How to Lay Out an Elliptical Arch

Measure from the top of the board down 24 inches and draw a straight line across the board. This is your y-axis.

Turn the board sideways and measure from the top down 20 inches. Draw a line at 20 inches across the board. This line crosses the y-axis and is called the x-axis.

Locate the center where the two lines cross. Measure 8 inches from the cross on each of the four lines, which is the two sides of each axis. Place a mark 8 inches from the axis

Mark your trammel at zero, 11-1/2 and 21 inches. Pivot from zero and 11-1/2. Drill a hole at the 21-inch mark large enough to insert a pencil into it.

Place the trammel over your first 8-inch mark on the y-axis. Insert your pencil into the 21-inch hole and swing the trammel, drawing a half circle. Repeat this action on the other side of the y-axis. Position the trammel so you are drawing the half circle on the opposite side of the cross in the center of the board. For instance, when you have zero over the south y-axis, you will draw a half circle from the 21-inch hole on the north side of the y-axis. See the illustration in the References section for an example.

On the x-axis, place the 11-1/2-inch mark on the trammel over the 8-inch mark on the x-axis. Insert your pencil into the 21-inch hole on the trammel; swing your trammel to draw a half circle on the opposite side of the axis. Repeat this on the other side of the x-axis.

Cut along the ellipse pattern. You can see a modified oval shape on your MDF drawing. Cut along the curves you drew, but do not cut into the other curves. For instance, cut the half circle at the top, but when it is met by the half circle on the right and left, follow those curves.

Cut along the x-axis, the widest line in the oval, for the bottom of the elliptical arch. You can cut two arches out of this one piece of MDF if you cut carefully along the lines. This arch will fill a 3-foot doorway space.