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Although they're rare, I've seen a few instances where a baseball player breaks their bat and still manages to hit a home run. Two examples:

I feel sure there are other instances, but this will give the idea.

Broken bats are not especially rare, but usually any hit resulting from a broken bat is weak. When the bat shatters or the head breaks completely from the handle it is not unusual that the fragments of the bat may go farther than the ball. When the bat cracks but does not fully break, it's not unusual for the ball to make it to the outfield, but these hit usually do not carry as far as if the bat stays intact.

In the two examples above, however, the bats snap completely, leaving the player with about 8-12 inches of handle in their hand and the ball carries over the wall, so let's say greater than 375 feet. The Harper home run was estimated at 406 feet.

The physics of these broken-bat home runs is not obvious to me. Once broken, the player cannot provide torque on the head of the bat, so they should have much less ability to change the momentum of the ball, and some energy must go into breaking the bat. I saw the Chris Davis home run above when it happened on television, and in the slow-motion replay, as I recall it, it also wasn't clear when in the swing the bat broke. I got the impression that it might have broken after contact with the ball was complete. (The announcer says the bat head ended up "in the Oriole's dugout," which is a clue to where it became disconnected from the bat. The dugout is more or less behind the left-handed hitting Davis in foul territory, and the ball cleared the wall in fair territory. Likewise, the announcer on the Harper home run says the bat head "hit the screen," which suggests that it flew reasonably far into foul territory while the ball cleared the wall fair.)

Is there some vibrational mode or other failure mode in the bat that would allow it to break in the follow-through? Could it be that the bat head already has sufficient momentum to redirect the ball, so the loss of connection to the hand doesn't matter? I think the former is more likely, but I'm not sure how that would manifest in the bat.

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  • $\begingroup$ If you slow down the video and turn up the quality, you can barely see that the bat breaks apart (the pieces separate) AFTER the ball has left the bat. If this observation holds, then the transfer of momentum from the broken bat that is still together to the ball is essentially the same as if the bat did not break. $\endgroup$ – N. Steinle Sep 30 '18 at 16:04
  • $\begingroup$ @N.Steinle That's consistent with the last part of my observation too, but it still leaves the question of what physical failure mode occurs in the bat and how the energy necessary to trigger that mode relates to the energy necessary to propel the ball so far. $\endgroup$ – Brick Sep 30 '18 at 16:28
  • $\begingroup$ I suppose it depends on whether the bat is brand new or if it is used meaning it will have microfactures already inside the barrel, which will make it stiffer and thus cause the ball to go farther. ac.els-cdn.com/S1877705810003012/… $\endgroup$ – N. Steinle Sep 30 '18 at 16:55
  • $\begingroup$ It also depends on how the bat was constructed, see the bottom of rockbats.com/techNotes/RB-TN-003.pdf $\endgroup$ – N. Steinle Sep 30 '18 at 16:55
  • $\begingroup$ Depending on these things, I think it could go either way: either the energy that causes the physical failure is correlated with the the energy to break the bat, or not. I.e. if the bat has a lot of microfractures along a grain of the wood already, then they are correlated certainly, since it won't require as much energy to break the bat which the leftovers can conceivably be imparted into the ball. I'm just speculating here $\endgroup$ – N. Steinle Sep 30 '18 at 16:59
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Nobody is going to break a bat just by swinging through the air. It breaks after the ball is hit.

If the weakest part of the bat is some distance away from the hitting point, it will break when the stress wave from the impact reaches the weak point. In fact, it might not break until the stress waves (two, one starting in each direction from the impact point) have traveled up and down the bat more than once.

The stress waves do not travel instantaneously along the bat. They move at the speed of sound in the material, which is typically about 4000 m/s in wood, compared with 340 m/s in air. Since that bat is about 1.1m long, and the ball speed leaving the bat from a fastball is typically about 50m/s, the ball has already travelled about 13mm (half an inch) away from the bat before the whole length of the bat has "felt" the shock of the impact.

For a simple model of the bat as a uniform cylinder, if the impact point of the ball is a distance $d$ from one end of the bat, the two stress waves will be superimposed again at distance $d$ from the other end, as they travel along the bat. The bat may break at that point, not where the ball was hit. Obviously this is an over-simplified model of a real bat, but it describes qualitatively what can happen - the two stress waves must meet again at some point, as they move along the bat in opposite directions and are reflected from the ends.

The bat may not break the first time the stress wave passes a weak point. it may take several passes to cause enough damage for the bat to fail.

To summarize all this: at the time when the bat breaks, the ball is already in flight.

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  • $\begingroup$ "The bat may not break the first time the stress wave passes a weak point. it may take several passes to cause enough damage for the bat to fail." - I think that that's a good point. Reverberations in a bat long after the ball has been hit are certainly very noticeable in aluminum bats. Reverberations also exist in wooden bats. $\endgroup$ – Samuel Weir Sep 30 '18 at 17:21
  • $\begingroup$ This is interesting and probably heading in the right direction. For sure the bat doesn't break before the ball makes initial contact. The ball remains in contact with the bat for finite time, however. A quick search shows an apparently credible estimate of 0.7 ms time in contact with the bat while the ball deforms. That is longer than the time that a wave propagating at the speed you suggest would take to pass the whole bat, (1.1 m / 4000 m/s = 0.275 ms). Could be that's just within the error of the approximation, I guess, but this is a little short of convincing to me so far. $\endgroup$ – Brick Oct 1 '18 at 16:25
  • $\begingroup$ Broken bat on a swing-and-miss: mlb.com/cut4/noah-syndergaard-breaks-bat-on-swing-and-miss/… $\endgroup$ – Brick Oct 1 '18 at 17:03

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