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Vincent Le Chevalier




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PostPosted: Wed 01 Aug, 2007 2:34 pm    Post subject: Linking harmonic and dynamic balance         Reply with quote

Hello all!

In keeping with my sword/math geek usual behaviour, I was crunching some ideas and concepts earlier this evening, and much to my surprise, came out with something rather simple and yet midly interesting. This is rare Happy

So there has been quite a lot of discussion recently about CoP, CoB, how they interact and how they are defined, how you can find them, etc. There are currently two ways of understanding swords: the most anchored in the community is based on vibrations of the blades, and there is another, that I think is promised to a bright future, based on dynamics of the sword considered as a rigid body. In the first, vibration nodes are the key, in the second, pivot points are.

Ever since this previous post I've had in a corner of my head that both are in fact closer than it seems. Well, now I have a mathematical proof...

So tonight I took all my steel swords (Atrim Type XI, A&A Milanese rapier, Darkwood Armory rapier) and located both the hilt and blade nodes on each. On each and every sword, they were associated pivot points (within the precision of my measures, about half an inch I would say). The blade node was the pivot point of the hilt node. Then I tried that with my wooden swords (you can locate the node by the special sound they make, though it's difficult): same result. On five object so different, coincidence was beginning to be unbelievable Wink

I then decided that for good or ill I'd have to sort this out, and took my pen and paper Happy The result is not as perfect as we could wish, but is already a huge step for me...

In fact, they are not exactly associated. More precisely, it depends on the shape the blade takes when it vibrates. See http://www.tinkerswords.com/harmonics.jpg for an example shape. Well, if the shape is a parabola, the equation magic happens, and the nodes are indeed associated pivot points, exactly. That's three lines of calculus if you know the definitions and the properties of pivot points and center of gravity. I can post them if anyone wants to see...

Of course, a vibrating blade, in general, does not take a parabolic shape. However, it is never so far away. The parabola is simply the most simple curve showing, as depicted, a belly and two nodes. So even though the two primary nodes are not associated pivot points, they are very, very close to being so on reasonable objects.

One could ask how this is important... Well there are several reasons:

- The definition of the CoP can be seen in a dynamic or in an harmonic sense, minimizing shock or vibrations in the hand, respectively. What the relation shows is that, on a nicely balanced sword, both are equivalent in a sense. On an harmonically balanced sword, there is one vibration node in the hilt. If the impact happens on the vibration node on the blade, two results are achieved: least vibration in the hand (since we are striking with a node), least shock in the hand (since the point of impact is the pivot point associated to part of the hand). That's why an harmonically balanced sword feels right upon impact on the node, I guess. There is more to it than just wobbling.

- There was a bit of noise after the parution of George Turner's article, that was dismissing harmonic balance in a way its supporters found a bit offensive. It turns out that as far as impacts are concerned, both sides were right Happy Make an harmonically balanced sword, and the resulting pivot points will be ideally placed for rigid body impact as well.

- I never liked CoP as a statistic in reviews, because I consider it is difficult to link to handling. Turns out that if the position of the node on the hilt was published as well (a big if, it is mostly absent), I would have a near exact set of pivot points, from which I can deduce any handling property I like. Which means that if someone feels comfortable with harmonics, he will measure the nodes, if I am comfortable with pivots, I will get them, and in the end, for handling we have the same information.

That still does not give a formula for the position or modification of the nodes, only a relation. That is, I know they are associated pivots, but if I don't have one of them, I can't find them both. And if we want to play with semi-nodes and such, the link to inertia is lost. There is also the issue of the precision of these measurements... Well in theory, at least, it works.

Of course everyone will tell me that all this is known since the dawn of time, obvious to someone with experience, etc. Well, I'm still happy to have a somewhat more unified theory to explain what we observe Cool Kind of feels like being able to tell why the sun rises every morning, not just how Big Grin

Wishing you all good night from my part of the world...

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Angus Trim




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PostPosted: Wed 01 Aug, 2007 3:14 pm    Post subject:         Reply with quote

Hi Vincent

Now all you need to do is factor in how the handle shape affects handling........*g*

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Vincent Le Chevalier




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PostPosted: Thu 02 Aug, 2007 2:05 am    Post subject:         Reply with quote

Angus Trim wrote:
Hi Vincent

Now all you need to do is factor in how the handle shape affects handling........*g*


Hey Gus, I'm trying to progress step by step here Wink If I was understanding too many things at the same time, I fear the resulting loss of magic would make the universe collapse Laughing Out Loud

Seriously, science, much like swordmanship, is not a result but a process. There is no end to reach... It's just a path I take.

Back to the subject, in fairness, I must point out that Leonardo Daneluz, back in April 2003, was very near the mark in this thread:
http://forums.swordforum.com/showthread.php?t=18278

Leonardo Daneluz wrote:
My conclusion is that two swords with the same vibration nodes, same c.o.b. and weight will also have the same oscilatory behavior [ed: that's how he calls properties based on pivot points]
[...]
But the meaning of all this to me is that a sword well made with the "vibration node" concept in mind won't perform significantly different than other made with the "oscilatory" concept.
Both swords would be made taking care of pnenomena that derive from the distribution of mass.
[...]
Claryfing: I not saying that a sword with the VN properly placed will have an oscilatory c.o.p. near the point but only that Vibratory and oscilatory behavior are closely related.


Unfortunately, he never got to the point of proving in which exact case what he suggests is true, apparently. He also focused on the pivot point associated to the cross, which is not as near to the node in the blade than the pivot point associated to the node in the hilt. Especially on rapiers, and possibly on certain kind of thrusting longsword, from what I understand.

In fact I have a question related to that: Where is the hilt node located on two handed swords (as in, handled with both hands, not necessarily true two-handers)? Cross? Back of the lead hand? Is there an empirical known relationship regarding the link between its position and the intended use of the sword?

I have an idea about that, but if there are well-known facts, I'd like to know them too...

Kindly,

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Angus Trim




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PostPosted: Thu 02 Aug, 2007 7:40 am    Post subject:         Reply with quote

Hi Vincent

If you want to be able to use a math formula to figure where the handle node is, its a bit like that old "mass distribution" thing......

How long is the blade? How thick at the base? How wide at the base? How much distal taper, and how does it taper? How much profile taper, and how does it taper? What does the contour look like { blade geometry and crossection}? Hilt length? Width and thickness of tang? Taper of tang {distal and profile}? How much does the pommel weigh, and where is the weight on it?

A lot of variables........

One thing to consider, the handle node moves from the "naked blade" to the mounted blade. Before mounting, its not unusual for it to be up on the blade proper a bit, once mounted its on the tang..........

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Vincent Le Chevalier




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PostPosted: Thu 02 Aug, 2007 12:36 pm    Post subject:         Reply with quote

Hi Gus!

Angus Trim wrote:
If you want to be able to use a math formula to figure where the handle node is, its a bit like that old "mass distribution" thing......
[...]
A lot of variables........


I agree, but fortunately I'm not trying to do that Happy I'm not aiming at finding all the properties from scratch, just from geometry and materials. I doubt it would be of much use to anyone... If you are able to have this level of detail and precision for measuring geometry, for example, it's likely that you have access to the object, and so you don't need a formula.

My original goal was to find a few parameters that give a correct idea (not exact, mind you, just correct) of the handling. At the beginning I was also looking for "the best part to cut with", but since then I figured that it depended much too heavily on considerations external to the sword. So I'm concerned with handling prior impact. Or post miss, eventually Happy

For my primary goal I do not really care about vibrations, since through handling they won't happen much. Pivot points, center of gravity, on the other hand, are definitely important in defining how the weapon can be moved, how it reacts to actions.

(Btw, concerning that, I tried to make this diagram to explain how I see things. I don't know if you've seen it, it faded from view pretty quickly... But if you have comments, I'd be glad to hear them and modify the thing accordingly)

Nevertheless, due to their significance in hard impacts, vibration nodes are commonly measured, and recognized as important parameters. So the obvious counter to my approach is "you cannot just forget nodes and expect good results". Which kind of makes sense... So either I explain how the nodes have no effect on anything (well, I can't, because they do have an effect Wink ), or I prove that they are linked to the rest of the parameters, so that having them utterly wrong is not possible. I was quite happy yesterday, because it turns out that last part is actually not that hard Happy

Besides, combining that with what I know of impacts and cutting, a lot of the observed effects of the nodes start to make sense, precisely because they are so closely related to pivots. Given the amount of heat that George Turner's article generated at the time, I think it's comforting to reach such a conclusion Happy

That being said...

My question about the position of the handle node was not about how it moves, or how its position can be computed. I was looking for observations about its location, particularly on long-handled swords, because I do not own one. If what I'm thinking holds some water, its position can give an idea of the perceived tip control or blade mass. I'd like to know if I should keep looking this way or if there are obvious known counter-examples...

Angus Trim wrote:
One thing to consider, the handle node moves from the "naked blade" to the mounted blade. Before mounting, its not unusual for it to be up on the blade proper a bit, once mounted its on the tang..........


Indeed, and Peter Johnsson made an illustration of that on Albion's website:
http://www.albion-swords.com/articles/images/sword-dynamics.pdf

Well at the moment, I can explain the motions of all the points, save the small displacement of the blade node. Even the huge motion of the hilt node is easily explained without having to know all the details from blade geometry, weight everywhere, etc. precisely because it is tied to pivot points, whose motions are easy to predict.

Thanks for your interest!

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Angus Trim




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PostPosted: Thu 02 Aug, 2007 1:34 pm    Post subject:         Reply with quote

Vincent Le Chevalier wrote:
Hi Gus!

Angus Trim wrote:
If you want to be able to use a math formula to figure where the handle node is, its a bit like that old "mass distribution" thing......
[...]
A lot of variables........


I agree, but fortunately I'm not trying to do that Happy I'm not aiming at finding all the properties from scratch, just from geometry and materials. I doubt it would be of much use to anyone... If you are able to have this level of detail and precision for measuring geometry, for example, it's likely that you have access to the object, and so you don't need a formula.

My original goal was to find a few parameters that give a correct idea (not exact, mind you, just correct) of the handling. At the beginning I was also looking for "the best part to cut with", but since then I figured that it depended much too heavily on considerations external to the sword. So I'm concerned with handling prior impact. Or post miss, eventually Happy

For my primary goal I do not really care about vibrations, since through handling they won't happen much. Pivot points, center of gravity, on the other hand, are definitely important in defining how the weapon can be moved, how it reacts to actions.

(Btw, concerning that, I tried to make this diagram to explain how I see things. I don't know if you've seen it, it faded from view pretty quickly... But if you have comments, I'd be glad to hear them and modify the thing accordingly)

Nevertheless, due to their significance in hard impacts, vibration nodes are commonly measured, and recognized as important parameters. So the obvious counter to my approach is "you cannot just forget nodes and expect good results". Which kind of makes sense... So either I explain how the nodes have no effect on anything (well, I can't, because they do have an effect Wink ), or I prove that they are linked to the rest of the parameters, so that having them utterly wrong is not possible. I was quite happy yesterday, because it turns out that last part is actually not that hard Happy

Besides, combining that with what I know of impacts and cutting, a lot of the observed effects of the nodes start to make sense, precisely because they are so closely related to pivots. Given the amount of heat that George Turner's article generated at the time, I think it's comforting to reach such a conclusion Happy

That being said...

My question about the position of the handle node was not about how it moves, or how its position can be computed. I was looking for observations about its location, particularly on long-handled swords, because I do not own one. If what I'm thinking holds some water, its position can give an idea of the perceived tip control or blade mass. I'd like to know if I should keep looking this way or if there are obvious known counter-examples...

Angus Trim wrote:
One thing to consider, the handle node moves from the "naked blade" to the mounted blade. Before mounting, its not unusual for it to be up on the blade proper a bit, once mounted its on the tang..........


Indeed, and Peter Johnsson made an illustration of that on Albion's website:
http://www.albion-swords.com/articles/images/sword-dynamics.pdf

Well at the moment, I can explain the motions of all the points, save the small displacement of the blade node. Even the huge motion of the hilt node is easily explained without having to know all the details from blade geometry, weight everywhere, etc. precisely because it is tied to pivot points, whose motions are easy to predict.

Thanks for your interest!


Hi Vincent

To make things clearer, the handle node of a long handled sword will depend on all of the variables above, and more, and who made the sword...............There's no uniformity here.......

However, I think you're on the right track, so keep things up. When I ask a question, or toss something at you, I'm just trying to get you to see another variable. I suspect that what you'll come up with is something that will work in most cases........

I'm going to tell you a story, something to get you to think a bit.......

Once upon a time, there was this AT sword collector named Eric McHugh. This was....long ago........

He wrote me about a problem, and this resulted in a telecon. He had these two AT type XIXs, different hilts. One cut up to his expectations, the other did not.....

When he told me of this, wanting to know if I had an answer, I was speechless. Had no idea......

Since it just so happened that I had a couple of these blades thru heat treat at the time, I mounted them, and did a few experiments.......

Unfortunately before I could get back to Eric about my initial thoughts, a major online sword makers war broke out, and the info never was passed on.

To make an incredibly long journey short, a few months later, I was at Livermore talking to a couple physicists about harmonics in swords, when part of the discussion caused a light to go on......When I got back, I did more playing with these two pieces, and came up with the problem being the way the deminodes were positioned........

Yeah, a subtle harmonic thing. Looking at things by banging the pommel on the side, both looked good. By knowing a bit more about the phenomena, one didn't look so good........

Still haven't passed on what I found out..... probably should one of these days.......*g*

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Vincent Le Chevalier




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PostPosted: Fri 03 Aug, 2007 1:53 am    Post subject:         Reply with quote

Hi Gus!

Thanks for the story... Unfortunately I do not own any sword that shows "deminodes" as far as I understand what that means, which is not much. On the illustrations I've seen they don't look like nodes at all... Not having as much info as I would like to have on the weapons (I don't suppose you measured pivot points on your type XIXs?), it's difficult for me to draw conclusions.

Perhaps the existence of deminodes also implies that in the first mode of vibration, the blade takes a shape that is sufficiently far away from the parabola, so that the blade node and hilt node are further from being associated pivot points. This would mean that their placement is not representative of dynamic balance, explaining some of the differences. Really just throwing out some thoughts here...

Isn't there some hierarchy of the effects, though? Assuming we are cutting a hard, unyielding target:

- If the impact happens too far from the blade node, the blade will vibrate with a disturbing amplitude, thus preventing the "bite" somewhat. That's the only real reason to strike with the CoP that I can see nowadays.
- If it happens at the blade node, there is not much amplitude in vibrations anyway, so the position of the handle node is not important vibration-wise (I suspect that's why it is rarely measured). However, since it is more or less the associated pivot point of the blade node, its position is important because it determines whether the hand feels the impact force or not, or rather what amount.

So what is termed "harmonic balance" mixes two different effects: the position of the node on the blade, and the pivot point associated to this node. It just so happens, on swords that do not have funky waveforms in their first mode, that the hilt node is very close to being the said pivot point. That's how, by checking the "harmonic balance", we end up checking for an approximation of dynamic balance as well.

Problem is that deminodes could disturb this equivalence, so that part of the dynamic balance is missed when just looking at how the weapon vibrates. I doubt it would end being really far off the mark, but perceptibly, it's possible. If you have the same blade node, the same primary hilt node, but deminodes in one case and not in the other, pivot points will probably be different, so the difference would be felt not only in cutting but in handling. Whether it is possible to feel the difference without cutting is another question...

I don't know, what do you think?

Best,

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Marton Pap




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PostPosted: Fri 03 Aug, 2007 3:37 am    Post subject:         Reply with quote

Hi all!
Could anyone tell me what deminodes are?
An other question: Are aft pivot points important because there is the other hand on a longer grip?
Regards!
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Bram Verbeek





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PostPosted: Fri 03 Aug, 2007 4:57 am    Post subject:         Reply with quote

just a thought: if the hand grips tightly and the rest of the grip is constructed using dampening materials, will it not be possible to calculate the exact pop using the speed of sound in steel and the tone a sword generates when struck? If the first node on the blade is exactly on the hand (where you want it) and you measure the tone (in Hz) the sword generates when struck, you can simply calculate the distance where 1/2 of the sinoid would be, using 5130/(2*Hz) from the first node (5130m/s is the speed of sound in steel, if I recall correctly, on 1/2 of the sinoid would be the second node so the time would have to be half that of a complete sinoid, and thereby half the distance, Hz is simply 1/T)

the distance of the calculated pop for a tapering blade would still be the same, but you would have to calculate the average frequency a lot harder, I will look into this after I am ready working for the day.
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Vincent Le Chevalier




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PostPosted: Fri 03 Aug, 2007 6:50 am    Post subject:         Reply with quote

Hi Marton,

Marton Pap wrote:
Could anyone tell me what deminodes are?


I'm not quite sure myself Wink There is an article by Michael Tinker Pearce here:
http://www.tinkerswords.com/Harmonics.html
I do not agree with everything written there, but at least there is a picture... Surely Angus could tell us more...

Marton Pap wrote:
An other question: Are aft pivot points important because there is the other hand on a longer grip?


Aft pivot point is important for handling but has nothing to do with vibrations. My interpretation is that it gives you sort of a dynamic length for the weapon. The shorter the distance between the rear of your grip and the aft pivot point, the quicker the blade will realign itself in cutting motions. Note that quicker is not necessarily better, since the position of this pivot is the result of a compromise in the design of the sword.

In general you won't find a vibration node close to the aft pivot point, I believe. Unless you consider higher harmonics that are barely visible to the eye or felt in the hand...

Bram,

Maybe it would be possible, but I think there is little point in doing so, as was said in the other thread... Because if you are able to make the experiment you describe, you can certainly grab the sword, hit the pommel or the flat, watch it vibrate and locate the CoP with all the precision you need. We don't need a millimetric position, because CoP matters for impacts, and you will rarely have the control needed to strike with such a precision, assuming your target is even that small...

The problem with the CoP is not to measure it, it's to know what it means, how to use it, what knowledge it brings us as well as what we cannot deduce from its location.

Regards

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Marton Pap




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PostPosted: Fri 03 Aug, 2007 7:36 am    Post subject:         Reply with quote

Thank you for the reply Vincent!
btw: I didn't ask the AP because of vibrations, I was just wondering about what would be the practical meaning of it (I mean correlation between the practical use and the physical meaning of pivot points), just like you said above. My first guess was the importance because of the rear hand, the second was that it tells much about the blade itself, the third was that I guess most of the parrying happens somewhere around the AP on the blade (Now I got an idea to examine the distribution of nicks on original blades to see if that might be true or not Happy ) I didn't think of the realignment part what you sad, so now that is the fourth one Happy . The thing that bothers me much is that I assume some correlation between the pivot points and Döbringer's advice not to grab (and pull) the pommel but I don't really know what it is Sad At least I have some ideas about the forward pivot point and its part in cutting and thrusting Happy
Sorry for being a bit off-topic
Regards!
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PostPosted: Fri 03 Aug, 2007 7:46 am    Post subject:         Reply with quote

Vincent Le Chevalier wrote:


The problem with the CoP is not to measure it, it's to know what it means, how to use it, what knowledge it brings us as well as what we cannot deduce from its location.

Regards


Hi Vincent

Most cutting actions are somewhere on the foible, and most times closer to the tip than the cop. So, really, the cop in itself isn't as important as we used to think eight years ago. Its just the primary node........

Ok, true, if we're cutting a difficult modern target, like 1/4 inch plywood, and/ or thick cardboard tube, the place on the blade to get the best results in a cut is the cop. No question..........But if we look at the sword as a weapon, then we have to admit that we're not going to be dueling 1/4 inch plywood or cardboard tubes. Cutting these up are fun, and educational to a degree, but only a degree.......

Oddly enough, with a well balanced sword, the softer targets {tatami, 2L bottles, pork shoulders, etc} are cut best with a portion of the blade much closer to the tip. This is where "harmonic balance" comes into play.........With targets like these, if a sword needs to be used at the cop to succeed in a cut, then its not balanced.........

The practical reason for this, thinking of the sword as a weapon, is that its a bit impractical to step close to an opponent trying to stick or cut you, and use the primary node as the striking point. Before that happens, its likely the opponent will use his tip to poke your eye out, or cut your wrist off, {or something unpleasant like that} or even take your sword from you.

The sword's tip, and just behind the tip, needs to be practical. You need to be able to use this.........

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Vincent Le Chevalier




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PostPosted: Fri 03 Aug, 2007 11:40 am    Post subject:         Reply with quote

I agree completely with what you say, Gus, and that's why I precised in my former post "a hard, unyielding target"... In fact I'm more and more convinced that many swords were designed not to achieve the highest performance in a very specific set of conditions, but rather to perform decently in a variety of conditions.

I have also experienced first-hand what you say about tip-cuts (or rather just behind the tip). In fact part of that can be explained with rigid body dynamics, and I think the rest is due to blade profile (given that many cutting swords are thinner at the tip). All other things being equal, a lighter target shifts the most efficient spot of the sword towards the tip. And the more mass there is in the hilt, the more dramatic the effect. So this is almost not noticeable with an axe for example.

So obviously the balance has an influence here, and we saw that a harmonic and dynamic balance are linked, so a sword that does not perform well you will perhaps see as ill-balanced harmonically, and I will perhaps see as ill-balanced dynamically, and possibly we'll both be right Happy

I do wonder however if the discomfort that can be experienced with a "bad" sword is really due to vibrations or if it's the shock that is mostly felt. Or if the cut feels bad because the effect on the target is not what we expected given what our hands felt. I guess I do not have enough "bad swords" to experiment Wink

Marton,

No problem for the slight off-topic, I've done enough of it myself Big Grin After all, the thread is about harmonics and dynamics Wink
Im afraid I can't help you much with Doebringer and the pommel. As far as I know, he is the only master to give an advice specific to that, and there are plenty of illustrations that show gripping the pommel. So I'm not sure you can reach a definitive conclusion based only on pivot points... You'll also find that the aft pivot point does not move all that much, whether you take it relative to the pommel or just in front of it. At most, it will move as much as your reference point. And the distance between them (the important thing when launching a cut) changes even less...

Regards

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Angus Trim




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PostPosted: Fri 03 Aug, 2007 12:11 pm    Post subject:         Reply with quote

Vincent Le Chevalier wrote:


So obviously the balance has an influence here, and we saw that a harmonic and dynamic balance are linked, so a sword that does not perform well you will perhaps see as ill-balanced harmonically, and I will perhaps see as ill-balanced dynamically, and possibly we'll both be right Happy

I do wonder however if the discomfort that can be experienced with a "bad" sword is really due to vibrations or if it's the shock that is mostly felt. Or if the cut feels bad because the effect on the target is not what we expected given what our hands felt. I guess I do not have enough "bad swords" to experiment Wink



Hi Vincent

Just so we're clear, I suspect that you and I use dynamic balance differently. When I first started using the term, dynamic balance, some 6, 7 years ago, on SFI, to describe how a sword reacts in motion, it was before pivot points were part of the "discussion". Pivot points weren't a part of the discussion, 'til after an article posted elsewhere......

Not to discount pivot points, but for me they're a subjective measurement, so I don't use them. I'm more interested in how a sword moves, how it "follows the point" in a thrust, linear or looping {possibly the curved thrust can be discussed using points of rotation, which are different from pivot points}, and how a sword "tracks" in the cut, or a cutting motion. How fast it recovers, etc, and so on........

Not to knock your study of pivot points, but they're useless to me. THough I'm not surprised that you find a correlation between pivot points and and the nodes......

Something I discovered years ago, and wrote about, is that a truly harmonically balanced sword, is also a sword with good dynamic properties. The two go hand in hand........ I do not the reason why, and frankly haven't worried about it.....

So please, keep up the study......

In a bad cut, shock will come back to the hand. The lighter the sword, the more shock you're going to feel, even with a sword with decent harmonics. If the harmonics are off, the shock will be worse.......

I think pivot points can describe part of dynamic balance, but dynamic balance is much more than pivot points......

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Vincent Le Chevalier




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PostPosted: Fri 03 Aug, 2007 1:00 pm    Post subject:         Reply with quote

Hi Gus

Angus Trim wrote:
Just so we're clear, I suspect that you and I use dynamic balance differently.


Hmm yes I'm beginning to realize that as well. I can't remember when I first used that term myself Worried

Angus Trim wrote:
Not to discount pivot points, but for me they're a subjective measurement, so I don't use them. I'm more interested in how a sword moves, how it "follows the point" in a thrust, linear or looping {possibly the curved thrust can be discussed using points of rotation, which are different from pivot points}, and how a sword "tracks" in the cut, or a cutting motion. How fast it recovers, etc, and so on........


Which I believe is explained entirely by actions of the user, and dynamic properties of the weapon, namely mass, center of gravity, inertia. You could add perhaps one mode of vibration if really the blade is flexible enough to start wobbling in handling (but even on my practice rapier, it's second order).

It's not that I specifically care about pivot points, but for sure they are a way to measure inertia (and that's not subjective, it's proven), and when I start to quantify all the effects you describe, I find a direct interpretation of the result in terms of where some pairs of pivot points are located. It's just so much more easy to visualize with them...

Angus Trim wrote:
I think pivot points can describe part of dynamic balance, but dynamic balance is much more than pivot points......


There are the properties I cited above, and there are actions from the user. Every motion of the weapon is driven by that. So if we don't want to pull the whole user into the study (I wish to compare swords, not users), I cannot really think of something else to add (though I'll grant you that an ergonomic study of the grip would be interesting). I'm talking of the motion here, impacts as I said somewhere already are way, way more complicated.

I think part of your opinion is caused by some kind of a restrictive view on what pivot points really are... And I have the exact same problem with the harmonic theory, in fact Happy We're complementary in a way Big Grin

Best,

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Angus Trim




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PostPosted: Fri 03 Aug, 2007 1:47 pm    Post subject:         Reply with quote

Hi Vincent

I don't think we're that far apart, really, on pivot points and harmonics. What I said about pivot points and subjectivity, is the measurement, not the actual location of the pivot points. It makes sense to me that pivot points have a correlation to the nodes.

I have been able to get different readings on pivot point locations, by trying to find them with the blade held horizontally, vertically tip up, and vertically, tip down. Also by moving my hand position back on the grip. Then one night, being tired, I unintentionally "muscled" the movement, and the apparent pivot points were several inches off.........

So I don't use it....

To check dynamic balance, I go outside, do my form. Take the sword thru several different paces...... And then I cut with it, to check tracking and behavior. Then do a straight thrust into a target, and a looping thrust into a target.......

But part of the reason that I think that pivot points are only part of the answer for dynamic balance, is I don't see how they can describe things like blade and edge geometry. If the nodes and thus pivot points are in the same postion on three different swords, only real difference is the edge geometry, how can the pivot point describe the dfference in handling?

For instahce..... take three swords, everything the same except edge. One has a blunt edge, .06 inch {1.5mm}. Another has an .03 thick edge, fairly robust edge geometry. the third has a really acute edge........

Handling is similar, but is subtly different. Many folks will tell you that the sharper of the three, has a more "alive" feel in movment........but won't be able to tell you why...... I certainly can't, yet its a phenomena I've experienced a lot......

You mentioned handle, here's something that affects dynamic handling.... and thus the balance.....

How does the pivot point location describe the difference in handling between blade contours? Flattened diamond, vs hex vs fullered, if all weigh the same, and cog is the same?

Again, I can't explain it, but have experienced it........

Pretty subjective stuff, this......Some swords have been described in the past as having an "organic" feel to them. Definitely a subjective term for a subjective feel..... but I'm in line with this at times........

Pivot points are valid. Every bit as valid as nodes....... but they cannot describe a lot of what happens when a sword is in motion, no more than the nodes can.........

Because pivot points are valid, I'd like to encourage you to continue. My thought on this though, is don't expect these to tell you the whole story..... because I don't think they will......

swords are fun
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Jared Smith




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PostPosted: Fri 03 Aug, 2007 2:16 pm    Post subject:         Reply with quote

I do not mean to hijack this thread, and consider this related when honestly contemplating Angus's position (I am interpreting it as refining design of swords by feel and handling.)

If the standard for giving the statistics of CoP/ CoB is from the guard, how appropriate is this for those long grip models such as an ATrim 1593, or Albion Munich? CoP is still a good place for a hard impact, but if the user wants docile handling, might they not appreciate the CoP/CoB being a little closer to the "strong" of the blade?

Absence of evidence is not necessarily evidence of absence!
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PostPosted: Fri 03 Aug, 2007 2:46 pm    Post subject:         Reply with quote

Jared Smith wrote:
I do not mean to hijack this thread, and consider this related when honestly contemplating Angus's position (I am interpreting it as refining design of swords by feel and handling.)

If the standard for giving the statistics of CoP/ CoB is from the guard, how appropriate is this for those long grip models such as an ATrim 1593, or Albion Munich? CoP is still a good place for a hard impact, but if the user wants docile handling, might they not appreciate the CoP/CoB being a little closer to the "strong" of the blade?


Good question, and since I'm pretty sure I don't know what you're getting at, I'd have to add, I'm not sure what the point of owning a docile dueling longsword would be. *g*

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PostPosted: Fri 03 Aug, 2007 3:45 pm    Post subject:         Reply with quote

I consider the Munich to be very docile. I can execute my poor zwerchau technique as fast (actually faster) with it as I can with any other sword I have been lucky enough to use and test cut with. The leverage afforded by the long grip undoubtedly influences my impression of the sword.

My point, in such a case, is that the guard is probably not very close to the location where the wielder's perception of handling traits are likely to be derived. I suspect the relevant location is nearer to the center of the two handed grip.

This line of reasoning could be all wrong, but similarly for one handed grip I would expect the most relevant location would be closer to the center of the one handed grip (roughly 2" down along the grip from the guard, rather than right at the guard.) As far as harmonics go, I think Vincent has already stated that they do not vary as greatly within a well designed tang and grip. Balance and inertia are still fully relevant relative to where one holds the sword though, rather than at the centerline of the guard.

My "nit pick" here is that CoP is relative to where you define it. In any practical engineering calculation, CoP is defined relative to some location where a motor, gear, or possibly a wrist muscle (such as center of hand grip area on a baseball bat..actually dictated by an ASME standard for giving CoP of bats) applies a torque to make something rotate. There are an infinite number of them for any object. If you hold a blade for a "murder stroke", there is a completely new CoP for that application located down somewhere near the guard, and it depends upon where you grasped the blade. Vibrational nodes are not the whole story here either. They do matter, but you can probably relate to the concept of a baseball bat being gripped in the "wrong location" with resulting hand shock, even though it was an o.k. bat. Everything is relative to where you hold or pivot a rotating object when discussing CoP.

I consider most forum participants here to be quite sharp mentally, and capable of estimating rough rotational characteristics of swords with greatly similar geometries and grips (using only CoB/CoP and weight) regardless of where CoP has been defined. However, if you want to compare two swords where the grips are drastically different, blades similar, now the true perception in actual handling might be much harder to predict using the guard as a reference point for CoP.

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Vincent Le Chevalier




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PostPosted: Fri 03 Aug, 2007 4:10 pm    Post subject:         Reply with quote

Angus Trim wrote:
I don't think we're that far apart, really, on pivot points and harmonics.


I don't think so either... In the end it's just a different way of looking at the things, with perhaps slightly different goals and constraints.

Quote:
What I said about pivot points and subjectivity, is the measurement, not the actual location of the pivot points.
[...]
I have been able to get different readings on pivot point locations, by trying to find them with the blade held horizontally, vertically tip up, and vertically, tip down. Also by moving my hand position back on the grip. Then one night, being tired, I unintentionally "muscled" the movement, and the apparent pivot points were several inches off.........


On that, perhaps you won't mind if I give some general advice... Might be useful for pretty much everybody.

The measurements of pivot points is indeed not so easy at the start, because it needs to be both dynamic and controlled. I think that when the "waggle test" was described by George Turner (it's the first place where I've seen it, but I'm sure others did it before), the best way to perform it was not given.

There are two key points for the waggle test: no torque must be applied, and the motion of the hand must be as quick as possible. So you choose a point, grab the weapon ideally between two fingers, as lightly as possible, and you move your hand as fast as you can from side to side. The motion need not be ample, more than 8in is not necessary and actually disturbs the measure.

You cannot really do that with the blade horizontal, because in this case you must press the handle to keep it horizontal, and this creates torque. A bit as if you were trying to measure harmonic nodes with the blade in a vice, gripped right at the middle, if you see what I mean.

George Turner exposes that holding the blade vertically upwards. But in this position, it is not stable. Especially with a sharp blade, you cannot do the test in a relaxed fashion because the sword could as well fall on you. So I prefer to do it vertically downwards. The goal must be to move just the handle, just the spot where your fingers are. Trying with sticks first is less demanding, because they are lighter and not sharp Happy

The test is sensitive to the frequency of your motion. Mathematically it is exact if the back and forth motion is infinitely fast, but fortunately it reaches a decent precision at a far slower speed than that Happy Indeed you can make the observed pivot point move towards your hand if you slow down too much. Really the idea is to observe the behaviour of the weapon as a pendulum. The goal is to find where the head of the pendulum would be, if it was a mass hanging from a string. So technically one could even train on pendulums first, to see the effect... You'll see with a pendulum that you can make the thing pivot around some random point on the string if you slow down sufficiently.

You said that the pivot point depended on your hand's position, but that's perfectly normal and expected. Pivot points go by pairs. For every reference point on the weapon, there a unique associated pivot point. If you change the reference point, the pivot point moves.

Visualising the weapon as a pendulum with a varying length, depending on the part on which I apply forces, has prooved enlightening to me, and I wish other experience that...

See Marton? That's what happens when I go off-topic Big Grin

Back to your message, Gus, I think I've found a difference in the way we think. As a sword maker, you seem to be thinking in terms of blade (and whole weapon) features: tapers, edges, fullers, cross-sections... And that's quite natural. Since I don't know about them as much as you do, and have not experienced with them as much as you, I abstract them in higher level concepts like mass distribution, that are of little meaning to you... And from these I extract the properties I'm looking for. So they are all taken into account, but I do not make a special case for each (I don't know them all Wink ).

Note also that I've shown that pivot points and nodes are approximately related only. So for all we know, all the examples you have given might as well have been different in pivot points. It's not very likely, but it's possible, and without measures we cannot reject this hypothesis.

Quote:
Because pivot points are valid, I'd like to encourage you to continue. My thought on this though, is don't expect these to tell you the whole story..... because I don't think they will......


Nothing will tell the whole story, it is endless Happy . Even handling, I suspect some qualities of weapon are missed by some people at times, because they are not looking for them. I'm really just looking for a bit more from the story....

Thanks for your encouragements!

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