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A circle is easily drawn with an ordinary compass, but there is no compass yet invented for drawing an ellipse. There are ellipsograph instruments used by draftsmen and engineers, but these are too expensive to recommend for carpet layers and estimators. A simple but accurate method, employing only string, tacks, and tape measure is as follows:

You first have to know the lengths of the major and minor axes before you can draw any ellipse. Assume these are 12 ft and 8 ft respectively, as in Fig. 4.14. Draw to scale a line AB equal to the 12 ft axis; bisect this line and erect line CD perpendicular to AB at the midpoint. (Use a carpenter's square to obtain a right angle above and below AB at the midpoint O.) Draw OC and OD each equal to 4 ft.

Fig. 4.14. Drawing a true ellipse with string and pencil.

With a line equal in length to OA, describe arcs from point C inter- setting AB at X and Y respectively. These are the two centers or foci of the ellipse. To draw the curve itself, place a tack at X and Y, and also one at C. Tie the end of a no elastic cord or string to the tack at X, pull it taut around the tack at C, and fasten the other end to the tack at Y. Now pull out the tack at C and replace it with a pencil or a piece of chalk. Keeping a steady tension on the string, move the pencil or chalk as far as possible in one direction, then on the other side of the long diameter, and so around the entire elliptical path, giving a mathematically true ellipse. This is to be distinguished from the so-called "oval" of a racetrack or football field, as shown in Fig. 4.15, which is actually a rectangle with a semicircle at either end.

Here the measurements are simply those of an ordinary rectangle and a circle, whose diameter is equal to the short side of the rectangle. The center of each semicircle is established in the same manner as for the center of the circle in Fig. 4-10; these centers in turn establish the length of lines AD and BC, with lines AB and DC equal, of course, to twice the radius of the respective circles.

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Sometimes when you are taking measurements you don't quite know what carpet is going to be used, or there is the possibility that the customer may have had or will have a change of mind.