Methods for radius layout

Alternatives to using a trammel for laying out an arc. September 19, 2001

Does anyone know a better way to lay out arcs/radius work than by using a trammel? I know you can use a triangle template of sorts (I believe it's a ship building technique), but I've not been able to find anything in writing on this. I am interested in any way that I can lay out arches up to twenty feet.

Forum Responses
The simplest way is with CNC. If you would like, I could cut some templates fairly inexpensively.

The next simplest is to make a scale drawing on graph paper and 'explode' it.

If you're looking for mechanical jigging, look up the book 'Plastering Skills' by Van Den Branden/Hartsell. In the section on ornamental plaster, there are various trammel and pivoting gig stick arrangements that may suit you.

From contributor D:
The easiest/quickest way is to take a thin wood slat and mark your radius distance on it. Then drill a hole for a pin or screw at one mark and a hole for a pencil or scribe at the other mark. Cheap, simple fast.

Isn't that the definition of a trammel?

From contributor D:

He could build a 20' triangle and get you to build an arc tangent curve for him on your CNC router. I would change my recommendation, though. At lengths such as were mentioned, I would suggest daycron string because it does not stretch.

From contributor J:
About 40 years ago I helped a guy lay out a small bridge and he used a formula for figuring out a circular curve. I can't find the scrap of paper I had it written on but it goes something like this. Say the distance is 20 feet and you want a 3 foot rise. You lay out the distance of the chord and each 1 foot point across the chord is a fraction of the distance across the chord and the rise. I'll keep looking for the formula and try to scale it out. I remember it wasn't too complicated and used simple fractions.

H=height L=length
10MM height 50MM length

From contributor J:
I have found two methods. To make a curve with a set triangle, set points (awls) at the width and the height. Put two wood strips against the width and the height and brad them together, then brad a brace piece across the strips to hold them in place. To mark out the curve, move the point toward either of the end points (width) either way keeping the strips tight against the awls, and the point will mark out a curve.

The other method is to measure the width and set a perpendicular for the height equal to one-half the width and connect this point to each end point. On this line, divide it into any number of equal parts (say 6 or 8 for a 12 foot width). Both sides must be divided equally. Count up to the apex on one side and down from the apex on the other. Connect lines from No.1 to No.1, No.2 to No. 2., etc. Where these lines cross will give you points on the exact part of a circle. This formula is in a 1904 book and is the one to make curves for brick and stone arches.

The comments below were added after this Forum discussion was archived as a Knowledge Base article (add your comment).

Comment from contributor A:
Need to find the correct radi? Measure the cord exactly (say it's 54"), divide this sum in 2. So 27"x27"=729", now measure the height from the cord to the highest point of the ellipse (let's say it's 6 1/4"), now x 6 1/4"x6 1/4"=39.06", now add 729"+39.06"=768.06", now add the sum of the rise 6 1/4" x 2=12 1/2". Divide this into 768.06" = 61.44" (61 7/16"). This is the true radius.