How does making a brick wall *curvy* save material?

Question

Recently, I visited a college. The University of Virginia, to be exact. Just more of a sightseeing tour than anything. Whilst walking through a part of campus, I saw a brick wall that was built somewhat like this:

I inquired about its curvy shape, and was told it was to save brick when building. I found this rather strange, considering each curve is one half times π times the diameter until it reached the same depth.

And we know that the circumference will be larger than the diameter, so how could this save material of any kind? Was I just lied to?

Thanks in advance, Joe

Answer 1

You are correct that the wall is longer than a straight wall. What you are missing is that such walls can be built thinner than straight walls, which can more than offset the increase in length.

From Wikipedia (emphasis added):

The sinusoidal curves in the wall provide stability and help it to resist lateral forces, leading to greater strength than a straight wall of the same thickness of bricks without the need for buttresses.

Note that such walls are described as "sinusoidal", i.e. based on sine waves, which means they wouldn't be made up of semi-circles as in your diagram. Of course, any individual wall might not conform to any exact mathematical pattern...

Anyway, I found a blog post that does the math on the length of a sinusoidal wall:

...consider a section of wall 2π long. If the wall is in the shape of a sin(θ), then we need to find the arc length of this curve. This works out to the following integral.

$$\int_0^{2\pi} \sqrt{1 + a^2 \cos^2(x)}\, dx$$

The parameter a is the amplitude of the sine wave. If a = 0, we have a flat wave, i.e. a straight wall, as so the length of this segment is 2π = 6.2832. If a = 1, the integral is 7.6404.

The author concludes that if you replace a two-brick-thick straight wall with a one-brick-thick sinusoidal wall, you will save on bricks as long as the amplitude of the sine wave is below ~1.4422 (i.e. the point at which the wall has doubled in length).