Parametric Rocket Nozzle

This is an attempt at a parametric Convergent-Divergent Nozzle, also called a De Laval nozzle.

There are two types available: a simpler nozzle with a conic nozzle extension; and a more complex and efficient nozzle with a parabolic bell extension.

I modeled the conic first, and built upon that foundation to model the parabolic bell by using a bezier curve.

It is close, and is a very good approximation, but could use a bit of help from someone more mathematically inclined.
Please contribute at:
https://github.com/Buback/ParametricDeLavalModel

Updated 3/24/2014: added correct combustion chamber and throat supports. the supports should make the printed piece stronger, but the slicing is more complex and error prone.
updated again 3/25/2014: thanks to Bill Waters for help finding p1. Bell is now modeled correctly. I've also been messing around with an intake, and flipped the whole engine upside down for printing the combustion chamber. the intake will really only work with steam or pressurized gas, for playing with.
4/18/2014: the newest version doesn't have the intake, but the geometry of the bell is now based on the expansion ratio instead of hard dimensions. you enter in the throat radius and the expansion ratio(Exit area/throat area) and it will calculate the proper exit radius. there is still the variables there to enter in fixed radii, and there's an echo to tell you the expansion ratio if you need a certain exit radius.