The CoP is a rigid body property of the bat determined entirely by its mass distribution. The location maximizing BBS is a delicate balance among different factors, including the mass distribution, but also including the vibrational properties of the bat, the speed and axis about which the bat is swung, and the pitch speed. Moreover, it is now believed that the CoP is not even the location that feels best to the batter. The unpleasant sting in the batter's hands has to do with vibrations rather than rigid-body recoil. Dan Russell has done the most recent research on this issue, as described here on this issue. So, the author is wrong on both counts: The CoP is neither the location that performs best nor the location that feels best.
The author can be forgiven for confusing the different sweet-spot definitions, given that they are physically very close to each other. But he can't be forgiven for his discussion about the statement about the bat being "swung for one-twentieth of a second with a force equivalent to 44 horsepower." The author seems to be confused about the distinction between the energy that the batter transfers to the bat and the energy that the bat transfers to the ball. Let's take a look at both of those sources of energy.
We first examine the energy that the batter transfers to the bat. In the classic book The Physics of Baseball (3rd ed, p. 33), Adair says that for a bat to have a speed of 70 mph at the sweet spot, assuming it is rotated about the knob, the resulting energy of the bat is about 0.6 horsepower-seconds (equivalent to 448 Joules or 330 ft-lb). Now it is unrealistic to think that this entire energy can be transferred to the bat in 1/20 seconds (50 ms). Adair says it is more like 150 ms, in agreement with what is found from high-speed video analysis. In fact, all you really need to do is play back the swing of a typical MLB player one frame at a time and count frames to figure all this out. In any case, using the Adair estimate of swing time, we find that the average power of the batter (i.e., the rate at which energy is transferred to the bat) is about 4 horsepower, a factor of 10 below what the author claims. One might quibble with the various assumptions (e.g., making the bat heavier or lighter, the swing time faster or slower, etc.), but it is hard to come up with a factor of 10. So, the author is way off with that estimate.
Now let's look at the energy transferred by the bat to the ball. We first estimate the post-impact speed of the ball. Let's take it to be 120 mph, about as large as has been observed in MLB using HITf/x or TrackMan data. That corresponds to an energy of 0.28 horsepower-seconds (208 Joules or 153 ft-lb). So the energy transferred from bat to ball (in the form of kinetic energy) is actually lower than the energy transferred from batter to bat. The extra energy goes partly into heating up the ball and partly into keeping the bat moving after the collision. Now, the energy transferred from bat to ball occurs very quickly, in about 0.001 s (1 ms). That means that the power is 280 horsepower, which is considerably larger than the number quoted by the author. It is very hard to know how he arrived at 44 horsepower.
This discussion is a good example of how the batter supplies a certain amount of energy to the bat by applying a relatively small force (few hundred pounds at most) over a somewhat long time (150 ms), followed by the bat transferring a large part of that energy to the ball by applying a much larger force (thousands of pounds) over a much shorter time (1 ms). The batter does not directly apply a force to the ball. He applies a small-ish force to the bat, which then applies a large force to the ball.
Return to Article
Physics of Baseball Home Page