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Why Does a Curveball Curve?

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Adam Wainwright delivers. St. Louis, MO, 2008. (bk1bennett/Flickr)
The St. Louis Cardinals’ Adam Wainwright delivers. St. Louis, MO 2008. (bk1bennett/Flickr)

With the World Series in full swing, most Americans would probably say they know the basic rules of baseball: the pitcher throws it, the batter hits it, three strikes and you’re out.

But underneath it all, the rules that truly govern this game are the laws of physics.

“When you go to a ballgame you’re seeing all the interplay of force and velocity and projectile motion,” said Paul Robinson, a physics teacher at San Mateo High School and a passionate baseball fan. “It’s a beautiful thing to see and watch.”

Robinson, who was interviewed several years ago by KQED for a TV story on the physics of baseball, uses the sport to teach his students how the universe works. To illustrate a sample lesson, he draws a baseball on a white board. Then he draws one arrow pointing forward from the ball, as if it’s going straight from the pitcher to the hitter, and one arrow angling up, to show the angular displacement of a curve ball.

“Physics is a beautiful way to see the world we live in,” Robinson said. “Being a student of physics just makes the game that much more interesting and fascinating.”


In the lab

The great pitchers put power into their arms by building momentum from a twist of the hips and that huge step with the front leg. “The phrase we like to use,” said Dan Hubbs, former pitching coach for the Cal Bears, “is ‘let your arm just go for the ride.’”

But sending your arm on that ride is a surprisingly complex task. It takes a biomechanical analysis to see just how intricate the throwing motion is. Big league pitchers get this done in a lab, using a 3-D, high-speed, infrared, eight-camera motion analysis system that tracks every aspect of the throw.

The players wear skin tight clothing with reflective markers that the computer can pick up. These markers allow the computer to calculate the exact body angles, joint velocities, and timing. It can also analyze the physical kinetics (or joint forces and torques) placed on the body.

Seeing the relationship between timing and velocity, between angles and spin, can help big leaguers make subtle changes in biomechanics to enhance their performance and reduce injuries.

San Francisco Giants starting pitcher Tim Lincecum delivers against the Colorado Rockies at Coors Field on April 11, 2012 in Denver, Colorado. (Doug Pensinger/Getty Images)
San Francisco Giants starting pitcher Tim Lincecum, against the Colorado Rockies at Coors Field on April 11, 2012 in Denver, Colorado. (Doug Pensinger/Getty Images)

“Baseball pitchers are great experimental physicists,” Robinson said, “because they’re constantly trying this, trying that, to see what works.”

What works, that is, to get the ball to do exactly what the pitcher wants it to do—like get there fast. A 95-mile an hour fastball will get to the batter in four-tenths of a second.

Newton’s second law of motion tells us that the acceleration of an object is dependent upon two things – its mass and how much net force is acting on it.  Translated: the harder you throw, the faster it goes. But pitching takes more than throwing hard. There are also external forces in play. Each pitch is fighting gravity and friction.

“When a pitcher throws a ball,” Robinson said, “it has to push the air out of the way. When it leaves the pitcher’s hand it’s going as fast as it’s going to go. From that point on, friction slows it down.”

While external forces may cut down on momentum and velocity, a good pitcher will be able to use this to his advantage.  Friction and gravity can make the ball do nasty things. A splitter, for example, looks like a fastball until it loses velocity; then it suddenly drops down toward the batter’s knees.

And in case you’re wondering, that curve ball is not an optical illusion—it really does curve. How much it curves depends on how fast you spin the ball. A curve ball that spins 30 times a second can break as much as 17 inches.

The reason the ball curves is a force called “lift.” Lift is the reason airplanes can fly, and it’s the force that allows sailboats to go faster than the wind.

“When a ball spins it generates greater pressure on one side as it moves through the air than on the other side,” Robinson said. “The difference in pressure is a form of lift. It’s called the Magnus effect.”

Can’t quite see it? Try this: Imagine a baseball spinning clockwise on your computer screen, in slow-motion. Now imagine smoke streaming from left to right past the ball as it spins. The smoke streams easily over the top of the ball; it’s almost pushed along by the clockwise motion. But the smoke underneath is going past the ball in the opposite direction of the spin. So that smoke makes a bigger curve to get around the ball. The ball is going to break the other direction, toward the easier flow of air. (If your imagination needs some assistance, just go to 5:43 on our video.)

But how does the batter know in which direction the ball is going to break?

The answer, said physicist Linda Shore of the San Francisco Exploratium, is simple. Just figure out which direction the front of the ball is spinning.

Oh. That’s all it takes?

Step up to the plate

Once the ball leaves the pitchers hand, the batter has barely the blink of an eye before it crosses the plate.

“You’ve got to decide swing, don’t swing, what kind of ball,” said Robinson. “Curveball, fastball, slider—you’ve got to make all those decisions in .2 seconds. It’s almost a reaction instead of a thought process. Some say it’s the hardest thing to do in sports. A round bat, hitting a round ball, that’s not easy.”

The batter wants both power and accuracy. And bat speed is the key to power, said Jon Zuber, a former major leaguer with the Philadelphia Phillies and member of the University of California Hall of Fame.

As part of KQED’s visit to Cal’s Evans Diamond to film the physics of baseball TV story, Zuber demonstrated that distance a batter’s hands have to move to get from ready, to the point where the bat makes contact with the ball. “I need my hands to get from there to there, short and quick, as fast as possible,” he said.

He slapped his thigh and hip to demonstrate that the batter does the same thing the pitcher does: he uses a twist in the heavy parts of the body to build momentum. “I need this weight and that muscle and torque and force,” Zuber said, “and now I have a whole lot of stuff hitting the ball at the same time, which is going to propel it out towards the field.”

When the bat and the ball collide, the ball squishes up close to half its size. “And it compresses like a spring,” Robinson said, “and then in a thousandth of a second it springs off the bat, leaving faster than it came in, maybe 110, as much as 120 miles per hour.”

San Mateo High School physics teacher Paul Robinson says heavier bats hit the ball with more force, but baseball has moved toward lighter bats, that can swing more quickly. (Chris Bauer/Quest)
San Mateo High School physics teacher Paul Robinson said heavier bats hit the ball with more force, but baseball has moved toward lighter bats that can swing more quickly. (Chris Bauer/Quest)

To get the most out of the hit, the batter can’t rely only on power; he needs accuracy. He needs to slam the ball with a particular part of the bat, known as the sweet spot. The reason? Physics, of course.

Newton’s 3rd law of motion states “for every action, there is an equal and opposite reaction.”

The collision of a ball on the bat lasts only about 1/1000th of a second. In that instant the batter can exert up to 8,000 pounds of force on the baseball. The ball is now headed across the field; what’s the equal and opposite reaction?

The bat trembles.

“When you ring a bell it vibrates,” Robinson said. “Or when you hit a gong, you can see it vibrating. When a ball hits a bat, the bat actually vibrates too. But there’s a point on the bat where it doesn’t vibrate. The so-called node.”

A node is the point along a wave where the wave crosses the zero line—where it has minimal amplitude. When a ball hits a bat it causes waves of vibration.  So when a hitter gets the sweet spot onto the ball, there’s less vibration and the bat imparts all that kinetic energy into the hit. You know you’ve hit the sweet spot by the sound of the crack.

So next time you’re watching the St. Louis Cardinals’ Adam Wainwright throw a curveball to a Red Sox slugger, listen for the sound of physics at work in America’s favorite pastime.




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