Elliptical Shapes Using Simple Geometry – video

In our soon-to-be-mailed August issue, furniture maker Freddy Roman discusses the use of elliptical shapes. Freddy uses them frequently in the Federal-style furniture he makes. In the article, he shows three easy ways to generate the shapes using simple geometry. Not only do these techniques allow you draw the shapes, but they can be applied in the shop to actually cut the shapes. How? Once you know how to find the radius points, you can use a trammel beam with a cutter for handwork or swing a router attached to a circle cutting jig.

Describing the layout steps makes the process seem far more difficult than it actually is. In the video I lay out a false ellipse using the most complicated of the three methods (it’s also the most versatile) and describe how it’s done in about three minutes. Check it out.

– Steve Shanesy

If you liked this, you may also be interested in the “Drafting & Design for Woodworkers Collection,” which includes a hardcover book and two CDs.

17 thoughts on “Elliptical Shapes Using Simple Geometry – video

  1. McDara

    Steve,
    It has been more years than I would like to admit that I have done the exersize you have shown (7th grade drafting class, I’m now 60). Just for my morbid sense of curiosity I duplicated your instructions using a CAD program. Then I used the Ellipse function to draw over the “false ellipse” in a different color. The difference is increadably minor.
    If you draw a line from the center of your right or left arc at a 45 degree angle crossing the false ellipse and an actual ellipse you will see about 1/16″ departure at the 45 degree line.
    Yes I know I am a geek.

    1. larrydwilliams

      You will find that as the difference between minor and major axis becomes larger, so does the variation between an oval (what is being produces here) and a true ellipse. Most of the time, the oval generation is good enough for woodworking. However, if I am doing something like a Stickley style bracket, I prefer to use a hyperbolic curve generation so that the curve radius constantly changes.

      1. Steve ShanesySteve Shanesy Post author

        Hi, Larry,

        Yes, there seem to be limitations of the false ellipse with regard to the ratio of major to minor axis. While elongated shapes or fatter elliptical shapes may be useful for some applications, I’ve found the sweet spot for pleasing false ellipse shapes has the length of the minor axis somewhere between 55% and 75% of the major axis.

        Steve

  2. keithm

    Yes, technically not an ellipse (the set of all points the sum of whose distance from two points (the foci) is equal) [cf. circle, the set of all points whose distance from a single point (center) is equal (the radius)]

    x^2/a + y^2/b = c (an ellipse)

    x^2 + y^2 = r (a circle)

    What Steve has constructed is often called a draftsman’s oval and is really close, but not exact, to an ellipse. A good article on this (see the diagrams) at http://en.wikipedia.org/wiki/Oval

    But I really love compass and straightedge constructions. Many of which quit being used after my grandfather’s generation.

    Are my two math degrees showing?

    1. Steve ShanesySteve Shanesy Post author

      Hey, Keith, now you are making me feel old!:). When I was went to night trade school for cabinetmaking, we learned how to do this geometric work for false ellipse, gothic headers, French headers and more. When I went to work for a custom furniture company in Los Angeles, we used the false ellipse geometry to make some remarkable conference tables, some being up to 40 feet long.
      Thanks for your comment, and yes, your math degrees are showing. Heck, one of the main reasons I elected journalism as a major was there was no math requirement.
      Steve

  3. Gary Laroff

    Steve, the geometric figure you were making is not an ellipse, but an oval. If you are not sure of the difference, please ask George Walker, who can describe, better than I, that an ellipse cannot be described at any of its points by circles. A true ellipse is a much finer and esthetically pleasing shape. There is an adjustable and quick device that you can make with a single stick, two nails and a pencil that will enable you to make ellipses.
    Regards,
    Gary Laroff

    1. hutchjo

      Let’s give Steve a break. He clearly states that what he’s generating is a “false ellipse.”
      Something that I find interesting is the superellipse. It falls somewhere between a rectangle and an ellipse and is touted as the most democratic shape for a table. There’s endless information regarding this shape on the Internet.
      Given Steve’s dexterity with wire rod legs and pencil edges, as demonstrated in his Tornado Table, I’m sure he could knock out a killer superellipse table. It might even be an answer to his recent dining table dilema.

      1. Steve ShanesySteve Shanesy Post author

        Hutchjo,
        Hmmmm, superellipse. Maybe that is a good idea for a tabletop shape. Gonna give that one some more thought. It’s certainly more interesting than a race track oval. Thanks.
        Steve

        1. hutchjo

          Steve,
          Fritz Hansen, a furniture manufacturer in Denmark, is still making the Superellipse Table in various configurations. Unfortunately, they only seem to be offering them with a white laminate top. We had two in our conference rooms in Columbus with teak tops and pencil edges. They do give you the feeling that there is no “head of the table.”
          If you’d like to pursue the notion of a superellipse table any time in the future, I’d be more than happy to be your go-to guy for some full-scale drawings. I thing we made a good team on the Tornado Table and I’m aure we could do it again. Think of the great sidebars!
          John Hutchinson

            1. hutchjo

              Steve,
              I don’t want to turn this into a superellipse promotion but I was thinking about building one a few years ago. The only thing (only thing?) that stopped me wewe the wire-rod legs. When I looked for a sourced leg, I hit the wall until I saw the Egypoid Leg on the Doug Mockett website. It’s not wire but rather “intersecting planes of inverted triangles.”

          1. Steve ShanesySteve Shanesy Post author

            I thought that was probably you, John. Hello! Long time, etc. Yes we made a very good team on the Tornado Table project. It was truly a collaborative effort that produced excellent results. I still have (and cherish) the two I built.
            I’m still uncertain where I’m heading for the dining room (space) table, but the superellipse is very interesting and something I want to look into more. Thanks for introducing the idea. Perhaps another collaboration is in the cards.
            Steve

            1. hutchjo

              Rats. Busted. The first thing I was going to do after my last reply was throw out my laptop. “IT” decides when to send things before I get a chance to proof-read or finish what I was starting to say. “IT” decided that “wewe” was funny when I was trying to say “were.” Reading it once again, however, makes me wonder if “IT” was right. The thought of making wire legs DID make me want to wewe (or weewee or whatever).
              Lastly, before “IT” deciced to send, I wanted to say that the Egypoid legs seem to capture the basic look and proportions of the original Superellipse Table legs without getting into the realm of bent wire. Mockett uses metal plate but I’m wondering if they could be fabricated from Baltic Birch plywood?
              And that’s all I have to say about that.
              Nice chatting with you again, Steve. I miss it.
              John
              Disclaimer: I swear that any mistakes in the above text will remain uncorrected.

    2. Steve ShanesySteve Shanesy Post author

      Gary,
      Just a couple points. I’ve found very little actual difference between the shapes of a true ellipse and a false one. Generating a false ellipse using the compass points easily translates to the ability to generate those same curves to actually cut the shape. I’ve seen this done first hand many times (usually to make a template) that can then be used machine parts with great accuracy. Can’t do that with a string and pencil; great for drawing, of no use in making parts.
      Steve

    1. gumpbelly

      You are correct, people have been using 2 nails, a string, and something to mark with (pencil) for as long as mankind has been making ovals. The problem associated is trying to figure out the distance of the nails apart, and the length of the string to make your ellipse/oval the size you want. The following link may help you figure that out. Don`t just look at the math. scroll down to the calculator :-)

      http://www.anvilfire.com/21centbs/math/ovals.htm

      I can`t view the video, so I`m limping here, but the jig Marc Adams showed at WIA 2 years back for a router ellipse/oval class was a life changer for me. Possibly PWW has video in their library, or you can get the info from Marc via a DVD, down the list a ways under “routing”

      http://marcadams.com/videos

      While not being the same jig, this jig shares many attributes, and all I can say is, if in your life you plan to make 3 to 5 items with an ellipse/oval shape it`s worth it to make a jig like this. The jig is pretty easy to make, and it is definitely worth having. Hopefully this isn`t what the vid is showing.

      http://www.popularwoodworking.com/projects/oval_layout_jig

      Tips of the day:

      An ellipse always has two axes of reflection; an oval has one or more.

      Drink more fluids in the HOT weather, Beer is a good fluid, but a poor hot weather choice, chug Margaritas, when you fall down it hurts less :-)

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