Thrown a curve

Well, as you can see, it’s not Friday anymore, but I did start this on Friday, so we’ll just pretend. As I started this week off with a special request, it seemed appropriate to finish the week with another special request. So, Dad, here’s the post you asked for on baseball. The beautiful game is about to collide with some elegant equations, and produce a gorgeous body of physics.

Most things in life can be somehow described by a cool equation, but the physics of daily life really shines in baseball. Here is a sport in which, at its heart, the whole point is the collision of two vectors, with the result of one vector altering course, and moving in a certain direction at a certain speed. To further complicate matters, the source of each vector is angling the vector in such a way as to achieve a different result. In other words, baseball is fundamentally about hitting a ball with a bat in such a direction that a run is batted in, or the batter is struck out (depending on whether you consult the batter or the pitcher).

So, let’s look a little more at one of these two vectors, the pitch. The pitcher is trying to either trick the batter into swinging at a ball the bat won’t connect with (strike), hitting a ball in such a way that one of the fielders will quickly catch is (strike), or not swinging at a ball that the batter could theoretically hit (strike!). How does the pitcher accomplish this?

 

Now, with a gravitational acceleration of 9.8 m/s, and an initial velocity of 153000 m/s, what air drag can I expect on this pitch?

Here’s where we get into the different pitches, and differences in how the ball is thrown. So, you have a ball moving through the air. The ball is moving straight (more or less) towards the batter. The flight of the ball is a result of the interplay between the inital force behind the ball (the throw), the force of gravity, and the resistance of the air to the ball’s movement. The ball is also spinning - in any pitch, the ball rolls off the pitcher’s fingers, and continues to spin as it makes its way towards home plate. Not all spins, however, are created equal, and here’s where the fun begins. Pitches can be roughly divided into curveballs, fastballs, sliders, screwballs and knuckleballs (obviously, there are further variations within these categories). What differentiates each pitch, and makes each ball behave differently, is the amount and direction of spin on the ball.

 

Let’s take a look at curveballs. In order to throw a curveball, the pitcher includes a snap of the wrist in the pitch. This makes the ball roll of the pitcher’s fingers in such a way that the ball is spinning in the same way that it is travelling. Visualize the ball moving toward the batter. As you look over the ball, the top of the ball appears to be rotating towards the batter. As you look under the ball, the ball appears to be rotating away from the batter. Now, what does this do to the pitch?

One more point about baseballs before we answer this question. A baseball does not have a smooth, uniform surface. Instead, a baseball has two rows of stitching, creating parallel seams on the ball.

When the pitcher throws a curveball, the spin on the ball teams up with the stitching to manipulate the forces acting on the ball. On the top side of the ball, the ball is spinning towards the oncoming air - oncoming air rides up over the seams, and pushes the ball down slightly. On the bottom side of the ball, the ball is spinning away from the oncoming air - there is no corresponding force to counter the downward push on the top of the ball. The difference in pressure is slight, but it is enough to make the ball curve down. Properly executed, a curveball approaches the plate at one height, but when the batter goes to take the swing, the ball has dropped down, and the batter fails to connect. Strike!

Even if the batter were able to anticipate the sinking ball, curveballs also, well, curve. The spin imparted to the ball, in addition to creating unequal air pressure, also creates unequal air drag on the ball. The difference in drag imparts a horizontal curve, as well as a downward curve, to the flight of the ball. Like the downward direction change, the horizontal change happens late in the flight of the ball - again, the batter winds up swinging at a ball that is not there.

The opposite of the curveball is the fastball. Here, the pitcher does not make any additional twisting motion - the ball is spinning in the opposite direction of travel. So, the top side of the ball moves away from the oncoming air, while the bottom side moves towards the oncoming air - just like with the curveball, air piles up around the seams, but on the bottom this time. The effect is enough to slightly counter the natural tendency of the ball to sink towards the ground over time (no matter how well thrown, a baseball is still subject to gravity), leading to a ball that doesn’t sink as fast as the batter would expect. So, the batter goes to take a swing, but misses the ball again, this time with a ball that is above the bat. Strike!

The top line indicates the actual path of the ball, the bottom line indicates where the batter expects the ball to be.

Sliders are interesting, in that there is no lifting or sinking involved - the ball is thrown to spin perpendicular to the oncoming air. Sliders are all about unequal drag on the ball causing said ball to curve either to the left or the right. It is harder for a batter to connect with a ball moving towards the bat, rather than away from the bat (counterintuitive, right?), and handedness influences both sliders and batting. So, a right-handed batter with have a hard time hitting a slider thrown by a left-handed hitter, and vice versa. This is where switch hitters, batters who are equally comfortable batting right and left-handed, can make a real contribution to a team, and ruin a pitcher’s day.

Screwballs dip down like curveballs, but curve laterally in the opposite direction. While a curveball thrown by a right-handed pitcher will curve slightly away from a right-handed batter (making it hard to hit), a screwball thrown by a right-handed pitcher will curve slightly toward a right-handed batter (making it harder to hit). Screwballs, unfortunately, require a rather unnatural twist of the wrist, and are thus not commonly seen in baseball.

 Just try and hit this one

Finally, we have the knuckleball. The deeply weird knuckleball. The four pitches we just looked at are thrown quickly (90 mph or more). The point of any of these four is that the curve kicks in late in the ball’s trajectory - given how fast the ball moves, the batter must make the decision to swing before the curve, dip or lift becomes apparent. The knuckleball doesn’t work like that at all. It is thrown at the comparatively lackadaiscal 65 mph, and with minimal spin on the part of the pitcher. This allows the knuckleball to experience the full range of irregular air drag made possible by the stitches on the side of the ball - the ball takes longer to reach the plate, and has less initial force from the throw to overcome air drag. The result is a ball that weaves erratically through the air, and is most difficult to hit. Pitchers have many tools at their disposal with which to psych out and strike out batters, and the simple physics of interacting forces and friction can explain many of them. Batter have a number of tools at their disposal with which to hit back, and we’ll look at those in a future further exploration of physics in baseball. But for now, sit back, watch the game, and envision all of the lines, arrows and force diagrams going into each pitch. Trust me, it makes baseball that much more fun.