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Q & A: Gothic Arches

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Most recent answer: 10/22/2007
Q:
Hi Van I would like to know how a gothic arch can stay up in place without falling. could you send me a discription or diagram of the angles and froces involved in the construction of a gothic arch. Thanks you very much. Great site by the way!
- mark (age 13)
international school of paris, Paris France
A:

Mark -

The thing that holds any kind of arch together is gravity. Gravity is a force that pulls everything on the earth straight down. The key to a gothic arch is that it has a (basically) triangular piece at the top:

Credit: https://matheducators.stackexchange.com/questions/7528/real-world-examples-of-more-obscure-geometric-figures/7548


Since gravity is pulling the top piece straight down, this means that all the forces produced by gravity on that top piece have to add up to being straight down. But it can only push against the flat edge of the bricks next to it. So what actually ends up happening is that it pushes the brick on its left a little bit to the left and a little bit down, and it pushes the brick on its right a little bit to the right and a little bit down. The "to the right part" and the "to the left part" cancel each other out, so that the total force being produced by gravity on the triangle is just straight down. The force on each brick to the side is then transfered much the same way to each of the rest of the bricks the rest of the way down. If this doesn’t exactly make sense, you can think of it in terms of some of the basic laws of physics. One of these laws is that "every force has an equal and opposite force" (for something that’s standing still). This means that the force of the top brick pushing down (gravity) is equal to the force of the bricks below it holding it up. Also, this means that the force that the top brick applies to the brick on its left is equal to the force that it applies to the brick on its right. The reason that the bricks to the left and right don’t just slide off to either side is because there’s a lot of friction (or mortar) between them and the bricks below them, so they won’t budge to either side.
Hope this is what you’re looking for.

-Tamara


(published on 10/22/2007)

Follow-Up #1: Gothic arch construction

Q:
You answered a question Mark (age 13) asked about how gothic arches stay up and not fall. However, my questions are: How are gothic arches constructed? How are the stones "put" in place so that they don’t fall while constructing the arch? How are the side walls of the arch kept in place so that finally they come together at the top with the top center triangular stone? Thanks. Respectfully, Armand
- Armand
San Francisco, CA
A:
Ah, this is one of the triumphs of the ancient Greek and Roman engineers -- how to build a stone arch that relies on its compression forces to stay up. In the process of building it of course not all the stones are yet in place, and so something else must be there to keep it up during construction.

The easiest solution is to build a wooden frame with supports for the stones of the partially constructed arch. Once the arch is in place, you can disassemble the frame and leave the arch free-standing.

Arches of course have lateral spreading forces from the rounded top on the supporting columns. Either the columns must be thick enough to handle the torque without collapsing, or secondary arches can be put on the side of the supporting columns so they do not fall over sideways. These can be constructed at the same time as the main arch with wooden supports.

Tom

(published on 10/22/2007)

Follow-up on this answer.