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Hi Marv,
I must confess that I too had to think about it for a
while, unfortunately I must still disagree with you ;)
let me see how well I can put my thoughts in words.
[...set that angle of attack and then set the power to
simply hold altitude, you'll be flying at a
significantly reduced airspeed than that which you'd
normally cruise at. This would give you the lowest
fuel burn at which you could maintain altitude, and
keep you in the air the longest.]
In the operation you describe here, you are setting
power to hold altitude AT A FIXED AOA (Angle Of
Attack), which in this case is the one that gives you
L/D Max (= Maximum Lift for minimum Drag). If from
here you reduce power further you will have to choose
between losing altitude (and maintain the same AOA) or
maintaining altitude (and increase AOA). *** You can
still reduce power significantly, fly at an airspeed
that will be closer to your stall (high AOA) and still
maintain altitude ***.
That high AOA, in a power off glide would be the
airspeed that gives you your slowest descent (feet per
minute). At that airspeed you will not perform a long
glide in terms of distance, but a long glide in terms
of time.
That, is the airspeed that will give you the greatest
endurance. The airspeed you could use in a hold, apart
from the fact that you will be close to a stall, and
maybe overheating your engine.
To get the greatest range, however, you must fly the
airplane where it gives you the minimum drag for the
maximum lift.
That airspeed in a power off glide will let you go the
farthest distance from where you are, and with power
will give you the biggest range. An airspeed to use if
your fuel reserves are going low and you wonder
whether you will make it to your next airport.
So in conclusion, what I believe is that both maximum
range as well as endurance can be got by flying an AOA
(once you've established what it is in either case)
and you don't need complicated equations to calculate
either. You will however as you point out have to
calculate fuel burn and airspeed to know WHAT that
range will be.
Max. Range = L/D Max AOA
Max. Endurance = AOA that gives you slowest descent
I take it for granted that your engine burns less fuel
holding altitude at slowest descent AOA (slower
airspeed) than at L/D Max AOA (higher airspeed). Is
that where I am wrong ? I don't see where else.
see you at the fly-in,
Regards, fili
[Fili, the problem with your theory is that you are operating from a
flawed premise. In your third paragraph you state: *** You can still
reduce power significantly, fly at an airspeed that will be closer to your
stall (high AOA) and still maintain altitude ***. That won't work. Once
you pass into an AOA range that is greater than L/D Max you are operating
in reverse command, or behind the power curve. At that point it will
take MORE power to fly slower (and maintain altitude), not less. This is
why L/D Max is such an important angle of attack, it's at the bottom of
the drag "bucket". If you're flying along in equilibrium at L/D Max and
pull back on the stick you will see a temporary increase in altitude, but once
the excess energy that was traded (airspeed) goes away, you will start to
descend because the drag has gone up and it's going to take an increase in
power to overcome that additional drag. This is why you fly L/D max when
the engine goes out, as you don't have the benefit of thrust in your
pocket to overcome additional drag, so with the engine out you get your
best possible glide (most lift, least drag) at that particular AOA. The
place where I have a problem equating max endurance with max range is
when you factor in fuel burn to fly the airspeed that gives you L/D Max and
then go to cruise, without knowing the fuel burn at that speed you don't
know exactly what's going to happen. If you really want to extend the range
you could also trade off altitude to minimize the thrust requirement, thereby
cutting back on the fuel burn even further, but as you can well imagine, you
would still be dealing with finite amounts of both fuel and altitude, so
there still is a limit to just how much range you're going to get out of
a particular amount of endurance. All I know for sure is that thinking
about this stuff in 3 dimensions without having a set of performance figures
available makes my brain hurt.
<Marv> ]
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