McImes, I went through the same process a few months ago getting my Ion set up properly for downwinds. There is a lot of info on the web but not specifically to paddling and downwind. Surfski.info had an article years ago worth a look -
here-
although I disagree with the author's conclusion that ellipticals are the most "efficient". Here's my take on the design parameters in question:
Sweep/rake: Less sweep (more vertical) rudders are more responsive and powerful, requiring smaller pedal input for effect. More sweep is more forgiving, so if you have a hull that is very easy to turn like the SF, you may find that really low angle of sweep is too reactive/twitchy and the boat whips around when you don't expect it. The lowest sweep I've seen on ski rudders is about 10-15% although some OC1 downwind rudders are almost vertical. You used the term "angle of attack" when describing this parameter, which may confuse people since AOA refers to the angle at which the chord line intercepts the medium. So for us, if the rudder is perfectly in line with the hull and pedals even, AOA is zero.
Depth: The major consideration is whether or not you have enough depth to keep adequate surface area in the water when the boat is nose down on a bump. Steep short wavelength needs a deeper rudder than longer/bigger swells since the tail of the boat breaks out the back and overhangs the water more in the short/steep stuff. I believe ellipticals are inferior because they don't have enough surface area at the tip of the rudder, which often is the only part of the rudder in contact with the water when you are nose down on a steep short bump.
Chord length: Longer chord for a given depth obviously is more surface area and powerful. But it also is my understanding that a longer chord is able to handle a higher AOA before stalling. If you imagine laminar flow of water wrapping around a rudder with, say, 20 degrees AOA, a shorter chord length forces the water flow to make tighter sharper turns, so it's more likely to lose that smooth flow, create turbulence and lose lift/ power/ and stall. The downside is for a given depth, you have more surface area therefore more drag with higher chord, assuming laminar flow. But if you are stalling, then that creates tons of drag in addition to the fact that you can't steer, and will broach.
Foil thickness: This is what people are talking about when they refer to "NACA" foils. Basically, how wide of a hole in the water is created when the rudder passes through? Relatively thin foils have less drag but require more speed for the same amount of turning power. So airplanes (or America's cup catamarans) that go really fast have razor sharp wing foils and slow Cessnas etc. have chubby fat foils. So a good designer will take into account the speed of the craft when selecting the foil thickness.
In my case, I asked Don for a rudder that had the necessary depth/surface area at the tip to handle big hawaii downwind, and also very resistant to stalling. The Ion has relatively stiff handling so it needs a fair amount of rudder power to hold a diagonal once you've committed to dropping down the face when making connections. This is what I got:
And it's great. 9 inch depth, 15 degree sweep. Actually looks pretty similar to Pete's "reef buster" with mine having a bit more chord. Although it is optimized for downwind control, I'm not able to measure any speed difference in the flat compared to the stock 7 inch.
I recommend going my route and just asking for the qualities you want, based on the conditions you paddle in and your skill/ style, and just see what shows up in the mail!
-Patrick