When a bowler runs towards the bowling pin, he transfers his momentum by running towards the ball. Let’s apply the law of conservation of momentum and Newton’s laws of motion to the moving ball before and after the pitcher throws it.
Mechanical Run Length:
By the Law of Conservation of Momentum, we write the equation that describes the relationship between the human mass, the speed of the bowler, the mass of the cricket ball, and the speed of the ball.
Mass of the human being * Stride speed = Mass of the ball * Throwing speed… (1)
For a launch speed of 140 km/h on the ball
Ball mass = = 1.5 Kg
Human mass = 70 Kg
Going by equation (1)
1.5*140=70*V stride
V stride required of 70 kg human = 3 km/hr
V stride required of 60 Kg human = 4 km/hr
V stride required of 80 Kg human = 2.5 km/hr.
If a bowler wears a 500g watch, he needs to run slower to achieve the same pitching speed on the cricket ball compared to when not wearing a watch. This is clear from the three equations above, that a heavier human needs to run slower towards the crease to impart the same velocity to the ball.
The length of the run is a critical factor for 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 run.
V * V = 2 * a * S (2) (Newton’s laws of motion)
For a ball toss at 140 km/h with a human pace of 3 km/h or 0.88 m/s
(the fastest human speed is about 10m/s)
0.88 * 0.88 = 2 * acceleration * 10 (stroke length)
Required acceleration = 0.032 m/sec * sec. If the length is shortened, the bowler has to provide more acceleration, which charges more quickly to achieve the same speed. If the length of the run is greater, the bowler can progress more slowly towards his run.
Ball kick:
The bounce of the ball is determined by the coefficient of restitution. A ball will slow down after throwing and 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 about 1.8 to 2.2 meters. At a vertical speed of 140 km/h with a coefficient of restitution = 0.5, a ball would recoil up to half its height. But the observed speed (140 Km/Hr) will not be released vertically.
For a launch angle of 45 degrees to 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 the energy expended while dashing up, it seems that a perfect horizontal launch where the launch angle equals 0 degrees would make the discharge velocity 140, all other launch angles would damp the launch velocity at the ball. The kick height or the height the ball bounces after launch will not be affected by the launch angle of the ball. It depends only on the height of the delivery.
Short Ball and Good Length Mechanics:
The short ball and the long ball depend on the height from which the ball is thrown and the angle from which the ball is thrown. The speed at which the ball is thrown does not influence where the ball lands. The mechanics of the ball will be influenced only by the gravitational force of the Earth and no other forces. Where the ball lands after leaving the bowlers hands will depend on the horizontal component of the pitch velocity.