Heavy bat vs light bat

Link to Mailbag item: http://www.straightdope.com/mailbag/mbat.html

In the question about which is better: a heavy bat or a light one, SDSTAFF Ken
appeals to F=ma. I strenuously object:
1) F= ma is not applicable here
2) Ken applied it incorrectly
3) acceleration magically becomes synonomous with velocity (ack! choke!
gasp)

Yes, application of a bat to a ball will cause a force on that ball,
but a lot of that force goes into deforming the ball. (Imagine the
differences in batting a rock, a baseball, a tennis ball, and a
water balloon. In that last case, the deformation is spectacular.)
The baseball will spring back into shape and this whole complex
process is what makes the ball switch directions. This complex
process cannot be described with the simple F=ma equation.

Ken also seems to think that the force on the *ball* is equal
to the mass of the *bat* times the acceleration of the *bat*.
Yeesh! This is why we teach freshman to draw plastic bags
around their objects. The force on the *ball* is equal to
the mass of the *ball* times the acceleration of the *ball*.
In Ken’s interpretation, if the bat has zero acceleration (I think
this is called *bunting*), then it applies zero force to the ball,
clearly absurd.

And last, acceleration is NOT the same as velocity. Acceleration
is the change of velocity with respect to time (dv/dt).

The physics that Ken should have appealed to is the impulse
(the change in momentum) where the momentum of the bat (its
mass times velocity) can be transfered to the ball.
(think billiards). What’s weird is that all the rest of
Ken’s remarks are correct, namely a heavy bat has plenty of
momentum but a light bat swung faster has plenty of momentum
too. Ken’s quips about Popeye and robots are far superior
to anything I could inject.



[Note: This message has been edited by CKDextHavn]

Karen: the ball is deformed due to the absorbtion of the energy (the ball's made of rubber and a few other things). Thus, the ball, upon meeting the bat, comes to a stop and is then propelled by the force imparted in the opposite (one would hope) direction to its original path.

According to Ken Burns' miniseries on the history of Baseball (which was shown on PBS under the ever-so-original title of _Baseball_):

"[Ted Williams] did a scientific study of bats, and discovered that speed, not weight, made the ball travel farther."

In other words, according to .400 hitter Ted Williams, it's how fast you swing the bat, not how heavy the bat is, that contributes the most to the initial velocity imparted to a baseball. And who am I to disagree with Ted Williams? Especially when he's got a baseball bat he cound hit me with.

My guess is that the momentum the bat already has when it first contacts the ball is not as important as the additional force imparted to the ball by your arm muscles across the whole duration of your bat's contact with it. The bat acts as a kind of lever, extending your arm; the faster you can get that lever going, the faster you can push the ball with it.

Of course, there's a simple way to test this hypothesis: allow aluminum bats in the Major Leagues. If we start seeing unprecedented numbers of over-the-wall home runs begin hit, then we'll know.

I can assure you that a lighter bat produces greater power, to a point. (I play baseball and softball, and this is from experience)
First off, there is a limit to how fast you can move your arms in the motion of swinging a bat. I cannot swing a 24 ounce bat any faster than I can swing a 28 ounce bat. Between these two, the 28 ounce is better, because the power generated is greater.(I have a 24 ounce softball bat, and it was too light to generate meaningful power) I also have a 32 ounce baseball bat(plus the 28 ouncer). The 32 ounce bat produces a marked difference in my batspeed. I hit much farther with the 28 ouncer. I believe it depends on the person, the stronger you are, the heavier bat you could use at your maximum swing rate. These physics 101 formulas dont take into account differing swing speeds for different weights. Also. aluminum bats are hollow and tend to have a trampoline effect(at least the expensive bats do) on the ball that a wooden bat does not. With my new 28 ounce bat, I can assure I am driving the ball further than I ever did in high school with a 32 ouncer.

I agree with roksez when he says that the Physics 101 formulae are
completely inadequate to describe all the nuanced effects going on
in batting. The original questioner specified a fixed torque, and
I am pretty sure we can quarantee that humans don't bat that way.
The physiology of applying torque to the bat is certainly not
understood by me. I'm sure the shape of the bat is a factor
(imagine a bat with no narrowing at the "neck", or a bat that
didn't have that little "lip" at the end). And third, at
some point the deformation of the bat causes effects. For
example, a cardboard roll of wrapping paper is very very light,
but you don't see major league players lobbying to get THOSE
approved for use, do you? And aren't you excommunicated or
something if they find cork in your bat?

And lastly, I hate to get all physicist-y on y'all, but I am
skeptical about the scientific experiments Ted Williams did
(did he measure the speed and momentum of his bats?) and the
reason for roksez's batting improvements since high school:
do you really attribute all that to your choice of bat?
Or practice and increase of skill, and possibly better
physical condition?

Karen Lingel, PhD
Physicist and Penguinist

I believe there is a trade off between weight and speed. A ten ounce bat will do you no good, no matter how fast you swing it.
A ten pound bat will do you no good, because you couldn't generate any speed. I'm sure someone could come up with a graph that shows two curves, one for speed, the other for weight, and their intersection would be the ideal point. But then, you would have to adjust it for each person. And adjust it for the material of the bat, and where the weight was distributed, and for the fact that the barrel is moving much faster than the handle. Anyone want to take a crack??

Not really adding anything to the debate, but...

I was watching a game on ESPN last night and noticed that they now have two speed indicators on every pitch. One shows the speed of the pitch while the other shows the speed of the bat. I thought that was pretty cool! Now, if we could just get ESPN to show the length and weight of the bat, maybe we could get somewhere.

------------------
The overwhelming majority of people have more than the average (mean) number of legs. -- E. Grebenik

[As board monitor, I have copied and pasted this post here, to keep the thoughts/thread together.- CKDextHavn]
------------------------------------------

Posted by: cmzeman
Posted on 06-14-99 05:11 PM

Ken,
I must beg to differ with your analysis of the bat weight question. Since the bat/ball interaction constitutes a transfer of kinetic energy, rather than force, I believe that the germane equation would be e=1/2mv2 *(squared, that is). Therefore, it would be to the batter's advantage to use the lightest bat possible. From this truth arises the time honored (and illegal) practice of corking the bat.

1) Both momentum and energy are transferred; both equations must be satisfied.

2) Human arms have a maximum speed.

------------------
John W. Kennedy
"Compact is becoming contract; man only earns and pays."
-- Charles Williams

Simple explanation- you want to use the heaviest bat possible that you can still swing at your arms' maximum swing rate.

Also, this occurred to me as I took batting practice today- for the most part, lighter bats are lighter only in the handle and the cup at the end of the bat. Bats are allowed only a maximum width. Many 2.75 inch barrels weigh 34 ounces, my 2.75 inch barrel weight 28. My bat has an extremely thin handle and a tapered barrel, as well as the cup at the end. The weight of my bat at the point of impact is probably the same(or very close) to a heavier bat, so again, lighter is better.

I'd like to make two small points, just for thought:

1. I would say speed would be very important, mailnly because most of the force imparted to a ball probably comes from the continuing force imparted to the bat from the batter's arms.

2. However, it is also instructional to see what the results might be of two "limiting" cases. First, picture a batter swinging a 100 pound bat at 10 miles per hour. Clearly, the ball wouldn't go very far. Second, picture a batter swinging a 2 oz. bat made of carbon fiber or some similar material, at 200 MPH. What might happen in this situation is that, even with the continuous pressure of the batter's arms on the bat, the end of the bat might not have enough force to reverse the direction of the ball. Perhaps there is a critical directional force (similar to and escape velocity?) that must be present at the point of contact?

Do these points provoke any insights?

I disagree that cork bats are banned because they are lighter. I believe they add to the "spring" of the bat. For instance, if you can't get pitchers to pitch you tennis balls, you cheat by trying to get the "tennis ball" effect from the bat instead.

Are tennis balls banned in baseball?

-k-
Karen Lingel, PhD
Physicist and Penguinist

Dunno about that, but other way around (using a hardball in tennis) is hell on the racket.

Corked bats are banned because they make the barrel lighter. Wooden baseball bats do not compress much if at all. The bat would likely shatter if a hollowed bat compressed too much. They are made of hardened wood. Now, the new composite aluminum bats have walls that are so thin that they do compress and provide the "trampoline" effect. Many of these bats were recently banned by the NCAA. I believe the new rule is the weight (in ounces) cannot be more than 4 ounces less than the length(in inches).

Also, I highly doubt any baseball player of skill could hit a tennis ball farther than a baseball. You lose too much energy when the ball is deformed. A child, with low bat speed, probably would benefit from the compression, however.


[Note: This message has been edited by CKDextHavn]

When reloading ammunition, doubling the weight of the bullet doubles the energy. Doubling the speed of the bullet quadruples the energy. (E=MC squared, or a variation of that). Using the heaviest bat possible while keeping maximum swing speed would result in the most energy.

Not to break the spirit of the thing, but some actual info can be found in _The Physics of Baseball_ by Robert Kemp Adair (ISBN: 0060950471).

In _The Physics of Baseball_, it is suggested that a heavier bat is better for fastballs, a lighter one for breaking and offspeed pitches. To the extent that lighter bats are in favor it's an indication that pitchers throw fewer fastballs than they used to.

about Ruth:
He was about power. 30 probably would have been like swinging a candy cane around to him.

I'd bet there's at least five guys on every current team that are stronger than Ruth. Nutrition and sports medicine are just that much better.

In MLB, the bats have gotten steadily lighter over the years. From what I've read, Ruth never used a bat lighter than 38 ounces, and favored ones around 42-46. Massive hunks of wood. My "Yaz" model, which was my father's, is a hefty 40.

These days most everyone goes for the light bat. I doubt anyone in the big leagues uses anything heavier than 36, and those would be older, power-hitting veterans. 28-32 would be par. I'm unfamiliar with what McGwire and Sosa used last year, but I would guess they used at least 33-34, they're both big guys.

I think it mostly depends on your size and what you feel comfortable with more than any physics questions. I doubt Ruth could have hit 714 homers with a 30 ounce bat, even though it might theoretically have given him more control, more batspeed.

He was about power. 30 probably would have been like swinging a candy cane around to him.

Yes, it would make sense that stronger people would use heavier bats, because they would have a higher maximum swing rate. I have found that I can't swing a 23 ounce bat any faster than I can a 28-29 ounce bat. So for me, a 28 ounce bat gives me the most power. If McGwire can swing a 34 ounce bat at his maximum arm speed, then he would create the most power with that weight. It's hard to compare Ruth, because the technology behind the bats was so different, as well as the balls. Also, some bats have thick handles, different lengths, etc. All these factors would also make a difference.

I think it gets even more complicated than that. A lighter bat will transfer more energy back into the batter's arm, where it will be absorbed by the muscles. There may be some impedance issues here too. Finally, shock waves from the impact may travel up and down the bat, and the resonant frequency of the bat may change how much energy is imparted back into the ball.

Robert Byrne did some experiments with billiard cues, to see whether lighter cues worked better than heavier ones. He took the end rail off of a pool table, then he and some friends who were all professional pool players started shooting cue balls off the end of the table with different cues, and measuring their impact points on the floor to calculate velocity. The conventional wisdom was that a heavier cue would provide more power, but they found that almost all of them could hit the cue ball farther with a 19oz cue than with a 21oz cue.

That might be a case of apples and oranges. With a bat, you have rotational force, and almost no compression at the hitting surface. A pool cue is pretty soft, and is struck no where near as hard as a baseball bat. And it is a linear motion.

You may be right, but it also suggests that the issue is more complex than a simple mass/velocity relationship. Another thing they tried was putting tips of differing hardness on the cue. First, a cue with no tip at all was tried, and didn't work very well at all. Then a very spongy tip was used, and didn't work all that well. A hard leather tip provided the best results. So there are some transfer of energy issues here as well.

Getting back to bats... When you hit the ball, a shock wave might travel up and down the bat. If the ball is still in contact with the bat when the shock wave comes back, the energy would be transferred to the ball. If not, the energy would be lost as vibration. The wrist and arm would also absorb some of the collision energy, and that amount would differ with different shapes and sizes and weights of bat.

Yeah, and another thing is that you may use a 34 ounce bat, and I use a 32, but my bat has more weight in the hitting zone. Yours could have a thicker handle, and I could have the cupped out end on my bat too. Also, different lengths of bats matter, since the longer the bat the greater the speed at the end. Speaking from experience, I hit with the most power using the heaviest bat that I can swing as fast as my arms will allow. Right now, that is a 28 ounce 33 inch long bat with a 2 3/4 inch barrel. It's a composite aluminum alloy.

I'm gonna throw this in here too. I have a baseball game today at 2:00. Now last week, the temp was 92 outside, but 125 on the field. It is supposed to be 98 today. I don't want to go. :(

[The Ryan]

dhanson
Member posted 07-30-99 02:40 AM
"Getting back to bats... When you hit the ball, a shock wave might travel up and down the bat. If the ball is still in contact with the bat when the shock wave comes back, the energy would be transferred to the ball. If not, the energy would be lost as vibration. "

I read somewhere that the point where the shock waves reinforce is what's called the "sweet spot". Is that true?

As for the central question of what's the best bat: it seems to me that as far the initial impulse is concerned, the mass of the bat is irrelevant; what matters is the inertial moment , which is basically a measure of how much mass is how far away from the batter (in the rest of my post, "light" and "heavy" shall refer to m.i.). The mass in the handle does very little, while the mass at the end of the bat does a lot.

In the first part of the swing, the impulse should be proportional to the velocity of the bat times MI2/(MI1+MI2) where MI1 is the m.i. of the ball, MI2 the m.i. of the the moment of inertia of the bat. Therefore, in this part of the swing heavier bats are better, up to the point at which the bat is too heavy to be brought to the max speed.

The second part of the swing is the brief moment of impact. During this time, the total moment of inertia will be the moment of inertia of the bat added to the moment of inertia of the ball (the farther the ball is from the batter, the more force it takes to move it). The ball will therefore receive a force proportional to MI1/(MI1+MI2). The lighter the bat, the more force the ball receives, but this advantage becomes less and less important the lighter the bat.

So in the first part of the swing, heavy bats are good, at least up to a point. In the second, heavy bats are bad. Which part will count for more will depend on many factors, such as arc of swing, arm strength, amount of ball deformation, etc. Of course, this is just a cursory analysis, so it doesn't come with any guarantees.

BTW, what's the URL of the column that started this?

------------------
-Ryan
" 'Ideas on Earth were badges of friendship or enmity. Their content did not matter.' " -Kurt Vonnegut, Breakfast of Champions

[C K Dexter Haven]

Ryan -- I have now modified the first post in this topic to provide the link. Thanks for your comments and for pointing that out. The "please provide link" policy just started in the last few weeks, so some of the older threads don't have it. If I get some spare time, I'll try to go back and correct.

[DSYoungEsq]

If anyone wants to see what is going on when the bat and ball meet, there is an excellent photo of it taken by the old master of high-speed stop photography, Harold Edgerton, of MIT. I imagine most any physics text would have it in the chapter on collisions. The ball deforms quite nicely around the barrel of the bat.

By the way, most of you seem to be ignoring the factor of strength of the batter in the equation. On one hand, strength will help increase bat speed for heavier bats. But on the other hand, strength will help power the bat through the collision. Thus, even if I can swing a 35 ounce bat to 'maximum' velocity at initial impact, I may prefer a lighter bat which will be easier to force through the ball during the time of impact. Someone with WAY more understanding of collisions would have to calculate the relative importance involved.

[WallyM7]

The question of heavy v light bat has not been resolved to everyone's satisfaction.

I humbly submit the following for your consideration:

a: The benefits of each cancel out.
b: The benefits of each very nearly cancel out.
c: It depends on the circumstances. (the batter, the pitcher, the humidity, etc.).
d: Unknown variables. (Suns spots, Camllurdian phase loops, inverse dimensional di-polarity, etc.).

------------------
You are unique - Just like everyone else.

[Polycarp]

Both are valuable...

You want a light bat if you're trying to get rid of pesky insects.

You want a heavy bat if you're trying to dispose of rotting fruit.

Oh, wait a minute, you mean the other kind.... ;)