[Gordon Alexander]

I suspect that I understand the physics determining where a COP is (especially once one can identify the relevant inertial moment). Even after watching Peter's lectures and reading all of the sword mechanics essays and discussions that I could find I still find that I may not know the advantages and of moving the COP in or out. All other things being equal (which I realize is not possible), for instance, why/when would a COP at 65% the way out on a blade be better (or not) than one at 50% or 80%?

Thanks in advance for your help.

[Timo Nieminen]

The 19th century European sword writers wrote about the importance of the COP in terms of force on the grip/hand when hitting with the sword. (From this, we have the modern misuse of COP for nodes of vibration.) If you swing the sword so that it's pivoting about the grip (so the hand is stationary, and the sword is rotating to strike), and you hit at the COP, there won't be any force at the hand due to the hit. This is good. If you hit like this, you want the COP to be where you hit.

If you strike between the COP and the hilt, the force is into the back of the hand. If you strike past the COP, the force is against the fingers, and on a bad day, you could lose the sword. So have the COP fairly far out on the blade.

If, instead, you make slicing draw cuts (e.g., Viking sword in hammer grip, tulwar, and more), the rotation is about the shoulder, not the hand, and the location of the COP is irrelevant. As far as I can tell, sword makers didn't care about location of COP on antique Chinese dao.

It's very important for thrusts. The COP is also called the forward pivot point. Move the hilt sideways, and the COP wants to remain stationary; the sword will pivot about this point. This is why we see lots of cut/thrust swords with COP very close to the tip (longsword, jian, and more). Move the hilt, and the point remains in about the same place - very good for changing the angle of a blade for a thrust. This is often a far more important reason for the placement of the COP than force on the hand when hitting.

Apparently rapiers have the COP at about where you expect the blade to be in contact with the opponent's blade, so as to easily pivot about the point of contact.

[S. Issara]

If you study different types of swords, or study dynamics data from other people's measurement like Vincent's http://blog.subcaelo.net/ensis/dynamic-method-weighing-swords/ you will see a pattern.

Stick like objects such as waster, boken and poorly balance ninja-to tend to have 50-60% of dynamic length (measured from pivot point to it's rotational point) of its total length.
Swords, cut and thrust, tend to have the number in the range of 60-70% and thrusting swords have the number 70% or so.

To determine sword type and usage, there are others factors involved as well. But dynamic distance is a hint of sword. By just looking at the numbers and compared with those of historical ones, you may differentiate bad repro from good repro.

[S. Issara]

Keeping other parameters (length, weight, CG) while changing dynamic length or radius of gyration is theoretically possible. Because you will have to play with mass distribution, so, practically, you get a totally different type of sword.

[Peter Johnsson]

The node of no vibration in the blade is located between one quarter and one third of the blade length from the point.
This is a place where vibrations are cancelled out. The nodes of no vibration are a result of cross section (stiffness) and distribution of mass.
There is a second node of no vibration in the hilt.
Apart from this pair of primary nodes there are nodes of higher frequencies (like the overtones of the string on a string instrument) that straddle the primary nodes on each side outwards. They also play a role in how the sword vibrates, or does not vibrate.
The vibration nodes have been focus for much interest since they are easy to observe, but they are not alone in defining the function and performance in a sword. Just one aspect of the dynamic profile of a sword.
You cannot judge the performance of a sword by just looking at where the node of no vibration is located in the blade. Just like you cannot determine the handling characteristics of a sword just by looking at where the point of balance is located.
Each aspect will tell you just that: one aspect of the swords characteristics, one aspect of its dynamic profile (Dynamic, as in how it moves and how it responds to impacts).

Pivot points are something distinct and different from nodes, but they interact with the nodes in the dynamic profile of the sword. Pivot points are an effect of rotational inertia (largely an effect of distribution of mass and distance).
On each given point in the grip or hilt of a sword, there is a corresponding pivot point, usually located somewhere in the blade. On badly balanced swords (too little distal taper and too heavy pommel, for example) the forward pivot point may be located outside the length of the blade, forward of the point. This results in very strange handling characteristics that is nothing like that of an authentic sword. If the point of balance is pushed too far towards the hilt, the result may be that the forward pivot point in the blade is pushed far outside the point of the blade.
The placing of the pivot points is a key to understanding how a sword will tend to react when put in motion. Pivot points are also responsible for dampening feedback into the hand when a blow is delivered. It is often said that this is an effect of the vibration nodes, but that is not entirely correct. Vibration nodes cancel out vibrations, pivot point determine handling characteristics and dampen shock.

Different types of swords have different combinations of the placing of the vibration nodes and the pivot points. There is not one single placing that is *the best*. Different types of swordsmanship, different ways of using the sword will demand different dynamic profiles.
Looking at historical swords there are certain trends to be observed.
It is not unusual that modern replicas have very different dynamic profiles than the swords they are intended to represent. That means that a modern sword may look pretty much spot on, but have dramatically different properties in heft and performance from that of an original weapon. The effect of this is that modern swordsmen cannot know if their training equipment gives correct feedback. Unless you know that your training sword *behaves* and *performs* like an authentic sword of a type that is correct for the school of swordsmanship that is studied, you can only speculate wether the interpretation of the techniques you are studying is correct or not.
Just because a replica sword has the same overall size, weight and point of balance as that of an authentic sword, there is no guarantee that it behaves like the original sword. Subtle changes in distal taper and cross section can have great effect in the placing of pivot points and nodes of no vibration. The replica may well move in a way that is dramatically different from the original. It may also deliver thrusts and cuts differently.
The devil is in the details. As we are looking as a complex interaction between many factors, there are many points in the design that has to be met, many more than just overall dimension, weight and point of balance.

Back to pivot points and nodes of no vibration: sometimes there is an overlapping of nodes of no vibration and a pair of pivot points, but this is not automatic or universal.
The maker of the sword will have to strive for a certain dynamic profile (placing of balance point, vibration nodes and pivot points) for this to happen: many aspects will have to be adjusted just so, for this to happen.
Even if the pivot points and vibration nodes overlap, they are still different and separate aspects of the functional properties of a sword. It is a good idea to keep them clearly defined.

This is all pretty technical and I do not have the knowledge in physics and mechanics to describe the cause in a clear and scientific way.
These aspects of dynamic properties of swords can be more or less clearly observed, however. Some are more fiddly to locate precisely, but you can normally come close enough to get a pretty good understanding. It takes some practice to do, however. Two people reading the pivot points in the same blade, may or may not come to the same conclusion. This because a variation in how the sword is gripped and swung: you´ll get a different reading as a result.

In ancient times they surely had other ways to define what was important in how swords felt and functioned. Nodes of no vibration and pivot points are mostly modern concepts, but we can use these to pin point and describe the dynamic properties of the function of swords. That is why they are useful.
Each aspect, or element is only one part of a complex whole, however. This is important to bear in mind.
By having nifty definitions for the balance or performance of swords it is easy to jump to the conclusion we know *all* there is to know about swords. We may fool ourselves into believing we have the secret to all successful designs.
OVer the years when I have documented original swords I have seen quite a bit of variation on these themes. It is not just one solution that goes for all swords. And there are trends, or typical profiles that goes along with different types of swords. You can read something about how the sword was intended to be used by looking at its dynamic profile.
This shows us that ancient swordsmen and sword smiths strived for certain things. Some qualities were more sought out than others and this varied over time and between different styles or techniques of swordsmanship.

-So this was a very long winded reply to the question: Why is a forward placing of the COP a good thing.
It can be, but it will sometimes come at a price that you are not prepared to pay, given the situation and sword type. The COP is not the dominant feature of sword function. It is simply one of several important aspects.
Saying that all else is equal, makes for a very simplified situation that actually loose meaning since all things are never equal. You always have the weigh different aspects against each other.
It might also be a good idea to strive for dynamic profiles that are closely patterned after historical examples, since these swords were made for use: we can learn from this both as makers and swordsmen.

[Craig Peters]

If I may be permitted to go-off topic a bit, for the sake of analogy:

As part of my current work, I have to teach high school students how to read and analyze poetry. What I have found, to some extent, is that there is a general impression among students and probably a fair number of laymen and laywomen that poetry is all about "secret meanings" (perhaps interpretable in poetic terms as "symbolism" or "allegory") that the student has to uncover within the poem. This belief is no doubt partly as a result of the fact that poetic meaning can often be particularly challenging and demanding, especially for readers with relatively little experience in reading challenging texts.

The reality, of course, is that poetry is a composition of many different literary and rhetorical elements placed together and acting in concert with, or sometimes even in opposition to, one another. We can look at a poem for the type of imagery used and any patterns of imagery found therein, including images created by comparison: metaphor, simile, and personification. We can examine a poem in terms of its potential symbolic meanings. We can also look at the tone, and how it helps to inform us about the persona and character of the poem's speaker. We might look at structure, particularly as the structure relates to meaning. We might also discuss the auditory elements of the poem: rhyme, assonance, alliteration, consonance, and so forth, and how they affect the experience of the poem and their relation to its meaning. We can also consider the themes: what sort of views, opinions, and beliefs are implicit in the poem based upon the speaker's response to, and way of shaping, the poetic topic or subject. And there are certainly numerous other things we might consider as well; this list is by no means comprehensive.

I think many of us, when it comes to the mechanics and dynamic properties of swords, are laymen like some of my students are laymen when it comes to poetry. We want to dissemble a complex and multifaceted thing by trying to reduce it to a few simplicities, whether these simplicities are weight, center of gravity, center of percussion, or "hidden meanings" in a text. We forget or perhaps do not know that swords, like poems, are combinations of multiple factors interacting with one another, and that merely because we know or understand one or two elements does not mean that we have the whole picture. And, like poetry, the more we begin to understand how the various elements interact and inform one another in rich and dynamic ways, the more we can appreciate the immense skill and craftsmanship that went into these ancient tools of war.

[Jeffrey Faulk]

A sword is a highly individual object. Even factory-made swords such as the Hanwei Tinker line and CNC-machined blades like Albion swords and Angus Trim blades will end up having minor variations in their metrics.

So worrying about precise COP's and such is not really necessary. Choose a sword based upon your purpose for it. If it is fit for that purpose, it will do well in your hands as you move it, and in turn you will move with it. Swords are not meant to be static, and neither are those wielding them.

[Gordon Alexander]

This topic wasn't intended to be about choosing a sword but rather trying to further my understanding of sword mechanics, dynamics, forms, etc. Like others here, I have compiled tables of sword data and created models in CAD to play with mass distributions and see their implications. I do suppose that I will have to start actually at least picking up a sword or two though. This is a bad behaviour of mine, I have done things like studying aircraft design, bought plans, modified them, and built the thing without actually being a pilot. I never even flew in the thing, but the new owner tells me that it flies very well and he likes it very much.

[Glen A Cleeton]

Vincent Le Chevalier has initiated quite a few discussions regarding the theoretical and practical mathematics for sword design.

http://www.myArmoury.com/talk/viewtopic.php?t...highlight=
http://www.myArmoury.com/talk/viewtopic.php?t...highlight=
http://www.myArmoury.com/talk/viewtopic.php?t...highlight=
http://www.myArmoury.com/talk/viewtopic.php?t...highlight=
http://www.myArmoury.com/talk/viewtopic.php?t...highlight=
http://www.myArmoury.com/talk/viewtopic.php?t...highlight=

http://www.myArmoury.com/talk/profile.php?mod...amp;u=3770


Cheers

GC

[Vincent Le Chevalier]

Hello Gordon,

As you say, all other things rarely are equal, but if they were then here is what can be said. I'm assuming same CoG, same total mass, and same reference point for the CoP.

If you put the CoP further down the blade towards the tip, you will have a higher apparent mass further down the blade. Apparent mass is what hits the target, so that's the good side. The bad side is that you also raise moment of inertia, which means that the sword will be less easy to turn around. It will be more floating, less eager to swing. You will also move the hilt node of vibration towards the pommel.

If you put the CoP further up the blade, the effects are pretty much the opposite, as you'd expect. The apparent mass is lessened, and the sword very much wants to swing, which at a certain point starts to feel uncomfortable and hard to control. And the hilt node naturally goes towards the blade.

Observation of quality swords tends to indicate that neither extreme are desirable. You want to hit the appropriate compromise. Measuring original swords as Peter did gives you a good insight on where that compromise lies for different sword types. There are no real scientific deductions that will give you the optimal position, as it varies depending on the technical means available and the intended use, of which we know very little at that level of detail. Actually, even picking one particular CoP to study is difficult. Which one do you pick? Just at the guard? just a bit behind the guard? At the heel of the hand? These are all different and the pattern of their placement differ. This is one of the reasons why I focus much more on radius of gyration and try to minimize arbitrary choices of points of reference. All work in progress

Hope this helps,