Home Run Forces
An activity from the Burroughs Wellcome Student Research Program
The Science of Sports

Problem:

Barry Bonds currently holds the record for home runs in a season. Many think this is due to his brute strength. Yet players with smaller biceps are still able to hit home runs. How can you maximize the force on the ball when you are at bat? Where, on the bat, should you hit the ball to make a home run?

Introduction:

There are several places on the bat where contact with the ball can produce varied effects. Many players refer to these as sweet spots. Physicists call these spots the center of percussion and vibrational nodes.

A bat is essentially a big stick. When you hit a stick off center, two things happen: The entire stick feels a force straight backward and it also feels a rotational force around its center. It is this rotational force or torque that causes the bat's handle to push back on or pull out of your hands. When the ball hits the bat's center of percussion (COP), you don't feel a push or pull as the bat tries to spin. As the bat spins, it pivots around one stationary point and when you hit a ball at the COP the stationary point coincides with your hand so it feels no push or pull one way or the other.

If you bounce a ball off a bat you will most likely hear a ringing sound. This happens when the force of the ball adds energy to the bat causing it to vibrate. However, if the ball strikes the bat at a vibrational node the force or energy will not cause the bat to vibrate and will stay with the ball. Vibrations or waves travel up and down the bat and nodes are the points where they always cancel out. There are two significant modes of vibration(see below): the fundamental which has a longer wavelength and a deeper pitch, and the second mode which has a shorter wavelength and a higher pitch. It is not possible to hit the bat at the node of both modes since they do not overlap but hitting the bat between the two nodes would only cause vibrations of a low amplitude in both modes and take the least amount of energy away from the ball.

Materials
Computer ULI and MacMotion software or Data Logger OR LabPro and LoggerPro software baseball bat force probe baseball or tennis ball rubberbandst masking tape ring stand meterstick hammer string

Exploring I:

Calibrate the force probe. Set up the software (MacMotion, Data Logger or LoggerPro) so that the computer displays a force graph (probe 1) and takes data for 2 minutes. Place small strips of tape along the barrel of the bat about every two inches. You may wish to label each strip. Place the handle of the bat on the force probe - use a small piece of rolled tape to keep it from rolling - and suspend the other end using rubber bands and a ring stand as shown below.

Determine a method for delivering a consistent force to the bat. Some ideas to try: dropping a ball from a specified height, letting the meterstick swing through a specified arc . . . .At each of the positions you marked with tape apply a force. Record the maximum force felt at the handle as measured by the force probe. You should take several (6+) measurements at each position to reduce error. Make sure the bat is stabilized before each measurement. Also record any other observations (listen!)

Discussion I

Where is the center of percussion of your bat?

On the diagram above draw all the forces on the bat when a ball strikes at the center of percussion.

Did you notice any positions that sounded different from the rest of the bat? Explain.

What do you think these positions correspond to?

Make a graph of the average change in force at each position.

Repeat the exploration but this time hold the bat in one hand. Notice how the bat feels when you strike it at the center of percussion, closer to the handle and closer to the end.

Exploring II

Hang the bat by a string from the handle. Attach the string so that the bat hangs straight (like the handle on a basket). Use the hammer and strike the bat fairly hard at each of the taped positions. Record all of your observations.

Discussion II

At what position did you strike the bat so that it swung through the smoothest arc with little additional movement and the greatest amplitude?

How does this position compare to those found in Exploring I?

Exploring III:

Hold the bat horizontally. Have a partner drop a ball several times at each position from a predetermined height and record how high it bounces. Make a graph of bounce height versus position.

Discussion III:

At what position did the ball bounce the highest?

How does this position compare to those from Exploring I and II?

Conclusions

Make a diagram of your bat below and label the center of percussion and vibrational nodes.

Where on the your bat do you think you should hit the ball to hit a home run? Explain your choice.