Article about sword mass distribution

[Mink]

Hello all!

Finally, after more years than I care to count playing with the concepts, I've managed to finish an article about sword balance and mass distribution...

It focuses on how to measure meaningful properties directly on the sword with as little calculus as possible (perhaps an addition or a subtraction somewhere ). The properties have some intuitive interpretations in terms of handling for example, at least in my opinion... Of course I've left some things out and a more advanced interpretation is still a work in progress.

Read the article here!

Please don't hesitate to comment! It's the only way I'm going to be able to iron out the parts that are not clear...

I hope the method described can be used in reviews to introduce some more objectivity in the appreciations of handling and ease comparisons.

In appendices you will find raw data measured on swords and some mathematical demonstrations that could be of interest to the maths/physics geeks out there

Regards,

[Fab]

I'll read that once me brains is in better shape...

[admin]

Thanks Vincent!
Like Fab, I'll read this properly when I am able.

[Mink]

Yes having a functional brain for that kind of thing is perhaps... advisable
That being said I've tried to make the matter as simple as possible, unless you dig into the mathematical appendix. It's really meant for everyone. At least I've tried, whether I've succeeded remains to be determined

Regards,

[Colin F.]

Having read the main article I can understand what you are trying to explain and I think it would make a very useful system in trying to compare and contrast swords without necessarily having to handle them. I then tried to read the appendices and gave up.

[KeithFarrell]

Ohhhhhh... I thought this article was going to be along the lines of how swords were mass distributed throughout Europe by merchants or armourers or the like, and I was wondering why calculus had anything to do with the subject. This looks much more painful

That being said, it looks very interesting, so when I have a spare couple of hours this evening I will forge myself some coffee and will read it through in more detail.

[Mink]

Hello!

I have just updated the page with a new format for the video, that will hopefully be supported almost everywhere...

Still at the same place!

Regards,

[Mink]

Ohhhhhh... I thought this article was going to be along the lines of how swords were mass distributed throughout Europe by merchants or armourers or the like, and I was wondering why calculus had anything to do with the subject. This looks much more painful

That's a misunderstanding I had not anticipated

[KeithFarrell]

I had a read through, and it makes sense. Quite an interesting read, and I notice you wrote it in LaTeX always nice to see other people using that for their formal documents.

I have a question though. At the risk of sounding stupid, how does one calculate cross weight? Is it really just as simple as totalWeight - bladeWeight? Or is the value H calculated in a different manner, in which case, how might it be calculated? What role does the pommel play in calculating H if the sum is not as simple as totalWeight - bladeWeight?


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Edit:

I just saw this paragraph, I must have missed it while reading through for the first time:

"Let us assume that we have a way to determine the dynamic length. Then it is
trivial to measure both masses: one just has to rest the sword on two scales, at point
H on one side and at point F on the other side, and read the values. That procedure
can be further simplified and involve only one scale, the other being replaced by a
simple resting point. That way, one of the masses is measured, and it is easy to
obtain the total weight of the sword, hence the value of the other mass."

So we pick point H, and do the waggle test. This shows us point F. We then get two sets of scales, place them directly under points H and F, and read the respective values. This gives us the weights at these two points.

Also, to find out the blade presence value, we simply do bladeWeight / totalWeight? So a weapon with totalWeight = 1000g and bladeWeight = 300g would give:
bladePresence = bladeWeight / totalWeight = 300 / 1000 = 0.3 = 30%

I'm quite interested in working out some of these values for my own weapons, and I'm certainly interested in reading any further articles on the subject!

[Mink]

I had a read through, and it makes sense. Quite an interesting read, and I notice you wrote it in LaTeX always nice to see other people using that for their formal documents.

Thanks!
Well LaTeX is more or less the best tool for the job in this case, and I've developed a deep aversion to other word processing packages for documents of more than one page anyway

I have a question though. At the risk of sounding stupid, how does one calculate cross weight? Is it really just as simple as totalWeight - bladeWeight?

Yes, it's exactly that simple.
Remember that the equivalent object has the same mass as the original sword, so since it is composed of only two masses in this case, if you have one mass and the overall mass of the sword you have the other one...

The mass of the pommel in particular, or of any other component of the sword, influences the result both of the waggle test and of the weighing procedure. So you don't have to compute anything related to it later, as the measurements already give all the info you need...

Also, to find out the blade presence value, we simply do bladeWeight / totalWeight? So a weapon with totalWeight = 1000g and bladeWeight = 300g would give:
bladePresence = bladeWeight / totalWeight = 300 / 1000 = 0.3 = 30%

That's right.
The interest is that it gives a simple indicator varying between 0 (all hilt and no blade) and 1 (all blade and no hilt). In my experience we feel that ratio very well, i.e. we are able to sort weapons according to that factor even though we generally suck at judging relative masses. My hypothesis right now is that our brain uses that ratio (or some function of it), among other things, to build some sort of "control architecture" that enables us to swing things around... But that's kind of hard to prove

I'm quite interested in working out some of these values for my own weapons, and I'm certainly interested in reading any further articles on the subject!

Well I hope you'll be able to use the method, and I'm in turn interested by the stats of your weapons... Always nice to see more data points. Really the only thing that can go wrong is the waggle test, the rest of it is not really error-prone. I've got means to check for errors during the waggle test, but the computations suddenly become a lot more complex. I'd have to publish a tool for that...

Regards,

[Mink]

Hello all,

Just a notice that I have made some minor corrections to the article (nothing really significant) and added a word of caution in the intro, that I'll repeat here just in case:

Measuring a weapon involves some handling. Be careful when you do it with sharp blades. In fact be careful in general! I do not want people to get hurt while just trying to measure swords. If you feel your grip is not secure enough, if there are any living beings nearby (including yourself obviously) that could be hurt by a sword falling down, just lay the sword down and rest. If the sword falls and is not worth any piece of your own skin then do not attempt to catch it. Do not take chances...

The risk is nowhere near that posed by actual martial moves but better be safe than sorry...

Still at the same place!

Regards,

[Penderyn]

Hi, that’s quite an interesting read and I can appreciate the huge amount of work and effort you've put into this. I've thought of trying to characterise the qualities of swords since it would help in the creation of simulators but a combination of laziness and not being able to find an approach that I would be happy with has prevented me, looks like you overcame those hurdles . I haven't properly looked through the maths in the appendix but on first glance everything looks good, it did remind me how rusty I am at mechanics though .
Two very minor things in section 2.1, I'm not quite sure what you actually mean by density of mass, do you mean density or the distribution of mass?
When you say an infinite amount of data, while it is mathematically true there is a fixed volume and a fixed number of atoms in the object which in my opinion would mean there isn’t an infinite amount of data and while impractical for most people some x-ray diffraction and x-ray fluorescence would allow you to have a fairly good estimation to the distribution of atoms and the elements present in the sword allowing you to calculate the mass distribution of the sword to a very high degree of accuracy. But I'm just trying to be a smartarse and it would be a massive overkill and a waste of time and money since you can make a good enough estimation with the far simpler methods that you've used.
Personally I would like to see an approach using beam theory and other aspects of solid mechanics to distinguish how the blade profiles change the behaviour of the rigidity of the sword, it would benefit those wanting to make a simulator that is safe in the thrust but doesn’t wobble about too much. But doing that would require some fairly horrendous maths, a 3d model rather than a 2d one and some computing and I don't really have the time or the desire to start a project that big.
Keep up the good work!

[Mink]

Hi Penderyn, thanks for the comments

Two very minor things in section 2.1, I'm not quite sure what you actually mean by density of mass, do you mean density or the distribution of mass?

I mean density of the distribution of mass, mass per unit length at the spot, if you like...

When you say an infinite amount of data, while it is mathematically true there is a fixed volume and a fixed number of atoms in the object which in my opinion would mean there isn’t an infinite amount of data and while impractical for most people some x-ray diffraction and x-ray fluorescence would allow you to have a fairly good estimation to the distribution of atoms and the elements present in the sword allowing you to calculate the mass distribution of the sword to a very high degree of accuracy. But I'm just trying to be a smartarse and it would be a massive overkill and a waste of time and money since you can make a good enough estimation with the far simpler methods that you've used.

Yeah, indeed not infinite, let's say the amount of data and the measurement process still makes it impractical Plus, in order to get something useful out of that measurement, you'd have to build some interpretation that would probably look quite like what I describe.

Personally I would like to see an approach using beam theory and other aspects of solid mechanics to distinguish how the blade profiles change the behaviour of the rigidity of the sword, it would benefit those wanting to make a simulator that is safe in the thrust but doesn’t wobble about too much. But doing that would require some fairly horrendous maths, a 3d model rather than a 2d one and some computing and I don't really have the time or the desire to start a project that big.

I did something of the kind earlier, see this thread. It's actually easier than you'd expect, because you can keep most of the approximations I've made in the article, so the model is still 1D. I did that to explore vibrations but I guess it would be possible to use the same thing to evaluate flexibility...

Regards,

[Penderyn]

That’s some good work, I was thinking of looking more at buckling and simulators, I'm not a blacksmith but I imagine the methods are fairly well known and almost instinctive to some blacksmiths. But working with plastics to make a safer simulator is new ground so a mathematical model would help in perfecting the simulators. I'm curious about something, all the simulators I have seen have an edge thickness in the order of the blade width, have you tried your previous model with a simulator to see how the approximations stack up?

Regards