MO, I still haven't had time to study your drawing; try to get back later. What's the width of the timbers?
Laying out and calculating points on ellipses isn't difficult, it's mostly Euclidean geometry and the Pythagorean Theorem.
Geometry: Ellipse Layout (aka "String Method") Geometry: Finding the Slope at any Point on Ellipse Formula for Slope at any Point on an Ellipse