Q&A: Why Some Balls Bounce Higher Than Others

Question: I love pretty much all sports but I’m not much into science. So I have a basic question for you. Why do some balls bounce higher than others even when they’re dropped from the same height onto the same surface? — TB, Indian Creek, FL

Answer: It’s all about a physical property known as coefficient of restitution (COR), a number between 0 and 1 that quantifies the “bounciness” of a ball. Higher CORs are bouncier. The rules for any sport specify the COR of the ball used for obvious reasons of consistency, predictability, and fairness. Whatever COR is desired, sports manufacturers can design that into the ball either with internal composition or air pressure.

The video shows a tennis ball (COR ≈ 0.7) and a ping pong ball (COR ≈ 0.8) dropped simultaneously onto the same hard surface. There is no air drag. Motion is slowed down to around 1/3 normal gravity for easier viewing. Only the first 5 bounces are animated. Notice how quickly the balls get out of sync.

COR = √(h / h’) where h = height fallen from, and h’ = height rebounded to. So the tennis ball rebounds to around 67% of the previous height, and the ping pong ball to 82%. If the animation were allowed to continue, both balls would bounce “forever” sans air drag. And you would be bored. The 5 bounces shown are sufficient to demonstrate my point about COR.

Here’s the specified COR for some common sports balls, ranked highest to lowest:

super ball
golf ball 0.89
basketball 0.82
ping pong ball 0.81
soccer ball 0.81
billiard ball 0.80
hand ball 0.75
cricket ball 0.62
baseball 0.60

Yes, I know super balls are not “official” sports balls, but I thought it would be informative to include their COR. The Super Ball™ was invented in 1964 by chemist Norman Stingley. The ball is made of a synthetic rubber he called “Zectron,” using a polymer polybutadiene and other materials. It was a hugely successful fad toy back in the 1960s, much like the Hula Hoop™.

So here’s the real science behind COR, and why some balls bounce higher than others. The graphic below shows the instant a basketball (with no spin) vertically impacts the floor:

When the ball impacts the floor it distorts from its spherical shape, flattening slightly on the bottom (exaggerated in graphic). This decreases its volume and raises the internal air pressure briefly from the NBA-prescribed 7.5 – 8.5 psi by a few tenths of a psi.

Newton’s 3rd Law says the forces between the floor and ball must be equal and opposite. That would be true even with a ball made of modeling clay (COR = 0) that just sticks to the floor. But when COR > 0 something different happens — it bounces.

Unlike modeling clay, balls with COR > 0 compress and store energy in a returnable form. As the ball resumes its original shape, it propels itself upward to a height determined by its COR. The COR is a function of the ball’s surface hardness and the elasticity of it’s internal components (solid or air). And the elasticity depends strongly on the internal density of the ball … that’s why the Super Ball™, formed with 3,500 psi of pressure, bounces as high as it does!

One should not underestimate the forces involved in a ball impact. You can easily squash a Nerf Ball™ to a fraction of its original diameter. Ever try that with a golf ball? The forces involved when a golf club strikes a ball are quite large. Take a look at this strobe photo showing the distortion of a golf ball on impact with the club, and imagine how much force that would take:

Even steel ball bearings and glass marbles, not usually thought of as deformable, will distort and bounce like a ball. The distortions will be smaller, but the forces greater. The COR for these materials is around 0.67. Of course, there’s a limit to the impact speed of glass beyond which it will shatter.

Bottom line: This is why it’s important to check the air pressure in inflatable balls before a competition. With hockey pucks, and croquet and billiard balls, it’s not an issue. Manufacturing standards take care of that. But whatever the sport, COR is an important part of the game. It controls how the ball behaves.

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