Calculated Curvature · The notes
Field guide: the bend that stands
Notes on the word, the wall, and the calculation.
The word
Crankle is both a noun and a verb. It means a bend, a twist, or a crinkle in something that was expected to be straight. The word appears in the late 1500s, formed from crank by adding -le, the same ending that turns crack into crackle. Shakespeare had already used it of a hare that “cranks and crosses,” in Venus and Adonis, in 1593.
Crinkle-crankle is the doubled form of the word. It names a wall whose plan bends from side to side along its length. This site uses the shorter word.
Why the wave stands
A straight wall only one brick thick has little resistance to wind, which is why a builder will make it two bricks thick, or brace it with piers every few metres. Bend the plan, first to one side and then to the other, and each bay behaves like a shallow arch laid flat. The shape is the brace. Many of these walls survive in Suffolk. The Dutch called them slangenmuur, or snake walls, after the shape of the plan.
The bays had a second use. A curve of brick holds the heat of the afternoon and shelters a fruit tree from the wind. The fruit is not part of the brick count, but it is one reason the walls were built.
The instrument on the front page also asks whether the wall stands. It sets the same breeze against three bases: the curve, a straight wall two bricks thick, and a straight wall one brick thick. The breeze is 0.15 kilonewtons on a square metre, about 35 miles an hour. The brickwork is taken at 19 kilonewtons a cubic metre, so that one brick is a little under three kilograms in the hand. The wall stands when its own weight can still keep the whole of the base in compression. A curve does that by placing brick away from the centre line. The figure is a model of that idea. It is not a calculation a building official would approve.
The ledger
The table is working the same sums as the instrument on the front page. One thickness of brick follows the curve, and two thicknesses follow the straight run, on an English module of 225 by 75 millimetres. These three examples may be looked at freely. The writing that follows them is the guide.
| Preset | Arc | Wavy | Twin | Saved |
|---|---|---|---|---|
| Suffolk garden | 18.05 m | 1,760 | 2,728 | 35% |
| Lawn bay | 12.44 m | 990 | 1,512 | 35% |
| Tight ribbon | 22.05 m | 2,646 | 2,862 | 8% |
Where a row shows 35%, that is the saving for a bay of that shape, in this model.
How the count is made
The wall may be written z = A sin(2πx / λ), taken over a straight run. The bricks do not travel that run. Each small step forward is accompanied by a small step sideways, and the brick walks the sloping side of that little triangle. Add the sloping sides and you have the arc, which is the integral on the front of this site. The curve grows longer if the wave is made steeper, or if the bends are set closer together. The sum is nearer the truth than a tape laid on a drawing, and further from it than a mason counting the bricks in the barrow.
The courses are the height of the wall divided by 75 millimetres, and then rounded, because a course has to be a whole number of bricks. The bricks in one course are the long path divided by 225 millimetres, rounded in the same way. Multiply the two, and you have the wavy wall: one brick thick, about 102.5 millimetres through. The straight twin uses the short distance instead of the long one, and is then doubled, since it is two bricks thick. The saving is the difference, divided by the twin. If that percentage turns negative, the wave has been bent so far that the advantage is gone. Ease the amplitude, or lengthen the bay, and it will come back.
How to look at one
Stand at one end and look along the coping. You are looking for a rhythm, not for a ruin. A bay is one bulge. The wavelength is the distance from the start of that bulge to the start of the next, and the amplitude is how far the belly of the wall stands off the straight line between the ends. A tighter garden wall may bulge less and still be doing the work it was built for.
After that, look at the thickness. If you can see a single long face of brick, the wall is about 102.5 millimetres thick, one brick. The coping, the piers at a gate, and the square returns at the ends are extra, and they may be straight. The curve is what stabilizes the middle.
What this model leaves out
The model leaves several things out, and it ought to say so. It leaves out the mortar that gets spilled, the bricks cut where a bay turns, a thicker footing, and any pier the original builder still decided to add. The tally uses the English module. A wall built with a different brick would need its own count. The comparison also assumes that the straight wall really does need two thicknesses. A straight wall that uses piers instead would need its sums done again.
Nothing here is a specification. A wall that keeps people off a drop, or that holds soil, is an engineer’s wall, and it should be left to an engineer. The model is only a way of seeing why a curve that looks a little odd was the economical one.