Normally when folks talk about propellers, they are described in terms of pitch and diameter. Diameter is obvious, that's the distance from tip to tip. Pitch is the distance the prop would travel through the air, if the air weren't a fluid.
If the air were made of metal, the prop would screw through it perfectly; like a nut on a bolt. Fluid dynamics, induced flow, Reynolds number, and on and on... make sure that a prop will never be 100% efficient. And, optimizing a prop to get that last bit of effenciency is beyond the scope of this article, not to mention my abilities..
However, the fundamentals of prop design are easy to understand. And will make building propellers that are "good enough" possible for us ordinary mortals..
Take a point at distance "r" (radius) from the hub. It travels in a circle while the prop goes forward according to the pitch, "p"...
If you've looked at a prop, you've seen how the blade is twisted from a large angle near the hub to a flatter angle near the tip. Why? That's because the tip, going through a larger raidus circle must screw through the air at the same rate as the blade section near the hub. The prop blade near the hub must be at a higher angle because the circle it goes through is smaller than the circle the blade goes through near the tip, but it must advance at the same rate if the pitch is to remain constant across the length of the blade.
a = arctangent ( P /2 * pi * r)
Or, if ya have a prop of unknown pitch
P = tangent (a) * 2 * pi * r
Will give ya the pitch.
Once you've made a few, it gets way-easy. I've been known to, during one evening, crank out four prop forms, in four different pitches, from balsa blocks; while paying marginal attention to TV sitcoms...
Once ya have a form, anything goes. Wanna lay up a composite prop blade? Go for it. I like to build light, so I make most of my prop blades out of thin balsa. The balsa prop blades get soaked in ammonia to soften them. Then they get held to the form by wrapping them in a chunk of Ace bandage. Bake in a low oven until dry. Et voia, nice prop blade.
For my small models, I usualy form two prop blades at once. Just put 'em both on the form, bandage, and bake...
Supply your own units.
Millimeters, inches, cubits...
The equations should work in your units. Except for degrees,
which are, degrees...