Understanding the Ellipse

Basically speaking any true ellipse can be laid out from two simpler shapes, the rectangle and circle. The term true implies that the ellipse follows the form {a² = c² - b²}.

Lets say you want to create an ellipse that is 100" long by 40" wide. You could first construct a rectangle with the measurements 100" by 40" it is colored orange in the drawing. Drawing two perpendicular lines from the centers of the long and short sides of the rectangle. This will give you the major and minor axis's of the ellipse, their in blue and black. Ellipses are laid out using their major and minor axis's. Actually, you only need know 1/2 of each value, these are known as the Semi Major and Minor Axises. In this case 1/2 the major axis(the semi major) will be 50" and 1/2 the minor axis (the semi minor) 20".

To construct this ellipse you will need to locate it's focus points, you can use the formula {a² = c² - b²} but, why bother, it's much simpler to use the radii of the circles that corresponds to this ellipse.There are two circles that will correspond to any regular ellipse. The two graphics at the right bear this out.

Since the diameter of one of these circles is equal to the length of the ellipses major axis (and the radius is equal to half that), all one needs to do is locate the center of this circle (point "A") at the top of the minor axis and scribe the circle. Where the arc of the circle intersects the major axis is the focus points, there will be two points F1 and F2.

Once you have located these points you can construct this ellipse by the String Method. Driving nails at each focus point and one at the top of the minor axis, you then stretch a string around all three nails, one other option would be to use picture hanging wire because it has less give then string, pull it as tight as you can and "tie" it together.

Now remove the nail at the top and place a marking device there and just begin to move it, it will follow a path that is defined by the string and trace out your ellipse. Now you have all you need to know on how to layout any regular ellipse, just plug-in you numbers to define yours.

A great book on this subject is by George Collings

Building Your own Ellipse Cutting Jig

The whole jig consists of Two pieces of 2" aluminum "C" channel. One 40" long. One 25" long. One piece of 3/4" plywood,3-1/4" x 40" to make the beam. Two small pieces of Oak to form the focal points, 4-3/8" x 1-7/16" x 1-1/16" with a 1/4" chamfer on two sides. Two 2" x 3/16" carriage bolts with some wing nuts and washers. An auxiliary plate for whatever router you might use.

Some other useful information on ellipses is how to figure the area and circumference.

The area K is equal to pi(ab) or K = pi(ab)

Where a and b are the semi-major and semi-minor axis respectively

The Circumference is C = pi(a+b)[1 + x²/4 + x4/64 + ...]

To as many terms as you like. Where x = (a-b)/(a+b).

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