So that was last week and seeings this week has started, I've been looking at the shape of the vault and have some questions to answer.

Initially, I thought that the vault was a segment of a very large circle resting on the corbel and ending at the compression ring and that the arc was a single radius, as it would be if it was a part of a circle.

So I started to look at the theory of parabolic conoids, masonry arches and stuff like that. And came across a theory by a chap called Hooke, who was a contemporary of Wren. (That's 17th century stuff but the fan vault was a 13th century and onwards thing).

Hooke came up with a way to describe the perfect shape for a self supporting arch with no thickness.

*"As hangs the flexible line, so but inverted will stand the rigid arch." *
I'll try and explain what it means and it involves a chain, no computers in those days.

If you suspend a chain between two points you make a catenary. A catenary has gravity acting on it, so it hangs down in and forms a uniform curve, called a catenary curve (I'll assume that the chain has a uniform thickness and weight for simplicity, no need to over complicate things which are already a bit complicated).

This curve is called a hyperbolic cosine (a bit like a parabola). There's a formula for those, but I'm not going to use it, and I reckon master carpenters and Masons in the 14th century didn't either, but they could have used a chain to plot the curve and experimented with smaller vaults before doing the big stuff.

Below is Polenis' drawing of Hookes' theory.

At the bottom is Hookes' chain catenary, which is under tension. When you make it rigid and flip it up about axis DE you get an arch which is under compression, due to gravity.

This is Hookes' perfect arch and it describes the precise load path for compression forces acting on the arch. Notice it doesn't get to be vertical at the ends BC, that's an important thing. All the timber vaults that I've looked at have a single piece of timber where all the ribs come together and load the corbel. The rest of the vault without that piece of timber look like Hookes' arch.

If you build an arch of masonry with no mortar, it has to contain all of Hookes' hyperbolic cosine catenary curve within the depth of the masonry, otherwise it will collapse into a heap on the floor.

So this weeks question is;

Did the carpenters and masons who built this stuff in 1400 know all about this before Hooke described it?

Actually there's two questions.

And;

Do timber vaults need to pay attention to this like masonry vaults do ?