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Draw an Ellipse

Suppose we want to make a platter that’s oval (elliptical) instead of round.  Obviously some carving will be involved in addition to what turning we may do, and we’ll need to draw the oval outline on the blank to guide us during the carving phase. This brings up the problem of drawing an ellipse, or at least an oval that is accurate enough to guide the carving.  

The method of drawing an ellipse using a string whose ends are attached to two nails is well known.  The pencil is moved all the way around the figure while always keeping the string tight.  

The nails are driven at the foci (plural of focus) of the ellipse, which  are located on the long axis at equal distances from the center.  The farther apart the foci are, relative to the length of the string, the more eccentric the ellipse will be.  

This provides an easy way to draw an ellipse, but to draw one of a predetermined, specified size is a bit more involved.  The question is where to drive the nails and how long to make the string.

Construct an ellipse of a definite size.

The first step is to mark the ends of the long axis (points A and A’).  Draw a line between the marks, and find the midpoint (C) of this line.  This will be the center of the ellipse.

Next, draw a line perpendicular to the long axis at the center of the ellipse.  On this line, mark points B and B’ at equal distances from the center to locate the ends of the short axis.    

Now use a large compass (or its equivalent) and set the distance between the points equal to one-half the long axis of the ellipse.  That is, set the compass to the distance between A and C or C and A’.  

Set the pivot of the compass at either end of the short axis, at point B or B’.  Swing the compass to make marks on the long axis, one on each side of the center.  These marks are the locations of the foci and are where the nails should be driven to hold the string.



How long should the string be?  Answer: the same length as the long axis of the ellipse.  However, a method is given in suggestion 4 below for setting the length that does not involve any measuring.  

Suggestions

1.  Small finishing nails work well.  Be sure to drive them in far enough so they don’t pull out when you put tension on the string.  (If you’re making a template, put a suitable backing board underneath the template material to help hold the nails.)

2.  Choose a string that is fairly small in diameter but strong.  Hopefully, the string will not tend to stretch when you put it under tension.  Be sure CA glue will stick to the string.

3.  Make a loop at one end of the string.  Place the loop over the nail at F’.  

4.  Drive a third (temporary) nail at one end of the short axis, B’.  Run the string from where it is looped over the nail at F’, around the temporary nail, and then to the nail at the other foci, F.  Wrap the string twice around the nail at F, then bring it back and twist it around the section running from B’ to F.  Pull it reasonably tight, then apply a drop of thin CA to the twist. (Don’t apply CA to the string near the nail.) Once the CA sets up, the string is ready to use.

5.  Remove the temporary nail at B’.  You are now ready to draw the ellipse.

6.  The accuracy of this method depends to some extent on the diameter of the pencil or pen used to draw the ellipse.  A Pilot Precise V5 Rolling Ball pen is ideal if the surface you’re marking is smooth enough to take the ink.  Or, make a small notch near the point of a pencil for the string to run in.  

7.  An obvious alternative to constructing the ellipse directly on the workpiece is to construct the ellipse on a piece of cardboard and then use this as a template to draw the ellipse on the workpiece.  An added benefit is that you may use the template to mark more than one piece.