# The Elusive Ellipse

Plot an ellipse using simple geometry in 4 minutes or less – really!

By Freddy Roman
Pages 54-57

As a furniture maker with a fondness for the Federal period, I’m interested in the ellipse-shaped decorative details that regularly appear in furniture from the era. When I study these details, I think of master craftsmen of the day and wonder how they drew and cut elliptical shapes.

So I turned to one of today’s masters, Will Neptune, to learn more about drawing and cutting this intriguing shape. Here, I’ll share with you several of the tricks and techniques he taught me.

Like the old masters, you need to have a basic working knowledge of geometry that can be used to lay out the cavities for ellipse-shaped inlays and stringing, and to generate pleasing elliptical shapes for tabletops, door panels and more.

Ellipse – True or False?
When working with ellipses, the first thing to understand is the difference between a true ellipse and a false ellipse. A false ellipse is two different-sized radii blending together at four intervals around an oval shape. A true ellipse, on the other hand, is an ever-changing series of radii. But if you lay out a false ellipse on top of a true ellipse, you’ll see they are very close to being exactly alike.

Why is this important to furniture craftsmen? The difference comes when laying out an ellipse. If you first lay out the false ellipse on paper, you know the four key center or swing points. Knowing these locations, you can connect a hand tool to a trammel-beam or a router to a circle-cutting jig and swing the arcs of the ellipse. Using the false ellipse provides accuracy and repeatability, and it saves time. In many cases, using a false ellipse is the smarter choice.

While it is easy to draw a true ellipse using the old “string and nail” method, it isn’t always easy to apply that method to a tool in the shop. But it helps to understand the true ellipse and how it’s drawn. Nails are driven into two points known as the foci (the plural of “focus”). The size of an ellipse is determined by the total distance between these two points and the length of the string that moves around them. To set the string length, a third nail is placed on the minor axis at the widest point of the ellipse and the string is then tied as it loops around all three nails. The third nail is then removed.

Once the nails are set and the string is taut, you are ready to scribe an ellipse. When you draw it, notice that the length of the string on either side of the pencil tip changes as it moves along. This variance occurs throughout the scribing of the ellipse, but the total length to the foci is continuous at every point throughout the ellipse.

Endless arrays of ellipses are formed by the location of the foci. The farther away from one another the points are, the more squashed the ellipse. The closer together the points, the more the ellipse resembles a circle. In fact, if the foci are at the same point, it forms a circle.

Video: See an ellipse plotted in less than four minutes using “Method 1” as described in this article.
More video: See a true ellipse drawn using two sticks that slide in perpendicular grooves.
Web site: Visit Freddy Roman’s site to see his furniture, cabinetry and restoration work.

From the August 2012 issue #198