The physics of baseball: batting

Since I’ve gotten back to playing ‘ball’ (softball) this summer I’ve been thinking a lot about my hitting. Once I got back to playing second base I fell into my old routine with fielding and have played fairly well (2-3 total errors in six games) even though I’m playing softball this summer and I used to primarily play baseball. Second base seems to come fairly naturally to me. My hitting, however, is another matter.

When I played baseball I was never a great hitter. During my first stint at softball I had a solid on-base percentage (OBP) and usually reached on a hit, though the vast majority were singles. But that was a college ‘beer’ league. The league I’m in this summer is a very competitive co-ed league and my hitting has taken a subsequent turn-for-the-worse. Somewhat concurrently I have been coaching T-ball which is the entry-level game in little league. Despite being average I always prided myself on having ‘good form’ and, as a teacher, have worked hard teaching these kids how to swing (no one keeps score in T-ball since it’s really about learning the fundamentals).

Put all this together and I started to think seriously about batting. While this may be known to those who have been involved with the game for a long time, I realized that the advice I (and countless others) have received (and given) to ‘choke up’ on the bat, is bad advice. Physics – and a little common sense – tells us why.

When a person bats they’re (usually) seeking to maximize the force of contact between the ball and the bat through efficient use of their body. Since the person is swinging, the action is akin to pulling a lever. That is, something is (approximately) rotating about a point or axis. There are a lot of variables that go into this, but roughly the force of contact is related to a torque created by the motion of the arms and bat (as well as a portion of the torso). The strength of this force partly depends on the distance, r, the contact point is from the axis of rotation. Take a look at the picture below that I’ve doctored up a bit (Note: I found this on Flikr via a Google search and it apparently was taken by a guy named Wil C. Fry. Hope he doesn’t mind.).

So the torque at the point of contact, independent of the action of the ball itself, is \tau = I\omega where I is the moment of inertia for the bat/arm combination. Roughly, we can approximate it as a cylinder pivoting around one of its endpoints. This is not a perfect analogy, but it will work for the argument here. \omega is the angular velocity of the bat/arm combination, i.e. how fast the batter swings the bat. So the torque can be determined without even considering the ball. However, the contact itself also creates a torque since torque also happens to be \tau = \mathbf{F} \times \mathbf{r}. Note this is a cross product. That means only the components of the force and vector, r, that are orthogonal (perpendicular) to one another multiply. If you’re not sure about that, let’s assume the batter hits the ball dead on (i.e. he/she didn’t swing late or early – no pulling or hitting to the opposite field). In that case it’s just a regular multiplication. So if you know the torque from the other stuff and you know where the bat and ball connect, you know the force of contact. Essentially, this is the same principle behind closing a door. Remember, the batter is trying to get the ‘biggest bang for the buck,’ so-to-speak. When you close a door you need to push harder to get it to close the closer you push to the hinges. Don’t believe me? Try it. This is why you should hold wrenches and hammers as far from the head (as close to the end of the handle) as possible. Hitting a baseball is a lot like hammering a nail.

This summer, despite my team’s plethora of bats, not one is less than (nor greater than) 34 inches in length. Now, I’m not a big guy (5’8″) and was always taught to either use a shorter bat or to choke up. Take a look at our picture above again. Naïvely we might assume that choking up might help the fellow. Of course, for the guy in the picture, the ball’s likely to just hit further down the bat. But for someone like me, who seems to always make contact on the tapered part of the bat, this is seen as an improvement (the ball tends to go more where you want it to, for one). But, this summer, despite choking way up on the bat, contact kept happening along the tapered portion most of the time (not to mention the fact that choking up just doesn’t feel natural). Then someone told me to not choke up, but instead move further back in the batter’s box. Let’s assume the ball always goes right over the plate for now and let’s only consider times I actually make contact. In this case, moving me back has the effect of increasing r! Just like closing a door, that either means I don’t need to swing as hard to get it to do the same thing, or, if I swing just as hard, it should result in a larger force of contact (think about using the same force to close a door by pushing right next to the hinge and likewise by pushing on the handle). In my last at bat (AB) in my most recent game, I did not choke up, but rather moved back further in the box (assuming the umpire would tell me if I was outside the box) and laced a nice single to left-center.

Now, my teammates were also talking about the fact that many batters actually ‘choke down‘ on the bat to get more power. Specifically, the very bottom of the bat is gripped by either the middle or ring finger of their lower hand, leaving one or two fingers gripping at air. Then, right around the time of contact (ideally at the time of contact), they flick their wrists a bit (the grip simply makes this action a bit easier). This applies a secondary torque since, briefly, the bat is also pivoting around its base (in addition to the bat/arm combination pivoting around the axis along the body). Since torques and forces are additive, this increases the force of contact slightly. It’s a nifty little trick of physics – if you can get the timing right. Get it wrong and you’re likely to pull the ball foul.

Now we could also look at all of this from the standpoint of momentum. In the above case, the momentum of both the swing and the flick of the wrist is associated with some angular motion and is thus called angular momentum. Nonetheless, a linear momentum is associated with this at the point of contact and, like forces and torques (and, indeed, all vectors) momentum is additive. This helps explain one more trick batters often use. Frequently batters will, just before their swing, pick their leading foot up and step forward a bit as they swing. This effectively transmits a small amount of linear momentum to the entire body and thus to the contact as well. This gets added to the other two pieces of momentum and, if perfectly executed, is the recipe for a great hit.

Ah, but how does one perfectly execute something like this? Well, it’s all about timing. Take a look at the following analysis based on numbers crunched by Yale physicist Robert Adair. Granted, this is for a 90 mph fastball. In theory it should be easier in slow-pitch softball, but in the latter the ball is not coming directly toward home plate (if it is, don’t swing – it’s a ball since it has to arc to be a strike in slow-pitch). In any case, at least in baseball and fast-pitch softball, timing, which is largely physiologically determined, is what separates a good hitter from a great hitter.

Update: I wanted to clarify the first torque equation (I wrote this when I was exhausted). So, if we approximate the bat/arm combination as a cylinder rotating about one of its ends, then the moment of inertia would approximately be ^{mL^2}/_3 where L is the length. Let’s, for the sake of argument, assume that the ball makes contact with the bat at the very end of the bat every time. As such, we can approximately say that L \approx r. According to Adair, the bat is moving at about 80 mph when it hits the ball. That’s a linear velocity. Angular velocity is ^v/_r where v is a linear (tangential) velocity. Substituting all that stuff in, the torque becomes \tau = ^{mLv}/_3. Thus we see that if we choke up, we’re reducing L thus producing less torque and reducing the force of contact!

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28 Responses to “The physics of baseball: batting”

  1. “Hitting a baseball is a lot like hammering a nail.”

    The nail isn’t moving.

    The torque generated on the bat tells you the bat speed, and the act of actually hitting is more appropriately analyzed as a collision. Assuming a constant torque, not choking up (or choking down) is appropriate if you can generate sufficient bat speed and contact the ball while it’s over the plate by doing so. Those are the adjustments that dictate whether one should choke up or not — compensation for a bat that’s too heavy. I’ve never heard it to be a mechanism for adjusting which part of the bat contacts the ball.

  2. quantummoxie Says:

    True the nail isn’t moving, but from the standpoint of the ball the ball isn’t moving either. The only difference in my book is that the ball possesses momentum when you hit it while the nail does not.

    As for choking up, I was taught to do that when I kept hitting on the tapered part of the bat and that’s what I originally taught my T-ball players. The problem is that people have a tendency to reach out over the plate when they swing so, if they choke up, they’re more likely to hit the sweet part of the bat. Choking up to compensate for weight doesn’t make sense to me since, regardless of where you hold it it weighs the same.

    • “regardless of where you hold it it weighs the same.”

      It doesnt change the weight… obviously. But it does make it feel lighter

    • Well it can change the “weight of the bat.” Of course the bat will not physically change in weight, but the distribution will cause a weight shift. As a D1 player we’re taught to choke up when we have two strikes. The reasoning behind that is were trying to stay late and poke it to the outfield (aka Choke and Poke)

      • quantummoxie Says:

        The choke and poke technique actually sounds like it makes some sense because you wouldn’t maximizing your torque which would make it more likely to maybe just drop into that dead zone between the infield and outfield.

        One of the reasons I was always taught to choke up, was when you repeatedly are hitting the ball off the tapering part of the bat. But if you’re doing that you’re either standing too close to the plate or you’re leaning forward when you swing.

        Nevertheless, from a pure physics standpoint, if you want to maximize the force with which you hit the ball, choking up is not the way to do it.

    • I know this I is an old thread, but I feel the need to comment on extremely poor advice you were given to choke up on the bat. I played D2 and D1 baseball and have coached for the last 8 years. The advice to choke up isn’t what bothers me, because there is a viable reason to choke up, but the reasoning you were taught was terrible advice. The responsibility to hit the ball on the sweet spot of the bat is solely up to your hand-eye coordination. Choking up on the bat will not fix where you are making contact on the bat, although I can see how someone would think that. But as someone who played the game for a long time, I can tel you that your mind and reactions don’t work like that, they try to hit the ball on the sweet spot every time and if not then you need more bp and/or to fix your swing mechanics. In all actuality, choking up does help players make better contact only because it gives them more bat control, hence why you’re told to choke up with 2 strikes so you have less of a chance to strike out. But choking up to hit it on a certain part of the bat is just poor advice and it makes me angry someone would give advice to you as a player who wants to succeed.

  3. “Thus we see that if we choke up, we’re reducing L thus producing less torque and reducing the force of contact!”

    Torque is something you exert in order to accelerate the bat, not something the ball feels. All the ball feels is the velocity and direction of the bat. Your torque equation proves that when the batter increases his swing length, his bat velocity will actually decrease for the same amount of exertion. Your advice of ‘adding power’ would have us working harder for the same result. In fact, reducing L will make the bat go faster and hit the ball harder, for the same amount of exertion.

    “Choking up to compensate for weight doesn’t make sense to me since, regardless of where you hold it it weighs the same.”

    It’s not just the weight of the bat that’s important, it’s also the weight distribution and where you hold it. It’s obviously easier to keep the bat parallel to the ground when you hold it in the center because you don’t have to apply a torque to keep it from rotating. Choking up makes it easier to manipulate the bat like a pendulum. This makes it easier to add speed to the bat from multiple rotations, and also makes it easier to control, so you are more likely to hit the ball.

  4. quantummoxie Says:

    Joseph,

    OK, let’s look at it another way. Just before and just after the ball and bat meet we can roughly approximate this as a linear elastic collision. As such, conservation of momentum tells us that m_{ball}\bar{v}_{ball,i}+m_{bat}\bar{v}_{bat,i}=m_{ball}\bar{v}_{ball,f}+m_{bat}\bar{v}_{bat,f}. Now, what is the initial velocity of the bat just prior to the collision? Well, since it represents the tangential velocity at that instant of the rotating bat/arm combination, it can be determined from v=\omega r as stated above where \omega is the angular velocity of the bat/arm combination. Let’s assume that’s a constant regardless of where you hold the bat, i.e. you swing at the same rate (I’ll deal with the weight of the bat in a minute). As such, the only way to increase the velocity is the lengthen r, i.e. choke down on the bat.

    Now, you contend that doing so causes you to have to exert more effort in order to simply hold the bat level since you’re now holding it at the end instead of the middle. While this is true, you’re forgetting that you’re swinging very fast and thus your muscles, which take a moment to react to that heft (since it’s not like you’re holding a lead bar), don’t have as much time to “tire” so-to-speak. Thus, unless the bat is excessively heavy (which, if it is, then don’t use it) this effect should be minimal. Perhaps an adjustment of the swing to bring the end of the bat up a tad would help. But the physics can’t be denied.

    Please note that, while I’m a physicist who plays softball (poorly) and think I have proven this mathematically, you can always just ask David Ortiz who chokes so far down on the bat that he’s only using two fingers on his bottom hand (technically that’s to also introduce a secondary flip of the wrist as well that adds even more power through a secondary torque).

  5. Hi quantummoxie,

    “\omega is the angular velocity of the bat/arm combination. Let’s assume that’s a constant regardless of where you hold the bat, i.e. you swing at the same rate.”

    I think it is more appropriate to assume a constant torque rather than a constant angular velocity. Torque represents the batter’s strength and determines how hard he or she can swing. When you assume that \omega is constant you are implying that the batter is working harder for a longer r. According to your torque equation v = ^{3 \tau} /_{mL}. So L (or r) and v are inversely proportional. Thus, in your model (cylinder rotating around its endpoint) increasing the radial length of the swing decreases its velocity for a given torque.

    “you’re forgetting that you’re swinging very fast and thus your muscles, which take a moment to react to that heft (since it’s not like you’re holding a lead bar), don’t have as much time to “tire””

    You can’t just swing the bat, you have to aim it, too. At a moving target. In your model, power comes from rotations at the waist, shoulders, and elbows. But precise aim also requires the use of the wrists, which are not as strong. Aiming is controlled by a feedback loop between the eyes and hands that allows the batter to make fine adjustments to the trajectory of the bat with his wrists. Choking up reduces the amount of torque required to make these adjustments by shortening the length of the pendulum. This makes aiming easier and also makes it easier to add speed by secondary rotation at the wrists.

    So choking up is a good solution for certain kinds of batters. Specifically, a newer T-ball player who is having a hard time making contact, or someone who wants more precise control over his swing, like a coach hitting flies to his outfielders, or anyone else who stands erect when batting.

    I do agree, however, that a batter should not choke up if he wants power. To explain the reason for this requires a modification of your model so it includes the batter as well as the bat. Instead of a cylinder rotating around one of its endpoints, consider a cylinder being swung around it’s endpoint, counterweighted by a large rotating mass with arms and legs. When the batter swings the bat, he also swings his body. Rather than a cylinder rotating around its endpoint, he is more like two masses connected by a rigid rod, rotating around a common center. In Will C. Fry’s picture, notice the extreme angle of the batter’s weight-bearing left leg to the ground. He is leaning way back in his stance, balancing himself with the weight and momentum of the bat, like a discus or hammer thrower.

    Analyzing the batter as a rotating system of counterweights makes it easier to understand why we shouldn’t choke up for power. By extending his reach, the batter ends up leaning back further during his swing. This takes his body off the rotational axis, and requires us to account for its mass and the force from his legs when analyzing energy and momentum. The further back he leans, the more torque he adds to the swing, the faster the bat moves.

    A note on torques:
    What we want is to increase the speed of the bat. We can do this in two ways:
    1. Decrease the amount of torque required, or
    2. Increase the amount of torque available.

    In your analysis, you counter-productively attempt to increase the torque required to swing the bat. Notice that by leaning back, we shift the rotational pole closer to the head of the bat. Thus we are simultaneously increasing the amount of torque available to move the bat, and decreasing the amount of torque required to move the bat by reducing the swing length.

    P.S. I’m a physicist too. 🙂

  6. quantummoxie Says:

    Joseph,

    I think the difference here is how much either of us thinks the wrists actually do. I think, if you have strong wrists (which, granted, not everyone does) the increased work you have to do is minimal enough that it shouldn’t change your rotational speed all that much. In other words, both of us know the physics and, really, it’s a question of biology.

    Here’s what I observed while coaching this summer: every time I had kids choke up they had a tendency to want to lean further over the plate (T). I think it might have something to do with the fact that choking up just doesn’t feel natural (think about anything you swing – a hammer, a sword, etc. – it doesn’t feel natural to choke up). As such I think people subconsciously overcompensate for that tendency.

    Anyway, what I had them do (and this worked well), was a) don’t choke up b) stand back from the plate (T) and c) don’t hold the bat in the ready position over their shoulders – instead hold the bat almost parallel to the ground with their arms extended but rotated out to their right (or left) – kind of like holding a sword preparing to slash something. It seemed to work pretty well.

    Not sure I understood your final point though. I never said anything about leaning back. My idea is that everything about your swing and stance remains the same except where you hold the bat. Now, as I just mentioned, maybe there’s some inherent “feel” to it that causes a similar reaction when we choke down (i.e. maybe we stand up straighter). In that case you may have a point, but see my observation above about my experience this summer.

  7. I’m Wil C. Fry. I appreciate the fact that you gave me credit for the photo you used — many bloggers don’t feel the need. Thank you for that. (In general, most photographers would appreciate a request for permission, FYI).

    A very interesting article overall, and a good use of my photo, I think.

  8. quantummoxie Says:

    Wil,

    You are absolutely correct. I should have probably asked you for permission first. I am glad you like the use, however. Many thanks!

  9. Hi,

    I really enjoyed reading the discussion about the physics of hitting a baseball. Let me say right off the bat, I am not a physicist. I am a baseball coach. I have played quite a bit of baseball, from little league through the minor leagues, and I am currently a coach for the Los Angeles Dodgers. As a coach I am very interested in the science of my sport, so I periodically look on the internet to see what kind of information I can find. I have read several studies on the physics of baseball, and I have found some very interesting result. Even though I try to use some of the information that I find to help educate athletes that I work with, there is a lot more to it than plugging numbers into formulas. For a hitter to generate the best possible bat speed at the point of contact, or hit the ball hard on a regular basis depends on many factors. So, you might be able to determine how far a ball will travel if it is pitched at a certain velocity and contacts a bat that is moving at a certain velocity, if it leaves the bat at a certain angle. All of this is great to know but it is usually determined in a controlled environment. You control the pitch speed, bat speed, angle at which the ball leaves the bat, and where on the bat the ball makes contact (sweet spot). But as a person trying to hit a ball (which is no easy task) it is more important to know what to do from a mechanics stand point so you can hit a baseball as consistently well as possible.

    Choking up on the bat or staying down on the knob does not determine how consistently you make contact on the sweet spot. Moving up on the plate or back from the plate, or even up or back in the box does not determine how often you get jammed. About David Ortiz staying down on the knob, yes he does. But Barry Bonds chokes up on the bat about 1.5 to 2 inches, and he has proven himself to be a pretty good power hitter. Understanding the mechanics of the swing (and your own physiology) and being able to execute those mechanics as consistently as possible will determine the type of hitter you will be. Proper hitting mechanics will allow you to generate better numbers to put into those formulas. Your mechanics will help you maintain balance throughout your swing, which allows you to generate maximum bat speed. Your mechanics insure that the energy you have generated from your lower half (legs, glute, and hips) will transfer properly to your upper body and out your arms, hands and bat head and into the baseball.

    Let me stop here, because even though there is so much more we could discuss about hitting mechanics, I don’t want to bore anyone. If you would like to continue the dialogue, please contact me. Let me finish by saying a couple things. First, I would not teach young kids to hit the way you described. There are a lot of books and videos that teach the proper mechanics of the swing. I am not saying this to be a jerk. I am saying this because it sounds to me like you have a love for the game and with that in mind I would think you would want to pass on the best possible information to these young athletes. Lastly, let me say I truly enjoy learning about physics, especially how it relates to sport. I understood some of what you had to say, but I must admit a lot of it is way over my head. Maybe you can help me better understand the physics of baseball and I can help you understand the mechanics hitting. Once again I really enjoyed the discussion on this topic.

    Thank you!

  10. quantummoxie Says:

    Rob,

    Thanks for the post!

    Let me just say that my grandfather on my father’s side was a HUGE Dodgers fan – until they left Brooklyn. 😉 My mom was a big Dodgers fan too until then. Sadly, Grandpa became a Cubs fan and since he died in 1974, he’ll never see them win a championship. Personally, I’m a Red Sox fan as are my parents, though I just love the game so any team is cool with me (except maybe the Evil Empire).

    I appreciate the input and I will definitely e-mail you as I have some more questions about coaching these young kids.

    Your reply brings up an important point. We can put all the physics into it that we want but there are equal parts physiology and psychology as well.

    I didn’t know Barry Bonds actually chokes up on his bats. On the other hand, if he has stronger arms than most players, this would still make sense from a physics standpoint.

    What really got me with the kids was that they swing down with the bat. As for myself I’ve been thinking all winter about this and I think one problem is that I’ve been swinging too late. I need to swing earlier, I think.

  11. Hi, Rob again.

    Thanks for getting back to me. I’ve never really had conversations over the internet. I am usually considered an over explainer (by my wife and son), so it is difficult for me to describe hitting in writing. With respect to Barry Bonds, he was incredibly strong, but when you think about hitting and hitting for power or just hitting the ball hard think about your power coming from your lower half. That is where all your power originates. Think of it like a bull whip. When you crack a whip, you throw the handle and that energy moves down the whip to tip. The tip of the whip then makes a cracking sound. That crack is the tip of the whip breaking the sound barrier and creating a mini sonic boom. Well, we both know that the handle of the whip was not moving at that speed. That means that the bigger handle generated a certain amount of energy that was used to move the tip of the whip at a much greater speed. I would imagine that you could understand the science of that much better than I, so if you have some insight, please pass that on. Now, if you think of your lower half (legs, gluts, hips) as the handle of the whip from which the energy is generated, you can visualize how that energy would move up your body to and through your core (which is why having a strong core is important) through your shoulders, down your arms and hands and out the head of the bat. The last part of the swing must remain loose and relaxed in order to create the same whip type effect as the bull whip. As you can imagine there is a sequence to the firing of each of these parts and if that energy moves through the body in the correct sequence, you will achieve maximum effect. Think of it like this, if the tip of a bull whip tried to do its part before the middle of the whip had a chance to relay that energy the tip would not get the same results.

    The next time you hit, think of the bat head as the tip of a whip. As you execute your swing, that should be the very last thing to move to the point of contact. Sometimes hitters will let the bat head start moving to the contact point before their hands have done all their work. Keeping the bat head back is what we call bat lag. If the bat head moves to the ball too early in the swing, this is one way that you slow your swing speed, which is not conducive to hitting balls hard. We want to generate the best possible bat speed with as much control over our bodies as possible(balance).

    I really admire the fact that you take your time to teach young kids baseball. I have an 8 year old son who plays little league, and I am grateful to all the volunteer coaches in his league, because without them these kids, including mine, would not have baseball leagues to play in. As I said before I could talk all day, everyday about baseball, so if you have something specific about hitting that I can share with you or if there are just some general questions I would love to try to answer them.

    I am sorry to hear that your family was upset about the Dodgers leaving Brooklyn (not that I had anything to do with it), but I do hear that a lot. I think we will be losing some more fans this year because of our move from Vero Beach to Glendale, Arizona for spring training. Being a Boston fan yourself, I am sure you have a strong opinion about Manny Ramirez. Whatever your opinion, he is a great person to study from a hitters stand point. I personally considered it a privilege to be able to watch him work for the last two and a half months last season. Like Barry he has some baggage, but they are both the very best at what they do.

    Thanks again

  12. quantummoxie Says:

    Rob,

    Sorry for not replying sooner. I’ve been crazy busy. But I actually like what you’re saying here. So the difference is really in how fast you can whip your hips/waist around. This is actually directly related to what I noted above from the physics standpoint. What you’re doing is increasing your angular velocity and thus increasing the momentum transferred to the ball.

    As for Manny, I actually liked the guy and miss him. I know he pissed off management for whatever reason, but the guy plays the game because it’s fun. He seems to have a better perspective on it than a lot of other people. It’s a game. Yes, it’s a business, but it’s also a game. He’s goofy and funny and I miss him here in Beantown!

    And for the Dodgers, I certainly have never known them as anything but the LA Dodgers so I’m not too upset one way or the other. I certainly rooted for them in ’88 and will never forget Kirk Gibson’s HR in Game 1!

  13. Assuming the batter has the correct mechanics and positions himself in the box properly. Does not “choking up” change the center of gravity of the bat thereby allowing the batter to swing the bat faster?

  14. quantummoxie Says:

    Choking up does not change the center of gravity/mass for the bat. That is a fixed property based on the dimensions and structure of the bat itself. It changes where, in relation to the CG/CM, the batter is holding it thus relieving some of the energy the wrist muscles must expel in order to hold the bat level, thereby theoretically allowing the batter to swing faster. But my argument is that the amount of energy saved in doing this is minimal and more than made up for when choking down in the extra power on gets from the added torque. I’ll add some numbers later this weekend to show you what I mean (I have to run to my daughter’s dance recital).

  15. I enjoyed this Read…Not a scientist, just played the game a few times…but have we all missed something?
    You speak of “BAT SPEED” being so significant. Can we also use a Heavier Bat to increase distance even if you will Lose a few mph from a lighter Bat. 28oz-32oz- 34oz-36oz. You spoke of choking up & how it has a mechanical effect to shortent the bat but to increase place hititng…but never offered an exact or approx speed @ which the Bat must travel to make a ball move 300 – 400 feet. Maybe a new instrument can be invented which could calculate weight of bat & speed of bat (swing) which can be convert to determine distance of ball to travel, (radar gun + bat weight+ball size) for all to use, instead of everyone needing to fetch balls, then hit so many of them to get blisters. Only to practice swinging for speed & the mechanics. We can all worry about eye & ball timing later.

    Could we set aside the mechanics of each indivduals swing. & disregard each individuals physical strength & weight/ height characteristics.
    I have seen little thin whimpy guys Crush a ball. The objective here is to move a ball 300-400 feet. I am not looking to move it 401 feet or 1000 feet.

    Can we all agree that The moment of impact is a micro second, & would be better to have the most possible weight into this equation. Bat Weight?

    You also never explained the dynamics of the sphere (ball) upon meeting the (cylinder) bat. The Tiny area which makes contact with the ball & The Bat upon impact. If you look at the point of impact with the 2 moving objects (bat & ball) in opposite directions, the impact point is so little, so perhaps the wieght of bat & speed are the most signicant part to moving this ball 300-400 feet. Can Luck also Lie in where the Bat meets the Ball… On its strings or the smooth cover for that micro instant of impact?

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    • quantummoxie Says:

      Hi there! Are you trying to measure the torque in a problem related to this one, meaning for the purposes of baseball? If so, do you have access to a camera and some video editing software?

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  20. D1 ballplayer Says:

    Hi,

    I just want to start by saying that this discussion has been a very interesting read for me. I am currently an NCAA baseball player with a pre-med biology major, and I wanted to clarify an issue.

    The above mentioned mentioned reasonings behind “choking up” are wrong.

    1. You do not choke up to avoid hitting the ball off the tapered part; that in no way makes sense.
    2. While there are a few players who choke up to alter weight distribution, this is not the the typical reasoning behind the strategy either.

    You see, baseball is not golf – hitting is a skill based on timing and reaction. What most have failed to grasp is the importance of angular velocity.

    Let’s take technique and fundamentals completely out of the equation – your physics is spot on: increasing the length of the lever arm will inarguably increase power. The trade-off, however, is a resulting decrease in angular velocity. If torque is held constant, altering a lever’s moment of inertia will inversely alter the angular velocity.

    A reduction in angular velocity means a longer time for the swing to reach its point of contact – meaning the hitter has less time to react to the ball moving towards him. By choking up, you decrease the lever arm = increase angular velocity = more time to react to the pitch.

    A 95 mph pitch reaches homeplate in .434 seconds. Not a lot of time for the hitter to react to the pitch. But by increasing his swing’s angular velocity a hitter can maximize the time he has to read the pitch before he swings. Again, this is why some hitters choose to choke up with two strikes – to avoid striking out, hitters will trade off some power in exchange for higher contact percentage.
    less MOI = more angular velocity = longer time to react = greater chance of hitting the ball

    Hope this helps, and let me know if I’m incorrect in any area.

    • quantummoxie Says:

      Thanks for the reply! By “angular velocity” do you really mean the velocity (in non-radial terms) that the end of the bat is moving at when it meets the ball or do you mean the radial velocity (the rate at which the angle is changing)? Choking up *might* increase the radial velocity, *but* only because, if held properly, it would reduce the surface area and thus the force of drag allowing you to swing faster. Recall that v=\omega r . If you increase \omega by simultaneously reducing r, there’s no guarantee that v will change. And v is what determines how far the ball goes, not \omega .

  21. […] a batter you want to get the biggest bang for your buck. You don’t necessarily need to know any special equations to improve your batting average, but knowing how the force of your swings connects with the force […]

  22. What you guys are forgetting, or maybe simply don’t know is the most important step that will improve your swing is…….. keeping your should turned in. Remember. … get out in front of the ball.

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