It has been quite a long time since I did any rotation of geometric shapes or mechanical drawing, and I need a refresher to jog my memory.
The goal is to make a template from construction paper which can be used as a guide when cutting sheet metal to make a pipe boot that sits over the ventilation pipe on the roof. The boot consists of a flat rectangular base (with a centered cutout for the pipe) and the cylinder that fits over the pipe. The two are soldered together.
For the sake of simplicity, assume the pipe on the roof has a 100mm O.D.
The roof pitch is 28 degrees.
The cutout hole for the pipe must be adjusted for that angle of rotation.
The flat sheet which gets formed into the cylinder must be curved on the bottom, so that it will have an oval-shaped base. Where to position the stationary leg of a drawing compass to form that oval curve?