# Sweet Spot on a baseball bat

caz
Gold Member
Back in grad school, a friend of mine became interested in the center of percussion and hammers. He couldn’t find one on the market that took advantage of the effect, so he designed one, patented it, and tried to sell it to a hardware company.

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berkeman
Mentor
Back in grad school, a friend of mine became interested in the center of percussion and hammers. He couldn’t find one on the market that took advantage of the effect, so he designed one, patented it,
Interesting. What did it look like?

Homework Helper
Gold Member
2020 Award
That part is okay, I gave some analysis in #6 to a similar conclusion.

My objection to #20 was that there does not exist a point on the bat about which the total angular momentum is zero, and even if one did, it would be an accelerating point so you'd also need to take into account inertial forces and impulses acting at the centre of mass.

So what Sears and Zemansky wrote sounds wrong, if that is an accurate reflection of their argument!
The calculation is done simply at the moment of impact, and it is assumed the bat pivots at a point near where the hands are. The speed of the bat is in the same direction all along the bat, and is ## v=\omega r ##. It is the same thing as the door and the doorstop.

etotheipi
caz
Gold Member
Interesting. What did it look like?
This was 20+ years ago, so memories are a bit fuzzy. He purposefully designed it to look like a normal hammer. Basically, he added internal weightings to adjust things. I think he also added some weight above where the hammer head connected to the shaft, but nothing that would stand out under a quick inspection. I believe he also found a couple of other physics related improvements, but I cannot remember what they were.

Homework Helper
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2020 Award
It sounds like he designed the hammer so that the center of percussion of the hammer, when pivoted about a typical hand position, was right in the center of the head of the hammer, where it meets the nail.

etotheipi
The calculation is done simply at the moment of impact, and it is assumed the bat pivots at a point near where the hands are. The speed of the bat is in the same direction all along the bat, and is ## v=\omega r ##. It is the same thing as the door and the doorstop.

It is still insufficient. Consider a point on the bat which is a distance ##\xi## from the pivot. The angular momentum about such a point is of magnitude$$L = M \omega \left( \xi - \frac{\mathscr{L}}{2} \right)^2 + \frac{1}{12} M \mathscr{L}^2 \omega$$Note that this is strictly > 0. Hence, there is no point on the bat about which there is zero angular momentum.

Further, it does not matter that the calculation is only performed within an interval ##[t_c - \epsilon, t_c + \epsilon]## around the collision. If the coordinate system has its origin connected rigidly to the bat then you must still account for an inertial impulsive Dirac delta force through the centre of mass.

caz
Gold Member
It sounds like he designed the hammer so that the center of percussion of the hammer, when pivoted about a typical hand position, was right in the center of the head of the hammer, where it meets the nail.
That was the initial idea. As he got into it, he found other physics improvements.

Homework Helper
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2020 Award
Angular momentum ## L= \int \delta \, \vec{v} \times \vec{x} \, dx ##, where ## \vec{x} ## is measured from the sweet spot, and ## \delta ## is the mass per unit length. The cross product will have opposite signs on either side of the sweet spot to make ## L=0 ##, when the proper spot is picked for the origin.

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etotheipi
etotheipi
Ah, you are considering instead an inertial frame with an origin fixed at the position through which the sweet spot passes through at the lowest point in its swing! Okay, yes the argument works, we understood each other.

I thought you had meant a coordinate system with body-fixed origin, in which case angular momentum is as written in #31.

caz
Gold Member
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berkeman
Mentor
I found a patent description
https://patents.justia.com/patent/20070151421
Looks like it's just a patent appliction. Do you know if it ever issued? Also, I was not able to find the diagrams/drawings -- do you see a link to them?

caz
Gold Member
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sophiecentaur
Gold Member
2020 Award
Looks like it's just a patent appliction. Do you know if it ever issued? Also, I was not able to find the diagrams/drawings -- do you see a link to them?
Thing about patents is that the only requirement to be granted one is that the description of the item has to be legally robust enough to challenge anyone who tried to copy it. There is never any guarantee that a patented device will actually work. The patent agents earn their money on all items and they just don't care about them, once the patent has been granted.

I think that quoting a patent is not a good argument about the Physics involved. That is, unless the device has sold well and has been seen to work for the customers. The Horse and Cart argument applies there.

caz
Gold Member
I think that quoting a patent is not a good argument about the Physics involved. That is, unless the device has sold well and has been seen to work for the customers. The Horse and Cart argument applies there.
According to his webpage,
https://www.novacentrix.com/team/kurt_schroder
”He is also the inventor of the antivibration technology contained within most hammers sold in the United States, with sales exceeding $2B” The story started with me saying that a friend from grad school after learning about centers of percussion in a classical mechanics class (in 1993) saw that hammers were not taking advantage of the physics and tried to do something about it. I thought it a nice story about physics being around us in everyday life. I then started getting questions. After looking at the patent I remembered more. He started with adding/removing weight from the hammer and saw that it improved performance via testing. He then figured out that you could move the pivot point and improve performance and designed a handle to do that which he patented. While I cannot verify the word ”most,” I do know that multiple major tool manufacturers in the US brought out hammers with his idea. Last edited: sophiecentaur and Charles Link caz Gold Member Physics World did an interview with him http://live.iop-pp01.agh.sleek.net/...edition/editions_nano_2018/article/page-26031 Here’s a quote ”I happened to walk into a Walmart and as I was looking at their hammers I realized every hammer that had ever been made had been designed incorrectly. If you hammer things all day long with an ordinary hammer, the shock and vibration will eventually give you lateral epicondylitis, or tennis elbow. Manufacturers knew this and designed the shape of their hammer heads to minimize this effect, but that leaves you with a hammer with reduced momentum transfer. I figured out that if you put air into the hammer’s grip in certain strategic locations, you can eliminate most of the shock and vibration, and that allows you to change the shape of the hammer to give it greater momentum transfer. Now, almost all hammers sold in the US have this technology in them. The invention has sold about$1.5bn in total,”