prop formula

Wed Oct 20 13:04:20 AKDT 2004

Hi Jeff, Nat, and All,
When you say equivalent, that's not the whole story. You could be looking for equal thrust at the same RPM, but the horsepower absorbed will be different, for different diameter props! The most useful equivalent, for our purposes is for horsepower absorbed. That determines the RPM the engine will reach. That's what you did in MotoCalc, you held the power absorbed constant. Good approach.

I can attest that a two-bladed  17 X 13 is about the same load as a 3-bladed 15 3/4 X 11, is about the same load as an 18 X 10 2 blader, is about the same load as a 4-bladed 15 X 11. I have tried all these props,and they turn within a couple hundred RPM of each other. When Dave Lockhart and I received the very first batch of 15 3/4 X 13 three-bladers, and found them to be more load than was practical, he started pitching down, while I clipped and thinned the blades, while keeping the 13 pitch. The clipped 3-blader that turned the number I wanted was a 15 1/4" diameter. That's close to what is in your list, too! My benchmark was always a 17 X 13 two-blader.

As it turns out, the better direction was to pitch down, as that let the in-air RPM reach the 8,600 RPM neighborhood, which is right where the torque peak for the OS occurs, with pipe lengths that produce civilized throttle response. See the Model Airplane News review done by Mike Billinton, for that last bit. Torque and horsepower curves may be a pain to produce, but they sure are useful when it comes to optimizing what you get from an engine.

Oh yeah:

Thrust for a given pitch and blade shape is proportional to RPM^2 times Diameter^4
Power absorbed for a given pitch and blade shape is proportional to RPM^3 times Diameter^5
these come courtesy of some dead guy named Renard.

This stuff is fun, ain't it ...

Dean Pappas
Sr. Design Engineer
Kodeos Communications
111 Corporate Blvd.
South Plainfield, N.J. 07080
(908) 222-7817 phone
(908) 222-2392 fax
d.pappas at kodeos.com

-----Original Message-----
From: discussion-request at nsrca.org
[mailto:discussion-request at nsrca.org]On Behalf Of Jeff H. Snider
Sent: Wednesday, October 20, 2004 1:59 PM
To: discussion at nsrca.org
Subject: Re: prop formula 

I messed around with MotoCalc to find a formula for "prop load".  My
goal was to find a formula that allowed you to replace one prop with
another of a different diameter but select the pitch so that RPMs
and Amps remained the same at full throttle static.  If the RPM
remains the same and the Amps remain the same, the "prop load" must
be the same.  Am I right?  I know motors are different from engines,
but (in theory) if the loads for two props are the same on a motor
at a given RPM, they are the same on an engine at that RPM.

The formula I reached is this:

Prop Load = Blades x Pitch x Diameter^4

That's Diameter to the fourth power.  I can almost justify the
fourth power with a geometry argument, but I'm not there yet.
Anyway, the formula works perfectly within MotoCalc.

As an example, a two blade 17x13 prop (think OS 160 here) turns the
same RPM as:

2 blade 17.34 x12
2 blade 17.73 x11
2 blade 18    x10.25
2 blade 18.15 x10

3 blade 15.36 x13
3 blade 15.67 x12
3 blade 16    x11

4 blade 14.30 x13
4 blade 14.58 x12
4 blade 14.91 x11
4 blade 15    x10.7

These props aren't all commonly available ones, just numbers to try
and get close to.

I don't have a good equation for thrust, but "prop speed" (meaning
theoretical mph of the air pushed by the prop) is a pure multiple
of RPM and pitch, so when moving up to more blades if you're keeping
the same RPM keeping roughly the same pitch seems like a good idea,
unless you want to change static thrust and your ultimate top speed.

(that was a long sentence)

Do those prop sizes sound reasonable to those of you who have tried
different props on your 160s?

	-Jeff

George Kennie writes:
> A little addendum to the prop formula that was on the list a couple
> of days ago.It was purported to be from Mike Nauman and went like
> this:
> No. of blades, X pitch squared, X diameter cubed.
> I tried the formula and felt that it didn't work. Then I tried it
> again today and felt that it corresponded to my experience. Then I
> tried it in a different range and it came up failing again. So I
> tried to simplify it a little and due to the fact that I find that
> the diameter is the most crucial component of the formula I decided
> to leave all else alone and just modify the diameter. So what I
> ended up with was:
> Number of blades, X pitch, times diameter squared.     Applying this
> formula in several ranges seems to work for me. See what you think.
> 
> 
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