Thinking About Propellers

So I keep thinking about propellers. 

Propellers are pretty wrong. (your average one, that is.)  This article goes into it with good depth.  http://www.eaa.org/experimenter/articles/2009-02_elippse.asp 

Tonight I broke out the spreadsheet and started trying to replicate the math.  In large part because Paul Lipps died, and his son is now working on drones, instead of the recreational aviation market. 

So starting with the most obvious, I started with this statement: Your available lift goes up with the square of speed.  And wing lift is also a linear relationship to area. 

I calculated the speed of the propeller at every 2" along the radius.  But that's only good for when you're not going anywhere.  As your forward speed goes up, you're adding to the perceived airspeed of the propeller blades.  This has some really funny effects on blade chord. 

With a 64" propeller, and an 8" hub, you'd need a 64 times more chord to provide equal lift! But as airspeed goes up, that ratio drops off rapidly.  The slower the prop speed, the faster that ratio drops.  At 100mph, and 3000rpm, that ratio drops to 22 times.  (for giggles, at 400mph, it's only 3:1, but the tip speeds are at a freaky 697mph)

While typing this I figured out that I am forgetting something.  Swept area.  All of the math I have done (or, in this case, OpenOffice Calc has done..) only tells me how to produce the same lift across the blade.  This would produce a lift profile like that of a constant chord wing. 

I need to think about how to compensate for that, if it's even worth compensating for.