Drawing an arc

[Paul Tinsen]

I was recently building a buffet and wanted to put an arc on the front of the top. The calculated diameter was 25' 4". I tried string, EMT (electrical metallic tubing) wood, you name it, I tried it. What are the secrets to drawing these arcs accurately?

[John Coloccia]

If you really want an accurate, circular, arc without using 25' of string, you can use something called a "long compass".

http://gicl.cs.drexel.edu/people/sevy/luthierie/compass/Long_compass.html

This is the simplest method I know. I've used this method in the vertical configuration to make a sanding dish with a router (the router is mounted in a carriage at the "peak". Don't do this...just buy the dish. LOL. It's a LOT of work!!).

By the way, to find your 3 points, you'll need to calculate the "sagitta" of the arc. That's the change in height from the peak of your arc to the two point the long compass is riding on.

So, let's say you have a 50" piece you want to put a 100" radius arc on (the numbers don't matter...just use all the same units). So you'll put your anchor points somewhat outside of the 50" (because you don't want to drive nails into your project). Let's say you're anchoring at 55".

Go here:

And calculate the sagitta.
r = 100
l= 27.5 (55"/2)

That give you a sagitta of 3.856" (so let's say 3.9"). What that means is that the peak of the arc will be 3.9" above wherever you sent the pivots. When setting it up, you would put you're workpiece 3.9" beyond the anchors, being sure to center the piece between the pivots. Now when you set up your sticks, place them on the pivots and just be sure that they meet at the far end of the workpiece at the centerline. Now you know you have the proper angle on your sticks for the anchor point spacing you've chosen.

If you just want to eyeball the arc, another method is just choose 3 point on your arc, drive nails at the outer point, make your sticks indexed on the inner point, and use. No need to do any calculations. You only need to calculate if you really want to nail a precise arc. Any 2 points and any stick angle will give you a circular arc.

This seems a lot more complex than it really is. I can make a long compass with a couple of sticks, a couple of nails and a drop of superglue in about 10 minutes.

[Chris Padilla]

Paul,

I sent you a PM (private message) regarding this.

[jerry cousins]

this may a bit simplistic but - mark the ends of the diameter - usually with a couple of brads - determine the rise of the arc and the center point - then put a spring pole up against the brads -push to the desired height at the center and scribe. the pole is merely just a thin piece of "springy" wood.
jerry

[Chip Lindley]

Hi Paul. You could draw out a full size template on a sheet of something to use as a pattern; cardboard, hardboard, plywood, etc. The radius would be 12'-8". You would need a board a bit longer than that, anchored at the pivot point, to draw the arc with a pen or pencil in a hole at the exact radius. That is a BIG, awkward way to draw a full-size arch template.

Or, you can draw the arc to scale on grid paper. The height of the arc from it's chord can be plotted every 3 to 6 inches from the center to the ends. The different height marks are joined to form the arched line.

Or, do it quick and dirty! Use a flexible strip of wood flexed to the bow-shape of the arc, on a sheet of template material, held in place with small brads. Anchor the flex strip at the centerline of the arc at it's maximum height. Adjust, and tack in place with the brads until the arc is symetrical on each side. Sometimes a variation from a perfect radius is more pleasing. This way you can eyeball it to your liking.

[Tom Esh]

I suspect what you're after is an elliptical section, which looks a lot more pleasing than a true circular section / arc and is much more common in furniture. These work pretty well:
http://www.leevalley.com/us/wood/page.aspx?p=44631&cat=1,42936,50298&ap=2

You can also make one easily. I made a 50" one from a strip of aluminum and garden twine. I originally tried ripping the bow from stuff in the scrap pile, but nothing I had would bend into a symetrical curve.

[Bob Wingard]

Here's a site that lets you plug in your variables, and it calculates the unknown.

http://www.delorie.com/wood/chord-radius.html

It sounds like you already have your numbers, and are seeking a method. Here's what I've done in the past. I made a huge trammel arm out of two pieces of lumber, and a door hinge on one end .. a router baseplate thingy on the other. Clamp or screw the hinge (with the pin oriented in the vertical) to a column, wall, anything sturdy .. stretch out the trammel pieces till you get the correct length .. orient the stock however you can to make the cut (this part can be tricky .. double sided tape is your friend) .. make the cut using shallow passes with a router. I've used this many times, but never anything quite as big a radius as you're contemplating, but I'm sure with a little adaptation, it will work for you.

[Darnell Hagen]

http://www.leevalley.com/us/wood/page.aspx?p=44631&cat=1,42936,50298&ap=2

If that's too short, a long thin strip of straight grain hardwood and a string will work.

EDIT- Oops, Tom got there first.

[Jamie Buxton]

Using two brads at the ends and a springy piece of wood gets you a nice curve. However, it is not a section from a circle. It is more like a hyperbola. That is, there is more bending happening at the middle of the curve than at the ends.