Physics of Baseball
The Sound of Sweetness
The Sweet Spot of the Bat
Hot dogs. Crackerjacks. The dog days of summer. The crack of the bat. All these things are associated America's Pastime, the game of baseball. What is so satisfying about the crack of the bat? Why is it a sound that brings joy to millions of Americans?
When the ball hits the bat, and the batter, pitcher, and everyone in the ballpark knows the ball is well hit just by the sound is what baseball is all about. This wonderful sound is the ball making contact with the sweet spot of the bat. The sweet spot of a bat can be defined in two ways.
The first way to define the sweet spot of the baseball bat is that it is the spot on the bat where the collision between the bat and the ball produces the least vibration. Typically when the two collide, two sets of vibrations are set off, at 170 hertz or 530 hertz. The sweet spot is the spot where the combined vibration is the least. Through experiments this sweet spot has been determined to be about 6 inches from the top or end of the bat. The sweet spot could also just be where the lower frequencies drop off, lowering the sweet spot by as much as an inch. Making contact with the ball at this point on the bat causes the ball to come off the bat faster and, therefore, travel farther. By hitting the ball with the sweet spot, 3-4% percent of energy is conserved and put into the ball, causing it to travel farther (Chang).
There are the least vibrations at the sweet spot because it is the node of the bat. When the ball hits the bat, the bat will bend somewhat, since wood is an elastic object. This causes the vibrations in the bat. The ball hitting the bat also causes two different waves. The first is when the ball hits the bat. The second is when the ball leaves the bat. The point where the amplitude, height of the wave, is greatest is called the anti node. The point where the two waves meet is the node (amplitude is zero), and this point produces the least vibration. Since the energy transferred through waves is proportional to the square of the amplitude then the anti node would produce the greatest transfer of wave energy, causing the bat to vibrate, instead of causing the ball to travel farther. Therefore, the node causes the least vibration and is known as the sweet spot of the bat (Physics).
The second way to define the sweet spot of the bat is at its center of percussion. This point is where the collision between the ball and bat causes the least shock to the batter's hands. The closer the ball hits to the hands, the more the bat pushes into the palm of the top hand of the batter on the bat. The farther toward the end the ball hits, the more the bat will push on the fingers in the opposite direction, trying to open up the batter's grip.
To understand why the bat exerts a force on the batter's hands, you should first think of the bat as a stick. If the ball hits the stick off center, the stick wants to move backward and also rotate around its center. This spin is what causes the bat to either push into the batter's palm or in the opposite direction into his fingers. When the ball is not hit at the sweet spot or center of percussion it causes the bat to swing into your hands and some of the energy of your swing goes into moving the bat in your hands (Sweet Spot).