The physics of the elusive "sweet spot" unraveled

Apr 25, 2003

Just what makes the "sweet spot" sweet is the focus of Dr. Dan Russell's seminal research into the physics of composite baseball and softball bats.

Just what makes the "sweet spot" sweet is the focus of Dr. Dan Russell's seminal research into the physics of composite baseball and softball bats.

Russell, associate professor of Applied Physics at Kettering University, originally used baseball and softball bats to engage students in his acoustics and vibration course. "I wanted something simple for students to test the physics of vibration in the lab,"he said, "baseball bats are simple to test but provide interesting characteristics at the same time."

As part of his acoustics animations web site, Russell posted his original baseball bat research on the internet, and that is where CE-Composites Baseball Inc., of Ottawa, Canada, found him. Having proved successful at producing composite hockey sticks(ballistikhockey.com) the company is now branching out into composite baseball and softball bats (combatbaseball.com), and was looking for a way to improve bat performance.

Composite sticks and bats (made from woven layers of carbon fiber, graphite fiber or glass fiber) "are the rage in the hockey and softball markets right now," said Russell, "they are stronger, they don't break, and they are lighter than both wood and aluminum."

The composite baseball and softball bat market is relatively new, but all of the best bats currently available are composites or composite-metal hybrids.

Russell's research explains some of the physics of the sweet spot based on how a bat vibrates. Last summer CE-Composites Baseball Inc., contacted him about applying his tests to their bats to determine the characteristics of a good bat.

"The first phase of the project was a little reverse engineering - testing good and poor commercially available bats to see what makes a good bat. The second phase is applying our findings to new bat designs," Russell said. "During the past six months they sent me prototypes, and I tested them to see how the prototypes compare to what they expected them to do," he said.

Both phases of this research involve a test called experimental modal analysis in which Russell uses a special hammer that measures force and an accelerometer that measures vibration. He taps the bat at 1-inch intervals marked along its surface to determine how it vibrates. Results are input into a computer program that creates two-dimensional movies showing the vibration and frequency.

Two things he looks for when testing are the mode shape and frequency. Mode shape is the way a structure vibrates and the pattern that it has while it's vibrating. The frequency is how many times per second that particular pattern flops around.

The mode shape of a baseball or softball bat is a simple flexing bending shape that has parts that move and parts that don't. Every bat has a point about seven inches in from the tip of the bat that doesn't move, that doesn't vibrate, called a node. The node is related to where the sweet spot is - where the bat does NOT bend or vibrate. If the bat vibrates when struck by the ball it is taking energy up, Russell said, which means the more energy the bat has, the less energy is transferred to the ball. The more energy the ball has, the faster and farther it goes.

"The sweet spot feels better because the bat is not vibrating, and the ball goes off better because the bat is not vibrating. There is about a two-inch range where a batter gets the best performance; if an impact occurs in that range it's not going to excite that bending pattern very much," Russell explained.

"Knowing how it vibrates, what frequencies, what shapes, I can figure out where the sweet spot on a bat is," Russell said. I can predict if it's going to have some sting properties, I can predict if the frequencies and the behavior of the bat are doing what they are supposed to in order to give the ball most of the energy after it collides with the bat," he said.

Composite bats, like aluminum bats, are hollow, causing them to have what is called trampoline effect. Because it is a hollow cylinder, the bat compresses when struck by a ball. "It can squish like a spring, like jumping on a trampoline," said Russell. A wooden bat can't compress because it's solid. The actual shape of a hollow bat changes from a circle to an oval and then, when it springs back, the shape goes oval in the other direction - round to horizontal oval, back to round then vertical oval. And, depending on how the bat is designed, it can either diminish the energy transferred to the ball or increase the amount of energy transferred to the ball.

Russell believes that a well-designed bat can be "tuned" so the natural vibration shape coincides with optimal transference of energy to the ball. "If the contact time of the bat and the ball matches the time it takes the barrel to squish and push back, you can get a really good performing bat," said Russell. "At least that's what the data we've been seeing seems to suggest, and the best bats on the market seen to be going in that direction," he said.

"Once the vibration and frequencies are established, then you can ask 'if you have a bat which is a good performer, how are its vibration characteristics different than a bat which is not a good performer?'" said Russell.

It all depends on how well the bat is designed. But exactly why does one bat sting more than another? Russell does not have the answer - yet. "The tests I do are very low impact," he said, "when you're playing a slow pitch softball game you have a ball coming in at about 20 miles an hour and you're swinging at about 60 miles an hour, so there is about an 80 mile an hour collision. In adult baseball the speeds are much higher. The physics of what is going on is very different at high speeds than it is at low speeds. I think there is more to it in a game situation with very, very large impact, big force and high speeds, that I'm not able to test right now."

"But, I'm trying to come up with ways of figuring it out," he said. To better be able to predict game forces on a bat, Russell is developing a physical model of what goes on when the ball meets the bat. He got the idea for modeling the frequency of baseball bats from research into the trampoline effect that has already been done with golf clubs.

"I'm hoping the model will show the same trends that the data is showing - that the qualities of the good bat have certain frequencies and certain shapes. I'm half way through the development, I'm at the hard part where I'm in-putting information I know about the properties of the bat moving and properties of the ball, and I let them interact with all the physics equations,"Russell said. The physical modeling is purely for scientific understanding, said Russell, it is not part of his research for CE-Composite Baseball Inc., though it may influence some of his recommendations.

Developing the model will enable Russell to identify the target frequency. "What we don't know for sure is exactly what is the best frequency? Where does it have to be, to be as good as possible but not exceed the required performance standards for amateur baseball and softball," said Russell.

"The Amateur Softball Association of America has an interest in potential findings because they have to certify bats for amateur play. There are regulations on how well a bat can perform," he said.

Russell feels that unraveling the physics of the sweet spot is a new approach to bat design. "Manufacturers and designers have all these ideas that they are implementing to improve bat performance, but I'm not sure they know the physics behind WHY their ideas work. I think there is a simple reason why a particular bat works," he said.

"Industry-wide, there has been a lot of focus on making hollow bats thinner, or using double walled barrels. "Whether they understand the physics of it or not," said Russell, "what they are doing by making the walls thinner, or adding a second layer in the barrel, is dropping the frequency, in effect 'tuning' the bat."

"If you look at all the bats I've tested, the best performing bats all approach this magic tuning idea. Whether manufacturers understand why it works, they are making new bats perform better," he said.

Russell's pursuit of the sweetest part of the sweet spot may someday help improve the amateur's batting average, but the pros are on their own. Professional baseball players have to use wood bats in both the minor and major leagues to maintain the integrity and purity of the game. "There is not much you can do to improve the sweet spot on a wood bat," Russell said.

Russell's baseball bat research may be found on the WWW at www.kettering.edu/~drussell/bats.html.

Written by Dawn Hibbard
810-762-9865
dhibbard@kettering.edu