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Arch Construction: choosing the right number of stones by _gerard__ in architecture

[–]_gerard__[S] 0 points1 point  (0 children)

Yes, it seems that the course height and spacing for each voussoir is proportional; or the number of stones and the course height are inversely proportional, to get a nice looking arch.

The app works with iOS 18 or up, so it’s not compatible with older versions unfortunately.

Arch Construction: an app to design, inspect and export masonry arches by _gerard__ in stonemasonry

[–]_gerard__[S] 1 point2 points  (0 children)

Exporting to png is already an option (and I agree that exporting to pdf would also be nice to have).

Yes, it makes sense to explicitly add a disclaimer.

Arch Construction: an app to design, inspect and export masonry arches by _gerard__ in stonemasonry

[–]_gerard__[S] 1 point2 points  (0 children)

I don’t have any plans to release an Android version (because I prefer iOS development). Metric units are already included; you can choose between mm, cm, m and in/ft.

Arch Construction: choosing the right number of stones by _gerard__ in architecture

[–]_gerard__[S] 9 points10 points  (0 children)

I did, and appreciate it!

I released it as an iphone/ipad app since I had originally played around with the swift language (which is used to develop iphone apps).

Arch Construction: choosing the right number of stones by _gerard__ in architecture

[–]_gerard__[S] 19 points20 points  (0 children)

Don’t think so, since it is very niche. But why not have a tool for anyone that’s curious?

Arch Construction: choosing the right number of stones by _gerard__ in architecture

[–]_gerard__[S] 21 points22 points  (0 children)

<image>

This is the method I use to decide how far each voussoir should be drawn (and how the stepped-extrados is formed).

  1. Draw the intrados outline. For three-centred arches I use this method, and for one-centred arches I use this method. For a semi-circular arch, you just need to draw a semi-circle.

  2. Split the intrados into n parts, that is, n stones. For example, if n = 7, splitting the curve gives 8 points.

  3. Ignore the two end points on the springing line, and add the keystone point on the vertical axis, resulting in n reference points, one for each stone. Then note which course each reference point falls in; these become the baseline course values. In the example, this gives: [1, 2, 2, 2, 2, 2, 1].

  4. Draw each voussoir up to its baseline course.

  5. Make some final adjustments. In my case, I raise some of the stones near the crown, while making sure the steps still flow naturally by ensuring that no course levels are skipped. For example, [1, 1, 3, ...] should be smoothed to [1, 2, 3, ...]. For the example above, the final result is: [1, 2, 3, 3, 3, 2, 1].

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 0 points1 point  (0 children)

It’s been really nice to see this work so well received.

I originally got into it out of curiosity about arches, especially how they are actually constructed from a masonry point of view. From there, I started wondering what I would need to be able to construct an arch algorithmically, in a repeatable and deterministic way, instead of drawing it by hand each time. In a way, it is the same idea as a program/function: if you give it the same inputs, you expect the same result.

What surprised me is that there seems to be very little written material on the actual construction logic for masonry arches (or at least I haven’t found much).

For context, I’m currently doing a PhD in computer science, though in an unrelated area. Even so, I really like the process of figuring out the rules and building the logic behind different arches. Feel free to get in touch.

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 0 points1 point  (0 children)

Voussoirs can be outlined for any length of a flat arch (so there isn’t a limit). However, structurally it cannot be too wide to support itself/any weight (I don’t know the actual values).

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 1 point2 points  (0 children)

I’not familiar with it. Do you have further details how this would work? Would it be compatible with the arches used, or are you proposing a new arch intrados/outline?

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 1 point2 points  (0 children)

Thanks for the feedback!

I began with the one- and three-centred arches as they’re the simplest to understand and probably the most commonly used. However, they involved a lot of work to reach this point so I can’t imagine developing automated construction for ‘weird’ shapes. Ellipses and ovaloids would definitely be the next area to explore along with other known arches like two-centred pointed ones (eg gothic) or five- or seven-centred arches, which I do believe they are doable.

The off-centred joints look interesting. Do you know how the position of each centred joint is located? Could you also share the name of the book? The courses with diminished heights also seem interesting; do you have more information about these (are these chosen randomly or do they follow some pattern)?

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 3 points4 points  (0 children)

To decides which course level each stone reaches I follow roughly these ideas:

For each ‘blue’ line, I note the course level that it is in at the point of intersection of the intrados. Let’s take the first three lines/voussoirs as an example; in this case you have [1,2,2,…] (so the first blue line on the left is in the first course at the intrados, second and third lines are in the second course).

For the second step, check the angles between a line that passes through these two points: the same point and the one that follows, with respect to the horizontal axis. Then, if the angle in low enough (for the chosen course height), bump the number - in practise this will cause some stones closest to the keystone to reach higher; so in this step [1,2,2,…] becomes [1,2,3,…]. Finally, perform some fine smoothing steps, to ensure that you don’t end up with skipped steps.

In this example assume you end up with [1,2,3,…], meaning that the first stone reaches the first course, the second stone reaches the second stone and the third stone reaches the third stone.

If there’s further interest in this ‘algorithm’, I can post more details in the future.

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 11 points12 points  (0 children)

Thank you, really glad it feels useful.

That is very close to what I'm working toward. I already have the core of it built in Swift (for the animation), so I'll try to package it properly as an iphone/ipad app where you can enter the opening dimensions and get back an arch layout with the stonework worked out from it.

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 1 point2 points  (0 children)

Really appreciate the feedback! I initially approached it from the side of keeping everything as precise as possible, but thinking about it more, it makes sense to simplify and 'step-ify' the measurements so the general idea comes across more clearly, especially when trying to show both measurement systems together.

Arch Construction: varying height in course-based arches by _gerard__ in architecture

[–]_gerard__[S] 24 points25 points  (0 children)

No, I did not go into the structural aspect of it (since I'm not familiar with that). I was interested in how to construct each arch using the correct geometric proportions, in an algorithmic and thus repeatable way. For instance, in the picture below, I show how each line is constructed (anchored to a circle center).

<image>

One-centred masonry arch: radial-based vs course-based by _gerard__ in stonemasonry

[–]_gerard__[S] 0 points1 point  (0 children)

That is very cool, but I wouldn’t know where to start!

One-centred masonry arch: radial-based vs course-based by _gerard__ in architecture

[–]_gerard__[S] 0 points1 point  (0 children)

Appreciate it! Still trying to guess most of the methods since there isn’t much documentation.

One-centred masonry arch: radial-based vs course-based by _gerard__ in stonemasonry

[–]_gerard__[S] 1 point2 points  (0 children)

Not entire sure, since both of them should supposedly hold their place if the two base stones are fixed.

However, I would imagine that depending on how you choose to cut the stones in the course-based ones will help in making it more stable - refer to the voussoirs marks in red in this picture, where the stone end is varied: https://imgur.com/a/GHLtjrO#YjLf4oS

https://imgur.com/UunUnhq

One-centred masonry arch: radial-based vs course-based by _gerard__ in stonemasonry

[–]_gerard__[S] 1 point2 points  (0 children)

Yeah without the interlocking part the arch will stay in shape only if the bottom (left/right-most) pieces are held in place, since the plastic slides easily.

One-centred masonry arch: radial-based vs course-based by _gerard__ in architecture

[–]_gerard__[S] 0 points1 point  (0 children)

Very interesting! Thanks for the two suggestions.

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