I would guess they substituted charcoal for the pencil but probably stuck with the road.Interesting day today.
I found out that Hyperbolic functions were introduced in the 1760s by Vincenzo Riccati and Johann Heinrich Lambert. But that's in Wikipedia, so I'll have to check the source properly.
I also managed to plot 1:3 scale drawing of the vault as a very tidy hyperbolic cosine using Hooke in about an hour. It was easily done with a piece of rope and a pencil. Which has got me thinking about how it was done in the 14th. century.
I think I have a credible answer, but I'll try it out on a full size drawing of the vault I'm planning first and use it to make a plywood template to cut the principal rib from.
In England, master carpenters and master masons acted as both architect/designer and builder up until the 17th century, when architects with no practical training or trade began to appear on the scene.Adam would the woodworkers have been consulted during the planning stages of a roof build or would they have been tasked with decorating after the masons were done? I realize there would have been an overall drawing of the building and detail drawing of sections but have the feeling they would have had to match the wood to the building to fit. I'll sit corrected if off but I doubt they were calculating curves etc to any extent, just fitting and adapting to make the work match the designers vision. Different in a building where the timber was the main load bearing structure, basically what you are working on, then the math fell on their laps.
I read (somewhere) that full size layout drawings have been found scratched on floors of churches and temples. It'd make sense as complicated curved shapes were ancient technology in ship building and "lofting" must be as old as ship building itself. Lofting - WikipediaIn England, master carpenters and master masons acted as both architect/designer and builder up until the 17th century, when architects with no practical training or trade began to appear on the scene.
Buildings such as the 14th. century timber lantern at Ely cathedral would have been the responsibility of a master carpenter working in conjunction with a master mason to produce the whole cathedral.
I doubt very much that something like this is just made to fit and plonked on top of a load of masonry and must have been designed at the same time as the stone tower by people with a deep understanding of material properties.
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To produce something like the lantern at Ely, which is vast, would have required a certain amount of working out by someone with knowledge of practical geometry and structural mechanics. I doubt very much if it was just built to fit, as it's a complex piece of timber engineering consisting of many layers all acting as one, and I would imagine that modern engineers and architects would struggle to design a timber structure like it today and sign it off.
In the east of England we have a tradition for building enormous timber structures, such as the barns at Cressing Temple, built in the 13th. century. These stand on a brick plinth, as there is no natural source of stone and a carpenter has had to do the maths to make it stand up. There may have been even larger timber structures at the time which have been lost due to decay or fire. So the knowledge possessed by carpenters at the time was equivalent to that of a master mason, and they both acted as designer working to the clients specification.
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The vault which I'm planning is inspired by a later insertion into a Norman stone tower at Winchester and is suspended from a hidden timber structure, much like the decorative vault at Ely. The real load bearing engineering is in the hidden parts, which consist of massive timber structures, much like the barn above, resting on masonry designed to support them and then clad in fancy timber vaulting by highly skilled carpenters.
It may even be the point at where carpentry and joinery began to be viewed as slightly different disciplines, as the vaults were scaled down to produce decorative rood screens in west country parish churches, such as the 15th. century one at Long Sutton in Somerset.
Is it joinery or carpentry when it becomes that size ?
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The curves may have been based on the rope catenary, which is why I'm messing about with it, as it's the easiest way to produce an arch, which isn't just a segment of a circle and avoids the use of complex maths.
My rib layout without the use of maths (below) which is also the precise description of the load path for a vault of that size. I'm beginning to think that fan vaults without maths are easily laid out, even though they look very complicated at first glance.
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So I think the short answer to your question is yes and no.
Sounds exciting!@Jacob That's interesting, I had the very same conversation yesterday with the resident geometry master.
His father worked at British Aerospace and he said that they laid out all their stuff on massive steel sheets in a huge loft. He also reckons that there's a framing floor in York Minster and I'll see if I can track it down.
I'm now starting on laying out the drawing for the vault and I've decided to make it as a tester, which is a canopy over a tomb. So it's going to be scaled down to about 5'6"x 3'3".
I'll post some photos once the full size drawing is under way, and I plan to show the drawing at the MA show in October along with the graduating MA's before starting on the joinery.
It's getting pretty exciting and attracting a lot of attention, so I hope I don't screw it up.