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Author Topic: Prop block formula  (Read 327 times)
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ffadict
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« on: November 21, 2019, 01:20:28 PM »

Hello all,

I'm getting a friend to 3d print me out a prop forming block, and I'm having a little trouble figuring out if my formula is correct. I've solved it as taking

Inverse tangent [(pitch in inches)/(2pi*distance from origin)]

I think this means that when I plug in the pitch and the length from zero, I should get the tip angle. Is this the correct formula? I've checked it against the figures in Ron William's book, but they are off slightly. It could be my formula, or that my TI-84 is more accurate than what he was using.

I know there's already a thread on this, but I didn't find a general formula in it. I need something that I'll also be able to use for carving, so not in code.

Thanks in advance,

Paul
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Bredehoft
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« Reply #1 on: November 22, 2019, 08:10:56 AM »

Your formula is correct and will yield the angle from "flat" (perpendicular to airflow) at the specified radius.  That is, at the hub, the angle will be close to 90 degrees. 

Infinitely close to zero radius, the angle will be 90 degrees and at near infinite radius, the angle will approach zero for ALL pitches. 

However the rate of change between those two infinite points is different for each pitch. (And the rate of change between each radius station is different - and different for each pitch.)

There IS an interesting phenomenon for these pitch angles:  the angle 32.48 degrees occurs at the same relative radius on every pitch.  This angle occurs where the blade pitch is equal to the number of 1/4" radius points.  32.48 on a 5 Pitch occurs at 5/4" (1.25"), on a 6 Pitch at 6/4" (1.5"), 7 Pitch at 7/4" (1.75"), and so on.  A standardized and adjustable pitch-setting jig or pitch-checking gauge can be constructed with this information.  Superior Props used to sell one when we took over, but I figured demand for such would be so low that sales would not justify any bench stock.

--george
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ffadict
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« Reply #2 on: November 23, 2019, 03:04:31 PM »

Thanks for the verification. The differences between tables really threw me for a loop.

There IS an interesting phenomenon for these pitch angles:  the angle 32.48 degrees occurs at the same relative radius on every pitch.  This angle occurs where the blade pitch is equal to the number of 1/4" radius points.  32.48 on a 5 Pitch occurs at 5/4" (1.25"), on a 6 Pitch at 6/4" (1.5"), 7 Pitch at 7/4" (1.75"), and so on.

That's an interesting method of determining pitch! I was making props with the laminated fan method for a while, and used the formula that the pitch divided by two pi was the distance from the hub of a 45˚ angle. I wonder what the math is behind the 32.48˚, but my Trig is failing me.
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dslusarc
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« Reply #3 on: November 23, 2019, 10:19:23 PM »


Here is why:

pitch = 2*pi*r*tanA
tan 32.48 = 2/pi
pitch = 2*pi*r*(2/pi)
pitch = 4 * r
or radius = pitch/4

similarly an angle of 38.51 degrees gives
pitch = 5 * r
or radius = pitch/5

Don
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ffadict
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« Reply #4 on: November 28, 2019, 07:39:30 AM »

Hmm, that makes more sense. But all that trig is going to have me holding up my fingers into triangles and pondering awhile  Grin

Thanks,

Paul
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