Study of Cor of Cricket Bat Ball Experiment

ABSTRACT:

The performance analysis of a cricket bat is best carried out by comparing experimental results with results obtained through finite element analysis. This paper studies whether COR (Coefficient of Restitution) can be considered a performance characteristic of the bat. The paper considers COR as the ratio of ball exit velocity to the ball inlet velocity. Further, the relationship between COR and the position of impact on the bat is studied. Similar studies have been carried out concerning baseball bats. It is the aim of this paper to see if the same approach may be used in the case of a cricket bat which has a more complex geometry.

INTRODUCTION:

Cricket is a very popular bat-and-ball sport played in many countries all over the world. It is believed to have originated in the 18th century in England. The main equipment used in cricket is the cricket bat and ball. The laws of cricket limit the size of the bat to not more than 0.965 m in length and the blade to be not more than 0.108 m wide. Cricket bats typically weigh from 1.1 to 1.4 kg though there is no restriction on the weight of the bat [18].

The cricket bat consists of a handle, shoulder, blade and toe as shown in fig. 1. Until recently, the quality of the cricket bat was based only upon the grain structure of the face of the blade. The modern tendency is to use heavy bats since most batsman believe that a heavier bat allows them to hit the ball further. The blade of the bat is commonly made of Kashmir or English willow [18].

LITERATURE SURVEY:

Baseball, a similar bat-and-ball sport has had a lot of research being carried out in the past few decades. The pioneering work that that viewed baseball scientifically spawning future interest and research in its development was Adair's "The Physics of Baseball".

The term 'sweet spot' of the bat generated interest and a lot of research has been carried out to find the location of this area on the bat. The sweet spot has three interpretations. The sweet spot is commonly known as the location on the bat that produces maximum batted-ball velocity. Often, it is also understood as the location on the bat that produces no sting to the batter's hands. A third interpretation of the sweet spot is the location on the bat where the amplitude of fundamental vibrations is zero (node point).

According to Noble, L., the sweet spot exists because it is close to the COP (center of percussion) and because the amplitude of fundamental vibrations at this location is minimal (close to node). Using modal analysis, Jaramillo P. et al resolved a deflection pattern of the baseball bat into a set of simple mode shapes with individual peak frequencies. The point of zero vibration is taken to be the sweet spot. Crisco J.J. et al obtained the sweet spot graphically through experimental values obtained using experienced players in a caged facility. The graph used to determine the location of sweet spot on the bat, was the Batted Ball Speed v/s the Impact Location graph

The centre of percussion (COP) was another parameter of the baseball bat that was studies to measure its performance. The center of percussion (COP) is the impact point on the bat that produces minimal reaction to the batter's hands.

The center of percussion was initially considered to be the same as the sweet spot (location on the bat producing maximum-batted ball velocity). However, the sweet spots and COPs on bats are very close to each other but are not necessarily at the same position on the bat. A paper by Weyrich et al demonstrated that the COP is the impact location that produces the greatest ball-exit velocity with a stationary bat. Also a theory developed by Brody to determine the impact location on the bat that would result in the greatest post-impact velocity shows that this location is not on the COP but is a function of velocities of the bat and ball, their mass and also the inertial and material properties of the ball.

When the ball strikes the bat, there is vibration produced in the bat. Hence, researchers have also analysed the vibrational behavior of the baseball bat.

Sutton, A.D. and Sherwood, A.J. used vibrational analysis to determine the batted-ball performance of baseball bats. They concluded that metal bats perform better than wood bats because of the trampoline effect. The hoop frequencies of the aluminium, composite and wood bats were found out through modal analysis. Graphs were plotted for hoop frequency v/s BBCOR (Bat-Ball Coefficient of Restitution), BBESR (Batted Ball Exit Speed Ratio) and BBS (Batted Ball Speed) which were calculated separately. It was observed that the bats gave better performance at lower values of hoop frequency. They also concluded that the ideal value of hoop frequency is 1200 Hz.

A node point is the location where the amplitude of vibration is zero. Therefore, an impact at a node point will cause minimum vibration in the bat. Hence, less energy is lost in the bat vibration, and more energy will be transmitted to the ball. Cross, R. has defined the region between the two fundamental nodes of a bat as the 'sweet zone' for impact which will cause minimum vibrations in the bat and maximum energy is transferred to the ball which gives it an optimum exit velocity. A study by Van Zandt, L.L shows that the ball exit velocity is relatively lower at any location other than the node point.

In addition to experimental analysis, researchers have used analytical methods to evaluate the performance of baseball bats. Most prominently the previous authors have used the technique of FEA (Finite Element Analysis) for such purposes. The use of ANSYS/LS DYNA has been explained in detail by Nicholls. R. L. et al. This work tries to analyse the importance of parameters like coefficient of restitution, ball exit velocity etc. using FEA. Shenoy, M. et al used FEA to evaluate the baseball bat performance using models replicating the experimental hitting machine setup.

A model of baseball bat impact based on the 3D kinematics of a bat of different design, hence quantifying the factors important in production of ball exit velocity has been studied by Nicholls, R. L. et al.

Due to the similarity between cricket and baseball, researchers have adopted similar methodologies to do research on cricket bats.

In his post-graduate thesis, Singh carried out experiments to measure the coefficient of restitution (COR). He used batted ball speed (BBS) as a parameter to measure the performance of the cricket bat. A dynamic finite element model was employed to simulate