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Date: Mon, 07 Jan 2002 08:52:57 -0800
From: Brent Regan <Brent@regandesigns.com>
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To: Lancair List <lancair.list@olsusa.com>
Subject: RE: Thrust and np
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Eric Writes:

<<I have to wonder where this idea of "percentage" came into use 
regarding the propeller efficiency factor "np".  "np" is a dimensionless 
number represented by the product of the advance ratio (J) multiplied by the 
ratio of thrust vs. power coefficients.  It is NOT a percentage of anything. 
<<snip>>

T = 550 * np * HP / V

Where:
T = thrust in pounds;
HP = brake horsepower imparted to the propeller, SAE net for all you gear 
heads;
V = velocity in feet per second;
550:  necessary to convert HP (ft.*lb./min) to comply with V in fps;>>

Let me help you out here, Eric. A horsepower is defined as the ability
to lift 550 pounds one foot in one second (not 1 minute) (or 1 pound
550 feet in one second, or ....) so if we multiply Horsepower by 550 
we get Work expressed in foot pounds/second. If we now multiply by
velocity (feet / second) the feet and seconds cancel leaving us
T = np * Tp(pounds of thrust the prop should be developing if there were
no losses). Rearrange the equation to T/Tp = np where np is the ratio
between actual thrust and theoretical thrust or, as you point out,
Efficiency Factor. If you multiply by 100 you can express it in PerCent.
0.84 = 84/100 = 84%. 

Now I think that most of the learned readers on this list appreciate the
fact that if you tie the tail of your plane to a tree   and firewall the
throttles you will produce a lot of thrust (force) but no velocity (if the
tree is big enough) so the ability of the propeller to convert horsepower
into USEFUL work is zero (My coffee cup is exerting force on my desk but
there is no motion so there is no work being done). How can this be? The
engine is faithfully turing gasoline into torque and rpm. Where is the
horsepower going? If you put your head out the cabin door it will become
immediately obvious. 

What "np" is depends on what you are calling thrust. Is it the force that
propeller exerts on the crankshaft in the direction of flight? The tension
in the rope that is tied to the tree?

If Thrust is defined as the force required to pull the airplane through
the air and V is the velocity of the airplane then would not "np" be the
"Propulsion Efficiency" you mention?

Curious readers want to know.

Regards.
Brent Regan
Regan Designs
Idaho
USA 
Earth





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