Above: Baseball (vedub4us, Wikimedia Commons)

Have you ever watched a pitcher throw a baseball so it curves as it crosses the plate, causing the batter to swing and miss? Or maybe you can throw a curveball yourself. But do you know what causes the ball to curve in mid-air? Magic? No, physics!

Did you know? Velocity isn’t the same as speed? Speed refers only to how fast something is moving. Velocity also refers to an object’s direction of movement.

Bernoulli’s equation is key to understanding why curveballs curve. It’s a formula that explains the flow of fluids. It takes into account key factors such as velocity, pressure, and height. In the case of a curveball, the fluid in question is air.

Bernoulli’s equation

P + ρgh + (½)pv2 = 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.

Gases as fluids

When you think of fluids, you might automatically think of liquids. But in physics, fluids are any substance that flows and conforms to the shape of its container. Fluids can be liquids, like water, that have free flowing particles that can be poured into a container. But they can also be non-visible gases, like air, that 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. Otherwise, you would have to stand in specific places in a room to be able to breathe.

Ideal fluids

To be more precise, Bernoulli’s equation applies to ideal fluids. Ideal fluids are missing some important traits of real fluids. For example, they don’t have viscosity, which means they don’t resist flow like syrup or other thick liquids do. Ideal fluids also can’t be compressed, don’t contain turbulence, and have irrotational flow.

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 if you are dealing with a continuous ideal flow, the sum of height, pressure, and velocity must stay the same at any given point within the ideal fluid. So if the velocity of a moving fluid were to increase at a constant height, its pressure has to decrease. And if its velocity decreases, its pressure has to increase to keep K constant. This is the phenomenon that causes curve balls to curve.

Did you know? Bernoulli's principle helps explain why a curveball curves and part of why airplanes, gliders, and helicopters can fly.

Curveballs, velocity and pressure

Think about a baseball spinning counter-clockwise on a vertical axis while moving north toward home plate. As the ball spins, it pushes the surrounding air in the same counter-clockwise motion. The friction between the spinning ball and the air causes the air molecules on the east side of the ball to move north. The air molecules on the west side of the ball move south.

But since the ball is moving north, air molecules on the east 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. These collisions between air molecules slow the velocity of the air and create a zone of high pressure on the east side of the ball.

Illustration shows the forces acting on a curveball as described in the article text
Illustration of the forces acting on a curveball. Click image to enlarge (Alex Beaumont)

Meanwhile, air molecules on the west side of the ball are being pushed southward by to the spinning ball. As a result, they won’t collide with other air molecules as the ball heads north. This increases the velocity of the air on the west 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.


So the next time you see a pitcher throw a curveball, just think about how the air is moving around the ball. Can you think of any other ways the spin of the baseball and might cause it to move in different ways? Using Bernoulli’s equation, you can figure out how air pressure relates to velocity and why different pitches move the way they do!

Learn more!

Websites explaining the physics behind different pitches:

The Physics of Pitching
Schlumberer Excellence in Education Development

Thrown for a curve

The Physics of Baseball (1995)
Robert K. Adair, R., Physics Today

Alex Beaumont

I am a student at the University of Manitoba and I am completing a science degree with a major in microbiology and minors in biology, chemistry and psychology. I am passionate about healthy living and science and I love sharing these passions with others!

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Avatar  Brian

This is an inspired and well written article! It clearly explains the scientific principals of fluid dynamics and how they apply to everyday life. It is filled with interesting questions and tidbits of information. The author did a fantastic job! Perhaps one day I will be lucky enough to hear this information presented in person.