[Vincent Le Chevalier]

[Robert Subiaga Jr.]

Timo, if I'm interpreting your response correctly, you're missing my point.

Take the most extreme simplified form of what I described--sword and body taken as a unit--consider the two extremes of a singular wrist point of rotation and a singular shoulder point of rotation. In my own case, that's a twenty inch variation. Just as importantly, consider the supposition (not always correct) that the pommel's function is at least in part as a "counterbalance." In the first simplified case, a wrist rotation, this is true. In a simplified shoulder rotation--full arm extension--the pommel serves NO counterbalance function whatsoever.

Thus, the moment of inertia of a sword as a sole object might be calculable, but the variation within the set when the sword and arm are treated as a unit is far greater than between any swords. This considerable variance in moment of inertia even among the same sword in different strokes might well make something as subjective as "feel" not dependent on it--and would corroborate others' claims. (Which, albeit subjectively, I must concur with. I too seem to find that any two swords with identical weights and balance points "feel" extremely similar. Now, maybe that's an artifact and I actually do unconsciously "feel" a difference due to MoI and am consciously ignoring it, but I'd need some physiological evidence of that to believe it.)

This of course is in a sense true for weight and point of balance as well. For example, if I hold a sword vertically and/or close to the body, the sensation of weight or imbalance is lessened. But I'm under the current impression that it is less easy to fool the senses about these factors. A significant difference in overall weight is hard to miss, and even if the hand is not the center of rotation a significant difference in the distance of balance from the hand is also something probably felt on a more gross level.

Which is the operative point here: how a blade feels, both statically and in motion, not how it cuts. (Which itself is far more variable based on blade geometry than MoI anyway!) Not only is it true that physics per se often shows us "a distinction without a difference," regardless of whether a physical difference exists if our sensory apparatus is not built to care, it doesn't care.

[Vincent Le Chevalier]

It's just a matter of paying attention to the feedback of the sword.

I can feel the position of the pivot point on most objects (sticks, swords, etc.) with my eyes closed, just by twirling the thing around. I'm pretty sure Michael could too if he wanted to, as would most martial artists. I'd go as far as saying that when you close your eyes, the only indication of length you have is that distance to the pivot point, that your body is perfectly capable of feeling, and that is used to control the weapon when you don't see it.

My interpretation of Michael's point is not that pivot points are unimportant, or somehow not perceived by our body. It's that they are heavily correlated to other indicators depending on the type of the object. That's quite a different thing.

Regards,

[Timo Nieminen]

[Maurizio D'Angelo]

I'm lucky to have a relationship with a museum. I could hold many medieval swords excavated. These are not exposed. My work now is whether in fact the old smiths, without knowing the physical applications, builds swords respecting the parameters of which we speak. The thing that amazed me at the moment is its lightness and handling that I did not think they had. Almost is not believed to have been used in battle, but it's true. Weight distribution at the tip, has a lot to do with what we call, tensor of inertia. It seems to me that the POB not assume too much with very light weights on average. My idea is that a sword is not meant to be balanced on a plan to which the POB is of great importance, but rather seeks a balance when it is in the air (inertia tensor). I think that the POB at the end is the result of research of inertia tensor for the balanced use of the sword. In other words, the ancients, don't sought POB as the final goal, but, it was just an effect of balance in the air that he wanted that sword. Eventually if you adopt these principles, some swords have very different results. But I'll be more precise, when I finish, this long work ..., their analysis may help us understand something more.

Now a question for experts in the moments of inertia.
Has been said, here, that the most important point in space is in the direction Y.

Another engineer told me that the matrix is made of infinite points in space. Usually the most significant nine points . Three for each axis.
These, depending on how the sword is in point in space, may or may not take more or less importance.
A vertical sword is different from a horizontal, a guard rotated by a non-rotated, the question is: what studies have been done on the X axis influence in air , on Y or Z?

[Robert Subiaga Jr.]

Yup, Timo, you're definitely missing the point, though your example helps demonstrate it. You asked us to compare a 20" and 30" blade with the same weight and balance point, but obviously different MoI. True, there are 20" and 30" bladed examples, but that pretty much is an example of extremely different sword types.

Consider, as a general set, swords for one-handed versus (mostly) two-handed use. Single-handed swords definitely cluster around the 30" blade length, give or take maybe three inches; longswords perhaps around 34-35", w/ the same give on each end?

That's a six inch range, if we're generous (and statistically I'd like to see a compilation, as I suspect it's less). As I pointed out, even a slight variation in the kind of swings one might realistically use is well over double that variation from the sword alone, if not triple. In short, for a given sword type, MoI just doesn't vary enough; using a dynamic measure, the sword alone is too uniform compared to the body

On the other hand--pun intended--the hand is the point from which one gets the feel of an object the most, particularly because of the preponderance of touch receptors. And the total weight and point of balance will not change from that point.

The question is: upon what is both unconscious proprioception and conscious perception of the handling depending?

If it is upon MoI, which it very well might be, as the brain unconsciously needs to calculate movement, it CANNOT be on the MoI of the sword alone, but needs to be on the particular MoI of the sword and arm moving together. Thus the MoI of any given sword alone is indeed a distinction without a difference! The brain very much needs to tune it out, as it's the unusable data that would open up the door for a control error.

By their very simplicity, it would make sense that static measures like overall weight and point of balance, which don't factor in the body and the body treats as external to itself, are much harder to ignore, especially on a conscious level.

[Robert Subiaga Jr.]

Just as an aside, but one pertaining to this thread, on how better physical analysis as often as not can show the lack of a factor's relevance, especially when the biomechanics are factored in, lets take the issue of overall weight.

We all know a sword or other weapon can weigh too much. But based on the weapon alone, there should be no lower limit on weight. An actual sword of actual steel needs a minimal mass to be robust, true, but what if we had something, like, say, a science fictional lightsaber? Something that weighed only a few ounces, with the blade essentially weightless?

Run the physical calculations based on the weapon alone and the implication would be that no one could defeat a trained Jedi--the ability to accelerate such a light object and near-weightless blade would make it many times faster than any existing sword. (Hell, even with existing swords, the implication would be that anyone with a three pound sword should have NO chance against anyone with a two-pounder of similar reach.)

The only problem with this? Such a calculation is based on the sword alone, when it's the sword and body that are the system--and the limiting factor is the physics of the body. Human muscle fiber not only has a maximum contraction speed--that maximum contraction speed actually maximizes under a certain load. (Yes, Martha, we're actually a bit slower pushing against nothing at all than we are pushing against something.)

Factor in the physics of the whole system, and you can often find that the relevance of a particular measure within the system disappears.

The measure is still there, of course. Could an overlooked measure end up having relevance in some context? Of course. "Small changes in initial conditions" and all; that's what chaos theory shows. You can't deny the existence of a measure in the abstract.

But, just like one ignores what's going on with any particular molecule of a gas when looking at the pressure exerted on the wall of a container, getting an accurate overall picture also means treating that measure AS IF it's not there, even when we know it is. We're just as likely, if not more so, to miss the forest for the trees and get lost in details as overlook a key detail.

[Vincent Le Chevalier]

I'm sorry Robert, but I see a lot of speculations in these posts and little foundation on facts. By your reasoning pivot points should be all over the place on swords, because our brain "tunes them out" and we are not sensitive to them in use. The fact is that they are not all over the place at all. I have measured enough good reproductions to know that. Good swords have a mass distribution that has to be precisely controlled and that can be wrong because of the positions of pivot points.

Your arguments can mostly be used the other way around, to point out that CoG and total weight should be neglected. For example:

[Timo Nieminen]

[Robert Subiaga Jr.]

Sorry, Vincent, but regarding MoI I'm afraid you're displaying a definite cultural bias. MoI does indeed vary considerably among historical swords--if you're not restricting yourself to European swords. Not to mention swords period, but cutting weapons as a whole. While an axe designed for war indeed usually has a MoI noticeably different from one for chopping wood, are you telling me it's not also notably different from a sword?

As for the brain employing a "folk physics" that cognitively employs "tuning out" data as often as calculating with it being mere "speculation," I wish I could lay claim to it. Instead I'd direct you to quite a bit of literature on cognition, from the work of JJ Gibson on how we perceive a moving object heading straight toward us via geometric size increase to Stephen Pinker in sources like The Blank Slate.

Not that our methods of perceiving based on folk physics are universally correct. In the former case a screwball pitch messes with our perception remarkably well, while in the latter, for example, Pinker points out that even professional scientists who've had physics class will commit the common mistake of thinking a marble exiting a spiral tube will continue on a curved, rather than a straight, trajectory. (While having little on the matter of folk physics per se, I'd also plug Malcolm Gladwell's Blink in there for the lay reader too, which speaks both to the strengths and weaknesses of "thin slicing" or quick cognition.)

In any case, the idea that, sometimes accurately, sometimes in error, or brains perceive based on something other than what is actually physically going on--or to be more accurate only a select part of what's physically going on? That is hardly mere speculation.


But you're just dead wrong about the "Jedi advantage," I'm afraid. It's basic physiology and biophysics, with decades of references about the matter.

First of all, muscle contraction has a maximum speed, period. While the Wikipedia entry on Muscle Contraction is more sparse than I'd like, go to it and check the last graph and the language of Force-Velocity Relationships. "the muscle generates no power at either isometric force (due to zero velocity) or maximal velocity (due to zero force). Instead, the optimal shortening velocity for power generation is approximately one-third of maximum shortening velocity.
These two fundamental properties of muscle have numerous biomechanical consequences, including limiting running speed, strength, and jumping distance and height."

Any load light enough that maximal speed on contraction is already being approached will result in no significant difference in added velocity, period. In the Power-Load Relationship there is an optimal load (~40% of max) which allows for the greatest power development-any load less than or greater than this decreases power output; summarizing force, power, and velocity relationships in muscle and integrating the force-velocity and load-power relationships, power and shortening velocity are maximized at a load of ~20% of maximal.

And this lower limit of relevance also requires the human factor is included in the mix: a muscle fiber must be able to push its own weight as it develops tension before it is able to move, all contraction up to that point being isometric (no motion yet). Only at the point does the force developed become isotonic motion.

The reason swords and indeed most handheld weapons fall within a narrow range of total weight (and in this case can be split between those for one- and two-handed use) is consistent with the relation of a handheld object as a proportion of the weight of the moving body parts themselves. Any heavier and the slowdown in the strike becomes significant; any lighter doesn't increase speed but only makes the weapon itself more fragile, and thus has no benefit.

Not that believing me requires complex mathematical analysis--but that ironically goes back to my original point. Just grab a video camera and track the speed on a sword stroke with a sword and an arm stroke with nothing in the hand, modeling the same stroke. Compare the velocity of the sword in the hand versus a pretend massless sword in an empty hand. Find a significant difference and we'll indeed have data for a groundbreaking paper!

[Robert Subiaga Jr.]

Sorry, I should've included a reference about optimal load being ~40% of max and power and shortening velocity being maximized at a load of ~20% of maximal.

http://www-rohan.sdsu.edu/course/ens304/publi...Muscle.htm

[Vincent Le Chevalier]

[Robert Subiaga Jr.]

[Chad Arnow]

[Timo Nieminen]

[Vincent Le Chevalier]

Hello Robert,

[Michael Edelson]

I don't want to offend anyone here, but this type of discussion is exactly why some of us roll our eyes and mutter "not those engineering nerds again" whenever someone mentions moment of inertia or pivot points.

[Vincent Le Chevalier]