Baseball and Cricket

I'm pretty sure a batter can hit a ball farther (faster) than when it's pitched, so most batters must be operating at more than "100 percent power transfer ratio".

It doesn't sound like Mr Wood (great name for a batsman, btw!) is an engineer. I think he is using phrase 'power transfer ratio' in a non-rigorous way simply to create a 'figure of merit' for determining how much improvement a batter can achieve. The typical sportsman doesn't care about the nit-picky details of how much power is transferred, nor how efficient the transfer is. He simply wants a way of knowing how to hold and swing the bat to drive the ball farther. This at least gives a measureable quantity to help determine that.

Nothing wrong with creating empirical figures of merit until you start calling them something erroneous and spouting bull.
I'm a great fan of the practical and even mixing units if necessary, but one still needs to be precise about defining what you are measuring.

Del

The premise is complete baloney. A batter's hands don't move anywhere near 80 mph.

There are several other editorial clinkers in that article.

Tell Mr. Wood to watch the next baseball World Series. These are the games where they use radar guns to determine the speed of the ball as it is thrown by the pitcher to the batter. It is also used for the speed of the ball as it travels from the bat to it's destination. Runners speed, bat speed and several other objects that the speed of have been attempted to be determine. Who knows, maybe they even radar to clock the beer vendor!

Have him listen to a radio broadcast and look at a TV broadcast at the same time. They utilize different styles, radio is much more descriptive, of broadcasted information to overcome the lack of sight for radio listeners.

Also since the radius of the arm that the hand is attached to is shorter than the radius of the cricket bat and the arm that holds this hand the "hand speed" is not an accurate source. For an example, try to hit a golf ball as hard as you can with a wood driver and a putter. Longer radius = greater speed.

Good Luck, Old Salt

I strongly suspect that Mr. Wood has a good idea what he is doing, and, that the problem with this article lies with the reporter.

That is a very generous point of view, but the story has been widely reported. Not all the reporters could have made the identical mistake.

This mystical power transfer ratio is spreading further, including this golf website, which states that the laws of physics do limit the PTR but then succeeds in mis-defining the coefficient of restitution. Apparently a COR of 1 means that all the energy in a collision is transferred from one object to the other.

On this other golf website it is correctly pointed out that the PTR cannot be less than 100%, since otherwise the ball would be travelling slower than the club face.

It appears that tennis has yet to succumb to the PTR, likewise football in any of the many codes.

For your homework:-
"If all the power in the bat was transferred to the ball, then the bat must cease to move forward after the ball has left the bat"
Discus

Del

If the mass of the ball is m, and its speeds are v1 and v2 coming and going, and the mass of the bat is M, there is some speed of the bat V such that M(V-0), the change in momentum of the bat, equals m*(v1+v2) , the change in momentum of the ball.

MV = m*(v1+v2).

The center of mass of the ball + bat system is not necessarily stationary. If you reference velocities to the center of mass, the ball will rebound from the collision point at the same velocity as it entered and the bat will also rebound with its same velocity.

The batter swings the bat and in essence determines the velocity of the center of mass (taking into account the relative mass of the ball and bat). At some velocity of the bat, the final speed of the bat with respect to the batter will be zero. I assume that is your 100 percent efficiency point. It does not necessarily occur if v2 = v1, it depends on the relative mass of the ball and bat.

If the batter swings the bat harder, obviously the ball will rebound faster and the bat will continue to follow through. More energy will be transferred to the ball, but some energy will remain in the motion of the bat.

I don't see the advantage of just hitting hard enough that the bat comes to a stop.

Quite so. In real life the baseball batter, cricket batsman or golfer always follows through, so the power transfer is always less than 100%. The power transfer ratio as defined by velocities, on the other hand, can never be less than 100% (unless, of course, you are Mr Wood and use hand rather than bat velocities in the calculation).

Exactly...
My aim was to illustrate that 100% power transfer was a nonsensical concept.
You have effectively proved this by reductio ad absurdum! Showing it is nonsense.

"If the batter swings the bat harder, obviously the ball will rebound faster and the bat will continue to follow through. More energy will be transferred to the ball, but some energy will remain in the motion of the bat"

Exactly

Del