Why Do Curveballs Curve?

Pitcher holding a baseball (Pgiam, iStockphoto)

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Alex Beaumont
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Bernoulli’s equation is key to understanding why curveballs curve.

Do you ever watch or play baseball? Have you ever seen a pitcher throw a curveball? That’s when the baseball curves as it crosses the plate, causing the batter to swing and (maybe) miss. You might even be able to throw a curveball yourself. But do you know what causes the ball to curve in mid-air? It’s not magic. It’s physics!

Surprisingly, one of the keys to understanding curveballs is a formula normally used to explain the flow of fluids. Bernoulli’s equation considers velocity, pressure, and height. In the case of a curveball, the ‘fluid’ in question is air.

Bernoulli’s equation
P + ρgh + ½pV2 = K
P = the pressure of the fluid
ρ = is the density of the fluid
g = gravity on Earth (9.8 m/s2)
h = height of the fluid above a given location
V = velocity of the fluid
K = constant

At any specific point in the fluid, the constant (K) will equal the sum of the three other values in the equation (velocity, pressure, and height).

Velocity isn’t the same as speed. Speed refers only to how fast something is moving. Velocity refers to how fast an object is moving in a specific direction.

Gases as fluids

When you think of fluids, you might automatically think of liquids. But in physics, a fluid is any substance that flows and conforms to the shape of its container. Fluids can be liquids, like water. Liquids have free-flowing particles that can be poured into a container.

But fluids can also be gases, like air. Gases have particles that are more spread apart and that flow past each other more easily.

Gases not only take the shape of their container, they fill it completely. For example, air will completely fill up a room. That’s why you can breathe no matter where in a room you’re standing.

Ideal fluids

Bernoulli’s equation applies to ideal, or perfect, fluids. Ideal fluids don’t actually exist. Instead, they are theoretical fluids that are sometimes used in fluid-based physics to help physicists understand problems. Ideal fluids are different from fluids in the real world because they are missing some important traits. For example, they don’t have viscosity. That means they don’t resist flow like syrup or other thick liquids do. Ideal fluids also can’t be compressed (squeezed), don’t experience sudden changes to velocity (turbulent flow), and do not spin (irrotational flow).

However, the air acting on a curveball is a real fluid, not an ideal one. But for the purposes of explaining a curveball using Bernoulli’s equation, let’s pretend the air around the ball is an ideal fluid.

Bernoulli’s equation states that under ideal conditions, the sum of height, pressure, and velocity must stay the same at any given point within the ideal fluid. This means that if one value changes, another will also have to change to keep the constant the same. For example, at a constant height, if the velocity of a moving fluid were to increase, the pressure of the fluid would have to decrease to keep K constant. Or, if the velocity were to decrease, the pressure would have to increase to keep K constant. This phenomenon causes curve balls to curve!

Did you know?

Bernoulli's equation is most commonly used to calculate the flow of fluids. For example, it can be used to calculate water pressure flowing out of a firehose!

Curveballs, velocity and pressure

Think about a baseball spinning clockwise on a vertical axis while moving toward home plate. As the ball spins, it pushes the surrounding air in the same clockwise motion. The friction between the spinning ball and the air causes the air molecules on the right side of the ball to move backwards. The air molecules on the left side of the ball move forward.

But since the ball is moving forwards, air molecules on the left side of the ball that are being pushed toward home plate will collide with the air molecules the ball encounters as it flies through the air. The collisions between these air molecules slow the velocity of the air and create a zone of high pressure on the left side of the ball.

Meanwhile, air molecules on the right side of the ball are being pushed backward by the spinning ball. As a result, they won’t collide with other air molecules as the ball heads towards the plate. This increases the velocity of the air on the left side of the ball, creating a zone of low pressure.

The side of the ball with the most pressure will push the ball towards the side of lower air pressure, causing the ball to curve!

This example explains the path of a curveball that’s thrown with a clockwise spin. If a ball is thrown with a counter-clockwise spin, it will curve towards the left. If it’s thrown with a downward spin, then the ball will curve downwards.

Did you know?

The laces on a baseball are very important to the pitcher. They give the pitcher better grip, while also causing friction with the air moving around the ball.

So the next time you see a pitcher throw a curveball, just think about how the air is moving around the ball. Using Bernoulli’s equation, you can figure out how air pressure relates to velocity and why different pitches move the way they do!

Starting Points

• Have you ever played baseball or softball? Do you like pitching? Why or why not?
• Have you tried throwing a curveball? Have you seen someone throw a curveball? Why would a pitcher want to be able to throw a curveball?
• Have you ever put your thumb over part of the end of a garden hose? What happens to the flow of water?
• Is Bernouill’s equation only  important for sports played with a ball?  Can you think of other sports where Bernoulli’s equation has relevance?
• In which other fields is an understanding of Bernoulli’s equation important?
• What is an ideal fluid?
• Could a big gust of wind affect the success of throwing a curveball? If so, why?
• Why are baseballs replaced so frequently in major league games? How might this relate to Bernoulli’s equation and curveballs?
• What is a common calculation that is done using Bernouill’s equation?
• Baseball is a sport that has embraced advances in technology over the years (e.g., improvements to baseball helmets, pitch tracking technology, instant replay, etc.) . What factors have influenced this willingness to accept and invest in new technologies?
• This article can be used to support teaching and learning of Math & Physics related to fluids, pressure, kinematics and dynamics. Concepts introduced include Bernoulli’s equation, fluid, ideal fluids, viscosity, compressed, friction and low pressure.

Activity from Exploratorium showing students how to throw different kinds of pitches (fastball, curveball, screwball, slider) accompanied by an explanation behind the physics associated with the throws.

Video (3:11 min.) from Seeker explaining the different physical effects that a pitcher can use to their advantage while throwing a ball. Discusses the fastball, curveball, and knuckleball.

Article by Mike Petriello of Major League Baseball News discussing the fastest curveballs documented by Major League Baseball players, also includes a video of Seth Lugo’s record-breaking throw.

References

Diamond Kinetics. (2015, July 29). Bernoulli's principle applied to baseball.

Engineers Edge. (2019, July 3). Ideal fluid theory - Fluid flow.

Nave, R. (n.d.). Bernoulli equation. Georgia State University.

Princeton University. (n.d.). Bernoulli's equation.