Vibratory Modes; Sammy Sosa

[ivymike]

I'm sure that many here are familiar with the recent bat corking / Sammy Sosa incident (US Baseball stuff, for those who don't know). There has been plenty of conversation around my office about the physics behind a corked bat. I've got my own theory about why a corked bat helps, and I'd like to hear some feedback / alternative theories.

I know from a PBS special that I saw that a (wooden) baseball bat will primarily vibrate in a 2-node mode when excited by the impact of a baseball. The label location, which indicates the location of the "sweet spot" of the bat, indicates the location of one of the nodes (the other is down where the hands go). Hitting the ball at the node results in the most effective transfer of energy from the bat to the ball, and the least amount of bat vibration (those who have played baseball can probably confirm the relatively smooth sensation of hitting a ball right on the sweet spot).

My idea: Adding cork to the bat increases the internal damping, and reduces the vibratory amplitude when a ball impacts outside of the sweet spot. This in turn reduces the sensitivity of the bat to the location of the ball impact (relative to the node), and thus widens the effective sweet spot. Having a wider sweet spot makes it easier to hit the ball a long way, and that's why we see better/longer hits from corked bats.

other info:

http://library.thinkquest.org/11902/physics/bats.html

 

[ivymike]

... I'd like to use a more sophisticated damping apparatus in conjunction with a baseball bat to see if it really works as I suggest above... Perhaps a piezoelectric damper similar to those used for skis.

 

[Neilmo]

Hello Ivymike,

The technical term for the `sweet spot` as you call it, is known as the "centre of percussion" and is similar to the "centre of oscillation" of a pendulum. You can find the theory behind both of these concepts in most books on `Applied Mechanics`.

All the best,
Neilmo

 

[ivymike]

Thanks for that info (I wasn't familiar with the term "centre of percussion&quot. Searching on that led me to this site:

http://www.webball.com/skill/sweetspot.html

"... As a result, the fundamental and second vibration modes are both excited with about the same amplitude. These modes are shown in the bat diagram. Hence, there are two vibration nodes in the barrel. An impact at the fundamental node will not excite that mode, but it will excite the second mode. Similarly, an impact at the node of the second mode will not excite the second mode but it will excite the fundamental mode. The ideal spot to hit the ball is half way between the two nodes since both modes will be excited but only with small amplitude. This spot is also close to the centre of percussion. "

I still wonder how the cork affects this behavior...

 

[Scipio]

Here's one site that takes a little more fundamental approach on the topic;

http://www.mos.org/cst/article/5471/1.html

Basically saying the only real difference corking a bat makes is to lighten the bat giving it a faster swing - might improve your batting average, but is more likely to reduce your best distance than increase it.

 

[abdul]

Here is my technical guess:

The hollow baseball shaft now has a surface which deflects inwards more then when the bat was solid wood, during the impact of the ball. This increased elasticity increases the time of impact(in microseconds),which then increases the energy transferred from the bat to the baseball.

It is well known that increasing the elasticity of an object, increases the momentum transfer when impacted by another.

In my opinion, the cork has no effect on the batting improvement, as that is accomplished by the central hole. It looks to me that the cork dampens the "hollow sound", which is an instant giveaway that the bat has been tampered with.


abdul