Looking for crochet pattern

I could only find two Cheryl and they are both freebies. See if either is of use to you.

The first one doesn't seem to be very large but you could possible adapt it:

second one seems more likely from your description of what you want.http://www.lionbrand.com/patterns/chs-dayToNightPoncho.htmlBernadette

Fake it. :)

You're an engineer, so you understand the concept of the circumference of a circle doubling at predictable intervals.

I knitted a circular bed cape (please don't ask me to find that pattern for you). Start with a foundation row long enough to go comfortably around the neck, and every so often, do a massive increase row (calculate this from the mathematical formula referenced above). When it reaches the maximum circumference you want at the hemline, stop increasing. (Or, if you're crazier than I am, go ahead and make a perfect circle with a 20-yard-long hemline. See if I care.)

Then just work upward from the neck to create your hood. Probably the easiest way would be to just work a rectangle and seam the top together.