u/_gerard__

I made this animation to explore how changing the rise of a masonry arch affects the geometry of a course-based stone layout (sometimes called stepped-extrados).

To make the comparison clearer, the stone count stays fixed while the rise changes.

The first part shows a 3 m (9’10”) span with the height varying from 0.2 m to 1.5 m (8” to 4’11”), while keeping the stone count fixed at 19. Each case is shown first as a one-centred arch and then as a three-centred arch.

The second part does the same for a smaller span of 1.3 m (4’3”), with heights varying from 0.2 m to 0.55 m (8” to 1’10”), using 9 stones, again comparing one-centred and three-centred outlines.

What interested me here is that changing the rise affects not only the outline of the arch, but also the position, proportions, and shape of the voussoirs in a course-based construction.

The animation was generated with a Swift program (that I’m trying to turn into an app for working with arches.) For each frame, the main inputs are the span, rise, and stone count, together with a few construction settings such as course height and joint thickness.

More generally, it seems that with enough geometric and construction information (which isn’t a lot), an arch can be described precisely enough to reconstruct the individual stones that make it up.

Following on from a three-centred arch model I had posted, I made these 1:10 scale 3D-printed models to compare two different ways of setting out a one-centred arch (segmental arch).

Both use the same overall geometry: a 1.2 m (4 ft) span and a 0.2 m rise.

The arch on the left is a radial-based version. It uses 5 stones, with the three central cuts set out equally, plus two stones at the base so the arch meets the course more naturally.

The arch on the right is a course-based version. It uses 7 voussoirs, with the cuts along the arch set out at equal distances, except for the first stone, which is shorter along the curve.

I’m interested in how the same arch outline (intrados), can lead to quite different stone layouts depending on the how the stones are cut.

From what I have seen so far, a lot of the intuition/methods seems to have been passed down by word of mouth rather than written up clearly. If anyone here knows more about the theory, or about specific methods used by stone masons, I would love to hear about it. I am trying to build a tool for designing and setting out arches, so I am especially interested in how these methods were actually used in practice.

Following on from a three-centred arch model I had posted, I made these 1:10 scale 3D-printed models to compare two different ways of setting out a one-centred arch (segmental arch).

Both use the same overall geometry: a 1.2 m (4 ft) span and a 0.2 m rise.

The arch on the left is a radial-based version. It uses 5 voussoirs, with the three central cuts set out equally, plus two stones at the base so the arch meets the course more naturally.

The arch on the right is a course-based version. It uses 7 voussoirs, with the cuts along the arch set out at equal distances, except for the first stone, which is shorter along the curve.

I’m interested in how the same arch outline (intrados), can lead to quite different stone layouts depending on the how the stones are cut.

From what I have seen so far, a lot of the intuition/methods seems to have been passed down by word of mouth rather than written up clearly. If anyone here knows more about the theory, or about specific methods used by stonemasons, I would love to hear about it. I am trying to build a tool for designing and setting out arches, so I am especially interested in how these methods were actually used in practice.

I designed and 3D printed this three-centred arch based on the bossut method.

It is based on a 1.2 m (4 ft) span and printed at 1:10 scale. The model uses 7 stones in a course-based arrangement, with the joints distributed at equal distances along the curve.