Re: Back of the curve ? question
David J. Gall
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Excellent questions you pose. The "backside of the power curve" is most
easily described by describing the whole "power curve," first, then
isolating the "backside."
The "power curve" we're talking about is actually the "power-required
curve." We all know that the drage of the airplane is made up of two parts,
parasite drag and induced drag.
Parasite drag increases as the square of the speed. If you draw a graph of
the parasite drag as a function of speed, you get a curve that goes up to
the right, ever steeper the farther to the right you go. Of course, this
assumes that "to the right" is toward increasing airspeed, and that "up"
means more drag.
Induced drag, on the other hand, decreases with increasing airspeed, so its
curve goes down and to the right, ever shallower the farther to the right
you go because induced drag is "inversely proportional" to the speed.
Adding the parasite drag and the induced drag together gives the total drag,
and the curve for the total drag starts high at low airspeeds (high induced
drag), comes down to a minimum (just above where the two drags' curves
cross), then goes back up as parasite drag starts to predominate in the
higher speed range.
But drag is not power. In order to get the power required from the drag, we
must multiply the drag times the airspeed. This sounds kind of kooky to just
say it, but the end result when applied to the drag curve is that the power
required curve looks very much the same as the drag curve. The power
required is high at low airspeeds, diminishes at moderate airspeeds, then
goes back up at higher speeds.
The minimum power required point does not quite coincide with the point of
minimum drag, though. The minimum power required speed is a little bit
slower than the minimum drag speed. But the important idea to remember is
that the power required curve is bowl-shaped. And that, if you extend the
flaps, the whole curve shifts up (higher power required at all speeds) and
to the left (lower minimum power required speed).
The power available curve sets the limits on what our airplanes can do in
level flight. If you fly at too slow an airspeed (too far to the left on the
power required curve), the engine can't make enough power to sustain level
flight. When that happens, the airplane must descend in order to maintain
airspeed. (Fortunately for your "expert" pilot, the Q2/200 is capable of
climbing in this condition. Even at reduced power setting, your Q2/200 can
apparently climb at speeds close to stall speed.) At the other end of the
speed range, the only way to go faster than flat-out full power in level
flight is, again, to go downhill.
There's a difference in the airplane's behavior, though, between the
slow-speed case and the high-speed case. In the high speed level-flight
condition, a reduction of power results in the airplane slowing down. Slower
flight means less power required, so the airplane can continue in level
However, at low speeds, below the minimum power-required speed - in other
words, to the left of the bottom point of the bowl - if you reduce power and
simultaneously attempt to maintain level flight, you find it impossible to
set a steady airspeed. If you try to maintain altitude, the airplane
continues to slow down. Alternatively, if you hold a steady speed, the
airplane descends. The airplane demands ever more power as it slows down. So
to go slower you find that you end up using more power than you had been
using before you slowed down. You are now flying "on the backside of the
power curve." To go slower demands the counter-intuitive use of MORE power,
Enter the Quickie/Q2/Q200 and Dragonfly. Here's a unique situation! Here's
where the Q's and D'flys are different from ANY other canard or conventional
airplanes out there. Earlier, I mentioned that the power required curve for
a conventional airplane was different with the flaps extended. But on Q's
and D'flys the FLAP is also the elevator. In order to fly slower requires
that the elevator be deflected to a more "nose up" setting, but that is the
same as extending the flaps. So, the power required curve of the Q's and
D'flys is UNIQUE in that it is a blended hybrid of the two power required
curves described above.
At low airspeeds, the power required curve is that of the flaps-extended
case. As the airspeed increases, the flap (elevator) is retracted and the
power required curve becomes that of the flap-retracted case. Where is the
minimum power-required speed? Compared to a conventional airplane, the
minimum power required speed is much farther to the RIGHT. That's right, the
gradual extension of the elevator (flap) as the airplane slows moves the
power required curve points up and to the left, so the minimum
power-required point is way out to the right compared to conventional
airplanes since the elevator (flap) is partially extended right up to design
cruise speed. In fact, design cruise speed is probably right at the minimum
power required speed.
This explains a lot about the performance of these planes. Ever notice how
fast the best climb speeds are? That's because best climb speed is very
close to minimum power required speed. If minimum power required speed is
close to design cruise speed, then expect best climb speed to be nearby.
Ever wonder why these planes are so good on gas mileage? That's also your
answer: minimum power required speed (design cruise speed) is close to our
everyday cruise speeds.
Notice that I'm referring to the "design" cruise speed, not the 65% or 75%
power cruise speed. Chances are that the designers never put this much
analysis into the aerodynamic design of these planes, instead concentrating
on stretching whatever magic it was that Burt Rutan put into the Quickie
into a two seat airplane.
Back to the power required curve: the power required curve for these planes
is stretched out to the right compared to a conventional airplane's power
required curve. That means that the minimum power required point is faster,
and that the size of the "backside" of the power required curve is much
larger in terms of the range of airspeeds it covers. Whereas a conventional
airplane that stalls at 60 might have a "backside" up to 85 or so, ours
might extend to 100 or even more.
Granted, the effects might not be so noticeable since the curve of our
"bowl" is so much shallower. And the really bad stuff at the extreme left
end of the curve never really happens to us since the elevator (flap) only
goes to 22 degrees instead of the 40 or more on conventional airplanes. So
the "backside" effects are probably much less severe (or even unnoticeable)
on Q's than on Cessna's.
Notice that none of this discussion even mentioned "stall."
To finish up, let me point out that the "frontside" of the power curve for
these planes is also different from conventional airplanes. Here, the
continued deflection of the elevator more trailing-edge up as higher speeds
are attained, and the use of reflexors for high speed trim, may give an
advantage over conventional airplanes. In other words, the power required
curve may be flattened somewhat allowing "more speed on less power" than
other designs. Let's hope that's true, but note that it would require a
reduction of parasite drag more than anything else. One form of parasite
drag is so-called "trim drag." Could it be that the trim drag of a Q is
significantly less than that of a conventional airplane? That is another
excellent question for another day....
David J. Gall