When a bowler runs into the bowl, he transfers his momentum by running toward the ball. Let’s apply the Law of Conservation of Moment and Newton’s Laws of Motion to the ball in motion before and after the bowler throws it.
Run Length Mechanics:
By the Law of Conservation of Moment, we write the equation that describes the relationship between the mass of the human, the speed of the pitcher, the mass of the cricket ball, and the speed of the ball.
Human mass * Stride speed = Ball mass * Throwing speed … (1)
For a launch speed of 140 km / h on the ball
Ball mass = = 1.5 kg
Mass of human = 70 Kg
Going by equation (1)
1.5 * 140 = 70 * V stride
V required stride of 70 kg human = 3 Km / h
Required V stride of 60 kg human = 4 Km / h
V required stride of 80 kg human = 2.5 km / h.
If a bowler wears a 500g watch, he must run slower to achieve the same release rate on the cricket ball as on the box when not wearing a watch. This follows from the three equations above that a heavier human needs to run slower towards the fold to impart the same speed to the ball.
The duration of the execution is a critical factor due to the following reasons. The speed of the stride near the crease will depend on the acceleration provided by the pitcher and the length of his stroke.
V * V = 2 * a * S (2) (Newton’s laws of motion)
For a 140 km / h ball throw at a human stride of 3 km / h or 88 m / s
(fastest human speed is about 10 m / s)
0.88 * 0.88 = 2 * acceleration * 10 (stroke duration)
Required acceleration = 0.032 m / sec * sec. If the length is shortened, the bowler has to provide more acceleration, charging faster to achieve the same speed. If the length of the run is longer, the bowler may move more slowly in his career.
The bounce of the ball is determined by the coefficient of restitution. A ball will slow down after being thrown and it will also slow down in midair. The recoil of a ball depends on the initial velocity and the coefficient of restitution. The launch height of the ball is approximately 1.8 to 2.2 meters. At 140 km / h vertical speed with a coefficient of restitution = 0.5, a ball will recoil to half its height. But the observed speed (140 Km / Hr) will not be released vertically.
For a 45 degree release angle 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 better utilization of energy expended while running, it appears that a perfect horizontal release where the release angle equals 0 degrees would cause the discharge rate to be 140, all other release angles would dampen the release rate by the ball. The recoil height or the height at which the ball bounces after the throw will not be affected by the angle of the ball’s throw. It depends only on the height of the delivery.
Short ball and good length ball mechanics:
The short ball and the long ball depend on the height from which the ball is thrown and the angle from which it is thrown. The speed at which the ball is thrown does not influence where it is thrown. The mechanics of the ball will be influenced only by the gravitational force of the Earth and not by other forces. The location where the ball lands after leaving the bowler’s hands will depend on the horizontal component of the throwing speed.