The Physics of Beach Balls and Fastballs

Beach balls are plentiful at Dodger Stadium. (via Teri Lynne Underwood)

Beach balls are plentiful at Dodger Stadium. (via Teri Lynne Underwood)

It is another beautiful day in SoCal, sunny, 78˚, with a gentle breeze. By some quirk of fate, the Boys in Blue actually spotted Kershaw to an early 4-0 lead. The ensuing giddiness would lead to the wave in most ballparks, but not at Dodger Stadium. Instead, the much maligned beach balls make their appearance.

The Dodgers Stadium security guidelines list the usual banned items; alcoholic beverages, fireworks, lasers, weapons, etc. In addition, they may be the only club that specifically bans “beach balls and inflatables.” The nearly constant presence of beach balls makes me worry about the team’s ability to control the aforementioned contraband.

Even Vin Scully struggles to maintain his constantly pleasant demeanor when a wayward inflatable wanders on to the field, as this quote from 2009 demonstrates:

Time called. The dreaded beach ball has shown up on the track in right field.
So Jeff Mathis will use the time and go out to talk to Jered Weaver…[Vin spends the coaching visit describing a connection between Weaver and Whitey Ford].

All right, Jered bends at the knees and — wait, that’s a joke. There’s two, three beach balls. I’ve always been amazed — I remember we were so thrilled just to go to a ballgame — but how people can make plans. Let’s go to the ballgame. Yeah, do you have your beach ball? Well, they do. All right, now we’re ready, two balls and no strikes the count…

Vin is right. It does make you wonder if the fans were actually headed out to the shore in Malibu when they decided the traffic was too awful and instead headed to Chavez Ravine.

Back in 2010 a beachball interrupted Hiroki Kuroda’s bid for a no-hitter. This is Vinny as angry as he ever gets:

“And time, there’s a beach ball out there. You talk about bad timing…And the crowd’s annoyed. Talk about a dull feeling for the dramatic. You throw a beach ball out on the field now, in the eighth inning? Wow.”

Many blamed the spherical bad omen as the following batter, Shane Victorino, drove a single to right.

Despite the negativity described above, it must be said that the motion of a beach ball is rather alluring. Since I tend to be something of a know-it-all, I have a theory as to why this movement is so entrancing. I think it is because its behavior is so foreign to our everyday experience.

If you toss a baseball upward then catch it when it falls back to your hand, it tends to slow down as it rises and speed up as it falls. This is the common type of motion we expect from most objects. It is explained by gravity. As the baseball rises, gravity pulls it downward, slowing it down as it heads upward. As the ball reverses course and begins to fall, gravity still pulls it downward and it speeds up.

A beachball appears to violate this normal motion. It seems like it is always moving at about the same placid pace. Even when a fan punches the ball, within less than a second it is back to its calm, gentle movements.

Physics explains the difference between the motion of a beach ball and a baseball in terms of the “drag force,” sometimes referred to as “air resistance.” The drag force occurs because a moving object must get the air in front of it out of the way.

The size of the drag force depends upon many factors, but the two that are relevant here are the cross-sectional area of the ball and the speed it is moving. The larger the object is, the more air it has to move out of its path. The faster it moves, the more quickly it must move said air.

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For decades, Roger Angell's writing has warmed us to the romance of the new season.

You can see the effect of the cross-sectional area by taking two identical pieces of paper. Crumple one up into a ball and leave the other flat. Holding the flat piece horizontally in one hand and the crumpled piece in the other, drop the two at the same time. The wad of paper clearly will fall faster, indicating more drag on the flat paper.

If you have your hand outside the window or a moving car, you can feel the speed effect. In a school zone you are hopefully moving slowly, and the force the air exerts on your hand is relatively small. As you travel down a highway, the force on your hand becomes quite large.

According to the Statcast Leaderboard, the fastest pitch in 2015 was a four-seam fastball thrown by Aroldis Chapman on June 29 to Brian Dozier. Here is a video of the pitch in question:

The PITCHf/x data agree to within half a percent with the Statcast start speed:

  • Start speed: 103.4 mph
  • End speed: 95.2 mph

The air slows the ball down by 8.2 mph in the 0.4s it takes to get to the plate. These values allow an estimate of the size of the drag. It turns out to be just a little larger than the weight of the ball.

Comparing a fastball to a beach ball is a bit of a challenge, but the main point is that a beach ball also has a drag force on it that is about equal to its weight. The difference is a fastball has a lot of drag because it is moving rapidly even though it has a small cross-sectional area. A beach ball has a lot of drag because it has a large cross-section even though it is moving slowly.

Back to the usual behavior of a baseball you toss upward and then catch back in your hand. The ball is moving so slowly compared to the Chapman fastball that the drag force is very small. So the ball’s motion is exactly what you would expect it to be.

For the beach ball, it has a large drag force even at the low speeds at which it generally moves. You can try to speed the ball up by letting it fall downward or by punching it, but the drag force will slow it right back down. It is this drag force that creates the serene and entrancing motion that is so alien to us.

So next time the game is interrupted by a beach ball, take a moment or two to enjoy its intriguing movement. Then feel free to scream at the morons for coming to the ballpark instead of going to the beach. As we said in the sixties, “What a drag!”


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.
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Roland Reich
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Roland Reich

Many thanks for the article.

I always wondered why a beachball when being kicked at slow speed with the left foot so that it spins clockwise often breaks to the left instead to the right. Baseballs or soccer balls never do. Any explanation for that?

Jetsy Extrano
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Jetsy Extrano

Roland, can you get a video of it? I don’t know how to get my beach ball to do that!

Roland Reich
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Roland Reich

Jetsy, give me a week or two until I get back home and I´ll try….

Roland

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