Some Propeller Fundamentals

And a blade angle calculator

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..

The Math Begins

Propeller Fundamentals

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"...

Now, imagine the prop comin' at ya. The helix traced by "r" becomes a circle. The distance traveled by r as it goes around is equal to 2* pi * r.
It Gets Twisted

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.

What's The Angle?
As a point on the prop blade travels around in a circle it advances according to pitch. From High School Trigonometry... The angle of the blade, at distance "r" from the hub, given a pitch "P" is:

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.

So What?
The math might look scary, but fear not. Making props is easy. Us old-time free flight modelers do it the easy way. Props get formed on a block of wood.

Carving a Prop Form.
Using your pocket calculator, or the javascript calculator below, it's easy to find the blade angle at some "r" distance from the prop hub. Then ya just lay out the lines on a block of wood, and carve away the material that's in your way..

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...

Then what?

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...


Input fields on left, output field centered.
You can change the fields on the left and see the results.
Once you've changed an input, click outside the box to force a re-calculation.

Supply your own units. Millimeters, inches, cubits...
The equations should work in your units. Except for degrees, which are, degrees...

P =
r =
a = Degrees

OK, ok,,,
Obviously, I'm ignoring induced flow and other prop efficiency variables. But, it's a start. And, an introduction to some of the math involved in propeller design.

If you want more, take a look at what Larrabee, and Drela (THE authorities of propeller theory) have done; and then explain it to me..;)


Email comments, questions and complaints to:
Del Ogren