteristics of a cricket bat”

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Physics of Cricket