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Peter Johnsson

Posted: Tue 03 Jan, 2017 1:19 am Post subject: 


The form of the parts seems fine. It is their relative proportion to each other that is off: guard width, grip length & blade width.
In part it was my evil intention with this exercise to show how tricky and possibly misleading it is to use photographs and published dimensions in this kind of analysis. There are too many levels of uncertainty involved. Simply taking the measurements has to be done following some sort of regime and with good enough precision to be useful. The Parallax from the camera lens is also also introduces more or less error.




Peter Johnsson

Posted: Tue 03 Jan, 2017 3:20 am Post subject: 


To keep the experiment going, here is a true to proportion rendering of the A457. I have adjusted the angle of the guard and normalised the blade and hilt on a central line, but not otherwise changed position of the parts.
You can compare this rendering with the photographs that are published to note any differences.
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Mark Lewis

Posted: Wed 04 Jan, 2017 8:13 am Post subject: 


Thanks for sharing the diagram! It is very helpful...
Overlaying the diagram on various photos shows that the ones in Records of the Medieval Sword and in the article by Edge and Williams are the most true to proportion, with relatively minimal discrepancies. It is still enough that I can tell my construction is invalidated... In particular, I had the shape of the pommel wrong (more or less as I suspected), the cross is a little shorter than I estimated, and there seems to be some very small inaccuracy in the published overall and blade lengths.
Working from the diagram, I have a new version, with a new ratio:
I have a much better feeling about this one. Once the correct(?) structure was in place, the rest of the details followed very quickly... unlike my previous attempts that required a lot of fiddling and trial and error.
I am kicking myself a little bit... I think I could have gotten something closer to this working just from the photos. I had completely forgotten to try using a type 1 structure with interlocking circles (to get a 2:x ratio) since this hasn't seemed to have come up with other swords I've tried to analyze so far. I had even been drawing circles of approximately the right size, but inscribing them within the erroneous type 2 structure I posted earlier.




Anthony Rischard

Posted: Thu 05 Jan, 2017 2:19 am Post subject: 


Hello everyone.
So the bad news (for me at any rate) is that I missed a plane to Budapest by 6 minutes this morning and now have cancelled meetings and a 10 hour airport wait ahead of me for the next flight...
The good news is that I now have a 10 hour airport wait ahead of me, cancelled meetings, a tablet, a stylus and a decent vector app to learn on said tablet.
So I get to play with A457 today.
Peter Johnsson wrote:  In part it was my evil intention with this exercise to show how tricky and possibly misleading it is to use photographs and published dimensions in this kind of analysis. There are too many levels of uncertainty involved. Simply taking the measurements has to be done following some sort of regime and with good enough precision to be useful. The Parallax from the camera lens is also also introduces more or less error. 
Absolutely Peter! I had the great pleasure for restoring the XIIth century romance ironwork for the church door at Mailhat (in Auvergne, France) in 2015. In preparing my initial bid for the job, I had only photographs to work with  and they were ALL distorted. One photo had, I later learned, even been "helpfully" skewed by a junior architect to "correct" for the fact that the 800 year old doors aren't true to square! This is exactly why I also work from drawings; photos are reference material, accurately drafted renderings are for study.
Archaeologists and paleontologists know this well!
In fairness to past collectors and curators of arms and armour, the intent of the illustration and description of these pieces was very different from that which is now beginning to emerge in our work.
Theirs was an intention derived directly from the study and conservation of art. Document the piece sufficiently to catalogue it, then identify the maker (if possible) and the materials, the provenance and history of the artefact, then describe it, with basic measurements sufficient to place it in a descriptive typology of FORM to hopefully do two things : identify forgeries (often unsuccessfully) and insert the weapon into a chronology by dating it (also with great difficulty).
Today we are still of course interested in these questions, but are seeking a deeper understanding of these weapons, as "living" objects (without going into the equally fascinating study of their existence as symbols). Determining their correct function as arms and their place in society, not as symbols but as tools and products of industry, requires much greater precision.
But, with too much time on my hands, I digress...
A457...
I had intuited a Type 3 structure in beginning to work with the photos last week and this seems to fit now that I have Peter's rendering (THANKS!)
Mark, I think I will take a different approach to yours for the hilt  I have a feeling that it can be achieved with a simpler construction, but we'll see!
I'll post something in the next few hours.
www.forgeart.com  www.blackarmoury.com 



Peter Johnsson

Posted: Thu 05 Jan, 2017 12:46 pm Post subject: 


Thank you for your continued interest and efforts, gentlemen.
I am really enjoying this :)




Jasper B.

Posted: Thu 05 Jan, 2017 3:15 pm Post subject: 


I'm also toying around with the three drawings posted earlier by Peter Johnsson. The geometry behind the design of No. III fell into place fairly easily. However, for No. I and No. II, I can't seem to find how the size/length of the handle and the dimensions of the pommel were derived.
Could anyone who has tried finding the geometry behind the design for those two swords, maybe give me a hint (without posting an actual image of your findings)?
Cheers,
J.B.




Anthony Rischard

Posted: Thu 05 Jan, 2017 3:18 pm Post subject: 


I'm fairly satisfied with my results for A457. Still need to polish it up for posting, and I only just got to my hotel  so I'll only get to that tomorrow.
Goodnight all.
www.forgeart.com  www.blackarmoury.com 



Mark Lewis

Posted: Thu 05 Jan, 2017 7:39 pm Post subject: 


Looking forward to comparing everyone's designs...
Jasper B. wrote:  Could anyone who has tried finding the geometry behind the design for those two swords, maybe give me a hint (without posting an actual image of your findings)? 
For number II, you've found the main structure? Add in a semicircle at the top and I think you'll find an alignment that measures the bottom of the pommel.
Number I seems the most difficult... does the guard appear to be a bit out of place from where it "should" be? I'm a little suspicious that the blade has the same markings as one in the catalogue that has "no coherent design"...




Jasper B.

Posted: Fri 06 Jan, 2017 4:01 am Post subject: 


Mark Lewis wrote:  Number I seems the most difficult... does the guard appear to be a bit out of place from where it "should" be? I'm a little suspicious that the blade has the same markings as one in the catalogue that has "no coherent design"... 
Try experimenting with an octagon for finding the position of the guard.
"no coherent design" I've been wondering if all three swords are completely designed using a geometric approach. For the sake of this little experiment, it would be interesting to see if we come up with a geometric pattern where none was originally there. So, from this line of reasoning, it would be plausible that we have been presented at least one sword where the design is not, or only partially, based upon geometric shapes. I'm sure that if I add enough lines, some will eventually match the lines of the sword, but I feel that the geometric design should not feel contrived.
Then again, maybe it is just my limited ability and somebody else will find some an elegant solution :)
J.B.




Kai Lawson

Posted: Fri 06 Jan, 2017 7:35 am Post subject: 


I was wondering about a similar thing. I am trying to finish up hilting up a blade with a wide cross and Brazil but pommel, and though it superficially resembles some of the swords shown here and originals were used as inspiration, it had no preplanning or geometry involved in its constructiononly aesthetics. It handles quite well, surprisingly, and it has evolved in shape following the forging of the pommel and the cross, which makes me wonder two things: can the geometry for a sword be altered to give a different pommel or cross width easily without changing anything else (as in, can a geometrically designed sword be repaired or altered according to specific, simple geometric rules or tweaks that could be easily applied), and how much are the basic design elements and visual style of these swords and the corresponding geometries linked? Obviously the proportions of any sword can be defined, and basic ratios will be present in a given visual design regardless of small variations, but can the Peter Johnsson geometry be easily (or moderately easily) applied to a sword conclusively NOT designed with geometric ratios? Is the geometry intrinsic to certain designs in some way, regardless of intent?
"And they crossed swords."
William Goldman, alias S. Morgenstern 



Anthony Rischard

Posted: Fri 06 Jan, 2017 12:54 pm Post subject: 


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.
The medieval, and ancient, approach to making anything was anthropomorphic.
If you live in a society where everything is traced out using straight edges and compasses, rather than algorithms and Bézier curves, and where you measure everything with bits of your body, well, everything tends to fit.
In reverse engineering the process, there's little wonder that Pi, and Phi, and natural ratios appear everywhere in this type of design.
I believe, however, that while many designs of the time will follow the "rules", they must do so as simply as possible. The simplest and fastest construction from an artisan's perspective must be sought.
I believe that the medieval artisan was not really interested in design. He was interested in producing something he could sell, and the concept of selling design time is a very modern one. Design was sometimes necessary, but when it was, it was to be quick and easy (the great architects, philosophers and theologians being, then as now, an exception).
So my personal approach, as it's developing, to all this (these are notes to self, not at all intended to be directive for anyone else):
 Start with an anthropomorphic bias. This means that bizarre measurement units like 119,125 cm are just fine, as long as they are coherent with measuring with your fingers, palm, arms.
 From that base, use the fewest possible manipulations of your tools as possible to get your result. This means if you're drawing circles, draw as many as you need before picking up the ruler again and that if you can get away with not even changing the spread of your compass, then even better.
 Where one single geometric form can set multiple parameters at once, then prefer it over using several forms to attain the same parameters.
 Remeber that it's easy to over complicate things when reverseengineering...
 Also remember that the often complex accumulation of geometric forms in these constructions is mostly an illusion. Necessary to visualize and formalize the concept Peter is exploring, but an illusion none the less. We don't usually need a full circle, we need the single point where the theoretical circle would intersect such and such line. We don't need a whole octogon, we need the length of one of its sides and so on. I imagine line segments and small compass arcs that form a "connect the dots" picture.
 Which means that it is likely much faster, once you "get it" to do these designs with compass and ruler on paper than it is in a vector programme (to be verified, but intuitively I think so).
This is how I approached the study of A457.
I took this exercise and turned it around a little. Instead of asking "what underlying geometry can I find in this sword?", I asked "What is the simplest and fastest way I can layout a geometry that will produce this sword with only a compass, straight edge and my hand".
I'll present my version in a follow up post in a short bit, with all the full circles, and squares, and triangles, and octagons that come with doing all this in a vector programme. But as soon as I'm home from this trip, I'm going to sit down with a ruler and compass and see just how much easier (I think) it is to whip this out with "fragmented" workshop geometry.
www.forgeart.com  www.blackarmoury.com 



Peter Johnsson

Posted: Fri 06 Jan, 2017 1:41 pm Post subject: 


Anthony Rischard wrote:  Hello Jasper, Hi Kai!
...This means if you're drawing circles, draw as many as you need before picking up the ruler again and that if you can get away with not even changing the spread of your compass, then even better.
 Where one single geometric form can set multiple parameters at once, then prefer it over using several forms to attain the same parameters.
 Remeber that it's easy to over complicate things when reverseengineering...
 Also remember that the often complex accumulation of geometric forms in these constructions is mostly an illusion. Necessary to visualize and formalize the concept Peter is exploring, but an illusion none the less. We don't usually need a full circle, we need the single point where the theoretical circle would intersect such and such line. We don't need a whole octogon, we need the length of one of its sides and so on. I imagine line segments and small compass arcs that form a "connect the dots" picture.
 Which means that it is likely much faster, once you "get it" to do these designs with compass and ruler on paper than it is in a vector programme (to be verified, but intuitively I think so).

Anthony, this is very much along the lines of my thinking as well.
I do think that geometry may have been a principle of planed construction, but also just like you point out, that once you are completely familiar with the method, you do not need to construct the full forms, only set out enough points to define the proportions you want. An economy of forms and dimensions is both practical and intellectually as well as aesthetically satisfying. It is also just what we see in the medieval geometric constructions that survive for us to see today (mostly from architecture).
It is a pity that this format of a discussion forum makes it difficult to provide full and well supported discussions.
I can only point at the articles I have published, where I try to provide som background and critical discussion of the hypothesis, the method and some critique of possible complications and pitfalls that must be kept in mind when undertaking this kind of analysis. A lot of what has been brought up are things that are touched upon in these articles.
The topic is far from unproblematic and I have tried to set out some of the basic concepts, principles and "rules" to keep in mind, previously in this thread.
It is important to see the use of geometry in the medieval period as part of a bigger picture before you can look for both questions and possible solutions. Context is important. We cannot look for geometry and proportions of swords as a thing separate from the world of medieval thought and aesthetic & religious philosophy.
Last edited by Peter Johnsson on Fri 06 Jan, 2017 2:15 pm; edited 1 time in total 



Anthony Rischard

Posted: Fri 06 Jan, 2017 2:05 pm Post subject: 


As I mentioned in my last post, I took a constructive approach to this exercise, trying to build the sword up as if I were designing it rather than interpreting it. This forced my geometry to follow a series of logical steps and allowed me to reject a fair number of "false positives" along the way.
I took a number of wrong paths along the way but I find the following progression pleasing. I also have definitely adopted the "start with the hand" approach. This single measurement will condition all that follows, with no other measuring required.
At the outset we trace a vertical guide, which will be the spine of our blade and will allow us to align all the other tracings.
First circle : We trace a circle of 1 1/2 palms or 1 palm and 2 fingers. As the ideal combat grip for this weapon style is a snug fit of the hand between pommel and guard, this will work very well to set the total hilt length. In our case with A457, this is just under 120 mm (119.125 mm) and works out fairly close to 1 1/2 palms Châtelet (114.9 mm), which is encouraging. Only 4 mm divergence from a much later standard measure is nothing, really.
This is the only time we measure  and we do so anthropomorphically to provide a functional base circle. From here out the entire weapon is constructed from the 1st circle, using only one square, one octagon and one triangle (or rather their intersections, one octagon side and the base and summit of the triangle).
Next we'll set our blade length. For this we'll say that our blade will be 7 hilt lengths. So we leave our compass set to the first circle and trace out seven more (in fact we are only interested in "walking" the compass seven radii down the spine to set the point of our blade).
Now we set the blade width. Putting down the compass and taking the straight edge, we construct an octagon around our first circle. The side length of this octagon is our blade width (in fact we only really need a piece of it  the right isosceles triangle with its base as the equator of the first circle)
Now that we have the blade length and width, we can construct the guard and pommel.
Since your compass is still set to your first circle radius, it is simple to trace out a square of two circles diagonal, centered on the intersection of the two first circles (here it's actually only the two points where the upper segments of this square intersect the blade width that interests us)
We will now simultaneously set le guard width and the centre of the circle that defines the lower pommel arc.
We trace line segments from the lower (not bottom) corners of the octagon to the intersection point of the large square and blade width. This forms an equilateral triangle which sets the guard width. We're almost done...
We finally place our compass point at the summit of the equilateral triangle and set the radius to the intersection of the square, triangle and blade width... and trace our final circle (or rather a lower arc that intersects with the first circle).
Let's see how this works on the A457 :
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Anthony Rischard




Peter Johnsson

Posted: Fri 06 Jan, 2017 2:39 pm Post subject: 


Anthony, I really like what you did in your analysis.
To add something more to be considered, I post a detail of my tracing of the original.
When you look at the original sword it seems the point has been resharpened or perhaps even reshaped after some damage.
A detail like this is difficult to make out from photos, since it is a 3D thing: it is how the edges are formed together with the outline of the point. In my tracing you will see how I estimated the original length and form of the blade.
I hope you forgive me from keeping this information to this later stage in the process. It might seem like a small thing, but it does have an effect in how the guard is positioned in a series of linked circles. Since this is the first step in an analysis (and also when you develop the design in the first place) it will affect all other solutions that come after.
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Peter Johnsson

Posted: Fri 06 Jan, 2017 2:57 pm Post subject: 


Kai Lawson wrote:  I was wondering about a similar thing. I am trying to finish up hilting up a blade with a wide cross and Brazil but pommel, and though it superficially resembles some of the swords shown here and originals were used as inspiration, it had no preplanning or geometry involved in its constructiononly aesthetics. It handles quite well, surprisingly, and it has evolved in shape following the forging of the pommel and the cross, which makes me wonder two things: can the geometry for a sword be altered to give a different pommel or cross width easily without changing anything else (as in, can a geometrically designed sword be repaired or altered according to specific, simple geometric rules or tweaks that could be easily applied), and how much are the basic design elements and visual style of these swords and the corresponding geometries linked? Obviously the proportions of any sword can be defined, and basic ratios will be present in a given visual design regardless of small variations, but can the Peter Johnsson geometry be easily (or moderately easily) applied to a sword conclusively NOT designed with geometric ratios? Is the geometry intrinsic to certain designs in some way, regardless of intent? 
Kai,
There are several aspects to this.
First: yes it is easy to change one or several elements of a design to vary the proportions of a hilt to a given blade, if you are looking for a different effect.
When you have spent some time playing around with a geometry based design system, you will find that there is a kind of "book of patterns" in your mind that provides easily accessible variations for you to use. You will also find that you can make associations between them, since various geometric forms and proportions share connections and points in the basic diagram. Various geometric solutions "talk" to each other. Using arcs and diagonals to cut the square will divide it into "zones". You will find that you can skip between these to increase or decrease the proportion of a part by applying different basic cuts and combinations.
It is another matter to apply geometry to a sword that is not designed on geometry in the first place. You will find that it often "resist" any attempt to make it fit structures in a simple and pleasing way. You will have to use many layers and combined forms to reach something that conforms to a structure and this is defeating the purpose of the activity: you want to use simple and straight forward structures that can easily be referred back to the sword itself.
However, if you adjust the blade´s length and /or width by a small amount you might find that it is easy to develop a satisfying geometric solution.
If you have a blade that is made with an overlong tang, it is usually pretty easy work out a geometry that fits the blade. A small amount of tweaking of the first circle will have a great effect of how a long series of circles falls out over the length of a blade.
Remember that the three basic lay outs divide the hilt in 1, 2 or 3 parts that are then multiplied to give you the blade length.
A small tweak of the first basic circle will also have minimal effect on crucial things like grip length, since you can often adjust the placing of the guard without breaking the geometry and you can always find smaller or larger diameters for the pommel to allow for different grip lengths. Once you have decided the proportions and dimensions of the pommel in the 2d diagram, you can work out how thick you must make the pommel to give it the correct mass.
This way, geometry can be used to design the hilt of a sword that you already have a blade for. It is sometimes more difficult to find a satisfying definition for the blade width that goes along well with the rest, but there are several ways to do this that provide options for you.
When you try out different designs for the hilt, you need only draw the circle(s) that are used to define the hilt, as long as you know they are of the correct diameter to be commensurable with the final complete length of the sword. This way you can easily work in full scale if you want and directly try out the effect of various alternatives.
The most simple solutions usually provides the most satisfying results.




Anthony Rischard

Posted: Fri 06 Jan, 2017 3:28 pm Post subject: 


Peter Johnsson wrote:  To add something more to be considered, I post a detail of my tracing of the original.
When you look at the original sword it seems the point has been resharpened or perhaps even reshaped after some damage.
A detail like this is difficult to make out from photos, since it is a 3D thing: it is how the edges are formed together with the outline of the point. In my tracing you will see how I estimated the original length and form of the blade.
I hope you forgive me from keeping this information to this later stage in the process. It might seem like a small thing, but it does have an effect in how the guard is positioned in a series of linked circles. Since this is the first step in an analysis (and also when you develop the design in the first place) it will affect all other solutions that come after. 
Thanks Peter,
I have adjusted to take this into account. My first circle goes from 119,125 to 119,5 mm. The effect on the hilt is as expected minimal and everything still "fits". The guard placement is, in my opinion, still within the margin of error for having normalized it. Would you also agree that the guard is the element most likely to have shifted by a few millimeters either way once the organic materials of the hilt have degraded?
Are there any other elements you can put into the mix to help me further evaluate my proposed solution?
Good night to all!
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Peter Johnsson

Posted: Fri 06 Jan, 2017 3:35 pm Post subject: 


Anthony Rischard wrote:  Peter Johnsson wrote:  To add something more to be considered, I post a detail of my tracing of the original.
When you look at the original sword it seems the point has been resharpened or perhaps even reshaped after some damage.
A detail like this is difficult to make out from photos, since it is a 3D thing: it is how the edges are formed together with the outline of the point. In my tracing you will see how I estimated the original length and form of the blade.
I hope you forgive me from keeping this information to this later stage in the process. It might seem like a small thing, but it does have an effect in how the guard is positioned in a series of linked circles. Since this is the first step in an analysis (and also when you develop the design in the first place) it will affect all other solutions that come after. 
Thanks Peter,
I have adjusted to take this into account. My first circle goes from 119,125 to 119,5 mm. The effect on the hilt is as expected minimal and everything still "fits". The guard placement is, in my opinion, still within the margin of error for having normalized it. Would you also agree that the guard is the element most likely to have shifted by a few millimeters either way once the organic materials of the hilt have degraded?
Are there any other elements you can put into the mix to help me further evaluate my proposed solution?
Good night to all! 
It looks good: a very elegant solution.
I have no further information about the sword that impacts the analysis :)
Promise.
I will comment on it further once we have seen a few more suggestions.
(If you don´t want me to show my suggestion right now).
I think that the placing of the guard can be shifted in many designs. Not all, it seems, but many.
Often it seems that it is enough if the guard somehow overlaps the defining line for placing of the guard.
I suspect that this is a way to adjust the grip length within a given design structure once you have chosen its overall dimensions.




Mark Lewis

Posted: Fri 06 Jan, 2017 4:13 pm Post subject: 


Great construction Anthony! Very different approach from what I have been trying...
We've both come up with constructions that give very similar arcs for the pommel, and we have almost identical intersection points that relate to the width of the blade. It seems to me (and I had the same thought as I worked on some previous diagrams) that varying the size of the small circle would be a simple way to generate variations of the same design with smaller or larger pommels paired with narrower or broader blades. Peter, would this be a useful technique for designing a pommel that will balance the weight of differentsized blades?
Using the reconstruction of the length of the blade actually reduced the margin of error in my design in several places and allowed some simplifications.




Kai Lawson

Posted: Fri 06 Jan, 2017 8:36 pm Post subject: 


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?
"And they crossed swords."
William Goldman, alias S. Morgenstern 




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