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Physics of Cricket Bowling
When the bowler runs into the bowl, he transfers his momentum from the run to the ball. Let’s apply the law of conservation of momentum and Newton’s laws of motion to a moving ball before and after the pitcher throws it.
Run Length Mechanics:
Using the law of conservation of momentum, we write an equation describing the relationship between the mass of the person, the speed of the bowler, the mass of the cricket ball and the speed of the ball.
Human Weight * Stride Speed = Ball Weight * Release Speed… (1)
For a release speed of 140 km/h per ball
Ball weight = = 1.5 kg
Weight of a person = 70 kg
According to equation (1)
1.5 * 140 = 70 * V step
Step V required for a 70 kg person = 3 km/h
Step V required for a 60 kg person = 4 km/h
Step V required for 80 kg person = 2.5 km/h.
If a bowler wears a 500g watch, he has to run slower to achieve the same release speed on the cricket ball as when not wearing the watch. It is clear from the three equations above that a heavier person needs to run slower into the crease to impart the same speed to the ball.
Run length is a critical factor for the following reasons. Pitch speed near the crease will depend on the pitcher’s acceleration and the length of his run-up.
V * V = 2 * a * S (2) (Newton’s Laws of Motion)
To launch the ball at a speed of 140 km/h at a human pace of 3 km/h or 88 m/s
(the highest human speed is about 10 m/s)
0.88 * 0.88 = 2 * acceleration * 10 (run length)
Required acceleration = 0.032 m/s * sec. If the length is shortened, the bowler must provide more acceleration, which charges more quickly, to achieve the same velocity. If the length of the run-up is longer, the pitcher can progress more slowly into the run-up.
Ball recoil:
The rebound of the ball is determined by the coefficient of restitution. The ball will be decelerated after pitching and also in the air. The recoil of the ball is dependent on the initial speed and the coefficient of restitution. The height of the ball release is approximately 1.8 – 2.2 meters. At a vertical speed of 140 km/h with a coefficient of restitution = 0.5, the ball would bounce up to half its height. But the observed speed (140 km/h) will not be released vertically.
For a launch angle of 45 degrees with the vertical, the vertical speed would be 140 * sin 45, the horizontal speed would be 140 * cos 45. This reduces the discharge speed or horizontal speed to about 100 km/h.
For the best use of energy expended in the launch, it seems that a perfect horizontal release where the release angle is 0 degrees would cause a release speed of 140, all other release angles would dampen the release speed on the ball. The bounce height, or height to which the ball bounces after pitching, will not be affected by the angle of the ball. It only depends on the height of the delivery.
Short ball and good length ball mechanics:
Short ball and long ball depend on the height from which the ball is delivered and the angle from which the ball is delivered. The speed at which the ball is thrown does not affect where the ball lands. The mechanics of the sphere will only be affected by the gravitational force of the Earth and no other forces. Where the ball lands after leaving the pitchers hands will depend on the horizontal component of the release velocity.
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