The Physics of Snapping a Bat Across Your Knee

In a game full of diverse, dynamic personalities, Yasiel Puig stands apart. Everyone agrees he is an outstanding defensive right fielder, but it is his demeanor in the batter’s box that really arouses the passion of fans.

The Dodgers faithful love his antics. Opposing pitchers likely find his behavior irritating; opposing fans rain down boos from the time he leaves the on-deck circle.

Puig is known to exaggerate the danger of inside pitches by flailing wildly out of the box or hoping up and down like the Easter Bunny. He’ll take his bat and whack himself on the helmet if he thinks he missed a pitch. He will also use the bat to pound his arm muscles between pitches. However, it is his love/hate relationship with his bat that provides no end of speculation.

While watching a recent game, I saw Puig break a bat over his knee after striking out with the bases loaded.

For Puig, this is not unusual. He has broken his bat many times before. He even missed at least once.

Breaking a bat across the knees is not an act unique to Puig. While I’m sure our readers can come up with earlier examples, the first time I can remember seeing a bat broken over a knee was Bo Jackson in 1993.

All of this bat breaking brings up a seemingly simple physics question: How much force does it take to break a bat? It turns out this is actually a complicated question, but we can make some reasonable estimates. First, let’s understand why the question is complicated.

There are three elements that factor into any estimate:

• The rate at which the force is applied.
• The application direction of the force relative to the grain.
• Estimating the appropriate values to calculate the force.

The force on the bat intended to break it can be applied rapidly or slowly. Or, if you prefer fancier language – dynamically or quasi-statically. Here’s a way to understand the difference. Go get an uncooked piece of spaghetti and hold one end in each hand.

Breaking it dynamically means very quickly snapping it in two. Put another way, you apply the force rapidly. Quasi-static means slowly applying the force so the spaghetti gently bends more and more until it eventually breaks. For most materials, the breaking force is different in the two cases.

In the case of breaking a bat in game situations, we know from high-speed video measurement that the force is applied dynamically because the entire bat doesn’t have time to bend before it breaks. Check out this famous broken bat hit by Hunter Pence off Joe Kelly in the third inning of the 2012 NLCS.

 

 

You can see the bat breaks before the entire bat has a chance to bend. This is a dynamic break, not a quasi-static one. It is harder to say whether a bat broken across a knee is also dynamic because the time it takes for the collision between the bat and the leg is many times longer than the collision between the bat and the ball.

The second complication has to do with the direction of the wood grain. As ballplayers know, a batter swings the bat such that the manufacturer’s label is either facing directly up or down when the bat contacts the ball. The label is placed on the bat so if a batter follows this rule, the ball will be hit along the grain where the bat is stronger. (This is actually not true in maple bats, where the label is placed such that when the bat breaks, it won’t splinter and go shooting off as happened at times in the early days of maple bat usage.)

One would assume that to break a bat across the knee, one would want to do so against the grain. That is, the batter would want the label directly up or down – exactly opposite to where you want to hit the ball. When a batter fails at the attempt, it is likely the intention was to break the bat along the grain, though we don’t know for sure.

I’ve stalled long enough. It’s time to stop fooling around and come up with an estimate. I’ll use data from the Pence broken bat and Newton’s Second Law to find the force. Kelly’s pitch came in at 95.2 mph, which is 140 feet per second and essentially came to a rest after the collision. Newton tells us,

where m is the mass of the ball, ∆v is the change in speed of the ball, and ∆t is the collision time. We know the weight of the ball is about 5.13 oz and the change in speed is 140 ft/s. The trouble is we don’t know the time of the collision exactly.

We do know the collision time for a well-hit ball off the barrel is about 0.0007 s or so. However, this is not the case here. Here we have a poorly hit ball off the handle. During the collision, the handle flexes, increasing the collision time. Let’s guess the collision time is at least 10 times longer and go with 0.01 s – yes, it is just a guess. These values give a breaking force of roughly 140 pounds.

Is this a reasonable result? To check, I had to learn something about the bending or flexural strength of wood. I’ll spare you the details, but the force needed to break a one-inch diameter piece of ash is measured at about 170 pounds. Note, this is the quasi-static breaking as opposed to the dynamic breaking. Nonetheless, the result is shockingly close to the Pence estimate.

We can also estimate the force Puig’s knee exerts on the bat by carefully examining the 15 fps video above. It takes one frame to move the bat from the brim of his helmet down to his knee, a distance of about three feet. So, the bat is averaging at about 45 ft/s. Since it starts at rest above his head, it will be moving about twice that, or 90 ft/s, when it hits his knee.

In the following frame of the video, the bat is completely broken. So, the collision time is much shorter than 1/15 s. How much shorter? We don’t know for sure. How about we try half of the frame rate, or 1/30 s? Using Newton’s Second Law, again the force comes out to 170 pounds – consistent with the other guesstimates.

All three estimates are “in the ballpark” with respect to each other. Nonetheless, you can see they are highly dependent upon the estimates of the speeds and collision times needed to calculate the force. Indeed, the question, “How much force does it take to break a bat across your knee?” isn’t that simple to answer conclusively.