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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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