Sliding weights

[Jeff D]

Hi All,

While it isn't a sliding weight, the sliding hilt does change the point of balance. This is from the Landesmuseum.

Jeff

[Jens Nordlunde]

Jeff, don't hold us waiting too long - which Landesmuseum?
There are several in the German speaking countries - so where is it?
BTW thanks very much for being the first to show a sword with a gliding weight

Jens

[Jeff D]

Originally Posted by Jens Nordlunde

Jeff, don't hold us waiting too long - which Landesmuseum?
There are several in the German speaking countries - so where is it?
BTW thanks very much for being the first to show a sword with a gliding weight

Jens

Oops Sorry Jens, this is the one in Zurich!

Jeff

[fearn]

Hi Jeff,

Neat sword! I think it's a solution to a different problem, though. There's a book out there (forgot the title) that's a translation of a late-medieval German swordmanship manual.

In that manual, they show the proper way to use a long sword (i.e. hand-and-a-half sword) against a foe in plate armor. Basically, you have to have gloves, on, because you grab the sword half-way up the blade and use the tip as a bayonet/pry-bar to attack the cracks in the armor at extreme close range. I say bayonet rather than short spear, because the the stance reminds me of the way one holds a rifle with for bayonet practice, as do the moves (short stabs and swings, using the pommel and guard in place of the rifle butt).

My suspicion is that this sword was designed with this half-sword grip in mind: Normally, one's finger holds the guard at the base, but at close quarters, you grab the pommel with the other hand, push the guard forward with the lead hand, and use it in a half-sword grip, without sacrificing the guard on the forward hand.

As far as swords with sliding weights, doesn't Stone's Glossary have a picture? I don't have my copy with me, but I have a memory that it does.

Fearn

[Rivkin]

In all honesty - I can imagine (barely) how one can use a movable weight in a throwing weapon, hoping to create some complex gyroscopic motion that would create a restoring force and stabilizing the trajectory as a result.

I can imagine using an adjustable grip or pommel to manage the balance and so on. I can imagine using an axe, the weapon with a high angular momentum.

I can't imagine any reasonable use for a moving mercury or anything in a sword. Suppresion of oscillations is most reasonably done by putting a tuned pitchfork into pommel. If this pitchfork is surrounded by an extremely viscous material, i.e. overdamped, you can have a very efficient transform of oscillations into heat (that's what they do in modern "professional" tools, like hammers). Another way is to design a sword in the way that all it's oscillations somehow negatively interfere with each other, so it basically damps itself (this method is way more complex, but that's what used in modern cameras to suppress the vibrations from shutter/mirror release).

Using a bottle of mercury for this purpose is rather strange.

[Jens Nordlunde]

Jeff, thanks a lot, I will try to have a look at it if possible.
Fearn, interesting what you write, but let us wait and see what I can come up with.
Rivkin, hold your horses till I - maybe can come up with something else.

Gentlemen it has been a pleasure

Jens

[Jim McDougall]

OK Fearn, I spent the better part of an evening thumbing through Stones, and didn't find any evidence of sliding weights or anything similar....but must say it was still enjoyable as always.I really love that book!! No matter how many times guys like to hammer away at Stone for the occasional errors, it's still fun to read so much very early data.He really set the stage for weapons research, and encouraged future researchers, such as us, to correct the inevitable errors with new evidence and revised data.
One thing I did find, and at the risk of mentioning something which applies only indirectly and is most probably irrelevant, I found:

"...Cestus: Heavy leather things, often weighted with lead or iron, wound around the hands and arms of Roman boxers to give additional weight to thier blows"
-Stone, p.168

Once again, leave it to the legacy of the ancients. Obviously, this note is purely speculative correlating the concept in dynamics and influences of many aspects of earlier cultures in application in later times. Clearly one would not need to seek such simplistic dynamics for the increase of force in a sword in ancient boxing, but the coincidence seemed worthy of note.

The search for the elusive sword with the slide continues

Best regards,
Jim

[Rick]

Originally Posted by Jim McDougall

OK Fearn, I spent the better part of an evening thumbing through Stones, and didn't find any evidence of sliding weights or anything similar....but must say it was still enjoyable as always.I really love that book!! No matter how many times guys like to hammer away at Stone for the occasional errors, it's still fun to read so much very early data.He really set the stage for weapons research, and encouraged future researchers, such as us, to correct the inevitable errors with new evidence and revised data.
One thing I did find, and certain unnamed parties will go berserk ranting about unrelated or irrelevant data or free association etc. by my mentioning it.....

<snipped>

Best regards,
Jim

[Jim McDougall]

Man you're fast Rick!!!!

[Andrew]

There is a tool used in orthopedic surgery for driving and extracting nails in bone. The concept is simple, but effective: the tool's head is placed on the nail head, and a sliding weight is forceably impacted in the desired direction. Forward to drive the nail, back to extract.

As with Jim's observation, this is not directly relevant, but may be edifying.

[fearn]

Jim, thanks for checking Stone's glossary for me. Now I'll have to figure out what stray memory I was thinking of. Possibly it was a sliding sleeve on a spear (for the forward hand, so you don't sand your palm off jabbing with the spear). Otherwise, I agree with you about the value of that book. I discovered my parents' original copy as an impressionable pre-teen. Now I'm here. Go figure.

Fearn

[Rick]

Originally Posted by Jim McDougall

Man you're fast Rick!!!!

Eight years of memories Jim .

[ariel]

The only such weapon I can imagine being workable is an ax. It necessarily goes only up and down. Anything staying for some time in a horizontal position and /or requiring lateral movements would be unworkable.

[fearn]

Originally Posted by ariel

The only such weapon I can imagine being workable is an ax. It necessarily goes only up and down. Anything staying for some time in a horizontal position and /or requiring lateral movements would be unworkable.

You don't like the idea of a pile-driver rapier, Ariel?

F

[Ian]

I have two engineers working on this problem.

To get them involved, I needed to rephrase the problem in terms of a baseball bat hitting a ball. They are baseball nuts, so this got their attention. While there is a book on the physics of baseball, as far as we know nobody has considered a bat with a sliding mass (probably not legal anyway ), so they want to work on this in case they come up with a "super bat" they can use in their Sunday softball league.

Engineers are like that -- give 'em a question they don't know the answer to, and they will worry away at it for hours. BTW, summer is a quiet time in our office.

Will be back in touch when, and if, they can find an answer.

Ian.

[Tim Simmons]

The sliding hilt is quite a good idea, how it worked in actual combat is another matter, but in theory it transforms a long thrusting weapon into something more general for close contact in the melee. Tim

[Jens Nordlunde]

Excelent Ian, but I think I on Google saw a training baseball bat with a sliding weight – only for training it said. It had some kind of sliding weight inside, but I am not sure what kind.

Imagine you had an arrow with a sliding weight on the haft. Before you took a shot, you pulled the weight back and when the arrow hit the target, the weight would make sure the impact was bigger than normal – would that work?

I hope to see the sword with the sliding hilt to morrow.

[Jens Nordlunde]

To day I went to Landesmuseum in Zurich, and found only very few weapons, and not the one Jeff show. When I asked where they were, I was told that they had packed them down, and no one knew when they would be on exhibition again, but to morrow a special exhibition would open with some weapons. I then went to the museums shop to ask after a book/catalogue showing weapons from the museums collection - no book, they had once had one, but it was sold out, and they did not plan another one.
Jens

[Ian]

Originally Posted by Jens Nordlunde

Imagine you had an arrow with a sliding weight on the haft. Before you took a shot, you pulled the weight back and when the arrow hit the target, the weight would make sure the impact was bigger than normal – would that work?

Jens:

I don't think this would have any effect, but perhaps it might if the weight shifted from the fletch to the head at the time of impact. Because we are talking about a piercing shaft, all energy would be concentrated at the point of impact, and the mass of the arrow lines up directly behind that point -- so however mass is distributed behind the point of contact would be immaterial, unless possibly if part of that mass is moving along the shaft at the moment of impact. Even then, I think the effect would be small and would need to be weighed against the effects of a rear-weighted arrow on its flight and accuracy. The small potential gain in penetrating power could well be offset by impaired accuracy.

Ian.

[Ian]

Here is what my engineering colleagues had to say about the question before us. I have translated from engineering-speak as well as I could.

The problem of a weight (mass) moving along a rod that in turn strikes another object is really quite complicated and we do not have enough information to answer your question. Here is a somewhat lay interpretation of the problem, which we have modified from The Physics of Baseball by Robert K. Adair.

Basically, the properties of a rod (sword, bat) relevant to striking another object squarely are defined by three weight distributions, or three moments.

1. The sum of the weight of each part of the sword, which is just its total mass (the zero moment)

2. The sum of the weight times distance, measured from the handle, of each piece of the sword (the first moment)

3. The sum of the weight times the square of the distance for each piece of the sword (the second moment or the moment of inertia)

There are three key positions along the sword that follow from these three moments.

a. The center of gravity
b. The center of inertia
c. The center of percussion

There are three additional factors that need to be considered.

d. The elasticity of the sword
e. The resonant frequency of the blade
f. The position of the vibrational node

Although the center of percussion and the vibrational node will be close to each other, they are not the same.

For a sword of fixed mass distribution, we can determine fairly simply the various points that correspond to the three moments.

The center of gravity is just the balance point. The center of percussion can be found by holding the sword lightly by the end of the hilt and striking the blade gently with a hammer; when the blade is struck at the center of percussion there is no detectable movement at the hilt. In most cases the center of percussion is very close to the vibrational node -- when the blade is struck at the vibrational node no vibrations are felt at the hilt.

The center of inertia can be determined by placing the sword on a frictionless surface (such as an ice rink) and pushed away. When the push is placed at the center of inertia the sword will move away without any appreciable rotation.

Each of the moments are manifest in obvious ways. The weight is felt by holding the sword vertically. The force required to hold the sword straight out in front of you at arm's length is proportional to the first moment. The force required to wave it back and forth vigorously when it is vertical is proprtional to the second moment. This second moment contributes most to the "feel" of the sword and is the factor most important to the user.

The elasticity is determined by the blade's resilience near the point of impact; a resilient blade may store energy upon impact and return that energy to the target.

The resonant frequency is a measure of the energy loss when a target is struck at a point along the blade away from the vibrational node. A higher frequency indicates a larger (i.e., longer) "sweet spot." Swords with longer blades and thicker handles will display higher vibrational frequencies and long sweet spots.

This is what we know about items that have a fixed mass distribution. When you add a varying mass distribution, the problem becomes more complex. When the weight distribution shifts, all of the moments change.

A sliding mass would create a tip-heavy sword, moving the centers of gravity, inertia and percussion away from the hilt. Depending on the fraction of the total mass that is moving and its final resting place along the blade, the respective moments may well be centered quite close to the tip, and essentially one would have a club. Such a shift in mass would likely make a clumsy and slow weapon.

We will think some more about this problem but it seems that any substantial shift in mass would produce a sword that could be difficult to control and would probably slow its action. How much of an effect would depend on the fraction of total mass that was shifting and the distance it traveled away from the hilt.

[Rivkin]

This list seems popular among the sword community - it's not the first time I've seen similar ideas expressed concerning the waves for example.

My problem is that for example it's hard for me to understand why the center of gravity is going to be a node for all waves (it should not be for at least for the waves with an odd number of halfwavelengths). Concerning the hilt, it seems more like a boundary condition to me, rather than a center of gravity. Concerning longer swords having higher frequencies and wider diaposon, it seems counter-intuitive to me - I would expect smaller swords to have larger frequencies and bigger separation in between of individual modes, but that's just my guess.

I'll be honest, I don't understand some of the ideas expressed above. Concerning the sliding mass question, again, what are the possible benefits of this construction vs. simply high momentum fixed mass weapon - nothing simple comes to mind.

[Ian]

Originally Posted by Rivkin

... My problem is that for example it's hard for me to understand why the center of gravity is going to be a node for all waves (it should not be for at least for the waves with an odd number of halfwavelengths).

The center of gravity is a balance point and the centers of inertia and percussion are located at different points along the blade. The respective centers are features of the weight distribution and mechanical properties of the sword (which mostly comprises the blade and the tang).

Waves do not originate from any of these centers. Waves are set up at the point of impact and spread out from that point. The further away the point of impact is from the vibrational node, then the more vibration will be transmitted along the blade and will be felt in the handle.

Originally Posted by Rivkin

... Concerning the hilt, it seems more like a boundary condition to me, rather than a center of gravity. Concerning longer swords having higher frequencies and wider diaposon, it seems counter-intuitive to me - I would expect smaller swords to have larger frequencies and bigger separation in between of individual modes, but that's just my guess.

The tang is continuous with the blade and would not be a boundary condition. Depending on the properties of the handle covering materials there may be some dampening of the vibration transmitted from the tang to the hand. My colleagues assure me that physics dictates that the longer the blade, the longer the sweet spot and the higher the frequency of vibrations.

Originally Posted by Rivkin

... Concerning the sliding mass question, again, what are the possible benefits of this construction vs. simply high momentum fixed mass weapon - nothing simple comes to mind.

I cannot see any real benefits to a sliding mass. That was the conclusion of my esteemed colleagues also -- they are skeptical that any greater force could be achieved, and the sliding mass would introduce unpredictable and inconsistent properties of the sword depending on how it was wielded.

Ian.

[fearn]

Hi Ian,

I think your overall conclusion is probably right--that a sliding mass is not beneficial, although it might be less troublesome in an executioner's sword.

I won't pretend to be a physics expert, but I do know a few things about swords and rods.

One thing that confused me was the difference between center of inertia and center of gravity. These are different because....?

So far as the vibrational nodes go, my limited observations are that straight swords are quite a bit like rods: the vibrational nodes are at the geometric center and the quarters. HOWEVER, the center of gravity doesn't have to be at any of these points. To give a crude example: imagine a rod two- thirds metal. It should be obvious to most people that the point of balance will be fairly close to the center of the metal part, because the wood is much lighter. In a sword with a heavy pommel and lighter blade, you can put the center of gravity and/or inertia pretty much where you want it.

So far as longer blades having bigger sweet spots due to higher vibrational frequency, I'll admit that I'm confused too. I agree that the longer blade should have a bigger sweet spot, but I'd bet a fair amount that it would have a lower frequency, just because it's longer. This is the same reason that cellos generally play lower than violins: the frequency is lower, not higher, in a longer string. I'm guessing that the word we're looking for is longer wavelength and bigger amplitude.

However, I'm still very glad that we had an engineer look at it. Now, if someone will get out there with the PVC tub and ball bearings, and find out what a sliding weight feels like when you swing it, we can all rest easily....

[Rivkin]

1. With given definitions the center of gravity and the center of inertia will be the same.

2. If its possible, I would really like to see the formula they use for sword's frequency as a function of length (do they consider it a string ? a thin and long prism ?).

3. Concerning tang not being a b.c., or even a separate body, I would prefer to hold a vastly different opinion.

4. Concerning waves propagating in swords and nodes - propagating waves usually do not have nodes. When people talk about nodes, they usually speak about standing waves, i.e. steady state solutions etc.
I suspect that the logic was that if sword can be considered a string, than a full wavelength standing wave will have a node in the middle, but it will basically be true only for even halfwavelengths mode... Plus I'm really too lazy to calculate the modes of a string with a variable mass, so I don't know how big percentage of the waves will have nodes at the center of mass.

5. Concerning the center of percussion - as far as I remember (and I remember it very poorly), the center of percussian is when you hit it, all the momentum is transfered into the rotation movement of the sword, without any daggling down or up.

[Jens Nordlunde]

Hi Ian,

Thank you for using your time on this topic, and thank you to your colleagues for their time. I had in the start expected the problem to be les complicated than it is, and I cant say that I can follow all the explanations, so I will have to read it one or two more times and see if it helps.

Fearn, I don’t have a sword with a sliding weight, only one with steel balls, and swinging that, the moving of the balls does not make much difference, it would not as the balls are not very heavy.

I think the conclusion is, like several has stated, that sliding weights on swords are non existent, and should such a sword be found, then it must have been made as an experiment – not for use.

[fearn]

Hi Rivkin,

You're right, of course: I'm thinking of standing waves, aka, the way the sword flexes when it hits something. The nodes are where it flexes the least, and those are where you want to hold it, unless you enjoy hand shock.

Hi Jens,

Yep, I think we've settled it. It's a good thing, too. Otherwise, we'd next have to deal with the mechanical advantage that the Chinese gain by putting those nine rings on the back of the nine-rings dao

Fearn

[Rivkin]

Originally Posted by fearn

You're right, of course: I'm thinking of standing waves, aka, the way the sword flexes when it hits something. The nodes are where it flexes the least, and those are where you want to hold it, unless you enjoy hand shock.

That's one of the things I don't understand - what is a node for one wave, will be a maximum for another wave.

[Ian]

Hi Kirrill:

You raise some interesting points and I will try to deal with them as best I can. My college physics is but a distant memory!

Both of my local contacts went on vacation on Friday, and will be out of the office for the next four weeks. Academics do very well with vacation time. I will do my best.

Ian.

Originally Posted by Rivkin

1. With given definitions the center of gravity and the center of inertia will be the same.

As described above, the respective moments vary with distance of the various components of mass from the handle, raised to the power of 0 (the zero moment, which is simply the total mass); with distance raised to the power 1 (the first moment); and with distance raised to the power of 2 (the second moment). The center of gravity relates to the first moment, the center of inertia relates to the second moment. If mass is distributed uniformly along the length of the rod, then I believe that the center of gravity and center of inertia will be the same. When mass is distributed unequally, then the two will be different. The difference will be demonstrated by the two tests I listed.

Originally Posted by Rivkin

2. If its possible, I would really like to see the formula they use for sword's frequency as a function of length (do they consider it a string ? a thin and long prism ?).

Need the experts for this one. I believe they modeled this as a solid rod.

The frequency we are talking about, then, is the resonant frequency of a solid rod, which (if I recall correctly) for a given diameter varies with the density of the material and its length. When we talk about a string, there is also a factor for the rigidity of the material or tension applied (a taught string resonates at a higher frequency than a slacker string). The resonant frequency is fixed for a rod of given dimensions and homogeneous construction. The amplitude of the vibration varies with the distance the rod is struck away from the resonant node.

An interesting example is the aluminum (aluminium) baseball bat, which has an outer aluminum shell and an inner core that is air-filled. Striking a ball with such a bat produces a brief, high-pitched "ching," and a lower-pitched "thunk." The higher pitched sound reflects the resonant sound of the metal shell, and the lower-pitched sound comes from resonance in the air-filled chamber.

These sounds are hard to distinguish with the human ear but apparently have been measured with sophisticated recording equipment. The low frequency sound is just a few hundred cycles per second, approaching the limits of detection for the human ear.

Originally Posted by Rivkin

3. Concerning tang not being a b.c., or even a separate body, I would prefer to hold a vastly different opinion.

For full tang construction, there should be no boundary condition because the tang is essentially an extension of the blade. This is the same situation as a baseball bat, and the handle presents no boundary condition in that example.

As I mentioned above, there may be dampening of the vibrations by materials around the tang. For partial tang construction, I am unsure how much of a boundary condition there may be. It probably varies with the width and length of the tang, and again the wrapping materials will be important in how much dampening of the vibrations might occur for the user.

Originally Posted by Rivkin

4. Concerning waves propagating in swords and nodes - propagating waves usually do not have nodes. When people talk about nodes, they usually speak about standing waves, i.e. steady state solutions etc.
I suspect that the logic was that if sword can be considered a string, than a full wavelength standing wave will have a node in the middle, but it will basically be true only for even halfwavelengths mode... Plus I'm really too lazy to calculate the modes of a string with a variable mass, so I don't know how big percentage of the waves will have nodes at the center of mass.

This one requires the experts. The test described above speaks to a property of standing waves, I think, but the center so defined also identifies the "sweet spot" which relates to properties of propagated waves also -- at least that was how it was explained to me.

With respect to analogous models, I believe that a string as we usually think of it is probably not the correct one. A string can have variable tension. If we exert enormous tension on a string, and essentially make it highly inflexible or "rigid," then we may approach a more representative model. A metal rod has a high degree of rigidity, which is essentially constant for the purposes of this discussion.

Originally Posted by Rivkin

5. Concerning the center of percussion - as far as I remember (and I remember it very poorly), the center of percussian is when you hit it, all the momentum is transfered into the rotation movement of the sword, without any daggling down or up.

Could be, but we need the experts for this one too.

[Rivkin]

Hi Ian,

I don't think rod vs. string makes too much of a difference.

1. Equations are basically the same - they are basically the same for all oscillations. What is important is that we have oscillations around the equilibrium. Exapnding potential in Taylor's series, and taking derivative with respect to the displacement (which is going to give us force), we'll se that constant force is not there due to the equilibrium requirement (there are no forces in equilibrium, the derivative of energy is zero), force linearly proportional to the displacement is what gives us oscillations, force proportional to the displacement squared exist only in anisotropic bodies (asymmetric problem), cube will give us a nonlinear oscillator, and that is something we don't whant to deal with.

So it's always restoring force linearly proportional to the displacement.

2. Now the shape determinces boundary conditions - but if something is very long in one dimension, since if it would be infinite, it would have plane waves as a solution, if it's just long it has something similar to plane waves - sin or cos (basically sum of 2 plane waves propagating in the opposite directions).

Now for other dimensions - if it's a rod, it's most likely going to have a Bessel function or something like this (since it's like a drum). I think the problem is somewhere in the books on diff. equations.

I think plank is more suitable than rod in case of swords, but again - we are interested in transverse oscillations along the longest dimension.

Concerning additional b.c. - I meant that the tang is coupled to a human hand, so it's either unmovable, but under stress, or it's coupled to an oscillator.

I still don't agree to the rest of the things...

Sincerely yours,

Kirill Rivkin

[Jeff D]

Hi Rivkin

I would like to address some of your questions and hope it can add to Ian's excellent answers.

Originally Posted by Rivkin

1. With given definitions the center of gravity and the center of inertia will be the same.

Inertia is the tendency for a body at rest to stay at rest or stay in uniform motion. It requires an external force to alter this state. With our sword example I think its relevance is more in the handling of the sword than in its ability to cut as per Jen's original question. So I would agree with you that for all intense purposes it would be OK to consider it the center of mass.

2. If its possible, I would really like to see the formula they use for sword's frequency as a function of length (do they consider it a string ? a thin and long prism ?).

I am not sure what model the engineers used, however I think it would be safe to use a bar with a clamped (fixed) end (similar to a hilt) as a model. Using this model the formula is;
F(1) = 0.162 {a/(L squared)} {the square root of(Y/d)} where a=thickness, L is the length of the bar, Y is Young's module (which is a variable of the elasticity of the material), and d is the density.

3. Concerning tang not being a b.c., or even a separate body, I would prefer to hold a vastly different opinion.

Using my model I would not consider the tang in the Length formula as the hilt and tang would be the fixed portion of the bar.

4. Concerning waves propagating in swords and nodes - propagating waves usually do not have nodes. When people talk about nodes, they usually speak about standing waves, i.e. steady state solutions etc.
I suspect that the logic was that if sword can be considered a string, than a full wavelength standing wave will have a node in the middle, but it will basically be true only for even halfwavelengths mode... Plus I'm really too lazy to calculate the modes of a string with a variable mass, so I don't know how big percentage of the waves will have nodes at the center of mass.

I think again we are confusing some of the issues. The vibrations only affect Jen's question in reguards to the energy transfer. The less vibration, the more energy transfered from the kinetic energy of the swing into cutting energy. If there is a lot of vibration then a lot of energy is wasted. The vibration will obviously affect the handling as well. I think a complex bar with varing thickness, fullers etc. would set up a series of standing waves that would cancel each other out so that there will be minimal palpable vibrations.

5. Concerning the center of percussion - as far as I remember (and I remember it very poorly), the center of percussian is when you hit it, all the momentum is transfered into the rotation movement of the sword, without any daggling down or up.

I am not sure of what your question here is but I think you are correct in that the center of percussion is where the blade strikes the sword, and should there for be where the resistance of the object balances.

Hope this adds a bit.
Jeff