Catenary Bowls?

[Russell Neyman]

I'm writing anther article about creating pleasing bowl shapes and this month I'm exploring the Catenary Effect. Basically, that shape follows the physics of a hanging chain. I'd like to add a collection of finished pieces that employed the principle. Anyone have examples I can publish in my newsletter, THE TURNIP?

[Kevin Jenness]

Not directly connected to woodturning but you could reference Antoni Gaudi, who used catenary models for some of his architectural work. https://mathstat.slu.edu/escher/index.php/The_Geometry_of_Antoni_Gaudi

[Richard Coers]

I'm writing anther article about creating pleasing bowl shapes and this month I'm exploring the Catenary Effect. Basically, that shape follows the physics of a hanging chain. I'd like to add a collection of finished pieces that employed the principle. Anyone have examples I can publish in my newsletter, THE TURNIP?
There are physics in a hanging chain? I thought it was gravity. How much do you pay for contributions?

[Jim Morgan]

The St. Louis Gateway Arch is a well-known example of the catenary shape.

517986

[Neil Strong]

.
I have what I think are some examples, but it's a fine distinction between some true parabolic and some catenary curves...



517990


And, of course, the catenary comes in many variations, depending on the suspension length (sag) and distance between suspension points.



517991

Also, the piece has to be photographed square to its side (something I rarely do), for the true curve to be seen. Anyway, here are a few that I think are close to catenary. In some cases you have to mentally complete the curve into the foot...



517992

517993


And with others you have mentally separate the curve at the bottom of the piece at which point it transitions into the upper part of the piece...



517994

517995

[Neil Strong]

.




And with others you have mentally separate the curve at the bottom of the piece at which point it transitions into the upper part of the piece...






I do have a few pieces where I've made an abrupt change from the catenary shape in the bottom of the piece into a closing form on the top of the piece, in which case the bottom catenary is more obvious...


517996

517997

517998



The flutes on many makes of bowl gouges are now described as parabolic, some of them erroneously so where they have a distinct V flute profile with straight sides. But, of those that are more genuinely described as parabolic, there are some that could be more accurately described as catenary. However, it is hard enough getting only those BGs with true parabolic flute profiles to be called that without adding another flute descriptor into the terminology we use to describe flute profiles.

For those with a geometry bent, the following is a link that explains how a catenary would have almost the the same curve as a parabola (given the same span and sag) if the catenary was formed by a cable/chain carrying no weight other than itself.

https://en.wikipedia.org/wiki/File:Comparison_catenary_parabola.svg

[Russell Neyman]

How much do you pay for contributions?

Sorry, I publish and distribute THE TURNIP for free and, therefore, have no budget to pay contributors. I'd be happy to consider your article, though. By the way, if anyone wants to receive my electronic newsletter, drop me a note with your email.

[Walter Mooney]

Russell, these are clearly not bowls, but, nonetheless, I think they fall into the catenary curve category. All are two pieces. The bulb portion has been hollowed, and the thread portion is ‘spiral’ carved (for lack of a better description). All are ~ 2-1/2” long.

[Don Stephan]

Just what is the process to turn a catenary curve on the outside of a bowl - constantly removing the blank to check against a hanging chain?

Make a negative cardboard pattern from a hanging chain and then shape the bowl exterior to match?

The concept of catenary curves is cool, but I don't see how practically to shape a bowl exterior as a catenary curve.

[Russell Neyman]

Just what is the process to turn a catenary curve on the outside of a bowl - constantly removing the blank to check against a hanging chain? Make a negative cardboard pattern from a hanging chain and then shape the bowl exterior to match?

Yes, you could make a cardboard pattern, but there's an easier way. Take a square blank and hang a chain from the two top corners, allowing it to droop to the base of the blank.
518220

Trace the pattern, either with a pencil or (per the example) spray with some paint. Mark a section at the bottom for a tenon. Repeat this process on a second side.
518222

Cut along the Catenary curve with a bandsaw. (For whatever reason, the site here has turned a couple of my image 90 degrees.)
518223

Reposition the cutoffs from the first side with tape, flip the blank on its side, and cut the second profile.
518224

This will give you a rough shape that looks like this. It can be mounted between centers, as shown, or on a faceplate.
518225

Now you can cut away the excess until all the facets are removed. You will end up with a shape that looks like this, perfectly following the Catenary Curve concept.
518228

This works for any size blank. If the piece of wood is shorter, just place the chains wider and have less droop. Kinda fun. I'll post photos of the finished piece both here and in my newsletter later.

Postscript: The difference between this and an actual parabola is that with the latter, you'd need a cardboard template. This method is a breeze.

[Russell Neyman]

Here's the finished bowl.
518289 518290 518291

I've made an unusual choice here-- The bowl and base have been left detached to underscore the "hanging chain" effect. There's a tiny brass pin in the base that matches a hole in the bowl for stability. The bowl is big leaf maple and the base is purpleheart.

[Neil Strong]

Postscript: The difference between this and an actual parabola is that with the latter, you'd need a cardboard template. This method is a breeze.

Russell

For those who haven't yet internalised these shapes your method gives them an excellent start with making some visually satisfying pieces.

Thanks for sharing.

PS - these shapes without feet also look great when held or suspended in minimal frames.

[Russell Neyman]

Here's another following the catenary principle. Again, I've left the bowl disconnected from the foot to underscore the hanging chain shape. These have been surprisingly popular and one sold before I could photograph it. Lignum Vitae, unfinished (polished wood only).

519060 519061 519062

The next one I do will be short and wide.

[Bill Dufour]

Take a metal tub and fill it with epoxy(maybe it was plaster of paris) slowly spin it until it almost reaches the edge. leave it spinning until it hardens. The resulting shape is a parabola more than good enough to focus at the quantam photon level.
Bill D