Complex Harmonics in swords

[Tapio Manner]

This is because it is easier for the blade to 'collapse' to the side, which defeats the rigidity of the edge axis

It actually buckles elastically, the energy to twist it is smaller than the one to bend it, the problem with narrow high beams. I once thought that one of the reasons for the saber shape is that it might not buckle as easily as a straight shape of the same thickness.

TLM

[Michael Tinker Pearce]

I think that you might be right about that- though the first sword that I had collapse catastrophically in this fashion was, ironically, a saber.

[Sam Salvati]

Sam, take another look at the drawing that Michael Pearce attached in the very first post of this thread. The idea is that a blade is an oscillator that can vibrate in the primary mode with two nodes... in exactly the same way that a xylophone key vibrates. All blades have harmonics... it is neither good nor bad to have them... it's just a fact. The character of the harmonics... the period of the wave (determined by the stiffness of the blade and the distribution of mass along the blade) and the location of the two primary nodes (determined by an even more complex interplay of factors) will determine how effective the sword is in varous types of use. By "effective" I refer to the efficiency with which muscular energy can be transmitted to the target via the sword's edge, and how effectively that energy is used to cleave the target.

Anytime you hit something with a sword some of the energy will go into oscillating the blade. But if the target is struck precisely on one node, and the hand is gripping precisely on the other... there is no opportunity for that energy to be absorbed in oscillation and it is ALL transferred to the target.

If you know three things about a sword... the weight, the balance point, and the nodal points... you can know a LOT about it.

HOLY CRAP! That is awesome. THANKS!!!!!!!!!!!!

[Tapio Manner]

Anytime you hit something with a sword some of the energy will go into oscillating the blade. But if the target is struck precisely on one node, and the hand is gripping precisely on the other... there is no opportunity for that energy to be absorbed in oscillation and it is ALL transferred to the target.

The energy required to make it extremely uncomfortable to hold a sword is a small fraction of the full energy of a properly executed cut. It's not really a question of energy efficiency but a question of comfort. Then again one would not like to do a full power cut if one knew in advance that the damn thing is going to ring.

TLM

[Sam Salvati]

So how would you locate the node points?

[Tapio Manner]

I have no reason to doubt the placing of the nodes on old good swords. The interesting thing is the effect of a heavy pommel on the node, I suspect it moves it inside the handle at least on bastard and two-hand swords. One wants to hold the sword on the node. Some FEM modeling is needed to solve it, while it might not at first give the exact place it certainly would show the effect of the pommel mass.

To be exact one wants to have hands at the least movement when the blade is vibrating, that basically is at the node. Depending on the mass and stiffness distribution it is possible to have reasonably little moving areas that are larger than the (theoretically) point like node.

TLM

[John VZ]

Anytime you hit something with a sword some of the energy will go into oscillating the blade. But if the target is struck precisely on one node, and the hand is gripping precisely on the other... there is no opportunity for that energy to be absorbed in oscillation and it is ALL transferred to the target.

If you know three things about a sword... the weight, the balance point, and the nodal points... you can know a LOT about it.

Just digging through old material...

Short introduction: I'm an architectural-, industrial designer and silversmith. In this thread another hobby came to mind: I'm studying and playing guitar for about 30 years now and these harmonics and nodes do exactly the same in strings. With several different tapping techniques in different places you can create very interesting sound effects. Even to the point where a "revolving" oscillating effect occurs. Playing on a node is such an effect, it kind of starts to amplify itself.
For guitarists: compare to "flageolet" in different positions.

When you "strike" a string in any position, it will have a tendency to CHANGE towards a harmonic vibration. I expect the same effect to be in a blade! Therefore I think that it makes more sense to concentrate on a flow of nodes within a blade towards a harmonic/natural node, than just finding typical nodes in one blade.

What also occurs with a string is that holding your finger exactly on a node MAY cause a "flageolet", but directly (only a fraction is enough) besides it ABSORBS all energy. Therefore I would expect a hand (because of it's size) on a node (blade) to absorb/dampen the energy and not attributing in a powerfull "blow".

Makes sense?

Cheers, John.

[RionMotley]

Because your hand is a non-rigid mount - think of it as a rope tied loosely to the sword. No matter how hard you grip, you're really just wrapping the handle in a bag of water and oil, with bone inside the bag. When you're transmitting force to the blade, you're accelerating your hand, then the blade, and when the blade strikes, it's the instantaneous effect which you are worried about, the transfer of momentum from the blade to the target, not the transfer of momentum between the handle and your hand. AFTER the blade strikes the target, your hand will be deflected by the reflected impuse traveling down the blade. Although this happens on the time scale of microseconds, you are still able to model the blade as a free-floating member in space. Unless you're wearing solid steel gauntlets, the weight of your hand is negligible, if only due to the loose fluid coupling between your hand and the blade. On longer time scales, i.e. more than one oscillation of the blade, you will notice damping, but the initial amplitude of oscillation should be identical whether you are dropping the sword from some given height or striking with it in your hand such that it has the same terminal velocity. Afterward, you will notice the blade either rings, or has a damped harmonic motion - it will always be damped, but the degree of damping will be orders of magnitude greater if your hand is not at a node. Insofar as blade construction goes, it should follow that a guard placed anywhere but at a node would loosen, and depending on its mounting method would thus dampen the oscillation of the blade. If you strike your target at the node of the blade, then you should feel very little reflected impulse, and the only shock on your hand will be simple momentum transfer - i.e. your hand is still moving, and the sword has stopped/slowed.

it's really more of a hand-comfort thing than a cutting efficiency thing when you're talking about hand/node orientation.

[B. Stamper]

To put this in a laymen’s terminology, would I be incorrect by calling this the harmonics or resonation/ring of the blade?
I have often thought that the Japanese tried to absorb and or cancel out this resonation/ring by the installation of ONE mekugi usually installed higher on the nakago.
I could be wrong but this single mekugi would allow the bottom of the nakago to flex and slide inside the bottom of the tsuka kind acting like a “harmonic” dampener.
In my inexperienced opinion I often question the use (and possible safety) of two mekugi because it seems to me like if you pin both the top and bottom of the nakago to the tsuka you eliminate the flex and slide of the lower nakago inside the tsuka.(this probably only being millimeters) Overall, the prolonged resonation and flexing of a blade with two mekugi would constantly stretch and compress the tsuka core mekugi holes and the mekugi them selves resulting in “harmonic” transferal to the hand and eventually faster tsuka core failure. Forgive me if this is way of subject but just something that came to mind here.
I know there are plenty examples of Nihonto with two mekugi holes but fewer than that with a single.

[RionMotley]

Essentially a sword can be modeled as a free-flying mass. You could even make a sword out of rope or cable or chain (under tension... weight at the end?) and the same rules would apply at impact with a target.

Actually, that's not a bad idea to look at it that way. grab something really flexible, and mark out 1/3 of the length from each end. Like a piece of plastic milk carton material, or a plastic ruler. If you smack something with it in between your marks, it'll buckle around the impact point, lengthening the amount of time it takes to transfer its momentum to the target (the blade flexes and the ends "keep going" past the point of impact, while the part that actually contacts will stop) thus, your kinetic energy, while constant, is spread out over a longer time, thus delivering fewer watts.

Think of it this way. You fill a bucket with water from a hose. It takes 30 seconds. Then, you dump the bucket out, which takes 1 second. If you're at a height of about 1 meter, then you've stored 10 joules of energy. To fill it, you expended 10 joules or so, plus whatever pressure losses in the hose, etc. But it took 30 seconds. This is 10 joues/ 30 seconds = 1/3 watt.

By emptying the bucket in 1 second, you release 10 joules in one second, thus increasing your POWER to 10 watts!!!!

There's no overunity, since the energy delivered isn't greater than the energy input, but Power is a better determinant of terminal ballistics than total system energy. i.e. a bullet made of jello will not perform as well as a depleted uranium bullet of equal mass and equal velocity, since the jello smooshes up and spreads its energy over a longer impact time. The depleted uranium, however, will blast through the target because it transfers its momentum to a much smaller mass of the target over a shorter period of time (think about how fast sound waves propagate in the target medium, and the further you get away from the energy transfer rate of the medium (speed of sound) the less damage you're going to do per unit mass of projectile).

In terms of a sword, you spend a second or so storing energy as the motion you give the sword through space with your arms/body. This is "filling the bucket". You empty the "bucket" at impact. This should show itself in the use of softer materials than high carbon steel, since these materials will deflect and deform microscopically and thus dissipate their kinetic energy over a longer period of time and larger area than a harder, sharper material.

Thus, if you have a sword that weighs 2kg moving at 10m/s, its kinetic energy is roughly 100 Joules. If it takes you one second to accelerate to this speed, then you have put out 100 watts.

*100 joules would bring 1cc of water nearly to a boil. Think about that next time you drive a nail into a board, then touch the nail. ~sizzle~*

if at 10 m/s it takes your blade .05 meters to stop inside your target, (say you hit a bone) then you're talking something like .005 seconds, so the delivered POWER is 100,000 Watts. This is the ideal case, with no deflection of your blade. If you hit at a node, this is roughly the case, minus frictional losses to heat - which still wind up in the target as joules, but don't contribute directly to terminal ballistics and damage.

If you hit at an antinode, then the ruler example applies, where the blade bends and bows around the target impact point and extends the energy transfer period.

Try the ruler thing edgewise and width-wise, and you'll get similar results. Don't hold the ruler too tight, though, since your hand is a significant factor heavier than the plastic ruler. Slacken your grip as you approach impact, and observe the deflection. Hit a hard object between the 1/3 and 2/3 marks, then hit it right on those marks.

Then post back in amazement!

Also, if you hold a sword at various points, and thump it with a wood mallet, you'll notice it rings, or kind of sounds like a dead anvil, depending on how you hold it, and how tight the fittings are. Find the point where it rings loudest, and you've found your nodes! On a non-constant section, the nodes will not necessarily be mutually equidistant, nor equidistant from any relative point on the blade/tang/etc.

Try it out on a ruler, then thump some swords, and let me know if you get a better grasp of all this. I might be teaching high school physics next year - I figure if I can teach you guys something, then I can teach anyone.

*nudge nudge*

;-)

[B. Stamper]

I have such a “Motley” combination of thought running through my head right now…….

[RionMotley]

At least I can sing, hmm?

:-p

DO THE RULER THING!!!

Seriously.

GO!

NOW!

Grab a ruler, and smack the edge of a table with it.

Seeeeeee? ;-)




One note, however... I was off by about a factor of 1000 on the amount of energy required to boil water... I've been doing work with electrolysis and got my nummahs mixxxedezzed uppeth.

Soooo... it's not a cc or a milliliter, but a microliter that you would boil. Your run of the mill raindrop is on the order of 10-100 microliters. It'll still get you sizzling tho!

[B. Stamper]

Well I don’t want to get to far off topic here but as far as Japanese tsuka are constructed, some questions arise in the physics of harmonic transferal to the hand comparing the single mekugi pin construction vs the double mekugi pin construction. On a single pin constructed tsuka I would imagine either one of the two occurrences happening (see fig. A) On a double mekugi tsuka I can only imagine more resonance transferal be sent through the hands and more compression and pull in a smaller area resulting in a earlier retirement? ( fig. B) Many swords have double mekugi claiming the extra for safety and this makes sense but in the long run I wonder what is better ie what one is going to result in a earlier tsuka loosening ect?

[B. Stamper]

Dang, a broke my ruler!

[B. Stamper]

Computing.......Computing..........Computing
ANSWER: 47

[RionMotley]

You're right about earlier fatigue.

What you've essentially got is a free, unpinned system - the sword itself - which operates on a cosine flexural mode. In other words, the ends go up and down, and the middle goes up and down, but the nodes are 1/3-ish from each end. As mentioned before, this varies depending on mass distribution, and to a degree, hardness/elasticity distribution along the blade/tang. Anything attached to this is singly or doubly pinned, or unpinned, depending on how firmly and in what manner the hardware is attached. The guard (Tsuba, right?), for example, can be seen as an unpinned member, since these are ostensibly loose-fitting, and held in place between the Habaki and the Tsuka.

*note... at this point my brain is farting loudly, and all my japanese sword terminology is floating out the window with the flatulence...*

Back on point - the Tsuba will contribute to your mass distribution intermittently, altering the resonance of the sword. If it is tight fitting, it can be assumed to be a singly pinned member, allowing free rotation about its center of mass, and can be used to tune the sword, based on position and mass. This can cause some interesting effects, since you can actually have several waveforms overlapping on the sword at once - if you manage to hit on the "sweet spot" node out front every time, then your tsuka should never loosen, but because of other hardware components, some energy transfer can occur, and non-cosine vibrational modes can set up which will place stress on your tsuka pins. The habaki would fit tightly enough in a well constructed sword to also count as a singly pinned, or integral member of the overall blade so as to simply work to alter the mass distribution, as the pommel and guard would on a western sword.

As far as the doubly pinned tsuka, I would say the wood part itself would contribute very little in the way of oscillation, since it is internally damped heavily by the fiber-on-fiber friction. I've not seen a piece of wood that would resonate like a piece of metal, or for as long, for just this reason - it's a microcomposite of many many cellulose fibers tightly packed and interspersed with the free space of empty cell walls. This is why wood floors make for a generally quieter space than tile or stone.

Further, the pins are themselves flexible to a degree, and less heavily damped due to the orthogonal relationship of the wood grain fibers to the direction of oscillation of the blade. They're set up more like a bow (as in archery). I suppose the ideal setup would be a very tough, flexible wood for the pins - say maple, hickory, or even mulberry (insanely elastic, dense wood) or perhaps even a willow or an oak. The scales, or the grip itself, would be best made from a not-so-hard wood, and perhaps spaced away from the blade a ways. This would minimize the shear forces involved, and allow the grip to flex, rather than undergo a more or less pure compression. On a microscopic scale, the two grip halves would flex outward, and the fore and aft pins would flex away from each other at the ends. If the grips are not spaced out from the steel (we're talking a strip of paper between the blade and the scales) then the pins are placed in double shear, and while this is a stronger configuration than single shear, the stress is concentrated on the center of the pin as shear, rather than a more gentle bending moment, and the pin will compress against the metal. Thus, upon disassembling a worn out doubly pinned tsuka, I would expect to find an incised ring around the middle of the pins where the edges of the hole have impinged on the wood and compressed it, allowing it to loosen in the hole, whereas the pin-scale join would more than likely be rather intact and quite tight.

On a spaced design (which may or may not exist in practice, I'm simply using this as an example to illustrate the forces and deflections involved) the double shear would less affect the pin-tang interface, and would cause the ends of the pins to inscribe a cone-shaped path, thus wearing the pin-tsuka interface, and loosening the scales on the pins, rather than the pins in the tang.

On a single-pinned handle, one has the same static forces exerted on half the pin cross sectional area, thus the static strength of the grip-tang interface is weaker, but the dynamic loads would simply not be transmitted, since the pin acts as a hinge point, and allows the grip to vibrate freely as a singly pinned member on the unpinned sword's oscillatory motion. This may or may not loosen other hardware such as the Tsuka-maki or the pommel cap, but the overall effect would be a more-or-less even wear on the pin by the tang hole edges, as well as the edges of the holes in the wooden grip scales.

I.e. the benefits are really neither here nor there - you lose some dynamic durability on non-sweet-spot cuts, but gain "let go" strength with two double-shear pins reacting the centripetal acceleration of the blade. You would actually be better off with a highly flexible thermoplastic handle carefully shaped to envelope the tang, and then friction stir or ultrasonically welded to it, thus providing a material property gradient from tang to grip that would even out any momentum transfer-induced strain.

I'm joking about the fric-stir weld. Though I've seen aluminum and brass friction stirred together! And clear acrylic and black ABS welded together without solvent!

Ok, back on point - the choice is yours. The decision to use a sword should be made on more important things related to the dynamic/harmonic balance, and the grip attachment is largely a maintenance issue, and not an overall reliability issue. The location of the pins would be critical in determining the relative strain levels, and you might consider pins more closely spaced vs. towards the ends of the grip - thus minimizing the net moment acting between the pins by limiting the effective lever arm.

Equal linear displacement of the tang would thus provide a smaller angular displacement of the pin axis relative to the handle material.

*breathes again*

I'm going to go to sleep now... Did anyone try the ruler experiment?

[B. Stamper]

Ill read this again after I’ve had fewer beers, go to bed Motley. :P

[RionMotley]

The pegs will still deflect as I described, but when I reviewed the geometries, it turns out the pegs would deflect in the SAME direction - i.e. both forming a U shape vs. a "u" and an "n" shape - there's no node between them (ostensibly) so the deflection would be in the same direction.

Included is a drawing I made in MotleyCad XP. Y'all should download it and give it a shot - especially since the new Service Pack 3 release.

:-p

It shows the deflection and impingement areas I was talking about.

The handle material will cause the deflection in the opposite direction from the tang, but I had another thought - use of a hardened material - perhaps steel? for the pins, and doing a press-fit into the tang, then a separate press fit into the wood scales for the handle would provide a somewhat more difficult to disassemble, but more durable joint... Just a thought.

[B. Stamper]

Im loving my copy of MotleyCad XP!
I have a lot of questions ect, Ill get back here shortly.

[RionMotley]

Im loving my copy of MotleyCad XP!
I have a lot of question ect, Ill get back here shortly.

Until you try MotleyCAM 2007 Enterprise Edition with Business Contacts Manager and Personal Firewall, with Secure AutoArchive. Also included in the download is a 30-day trial version of MotleyCad 2007, with Service Pack 1.

[B. Stamper]

Brass and or metal mekugi (pins) are really looked down at by the Japanese sword makers and enthusiast. This entire topic of node points just further deepens my respect for the sword makers of the past, I cant help but think that harmonics of the blade and what we call node modules or points was probably a kindergarten level class in there studies?

[B. Stamper]

Until you try MotleyCAM 2007 Enterprise Edition with Business Contacts Manager and Personal Firewall, with Secure AutoArchive. Also included in the download is a 30-day trial version of MotleyCad 2007, with Service Pack 1.

Tucows has it all for free!

[RionMotley]

While we continue developing our Harmonics Solver, Check out the new features of MotleyCAM:

Consider Upgrading to Motley Personal Firewall 2007, with even more features than Enterprise Personal Firewall.

------------------------------------------------------------

Yes, i know brass/steel pins are looked down on. The easier material is ALWAYS looked down on. Less skill to get it right.

Personally, I'd rather have it WORK right than "BE" right. This is not to say I prefer slipshod work... far from it, but being harder doesn't always mean better.

[B. Stamper]

“Back on point - the Tsuba will contribute to your mass distribution intermittently, altering the resonance of the sword. If it is tight fitting, it can be assumed to be a singly pinned member, allowing free rotation about its center of mass, and can be used to tune the sword, based on position and mass. This can cause some interesting effects, since you can actually have several waveforms overlapping on the sword at once”


A bandpass katana!

[B. Stamper]

Ill take a 7th order katana please…..