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Thread: Practical effects of 'complex harmonics'

  1. #26
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    Quote Originally Posted by Vincent Le Chevalier View Post
    One more question: How does all this affect the blade node? In a sword showing CH, is it different for all demi-nodes?
    CH swords tend to have what Gus describes as a 'long' blade node- where the zone of zero vibration appears to be spread over several inches rather than being a discrete point. Such swords also tend to be good tip-cutters.

    Or In other words, are there demi-nodes only on the hilt, or are they associated to other demi-nodes on the blade?
    The 'long' blade node noted above may actually indicate the presence of demi-nodes on the blade but we're not sure.

    If the blade node stays the same, is it possible, even on CVH swords, to find a primary hilt node by grabbing the sword at the blade node (still vertical with the hilt down), hitting somewhere and watching where the vibrations are the smallest?
    I just tried it on a 'whippy' XIIa. Didn't work... I suspect the vastly greater mass at the hilt end (as opposed to the tip of the blade) prevents getting enough oscillation going.

    If I understand what you describe, the blade node should be different for each demi-node gripped, but perhaps not significantly different, which is something that could be used...
    Using the same xiia above- which is a 'CVH' sword- I marked the center of the long blade node with the hilt gripped at the top of handle. I then gripped the hilt in two different placess, near the middle and near the pommel, and struck the pommel and checked the apparent COP. It was identical in all three cases-- 23-1/2 inches from the base of the blade. HOWEVER- the lower I gripped the handle (towards the pommel) the longer the node appeared to be! Interesting- I'd never thought to try that before. Great Questions.
    Tinkerswords.com Fine knives, swords and daggers in the style of the European Middle Ages and Viking Era

    "Then, one night as my car was going backwards through a cornfield an ninety miles per hour, I had an epiphany..."

    Luke 22:36 Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.

  2. #27
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    Quote Originally Posted by Andrea N. View Post
    And what's the most convenient way to find out if a sword is CVH? I don't feel that banging the pommel is enought (maybe I'm just not experienced for this) so how? I don't think that you can test cut with an antique...
    The two methods are simple and both depend on 'feeling' for the 'dead spot.' One method is the pommel-sriking method; the other is to bag the swords tip on something hard and seeing if you feel shock. Looking for either demi-nodes or CVH you want to grip the sword firmly in the circle of the thumb and forefinger.
    Tinkerswords.com Fine knives, swords and daggers in the style of the European Middle Ages and Viking Era

    "Then, one night as my car was going backwards through a cornfield an ninety miles per hour, I had an epiphany..."

    Luke 22:36 Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.

  3. #28
    For what is worth... Here is a tentative explanation of how I see things now.

    As you might know, there is not just one way for any object to vibrate. There are many shape an object can take, that are associated to vibrations of different frequencies. All these shapes are the modes of vibration. The first one has two nodes, the next one three, and so on and so on... And all these modes are excited and start vibrating together when an impact occurs. But the repartition of the energy among modes depends on the location of the impact, and on the external conditions affecting the sword, for example the hand, that imposes a force on the hilt. For a given energy, the first mode will show a greater amplitude in vibration than the second, which in turn will vibrate more than the third...

    If as you say the blade node stays at the same place and only appears more or less wide, I'm quite confident the center of this 'wide node' is one of the two nodes of the first harmonic mode of the sword, because this mode is the most noticeable.

    Now how can it get larger? As you said it depends on the location of your hand, which means that it is indeed your hand that causes the width of the node. I believe your hand sets the repartition of the energy of the vibration among all the other harmonic modes of the sword. For example, if your hand is near a node of the second mode, it will be easier to store energy in that mode than in the first. So the first mode will be vibrating a bit less, which in itself could cause an apparent change in the size of the blade node. What's more, the vibrations of the second mode become more noticeable, and that mode has two nodes on either side of the first mode's node. So in effect you have a larger CoP, but it could also become a bit more 'blurry', because of small vibrations of all the modes in this area.

    Of course the effect is probably not limited to the two first modes, especially on CVH swords. But you get the idea...

    In theory it is something that could happen on any object, but in practice we put only a limited strength in our hand. So on some swords we will not manage to ensure this energy transfer, and these are only HB. On some swords we will be able to do so just when close to the nodes of higher modes, and these will appear CH. And on some, it will be easy whatever the position, and these will be CVH. But this discrete repartition is an effect from our hand and not from the objects.

    An interesting property of this explanation is that the other node of the first mode should be at the location that generates the sharpest blade node. Looking at my simulations it should be the closest to the blade, which is also in line with the observations you reported in your previous post.

    Several things could cause this to appear. A hilt-heavy mass distribution will diminish the vibrations in the hilt, so the grip will be facilitated, and the nodes will be brought closer together as well. I think the flexibility of the blade towards the tip would also help. But the interaction of the effects is not something easy to figure...

    Well at least that's the beginning of an explanation. Looking at my type XI with this in mind I've been able to notice a weak semi-node on the handle, that indeed makes the blade node wider if I apply enough force. And it is precisely at the place where my simulation gives the first node of the second mode...

  4. #29
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    Vincent, I think that you are on to something here. How does someone observe secondary modes of vibration? Also-I have several CVH swords of different types and rigidity on-hand at the moment; can you suggest a simple experiment that might indicate or tend to disprove your hypothesis?
    Tinkerswords.com Fine knives, swords and daggers in the style of the European Middle Ages and Viking Era

    "Then, one night as my car was going backwards through a cornfield an ninety miles per hour, I had an epiphany..."

    Luke 22:36 Then said he unto them, But now, he that hath a purse, let him take it, and likewise his scrip: and he that hath no sword, let him sell his garment, and buy one.

  5. #30
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    Perhaps over simplifying but the easiest properties I understand about complex and variable harmonics are resonance and reverberation. Think of pretty much any stringed instrument. The sine wave can be altered through a great may variables of action.Especially true of more manipulative stringed instruments where primarily indcuded energy is happening on one end and manipulation/modulation on the other.

    It kind of goes back to a knowledgable user appreciating good instruments, while being able to get the best use of poor ones.

    I'll bet few swordmakers consider themselves luthiers but in a very true sense, there are parralells.

    Cheers

    Hotspur; just give me something that is fun to play

  6. #31
    Quote Originally Posted by Michael Tinker Pearce View Post
    Vincent, I think that you are on to something here. How does someone observe secondary modes of vibration?
    Observing a specific mode of vibration is alas tricky... As I said any force applied, impacts and so on, will stimulate all the modes, so the secondary mode is always more or less hidden in these situations.

    The only solution I can think of is to apply a vibration on the sword, with a fine-tuned frequency, and watch for a resonance as Glen said. Normally there should be one at the frequency of the first mode, then one at a higher frequency that would be the second mode. Watching the shape taken by the sword as it resonates would allow to really watch the second mode.

    I've seen this kind of experiment done with ropes, but never with solid objects like swords. The problem would be to find what could give a vibration with sufficient control, and with enough "punch", in the necessary range of frequency. Should be possible but it's an investment...

    The other solution is simulation, but you have to trust the simulator And have sufficient data...

    Other than that, in fact the experiments you already did are probably the furthest you can go with just your hands and your eyes.

    Also-I have several CVH swords of different types and rigidity on-hand at the moment; can you suggest a simple experiment that might indicate or tend to disprove your hypothesis?
    If you manage to identify a demi-node, it would be possible to test if it is indeed a node of the second mode. Perhaps on CVH swords it's not easy, on CH sword maybe the effect is visible.

    Basically you would clamp the sword in a vice at the place of the demi-node, then set it to vibrate. If indeed it is a node of the second mode, two effects should be visible:
    - The vibration should last longer than when clamped in another place, neither primary nor demi node
    - Two nodes should be visible on the blade, on each side of the primary blade node.

    That's roughly what you observe with your hands-on experiment, except that your hand still allows the first mode to vibrate. The objective of the vice is to prevent totally the first mode from vibrating.

    For this to work the vice must be really tight and with the minimum damping, i.e. no padding, so there is a risk for the sword to be damaged. Otherwise you'll just see the sword wobble slowly from side to side. Honestly I have never seen this done - I don't know how well it would work and it does not really prove anything if it doesn't. But if it does, the theory holds some water...

    I think it would be of some value, if you really want to understand what goes on, to build the simplest possible object that exhibits CH or CVH. For example a bar of uniform steel with a constant cross-section shape, but with tapering. I'm pretty sure all the details of the shape of a sword are not necessary for CH or CVH to happen. Then we would have a simpler starting point to figure the causes better.

    Kind of like I was taught to report software bugs: find the simplest sequence of actions that causes the misbehavior. Except here it is the desired behavior

    I should point out that all these problems are in no way specific to swords and were studied in other contexts. For example base-ball bats:
    http://www.kettering.edu/~drussell/Demos/batvibes.html

    There you have an illustration of the modes of a baseball bat. Of course they are designed with other objectives, but the physics stay the same, it's just how we use them. In fact I could make the same kind of animation for a sword...


    All these efforts have to be weighed against the benefits, of course. Personally I'm just looking for a physical explanation out of scientific curiosity, but I'm still very glad to play with my boken that has no vibrations whatsoever

  7. #32
    Quote Originally Posted by Glen C. View Post
    It kind of goes back to a knowledgable user appreciating good instruments, while being able to get the best use of poor ones.

    I'll bet few swordmakers consider themselves luthiers but in a very true sense, there are parralells.
    I very much agree Glen. Music instruments are works of art in their own right, mixed with very a accurate control of physical properties. It is this same mix I'm looking for in swords: beauty allied with efficient understanding of the underlying physics (empirical or not). That's what make sword making different from sculpture...

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