# The Physics of Throwing A Baseball

#### Adam O’Neill 20332770  JF COMMUNICATIONS BLOG

Baseball, it’s a game with a simple concept to follow, hit the ball and don’t get out. But hidden in a game with a very simplistic premise is a great deal of physics. A fielder being able to perfectly time his jump to catch a ball for final out or finding the optimal angle to hit a walk off homerun and win the game. However none are more interesting than the physics behind how pitchers throw their different pitches. There are two main components to look at, speed and movement. The emphasis that teams put on having good pitching is seen by simply following the money, with the average MLB (Major League Baseball) pitcher earning \$4.4 million per year, with the highest paid with the highest paid pitcher Max Scherzer  earning \$43.3 million per year. To earn the big bucks these pitchers must be able to throw all 3 different types of pitches, fastballs , changeups and breaking balls.

Highest paid MLB pitcher Max Scherzer in action (1)

While the fastball may seem like the most simple pitch the physics behind it is somewhat complex. The pitcher aims to throw the ball in straight line as fast as possible. Isaac Newton described the relation between how the force on an object is dependent on the objects acceleration in his famous equation F = ma ,where F is the force , m is the object’s mass and a is the object’s acceleration. Pitchers seek to move their arm as fast as they can to maximize the acceleration ,and hence force , on the ball.

The Magnus force on a baseball (2)

As the ball passes through the air the air moves in the opposite direction. When there is back spin the top half of the ball is moving in the same direction as the passing air while the bottom is moving in the opposite direction. As a result, the speed of the bottom relative to the air is higher than the relative speed at the top. This results in the ball speeding up the air moving over the top and slowing the air flowing under the bottom. This creates an area of high pressure below the ball and high pressure above it. This pressure differential causes a force , the magnus force , pointing from high to low pressure which pushes the ball upwards.

In the case of the fastball moving in a straight line enough spin is put on the ball do that this magnus force is the same as the force of gravity. We’ll look at other pitches with a greater spin rate and hence much more movement along their trajectory.

#### How about we slow things down a little?

Both changeups and breaking balls rely on decieving the batter rather than beating them with pure power. Changeups are in essence just slower fastballs. They are thrown is a similar manner, so the batter is set to swing at a fastball. When this is pulled off correctly a batter will swing early expecting a fastball and the ball will sail right past him. The physics behind throwing a changeup is similar to that of a fastball when it comes to speed. In this case the pitchers accelerate their arm less to reduce the force on the ball and hence the speed of the ball.

A key component of the deception used in both changeups and breaking balls is the increased movement. As discussed before this requires more spin on the ball which generates a greater magnus force and hence more movement. The spin on the ball is caused by the friction between the hand and the ball. A perfectly thrown ball won’t travel with spin, take for example a shot put. It travels with very little spin because relative to its low speed it leaves the hand at all points at the same time. However this is not the case for a baseball , where by using different grips the ball leaves certain parts of the hand before other.

Examples of grips for the three main pitch types

Lets once again look at the example of backspin on a pitch. A grip can be used such that the ball leaves the palm while still in contact with the fingers. There is friction created between the fingers and the ball causing a force on the that side of the ball , which causes it to spin.  The larger the friction the more force there is on one side of the ball and hence and increased spin rate. The force generated by the friction is given by the equation  f = uN  where f is the friction force and N is the force of the ball on the hand. is the coefficient of friction which is just a number which depends on the material of each surface.  By using different grips with different finger positions many different direction of spin and hence movement can be applied to a ball. As a result there are many different sub-types of changeups and breaking balls with varying magnitudes and directions of movement.

#### Putting the physics to use

That’s great but how can I use my newfound understanding of the physics to gain a competitive advantage? Well, by simply increasing the friction between the fingers and the ball you can throw pitches with more spin and hence more movement. This makes the pitch less predictable and harder to hit. The friction can be increased by increasing the value of in the equation for friction we looked at before. This can be done by using a sticky substance and applying it to your fingers. Unfortunately for you MLB rule makers also understand physics and have banned these substances from being used. They take this type of cheating very seriously and randomly inspect pitchers hands during games and if anything is found the player receives a ten game suspension. Despite this there have still been recent cases where they have found these substances showing that pitchers understand the benefit of the extra spin on the ball.

Max Scherzer being ejected from a game on April 4th 2023 after umpires allegedly found a sticky substance on his hands (3)

By understanding the physics of throwing a baseball hopefully you have a better idea of just how pitchers manage to make the ball blow away batters or swerve down at the last second to avoid the bat. If not at least next time you see a pitcher ejected from a game for having sticky hands you’ll understand what the fuss was all about.

REFERENCES AND OTHER INTERESTING SOURCES

An interesting youtube video on how pitchers cheating in baseball is on the rise again: