Swing weight of a cricket bat & batted ball speed! What are you on about now?

If you have 2 bats one heavier then the other and you can swing them at the same speed [assuming the ball speed is constant for both] then based on theoretical momentum equations the heavier bat will win….

Why! as the batted ball velocity depends on the mass of the ball and bat. The elasticity of the ball, bowling ball speed and the bat swing speed. The other bit of this is based on moment of interia and with this you get into the realms of coefficient of restitution and coefficent of precussion

The techie bits

Ok something quick on both Coefficient of Restitution [CoR] you can try this at home. Drop a ball from a fixed height onto the cricket bat and measure the rebound height of the ball - CoR is the square root of rebound height divided by Original height. [this just gives you a number]. But you will see / measure a rebound difference between two cricket bats. CoR is dependant on a number of things but in this context it is related to the cricket bat shape and where it hits [or lands] on the bat.

Centre of percussion [CoP] - hang a bat where you normally hold it and hit it with a mallet. At the point it swings like a pendulum that is the CoP. Or when playing it when the ball hits the cricket bat at a point that it neither pushes your hands forwards or backwards. 

Hold on your hats the Math

Ok it is getting a bit scary now so I should stop but I won’t [a sly grin] There varying articles on this [mainly baseball, some tennis and limited number on cricket bats!!!]

The general consenus though is this equation:

Batted ball speed = q x Velocity of ball + (1 + q)Velocity of bat

Where q is calculated as follow q is the Bouncabilty of a bat or Apparent Coefficient of Restitution [ACoR]

For CoR q = CoR - r / 1 + r
R is made up of many factors and it beings to get overly technical at this point and I dont want to go down that road…. you are bored already!!!!

In simple terms q can be defined as Velocity of ball after the collision [divided by] Velocity of ball before collision. [Velocity, by the way if you want to drop a ball on a bat and measure it for a baseline and rebound to calculate q, is Distance / time]

Ok some theoretical calculations for batted ball speeds

Which Cricket bat is better, stick with me here….

 [A Big Note: Made up numbers for the blog for q and velocity but proper calculations with those numbers]

A normal cricket bat our datum point….

q = 0.45
Vel of Bat = 50
Vel of ball = 60
Ball exit speed is 99.5

Now add 10% on the cricket bat mass resulting in a slightly lower bat speed lets say 10% slower and lets keep it 10% and increase in q [bouncabilty] which is Apparent CoR or [ACOR]

So
q = 0.5
Vel of bat = 45
Vel of ball = 60
Ball exit speed is 97.5

Ok let assume you have a bat and the swing weight is the same as first bat but has more mass therefore a higher q [ACOR]

q = 0.5
Vel of Bat = 50
Vel of ball = 60
Ball exit speed is 105

Are we still talking about Cricket Bats?

So what do those theoretical values tell us… Swing speed offset against bat weight is almost an exponetial curve it slowly raises and plato’s and then slowly drops off. Therefore there is a range of bat weights that with good pickup will allow you to have the same reaction time and swing speed but due the weight distribution in the bat areas of mass etc and ball impact points you can raise the ACOR [q] bouncabiity. Mass behind the sweet spot [hopefully in the main hitting area] will be ideal especially if the swing weight of the bat means you are hitting the ball at close to maximum speeds in the position and batting shapes you normally hit a ball at… [that is your normal ball impact areas] cricket bat middle postion etc etc

Does this mean there is an optimum weight for everyone, depending on their strength?
Yes this optimum weight would be where they could swing the bat fastest then without to much compromise on size of the bat.

Few is that it my coffee got cold?

Ok Willow is organic a live piece of timber and you will never really know how a bat will go until it is used. But being the person that I am I like to get an idea on the science behind it all and it is complex due to the numerous varibles associated to the timber and person using it and level at which it is all used.

My view is a bat with good pickup allowing someone to use a slightly heavier bat or wood mass distributed properly with the middle in the correct place will go a long way in to giving a batsman what he wants…. Can you get that from a machine made bat, it is debatable buy a handmade bat it is cheaper then you think

Finally…..
You don’t always slog the ball and I will agree with you pratical, theoretical and variation on ball, bat and bowling speeds doesn’t make it conclusive but you can get a good baseline and it makes for good article

I’m interested in this stuff scary but true!!!!!

Andy
Podshaver for San Andreas Fault Cricket Bats
Handmade Cricket Bats

Have a Cricket Bat related question email me