[Vincent Le Chevalier]

Greetings all,

As questions about sword balance tend to pop up from times to times on this forum, it seems to me that a kind of "literature review" is missing. There have been over the years a lot of discussions about that, some articles published on various websites, great insights given by sword smiths and users. I think we now need a place to give commented pointers to all that information. It could save some tedious search for someone who does not really know what to look for... Good keywords can be hard to find.

I shall start by articles that I think are essential in order to understand what is being discussed in many forum threads. I will then give links to some threads and posts that I found particularly enlightening...

I'll try to give a short comment on what each link is about and how I think it is relevant, while trying to stay as neutral as possible. Of course, since I was a participant in some of these discussions, and have my own opinion on the matter, that last objective will be hard to fulfill All the comments thus reflect only my own opinion, and I apologize in advance if I'm misinterpreting what is said. Feel free to correct me...

This will be a fairly long post, but I feel the topic deserves it.

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Let us start by the featured articles here on myArmoury:
http://www.myArmoury.com/feature_properties.html by Patrick Kelly

Covers briefly all the basic properties, geometry, harmonic balance, and some dynamic (CoG). It lacks a description of the pivot points, as well as a discussion of how all these interact, but admittedly there is no consensus on that last point at the moment. The terminology article at Albion's site can be used to see a brief discussion of pivot points (possibly based on insights from Peter Johnsson):
http://www.albion-swords.com/swords/sword-terms.htm

Another interesting feature is:
http://www.myArmoury.com/feature_heymister.html by John Clements

That covers some aspects of sword design, among which balance. It's a qualitative analysis of how the aspects interplay to make a sword that behaves historically. It doesn't go into much details about what to measure, however.

Basically, sword balance is split between what is termed harmonic balance (the way the blade vibrates) and dynamic balance (the way the weapon moves when handled). Harmonic balance has been abundantly debated for several years now, and is the theory most people are familiar with. Dynamic balance is perceived as being more obscure somehow (really, it shouldn't be in my opinion).

For a summary of harmonic balance, I'd recommend looking at the following "sticky" threads over at SwordForum, by Michael Tinker Pearce:
http://forums.swordforum.com/showthread.php?t=42946
http://forums.swordforum.com/showthread.php?t=51960

The whole threads are interesting as illustration of what the harmonic concepts can and cannot bring. I do not agree with everything said in the discussions, but the phenomenon remains true.

As far as I know, the first published work involving inertia and pivot points (fundamental for a study of dynamic balance) is the article by George Turner, from the ARMA:
http://www.thearma.org/spotlight/GTA/motions_and_impacts.htm

There is a more complete (and mathematically heavy) version of this article here:
http://armor.typepad.com/bastardsword/sword_dynamics.pdf

The first part is pretty much a must-read for mass distribution and pivot points. Even though I do not necessarily agree with the way the physics are presented, the author does a very good job explaining with as few equations as possible. The rest of the article I find less convincing, because it tends to simplify the situation too much. The author tends to focus on proving how the forward pivot point should be at the tip, which is not true in my opinion.

Sadly, this article suffered from some political orientation and use, and perhaps because of that was not debated and expanded as it should have been. It has also caused some kind of silence afterwards, as the simple fact of bringing up balance problems in a discussion tended to degenerate.

The only academic, scientific paper on sword balance that I'm aware of is the following publication:
Swordplay: an exercise in rotational dynamics, Mark Denny, 2006, Eur. J. Phys. 27, 943-950 (sadly, not freely available as far as I could find).

Interesting from the physics point of view, but it seems the author is not so much knowledgeable of swords and their uses. Thus, he misses several possible applications of his physics... It is a bit similar in the end results to Turner's article. Some of the assumption about mass distribution are too rough to be really useful for an analysis of real swords in my opinion.

Dynamic balance has also been talked about under the term Polar Moment, particularly in this other sticky from Michael Tinker Pearce:
http://forums.swordforum.com/showthread.php?t=51519

Overall I believe it brings little to the matter, as it is essentially observing the same things as those who works with inertia and pivot point, but calling them differently... Besides, it lacks clear relationship with an actual theory in physics, since a parallel terminology is used.

As a final note, I would like to point out that many of these concepts are not exclusive to swords. For example, see these articles on the COP and sweet spot on baseball bats:
http://www.kettering.edu/~drussell/bats-new/cop.html
http://www.kettering.edu/~drussell/bats-new/sweetspot.html

Not everything from sports is relevant, though. Generally, there are regulations on sporting implements, that put constraints on what is possible or not. Besides, baseball bats for example are not meant to fence with. All that matters is one swing and the impact. No recovery, no thrust, no flowing from guard to guard...

With all that, all the discussions that happen currently can be understood. And you can even start forming your own theories... That's what I did Looking at more recent discussions gives an intersting variety of viewpoints, though, hence the next section.

******************

There are in fact many areas of shadow in all these theories, and they are all quite complex to grasp. Thus, many discussions happen in forums about these subjects, that are sometimes very informative because they highlight the strong and weak points of each. Generally, they are started by people that do not consider themselves expert in the subject, asking simple questions that tend to bring long, but informative answers, often by noted sword smiths.

I like to split these discussions into three categories: questions about the very definition of the properties, questions about what values are expected for some properties (generally asked by users/buyers), questions about how to obtain the right values when building a sword (generally in answers by sword makers).

This spotlight thread is a mix of all three. It is full of good discussion of various properties, how they are linked, how to measure them:
http://www.myArmoury.com/talk/viewtopic.php?t=8088

The first type of questions is interesting because it can highlight inadequate or imprecise terminology, or overlapping between terms from different theories. For example, this spotlight thread was started on the definition of the Center of Percussion (CoP):
http://www.myArmoury.com/talk/viewtopic.php?t=6986

The heart of the matter is that there are two things that are called CoP, one for harmonic balance, one (at least, depending on whether you are looking for "least shock in the hand" or "maximum energy damaging the target") for dynamic balance. Sometimes the end up at the same place, sometimes not, and there is confusion as to what CoP we are talking about. That said the whole thread offers good insights, and as is often the case wanders on all the other aspects.

Questions about what values are expected for a given property are also numerous.

Many revolve around the efficiency in cutting. Sadly, these discussions are weighed down by the number of unknowns. There are quite simply too many things that change, from sword to sword, target to target, motion to motion. As far as I'm aware no discussions went further on that subject than the articles I referred to earlier. In fact I believe cutting has been given too much focus, as also said Matt Easton in this thread:
http://forums.swordforum.com/showthread.php?t=52099

Quite often, when asked about a particular metric, such as CoG recently, one can only answer "on its own, it does not mean much". Often the discussion ends up in exposing how all the other properties are important as well, as in this spotlight:
http://www.myArmoury.com/talk/viewtopic.php?t=3154

This has lead part of the community to discard the "scientific approach" on the basis that swords are too complex to judge that way. This view is expressed by several posters in this other spotlight thread:
http://www.myArmoury.com/talk/viewtopic.php?t=288

I agree that probably all these numbers did not matter in the old days. But I do think they matter now, because we have a communication problem. Many are buying swords without being able to handle as many as they would like before. Numerical stats allow us to clearly communicate, in reviews for example, objective aspects of the weapon. They also enable us to spread the information on antique specimens, to which few of us have access.

The stats we use today (various length and width, PoB, harmonic CoP at best) are not satisfying because they give very little information about handling. It does not mean that there are no ways to find some other stats that do...

Angus Trim kindly pointed out to me that Don Nelson proposed in 2002 a new metric that he felt was more directly linked to handling:
http://forums.swordforum.com/showthread.php?t=6821
http://forums.swordforum.com/showthread.php?t=9057
http://forums.swordforum.com/showthread.php?t=20110 (be sure to check Don's own explanations in these two last threads)

The first formula he used was closely linked to inertia. In fact, it was the formula for computing the moment of inertia of the weapon, assuming that the forward pivot point was at the tip. Unfortunately, the use of that metric was limited, perhaps because summing up everything by just one number is indeed impossible.

I have a different take on the subject, that I exposed in this post, in one of the aforementioned spotlights:
http://www.myArmoury.com/talk/viewtopic.php?p=83521#83521

I have changed the metrics a bit since, but I still haven't finished writing about it. The principles hold true, though... I will not expand on that here since I'm obviously biased

The third category is of special interest because it shows how sword smiths try to control the stats of the weapons they are making. Angus Trim, Craig Johnson, and Peter Jonhsson posted great info here over the years, as to how they design swords. Much of it can be found in this spotlight topic:
http://www.myArmoury.com/talk/viewtopic.php?p=31012

Apparently all stress the importance of the blade shaping, and conceive the pommel as only a final adjustment. There are differences among smiths, of course: Peter Johnsson pays more attention to the pivot points, Angus Trim to the harmonic balance, for example. I suspect these are just different ways to achieve the same kind of results.

I posted an outline of a theory I have on how adding/removing mass acts on pivot points and generally dynamic balance, and on why starting with the blade makes sense, but unfortunately it's not quite as developed or clear as it should be:
http://www.myArmoury.com/talk/viewtopic.php?t=10070

Peter Johnsson made a diagram for Albion showing the same kind of effects:
[url]http://www.albion-swords.com/articles/images/sword-dynamics.pdf

I also explained a simplistic version of that in this thread:
[url]http://www.myArmoury.com/talk/viewtopic.php?p=83236[/url]

The thing I was not able to find is how modifications of the mass distribution impact the harmonic balance. Or rather, what predictions can be made beforehand, as to how the nodes will move. I've seen a lot of empirical descriptions, but it seems that the effect is too complex to figure out in advance and predict. If I have overlooked something, feel free to correct me...

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That concludes this long post. I hope it will help enthusiasts to get a wider view of all the concepts involved...

If anyone has favourite articles/posts to add, they are most welcome. I'm quite sure many things have been said that I have missed... I'm also certain there have been articles published on other supports. I've limited myself to the Internet because that's what I've been reading specific to sword balance.

Kindest regards,

[Vincent Le Chevalier]

Another thing, going a bit off-topic in my own thread

While doing this literature review and wading through all the posts, I have drawn this little diagram that show how the various concepts interact with each other, and what we really measure.

This ends up looking like a bunch of noodles , but I still figured it could be of some help to have a more visual representation of what affects what.

The straight boxes are concepts, they are linked by arrows that shows the influence they have on other concepts. For example, Geometry affects Grip (through handle shape), Mass distribution (because it determines the volume and position of the elements), Stiffness distribution (through cross-section especially), and Cutting (edge geometry).

The curly boxes are measures, things that can be found in reviews, for example. I've put only three of these boxes: the Harmonic stats include CoP, grip node, and secondary nodes, NSHR is the metric I briefly described in the previous post, invented by Don Nelson, Dynamic stats (for lack of a better term) are what I would like to define, a set of numbers based on mass distribution (pivot points and center of gravity), hands position, tip of the sword... The blue dotted lines indicate the concept that is measured. Note that all these take the grip into account...

The last thing I've put on the diagram is perhaps the most subjective. It's all these percentages... They just reflect my opinion at the moment, I must stress that.

Around some concepts, you can see a percentage next to the arrow coming from another concept. These represent the relative influence on the central concept. For example, I consider that the Cutting behaviour is affected 40% by the target behaviour, 30% by the sword dynamic model (that includes user actions), 20% by geometry (without cutting edge, no cut), and only 10% by harmonics.

And next to the blue links, there are percentages that represent what fraction of the concept is actually measured. For example we rarely measure the grip fully (at best beginning/end). I've only attributed 50% of the harmonic model to the harmonic stats because really, we only capture part of the vibrating behaviour of a sword (proof is, a sword struck at the CoP also vibrates, just differently). In fact we see at best two harmonics, and without even the waveform.

As I said this last part is largely subjective, and open to debate. I felt it was necessary to include this, in order to keep a perspective on what has the strongest influence.


I'm sure this representation is lacking many things. Feel free to post any suggestion or criticism. I'm wishing to improve that...

Best,

[Jeffrey Hull]

[Angus Trim]

Good post Vincent. I suspect that what you have posted could become a very good resource........

[Vincent Le Chevalier]

Jeffrey,

[Jared Smith]

I am curious (not really arguing, had just not evaluated it before) about your comment about disagreeing with GT's claim that pivot points near the tip of the sword were a primary historical objective of large pommels.

A section of his article that might be what your are referring to reads; "If the desired pivot point was anywhere near one third back from the tip, why use a pommel at all? Just leave it off and have the sword pivot around a point about a third back from the tip, just like a saber. So I would say that if a sword has a real pommel, it would only logically be used to create a pivot point very near the tip."

I can see two sides of the argument; Wanting to make damage significant at maximum reach. Wanting to dampen hand shock from natural harmonics when striking at the CoP. Is it possible that historically accurate (heavy) pommels do a good job of achieving both?

[Vincent Le Chevalier]

Hi Jared,

As far as I'm aware, the fact that original swords would all have the pivot point of their cross located at the tip is unsupported... Which means that any explanation as to why this would be optimal must be missing part of the picture. For this I rely mainly on observations Peter Jonhsson made, because he has been documenting a good number of originals with respect to pivot points. A rough summary of the conclusions can be found on Albion's site (http://www.albion-swords.com/swords/sword-terms.htm):

[Joseph Fonzi]

[Vadim Palshin]

Great thread, guys, and the collection of links is priceless. I have only started thinking about this very recently, and it’s very enlightening to see all the discussion from the previous years. I would like to add my opinion to this, it’s certainly not original but I think this point needs reiteration: the key property which determines how a sword will move and respond (a.k.a sword handling, dynamic balance, etc…) is its Moment of Inertia. It's the axis that ties together most other variables: PoB, weight, length, mass distribution, pivot points, taper, etc. My PhD is in Materials Science, but I have enough Engineering background to see that George Turner is exactly right on this, even though his other points may be wrong. This article: http://www.iop.org/EJ/abstract/0143-0807/27/4/025 is also correct, although the model used to describe a sword is a little simplistic, basically a stick with a pommel. As my own modest contribution, I have posted a slightly more realistic calculation here: [url]http://www.thearma.org/forum/viewtopic.php?t=23300 [/url]
It takes into account distal and profile taper, which makes a huge difference. I am still waiting for volunteers with experience, access to many (good) swords and some free time on their hands to test it. Please? Anyone?

[Vincent Le Chevalier]

Hello Vadim,

[Joseph Fonzi]

Vadim

spot on!

i'll have to look at that formula you posted and compare it to what my 3d cad model tells me for a moment of inertia. where did you base the axises for I at the guard?

i completely agree with you post on http://www.thearma.org/forum/viewtopic.php?t=23300.
and yes of course to close the loop the big need is to find what the dimensions and weights are of swords (by type) that handle and cut very well and see what moments of inertia ( and radii of gyration , etc) are.

i might even turn out to be as simple as GT's paper said about most historic swords having a center of oscillation or percussion at the tip with reference to the base of the blade at the guard, then the pendulum test would be all you need.

so where are those volunteers with the spare time.

Joe

[Vadim Palshin]

Hurrah! Finally, I have found some sword enthusiasts who believe in physics. Thank you, gentlemen! We could give this a try, slowly building up a database of measured and calculated swords. If enough people contribute we could reach some critical mass where this project would actually become useful.
Josef - yes, it will work best relative to guard due to some assumptions I made to simplify the math. But it's not a bad thing - it could be used as a yardstick to compare different swords, and then one could use it to do more accurate calculations for any pivot point.
Vincent - I missed your recent thread; lately I have only checked the historical arms forum, and probably missed a lot of good stuff on the off-topic one. I must say that I like your approach better. A numeric solution should be more accurate than an analytical one. It's more universal and does not make as many assumptions. For example, the weakest part of my model is the assumption that the cross-sectional area changes linearly along the sword's length. It will work fine as an estimate, but you'd almost have to construct a new model for each sword shape to get any real accuracy. Yes, I'd like to see your type XI measurements - could you PM them to me? - and then we could compare the results.
Vadim.