The Physics of the Force on Spinning Baseballs

Dellin Betances had some of the highest spin rates of in baseball in 2016. (via Arturo Pardavila III)

Dellin Betances had some of the highest spin rates of in baseball in 2016. (via Arturo Pardavila III)

The origin of the phrase “spin doctor” is somewhat dubious. Most agree it was first in print as part of a New York Times editorial in 1984 describing the postmortems of the debate between Ronald Reagan and Walter Mondale.

Some argue spin doctor is derived from the expression “to spin a yarn.” I prefer to believe it is like “out in left field” or “that was so bush league.” I claim spin doctor is just another example of baseball infusing itself into our culture. After all, what is a better description of a pitcher than spin doctor?

The spin on the baseball is not confined to pitching. A ball hit to center field that would travel 350 feet with no spin will vary in distance depending upon the magnitude and direction of its spin. A graph of distance versus spin is shown below. The spin can change “a can of corn” to a pretty serious blast.

kagan-1

While I have written many times before on the effect of spin on the flight of a baseball (e.g. “The Physics of a Foul Down the Line,” “The Physics of the Pop-Up,” “Why is a sinker ‘heavy?'”), I always have referred to the spin-related force on a baseball as the “lift” or the “Magnus force.” Instead of just giving this force a name, the point here is to focus on the origin of the spin-related force.

Since it is the darkest part of the year – literally because it is close to the winter solstice and figuratively due to the absence of baseball – let’s think about the wintry frustration of getting your car stuck in the mud.

kagan-2

If the tire is spinning very slowly, it simply develops a coat of mud that spins along with it. At a more moderate speed, the mud works it way up along the tire a bit before is flies off instead of continuing to stick to the tire. At very high speeds, the mud flies off the tire before it goes up along the surface much at all. In summary, the faster the tire spins, the sooner the mud leaves the tire.

Here’s the key idea. The air moving around the surface of a baseball acts an awful lot like the mud on the tire. If you’re paying attention you should be screaming, “That’s ridiculous! Mud is thick and gooey while air isn’t.”

Actually, air gets pretty thick and gooey, especially as it moves over surfaces at high speed. Just think about the fact that air can support the weight of a huge, heavy airplane when the plane is moving fast enough. Don’t try this at home, but I have held my hand outside the window of my car. The faster I go, the thicker and gooier the air feels.

In the sketch below, a baseball is moving through air at, say, 90 mph to the right. In the left-most image, the ball is not spinning, so the air moves symmetrically over top and bottom the surfaces of the ball so there is no spin-related force. However, in the image in the center, the ball has topspin of, say, 1000 rpm, and in the image at the right, 2000 rpm.

kagan-3

The air at the surface of the ball acts much like the mud on the tire. That is, the faster the surface of the ball moves with respect to the air, the sooner the air is thrown off the ball. The only complication is the ball is moving through the air as well as spinning.

In the right two images, the surface of the top of the ball is moving faster than 90 mph because the top of the ball is spinning in the forward direction. On the bottom of the ball, the opposite is true. The surface of the ball is moving less than 90 mph because the bottom surface of the ball is spinning in the backward direction.

You might be more comfortable if I give you some numbers. The top surface of the ball in the rightmost image is moving at about 107 mph while the bottom surface is only moving at about 73 mph.

This results in the air leaving the top surface of the ball earlier than the bottom surface, causing the air to deflect upward. The faster the ball spins, the further upward the air is deflected, as seen in the far right image. So a ball with topspin exerts an upward force on the air stream as it passes through.

Now we need to discuss this matter with our friend, Sir Isaac Newton, who explained to us that objects (including baseballs) do what they do because of the forces that act upon them. So far, we have only thought about the force acting on the air, but we want to know about the force on the ball.

Baseball, You Make It Hard to Love You
Again, a scandal puts fans on the defensive about their game.

Sir Isaac reminds us to think about his Law of Action and Reaction: “When one object exerts a force on a second object, the second object exerts and equal and opposite force back on the first object.” Aha! If the ball exerts an upward force on the air, then the air exerts a downward force on the ball.

You know from experience that a ball with topspin will tend to drop faster than gravity requires. Now you see the downward force is caused by the air deflected upward from the ball’s surface due to the spin. This force is usually referred to as the lift or Magnus force, which is just a name, but now you see in a deeper sense the origin of this spin-dependent force.

Some of you sharp characters out there must have noticed that I ignored the seams on the ball. They do make a difference, but perhaps not as much as you might think. By understanding that the spin-dependent force is caused by the separation of the surface layer of air on the ball, we have a context to examine the effect of the seams.

The seams moving past the air will encourage the separation of the air from the surface of the ball. The seams on the top of the ball will strike the air with a higher speed than the seams on the bottom of the ball. So, they will be even more effective, causing the air to separate sooner and enhancing the break in most cases.

For a very slowly spinning ball, the primary cause of the air separating from the surface is just the seams. This is a knuckleball, but that’s a topic for another time.

References & Resources

  • Thanks to Evan Jones for the discussions that led to this article.


David Kagan is a physics professor at CSU Chico, and the self-proclaimed "Einstein of the National Pastime." Visit his website, Major League Physics, and follow him on Twitter @DrBaseballPhD.
newest oldest most voted
jim
Guest
jim

Excellent work. Even an intellectually-challenged person such as myself can understand this.

Eli Ben-Porat
Member
Member

Loved it. Enjoyed the explanation of how top of the ball is moving faster than the bottom of the ball. Would love an article about how the batter’s swing can affect spin (not sure if you’ve covered this in a prior piece). A “line drive” swing should probably be top-spin heavy, while a “home run” swing should be back-spin heavy.

Alan Nathan
Guest

Very nice article, Dave.

Martin
Guest
Martin

At the school where I work, a fourth grader has asked me different questions about the physics of a baseball’s spin just about every day for the past two weeks. This was very helpful, I will be sure to relay the information!

joe lavelle
Guest
joe lavelle

The spin of a golf ball works the same way. This is a solid application of basic physics. It would be interesting to compare the dimples on a golf ball, which serve to keep the laminar air flow close to the ball, to the threads on a baseball, which probably do the opposite.

At any rate, nice article, solid physics.

channelclemente
Guest
channelclemente

So how is it in Minute Maid Stadium in Houston, the seam height of the ball seemed to be the difference in carry between MiLB and MLB baseballs?

MGL
Guest
MGL

In the first graph you have distance versus spin rate and direction. At what launch angle and velocity? Doesn’t it depend a lot? Doesn’t that curve start to bend downwards? I.e, with too much backspin the ball travels less far (it “baloons” up). IOW for every EV and launch angle, isn’t there is an optimal backspin rate for maximum distance? You seem to imply (and in fact, say, in the FG article by Eno) that the more backspin the further the ball will go. That can’t be true, right?

Terjemahan
Guest
Terjemahan

Excellent work

ighack.net
Guest

This is the reason to be the instagram hacker online.

Fake Yeezy Boost
Guest

adidas Consortium aims to bring luxurious vibes to the hardwood with the coming “Day One” Collection featuring the adidas Crazy Explosive Low and the adidas Crazy Team