The Murphy Builders Site

I just did some math that brought some very interesting results.

Everyone knows that prop redlines are generally in the 2700 RPM range. And
I have found out from more than one source that a Chevy V8 should probably
be redlined at 4500 RPM for maximum reliability. So I came up with a 1.67:1
reduction ratio based on these figures. Applying 75% to the engine redline
gives me a cruise prop RPM with a 1.67:1 reduction of 2021 RPM. Here's the
interesting thing I found out by running some more numbers.

Assume max engine RPM of 4000 and max prop RPM of 2700:
4000/2700=1.48 gear reduction
4000*75%=3000 cruise engine RPM/1.48=2027 cruise prop RPM

Assume max engine RPM of 4500 and max prop RPM of 2700:
4500/2700=1.67 gear reduction
4500*75%=3375 cruise engine RPM/1.67=2021 cruise prop RPM

Assume max engine RPM of 5000 and max prop RPM of 2700:
5000/2700=1.85 gear reduction
5000*75%=3750 cruise engine RPM/1.85=2027 cruise prop RPM

Assume max engine RPM of 5500 and max prop RPM of 2700:
5500/2700=2.04 gear reduction
5500*75%=4125 cruise engine RPM/2.04=2022 cruise prop RPM

Just for fun Assume max engine RPM of 3000 and max prop RPM of 2700:
3000/2700=1.11 gear reduction
3000*75%=2250 cruise engine RPM/1.11=2027 cruise prop RPM

Is there something wrong with my math or do I get essentially the same
cruise prop RPM no matter what engine redline I choose? Don't I get the
same thrust from the prop if 100 HP is turning it at 2020 RPM versus 200 HP
turning it at 2020 RPM? Maybe therein lies the problem. Perhaps 100 HP
can't turn the prop at 2020 RPM if it's an 80 inch three bladed monster.

Mike Kimball
SR #044




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If your swinging an 80" prop at 2700 rpm, your static thrust should be
pretty consistent whether you're using 100HP or 200HP. What you're going to
lose with less power is air velocity through the prop... you'll have to fine
the pitch of the prop to keep it spinning at 2700 rpm as you use less power.
Theoretically you could spin an 80" prop at 2700 rpm with 100HP, but your
pitch would have to be so fine you would end up with a forward airspeed less
than your aircraft's stall speed! If you built it light enough though...
you could just take off vertically with all the thrust you're making. ;-)

The key to your math was that you adjusted your prop reduction ratio for
each engine speed to produce a prop speed of 2700... since all of these
ratios are linear, 75% of the engine speed is always going to be 75% of prop
speed... and 75% of 2700 is 2025.

What you have to consider here is how much cruise speed you're willing to
trade for climb performance... even with a constant speed prop, the larger
diameter prop will out climb a smaller diameter, but it will be slower in
cruise on any given engine. To swing that big prop fast with sufficient
pitch for a comfortable cruise speed is going to take a minimum amount of
power no matter what your engine rpm or reduction ratio.

Mike

----- Original Message -----
From: "Mike Kimball" <mkimball@gci.net>
To: <murphy-rebel@dcsol.com>
Sent: Friday, November 30, 2001 9:45 PM
Subject: Interesting math

I just did some math that brought some very interesting results.

Is there something wrong with my math or do I get essentially the same
cruise prop RPM no matter what engine redline I choose? Don't I get the
same thrust from the prop if 100 HP is turning it at 2020 RPM versus 200

HP

turning it at 2020 RPM? Maybe therein lies the problem. Perhaps 100 HP
can't turn the prop at 2020 RPM if it's an 80 inch three bladed monster.

Mike Kimball
SR #044


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Of course 75% of 2700 RPM at the prop is always 2025 RPM. Funny how I
didn't see that at first since I was coming at the math from a different
direction. The obvious was hidden from me while my attention was elsewhere.
It's why I shouldn't do math or write emails at 11:00PM at night.

As for the other stuff, I want to ponder those thoughts during daylight
hours, check my Aerodynamics for Naval Aviators book, and get back to you.

Cheers,

Mike Kimball
SR#044

-----Original Message-----
From: murphy-rebel@dcsol.com [mailto:murphy-rebel@dcsol.com]On Behalf Of
Mike Davis
Sent: Friday, November 30, 2001 11:12 PM
To: murphy-rebel@dcsol.com
Subject: Re: Interesting math


If your swinging an 80" prop at 2700 rpm, your static thrust should be
pretty consistent whether you're using 100HP or 200HP. What you're going to
lose with less power is air velocity through the prop... you'll have to fine
the pitch of the prop to keep it spinning at 2700 rpm as you use less power.
Theoretically you could spin an 80" prop at 2700 rpm with 100HP, but your
pitch would have to be so fine you would end up with a forward airspeed less
than your aircraft's stall speed! If you built it light enough though...
you could just take off vertically with all the thrust you're making. ;-)

The key to your math was that you adjusted your prop reduction ratio for
each engine speed to produce a prop speed of 2700... since all of these
ratios are linear, 75% of the engine speed is always going to be 75% of prop
speed... and 75% of 2700 is 2025.

What you have to consider here is how much cruise speed you're willing to
trade for climb performance... even with a constant speed prop, the larger
diameter prop will out climb a smaller diameter, but it will be slower in
cruise on any given engine. To swing that big prop fast with sufficient
pitch for a comfortable cruise speed is going to take a minimum amount of
power no matter what your engine rpm or reduction ratio.

Mike

----- Original Message -----
From: "Mike Kimball" <mkimball@gci.net>
To: <murphy-rebel@dcsol.com>
Sent: Friday, November 30, 2001 9:45 PM
Subject: Interesting math

I just did some math that brought some very interesting results.

Is there something wrong with my math or do I get essentially the same
cruise prop RPM no matter what engine redline I choose? Don't I get the
same thrust from the prop if 100 HP is turning it at 2020 RPM versus 200

HP

turning it at 2020 RPM? Maybe therein lies the problem. Perhaps 100 HP
can't turn the prop at 2020 RPM if it's an 80 inch three bladed monster.

Mike Kimball
SR #044


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Mike,
Using Murphy's numbers the cruise fuel burn is 14 gal/hour at 143 mph.
If we use 0.45 pounds/HP/hour we get about 185 HP.
So whatever RPM you want to cruise at you will need on the order of 185 HP
to maintain 143mph.
75% power does not have to mean 75% rpm.
At higher rpms (but same power) your throttle will not be open as much.
Like shifting down
a gear to climb a hill in your car - you can maintain the same speed but in the
lower gear you let the engine spin up more. This allows for lower cylinder
pressures and smoother running since the torque impulses are lower in
amplitude but higher in frequency.
John


At 10:45 PM 11/30/01, you wrote:

I just did some math that brought some very interesting results.

Everyone knows that prop redlines are generally in the 2700 RPM range. And
I have found out from more than one source that a Chevy V8 should probably
be redlined at 4500 RPM for maximum reliability. So I came up with a 1.67:1
reduction ratio based on these figures. Applying 75% to the engine redline
gives me a cruise prop RPM with a 1.67:1 reduction of 2021 RPM. Here's the
interesting thing I found out by running some more numbers.

Assume max engine RPM of 4000 and max prop RPM of 2700:
4000/2700=1.48 gear reduction
4000*75%=3000 cruise engine RPM/1.48=2027 cruise prop RPM

Assume max engine RPM of 4500 and max prop RPM of 2700:
4500/2700=1.67 gear reduction
4500*75%=3375 cruise engine RPM/1.67=2021 cruise prop RPM

Assume max engine RPM of 5000 and max prop RPM of 2700:
5000/2700=1.85 gear reduction
5000*75%=3750 cruise engine RPM/1.85=2027 cruise prop RPM

Assume max engine RPM of 5500 and max prop RPM of 2700:
5500/2700=2.04 gear reduction
5500*75%=4125 cruise engine RPM/2.04=2022 cruise prop RPM

Just for fun Assume max engine RPM of 3000 and max prop RPM of 2700:
3000/2700=1.11 gear reduction
3000*75%=2250 cruise engine RPM/1.11=2027 cruise prop RPM

Is there something wrong with my math or do I get essentially the same
cruise prop RPM no matter what engine redline I choose? Don't I get the
same thrust from the prop if 100 HP is turning it at 2020 RPM versus 200 HP
turning it at 2020 RPM? Maybe therein lies the problem. Perhaps 100 HP
can't turn the prop at 2020 RPM if it's an 80 inch three bladed monster.

Mike Kimball
SR #044


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