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Peter Johnsson
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PostPosted: Fri 06 Jan, 2017 11:39 pm    Post subject:         Reply with quote

Kai Lawson wrote:
Peter,

I thank you very much for your explanation. Mathematics and geometry were never my strong suit, and having some of the basic steps for various situations laid out helps my understanding quite a bit. I will try this the next time I work on a sword. I think the concept is very interesting, and have watched with a mix of confusion and interest as this thread unfolds.

Are there combinations of geometric layouts that indicate or can be used to locate ranges for handling points, like pivot points or estimates about balance or vibrational nodes, if thickness (and thus mass) measurements are known? Some of those would be harder to calculate, but I wonder if there could be geometric solutions that could be used to combine both the dimensionality and some of the gross handling characteristics?


This method for design is no short cut for dynamic properties of a sword. Balance and position of pivot points and vibration nodes are determined largely by distribution of mass ands that is mostly decided by variations in thickness and cross section.

You cannot once for all decide thickness or distal taper in a sword by a geometric layout. Volume cannot be scaled the same way as outline. A small change in dimension would then have disproportionate result in mass.

Once you have decided for a design you then work out how thick the blade shall be and the volume of the pommel.
Or you keep this in the back of your mind as you work, adjusting for the effects of proportion and dimension as you work.

Either way, mass and balance are separate things from the proportions of the sword.

The only way proportion has a direct impact on handling is the ration between blade and hilt. This *will* have an effect on handling and position of nodes and to some extent pivot points. But this is not enough to give you the complete solution.
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Peter Johnsson
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PostPosted: Fri 06 Jan, 2017 11:47 pm    Post subject:         Reply with quote

Mark Lewis wrote:
...Peter, would this be a useful technique for designing a pommel that will balance the weight of different-sized blades?



Mark, the geometry gives you no clue as to the thickness of the pommel. Only its proportion to the rest of the sword and finally its dimension in width and height, once you determined the overall size of the sword.

You make it thicker or thinner (and more or less hollow) to reach desired mass that is proper for the blade in question.

Look at some swords that have unusually large pommels: they are as a rule very thin.
I think they were made this way to meet demands on certain dimensions and proportions
.
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Guillaume Vauthier




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PostPosted: Sat 07 Jan, 2017 6:07 am    Post subject:         Reply with quote

This topic is more and more interesting, and I decided to try to size my "own" sword, according to my hand proportions. As I'm into HEMA I decided to choose a sort of "average" one-handed sword shape of the 13th/14th century, as I could use to do some I.33 stuff for example: a type XII, or hybrid XII/XIV, with a simple straight crossguard and type J pommel.

As I saw that several swords of this type had a handle that could be drawn from an equilateral triangle, I decided to use this method.

The proportions were very simple and accessible. With only a compass and a ruler (and a calculator...) I easily determined everything, using the circle to get the inscribed hexagon and equilateral triangle, and then the rectangle made with them: length and width of the crossguard, grip length, pommel length and diameter of the central part, blade length and width, fuller length...

In fact, the only problem is the pommel width. As you know, on original swords it is not a circle but an ellipse (it is wider than long, if you understand what I mean!). And I don't find how to calculate the adequate ratio between length and width... does someone have an idea?
Here on my following drawing, I tried to use the same dimension that the blade at guard, but it looks too flattened...



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Peter Johnsson
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PostPosted: Sat 07 Jan, 2017 6:41 am    Post subject:         Reply with quote

A possible example of the consequence of geometry deciding the proportions of the outline of a sword and how it has to be forged to meet those proportions can be seen in the well known Oakeshott XIII.4 sword.

This was a sword that Oakeshott published in his "Records" but that for a number of years disappeared into unknown location as part of one or several private collections.
It emerged again recently and was part of the exhibition "The Sword - Form & Thought" in Solingen that I helped curate.

When it came to light again, it had met a strange fate. Oakeshott gave an incorrect number for the length of the blade, but also make a drawing of what it looked like when he saw it.
It turns out that some collector saw fit to add a length to the blade to make it meet the dimension given by Oakeshott (some 14 cm longer than actual original length). This is clearly visible in x-ray, where the new tip has been welded on.

In the illustration you can see how the sword with its original length neatly fit a simple geometric structure, but also how it in its new lengthened form, fails to meet any geometry in a satisfying way.

If you just look at the sword it might come across as odd and perhaps even ungainly in its proportions, but knowing the underlying geometry you can appreciate that there is an original sense of beauty that defines it.

To make it possible for the pommel to be as large as the geometry sets out, it is made very thin. It is nearly 7 cm wide, but only 1 cm thick. If you take two digestive biscuits together they will be thicker in proportion to their diameter than this pommel is.

I think this may well be a result of a design defined by geometry that results in some creative and original solutions by the sword smith.



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Peter Johnsson
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PostPosted: Sat 07 Jan, 2017 6:47 am    Post subject:         Reply with quote

Guillaume Vauthier wrote:
This topic is more and more interesting, and I decided to try to size my "own" sword, according to my hand proportions. As I'm into HEMA I decided to choose a sort of "average" one-handed sword shape of the 13th/14th century, as I could use to do some I.33 stuff for example: a type XII, or hybrid XII/XIV, with a simple straight crossguard and type J pommel.

As I saw that several swords of this type had a handle that could be drawn from an equilateral triangle, I decided to use this method.

The proportions were very simple and accessible. With only a compass and a ruler (and a calculator...) I easily determined everything, using the circle to get the inscribed hexagon and equilateral triangle, and then the rectangle made with them: length and width of the crossguard, grip length, pommel length and diameter of the central part, blade length and width, fuller length...

In fact, the only problem is the pommel width. As you know, on original swords it is not a circle but an ellipse (it is wider than long, if you understand what I mean!). And I don't find how to calculate the adequate ratio between length and width... does someone have an idea?
Here on my following drawing, I tried to use the same dimension that the blade at guard, but it looks too flattened...





Guillaume, I am happy to see you are interested in experimenting with this.

The proportion of the not-circular pommel can be defined in several ways. I have already mentioned that there are many ways to cut or divide the square (the square around the first circle) that will give you some easily accessible ratios to try out. You can also try dividing the side of the square (or the diameter of the pommel) in a number of equal parts and see if that gives you a good proportion. You can draw a square around the pommel and rotate it, so that it is wider than it is broad: this might be a good proportion for an oval pommel. -Many alternatives.

For determining the blade length, you should set the point of the sword at a circumference of a circle, not in a vesica. At least, this is the rule I have followed myself.
The 15th C goldsmith Hanns Schmuttermeyer tells us that geometry as a design tool for artisans and craftsmen must be used following certain rules in drawing and setting out. He stress the centre of the rice and its circumference and being of greatest importance.

I also see no clear definition of the blade width. It looks like it is close to the golden section of the diameter of the circle, but it is not defined.
If you leave one element undefined, the structure is invalid. It is all or nothing. The fewer components you need to define *all* important elements of the sword, the more beautiful the result tends to be. -With some exceptions of course...
;-)

If you are interested in seeing many examples of various geometries that conforms to actual historical swords, I recommend that you get a copy of the catalogue to the exhibition "The Sword - Form & Thought". I have there presented analysis of some 48 swords. You can see which ones seem to follow a geometrical definition and which ones does not. You can also see examples of some common strategies and types of lay outs. In an article I also describe the method of construction and analysis.
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Mark Moore




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PostPosted: Sat 07 Jan, 2017 8:09 am    Post subject:         Reply with quote

Sorry to interrupt, and far be it for me to get involved in conversation obviously waaaay over my head.....but: Have any of you guys put any of these theories/equations towards the famous Cawood Viking sword? I'm talking about the--original--Cawood sword. The one in the museum, not reproductions. That might be interesting. Just wondering....I'll go away now. Happy ...McM
''Life is like a box of chocolates...'' --- F. Gump
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Guillaume Vauthier




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PostPosted: Sat 07 Jan, 2017 8:48 am    Post subject:         Reply with quote

Peter Johnsson wrote:
For determining the blade length, you should set the point of the sword at a circumference of a circle, not in a vesica. At least, this is the rule I have followed myself.
The 15th C goldsmith Hanns Schmuttermeyer tells us that geometry as a design tool for artisans and craftsmen must be used following certain rules in drawing and setting out. He stress the centre of the rice and its circumference and being of greatest importance.

I didn't want a blade that long at first but... looks better this way.

Quote:
I also see no clear definition of the blade width. It looks like it is close to the golden section of the diameter of the circle, but it is not defined.

I took the length of one of the sides of the equilateral triangle divided by three to get this blade width at guard. It is maybe more apparent on this picture, were I cut the rectangle inscribed in the hexagon in 3 rectangles that seem to have the same ration L/l. Totally intuitive on this subject I must admit.



Quote:
If you leave one element undefined, the structure is invalid. It is all or nothing. The fewer components you need to define *all* important elements of the sword, the more beautiful the result tends to be. -With some exceptions of course...
;-)

You know, I just made it for fun and to find out by my own, I'm a beginner! I didn't practice geometry since like ten years. When I see you talking about some golden section or square root ratios I'm completely lost. I need lots of time and learning to be at your level, guys! Big Grin
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Jasper B.




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PostPosted: Sat 07 Jan, 2017 10:16 am    Post subject:         Reply with quote

Anthony Rischard wrote:
Hello Jasper, Hi Kai!

Some personal thoughts...

I agree that given enough time and a little imagination one can find "planned" geometry in pretty much anything. Heck, entire cults, end of the world prophecies and conspiracy theories are based on just that - humans are brilliant at finding patterns even where there are none.

I believe, however, that Peter (and his predecessors working on medieval geometry in other contexts) are on to something. Not because every sword was intentionally and intricately designed using these "techniques", but rather perhaps because these geometric techniques describe a fundamentally different approach to design from ours that naturally embed them in these productions.

(...)


I also believe that Peter is on to something. I experimented with 'designing' a sword using geometry some time ago and found that setting up the proportions of a sword is indeed quite easy. What's more, it is easy to make the proportions 'look' historically plausible (I will immediately agree that this is not proof of anything, but if the resulting designs looked wrong, the idea would be far less likely be correct). I've also seen and read papers discussing geometric design in the proportions of medieval buildings, so it is only logical that they would apply the same methods in other fields.

My post mostly was about trying to retro-actively decipher the geometric design that may or may not have been present in the various details of the three swords presented by Peter Johnsson. For two of the three swords I find/found it hard to find the position of certain parts of the design, by using simple geometry.

Your example underlines my thoughts on the subject: the original proportions of the swords have most likely been constructed the simplest way possible. So, because I could not find the proportions using simple geometry (as opposed to continue adding shapes until at last something shows up), I started to doubt if either my skill was lacking (a real possibility) or that not every detail was originally laid out using geometry.
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Peter Johnsson
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PostPosted: Sat 07 Jan, 2017 10:17 am    Post subject:         Reply with quote

Guillaume Vauthier wrote:
Peter Johnsson wrote:
For determining the blade length, you should set the point of the sword at a circumference of a circle, not in a vesica. At least, this is the rule I have followed myself.
The 15th C goldsmith Hanns Schmuttermeyer tells us that geometry as a design tool for artisans and craftsmen must be used following certain rules in drawing and setting out. He stress the centre of the rice and its circumference and being of greatest importance.

I didn't want a blade that long at first but... looks better this way.

Quote:
I also see no clear definition of the blade width. It looks like it is close to the golden section of the diameter of the circle, but it is not defined.

I took the length of one of the sides of the equilateral triangle divided by three to get this blade width at guard. It is maybe more apparent on this picture, were I cut the rectangle inscribed in the hexagon in 3 rectangles that seem to have the same ration L/l. Totally intuitive on this subject I must admit.



Quote:
If you leave one element undefined, the structure is invalid. It is all or nothing. The fewer components you need to define *all* important elements of the sword, the more beautiful the result tends to be. -With some exceptions of course...
;-)

You know, I just made it for fun and to find out by my own, I'm a beginner! I didn't practice geometry since like ten years. When I see you talking about some golden section or square root ratios I'm completely lost. I need lots of time and learning to be at your level, guys! Big Grin


I see!
Of course. A third of the side of the triangle.
Sorry. I should have noticed.

I am sorry if I came across as harsh and commandeering. Not my intention! I just wanted to be clear to avoid misunderstandings. I really do appreciate to see how different people approach this idea. It is interesting and enjoyable.
-Please continue and please tell me to shut up if you don´t want critique!
:-)
I can sit back and enjoy silently, if I really concentrate :-)
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Guillaume Vauthier




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PostPosted: Sat 07 Jan, 2017 11:27 am    Post subject:         Reply with quote

Peter Johnsson wrote:
I can sit back and enjoy silently, if I really concentrate :-)

You know, if you stay silent that would be a shame Big Grin

Anyway, I'm glad to see that, even with my poor geometric skills, I'm able to draw a sword with some nice proportions without getting an headache at all. At the beginning of this topic, and seeing your youtube vids, I was impressed by all those combined forms, diameters, ratios and polygons. But in fact, with all your interventions (from you all, guys!) I begin to have a real technical understanding of the thing, and that's exciting. In fact, all the dimensions on my pictures were obtained with proportions : the crossguard length is the circle diameter, the crossguard width is 1/12th of the rectangle small side (i.e. 1/12th of the circle's radius), the grip length and pommel length were obtained with the rectangle, and so on. That's cool.

Except that pommel major axis. Big Grin I need to do some searching on this. I actually know what dimension would be the most appropriate by experimentation, but I would like to find it geometrically.

I feel like I will buy your The Sword - Form & Thought sooner or later...
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Mark Lewis





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PostPosted: Sat 07 Jan, 2017 11:56 am    Post subject:         Reply with quote

Guillaume Vauthier wrote:
Anyway, I'm glad to see that, even with my poor geometric skills, I'm able to draw a sword with some nice proportions without getting an headache at all.

Guillaume, it is very cool to see a design worked out on paper, and sized to your own taste and purposes. Happy

Peter Johnsson wrote:
A possible example of the consequence of geometry deciding the proportions of the outline of a sword and how it has to be forged to meet those proportions can be seen in the well known Oakeshott XIII.4 sword.

"Odd" examples can be the most interesting...

Have you ever had the chance to document the swords at the Hotel Sandelin in St. Omer? There is one there in particular that I wonder how similar it may be to XIII.4, with an extra-broad blade of almost exactly the same width... less unusual pommel though.

I worked from lousy photos and few measurements, so this may be no more than idle speculation... but I could not resist trying to sketch something, and I thought the result turned out surprisingly well (even if it exists only in my imagination).

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Peter Johnsson
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PostPosted: Sat 07 Jan, 2017 1:52 pm    Post subject:         Reply with quote

Mark Lewis wrote:

..."Odd" examples can be the most interesting...

Have you ever had the chance to document the swords at the Hotel Sandelin in St. Omer? There is one there in particular that I wonder how similar it may be to XIII.4, with an extra-broad blade of almost exactly the same width... less unusual pommel though.

I worked from lousy photos and few measurements, so this may be no more than idle speculation... but I could not resist trying to sketch something, and I thought the result turned out surprisingly well (even if it exists only in my imagination).



Indeed.
It is a very interesting and a bit odd looking sword. It has always struck me as a possible sibling or at least cousin to the XIII.4 as well as a sword found in the River Fyris of my home town of Uppsala. They are all similar in dimension and proportion. At least they form a little sub family of sorts. I have not yet been able to make a pilgrimage to the Hôtel Sandelin, unfortunately. Several of the swords in this collection seems highly interesting. I had hoped to have a chance to get access to them when they were exhibited at the Cluny museum, but alas, no such luck. It would have been extremely valuable.

The pommel of this type XIII from Hôtel Sandelin is unusual in that is is spherical and most probably hollow. On one side there is a pattern/decoration of some kind of trinity symbol (three arcs made with a compass).
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Mark Lewis





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PostPosted: Mon 09 Jan, 2017 7:14 pm    Post subject:         Reply with quote

Peter Johnsson wrote:
The pommel of this type XIII from Hôtel Sandelin is unusual in that is is spherical and most probably hollow. On one side there is a pattern/decoration of some kind of trinity symbol (three arcs made with a compass).

Interesting detail! The mark is visible in the closeup photo if you know to look for it. Now that you mention this, I just recalled that coincidentally one of the swords I posted at the beginning of the thread has a similar mark on the it's blade. I hadn't given any thought to it's symbolic meaning. Idea



Is anyone still working on interpretations of A457? If not, I'd very much like see your analysis... very curious if I or Anthony were able to detect any common features!
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Anthony Rischard




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PostPosted: Mon 09 Jan, 2017 10:40 pm    Post subject:         Reply with quote

I second Mark's "last call" for A457 - if anyone would like a little more time, please let us know, otherwise I too would love to see Peter's interpretation and see how what Mark and I have come up with compares.

I may have to bow out of the current exercise ( the three Swords by Peter analysis) for lack of time.... we'll see.

Good day to all!

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Guillaume Vauthier




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PostPosted: Wed 11 Jan, 2017 10:31 am    Post subject:         Reply with quote

Experimenting again on paper, with ruler and compass. Not as handsome and as precise as I would like, and a bit blurry due to the pencil, but the result looks correct!

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Anthony Rischard




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PostPosted: Wed 11 Jan, 2017 11:12 pm    Post subject:         Reply with quote

Très joli Guillaume !

I like the simplicity of your construction and really like what you've done to set the terminus of your fullers.

A pair of elegant weapons.

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Mark Lewis





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PostPosted: Thu 12 Jan, 2017 6:16 am    Post subject:         Reply with quote

Guillaume Vauthier wrote:
Experimenting again on paper, with ruler and compass.

I like the second one in particular. Happy

Anthony Rischard wrote:
I may have to bow out of the current exercise ( the three Swords by Peter analysis) for lack of time.... we'll see.

Hope you can find the time to get something together! There is no rush... so far I think I have a decent offering for II and III.

Luka Borscak wrote:
I would love to see analysis of A.459. Happy

In the meantime I've gone back to look at A459 and here is the result. The hilt-blade ratio is very close to 1:5, but using a type 2 structure to derive this seemed to offer more than a simple type 1. The design came together with a pretty minimal number of needed constructions. The pommel is not defined in a really solid way, but it's a very irregular shape, so I don't feel like this is a serious shortcoming...

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Luka Borscak




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PostPosted: Thu 12 Jan, 2017 1:40 pm    Post subject:         Reply with quote

Thank you! Elegant geometric solution...
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Guillaume Vauthier




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PostPosted: Mon 16 Jan, 2017 1:44 pm    Post subject:         Reply with quote

Another test with and existing sword: a interesting type XIV kept in the Musée de l'Armée, Paris.

The simple geometry I used precedently seems to work fine (the only real differences in the silhouette being the straight crossguard and the shorter fuller). Naturally it is lacking some parameters, like determining the pommel width or the clip point length for example), but I'm glad to have found this anyway. Here is a comparison between the original and the hand drawing that I made, cleaned of :





I just have a question: when there's a peen block on the weapon, should it be included in the global geometry? If that's the case, the handle has a 1:1 ratio (the crossguard length is 16cm, and the full handle length including the peen block is 16cm too)...
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Mark Lewis





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PostPosted: Tue 17 Jan, 2017 6:54 pm    Post subject:         Reply with quote

Guillaume Vauthier wrote:
I just have a question: when there's a peen block on the weapon, should it be included in the global geometry?

That is a good question... if it is included, then the underlying geometry of that sword might be something like this, but the pommel is left floating, a bit disconnected from the structure, so perhaps this is not a good approach to design. Worried



I hope the great experiment has not ended prematurely... here are my attempts at reverse engineering Peter's 2nd and 3rd designs.



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