How do I set up artificial
stability for a plane?
Austin published the following recently:
to the PlaneMaker page
Load an airplane in Plane-Maker.
Go to the EXPERT menu, ARTIFICIAL STABILITY screen.
This is where you can enter control-system constants to make your plane
feel stable even though, in reality, it isn't. This is especially
common in fighter jets and helicopters... fighters are most
manueverable if unstable, and helos just have nothing to naturally MAKE
them stable! So we design control systems to MAKE THEM SEEM STABLE.
These control systems typically do this by ADDING SOME INPUT IN
ADDITION TO YOUR STICK INPUT to make the plane do what you want.
A common case of this in the civilain world is the yaw damper... your
feet still move the rudders, there's no doubt about that, but the
yaw-damper system ADDS SOME ADDITIONAL RUDDER DEFLECTION FOR YOU TO
DAMP OUT THE ROTATION RATES OF THE PLANE. How much rudder does it add?
Well, that is a decision made be the controls-system engineer... in
this case known as: "YOU".
Let's imagine a yaw damper. The goal is to add some rudder deflection
to whatever the pilot hammers in with his feet to stop aircraft
rotation... this is seen in high-end Mooneys and most jets. So ask
yourself this: How much rudder do you WANT to add to stop rotation?
FULL rudder? Just 1/10 of the max rudder deflection? Obviously, if the
plane is only wagging it's little booty a LITTLE BIT, you only want to
add a LITTLE rudder to stop it. But, if the plane is shakin' dat thang
at a high rate, then you better put in a LOT of rudder to put a stop to
it NOW. So how do we decide how much rudder to put in? Well, there are
plenty of ways, but in X-Plane, we say that we enter some fraction of
the rudder input PER DEGREE PER SECOND OF ROTATION RATE.
So, imagine the plane is wagging it's little tail (from turbulence,
varying crosswind, the pilot stepping on the rudder, WHATEVER) at 90
degrees per second. (Now let's THINK about that for a second!!!!! HOLD
YOUR HAND IN FRONT OF YOUR FACE AND PRETEND IT IS AN AIRPLANE. NOW
ROTATE YOUR HAND THRU 90 DEGREES OF HEADING CHANGE IN 1 SECOND. THAT IS
90 DEGREES PER SECOND.) As you see, it is a moderate rotation rate, but
not a really huge rotation rate. However, when you are in the real
airplane, 90 degrees per second of tail-wagging will feel like a LOT.
(kicking the rudders a bit in a Cessna 172, for example, will shake
it's little booty at about 35 degrees per second). So, lets say that 90
degrees per second is so much rotation rate that we are willing for the
control-system to put in FULL RUDDER to oppose it. That means that if
the plane is rotating at 90 degrees per second, we want to put in FULL
rudder to oppose that motion, and at 45 degrees per second we want to
put in HALF rudder to oppose that motion, and at a measly 9 degrees per
second we want to only put in 1/10 rudder to oppose that motion. At the
35 degree-per-second tail-wag of a 172, the control system would put in
as much as about 35% rudder deflection to oppose tail-wagging and
yaw-stabilize the plane. This does not sound like an unreasonable
So what do you enter in Plane-Maker to make it happen? Well, for the
"heading: target sideslip" you might just enter "0" (the plane always
tries to stabilize at 0 sideslip) and for "fraction deflection per
degree difference" simply enter "0" (the system is not trying to
achieve a desired sideslip, only DAMP OUT the tail-wagging by opposing
ROTATION RATES) and for "fraction deflection per degree per second"
enter "0.0111". Why 0.0111? Well, take that 0.0111 and multiply it by
90 (the rotation rate that we would apply FULL rudder at) and you get
1.00.. or, translated: "FULL rudder deflection". Put another way, if
you want full rudder at 90 degrees per second yaw rate, simply take
1.0/max yaw rate and you will get 1/90 or 0.011. This is a reasonable
yaw-damper constant. Try entering it for the 172, save the plane in
Plane-Maker, load it again in X-Plane, and pop the rudders left and
right: you should see the plane damps out faster, as would a real one
if such a yaw damper were installed in reality.
Now, maybe you want even MORE stabilization... try entering 0.1 in the
"fraction deflection per degree per second". Now THINK about what that
means. That means that if the plane is rotating thru 10 degrees per
second, the rudder will move fully to oppose it. (10 degrees per second
times 0.1 control per degree per second = 1.00, which is FULL
DEFLECTION.) Move your hand at a rotation rate of 10 degrees per
second. This means it should take 9 seconds to move your hand thru 90
degrees. That is a SLOW rotation rate. Yes, with a constant of 0.1,
even this SLOW rotation rate will be opposed by FULL rudder.
YIKES!!!!!!!!! If you just BREATHE on this airplane now it will kick
FULL rudder to oppose it! Yikes! This is scary, because IF YOU TAKE
THIS THING INTO TURBULENCE I GUARANTEE THE AIR WILL KICK YOU AROUND AT
WELL OVER 10 DEGREES PER SECOND ROATION RATES, SO I GUARANTEE YOU WILL
SEE =>FULL<= RUDDER DEFLECTION FIRST ONE WAY, AND THEN THE OTHER,
AS THE PLANE WAY OVER-REACTS TO EACH ANGULAR ROTATION INDUCED BY THE
TURBULENCE BY KICKING FULL RUDDER TRYING TO OPPOSE THAT ROTATION! So,
as you can see, a constant of 0.1 is really pretty high.
Now, to give you an idea of how bad it can get, I have actually seen a
plane where someone entered a constant of 3.0... THIRTY TIMES HIGHER
than this hypothetical case. Think about what this means: For a
rotation rate of 1/3 degree per second (in other words, it takes 270
seconds (4.5 minutes) to move thru 90 degrees of heading, an EXTREMELY
LOW ROTATION RATE, the system would put in FULL OPPOSITE RUDDER! HOLY
COW! That means that the plane has even the tiniest, slowest-imaginable
HINT of rotation in a given direction, THE RUDDER SLAMS HARD OVER TO
THE STOP TO COUNTER IT. Needless to say, any time this plane entered
even the slightest hint of turbulence, the rudder would slam from one
stop to the other in a wildly exaggerated effort to counter the
turbulence.. ugh! If you must kill a fly buzzing around you in a
china-shop, don't go after it with a chainsaw... the results won't be
pretty. This particular plane handled OK if there was no turbulence:
Since nothing ever came along to ROTATE the plane, the flight controls
never had to move to OPPOSE THAT ROTATION... but, as soon as the
slightest imperfection came along to move the plane (in this case
turbulence, though it coudl easily be the pilot kicking a flight
conrol, a bird-strike, an engine-failure, a bumpy landing, flying into
changing winds.. ANYTHING. One thing that you can ONLY learn by
actually getting your pilots license and getting your butt in the sky
is that it is a VERY IMPERFECT WORLD UP THERE.. The plane is constantly
barraged by all manner of imperfections, perturbations, and external
winds and forces... and, much like with a BOAT, this must be EXPECTED
and anticipated in the design.
Now let's apply what we have learned to PITCH stability: Say your plane
is not very stable in pitch and you want to lock it down a bit. (First
of all, in X-Plane 8.30 RC-2 and later you can slide the "control
addition" sliders in the "Joystick" screen second tab to the right a
bit to add some aritifical stability to help stabilize the plane a
bit.. this simply engages a system that I designed for you to help
stabilize the plane). But let's say you DON'T want to use my sytem to
stabilize the plane, but really design your own to mimic the one
actually installed in the real plane! Well, enter maybe 20 degress for
the target angles of attack (enough to stall the plane) enter 0.1 for
the fraction deflection per degree difference (if the angle of attack
is 10 degrees off, then the plane applies full elevator to capture the
desired angle of attack.. a very agressive but not insane constant) and
enter 0.05 for the "fraction deflection per degree per second" (If the
nose is coming up at 20 degrees per second, then the system will apply
full elevator to stop it). These are some pretty agressive constants (a
lot of elevator is brought in to counteract a small amount of motion)
but I have my reasons: 1: The plane needs to have lower rates in pitch
than in yaw. Why? Because if you yaw a plane a bit, not that much will
change: the vertical stabilizer, which is being broadcast to the air,
is small! But, if you PITCH the plane a bit, then the WHOLE WING AND
HORIZONTAL STAB is shown to the air... the effect will be a lot greater
than in yaw where only the vertical stab is offset, because the wing is
so much bigger!!!! So, we got a lot more effect for each degree of
angle of attack than we do of sideslip, so we need lower pitch rates
than yaw rates to keep within comfortable (safe) G-loads, so we enter
HIGHER constants in pitch than yaw to really work hard to counter those
pitch rates. Also, there is another reason we can enter higher
constants than you think: 2: I cheat. X-Plane will AUTOMATICALLY REDUCE
THE CONSTANTS as you speed up, because it knwo that at hi speed it
better enter smaller control deflections to keep from busting anything!
So the constants you enter here are only fully applied down near the
stall where control authority is mushy... the controls relax and phase
out as the indicated airspeed (air pressure on the controls) builds up.
Now, are you ready to see this schieze in practice? Open up my VTOL in
Plane-Maker ("File" menu, "Open Aircraft", "Austin's Designs : Austin's
Personal VTOL" and look in the "Expert" menu : "Artificial Stability"
screen. Notice that I have only LOW-SPEED constants here, designed to
phase out rotation rates to make the thing easy to fly. Look at the
rotations I shoot for with full-scale stick deflections in hover: Max
of 30 degrees pitch, 45 degrees roll, and 45 degrees PER SECOND
ROTATION RATE in yaw. And now you know what the 0.02 and 0.01 do as
well. Now get into X-Plane and load up this little bird (it starts off
with thrust vector at 90 degrees, straight up). Add power and raise up
off the ground and work on your hovering. Slide left and right. Fore
and aft. Up and down. Do it with small control deflections. Now, see
that little switch on the panel called "ART STAB"? Turn it OFF to fly
WITHOUT stability augmentation. VIVA LA DIFFERENCE!
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