September 30, 2015

The Physics of Baseball

MLB Playoff Season 2015

Ever wonder why some hits feel good when the bat connects with the pitch, and others leave your hands ringing? Or exactly how a pitcher throws a ball that seems to curve just as the batter swings? Physicist Dr. Kasey Wagoner says, like most things in our universe, it all comes back to physics. Just in time for MLB playoff season, he talks about the forces involved in different pitches and how the "sweet spot" of the bat works.

For those of you who enjoyed the podcast, but are looking for more, we've got videos, websites, and equations for you!



Announcer: Ladies and gentlemen, it is the seventh inning stretch time! We invite you to join in sing “Take Me Out to the Ballgame!”

Rebecca King: Hello, and thanks for listening to Hold That Thought. I’m Rebecca King, and here in St. Louis, we’re getting really excited for baseball playoff season to cheer on our local St. Louis Cardinals. My guest today, physicist Dr. Kasey Wagoner, is also a big baseball fan, and he has spent some time exploring the physics behind the game, like, how pitchers manage to throw sliders or curveballs. Or why sometimes a pitch leaves your hands ringing after hitting it with the bat. Dr. Wagoner says, like most things in our universe, it all comes back to physics.

Kasey Wagoner: When it comes to physics in baseball, there are a lot of different things, but the thing people started out to be the most interested with is the idea of a curveball. A curveball curves more than a standard pitch. Every thrown ball will curve, because there is a gravitational force acting on the ball, pulling it down towards the earth’s surface. When we refer to a curveball, we mean a ball that curves due to another force in addition to gravity. That additional force is called the Magnus Force.

RK: And the Magnus Force affects any ball. Think of soccer and David Beckham’s ability to bend the ball—or kick it so it curves around defenders. Any spinning object moving through gas or liquid is affected by this Magnus Force.

KW: The direction of this Magnus Force is such that it will push the baseball whatever direction the leading edge of the baseball is going. It is kind of hard to describe without a picture.

RK: Alright, I can hear some of you all out there scratching your head. Don’t worry. For those of you who are more visual learners, there are pictures and animations from Dr. Wagoner on our website. But I’ll do my best to break it down a little further. So on any thrown ball, we’ve got gravity pulling it down; the drag force, which is basically air resistance, slowing the ball as it moves forward; and the Magnus Force, which curves the ball away from its principal flight path depending on its spin. So what does this look like? Well as Dr. Wagoner said, it depends on the leading edge—or the spin the pitcher gives the ball. So, if the ball was given topspin, which means the ball is spinning forward as it moves forward, it will drop faster than gravity alone, because the Magnus Force is also pulling it down. If the ball is given backspin, meaning the ball will spin backwards as it moves forward, the ball will actually fall more slowly as the Magnus Force is lifting it up. Finally, some pitchers add sidespin, which can cause the ball to move from side-to-side, and this kind of pitch is known as a slider. Which hand a pitcher throws with can also affect the curve of his throw.

KW: Generally, a curveball thrown by a right-handed pitcher will break from right to left from the pitcher’s point of view and the opposite for a left-handed pitcher (from left to right) based of the spin they’re putting on it. What pitchers do is they try to manipulate this Magnus Force. Now, I really doubt that any pitcher is standing out there thinking about the Magnus Force and how they are going to manipulate it; what they’re doing is just trying to throw a curveball and get the batter out in a way that has been effective for them before.

RK: But even if they aren’t thinking about the Magnus Effect in these terms, as Dr. Wagoner said, they do have control over several factors that effect where the pitch will land, how much it will curve, and how fast it will get there.

KW: One big control that a pitcher has is being able to affect the angle of the curve; this is just by the way in which they hold the ball. The second thing the pitcher does is he will affect how fast the ball is spinning. The amount the pitched baseball will curve depends dramatically on how fast the object—the baseball—is spinning. If it is spinning faster, then t will curve more. If it is spinning slower, it will curve a little less. What is a little bit funny and not necessarily intuitive is the general thought as a pitcher is I want to make it spin as much as I possible can, because I’m going to get the greatest amount of curve. It turns out that is not always the best way to deceive the batter. The idea of a late-breaking curveball, which is really hard for a batter to hit, is really those balls tend to have less spin on them. The actually curve a little bit less; it’s just the time at which they curve makes it harder for the batter to pick up. Anyway, the pitcher really affects the amount of spin he puts on the ball, and then in turn, that means how much the ball will actually deviate from a straight line. This is done by how much he flips his wrists—how violently he snaps his wrists.

RK: Of course, as any baseball fan can tell you, there are dozens of different pitches that professional pitchers choose from to fool batters, and most of these, according to Dr. Wagoner, are simply variants of the curveball. So, what about the fastball? Does that just mean the pitcher throws it really fast?

KW: Another thing that there is some misconception about from time-to-time is what happens on a fastball. Anybody that has played baseball knows that when you have a fastball that is pitched, it comes in and it is also spinning. Now, the pitcher is not necessarily trying to put spin on it, but just the act of throwing it imparts some spin to it. In general, this spin is put on the ball in such a way that it makes the ball rise. It’s not uncommon to hear of a rising fastball. There is an upward force on the ball that makes it appear it is rising, and it is again due to the Magnus Force. Now, any pitched baseball will not actually rise, because as a ball is pitched, and as it is travelling from the pitcher to the batter, there are two competing forces on the ball. There’s this upward force from the Magnus force pushing the ball up, but there is also the downward gravitational force that’s always there and you can’t escape. It turns out the gravitational force wins, but the ball doesn’t drop as much as it would without spin. That is why hitters perceive it to be a rising fastball. It’s higher than where they expect it. Same effect, same physics, just applied in a different way.

RK: Remember, the Magnus Force only affects spinning objects through a gas or liquid, so what if a pitcher was to throw a ball that didn’t have any spin? That brings us to the knuckleball.

KW: The knuckleball is a very interesting effect that is entirely different from the other pitched balls. Up until now, when we talked about a rising fastball or a curveball, the import forces on the ball were the gravity that’s just making the ball fall down and then the Magnus Force that is dictating the direction of the curve. Well, the Magnus Force comes about when you are talking about a spinning ball moving through the air. But the idea of a knuckleball is that you are throwing it without any spin, so the Magnus Force isn’t so important anymore.

RK: The knuckleball is notoriously unpredictable as far as what direction it will go, and Dr. Wagoner says you can actually see in videos even catchers have no idea where the pitch will end up. You can see them closing their eyes as the ball comes closer. So, some scientists got interested in this problem and did a few experiments to understand what forces are at work on the knuckleball if the Magnus Effect isn’t as strong.

KW: The results say that if a ball is traveling and not rotating very fast, like a knuckleball, then the direction of the force on the ball is very very different different for different seam orientation. The seams definitely play a role in any pitched baseball, but the role that they play in a pitched knuckleball, that role is kind of elevated over the role that they play in a curveball. This ball is travelling through the air, rotating just ever so slightly, and the force of the ball will be in any different direction. What it really comes down to is it is very unpredictable as a batter. It’s not near as predictable as the Magnus Forces. As a batter, as soon as you see the ball spinning in a particular direction, you know which way it is going to break. With a knuckleball, it is an entirely different thing.

RK: But pitchers aren’t the only ones relying on physics. Batters, too, feel the effects of physics at the plate, literally.

KW: Anybody who has swung a baseball bat and hit a baseball can tell you that when a ball hits the bat, it’s not the same every time. Sometimes it feels really good if you hit the sweet spot, but a lot of times, it will leave your hands ringing. From the batter’s point of view, what they’re really trying to do is just hit that ball on that sweet spot. It tends to be about six inches away from the barrel end of the bat.

RB: So what is happening to the bat to create these sensations?

KW: When a baseball hits a baseball bat, it creates a wave on the bat. If you had a super slow mo camera and you could zoom in and watch the baseball hit the bat, the bat will wiggle just like a string inside a piano. The bat will oscillate back and forth, up and down. There is a wave that goes up and down it. Well, it turns out there isn’t just one wave; there are multiple waves that go up and down the bat, but if you hit the sweet spot, it turns out to be what we say a “node” of one of these waves. When the ball hits the bat at that particular sweet spot, one of the waves does not go up and down the bat. You can imagine holding a baseball bat, and if a wave is travelling up and down it, the bat itself is going to wiggle back and forth in your hands. That is the vibration that you feel. But if the ball hits the bat right at the sweet spot, then one of those waves doesn’t actually travel up and down the bat; the bat is much more stationary in your hands, and it feels much more smooth. It feels sweet.

RK: It sounds unbelievable, but it’s true. The wooden bat does vibrate, or oscillate, after a hit. For those of you who want to see it for yourself, we’ve got some videos of this effect on our website: But getting back to that sweet spot, sure hitting the ball there feels better, but does it also translate to a better hit? Well, absolutely! Think back to your days in physics 101 to the lessons on energy and kinetic energy.

KW: In terms of physics, there is a little bit more to it in that because you have not created a wave that’s not travelling through this bat, the ball has actually given less energy to the bat. If there is less energy given to the bat, that means there is more energy that is going to ultimately stay with the ball and fly off and be a good hit. It is advantageous to hit the ball in the sweet spot because A) it feels better and then B) it’s actually going to produce a ball that is hit a little bit harder.

RK: These are just a few of the ways physics works in the field and specifically on the baseball field. As you tune in to cheer on your favorite baseball team in the playoffs next week, remember the Magnus Force as a pitcher seems to throw a ball that curves just as the batter swings or the transference of energy when the batter finds the sweet spot and sends the ball sailing toward the stands for a homerun. Many thanks to physicist Dr. Kasey Wagoner for taking the time to meet with me. I’m Rebecca King, thanking you, too, for tuning in to Hold That Thought. If you are interested in seeing visualizations of some of the pitches and forces we talked about today or to hear more of our episodes, visit our website at