Meaning of "center of mass" of weapons?

[Ed Rybak]

Hello to all. This is my first post here, after many months enjoying the articles and other resources. You've got a fascinating field of study.

I have a question which I hope is a simple one. Reading about swords and other weapons (even sporting goods, on other sites), the terms "center of balance", "point of balance", and "center of gravity" come up often. I think these refer to the same thing: the point at which the object, laid horizontally, will balance – something easy to find with just a fingertip.

What about "center of mass", though? Is that used with the same meaning as center of balance? Or – my guess – is it the point at which the object, if cut into two, would result in two parts of equal mass?

To clarify: For a uniform rod, that point would be the same as center of balance. But for a shaped object like a sword, it wouldn't necessarily be the same; the way mass is distributed could make the two points differ quite a bit. (This center of mass might also be hard to measure in real life, but still meaningful in mathematical discussions, where I've seen the term come up – though again, without clear definition.)

So: When a text mentions "center of mass", how should I understand that?

Thank you!

[Stacy Clifford]

Yes, the center of mass should be the point at which the mass on either side is equal. If you really want to delve into the science and engineering side of things, I recommend reading this article:

http://www.thearma.org/spotlight/GTA/mo ... mpacts.htm

[Ed Rybak]

Your recommendation is a good one; I've read George Turner's amazing essays on the physics of swords. I've never seen better resources on the topic.

With respect to my particular question, though, his essays are among the many resources out there that make separate reference to both center of balance and center of mass, without clarifying whether these are the same or not.

(To complicate things a bit more: While the two could have differing meanings, and while I agree with you that they also should, the Wikipedia entry for Center of Mass pegs it as being the same as center of balance. For what that's worth.)

So I still don't know the answer, but thanks for the input! If anyone else does know of an authoritative word on the matter, I'd love to hear it.

[Vincent Le Chevalier]

If you want to be really technical:

• center/point of balance is a point where you can apply a simple force (no torque) to support the object in a static situation
• center of mass/inertia is the average position of the mass of the object
• center of gravity is the point at which the actions of gravity on the object are equivalent to a simple force

If you are in a constant gravity field (which is the case at the human scale) and if you believe in the equivalence of inertial and gravitational masses (which you should because it's been verified to some tremendous precision), center of mass and center of gravity are precisely the same point.

Point of balance is more problematic. For example if you have a ring, all the points in the inner circle are points of balance, and of course none of them are the center of mass, which is actually at the center of the ring. In the specific case of swords, this usually refers to the point of balance that allows to rest the blade horizontally. This point is just right below the center of gravity when the blade is horizontal, which is why the names are used interchangeably in that context. Moreover, the position of the center of gravity along the longitudinal axis is the dimension that has the greatest impact on handling properties. The other dimensions can often be deduced directly from the axis of symmetry of the sword, and since swords are far longer than they are wide or thick, do not vary much.

The thing you describe here:

Or – my guess – is it the point at which the object, if cut into two, would result in two parts of equal mass?

Has no name, because it does not really influence the physical behaviour of the object. Look up definitions of mean (what center of mass/gravity is) and median (which is what you describe).

Finally if you're interested in sword physics you could read my own article

Regards,

[Ed Rybak]

Thank you for the very helpful response. That really clarifies some things. The example of a ring is an interesting one, though since my interest is bar-like weapons, with no unusual complications like non-constant gravity field, I understand that I can read center of mass, center of gravity, and center of balance (for a horizontal weapon) as referring to the same point along the weapon's longitudinal axis. Got it. (I hope.)

I discovered your article shortly before posting, and have since read through it. Your two-mass equivalent model is exactly what I had in mind when I was envisioning the median point of mass (yes, median is the word I was looking for; thanks!), as using such a model, shifting the two masses independently of each other will change the center of mass/gravity/balance without changing the median point of mass. Hence my question.

What I understand from your comment is that, yes, one could talk about that median, but it's not a particularly meaningful piece of data for weapon handling properties, and thus isn't likely to be what an author refers to when making an unclear mention of some point on a sword. Assuming I've got that right, I'll set aside the median point as an unneeded bit of data.

Your article is nicely succinct and clear, though there are a few simple points I'd like to confirm. Would this thread be an acceptable place to ask questions, or is there an existing thread on your article? (Or does this forum discourage threads that focus on weapon physics instead of fightin'?)

Thanks again!

[Stacy Clifford]

You're welcome to ask your questions here; this is a sword forum after all and we're curious about the answers too.

[Vincent Le Chevalier]

What I understand from your comment is that, yes, one could talk about that median, but it's not a particularly meaningful piece of data for weapon handling properties, and thus isn't likely to be what an author refers to when making an unclear mention of some point on a sword. Assuming I've got that right, I'll set aside the median point as an unneeded bit of data.

That's pretty much it yes... Actually I have no idea how you could measure that point if you wanted too, because it has no influence on the physical behaviour of the object. The only way would be to break the weapon into tiny pieces which is ordinarily unacceptable

Your article is nicely succinct and clear, though there are a few simple points I'd like to confirm. Would this thread be an acceptable place to ask questions, or is there an existing thread on your article? (Or does this forum discourage threads that focus on weapon physics instead of fightin'?)

That's really up to the mods, but if you wish to discuss my article specifically I had a thread about it here... I'd be glad to read your feedback!

Regards,

[Ed Rybak]

Thank you all for the replies. Vincent, I'll shortly direct my questions about your article to the thread you mention.

Before that, I have one last note on my "center of mass" question – particularly, an example of the jumbled usage out there that unfortunately leads to confusion.

Your excellent page of links at http://www.myarmoury.com/talk/viewtopic.php?t=10758 includes a link to Albion's Basic Sword Terminology page at http://www.albion-swords.com/swords/sword-terms.htm . That's a nice resource, though it does contain this oddity:

"CoB": The Center of Balance (also known as the "CoG"- Center of Gravity, or "PoB" - Point of Balance) is the point along the blade where the sword has equal mass on either side.

Hmm, that's saying that CoB/CoG/PoB are all the point of median mass! That seems to be a flat-out mistake (true for uniform rods, or other longitudinally symmetric objects, but not for swords). It's particularly surprising to see the mis-definition on a respected sword maker's terminology page. (I expect that it's simply a mistake that slipped through Albion's editing, and that the smart folks there know how CoB/CoG/PoB actually work.)

I mention that just as an example of why people like me get confused. : ) Anyway, unless I hear otherwise from an authoritative source, I'll stick with your earlier clarifications as the sensible definitions.

[Vincent Le Chevalier]

Your excellent page of links at http://www.myarmoury.com/talk/viewtopic.php?t=10758 includes a link to Albion's Basic Sword Terminology page at http://www.albion-swords.com/swords/sword-terms.htm . That's a nice resource, though it does contain this oddity:

"CoB": The Center of Balance (also known as the "CoG"- Center of Gravity, or "PoB" - Point of Balance) is the point along the blade where the sword has equal mass on either side.

Hmm, that's saying that CoB/CoG/PoB are all the point of median mass! That seems to be a flat-out mistake (true for uniform rods, or other longitudinally symmetric objects, but not for swords). It's particularly surprising to see the mis-definition on a respected sword maker's terminology page. (I expect that it's simply a mistake that slipped through Albion's editing, and that the smart folks there know how CoB/CoG/PoB actually work.)

Ah yes indeed, it's been a while since I looked there but this is a mistake.

Note that in practice this is of little consequence, because even when people think that they are measuring the median, all they can really measure physically is the average So there is no problem with some people giving the mean and others the median; everyone gives the mean. In a way the only confusion is in what people think they are measuring. It's important too of course... But at least the data is consistent.

I don't think that confusion affect Peter Johnsson's designs in any way (actually he might very well not be the person who wrote that page anyway).

Regards,