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.

Comments

[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?

[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.

[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]

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

[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)