Sometimes with woodworking, what seems crazy one day can be quite sensible the next.

I distinctly remember reading in the late 1990s a manuscript from an author who was building some Morris chairs. He used an 8′-long beam compass to lay out the shallow curves on the chairs’ stretchers and had to enlist his sons to help him strike the arc.

Fellow editor David Thiel and I chuckled about that detail when we read it. It seemed like a lot of trouble for a shallow curve that we would strike using a flexible piece of thin hardwood and a couple nails.

But this week I’m not laughing anymore.

This week I’m building a Stickley sideboard for the next issue of *Woodworking Magazine*, and one of the prominent features of the piece is a shallow curve on the front rail. When I built the prototype of the project I used the flexible-stick-and-nails approach to lay out the curve.

After staring at that curve for many months on the prototype, it bugs me. It’s not a perfect arc. It’s a subtle thing, but I think the arc is a little flat.

So yesterday I built a monster beam compass that was more than 4′ long. The beam itself is 1/2″ x 1″. At one end I drove a #8 x 2″ screw through the beam. At the other end I drilled a 1/4″-diameter hole. Then I whittled a pencil to fit snugly in that hole. (Good luck trying to find the right drill bit to fit a standard pencil. Are pencils metric?)

I drove the screw into my benchtop just a tad then secured my sideboard’s stretcher to the bench with a holdfast. I struck the arc then cut it out. It’s perfect.

What’s next? Am I doomed to build a jig that holds too-thick biscuits so I can sand them to perfect thickness? Am I going to build a router table with a micrometer built into the fence?

Shoot me if I do.

*– Christopher Schwarz*

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To Quote Chevy Chase playing Pres. Ford on SNL

"It was my understanding , there would be no math."

I made a really long, low bookcase and needed a very large radius curve for the front. I wound up doing what Bob Lang described: made a huge (14′) beam compass with my router attached to the end of it. I used that to create templates and then pattern routed the actual pieces after cutting off the bulk of the waste. My rig was huge! I made a plywood base and stabilized it with my toolbox, a 5 gallon paint can and other heavy things. My neighbors must’ve thought I was crazy. The arcs are PERFECT though. Tried the hardwood bow too, but the curve wasn’t consistent as others mentioned.

You’re in good company Chris!

Of course its not a perfect arc. If it was, model railroaders wouldn’t have been using the stick method for decades to draw easements. An easement "eases" into a curve, something that prototype railroads usually do, and something that those Lionel trains NEVER did. Remember how they would "slam" into the curve?

Cosmo,

I’ve done this. It works. You have to have good hand skills to keep the pencil at exactly 90°. Any deviation and your arc is off. Sometimes this doesn’t matter. Sometimes it does.

Chris

Didn’t I see a technique somwhere that uses a string to create an arc? Put two nails at either end of your arc. Tie a string to both nails so that the slack, when pulled taught, will create a third point at the exact apex of the arc you want to draw. Then mark your line with a pencil, pushed through a router collar,or sewing machin bobbin, by riding along the string from nail-end to nail-end. The result should create a perfect arc. No?

Dale,

I don’t have a plotter, so large curves require several sheets tiled and taped. The trammel was faster I think.

For small curves, I definitely make paper templates. Thanks for mentioning that.

Chris

How about going to the handy-dandy CAD drafting program (Sketchup), drawing an arc of the desired radius, printing it off on a piece of paper and tracing it on your project?

Chris, Chris, Chris.

It is dead easy to make an arc with two sticks and a couple of nails. No need for extra long trammels nor square roots. I’ll send you an article I wrote.

(I tried to post this earlier this morning but obviously did it wrong. Apologies if this shows up twice)

There is nothing wrong with using a (long) compass arm when drawing an arc. Even ARChimedes would have done so even if he didn’t have easy access to #8 screws. There are other applications than Stickley sideboards that require accurate arcs. Rocking horse rockers are the perfect example. When mass cutting a set of rockers from a long 4′ wide slab of laminated oak, I use a 5′ long oak 1" x 1" as the compass arm, a #6 screw at one end and a pencil in a 1/4" hole at the other. A kerf at the pencil end expands the wood enough to accommodate the first pencil I find. A similar length of 6" wide 1/4" plywood with the pencil replaced by a plunge router serves to cut the rocker ends smoothly in a perfect arc. (photos available in Chris cares)

Gary Laroff

Or you could tie a string the length of your radius to a nail, and to a pencil. Strike your arc while holding the pencil perpendicular to the board. Am I the first one to realize this technique? It is now hereby copyrighted and I’ll expect the royalty checks to start flowing in.

Hi, I’m Bruce and I’m a nutjob. Here’s my take:

Richinsd above has almost exactly my approach to this long radius problem, although I confess I like the bending stick approach, too. So, here I am, trying to figure out how to fair a leg with an arc only a half-inch high by some 29 inches long. How long a trammel will I need?

Whip out trusty 39-button calculator. Get envelope to draw picture. Set up formula from picture using Pythagorean theorem:

(r – 1/2)^2 + (29 / 2)^2 = r^2

r^2 – r + 1/4 + 210 1/4 = r^2

r = 210 1/2 or 17 ft 6 1/2 in

I don’t think I have a long enough anything in my shop to make this trammel, unless I figure a ball of string, which is what was used long ago, in days bygone when no tools had tails, except for this level imported from Egypt. For this shallow an arc, seems to me that the bending stick will work just fine (I hope).

As for filing down biscuits, isn’t that like shaving tenons with a shoulder plane?

And for router table fences with built-in micrometers, well, it might keep you from having undesireable fillets.

In short, as an old colleague from a completely life (in hospital finance – please, let’s not go there) once said, you can rationalize any insanity.

For what it’s worth, I have had marvelous results drawing long radius curves using a steel locking tape measure with the end stop removed. I drill a 1/8 hole near the end of the tape for the pencil lead to fit through and fasten the body of the tape to a small nail using a loop of string through the tape measure back. It’s rediculously simple, fully adjustable. Just feed out the length you need to get the curve you’re looking for and lock it in place. Since the tape is resting on the work piece and is only holdng the point of the lead, the angle of the pencil poses no significant issue.

I’ve done both, although my preference is accuracy and therefore a trammel bar and pencil/router. The longest trammel I’ve ever made measured in at 10 feet long with a router stuck at the other end. Interesting and challenging task indeed.

The other method I also use to ensure symmetry is using a flexible stick to mark out half an arch and then cut it to shape. Repeat the process for the other half. I’ve used this where a true semi circle is not needed and that a balances elliptical curve is just fine.

I much prefer a radius to a bent-stick arc. It just looks better.

There is another way to achieve a large radius that hasn’t been mentioned, the stick method. Jim Tolpin describes it in his book, Measure Twice, Cut Once.

http://books.google.com/books?id=V8L8y1J8YcgC&pg=PA76&lpg=PA76&dq=radius+draw+two+sticks&source=bl&ots=qHH8CmlMcs&sig=dh8qYhXUG-g-tq5Ly_WH1akvh4s&hl=en&ei=5ma5SdmqIIHwsAOxksE5&sa=X&oi=book_result&resnum=2&ct=result

Combining this method with Stephen Wilson’s formula (previous comment), and you can draw any radius you want if your sticks are long enough. I’ve posted a couple of photos of my jig on my blog.

http://stammerjohn.com/2009/03/12/drawing-arcs

1 Don’t build a boat – you would not be able to loft or make fair.

2 Do look at Ellsworth Kelly’s abstract canvases, made with compasses up to 100 feet long (out of the studio and across the yard).

Chris,

I’m just guessing, but were you looking for a height of your arc at around 2 1/4 in. given that the length is, I believe, 30 in.? Your radius should be 51 1/8 in. Did I come close?

"What’s next? Am I doomed to build a jig that holds too-thick biscuits so I can sand them to perfect thickness? …"

No need to — If the biscuits are too thick (I suppose from the absorption of moisture), just place them on a steel surface and give them a few whacks with a hammer. They’ll then slide easily into the slots.

Before I started doing this, I was throwing away lots of swollen biscuits.

The curve you get from bending wood is not the circular arc obtained with a trammel or compass. The shape from bending a flexible stick is a catenary(roughly) a parabola, and thus will always look slightly flat or slightly sharp. Looking at it mathematically trammels cut an arc of

y = sqrt(r^2 – x^2)

where r is the length between the trammel points. In contrast, the shape described using the bent stick method is

y = a*(e^(x/a)+ e^(-x/a))/2

Just to push the nuttiness to its limits, not just any stick will do. Consistent, tight and straight grain yield a better curve, and the thickness has to be just right to achieve what boat builders call a fair curve. I think the Lee Valley bow has an advantage, but I’d rather worry about the curve than spend the $26.50.

Bob Lang

There is a real geometric (mathematical) difference between curves produced by a batten and arcs. The first is known as a spline (b-spline, bezier curve, etc), and its shape can be manipulated to mimic other types of curves, but in the end, it’s still an approximation. Apparently, the difference is noticible.

The mathematical description of a spline is much more complicated than that of a circle, but in practice, it’s usually easier to layout a spline for large radius arcs.

Mr Schwarz,

Be afraid. Be very afraid. Bisquit jigs and fence micrometers are only the beginning. Dowel polishing and precision compass point sharpening wait just beyond the horizon.

Recognizing the problem is the first step to the cure.

Dan

When you bend a stick around nails, you are creating a "natural spline". A natural spline is tangent to the nails that it bends around. In between nails, the spline tries to relax so as to minimize the stresses inside the wood. It will do most of its curving near the nails and flatten out in between. You might say it speeds up as it goes around the nails and then slows down in between them. That gives you a flowing curve, but it’s definitely not a circle.

>(Good luck trying to find the right drill bit to fit a standard pencil. Are pencils metric?)

Pencils actually have a standard ("english") size – 1/4" across the flats. The Wikipedia has an article. In this case, a number "N" drill is the size you want (Dixon pencils). There is slop between pencil makers so the drill is not one size fits all.

Yeah, the bent wood curve can look a little strange because the radius is varying, but sometimes varying radii can look really nice when you start talking about bezier curves. The thinner the wood, the more it’ll bend along it’s length, giving less of that flat look. The bent stick almost appears to be more of a catenary instead of an arc (St. Louis arch is a catenary)

When the second sideboard is complete, I’ll post a comparison.

You can see the prototype’s arc here:

https://www.popularwoodworking.com/techniques/joinery/festool-domino-the-six-month-report

FYI I’m not using the Domino for the new one. It’s all traditional joinery.

Chris

The shape of the bent-stick curve will depend on many factors, including the precise "springiness" of the stick being used.

It’s essentially a case of beam deflection, but the normal beam formulas assume small deflections so they aren’t actually valid.

In general however I would expect the bent-stick curve to be of varying radius, which could cause subliminal dissatisfaction in a viewer expecting a circular arc.

Bob,

Your malaise over the stick drawn curve is caused by both reasons cited. You should feel a little guilty for taking the shortcut and the curve is at least a little bit bad.

In fact, you will notice the effects of the beam strength of the stick causing greater flattening of the ends of the arc as your radius gets tighter. One way to counteract the effect is to effectively load the beam at more points by driving more nails to smooth the curve.

But then the effort of calculating, laying out the locations of and driving those nails would probably be greater than the effort to construct a simple beam compass like the one Chris made.

I hear there will be a Nutjobs anonymous meeting in the hotel bar at the NWA Showcase on Saturday night 3/28. Maybe I will see you there.

Chris,

Your last comment surprises me, you always seemed a practical person, proud of having a "blended" shop where the tool used was the one most appropriate for the job.

In this case, the trammel was the tool, or properly the jig, for the job.

I find it inspiring that you would let the project percolate until the least satisfactory bits came to light, then found the way to right them.

Learning how to do it right is what I expect from you, not a specific "path of spriritual enlightenment" (grin)

Mike

I see you have out the files which orf course work well, but I was recently given a 113 as a gift, and found it to be a revelation when I was smoothing a very similar piece recently. I highly recommend them:

http://www.flickr.com/photos/chevy_chase_hughtos/2826283523/sizes/m/in/set-72157607001006126/

By the way, I used a stick. I’d been satisfied, but I think next time, I’ll follow your lead with the beam compass. Nice arc. Amazing how those subtle things make a difference.

I agree – but you’ve got to know how to get the radius in the first place. For the benefit of readers who do not know the formula:

radius = H/2 + (WxW)/8H

Where:

W is the length of the base line of the arc.

H is is the height of the arc measured at the midpoint of the base line

I have had good results with the "Symmetric Drawing Bow"

#05N55.01 from Lee Valley tools, when I built a Stickley Cabinet with a Harvey Ellis type design on the bottom stretcher.

Back when I did architectural work, we would get jobs at times that called for arcs with ridiculously long radii. I have successfully talked co-workers and employers out of cobbling together 20-foot long trammel jigs and swinging a 3hp router on the end of a 50+ foot rope. I’m a fan of the bendy stick for making arcs.

But I always wonder, and I confess that my stick drawn arcs almost always bother me. I can’t be sure if I’m really seeing a bad arc, or if it’s just guilt for faking it.

Bob Lang

I totally agree with your "eye." Those flexed stick arcs are not true and have never looked right to me either.

So can we see the two arcs together? How different where they?