The Physics of Bryce Harper’s Broken Bat Blast

Monday night at Citi Field, Bryce Harper demonstrated his hitting prowess yet again by turning a 96 mph pitch from Jacob deGrom into a home run. Statcast reported an exit velocity of 99 mph at a 30˚ launch angle traveling 406 feet – all common home run values. Why all the excitement when Harper averages more than 25 homers a year? Take a look.

As Harper trotted back to the dugout, he flexed his right arm as if to point out his broken bat homer was an extra special feat of strength. Don’t get me wrong, hitting a shot off a highly regarded major league pitcher is certainly a demonstration of strength and remarkable athletic ability. However, the broken bat homer is not an indication of anything more than unusual luck combined with the usual skill set of a major league batter.

At first glance, one is tempted to think that hitting a ball that hard as the bat is breaking apart would make a home run impossible. However, there is a flaw in that thinking. If there were super slow-motion video of the ball-bat collision in this case, we could look more carefully at just what exactly happened when horsehide met lumber.

Alas, there doesn’t seem to be any such video available. However, there is super slow-motion video that shows what’s going on during ball-bat collisions that result in broken bats. Here is a famous broken bat from the 2012 NLCS.

Notice that the ball collides with the handle of the bat and the bat snaps at this same point almost immediately. The result is a ball that is barely moving off the bat. A physicist would say something like “all the energy in collision is used to break the bat leaving no energy left to propel the ball.”

In this case, bizarre things began to happen almost immediately after the initial collision. The ball was moving forward so slowly that the broken part of the bat came around and hit the ball twice more. Try not to focus on that. Instead look at the initial collision between the ball and the bat handle, and the resulting dribbler that would have occurred but for the bat hitting the ball two more times.

The point is that if the ball breaks the bat by hitting the bat on the handle, the ball doesn’t leave the bat with much speed at all. In cases like this, you’ll typically see a gentle grounder in the infield. The sense that a broken bat can’t propel a ball indeed seems reasonable.

Looking back at the Harper homer, you will notice that the ball didn’t hit near the handle– instead it collided on the barrel. Let’s see what is different in this situation. Here is a broken bat where the ball strikes the barrel. Again, this super slow-motion video is from the 2012 NLCS.

You can see that again, the bat breaks near the handle. It makes sense that if the bat breaks it will break near the handle, because the handle is the thinnest and therefore the weakest part of the bat. So the mystery is, how does the bat break at the handle when the ball hits on the barrel?

The answer is that the collision between the bat and the ball creates a wave that travels up the bat toward the handle. If the wave is such that the handle bends too much, the bat breaks.

It takes a good fraction of the energy in the collision to initiate this wave on the bat. As a result, a ball hit off the end of the bat doesn’t typically have enough energy to become a home run. It turns out that the energy needed to make the wave is less than that required to directly break the bat on the handle. As a result, balls are hit harder from broken bat hits on the barrel than balls directly breaking the bat on the handle.

Another thing to notice in this last video is that the ball leaves the bat before the bat actually breaks. So this ball colliding with the barrel is not actually hit with a broken bat. Instead, the ball heads off on its trajectory and the bat breaks very shortly afterward. This answers the question as to how a broken bat can even propel a ball.

If it takes energy to initiate the wave along the bat and that energy comes at some cost to the outgoing speed of the ball, how can you get the right combination of barely enough energy to create a wave that will break the bat and still leave sufficient energy to propel the ball for a round-tripper? It turns out, the size of the wave depends upon exactly where on the barrel the ball collides.

Here is a video of a home run collision from the 2013 ALDS. You’ll notice the bat doesn’t appear to vibrate at all due to the collision. This spot where the vibrations are minimized is called the “sweet spot.”

If a ball hit off the end of the barrel causes a large amplitude wave to travel down the bat toward the handle while a ball hit on the sweet spot of the bat creates a very small or even negligible amplitude wave on the bat, then somewhere in between there must a spot where the amplitude of the wave is just barely enough to break the bat.

The size of the wave amplitude is proportional to the energy in the wave. So, to see a broken bat homer the ball must collide at exactly the right point to have the minimum amplitude required to break the bat, while leaving the maximum energy available to the ball. This must be a rather rare occurrence since broken bat home runs are always noteworthy.

This page at MLB.com contains a montage of broken bat home runs, as well as more videos of Harper’s recent addition to the collection.

Instead of thinking of a broken bat blast as a feat of super human strength and athleticism, we should think of them as a rare treat such as a perfect game or a natural cycle. All such treats involve a tremendous amount of luck, but the only people capable of having such luck are the superhumans who play major league baseball.