From: StarAerospace@aol.com
Message-ID: <10f.a6429fa.296fec24@aol.com>
Date: Fri, 11 Jan 2002 02:20:04 EST
Subject: Thrust, np, downwash, and misconceptions
To: lancair.list@olsusa.com
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<< 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. >>

Thanks for the help, but no, I'm afraid the V can't be ignored.  V at or near 
zero invalidates the basic thrust equations of 

T = np * 550 * HP / V 

and...

np = ( T * V ) / (HP * 550)

because we would have to divide or multiply by zero.  Gee, that means that np 
would be either infinite or zero (percentage or not <LOL>).  In fact, the 
inversely proportional relationship of T and V represents J, the difference 
between the angle of the helix wake field and the freestream. Thrust is 
nonlinear with V near zero and np does not apply.  Please stop interchanging 
np with Peff, which really IS a percentage.  Raymer and most texts do not get 
into this simply because it is too complex and not well quantified in current 
aero theory;  although I would point out that NO WHERE in Raymer's or many 
other texts is np called out as a percentage.  Heck, even Bombardier and 
Dornier still use actuator disc theory in their CFD of prop aircraft;  not 
very accurate.  

(BTW, I have a first edition of Raymer over a decade old among many other 
references.  Almost none speak of the differences between np and Peff since 
most work in the "installed vs. uninstalled thrust" area took place after the 
jet revolution.  However, the analysis of installed vs. uninstalled thrust of 
jets is highly detailed.)

There are MANY dimensionless coefficients that typically come out to some 
fraction of 1;  do we represent all of them as percentages???

How about lift coefficients?  For normal flight above stall, Cl is almost 
always less than 1, should we say that our Lancairs cruise at 15% lift 
efficiency and approach at 90%???  Absurd examples abound.  I go with 
convention of professionals.  In this case, transonic propeller engineers and 
aerodynamicists call out np as np, not a percentage.  

Behind the prop there is a helix of blade wakes that have been accelerated 
vs. the freestream.  Between these wakes are a helix of disturbed air that is 
at varying velocity depending on how close the blade wakes are to each other. 
 At low speeds the helix is very close to parallel with the freestream, so we 
get lots of thrust for not a lot of HP.  This is because the blades are at 
nearly flat pitch and the lift they produce mostly goes in the direction of 
flight.  Now, we need to stop thinking in Cl and start thinking in Cn.  As we 
go faster the helix stretches out and we create more blade lift off the 
thrust axis.  Conservation of energy tells us that since we are making lift 
someplace useless, we must give up some of the "useful"
lift in the thrust axis.  The Cn (or force coefficient normal to the blades) 
is still very high, but now the pitch of the blade is not perpendicular to 
the direction of flight.  So the Cl (thrust axis) has diminished (you guessed 
it!) in direct proportion to the velocity.

"np" cannot be represented as a percentage in the equation you used because 
the physical relationships you both are quoting Peff, not np.  We simply 
can't get away from that dratted velocity component because we are defining 
an acceleration, not a pressure.  In an ideal case, Peff = np.  The real 
world is different.  In your "aircraft tied to a tree" scenario, useful work 
IS being done:  A great deal of air is being accelerated from zero to some 
velocity.  Restricting the physical definition of "work" done by tying the 
aircraft down is poor physics.  Would you also say that a hovering aircraft 
is doing no "useful" work?  It too is motionless, so by your definition it 
should be producing no more "useful work" to accomplish this than the coffee 
cup.

"But wait!", I hear, "Wings produce lift and that's just a static force in 
level flight, right?  I was taught that by (insert pilot course, 
undergraduate or HS course, old salty CFI, etc.)"

Wrong.  This fundamental misconception of how lift is created and why we stay 
in the air exists not only in every pilot course, but also in all lower 
division aerodynamics classes (this misconception is corrected in upper 
division classes ... sometimes <LOL>).

Gravity is an acceleration, not a static force.  When we are in level flight, 
we are continually accelerating "up" at 1 G.  That's 32 fps/sec;  NOT 32 fps 
(Change your equation to represent lb.f of force instead of lb. of weight and 
this might be clearer;   better yet, use SI units and it becomes obvious).  
There just happens to be 1 G (down) that's offsetting this and making us 
think that everything is static.

To maintain 1 G level flight, we are accelerating the air flowing over the 
aircraft DOWN at some combination of mass and velocity capable of supporting 
1 G flight of our current aircraft weight.  The easiest way of thinking about 
this is to look at a helicopter and a Harrier, both at ~20,000 lb. weight.  
The helicopter will accelerate a vast quantity of air down at a small 
velocity change to maintain a hover or 1 G forward flight.  The downwash is 
the same whether the helicopter is in hover or at 100 KTAS.  The volume of 
air that can be worked with is governed by the rotor diameter, and that's a 
LOT of air;  so we don't have to move it very much.  Now look at the Harrier. 
 The "rotor diameter" is the size of the output nozzles.  Since the Harrier 
weighs about the same as some mid to large helicopters, we need to accelerate 
the air from these nozzles quite a bit faster to keep the same weight in a 
hover.

Now we transition that Harrier into 1 G 300 KTAS forward flight and let the 
wing do all the work.  Guess what?  The wing is now accelerating the same 
massflow of air down as the rotor system on the (equivalent weight) 
helicopter.  Rotary wing, fixed wing, or powered lift, we are pushing air 
DOWN;  fast.  It's dynamic, static force concepts fall hard about now...

To all on the list without a hard physics background, I apologize for this 
being so long.  But the fact is that thrust is inversely proportional to 
velocity and none of this babble about tip speeds managed to point that out.  
For the record, very few props available for general aviation use can 
maintain an np of greater than .8 at tip speeds above M.85.  However, single 
stage props in production use on the C-130J achieve np of over .85 at tip 
speeds well into the low M .9's and the counterrotating props on the An-70 
work all the way up to M.94 tip speeds and maintain np of over .85 at an 
aircraft speed of M.72 (almost 500 mph!).  The GE led UDF program of 
counterrotating propfans on an MD-80 led to np of over .80 at a cruise speed 
of M.81. 

None of this really helps C-182's at 120 KIAS, but it does make a difference 
to us in Lancairs (and other, planned aircraft) at M.5+.

The difference between what the prop does in the charts and the thrust you 
get on your aircraft is, in fact, a percentage.  This is the "propulsion 
efficiency" represented by the amount of installed thrust you get for the 
theoretical uninstalled thrust.  Since it is a fraction of a ratio whose 
maximum is theoretically 1 or 100%, it is appropriate and accepted industry 
practice to call it out as a percentage.  There is only one propulsion 
concept so far that has exceeded 100% Peff under this definition, and it did 
it by reducing drag not perpetual motion. 

((BTW, aren't you the guy who asserted, not long ago, that "...the PSRU's on 
all turboprop engines relied on helical gearing..."  ?? Seem to remember that 
being rather convincingly refuted.))

<LOL>, I should have said "the better ones".  Please refer to page 32 of 
AWS&T 1/7/02 issue or any issue that has a picture of the proposed engine for 
the A400M.  Primary reduction is helical, accessory cases are straight cut.  
In the case of the M88 derivative for the A400M, they are using a helical 
planetary.  In the case of the proposals made by GE for a geared fan engine, 
all the published data shows helicals.  So were the UDF's, all the post-PT6 
Pratts displayed in cut away form at Oshkosh, etc.  Disinformation?  Perhaps 
it's a conspiracy <LOL>  Focusing on what was acceptable a few decades ago, 
isn't really relevant.  Straight gears have their place, and that place is 
low cost when weight is not critical.  Otherwise the highest load, lowest 
weight, highest dollar applications would use them.

Eric
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