[Jared Smith]

In hope of starting a discussion of broad interest I decided to see if anyone wished to explore and attempt to contribute to the Center of Percussion (CoP) topic/ definition in more depth.

At least one issue I am wondering about now is how we determine our CoP values in the myArmoury reviews, and how the manufacturers are doing it.


I will save you from a lengthy read and point out going into this that the definition of CoP given in Patrick Kelly’s “Understanding Blade Properties” article… http://www.myArmoury.com/feature_properties.html closely matches what sporting goods companies refer to the “sweet spot” of a bat or racket. It is actually a complex interaction of harmonics, mass distribution, and “effective pivot point” based on how an average athlete really pivots a club like implement using their wrists and arms when they swing it.


One ARMA article proposes a “waggle test” predicated on a “pivot point”, which I am not sure is realistic in terms of handling. http://www.thearma.org/spotlight/GTA/motions_and_impacts.htm

Baseball/ softball bat true hitting distance performance are based on a “sweet spot” which is something distinctly different from the CoP determined by mass distribution relative to the center of the grip area. This discrepancy results from the fact that in a realistic swing, the athlete pivots a club like object around a location that is actually behind the center of his grip (typically at their wrists or even farther up the arm.) I speculate that there could be some analogy between this “sweet spot” and the best point for a sword blade to strike a target intended for cutting. http://www.kettering.edu/~drussell/bats-new/cop.html
http://www.kettering.edu/~drussell/bats-new/sweetspot.html
Actually finding the true “sweet spot”, and rating a piece of sporting equipment (with legal acceptance from a governing tournament sanctioning organization), is a fairly difficult thing. Relatively scientific tests that simulate true usage pivot locations are typically employed (and required by law) in addition to validation by handling performance trials using experienced athletes. The overall certification process usually takes over half a year in the case of a “tournament certified” baseball or softball bat which may be produced annually in quantities of around 1000 bats priced at roughly $300 to $500 each. I know since my spouse worked at one such company and had to handle customer relations and technical explanations for one year when recall issues were imposed by the governing organization (governing organization rule changes imposed several million dollars worth of accumulated expense due to months of technical testing, alteration, and recertification efforts of about 100,000 bats previously considered legal for the affected company.)


An engineer (regarded locally as a genius) I greatly respect balanced my first premium sword vertically with pommel resting in his palm. He then “wobbled” it in the cutting plane and pronounced an “effective CoP” to be at an appropriate location (about 8” from the tip of a roughly 36” long blade.) He also struck the blade with his hand and a stick along various locations (trying not to contact it other than where struck while supported at pommel) and orientations pronouncing that vibration was pretty well dampened near the “desired cutting location for striking blows” based on visual judgment of the blade vibrations. His whole examination took about 10 seconds. Although this individual does not collect swords, within my regional engineering area he is recognized as a genius. At the time, his analysis did not seem quite right to me in terms of physics and grip location. What he stated as the important “effective CoP” actually was an entirely different location than this premium manufacturer’s stated CoP for the sword. As I have thought it over many times since, it seems increasingly amazing to me how he quickly and decisively he chose this method of assessment.

Some here may strongly disagree. However, I offer some controversial stuff to discuss.

Best impact performance as proven in sporting goods applications is often not the mathematical CoP based on an assumed pivot point at the center of grip combined with mass distribution calculations made based on that grip’s center.

Vibration and “perceived hand shock / reaction forces” within bats and rackets typically are minimized if impact occurs at the true “sweet spot” that delivers maximum impact energy to a ball as wielded by someone proficient with that type of tool. This is difficult to define in terms of CoP unless there is a convincing assertion of where the true pivot point is when a competent athlete swings the bat or racket.

[Angus Trim]

Hi Jared

I've seen a lot of discussion over the years over where the best place to strike a target with a sword is...and it depends. Depends on the sword and on the target........

Take for instance, the typical AT cutting sword. The tip is generally shaped for cutting, the edge geometry generally a good one for cutting.

If the target is something like a milk jug filled with water, the best part of the blade to use for cutting is the tip. a 2L pop bottle filled with water, just behind the tip. Cutting Mugen Dachi tatami mats, just behind the tip. Cutting 1/4 inch plywood though, and targets that offer that much or more resistance, then the best place to cut with on the blade, is the node.

This isn't done with any math, or any real armchair calculation. This is figured the old fashioned experimental way.... cutting with said sword against several different targets, and recording the results.........

If function is the main criteria, its been my experience that most quality modern swords intended to cut with react similarly......

[Craig Johnson]

[Marton Pap]

Hi!
As I see, the main difference in determining the location of CoP is where you want the pivot point to be, namely the cross guard (ARMA), the center of the grip (baseball bats), the pommel (the engineer) or even further back. As the ARMA article points out, if we put the CoP to the tip to cause the sword pivot around the cross, the use of a pommel makes sense, and increases cutting power.
Regards
Marton

[Jared Smith]

Thanks for the interesting inputs.

I had overlooked how different types of targets (thick wood, thin plastic jugs filled with water, etc.) might signficantly alter the percieved "sweet spot" of a sword. I suppose this has to be true since resistance and hand shock resulting from a target the sword does not pass through (maybe a tree or thick piece of opponents armour) is going to become a bigger factor!

Another key aspect of this topic is "Does everyone publish their CoP numbers based on the same method?" Specifically, are well all basing this on the guard as the pivot point, or are the manufacturer's doing their best to assess all of these difficult interactions (vibrational nodes, effective pivot points, qualitative test/assesment, etc.) and basically estimating the "sweet spot" of the sword?

Some might say there is negligible difference between the sweet spot and the physics CoP based on a non-debatable pivot point (pommel center, guard, etc.) I have a suspicion that discrepancies could become more significant as grip length increases (hand and a half...true two handed grip.) Those who hit well with a bat should contemplate where they place their hands when pitching for themselves (tossing a ball up one handed and swinging the bat one handed.) One handed grip location is instinctively adjusted several inches differently than where hands are placed when hitting two handed.

[Chad Arnow]

When we publish reviews here, we use that term as defined in Patrick's piece as the primary node: the place on the blade that will transmit the least vibration to the hand(s) during a strike. It's determined by holding the grip lightly and whacking the pommel. The place on the blade where the undulations seem non-existent becomes the COP (that's perhaps an overly simplified answer). It's a static measurement based entirely on vibrational properties of a non-moving sword. As far as I know, everyone calculates it basically the same way. It's not based on any pivot points; it's simply a sword-at-rest static statistic.

Like any measurement, it's only part of the story. What is at least as important as COP and POB is a sword's pivot point and its overall mass distribution. Location of the pivot point will vary from sword to sword and won't always line up with the COP. This thread has great info on pivot points and dynamic properties: http://www.myArmoury.com/talk/viewtopic.php?t=3154

[Steve Grisetti]

[Vincent Le Chevalier]

Hi all !

In fact, I've been thinking about this issue since the publication of the cited ARMA article, so it's about time I share my thoughts... I promised a while ago to write an article regrouping what I've been able to establish, but decided to delay that until I have a coherent whole and not just bit and pieces.

I've understood, skimming through posts here and on SwordForum, that this was a controversial matter that has led to heated arguments in the past, so I shall try to remain as fair and neutral as possible. OK, it's an important subject, but not one worth fighting about

I will not develop any computations or mathematical theories here, but I pray readers to believe that I've done computations wherever they were required... I'm finishing engineering studies, and it's been great fun to apply what I learned at school to swords

Right, enough of an introduction, let's get into it.

My belief is that we are confusing two things in this. When speaking about COP, COB, pivot points, blade harmonics, etc. people ordinarily think of two aspects : behaviour during impact or cutting, and handling properties. I think that trying to apply the exact same theories and criterias to those problems is not a good idea.

True, there are common features. When analyzing the physical behaviour of a solid like a sword, it seems obvious to me (mostly coming from my engineering background) that one has to consider at least three caracteristics of the object : its mass, its center of gravity and its moment of inertia. The center of gravity tells you where the mass is on average, the moment of inertia tells you how far it is spread around this average position, that is, how difficult it is to make the object spin around the center of gravity. Indeed, it's a proven fact of mechanics that as long as you consider the objects do not bend or deform, those three quantities are enough to resolve completely the behaviour. So my idea would be to leave the blade harmonics (which result from its deformation) for the last step, and start by looking at those three caracteristics.

The main problem, you see, is that they are not all that easy to measure, especially the moment of inertia. The mass is easy, you just need scales... The center of gravity is not that hard either, it's just a matter of finding a static equilibrium, we've all done that. The moment of inertia is impossible to determine by a static measure, you have to put the weapon in motion to measure it. And even then, it's not easy to measure, you have to deduce it from indirect measures of length.

The easiest way to measure the moment of inertia (that I know of), is the waggle test described in the ARMA article. It allows you to determine a pair of pivot points, and from these, to deduce the moment of inertia. It's a reasonably accurate way of determining this, as far as I've been able to try. I like best doing that with the tip pointing to the ground, since I feel it's more safe and stable that way, but the idea is the same.

There are, however, two problems with that moment of inertia. First, it's relative to the center of gravity, and thus does not reflect the ease of rotation around any other point. And even then, it's not an intuitive thing at all. It is expressed in units to which we are not really used (hey, who has an idea of what a kg.m² feels like...). Thus, the definition of other, derived caracteristics, such as the COP or variants of it.

As far as impacts are concerned, I think the interesting quantity, which we all try to maximize, is the ratio between the energy of the weapon before the impact, and the energy that disappears in the target during the impact. That's where the troubles start. This is something that depends not only on the weapon, but on the target and on the motion of the weapon as well. I think it's reasonable in most cases to consider that the speed of the target is way inferior to that of the weapon. So we are left with : center of gravity, moment of inertia, mass of the sword, its motion (roughly, around which point in space it's rotating, and at what speed), and the mass of the target. After a painful enough computation, the result exhibits a number of interesting properties, that are fairly representative of what Angus Trim and your engineer friend said.

When the target is an infinite mass (that is, something that will not move upon impact no matter what, such as the plywood boards Angus refers to, I think) the optimal point impact wise is the pivot point associated to the center of rotation of the sword just before the impact. In my personal experience (but I'm no expert swordman) it's difficult to make the weapon rotate about a point closer to the blade than the pommel, without loosing much energy before the impact... So your friend was just determining the pivot point relative to the pommel, and it's truly the most efficient point if you manage to get your weapon to rotate about the pommel. Now, the second thing is that when the target is not of infinite mass, this "perfect" point moves toward the end of the blade. This is I think coherent with what Gus said about dependency on the target...

But there is another thing with impacts, it's the effect you feel on your hand. It's not something I'm quite sure of, since all the calculations I've made rely on models for the hand that are, I believe, much too simplistic. Nevertheless, there is a sure thing, when you hit sufficiently close to the pivot point associated to your hand, you feel no shock at all. From my experience and computations, it's not so much a sweet spot but a sweet zone, and so is the area of "perfect" impact described earlier, thus there is always a significant overlap, of which a skilled swordman will naturally take advantage...

Blade harmonics are mostly significant when the impact happens sideways on the blade, which is not really expected when you are cutting, except if you missed your cut and end up with a bad edge alignment. In this matter, I mostly share the point of view of the author of the cited ARMA article. I believe that the effect is second order with respect to the properties mentioned before... What confuses the matter is that the node of vibration can be quite close to the interesting pivot points, specially on cutting swords, so that people might well be looking at the right point but with the wrong explanation.

Now, on to the handling properties.

Interestingly enough, the "dry" feel of the sword seems to be widely believed as related only to the position of the center of gravity. As far as I understood the various reviews I read, the center of percussion and/or blade harmonics are given mostly to evaluate the behaviour during impact, and not during handling and motion. True, the static feel of a weapon (what you feel when holding it motionless) is related only to the center of gravity. But, well, most of the time your weapon is moving, so my guess would be that we miss a significant part here... It's the section I'm still not completely satisfied with in my study, but I do have some interesting results. Specifically, I found that the perceived blade mass of weapons, when you consider only actions relative to one point (your hand), is just the ratio of the distance between your hand and the center of gravity, and the distance between your hand and its associated pivot point. It seems to work best, maybe for psychological reasons, when you choose the index as a reference. It does not tell the whole story however, since it does not take into account the fact the hand is not a point... Still working on that, but I would appreciate if the collectors here could try this with their swords, and tell me if they feel it's significant. I think it is, I've chosen iaitos and bokens already with that, based on what I know I like as a blade mass. I've used it to compare all the weapons I've come accross, and I'm already quite happy with the result...

I believe as well, but that would need some neurological evidence, that the tip control you have is directly linked to the position of your hand's pivot point relative to the tip. I've seen evidence of this comparing sabers, cutting swords, thrusting swords, even foils and bokens... I like to compute a "tip behaviour" caracteristic, as the ratio of the distance from COG to the pivot point of the hand, and the distance from COG to tip. I used that as well for iaitos and bokens. Seems to work decently, try it yourself and please tell me what you think...

Now, I'm writing about that, because I think that when it comes to measurements, we tend to focus far too much on impact properties. I mean, a sword will do significant damage when it hits with a good edge alignment anyway, the dependency upon the point of impact is only a slight variation... On the other hand, handling caracteristics do vary, and affect what moves you can do with the weapon. In short, a good sword and a good axe both cut efficiently, but you should not handle an axe like a sword...

Sorry for the extra-long post (partially off-topic, maybe), but I feel that subject is well worth a lengthy explanation, and I've been working a lot on it so it's hard to stop I'd appreciate any feedback and questions, of course, and I shall still try my best at writing an article on that, but I really couldn't resist posting a reply

Cheers

[Angus Trim]

Hi Vincent

I hope you don't mind a bit of a disagreement with your analysis.......I agree it looks good if what we're talking about is stiff swords like katanas, or something like crowbars.... But most western swords aren't as still as katanas.........

There are both videos and stills, of antiques { a saber cut, from horseback, on a melon, in Australia} and modern swords that show both the edge alignment of the strike, and the blade action during and after the cut...... Quite often what you see, is a blade whipping both during the cut and afterwards {even with a strike with the edge alignment being spot on}. Quite often, the cutter is actually unaware of this happening. If the nodes are in the kind of alignment that a few of us call "harmonically balanced", then in a good cut its likely the cutter will be unaware of the blade action.

Years ago, before I began swordmaking, I was a sword reviewer. At one time, I had 7 type XIIs from 3 different makers, all within 2 inches of blade length, and 3oz in weight. But cutting in 1/4 inch plywood, one was outstanding, with consistent cuts in the 8.5 to 9 inch range, and one was poor in comparison, averaging 5 inch depth of cut. Most of the other swords were grouped around 7 inches, but it varied. I had newly met Tinker at that time, and mentioned my findings to him. At that time, he explained "harmonic balance" to me, and suggested I look over things again. I did that, and funny thing was that the "harmonically balanced" sword cut deepest, the one that stung my hand was worst, and where the hilt node was, also pretty much explained the rest of them too.........

It gets better........

Having experimented for years on this, a few years ago, I discovered that one needed to have the distal taper work with the wave action of the blade. If the character of the blade was just a bit off, and the sword cut something with enough resistance, it could very easily take a set in this one spot. The first time I saw this, I didn't believe it.... I made a model of sword that tested out pretty country fair. But the first three that were sold all came back bent, all in exactly the same spot. The heat treat was spot on......... After blade redesign, the model became quite successful.

After that experience, I tested new models for it, and managed to catch several before releasing them. Having made over 250 models {many of them one offs}, I've done a lot of experimenting and cutting.........The distal taper and the wave action of the blade have to compliment one another for best results........

Its my opinion that skipping harmonic balance in the discussion of the physical properties of the western sword is the biggest mistake some people make. You don't need to worry about it with kats, they're too stiff. But then again, even baseball bats have "sweet spots" where there is little to no vibration on impact, and these are the best spots to strike the baseball.......

The reason I mentioned target choice earlier, is if the target doesn't really give the blade any resistance, the blade can be thru the target before there is any sideways action to the blade. Once you get that resistance, then harmonics impact cutting performance, and durability..........

The reason I mention the blade node as the cop, is that I used to cut 1/4 inch plywood to measure some of this. Cutting on that node always produced the best results. Cut outside the node, cut inside the node, the cuts would measure less, and you'd get more blade action {depending on rigidity of course}........

The node and lethality of a sword cut? Not so much...... In unarmored combat, the tip is/ would be every bit as lethal as the cop. Particularly with a tip geometry for cutting....... The tip wouldn't do as well cutting in plywood, but would be more than good enough to take a throat out, remove a wrist, etc..........

[Jared Smith]

I suspect the statistic that is so often published as “CoP” in sword reviews is the correct and relevant dimension. It is probably extremely important that lessons from people like Angus should not be discarded.

I am not sure “CoP” is the right term for it. (Sort of advocating something like “sweet spot” here which is what other industries have adopted in recognition of the difference.) I admit that at some points we have to accept compromises (recent sword "point" versus "tip" terminology topic comes to mind.) Then again, not everything needs to fall apart technically, and has not in sporting goods industries that face a very similar issue as what I hope some might address here. If no one really cares for physics and precisely defined terms, the issue may go the same way as the automotive term for “radiator” (a device which in fact rejects something like 10% of it heat by radiation, mostly by convection… should have been called a “convector” or simply “heat exchanger.”)

A physics book will state nothing about vibrations resulting from striking something at the mathematical CoP. In fact, weird demonstration devices could be constructed for which CoP is “close to” the worst possible place for impact in terms of vibration nodes. If rotational form is absolutely perfect, the vibrations theoretically do not have to occur. Such an object would probably be worthless as a sword, but is possible.

One of my first regular paying jobs was at a golf course (almost two decades ago.) I noticed an old gentlemen (estimate octogenarian) who occasionally visited the driving range and consistently hit balls further than anyone else with deceptively gentle effort. One night I attempted to emulate him with no success. A couple of evenings later he returned with a “teaching tool” intended specifically for me. This tool was a wooden handle, with a rubber strap the length of a shaft appropriate for my size, and a club like metal head at the end of the strap. His teaching tool would reward only perfect form with good hits. It is not a perfect analogy, but an example of how CoP does not have to correspond with a variety of other complex and desirable aspects (stiffness for thrusting, vibration, forgiveness of alignment, etc.) of a club-sword like object’s physical characteristics.

[Vincent Le Chevalier]

[Vincent Le Chevalier]

[Marton Pap]

Really interesting!
This practicing tool reminds me what the Döbringer manuscripts says:

Know also that a good fencer should
before all things know his sword and be able
to grip it well with both hands, between the
cross guard and the pommel since you will
then be safer than if you did grip it with
one hand on the pommel. And you will also
strike harder and truer, with the pommel
swinging itself and turning in the strike you
will strike harder than if you were holding
the pommel. When you pull the pommel
in the strike you will not come as perfect or
as strongly.

This and the practice tool together underlines the importance of the pivot point related to the crossguard. As I see now it should be adjusted close to the tip with the mass of the pommel, and the blade should be light enough and the vibration node carefully adjusted far from the cross, so the pommelweight doesn't pull it back much, thus the two points (pivot and vibration) can stay close together and close to the tip.
The other thing I have been thinking about recently is the taper and the node, like Angus mentioned. If the node is mainly influenced by the taper and less by the shape [hexagonal, diamond etc.]of the cross section, than it would be extremely interesting to carefully measure the change of the cross section size [square millimeter] along the blade of some original swords. Does anyone know about such research? I think laserscanning is precise enough but I think it is quite expensive.

I really look forward to read your opinions!

(It would be exciting if the swords have the same overall taper, and even more if they don't have the same but could be categorized into two or three families.)

[Craig Johnson]

Excellent discussion guys

[Joel Whitmore]

[quote="Vincent Le Chevalier"]

[Jared Smith]

I honestly just happened to run across this relevant article.
http://en.wikipedia.org/wiki/Center_of_Percussion

I personally consider vibrations relevant to handling. I will admit that for typical longswords, vibration is primarily in a plane perpendicular to the cutting arc, and probably amounts to less than 5% of the total performance. That is not insignificant when one considers how many times a sword could have been swung (historical accounts of durations of battles and sword edges hacked up like saw blades after battles tell us a little...) A 2- 5% difference may be a life and death issue over the course of a few hundred swings with unimaginable fatigue progressing throughout such a day of battle.

I also admit that a "sweet spot" on athletic equipment is not the same for everyone. Those labels on bats or discolorations on racket strings (tyically 3 to 5" long) are generally large enough (based on testing) to encompass a large range of athletes' styles who have shown any decent performance capability with the equipment though. There is a statistical exact spot for the label as well. That "statistical center" of the sweet spot is actually pretty darn close to the perfect sweet spot for something like 75% of bat users according to the company my spouse worked at. When tasked to "reverse engineer" what the effective pivot point of a bat must be based on the empiraclly proven "sweet spot", it is generally much closer to the pommel like end of the bat, than it is to the grip area center. This tends to be an amazingly consistent truth of a wide range of club like objects (rackets, bats, golf clubs, etc.)

[Jared Smith]

A couple of more thoughts and speculation here. Let me preface it by saying I consider the Peter Johnson's and Angus Trim's to be the masters. My opinion does not count for 1% in my own estimation of what their opinions count for.

(Another over-simplification.) Take a piece of standard round pipe of very uniform dimensions. Hold it with your hand exactly in the center. Twirl it like a batton. In this instance there are two "CoP"s located at each tip of the balanced spinning piece of pipe/ batton. Hold it any where else, there is only one CoP. In fact, there are infinate CoPs for anything depending on how you grip it and what the real "effective center of rotation" actually is. CoP is entirely dependent on an assumption. There are an infinate number of CoPs for anything, including swords. They are greatly different in the case of "murder strokes" than they are for typical strikes. "CoP" without a qualification of what it is in relation too is meaningless.

Let's just say some correct expert has determined this perfect spot on a sword blade to hit some type of specific target with. I fancy myself better (admit I offer no proof) than a mental retard with regard to logistics. What will be of interest to me is how far that point is from the guard of the sword. That represents to me how far I can be between my last line of defense and my opponent while I do him optimal harm. Not all sword like objects have guards. But for those that do, what interests me is how far that "sweet spot" is out in front of that guard. When I read reviews, I often don/'t know exactly what the "CoP" or what ever you want to call it is being dimensioned from. I would like to see some type of "important blade point / sweet spot" defined with respect to sword guards. Right now, I am not certain what various manufacturer's are giving this dimension in relationship too.

Lastly, "CoP" does little credit to all that craftsmen who have spent years of making, testing, and refining have actually invested into these works of art. I do not doubt that they ascertain in mere seconds exactly what is important at some specific point on the blade of a sword.

[Chad Arnow]

As far as I have seen, any maker who talks about the CoP is referring to the blade node where vibrations are best dispersed. As far as I've seen, everyone measures it as a distance from the guard. I've never seen any confusion over this.

This stat does have some relevance, hence its inclusion in so many places. I check the CoP before cutting with a new sword, because my experience (whatever it may be) has shown that more powerful blows generally come from the CoP. More comfortable blows certainly do. Knowing where it is certainly helps me. I've used swords where off-CoP cuts vibrate badly, usually when I've struck behind (guard-ward, not tip-ward, of) the CoP. Certainly some swords and cutting media respond very well to slashes by the tip and other outer-part-of-the-blade cuts as well.

It's just one stat of many. How it mates up with pivot points and how a sword's overall mass is distributed is much more important. While it is relevant, I wouldn't try to make too much out of it.

It's a static measurement that shows a region on the blade where many cuts will be effective. How well the sword moves is determined by balance, weight, and mass distribution more than CoP.

But that's just my two cents.

[Jared Smith]

[Chad Arnow]