How to Draw Large Curves

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About: Craftsman of fortune. Less is more, and simpler is better.


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.

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    15 Discussions

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    aerayMikeSarrazin

    Reply 2 years ago

    Thanks. Let me know if you have any questions.

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    8bit

    8 years ago on Introduction

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

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    aeray8bit

    Reply 8 years ago on Introduction

    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.



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    Arano

    8 years ago on Step 2

    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

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    aerayArano

    Reply 8 years ago on Step 2

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

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    aerayaeray

    Reply 8 years ago on Introduction

    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?

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    Aranoaeray

    Reply 8 years ago on Step 2

    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

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    aerayArano

    Reply 8 years ago on Introduction

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

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    Aranoaeray

    Reply 8 years ago on Introduction

    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)

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    frazeeg

    8 years ago on Step 3

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

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    aerayArano

    Reply 8 years ago on Introduction

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