[Thomas Riley]

Hello,

I've been doing my own research, after reading the book "The Sword: Form and Thought" and working on applying the concepts to my own collection.

In it are graphs which describe the sword "at a glance":


I understand how all of these things have been measured and graphed, except for 2 aspects: The Oval and the Cones, which represents the agility of the sword. I understand the Oval represents linear transition agility, and the cones are some form of rotational agility.

I've read over George Turners "Dynamics of Hand-Held Weapons" to dive into the math for a lot of this, but in the end have not been able to crack the nut of these 2 aspects.

Perhaps someone here can help me with it. How exactly are they determining how to chart these things, specifically the magnitude of both the oval, and the angle for the cone?

[J. Nicolaysen]

I am probably wrong, but I assumed the oval and cone correlated as how far you'd move the hilt (oval) to get the tip and edge to the side of the cone. So basically, the smaller the oval and wider the cone, the more agile sword you have, minimal effort with maximum effect. I'm looking at the red dots to see this. If you mark a dot on the hilt traveling to a point on the oval, you can measure the dot on the cone...

But I am very interested to hear an expert's thoughts on this, it's just my quick understanding from the catalogue.


---edited to replace "Dots" instead of triangles, sheesh.

[Bram Verbeek]

I think it would not be hard to do.

Rotational: Set sword on a turning table with constant known resistance, centered on the center of mass. Give a constant known impulse at the handle, measure the angle the sword travels.
Translational: Set the sword at a slide with a constant known resistance, give the sword a constant known impulse at the handle and measure how far the sword travels.

The hard part is to gather why the ovals are not round.

[Thomas Riley]

[Vincent Le Chevalier]

Hello all,

I happen to be responsible for the construction of these graphs

The goal in that book was to get a visual impression of various aspects of the sword's balance, that could otherwise only be perceived sword in hand. It's not really mature as a comparison system; this is still a work in progress for me and Peter. We also had a fairly limited space and had to explain all the basic concepts first, and this is why the explanations are not sufficient on these diagrams.

The oval and the cone are meant to represent the potential for acceleration of the weapon when using several modes of motion. Mass is the primary factor in their size, and mass distribution influences the relative shapes. The bigger the mass, the smaller the shapes become, showing the difficulty in accelerating a heavy weapon. The oval represents how the sword accelerates in different directions when subject to a force applied at the cross. So if you push along the axis of the weapon, you meet the whole mass. If instead you push perpendicularly, you only meet part of it: the effective mass at the cross. That is why these are ovals and not circles. The cone represents how the sword accelerates when moved in rotation around the cross. It also takes into account leverage; these diagrams are computed assuming constant force at the end of the handle, basically. Otherwise two-handed swords would have a much smaller cone.

So to compute them you need:

M, the total mass of the weapon
H, the location of the cross
G, the position of the center of gravity
R and P, a pair of associated pivot points
L, the location of the handle end (pretty much the aft location on the handle), where leverage is applied

and then you compute:
J = GR*PG + GH^2

Width of the oval = ko/M
Height of the oval = ko/M * J / (GR*PG) [EDIT: made a mistake!]
Angle of the cone = kc/M * HL / J

The coefficients of proportionnality ko and kc were picked to give a proper spread. You should probably pick your own for your collection (depends on the units you measure in as well)...

Hopefully a much more complete publication about sword balance will follow in the future!

Hope this helps,

[Thomas Riley]

[Vincent Le Chevalier]

Looking good Thomas!

The whole thing hinges on accurate measurement of pivot points, and this is something we spent quite a lot of time exploring. Here I'm a bit surprised with the location of the aft and forward pivot that you have found; on this type of sword I'd expect the forward pivot to be in between the blade node and the tip, and the aft pivot further from the center of gravity. I'm not sure how you measured them, I guess some form of waggle test?

Things to look for with the waggle test:

• It is easier to do with the blade down
  
• As little torque as possible should be applied to the sword. I hold the sword just between two fingers
  
• The frequency of the motion must be as high as possible. If you move too slowly the fixed point tends to migrate back to the hilt
  
• Spotting the fixed point can be difficult on smooth blades. I use a hair tie on the blade that I move up and down until I see it fixed. Also makes it easier to measure, as you can move the sword around without losing the point.
  

The values on the curve are computed just like the hilt agility (inverse), so at point X:
value = M * GR*PG/(GR*PG + GX^2)

That should allow you to build a curve and determine the mass and fraction at node, consistent with the pivot points.

Regards,

[Thomas Riley]

Thanks! I was surprises by the location of the pivot node and vibration node locations, but I measured it multiple times... I like your approach of using a band of sorts to assist. I used a sticky note.

Anyway I'll incorporate your formulas in the future to make all this easier on myself.

Thanks Again.

[Thomas Riley]

Quick question, regarding the formula: J = GR*PG + GH^2

In this case GR represent the distance between the Center of Gravity and the pivot point #1, PG represents the distance between the Center of Gravity and the pivot point #2, GH represents the distance between the cross and the Center of gravity.

So when G = .375m, R = 0.77m, P=0.26m, H=.285m, L=0.06m
then
GR = 0.395m, PG = 0.115m, GH=0.09m, HL=0.225m and J = 0.053525

Am I doing this correctly?

[Vincent Le Chevalier]

Seems right yes!

Regards,

[T. Kew]

I agree with Vincent that the pivot points you've presented are dubious.

Maarten Kamphuis (of mBlades) has presented some results about the behaviour of swords, and how they're related to mass distribution, pivot points, and so on.

The most relevant one for this discussion is the following:

a * m * b = k

Where a is the distance from a pivot point in the hilt to the centre of mass, m is the mass of the weapon, b is the distance from the centre of mass to the matching pivot point in the blade, and k is a constant for the sword (determined by its overall mass distribution).

As a consequence of this, if you double the distance from your hilt pivot point to the centre of mass, you halve the corresponding distance in the blade.

This relationship doesn't seem to hold true for the set of data you've diagrammed on your sword.

(This also has a geometric expression - if you draw a circle through a rear pivot point and its corresponding forward one, the point at which that circle intersects a perpendicular drawn from the centre of mass is constant for all pairs of pivot points. That also doesn't seem to be true, but I've only poked the diagram a bit with a set square)

[Vincent Le Chevalier]

Indeed that is the manipulation I did too. It is pretty useful to check several pairs to make sure there isn't a faulty measurement somewhere, and realize that no measurement is perfect...

(See my article about the geometrical interpretation too!)

Pivot points should also correlate with pendulum tests, if that is how you computed the curve. The length of the pendulum should be the same as the distance between the center of rotation and its pivot point.

Regards,

[Thomas Riley]

I'll be revisiting the Liechtenauer this week brand new and fresh, re-measure everything, and use some of the methods described in this conversation.

[Nathan Robinson]

Have you seen this video?

Sword Dynamics - Defining the Agility of a Blade Using Physical Measurements

[Thomas Riley]

I have, that is me.

I will be updating my approach as I process and understand what was covered in this thread. This thread picked up after I had made that video.

[Nathan Robinson]

[Thomas Riley]

Preview of the new model for the Albion Liechtenauer:



You can see it is very different from my first version, and I feel it is much more accurate. Especially the vertical hilt agility. This is using only the formulas provided by Vincent.

With some help from a YouTube Commenter I can now provide this method for quickly generating the graph information on GeoGebra: https://ggbm.at/yqYH2F2h

Later I will build the final vector graphic for all of this, and will post the final version as an FYI for anyone following this thread.

Thank you all! This is really awesome.

[Thomas Riley]

Final version:



Thank you so much for all the help!

[Nathan Robinson]

That's pretty damn awesome.

[Thomas Riley]

As I look through the book, it strikes me that almost none of the swords have this kind of ratio for the linear agility, why am I getting such tall ovals in the sword I am trying this on?

was the constant "ko" different for the X and the Y axis?