How to Draw Large Curves

Here are three (or four) field-expedient methods for drawing curves that I use frequently when building houses and furniture. Each method produces a different type of curve, so pick whichever suits your application.

These are demonstrated here in small scale, but I usually use them in the field to draw curves from 1' or 2' long up to 20' or 30' long.

Step 1: True Arc

This method produces an arc, a segment of a circle. Mark the width of the arc and the height of the arc at the midpoint. Place a nail or other restraining implement at either end of the arc.

Place two straight strips of material so that they are touching the nails and intersecting at the midpoint. Fasten them securely at the midpoint and place your marking implement in the apex. Slide the contraption to one side and then the other, keeping the marker in the apex, and the "legs" in contact with the nails.

Step 2: Batten or Spline

This method is often used by boat builders because it can be used to make "fair" (smooth) complex curves. Here is a boat-specific example. It is the method I used to layout the curve for my trestle table. I'm also not sure what kind of curve it produces, mathematically speaking, but I'm hoping someone here at Instructables can tell me...

Mark the end points of your curve, and the height. Place to nails or other restraining devices at these points. I often use clamps. Use a long, thin, consistent strip of material (a "batten", PVC pipe works well for large curves) to "fair the curve". You may have to experiment with different batten materials and dimensions to get a good result.

For compound curves, mark several "waypoints" and use the batten to connect them.

Step 3: Catenary

This method produces a catenary, which is almost, but not quite, a parabola, but is usually close enough. This method doesn't work well if there is a breeze.

The surface to be marked should be vertical. Drape a limp piece of string or thin rope so that it hangs freely. The piece I used is not quite right. I use a marker and "dab" it over the string every so often and then connect the gaps in the dots later by hand.

Again, you'll have to experiment with material. Woven cord works better than twisted, which is why the string in the example photo isn't quite right.

Comments

[WackyPup]

You can make a really nice arc using string and two nails or other fixed points - https://www.thisiscarpentry.com/2012/03/30/drawing-an-elliptical-arch/

[jessi3535]

If i put pieces of cardboard on the line and have them touch the apex what i am looking at is a triangle. How do i get a curve out of this, and what is a contraption?

[aeray]

A contraption is an assemblage of parts.

To make a curve with the triangle, place a marking implement at the apex, then slide everything to one side, then the other, keeping the two legs of the contraption in contact with the fixed pins, and the marking implement at the apex.

[MikeSarrazin]

Thoroughly enjoyed this tutorial.

[aeray]

Thanks. Let me know if you have any questions.

[8bit]

for step 1, how would one compute the center of the circle which this arc is a part of?

[aeray]

You can find the radius using this equation, with "H" equaling the height or the arc, and "W" equaling the length of the chord (the width of the arc):

R=(H² + ¹/₄W²) / 2H

As for the angle of the arc:

Degrees arc=[sin(a)= ¹/₂W/R]*2, I think.

[8bit]

And the angle of the arc?

[Arano]

mathemathicaly this should be a function which should look like this(all characters besides x are constants): f(x)=a*x³+b*x²+c*x+d

besides that: well written ible

[aeray]

So... what do you call the curve produced by three points, using this method?

[aeray]

Sorry... using the spline or batten method, using two fixed endpoints, a uniformly flexible "batten" and a single pressure point, forming the curve, at the apex?

[Arano]

still the same... though it might happen that if you actually try to find the values of the constants some turn out to be zeros.... with 2 endpoints and one pressurepoint the constant a is likely to be zero but it doesn't have to

[aeray]

So is there an actual name (like "arc" or "catenary") for this type of curve?

[Arano]

well uhm... it's the graph of a cubic function... i think there are neither in english nor in german special names for something like that... (well in school we were told that this is sometimes called spline in connection to boatbuliding but thats no new information)

[aeray]

Thanks. Perhaps well-written, but sub-par pics.

[frazeeg]

Heavy cord (dense, not thick) works better than light cord as well. The weight smooths out the kinks in the rope better.

[Arano]

a thin metal chain works better too

[aeray]

Both correct, but string and rope are common on the jobsite, and fine chain isn't.