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Coefficient of Restitution and Compression in Baseballs

Imagine standing in the batter’s box, bat in hand, with your gaze fixed on the pitcher winding up. While physics might seem far from your thoughts in that moment, the Coefficient of Restitution (COR)—which quantifies the ball’s bounce-back energy—and compression, indicating how much the ball deforms upon impact, are crucial in the interaction between bat and ball.

In the realm of baseball ball performance, it’s essential to consider three key relationships: the Coefficient of Restitution (COR), compression, and the trampoline effect. Both COR and compression are intrinsic design elements of different types of baseballs, made to suit various age groups, whereas the trampoline effect pertains to the bat.

The COR measures the ball’s efficiency in retaining energy upon collision with a bat or glove, a higher value indicating a greater potential for energy retention and thus, a livelier response. Compression, conversely, assesses the ball’s firmness and its ability to maintain shape under force. These parameters are meticulously calibrated to match the ball’s intended use, aligning with the needs and safety considerations of different age groups and levels of play.

These three design factors impact the ball dynamics so let’s break it down step-by-step so you understand how they work together to provide a safe playing environment for young players.

Proper Context

In middle school and higher levels of baseball, the distance between the pitcher’s mound and home plate is precisely 60 feet and 6 inches. An average Major League Baseball (MLB) fastball, clocking in at around 94 mph, covers this distance in approximately 0.44 seconds.

A baseball is constructed by tightly winding yarn around a cork center, all encased within a cowhide shell. It features 108 stitches, weighs 5 ounces, and has a circumference of 9 inches. The difference between a ball being hit fair or foul can hinge on a timing difference of just 7 milliseconds. The bat-ball collision lasts for merely about 1/1000th of a second, yet it applies an enormous force of about 8,000 pounds, compressing the ball to roughly half its original diameter.

How much does a baseball weigh - baseball anatomy

The distance a ball travels after being hit is significantly influenced by the ball’s Coefficient of Restitution (COR) value and compression profile, along with the bat’s weight and the batter’s swing speed. Notably, each additional mile per hour of bat speed can add approximately 7 feet to the ball’s flight.

Baseball Crashing into a Bat

In baseball, understanding the dynamics of how the ball collides with the bat is crucial for grasping the nuances of the game, particularly in terms of the ball’s behavior upon impact. There are two primary types of collisions to consider: elastic and inelastic collisions.

Elastic Collisions

An elastic collision is characterized by the conservation of total kinetic energy between the ball and bat both before and after the collision. Essentially, there is no net loss of kinetic energy within the system; the energy is simply transferred.

In an ideal scenario, a collision between the ball and bat is nearly elastic, with the ball rebounding off the bat with minimal energy loss. For instance, when a ball is pitched and meets a bat swung with precise timing and angle, the collision approaches elasticity, maximizing the energy transferred back to the ball. This efficiency boosts the ball’s exit velocity, propelling it further into the field.

However, no collision is entirely elastic due to factors such as deformation and the energy absorbed by both the bat (and, by extension, your hands) and the ball. Nonetheless, baseballs used at the college level and beyond are designed to exhibit higher elastic properties.

Baseball Colliding with a bat
(Courtesy: University of Illinois)

Inelastic Collisions

In an inelastic collision, the kinetic energy between the ball and bat is not conserved during impact. Energy is lost in various forms, including heat, sound, or the deformation of the objects involved.

An inelastic collision in baseball might occur when the ball strikes the bat but does not rebound strongly, indicating a significant portion of kinetic energy was absorbed through deformation of the ball and possibly the bat, or lost as heat and sound.

A clear example of an inelastic collision is when a ball is caught in a glove. In this case, the ball and glove stay together post-collision, with the ball’s kinetic energy being absorbed by the glove and the player’s hand, effectively stopping the ball. The characteristic “pop” sound is a transformation of some of the kinetic energy into sound energy. Most baseballs used in youth leagues are more prone to inelastic collisions.

What is COR?

The Coefficient of Restitution (COR) measures the efficiency of an elastic collision between two bodies, expressed as the ratio of their final to initial relative velocities after colliding.

COR values range from 0 to 1, with values closer to 1 indicating more elastic collisions. This means a bouncier ball that retains more of its energy upon impact, resulting in higher rebound speeds.

In the context of baseball, professional players aim to minimize the effects of inelastic collisions by opting for heavier bats and employing fast swing techniques to reduce energy loss. However, completely avoiding inelastic effects is unfeasible due to the inherent physical properties of the ball and bat materials.

COR values for MLB and NCAA baseballs
The current COR value for MLB baseballs stands at 0.5460, while for NCAA/NAIA/NJCAA baseballs, the COR value is set at 0.555. The lower COR value of MLB baseballs, compared to those used in college baseball, is attributed to the advanced skills exhibited by MLB players.

What is Compression?

Ball compression, on the other hand, quantifies the ball’s stiffness or hardness by measuring the force required to compress the ball by a certain displacement.

Compression measures how hard a ball is, indicating its resistance to deformation under a specific load. Recall the principle that deformation absorbs energy. Consequently, a professional-grade baseball with higher compression will deform less than a youth baseball upon impact. This reduced deformation allows the bat to transfer energy back to the ball more efficiently, resulting in greater travel distance.

What is the Trampoline Effect?

The “trampoline effect” in baseball describes the phenomenon where a bat’s surface flexes or deforms upon impacting the ball, similar to a trampoline. This deformation temporarily stores energy, which is then released back into the ball, propelling it away with increased speed and force.

This effect is particularly pronounced in hollow metal or composite bats, whose walls compress and rebound during the collision with the ball. Such efficient energy transfer, boosted by the bat’s elastic properties, leads to a higher exit velocity of the ball than would be possible with a rigid, non-deforming surface. Therefore, the trampoline effect significantly affects how far the ball travels, with a more noticeable effect resulting in longer hits. The bat’s material, the thickness of its walls, and the ball’s properties, including its Coefficient of Restitution (COR), are critical factors determining this effect’s extent.

In many high schools, players have the option to use either a solid, one-piece wood bat or a BBCOR bat. The BBCOR (Batted Ball Coefficient of Restitution) standard ensures a uniform performance closer to that of wood bats, and these bats may also be referred to by their BBCOR rating of 0.5, with a -3 (or drop 3), indicating their weight to length ratio.

Ball Deformation vs Bat Deformation

You might wonder, how does the deformation of a ball dissipate energy while the deformation of a bat increases energy? This question is understandable and might seem contradictory initially. However, let’s delve into how energy is managed differently in the deformation of the ball versus the bat, especially within the context of the trampoline effect.

In essence, when a ball deforms upon impact, it absorbs some of the collision’s energy, leading to energy loss primarily through heat, sound, and the process of returning to its original shape. On the contrary, when a bat deforms, particularly in cases involving the trampoline effect, it temporarily stores energy before releasing it back to the ball. This action enhances the ball’s exit velocity due to more efficient energy transfer. Understanding these dynamics clarifies the distinct roles of deformation in ball and bat behavior during play.

Wrapping Up

Holding a baseball, its firmness is apparent right away, unlike its potential for bounce. Yet, similar to how a rubber ball rebounds, a baseball deforms and quickly returns to its original shape when struck. The more resilient it is, the further it propels off the bat. Choosing the right baseball is as crucial as selecting the perfect bat; both must be precisely suited to your needs. A misjudgment here can lead you to face unexpected challenges.

The COR (Coefficient of Restitution) value helps us understand the dynamics between the bat and ball, with values ranging from 0 to 1. COR, however, is more than just a figure; it represents the moment of impact, detailing the deformation and subsequent rebound of the ball. High-speed footage has unveiled the intricacies of these moments, showing how the choice of materials, ambient temperature, and even surface smoothness can influence the COR.

So, here’s to those impeccable pitches, the satisfying sound of the bat connecting with the ball, and the endless days spent under the sun on the baseball field. If you have any questions, thoughts, or curiosities about baseballs or any aspect of the game, feel free to leave a comment below.

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Let’s play ball!