# Bend it like Murali

*Solution to a puzzle thrown to college teams in an annual tech fest may soon cast its spell in the international cricket arena. Two students from the famed Indian Institute of Technology at *

In a student competition in IITs annual tech fest Shaastra 2006, General Electricals tossed eight puzzles for 125 college teams and one of them was 'Bend it like Murali'. In this puzzle, students were expected to come up with a solution for chucking, that gained fame by media hype over spinner Muralidharan's suspected bowling action.

A V Varun and Arun Manohar, Aerospace Engineering students of IIT Madras came up with the solution for the problem in their software 'Xiva' using Genetic Algorithm, a method for solving optimization problems in aerospace engineering.

*How Xiva Works*?

Cricketing laws have complex restrictions for bowling action to prevent chucking or throwing of the ball. Bowling law states that the process of straightening the bowling arm should not take place before the delivery of the ball, which is virtually impossible. Hence, this law was recently modified to allow 15 degrees of straightening.

The xiva software freezes the elbow flexing frame and uses an algorithm to measure the rate of change of angle of the elbow till the point of release of the ball. The on-field camera captures the images of elbows and the software would immediately determine the rate of change of angle, dq/dt

Figure shows the angles of concern, q, w_{L}, w_{u}

Figure illustrating the angles of elbow rotation while bowling

_{}

As the bowler swings his arm, this angle q, changes with time (t). Time difference for which the angle is measured is given by

dt = t2 - t1

t1 = time when the bowler's arm has reached the level of the shoulder in the delivery swing

t2 = time when the ball leaves the hand.

For t=dt, dq should be __<__ 15 degrees.

However, the rotation of arm cannot be assumed to be two-dimensional. The actual rotation of arm is three-dimensional as shown in the figure where

w_{L} = angular velocity of lower arm_{}

w_{u }= angular velocity of upper arm

_{}

The rate of change of w_{L}, and w_{u} is proportional to the degree of stretching q. Based on this, dq is calculated and if it is found to be > 15 degrees, umpire will be immediately alerted and the ball would be deemed a no-ball.

The students plan to submit their project to BCCI after sufficient testing and real time analysis.