Generating Large Ellipse for Woodworking.Overview of process

Below are pictures showing how to create a large ellipse (half of one but could also use to draw a full ellipse. I used this technique to make arc sections in a set of bookcases. No complicated jig to build; just a board, clamp and stick with slot for pencil and nail to set minor axis length. Some pictures of the setup, mathematics used and a simulation are included below.

Pictures illustating setup and drawing

The Mathematics

$x = \overline{E1 E3}*sin(\alpha)$ and $y = \overline{E2 E3}*cos(\beta)$ and from geometry $\alpha = \beta$

Using these as parametric equations and eliminate the angle $\alpha$ we get equation: