Why Does a Curveball Curve?

If you’re a science nerd or a baseball fan, you may think you already know the answer to this, and you may be right, but for the purposes of this article, i’m going to assume you don’t know much about baseball or aerodynamics. Even if you think you know the answer, give it a read anyway, it may be more complicated than you think it is, and you might learn something, or at the very least you might be entertained. 

Contrary to what you might expect, a curveball doesn’t move from side to side it actually dives. A perfect curveball is sometimes referred to as a 12-6 curveball, referring to the numbers on a clockface, that is, it moves downward from 12 o’clock to 6 o’clock. How does the pitcher make it do that? A curveball, like most baseball pitches, is all about spin. There are essentially two forces at work once the ball leaves the pitcher’s hand, gravity and aerodynamics. Obviously gravity simply is what it is, it will continuously pull the ball downwards with a constant acceleration of 9.8 m/s/s or 32 ft/s/s. Without aerodynamics, you have what’s called a ballistic trajectory, which means that the projectile (a baseball in this case) follows the path you set it on and simply curves continuously and predictably due to the force of gravity. Even with aerodynamics, because a baseball is round and symmetrical (mostly), if there is no spin, the only aerodynamic force that will act on the ball is drag (slowing it down), still resulting in a very predictable trajectory (as long as you assume the weather is perfectly still with no wind gusts, turbulence, or the like, we may dive into this more if I decide to do a knuckleball article). But predictable is not going to strike out professional baseball hitters, and that’s why “movement” is such an important part of Major League pitching. When baseball folks talk about movement on a pitch, what they’re really talking about is the ball moving off of that predictable trajectory. Since there’s no way for the pitcher to directly change what’s happening to the ball once it leaves their hand, everything has to be “baked in” to the pitch as the pitcher releases it. That means spin. 

Spin is the only way to produce a lateral force (read: not drag) on a symmetrical object like a ball. OK, brace yourself, things are going to get a little technical. I’ll try not to turn this into an aerodynamics textbook, but we do have some basic concepts to get through here. For any real life object, no matter how smooth it seems, there is enough friction between the surface and the air, that the air right next to the surface doesn’t move relative to the surface. Then you have an area just off the surface where the speed of the air changes smoothly from zero to whatever the speed of the air away from the object is (the free stream). This area where the air speed is changing as you move away from the surface is called the boundary layer, and whether we’re talking about wind blowing past a stationary object, or an object flying through the air, the effect is the same (just think of everything in the object’s reference frame. It’s like when you stick your hands out the window of a moving car and feel the wind pushing it backwards, there’s not actually a 60 mph wind blowing down the road if you were standing on the shoulder watching the car go past, but sitting inside, you’re in the cars reference frame, so to you, it feels like the wind is blowing.  You’ve probably experienced the effects of this boundary layer in your life whether you realize it or not. You may have noticed that a bug that’s sitting on your car’s window doesn’t get blown away even at highway speeds, but if you manage to dislodge it so that it’s not sitting directly on the window anymore, it will go shooting back (relative to the motion of the car) once it leaves the boundary layer. Even the Earth has a boundary layer which is why wind speeds tend to be faster the higher up you go in altitude (if you play golf, this is one of the reasons why it’s good to play lower shots when hitting into the end, and more lofted with a tail wind).

In the Boundary Layer, the air speed goes from zero right at the surface, to the free stream velocity a certain distance away from the surface

The size of this boundary layer region and the steepness of the wind speed transition is dependent on the viscosity and density of the air (more on this perhaps in a future article) and the roughness of the surface. A baseball is a pretty rough object, not only does it have a relatively well texted surface (run your finger over it, you can feel that it’s bumpy compared to, say, a steel ball bearing) but it also has those stitches which in the context of aerodynamic boundary layers, stick up like fricking mountain ranges. Now, remember that the air right next to the ball is going to be stationary relative to the surface of the ball, and the more friction there is between the air and the ball, the wider the boundary layer region will be. If the ball is spinning, that means that the boundary layer is also spinning. Effectively, the ball is “pulling” the air backwards (relative to its flight path) on one side, and “pushing” the air forward on the other. So the relative wind speed within the boundary layer is different on one side of the ball than the other.

The Spin on a baseball effects the air speed in the boundary layer differently on opposite sides of the ball

Why does this matter? Two words, Bernoulli’s Principle. Like I said, i don’t want this to turn into an aerodynamics textbook, but simply stated, Bernoulli’s Principle basically says that fast moving air is at lower pressure than slow moving air. Since the speed of the air relative to the baseball is different on one side of the ball than the other, there is a difference in pressure on one side of the ball than the other. You can do a lot of work with pressure differences, that’s how straws work (you produce a low pressure in your mouth and the atmospheric pressure pushes the liquid up the straw into your mouth), pneumatics/hydraulics (compressing the working fluid with a cylinder produces a high pressure in the line that can be used to move an actuator at the other end), and all types of engines (steam engines boil water and the pump the high pressure steam into a cylinder to drive a piston; internal combustion engines do the same thing, but instead of pumping steam into the cylinder, the expansion happens right there inside the cylinder in the form of an explosion, and rocket and jet engines use combustion to produce higher pressure right there in the thruster itself to force air to accelerate out the back and push the whole vehicle forward – I won’t go into the difference between a rocket and a jet engine here, that will have to wait for its own article). If you want to see Bernoulli’s Principle in action, hold a piece of paper on both sides at one end right at your chin under your mouth, letting it droop, then blow across it like you would blow across a bottle to make a sound, and watch as your breath blowing across the surface of the paper lifts the drooping end because the fast moving air of your breath is at lower pressure than the still air below the paper.

To throw a curveball, the pitcher holds the ball more or less sideways from a fastball with wrist and hand on the outside of the ball, and then snaps their wrist to pull their fingers down across the front of the ball as their arm action throws the ball towards home plate, giving the ball over-spin. Then, as described above, this over-spin pulls the air backwards on the bottom of the ball (thus speeding it up relative to the speed of the ball) and pushes against it on top of the ball (slowing it down) so that Bernoulli’s Principle causes a lower pressure below the ball than above the ball and force the ball downward faster than gravity alone would cause the ball to drop, thus altering the trajectory of the ball flight relative to what the batter would predict. And that is why a curveball curves.

Illustration of how a curveball is thrown

Bonus Material: What’s a hanging curveball?

You may have heard of a hanging curveball, it’s a term used to describe a curveball that doesn’t curve. What does that mean exactly, and how does that happen? Well, occasionally, a pitcher will screw up that wrist snap and instead of putting over-spin on the ball, they’ll put spiral spin like a football or a bullet (this is sometimes called gyro spin, more on that momentarily). Because the spiral spin is only perpendicular to the ball’s velocity, it can’t pull or push the air to change the speed relative to the ball’s flight, all it’s doing is adding swirl which stabilizes the ball’s flight and makes it even more predictable (this is exactly why bullets and footballs have spiral spin, it adds gyroscopic stability to keep the orientation of the projectile aligned with its trajectory because in shooting and football, you want a predictable flight path). So a hanging curveball is REALLY easy to hit because it’s EXTRA predictable. And there’s no such thing as a “gyro ball” for exactly this reason.


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