I have been looking for instructions on drawing an oval using two points and a string. What is the rule of thumb to position the pivot nails to get the size oval you want?
(Architectural Woodworking Forum)
From contributor P:
There are formulas for drawing an ellipse. A little difficult to get it all straight in your mind. Maybe you really don't want to know what they are. But I do have a free spreadsheet to download at this website. You enter in the semi-major axis and semi-minor axis, and you will get the distance between the foci, and the length of the string needed, to draw the ellipse you are after. There are also some drawings to give you an idea of making a router jig, if you want to go that route.
Spreadsheet Calculation Program
I hope this answers your question. I would not use this method for actually making patterns, but only for quick and dirty drawings. Also use only very thin low stretch line like spider wire fishing line.
A P C P B
Steps to drawing an Oval
1. Get exact center of your desired oval and draw vertical and horizontal lines. Mark C.
2. Measure Width (AB) of desired oval size. Center this on your board.
3. Measure Height (DE) of desired oval size. Center height on board.
4. Calculate Ĺ of the distance from AB(=AC or BC). This will be the length of your hypotenuse (the diagonal line PE).
5. From point E with a ruler, find the spot on AB where PE intersects it with a length of AC.
6. Repeat for the other side, so you now have 2 point Pís along the horizontal axis AB.
7. Nail holes at P, E, and the other P.
8. Take non-stretchable string and connect it P E P, typing the string together for a triangle tightly.
9. Take a Pencil and pull out E nail hole. Replace the E hole with a pencil inside the string.
10. With the string as your guide, move around the oval. The max size of the string will create a smooth line as you finish drawing it out.
11. You will have to maneuver around the nails when you get to point A and B.
12. You now have a perfect oval, cut out along the newly drawn outside perimeter.
Comment from contributor B:
The large radius is the hypotenuse and the short radius is the adjacent side and the distance from the center point on the long diameter to the pin is the opposite side. To determine this, take the square root of the large radius squared minus the short radius squared. This is the distance from the center to the pin. The pins are equidistant from the center of the large radius. The string length is large radius times two plus the total pin distance. With the string around the two pins and a pencil stretching the string draw an oval of the size needed.