THE BOOK--Playing The Percentages In Baseball

In my pedestrian understanding of hitting, the collision of ball and bat cannot be considered an instant contact and release though an approximation is usually sufficient.  The ball and bat deform and the ability to maintain the momentum of the bat through the contact time affects the speed of the ball coming off of the bat and I would assume spin also.  Thus the age-old advice to swing through the ball.

So the arms, upper body, trunk, lower body and feet must withstand the affect of the ball hitting the bat so that as close as possible to a perfectly elastic collision occurs.

A 75 lbs kid cannot withstand the incoming momentum of the ball as well as a 200 lbs man.  That is unless the kid is extremely strong and can resist absorbing momentum.  In other words as contact is made the bat slows as it absorbs (through the hands, arms, etc) the ball’s momentum since the kid cannot overcome it.

A too light grip on the bat will allow the bat to vibrate and absorb momentum.

The tests at UMass-Lowell typically use a very rigid grip and a swinging mechanism that does not react to the incoming momentum (it is rigily fixed). 

At the end of the day and circumstantially, increased mass and upper body strength can affect power hitting and hitting in general.  The ability to use that advantage still requires skill.

Response to #31:

Unfortunately the science, both theoretical and experimental, does not support your claims.  I am not sure this forum is the best place to carry on a scientific discussion, so I refer you to my paper on the subject:
http://webusers.npl.illinois.edu/~a-nathan/pob/AJP-Nov2000.pdf.

The paper is a theoretical/computational exercise.  However, the result is not “theoretical” in the sense that it is not backed by experimental data.  Lots of experiments have shown that the speed of the ball coming off the bat is completely independent of how the bat is supported at the handle:  free, clamped, pivoted, tight grip, loose grip, etc.  It simply does not matter. 

I realize that such a result does not set well with the intuition that many people have about batting the ball.  But that does not make it any less true. 

Just some quick remarks about some of your points:

1.  While the fate of the ball does not depend on what is going on at the handle, the fate of the bat certainly does.  Thus, when held loosely the vibrations will be less damped and the bat will recoil more than when it is held tightly.  However, all of that happens after the ball has already left the bat and therefore cannot possibly affect the ball.

2.  I agree that muscle mass, even upper body muscle mass, can affect power.  But it does so by increasing the speed of the bat prior to its collision with the ball.  As I said in my previous post, the batter could just as well let go of the bat just before contact with the ball and it would not make any difference in what happens to the ball.  Strange, perhaps (although not to me), but true nevertheless.

Your point about backspin on the ball is interesting ("By undercutting the ball, as opposed to hitting is squarely, the friction between the ball and surface of the bat causes the ball to spin, so that it comes off the bat with backspin.").  Will your paper discuss at all the extent to which players seem able to deliberately create backspin? 

It seemed to me back in 1998 that McGwire had developed a real ability to do this.  And the same seemed true of Bonds in 2001.  (Which isn’t necessarily to say either/both didn’t also benefit from PED use.) But that perception could easily be wrong.  Do you think any hitters have the ability to hit under the ball such that the distance gains from backspin exceed the loss from hitting the ball less squarely?

Guy (#33):  Your question: can a skilled batter control the backspin on the batted ball?  Excellent question and one whose answer I am unsure of.  I suspect the answer is “yes” but I wouldn’t bet the farm on it.  However, let me relate a story.

Last fall, I was hanging out with my Rawlings friends who were testing some new softballs.  One of their employees, whose name I forget, was hitting slow-pitch softballs and consistently hitting over 300 ft.  Those of you who play slow-pitch softball know that is no small feat. We had Rawling’s “SciFly” radar system set up to measure the speed of the ball coming off the bat.  I was surprised that the speed was not particularly excessive for many of these long fly balls, in the high 80’s or low 90’s mph.  So, I asked him how he was able to hit the ball so far.  He claimed he was purposely hitting the ball in such a way that it had a lot of backspin on it.  So, that’s my anecdotal “evidence” that a batter can control the backspin.  But, this was slow-pitch softball, which is a very different game. 

BTW, it is not necessarily true that undercutting the ball (to get the backspin) reduces the batted ball speed in any significant way.  But that’s a much longer (and more technical) discussion.

Alan, getting back to Dufman’s comments about grip pressure, upper body strength, the man versus the boy, etc....

Let’s say that you had a ball traveling at 80 mph approaching a bat.  One bat was held stationary at the handle.  Another bat was dangling in the air by a string.  The ball hits both bats.  Will the ball go further coming off the rigid stationary bat?  That would seem intuitive.  It would seem intuitive that the ball would hit the bat on the string and propel the bat in the direction the ball was traveling and the ball would barely, if at all, bounce back.  The ball that hits the stationary, rigid, bat would bounce off of it like a bunt.  Is this not true?

If that is true, what about if we gave both bats a little speed toward the ball - just barely enough for it to move.  Now, wouldn’t essentially the same thing happen - the ball would bounce off the rigid bat a little further - like a hard bunt.  With the dangling bat, even though we give it a little shove towards the ball, the ball is still going to propel the bat in the direction that the ball is moving and the ball is NOT going to bounce back very far, no?

If I am correct in my analysis above, and I would be surprised if I were not, then how can you say that a 40 pound boy holding a bat and swinging the bat at 3 or 60 mph is going to hit the ball as far as a 200 pound man, when the boy holding the bat is similar to the bat dangling on a string.  The 80 mph ball is going to propel the bat and the boy (essentially knocking him over), no?  Am I to believe that the ball will ricochet off a bat at the same speed and distance, whether the bat is moving or not, regardless of whether it is held by a rigid machine, a string, a 40 pound boy, or a 200 pound man?

MGL:  The experiment you describe has actually been done.  Namely, a ball is shot out of a high speed cannon onto a stationary bat.  In one case, the bat is held rigidly at the handle.  In another case, the bat is suspended with strings, essentially free.  In yet another case, the bat is pivoted at the handle.  The speed of the ball coming off the bat is exactly the same in all three cases (assuming the impact occurs in the barrel). 

Let me speculate as to why most people consider this result nonintuitive.  I think the reason is that people think of the bat as a completely rigid body.  For a rigid body, if I hit it at one end, the other end responds by recoiling immediately.  In fact, a bat is not a rigid body, at least not on the short time scale of the ball-bat collision.  When the ball hits the bat at one end, the bat starts to deflect locally where the ball is hit (i.e., it bends), and that bending wave propagates down the bat at a speed that depends on the properties of the bat.  For typical wood bats, the speed of propagation is such that the wave doesn’t reach the other end of the bat until the collision is essentially over.  In order for the support mechanism at the handle end to matter, the wave would have to reach the handle, then reflect and propagate back to the collision point prior to the ball leaving the bat.  The “information” about how the bat is supported is contained in the reflected wave.  All of this is explained in the paper I referred to in an earlier post.  And, just to be clear, this is not just some theoretical result having nothing to do with reality.  The experiments are completely in accord with the theory.  I have done experiments where I strike a bat at one end with a hammer and measure the movement the bat at different points on the bat with accelerometers.  You can easily see a distinct delay between the time the hammer hits the bat at one end and the movement of the bat at the other end.  And it agrees completely with the theory I have worked out.

So, the bottom line is that when the ball impacts the bat in the barrel, the outgoing speed of the ball is completely independent of the what is going on in the handle:  the size, shape, weight, or means of support *do not matter*.

As I said in my previous post, the batter could just as well let go of the bat just before contact with the ball and it would not make any difference in what happens to the ball.  Strange, perhaps (although not to me), but true nevertheless.

Alan, I think the problem I (and I suppose everyone else) is that we know (or have seen) those pictures where the ball hits the bat, and both the ball and bat change their shape upon contact.

So, it would seem to me that the point of contact does not last 1/infinity seconds.  And so, I don’t see how it would be possible that it doesn’t matter how rigid or not the bat is held, presuming all other things equal (bat velocity, mass and acceleration).

I would presume that the more rigid you hold the bat (all other things equal), then the better the follow-through, and therefore, the point of contact lasts longer. 

Obviously, you think about this 1000x more than we do, so I presume there is some assumption you are making that we are not.

Is it possible that the speed off the bat (velocity) is the same, regardless of the rigidness, but the acceleration is different (because the point of contact lasts longer)?

After all, the distance travelled couldn’t possibly be the same, could it? I’ll go on to your paper now…

Another way to get at Tango’s issue (I think):  even if the speed/mass of the bat were identical at the instant of impact, would the bat speed also be the same 1/1000 of a second later, while ball is still in contact with bat (but in process of changing direction)?  Of would Mark McGwire be able to maintain bat speed through the period of contact more effectively than our hypothetical 40-lb. child?  For most of us, it seems intuitive that there would be a difference.  (Of course, if intuition were always correct, we wouldn’t need physicists.)

Assuming Alan is correct, I think what makes this non-intuitive is the energy of the incoming pitch.  We assume the strength/mass of the hitter is relevant in “standing up” to that energy.  But if we think about this as t-ball, the problem disappears:  if a kid could swing the same bat as fast as a major leaguer, I assume the ball would travel as far.  Or golf:  if a kid could get a driver head accelerating as fast as Tiger, I think he could hit the ball 300 yards (come to think of it, when Tiger was a kid he nearly did).  So the question is:  does the fact the ball is traveling toward the hitter change things?  Thinking about it some more, I’m not sure it would. 

Of course, a 40-lb kid could not really get a bat moving this fast, which is another reason it’s hard to get our head around this....

I think that the ball is coming from the opposite direction makes all the difference in the world, in that the point of contact is longer.

Ok, I’m reading now.  Section D (energy conservation) seems to be what the rest of us are talking about.  That the stronger player (all other things equal) will have less energy lost in the compression/expansion of the ball.  Are you saying that our supposition is not true?

Wow, you guys are tough customers...and I do not mean that in a perjorative way.  You ask good questions and deserve good answers.

The experimental fact is that the far end of the bat does not matter:  the grip, the size or strength of the batter, the thickness of the handle, the weight or diameter of the knob, etc.  Please accept this as an experimental fact.  Now let’s see if we can understand this fact based on the physics.

The essential physics, as I have said, is…

1.  The bat is not a rigid body
2.  The ball-bat collision time is comparable to the time it takes the bending wave to travel down the bat from the point of impact to the handle.

As a result of these things, the ball has left the bat before the wave that reflects from the handle reaches the impact point.  Now, if the impact is not in the barrel but (for example) in the tapered region, then it is quite likely that the handle end of the bat does matter, for two reasons.  First, the bat is more flexible in the tapered region, which makes the collision time longer.  Second, the wave does not have as far to travel to reach the knob, then reflect back to the impact point.  So, my assertion only applies to a typical bat, say 33” long, impacted no less than 8” from the tip. 

BTW, I am not claiming that the collision time is infinitely small.  I am only claiming that the time is comparable to the pulse propagation time.  The collision time is mainly a property of the ball, not the bat.  The pulse propagation time is a property of the bat.  And for typical wood bats and typical baseballs, those those two times have conspired to give rise to the experimental result.  If a nerf ball were used, the collision time would be much longer and my conclusion would not be valid.  Or, if the bat were even more flexible (say, like a skinny cylinder), then the pulse propagation time would be longer and the conclusion would again not be valid.

Regarding the bat not being a rigid body:  think of the bat as like a slinky, where you shake the slinky at one end and can actually see the wave propagate to the other end and reflect.  I do this type of demonstration in my introductory physics classes to demonstrate wave motion. 

Regarding the question of whether the fact that both the ball and bat are moving alters the conclusion:  it does not.  In physics lingo, the collision is “frame independent.” For example, if you were running toward the pitcher at the same speed as the bat is being swung, then the bat would appear to be at rest and the ball would be coming at you faster than it appears to the batter.  But, the nature of the collision has not changed.

My friend and sometimes collaborator Rod Cross, an Aussi who is mainly interested in tennis, did a very interesting experiment about 10 years ago that I refer to in my paper.  He bounced superballs off aluminum beams and measured the speed of the ball after bouncing.  He found that when the ball hit one end of the beam, the bounce speed was completely indepedent of everything having to do with the other end of the beam, including the total length of the beam and its means of support.  The physics in that case is exactly the same.  Namely, the collision time was short compared to the pulse propagation time down the beam and back.

Alan, does the mass of the bat matter?  Or maybe the mass of the barrel portion of the bat (sorry if I missed this earlier)?  If the latter, how far down the barrel (generally) matters?

Or is the relevant mass the entire mass of the bat/arms system?

Also, is the distance advantage from metal bats due to the lighter weight allowing faster swings, or the greater coefficient or restitution from the hollow bat barrel transferring more energy to the ball?  Or maybe both?

I just realized that there are a couple of other points that I did not respond to.

Tom (#42):  This is not an energy conservation issue.  Since you have my paper, look at the discussion on p. 987, right column starting with “Perhaps the most interesting...” This discussion has nothing to do with energy conservation and everything to do with collision times and pulse propagation times. 

Tom (#41):  The ball-bat collision time at a given impact location depends on the relative ball-bat speed.  That too is frame independent.  So, that is also not a relevant issue here.

Don’t you guys have work to do ?  I am officially retired, so I can goof off all I want.  In fact, I recently retired mainly so I can spend *all* my time on the physics of baseball. 

OK, Greg (#44):  The relevant mass of the bat that matters is the mass in the vicinity of the barrel.  For impact near the sweet spot, the effective mass of a typical 34"/31-oz wood bat is about 20 oz.  That is the relevant mass to use when considering the momentum of the bat for the purposes of momentum conservation in the collision with the ball.

Regarding Greg’s question about aluminum bats, there are two effect, as he has said. One:  the aluminum bat has a smaller effective mass than a wood bat of the same actual mass and length (less of the mass of the aluminum bat is concentrated in the barrel).  This has two partially compensating effects:  higher bat speed but less effective collision.  Roughly speaking, these two effects cancel, at least for the type of bat used in high school and NCAA play (not so for LL).  Two:  the aluminum bat has a higher coefficient of restitution (COR) due to the “trampoline effect.” This is a whole other topic, about which I also have written extensively.  For NCAA-type bats, it is the higher COR that is mainly responsible for higher batted ball speeds.  However, most batters seem to prefer the tradeoff in barrel mass that an aluminum bat gives, since the lighter barrel mass means better bat control, even at the cost of smaller collision efficiency.

Alan:  Very interesting.  In the experiments you reference, how do you get a bat head moving at high velocity but not be anchored (or be loosely anchored) at the knob end when impact occurs? 

And to clarify:  are you saying that the batter could theoretically release the bat at the very instant of contact with no change in resulting ball velocity/distance?  And does that mean the batter contributes no additional force during the period of contact, beyond the momentum that existed at first contact?

Response to Guy #47:

In the experiments you reference, how do you get a bat head moving at high velocity but not be anchored (or be loosely anchored) at the knob end when impact occurs?

Some of the experiments are done by firing a ball at a stationary bat, where one is free to do whatever one likes to the handle end.  There have been additional experiments done by using a robotic device to swing the bat, but as you point out the bat is not free in that situation.  Also experiments have been done swinging a bat and hitting off a tee.  And finally, there have been (much harder) experiments done with a batter swinging at pitches fired from a pitching machine.  These experiments are harder since high-speed video needs to be used to track the ball and bat.  In comparing all these experiments, once has to be careful to compare them all in the same frame of reference.  But when you do, you find the result is always the same.  Namely, the batted ball speed (in the appropriate frame of reference) is independent of the end conditions.

Are you saying that the batter could theoretically release the bat at the very instant of contact with no change in resulting ball velocity/distance?

Yes!

And does that mean the batter contributes no additional force during the period of contact, beyond the momentum that existed at first contact?

Yes!

So, my assertion only applies to a typical bat, say 33” long, impacted no less than 8” from the tip. 

This is a great point to consider.  So, if you have a 100lb kid and a 200lb man, each swinging a 30oz, 40” bat at the same speed and acceleration at the same ball, and if the contact is made at say the a few inches from the tip, then it will have no difference in result?  Fascinating.

If a nerf ball were used, the collision time would be much longer and my conclusion would not be valid. 

So, if we had something more rigid than a baseball, say a golf ball, then you could have a much smaller length of baseball bat, say 15”, and again, it won’t matter how strong you are (all other parameters equal), because the contact time is so small, that by the time it reaches your hands, the ball is no longer in contact.  Fascinating.

Regarding the question of whether the fact that both the ball and bat are moving alters the conclusion:  it does not.

I only meant it in terms of contact time and compression.  But after reading your PDF, I see that this is considered (extensively).

In fact, I recently retired mainly so I can spend *all* my time on the physics of baseball. 

We’re also trying, but first we need those mortgages paid off.

are you saying that the batter could theoretically release the bat at the very instant of contact with no change in resulting ball velocity/distance?

I don’t think he’s going quite that far.  He is saying that by the time the ball is bouncing off the bat, the vibration or energy or whatever that has gone through the bat, by the time it reaches your hands, it’s useless, since the ball isn’t there anymore.

The point of contact lasts longer than 1/infintity, so you still need to bat in contact during the whole compression/expansion process. It just doesn’t matter, if I understand it correctly, whether you have a 50lb or 250lb person holding that bat (presuming they both had the same velocity/acceleration/batsize).

Does that about summarize it?

Alan: you should write this up in layman’s terms for the baseball world at Hardball Times.  You will likely find yourself with several thousand new fans if you do.

Yes!

Darn it, and I thought I understood it.

Tom..you were doing very well right up until the end and (except for the last point) you have a very good understanding of my points.  Re the last point:  Since the collision is over by the time the bending wave has reached the hands, the hands could not possibly have played any role.  So, the batter might as well not even be holding onto the bat.  That was the sense I meant when I said the batter could just as well let go of the bat just as it is making contact with the ball.

One of the statements people are having trouble with is that an 85 lb boy would hit the ball as far as a 200 lb man, given the same bat speed.  It is a true statement.  However, it is extremely unlikely that the boy would have the same bat speed as the man.  But, one of the common misperceptions about hitting is that the batter “muscles” the ball as it makes contact with the bat.  The analysis I have given shows that this is not true.  The batter’s job is to get the bat in the right place at the right time with as high a speed as possible.  After that, he might as well let go. 

Re your THT suggestion:  Rod Cross and I are working on a book on the physics of baseball.  It is not really meant to compete with Bob Adair’s famous book, which is hard to improve on.  However, what is missing from Adair’s book is a good accounting of a huge amount of experimental work done in that area over the past decade, a lot of it by Cross, myself, and others we work with.  As a result of this work, we now know much more that was known at the time of Adair’s book, especially in two areas:  the ball-bat collision and the aerodynamics of a ball in flight.  Our intended audiences will be a little different also.  Adair has written (in my view) a brilliant book for the lay person.  We will aim our book at people who are interested in baseball and who have at least a little knowledge of physics, at the level of a high school course.

I will consider writing a THT article.  Good suggestion.

The basic physics of this are definitely counter-intuitive.  It doesn’t seem right that a ball fired against a bat held in a vice would rebound just as far as one fired against a bat suspended by a string.  In one case the bat is left spinning like a top, so it seems to have absorbed more of the ball’s energy.  But I can accept it’s not true.

The other reason I think we find it so surprising is that we’ve all been taught the importance of “following through”, when hitting a baseball, a tennis ball, or a golf ball.  We learned that following through allows us to hit the ball harder/better.  That may be good advice, because following through improves the mechanics of a swing in various ways (and NOT following through might cause the hitter to decelerate prior to impact).  But apparently it actually has nothing to do with driving the ball.

This is amazing. I was just thinking about this exact topic yesterday and had conducted several thought experiments that seemed to point to the opposite conclusion. FWIW, Alan’s conclusions seem to contradict my own personal experience in hitting a baseball, however the science has me convinced that I’m drawing the wrong conclusion from my experiences.

This is fun stuff. I don’t intend to compete with the brilliance on these posts, only to add my two cents.

The reason we are taught to follow through is to generate the necessary bat speed to get the maximum distance from our swing. If we attempted to stop our swing just beyond impact (i.e. just as the ball leaves the bat), we would have had to make that cognitive decision much earlier in the process, because of the relative ‘slowness’ of the firing synapses carrying out the executive decision to the muscles. The result is that we will short-change our bat speed *before* impact, compromising on our max distance.

Following through is our assurance that we don’t short-change ourselves before the ball leaves the bat. I believe the same principles carry over in the golf swing as well, considering some of the ‘keys’ we are taught to maintain the clubhead angle and speed through impact.

OK, I have given up on the idea of getting any real work done today, so let me continue.

Guy #53:  Interesting point raised here.  In the case of the free bat suspended by strings, the bat recoils and spins.  In the case of the bat clamped at the handle, it does not.  It would appear that the energy transferred to the bat is different in the two cases, and therefore the energy that the batted ball has must also be different in the two cases.  But this is actually not the case.  The bat has the same energy in both cases.  In the free case, the bat energy is mainly in recoil and rotation, as Guy has said.  In the clamped case, the energy is contained in vibrations.  In fact, the primary vibration in the clamped case is the “diving board mode”, a very low frequency mode that you see when a diver jumps off the springboard.  It is also called the “cantelever mode” for obvious reasons.  You can see this mode in action by clamping a plastic ruler to the edge of your desk (or hold it there tightly), then deflect and release the free end.  A bat clamped at one end has a similar vibrational mode, albeit at a higher frequency than the plastic ruler.  Detailed calculations show that both the energy transferred to the bat and the speed of the batted ball are *identical* in both cases.  And it is not an accident that this is the case.  It MUST be the case, based on the argument I gave about collision and pulse propagation times.  The fundamental point is that the ball must have the same speed in the two cases.  Therefore the energy transferred to the bat must be the same in the two cases.  How that energy gets distributed between so-called rigid-body modes (i.e., translation and rotation) and vibration depends on the details of the situation, such as the method of support.

Regarding the follow thorough that we have all been taught.  You surely would agree that what the batter does *after* the ball leaves the bat cannot possibly matter.  I am taking it one brief instant further and saying that what the batter does just as the ball is making contact doesn’t matter either.  The follow through advice is given mainly to make sure that the swing mechanics use right up to contact is correct.

Brian:  sorry, without knowing more about your thought experiments, I cannot comment.

I agree with both John’s and Alan’s comments on following through.  I’m only speculating that this training we’ve all received is one of the reasons Alan’s findings “feel” wrong to us non-physicists....

an 85 lb boy would hit the ball as far as a 200 lb man, given the same bat speed.  It is a true statement.  However, it is extremely unlikely that the boy would have the same bat speed as the man.

I am pretty sure a 100lb boy will have a (much faster) bat speed than a 200lb man, if that boy was Barry Bonds and that man was Don Zimmer.  I don’t think this was our original issue.  Our issue was one of holding the bat rigid, rather than, as you are saying, releasing at point of contact, being the same thing.  The 100lb boy and the 200lb man simply gives us a human illustration. 

I think it’s very easy to understand that a 12-yr old Wayne Gretzky could have a slapshot that is just as hard as the 22-yr accountant.

I think it’s very easy to understand that a 12-yr old Wayne Gretzky could have a slapshot that is just as hard as the 22-yr accountant

...or the 62-yr old physics geek/baseball wannabe!

Alan -
I believe my thought experiments have all been covered in the posts above (bat hanging from string, bat fixed in position, bat fixed about a point, etc)...nothing more to add! I merely intuited the results incorrectly, which kind of makes me giddy actually. I love it when I learn something. lol

Just putting a demarcation point that all posts from this point on is since the new thread started.

I am not sure I understand the technical explanations by Alan, but I am certainly going to conduct a simple experiment today.  I am going to propel a baseball or golf ball (I already have a couple of hundred of those scattered around my back yard) against the something (maybe a board) that is held firmly and then against the same thing that is allowed to easily move - maybe I’ll suspend a board from a string.  Then I’ll simply see how far the ball rebounds.  While I obviously cannot get any exact speeds and measurements, I should be able to get some idea as to whether it matters or not whether the object (the board, which is the analogy of the bat) is held rigid or allowed to move.

Again, the intuitive supposition is that the ball with move the non-stationary board and that the ball will NOT ricochet back as much as if it hits a board that is rigidly held.  But apparently that is not the case.

BTW, in golf, which I study a lot (from a layman’s perspective) we see players (men, girls, boys, women) who are not necessarily big and strong at all, but hit the ball a mile. This alone suggests that the strength/mass of the person holding the golf club has little or nothing to do with how far the ball goes (it is only clubhead speed that matters, everything else being equal, like equipment, hitting on the sweet spot, launch angle, spin, etc.), but that is a little bit different from what we are talking about plus the ball in golf is not moving so it cannot propel the golf club.

I just read through this thread and am fascinated by it. My question is about the plane of the bat vs. the plane of the ball. Alan, are all the experiments you mention with “dead on” hits? Does the plane of the bat vs. the ball matter at all for ball velocity off the bat? I assume it would, since any bat speed wasted on a direction perpendicular to the ball’s plane is basically wasted velocity. Or is it?

While Alan’s arguments are non-intuitive, I think I get them, and I appreciate his detailed reasonings.

Some evidence that may be apocryphal—didn’t Jim Rice once hit a home run with a broken bat? Assuming the bat breaks at impact, it is roughly equivalent to a moving bat ‘on a string’ since it has no pivot point.

Don’t know about Rice, but I saw Jack Howell hit a broken bat HR in 1987.

Trying to understand the “counter intuitve” collision -

tell me if I am thinking this correctly.

1. Roll a ball across the floor at another stationary ball (same size, same mass). When they collide our rolling ball deflects away at a certain speed. The ball that was hit will also roll away, in the opposite direction, because it absorbed energy.

2. Roll the ball at the same speed, but into a wall. The wall absorbs the same amount of energy from the ball, but doesn’t move, instead vibrates, because it is held in place. The rolled ball should deflect away at the same speed that it did when it hit the stationary ball.

3. Roll both balls. At impact, they give each other energy, and bounce away. If the target ball was moving faster, our ball will absorb more energy than it gave away, so it will bounce away faster than it went in.

4. Pitch the ball at a moving bat. The ball’s energy is it’s mass times it’s speed, and the same for the bat’s energy. On contact they exchange energy, and the ball bounces off, likely with more energy than it came in.

And yes, I am at work

I’d really love to ask Barry Bonds about things like this. I’ve heard him quoted as saying that he could read pitches coming out of the pitcher’s hand, so it wouldn’t surprise me to hear that he was able to intentionally put backspin on the ball. Barry was obviously a physical freak, but his baseball I.Q. was off the charts too.

Re new #32 and #33:  I’ve watched all the homers the last three years, and I’ve seen a few where the bat broke.  One in particular, I can’t remember who hit it, but the bat head went flying a long way, nearly to the outfield grass, and the ball still made it over the fence.

However, broken bat homers may not be the same situation that we’ve been discussing.  Alan’s description of the vibrations not returning to the head of the bat until the ball is gone might not apply if the bat is cracked/flawed, or if the ball is hit too far up the bat.

Re Mark new #35, Bonds can’t put spin on the ball any differently than all the other players, which is to say that to do so, he would have to strike the ball off-center (below center to generate backspin), and/or with a swing plane that is not parallel to the incoming pitch.  Now, Bonds certainly had (has) exceptional skill at hitting the ball hard at a good angle, which generates backspin that adds to the flight distance of the ball.  I just don’t know that the backspin part ought to be considered distinct from the “hitting it hard at a good angle” part.  They’re totally intertwined…

You guys are really wearing me out!  Let me see what I can do in the next few minutes.

1.  MGL #31.  Nice idea for an experiment.  Here is another idea (and one the Cross and I were planning on writing up in our book).  Suspend a superball on the end of a string so that it can freely oscillate like a pendulum.  Then find something convenient to collide it with.  Perhaps a meter stick (ok, a yard stick will also do).  Figure out how to set things up so that the ball hits the stick on one end and the bottom of its path.  Always start the ball from the same initial height, then measure the rebound height.
Now compare the two cases where (1) the opposite end of the stick is clamped (say, to a table) and (2) the stick is suspended at the center from a string.  I haven’t checked out the numbers to see if they work out.  Remember, if the collision time is faster than the pulse propagation time, then the rebound height will be the same in both cases. 

2.  Doug #32.  Everything I have been saying up to now is for head-on collisions.  Things don’t change too much if the collision in not exactly head-on.  In terms of rebound speed, what matters most is the component of the ball-bat relative velocity that is perpendicular to the surface of the bat.  The angle can be quite large and still not lose much perpendicular speed.  For example, the cosine of 10 deg is 0.985, so the perpendicular component is still large.  So, the collision is quite “forgiving” for small misalignments.  Those misalignments are very important for the spin of the batted ball.  But that is a whole new topic (and the subject of another paper that I am currently working on--I think I may have said this in an earlier post). 

I have my own story about broken bats.  I was testing bats a few years ago and repeatedly impacted a stationary wood bat with a ball fired at about 120 mph.  After about the 8th impact, the bat broke.  But the rebound speed for that impact was identical (within experimental uncertainty) as all the previous impacts.  And the way I understand that is the whatever happened to the bat happened after the ball had already left it.

3.  Brian #34.  I would not compare a ball-ball collision to a ball-wall collision.  I am not sure what you would find, but I much prefer MGL’s experiment mentioned above (or my own version of it).  That is, you want to bounce a ball off one end of an extended object, then compare the bounce speed with different conditions for the opposite end (free, clamped, etc.).

Greg #36: I guess I’m wondering if Bonds, by virtue of his natural gifts, was able to find something approximating hitting the ball at an optimal angle rather than just at a good angle. There was some discussion earlier in the thread about players generating backspin, and specifically whether they could learn to generate backspin. My thought was that Bonds, as his numbers attest (and PEDs can’t possibly explain away), was operating on a something of a higher plane. Was this because he figured something out or was his coordination and vision and fast-twitch musculature just that much superior to everyone else? Or did his natural gifts allow him to figure things out that wouldn’t be apparent to other players?

For me it all boils down to one simple question: “Is the ball still in contact with the bat when the bat starts to recoil from the impact?”

If the answer is “no”, and this is what the science is telling us, then the strength of the batter makes no difference.

If the answer is “yes”, and this is what my intuition tells me, then the ability of the batter to reduce the recoil (ie. strength) does matter. Hell, I’ve even been told by coaches that I should improve my strength in order to keep the bat on the ball longer and hit for more power!

In the end, the experimental data appears to be solid, so I’ve got to admit my intuition is wrong.

Re Brian #39.  What exactly is meant by “start to recoil.” That statement is inherently a rigid-body concept, whereas the bat is not rigid.  The bat starts to move more or less just after the ball contacts it.  But it only moves locally, in the vicinity of the impact location.  That bending wave then propagates down the bat, reflects back up to the other end, reflects again, etc. etc.  After many reflections, the ultimate motion of the bat takes shape in terms of recoil, rotation, and vibration.  If you look at my paper, Fig. 13, you can get an idea about how the motion of the bat evolves.  The knob end of the bat, where the batter is holding it, does not even start to move until the collision is nearly over.  The batter can’t start to “reduce the recoil” until he feels the recoil, i.e., until the bat actually starts to move under his hands. 

The statement by the coach makes no sense to me whatsoever.  I don’t dispute what coaches teach batters to do.  After all, they know much more about swinging a bat, pitching a ball, etc. than I could ever hope to know.  However, I do dispute their reasons, if those reasons are not in accord with scientific fact that I know to be true.

Anyone want to start a debate about corked bats?

Wow, how’d I miss this discussion?

I can say with near certainty that power hitters intentionally put backspin on their hits. It’s one of the elements of power hitting along with bat speed and elevation. In fact, there’s a whole school of hitting based on this - Charlie Lau - which advocates a level swing and using generated backspin and elevation (by hitting under the ball).

There’s an article on the optimal batting parameters for hitting a baseball the farthest on Alan’s site. Sorry I don’t have time to find the link - I’ll post it when I get home. Anyway, it is a slight upswing with about 1” of undercut.

It is not accident that most batters miss the ball by swinging under it, especially fastballs. There’s more bat below their aimpoint than above it. It also explains how sinkerballers induce ground balls at the expense of strikeouts.

I have an article I have been working on about this very topic. I will probably be finishing it up next week (my vacation ).

Matt

The article Matt referred to is at this link:
http://webusers.npl.illinois.edu/~a-nathan/pob/AJP-Nov03.pdf. 

If I might digress for a moment, we will soon have new data from hitf/x that will tell us the speed and launch angle(s) of the ball coming off the bat.  Unfortunately, the missing ingredient that will will not get is the spin on the ball.  That kind of data is much harder to get because it requires cameras that have both high speed and high spatial resolution, since you need to pick out features on the ball and watch them evolve on a fast time scale to measure the spin rate.

Alan-
I was using ‘recoil’ as a catch-all term for any displacement/bounceback/vibration of the bat within the batter’s control that could negatively affect the speed of the ball after contact. Obviously there is a certain amount of ‘recoil’ in the vicinity of the contact that is entirely outside the batter’s control and is more a property of the materials involved. However, intuition wrongly tells me (and presumably the coach I referred to as well) that due to the deformation of the ball and bat at contact, the information from the contact reaches the batter and the batter’s response propagates back up to the barrel before the ball has left the bat. If the ball is gone before the information of the contact reaches the batter, then the question of whether or not some property of the batter (strength of grip) can influence the speed of the ball is moot. That’s all I was trying to say.

While that particular piece of coaching advice may be misdirected in light of your research, I have been told many things by many coaches that were much more ridiculous than ‘keep the bat on the ball longer for more power!’ Ridiculous and counterproductive coaching advice would probably make a good topic for another day.

Count me among those that finds this experiment hard to believe.  Not that I’m doubting you, Mr. Nathan, just that it is counter-intuitive.

Do you know if there are any videos on the web of this type of experiment? It would be cool to watch.

I respect the theory behind this discussion, but the issue of player strength vs. bat characteristics seems to come into play with a set of pitch-by-pitch statistics I derived from Sammy Sosa’s ‘97 and ‘98 seasons. Sorry if I’m coming in from right-field here (no pun intended), but:

From ‘97 to ‘98, Sosa increased his HRs from 36 to 66. Most of us know this. But lost in all of the discussion of Sosa being “more patient” at the plate in ‘98 is the fact that not only did he strike out at the same rate (’97: 174 Ks in 642 ABs, ‘98: 176 Ks in 643 ABs), he missed the same percentage of balls he swung at each year (31%).

But the most startling stat for me is the jump in the percentage of HRs Sosa hit for balls he put ‘in play.’ In ‘97, this was 8.1%. In ‘98, it jumped to 14.6%.

Maybe I am jumping the gun when I say this, but I interpret this increase due to Sosa’s fly balls traveling farther distances (imagine a distance distribution curve s-t-r-e-t-c-h-e-d to the right), which I attribute to an increase in strength. Even line drives and ground balls were hit harder, as his batting average jump from .251 to .308 seems to show.

According to the theory in these posts, though, the answer would be in Sammy’s/the bats mechanics, that his

[Sorry, my last paragraph was truncated in previous post. Here it is.]

According to the theory in these posts, though, the answer would be in Sammy’s/the bats mechanics, that his HR/INPLAY jump was due to an increase in bat speed, which I admit would have me confused - so were all those muscles just for show?

[This post has been fascinating to follow...]

The theory here does not say strength doesn’t matter.  Just that Sammy’s increased strength allowed him to swing with greater bat speed.  The bat speed is the cause of him hitting the ball farther, his strength in gripping the bat means little.

Alan,

Wouldn’t there be enough information to calculate a spin values by combining HITfx data with Hit Tracker observations? You’ve got initial launch angle and velocity, and then a location and arrival time. You’d be limited to homeruns, but that is the kind of hit most people are interested in anyway.

Matt

Rally #47:  perfect explanation!
Matt #48:  Yes.  Combining the hitf/x data with Greg’s hittracker data (landing point and flight time) pretty much constrains the spin on the ball and the whole trajectory.

Prof. Nathan,

A couple of questions from your papers, from a quantum physicist:

1. Why (in your Spin paper) are your statistics so low? 22 pitches seem like very few once you’re gone to all the trouble of setting up the experiment.

2. Is much known abort the effects of the seams on C_L and C_D? Only one of your references seems to care at all, and even then only in the two “symmetric” (2-Sean & 4-Seam).

3. Regarding the bathed collision: Bunting. With the hand farther up the bat and much lower collision speed, is the mechanism much different?

Cheers,

Devin Smith

Devin:  re your last question, the situation you describe is different in two respects.  First, at lower speed the collision time is a bit longer.  Second, the hands are closer to the impact point.  For both those reasons, the grip is likely to matter.  I would guess that with a strong grip, the ball bounces off the bat faster than it would for a free bat.  But, just to be clear, that situation is very different from the one we had been discussing in this thread.

Re your other questions:  those are a bit off topic, so contact me privately and we can discuss.

I would guess that with a strong grip, the ball bounces off the bat faster than it would for a free bat.  But, just to be clear, that situation is very different from the one we had been discussing in this thread.

Why is this different from what we have been discussing?  This is EXACTLY what we have been discussing.  What is going on?

Alan said this:

“Second, the hands are closer to the impact point. “

So, by the time the vibration reaches your hands from a bunt, the ball is still in contact with the bat.

For a regular swing, if the ball is at least 25 inches from your hands, the ball has already left the bat by the time the vibrations reaches your hands.

Hopefully, I got that right.

***

This also gives a better understanding when you are taught to hold a bat or stick or racket “not firmly”.  I guess there’s an implicit understanding that you want your wrists as loose as possible so you can generate power/acceleration, and having a tight grip on the bat simply doesn’t add to that (in fact, probably worsens it), and there’s NO tradeoff in terms of having the “rigidity” since the object has left the bat/stick.

***

Alan: any plans on doing this with hockey?  I’d like to know the optimal point to hold a stick when doing a slapshot.

Re:  MLG and TT (#’s 52,53).  Sorry, I should have explained that I was responding to #50, a question about bunting.  Tom, you explained my explanation perfectly!  And it makes it clear that the issue of whether or not the hands matter really comes down to a quantitative issue, and the two primary factors involved are the collision time and the pulse propagation time. 

Re hockey:  Sorry, no plans.  I’ve got too many other things on my plate at the moment.  Maybe someday.

If I haven’t said so already, let me say now that I have very much enjoyed this whole discussion.  You guys have asked very incisive questions and have forced me to work hard to try to answer them.  And, if you haven’t yet figured out, I love doing it!

Here is maybe a different point of view of what Alan is writing about. Please correct me if I am wrong.

In an ideal state, the batter wouldn’t even be touching the bat with his hands (if you can imagine that) because any ‘forces’ of the hands on the bat (e.g. gripping too tight) can only hurt the ‘system.’ The hands are there only as the ends of the lever system (wrists, arms, shoulders) that is trying to do one thing: Generate maximal bat-head speed through the plane of the ball’s direction.

Over-tightening of the grip works against the freedom for the wrists to rotate as the bat head accelerates through the hitting zone. Think Ken Griffey Jr.

The strengths of the legs, hips, and upper body (which certainly can be enhanced through weight training, etc.) all coordinate to channeling the energy for generating the bat head speed.

Does that make sense?

Alan: if I had a really rigid bat, would the vibration from impact get to my hands more quickly? 

And I hope this isn’t too off-topic, but are frozen baseballs really deader (in the perhaps apocryphal story where the pitcher sneaks one into a game)?  I would think that a frozen ball is more rigid, making for a more efficient energy transfer.  But this goes against my natural intuition (which admittedly comes from a small sample size of a few little league and high school games played in very cold weather--I guess the bats were affected then, also.)

I’m sure Alan is aware of Time Warp on Discovery, but I highly recommend that show.  Their super-slo-mo cameras catch wave motion through all sorts of “rigid” objects, like cymbals and skateboards, plus they like to film objects colliding into other objects.

Thanks for your participation in this thread, especially for answering questions that you have already addressed in your paper. saying “read my paper

Re John #55:  You are now treading into territory about which I have much less expertise.  I had better let others comment while I just read and learn from you.

Re Hizouse #56: 

Rigid bat:  Yes, the speed of the wave is faster for a more rigid bat, e.g., a fatter bat.

Frozen baseballs:  There are two not-completely-independent properties of a ball that matter as far as the ball-bat collision is concerned.  One is the “coefficient of restitution” (COR) or the “bounciness” of the ball.  It is a measure of energy dissipation in the ball.  The higher the COR, the less energy dissipation and the higher the batted ball speed.  Generally speaking, the COR goes down at lower temperatures.  The other property is the “hardness” of the ball, which really plays only a small role for wood bats.  The hardness determines the collision time--the harder the ball, the shorter the collision time.  Shorter collision times generally are more effective at exciting vibrations in the bat.  But, that is a small effect for a wood bat and the COR effect is dominant.

For an aluminum bat, things are different.  A harder baseball gives more of a trampoline effect.
So, if you can put the balls in a deep freeze (but keep the bats at normal temperature), I cannot say with confidence what will happen for an aluminum bat.  The ball will have a smaller intrinsic COR but the trampoline effect will be greater.  Rather than speculate, it is better just to do the experiment (which I have not done).
Good question.

Thanks.

Slow-pitch softballs are regulated according to their COR (higher COR balls go farther) and their “compression,” which I think would equate to hardness.  Compression is measured, I think, by seeing how many lbs of pressure it takes to compress a ball by a certain amount.  And in softball, with fancy metal bats, power hitters would rather have a low COR-high compression rating (harder) ball than vice versa.

Which in turn reminds me of another item touched on earlier: Before a Braves game last year at Turner Field, they had a softball home-run hitting demonstration.  Those guys unquestionably were intentionally putting tons of backspin on the balls.  It looked like they were hitting 7-irons.

Anyways, sorry for the softball diversion, thanks again, and go Illini go.

Not to keep rehashing the same issue, and I have not yet done the simple experiment we talked about (or some version of it), but won’t a moving ball displace an object, like a bat, that is not fixed, and won’t some of the energy of the collision which would otherwise go into the rebound velocity of the ball, go into the kinetic energy of the bat as it is propelled by the ball?  Thus making the ball rebound with less velocity? I guess my question should be, why is that not so, as I am conceding that Alan is correct as he is the physicist and I am a lay person, when it comes to physics and bat/ball collisions?

If I dangle a piece of fabric from a string and throw a ball at it, won’t the ball just move the fabric and not rebound?  If I put the fabric in a frame and it is not allowed to move, won’t the ball bounce off?  What about a piece of cardboard?  A thin piece of wood?  A piece of plastic?  A bat?

MGL:  Yes, some of the ball’s energy will go into moving the unfixed bat.  But an identical amount will go into creating vibrations in a fixed bat as well, so the ball exits with the same energy.  Now, if the ball stayed in contact with a fixed bat longer, I suppose it would gain additional energy when the fixed bat rebounded.  But Alan is saying that the ball is no longer in contact with the bat when this occurs. 

See Alan’s comment #25 (responding to my #22).

I was about to respond to MGL #59 when Guy #60 beat me to it with (more or less) the same response I was going to use.  I was watching Cramer get grilled on the Daily Show and missed the post.

Boy - I go to work for a few days and I miss then conversation.

To summarize what I kind of started -

Simple physics shows that the transfer of momentum/energy from the bat to the ball is mostly dependent on the mass and velocity of the ball and mass and velocity of the bat.  That is, as soon as the ball leaves the bat, nothing else matters.

The deformation of the ball and bat and wave propogation in the bat and “recoil” effects are nearly non-contributors to the exit velocity (I may have missed timing of ball deformation to the process).  COR of the bat and ball do have an impact to varying degrees.

So my original premise of rigidity in stance, bat grip, etc is only important in the aspect of getting the bat moving at a maximum speed.  If your grip is too light, you lose bat control.  If your stance is too light, you lose balance and thus bat speed.  If your lower body isn’t strong, you cannot torque your body to create bat speed.  If your upper body isn’t strong, you cannot generate bat speed.

Now I am off to read Alan’s paper over the weekend.

Two points:

1.  In looking back at some of what has been written, I just realized I said something not quite right in an earlier post, #13.  Here is what I said:

[\quote]Or, if the bat were even more flexible (say, like a skinny cylinder), then the pulse propagation time would be longer and the conclusion would again not be valid.

It is true that a skinny cylinder would have a longer propagation time.  It is not true that my “hands don’t matter” conclusion would not be valid.  The example I meant to use was a fat cylinder, which would be less flexible than a real bat so that the propagation time would be *shorter*.  Under such conditions, the “hands don’t matter” conclusion would not be valid. 

Just to emphasize the point, the hands won’t matter if the collision time is short compared to the pulse propagation time.  Sorry if my example caused confusion.

2. The “hands don’t matter” idea is crucial for the efforts to test bats in the laboratory at places like the Baseball Research Center at UMass/Lowell (where they certify bats for the NCAA).  See http://m-5.eng.uml.edu/umlbrc/.  I think they may even have some high-speed videos.  In their apparatus, the bat is clamped at two points in the handle and mounted on a device that allows it to freely pivot after being struck by the ball.  The manner in which the bat is clamped is very different from the way a batter grips the bat.  Thus, if the test results are to be a meaningful representation of performance in the field, it is important that the clamping method not matter to the ball exit speed.  This is an excellent example of how “theoretical” physics can be applied to a practical situation that someone might even care about.  That is, it is not just an academic exercise but of real practical value.

Here’s some physics page on Cricket:
http://www.physics.usyd.edu.au/~cross/cricket.html

Hat tip: David Barry.

Re #64.  Rod Cross is a frequent collaborator of mine on science of sports projects.  We have co-authored a bunch of papers together and have been working on a new book on the physics of baseball.

One more thing about Rod Cross.  He is one of my two go-to guys when I want to test out my understanding of something or try out a crazy idea (Adair is the other).  Smart guy and incredibly prolific.

I understand that there is an optimal launch angle for hitting a baseball the maximum distance under specific conditions, and that there is a backspin element that also factors in gaining even more distance.

Is there an optimal swing path angle of the bat barrel for achieving this maximum distance? I imagine that since the baseball is actually dropping as it arrives at the plate, the answer might be, “it depends.”

More loosely, I am wondering if there is a minimum ‘uppercut’ that is required to achieve the launch angle?

I am investigating the matter where singles hitters turned into power hitters (i.e. hit more HRs), and in doing so struck out more often. The question is did they strike out more because they went for the fences more, or did they strike out more as a result of adopting more of an uppercut swing to take advantage of their new found power (say through strength training) than in their singles-hitting days. The argument is that the slightly more pronounced uppercut is what increases the probability of a swing-and-miss, causing the Ks to go up.

Thank you.

The issue of optimum swing angle has been addressed in a paper (I am not one of the authors) that can be downloaded at this link:
http://webusers.npl.illinois.edu/~a-nathan/pob/AJP-Nov03.pdf.  The paper is pretty technical, so I can briefly summarize here.  The authors consider the optimum swing angle and undercut distance (i.e., amount by which the bat undercuts the ball) to get the longest fly ball distance.  To achieve that, one needs both the optimum launch angle and backspin on the ball.  Generally, this is achieved by swinging upward at an angle greater than the downward angle of the pitched baseball.  Such a swing is “less forgiving” than if the bat is swung in the same plane as the ball.  In the latter case, if the swing is a bit early or late, you can still make good contact.  By swinging upward, you stand a good chance of missing if you are early or late.