BACK WHEN I
was maybe 17 years
old, there was a
construction article
in the old American
Aircraft Modeler
(AAM) magazine for
an RC Aerobatics
(Pattern) model
called the
“Warlock.” Hello
out there, Jim
Wilmot. If you are
reading this, it may
please you to know
that your novel
design and amusing
article are
remembered.
It was a radical
design (even today
the Warlock would
be viewed as
radical), with
tandem retractable
landing gear and
wing outriggers, as on a U-2 spyplane; aggressive angular lines; and,
most intriguingly to me, an all-flying horizontal tail or stabilator.
This was cool, not only because all of the latest supersonic fighter
jets were being designed with all-flying tails, but also because all the
talk I’d ever heard at the local flying field about stabilators was that
they were tricky. Put the pivot in the wrong spot, and they would either
flutter off the airplane at speed or overload the servo and cause a crash.
Wonder of wonders, here were shrunk-down plans in the magazine
that showed a working stabilator design, complete with the correct pivot
tube location and construction details. I would appropriate this design
element and use it in an airplane I had been contemplating for a while.
The wing was swept an inch or 2 at the TE (please forgive the fuzzy
memory), with a tip chord something near 70% of the root chord, and
the symmetric airfoil was borrowed from the late Pappy deBolt’s Live
Wire Sonic Cruiser design.
My dad had built and flown the daylights out of one of these when I
was 8 or 9 years old. After its demise, I had made a CL flying wing
from the surviving outer one-third of both wing panels. It flew pretty
well as I remember. The airfoil was an NACA 64012, and further
homage had been paid to Pappy when Art Schroeder (long-time editor
of Model Airplane News magazine) used it in his popular and
successful Eyeball design series.
The fuselage moment arms (the length from propeller to wing
aerodynamic center and from the wing’s aerodynamic center to the
stabilator pivot) were lifted from yet another popular Pattern aircraft of
the day, and the fuselage had the popular, at the time, fishlike profile.
The triangular fin and rudder had a dorsal fin that ran all the way up to
the canopy in a stylish curve, because I liked how Dennis Donohue’s El
Tigre looked. The airplane was never properly named and oh, how I
wish I had a picture of it.
It was more an exercise in styling than aerodynamics, painted in
gold and bright-red automotive lacquer. An O.S. .60 Blackhead
provided the go, a World Engines Expert-series radio made it behave,
and on the ground it sat on Rhom-Air retracts.
It flew great, as I remember, and even through the rose-colored
lenses of nostalgia for my youth, I can accurately say that it was another
10 years before I was successful in designing anything that flew better.
What is the aerodynamic center, and what does it mean?
April 2009 83
If It Flies ... Dean Pappas | [email protected]
Lift Vs. AOA for Several Different Airfoils
An airfoil’s lift increases as the AOA increases. The diagram shows the relative shape of three airfoils. The symmetrical airfoil
produces no lift at zero AOA, while the undercambered airfoil produces lift at negative AOA. The straight slope in the
diagram represents an “ideal” condition of infinite aspect ratio (or wingspan divided by wing chord). This is similar to what is
measured in a wind tunnel when the test wing touches its sides. For realistic wing planforms, the slope is somewhat less.
Very low-aspect-ratio wings show a slope roughly half that shown.
Coefficient of Lift (unitless)
AOA (degrees)
Undercambered
Semisymmetrical
Symmetrical
Find the Mean Aerodynamic Chord and CG
Straight Wing
The mean aerodynamic chord
is the chord everywhere. The
AC is 25% of the way back on
the chord line.
Any Tapered or Swept Wing,
With Straight LE and TE
The mean aerodynamic chord
splits the wing into an outer
50% of the area and an inner
50% of the area. That line is
the mean aerodynamic chord.
This simple graphic method is
described in the text. The
aerodynamic center is 25% of
the way back on the chord
line.
It Even Works on Delta
Wings
Even though the tip chord has
zero length, the same
technique works. The mean
aerodynamic chord of a
“pure” delta is one-third of
the way from root to tip.
Again, the AC is 25% of the
way back on the mean
aerodynamic chord line.
04sig3.QXD 2/24/09 2:01 PM Page 83
Fast-forward to just a few months ago,
when I was thinking back to the unnamed
red-and-gold beast. In what can only be
described as one of those serendipitous
connections, I remembered that the Warlock
construction article was published in the same
issue of AAM as the CL Stunt (Precision
Aerobatics) Sweet-Pea that my buddy,
Dennis Adamisin, designed. (AAM was the
predecessor to MA as the AMA’s house
organ.)
Surely Dennis would have an old copy of
the issue with his design in it. One enjoyable
phone call later, a scanned version of the old
article showed up in my e-mail. Thanks,
compadre.
There it was: the stabilator design that got
the ball rolling in the first place. Armed with
just a bit more understanding than I had as a
teenager, I carefully measured the stabilator
plan, reproduced it in CAD, and did the
calculations to see if the Warlock conformed
to the usual rule for stabilator pivot
placement.
Sure enough, it did; the pivot was right on
the stabilator’s Aerodynamic Center (AC).
Maybe that’s why I never had a bit of trouble
with the elevator control on the old beast,
despite the earth-moving 45 ounce-inches of
torque that the World S-4 servo provided.
The airplane eventually died, when I
forgot to extend the transmitter antenna
before takeoff. (It’s always pilot error.) I lost
control of the model immediately after doing
the prettiest 8-point roll I had ever done.
It crashed through a thicket of saplings
that strained the mechanical and radio bits
from the lighter balsa bits like water from
spaghetti in a colander. It took a lot of help
from friends to find the crash site, too.
What is the AC, and what does it mean?
That is this month’s subject, and it is a lead-in
to a discussion about why moving the CG
(also called the balance point) forward or aft
changes an airplane’s flying characteristics,
making it more or less stable.
The textbook definition is simple enough,
but, as with most technical language, very
few words say a lot. The AC of an airfoil,
moving through the air, is the point at which
the pitching moment for the airfoil does not
vary with lift coefficient or angle of attack
(AOA). Remember that “moment” is another
word for “torque.”
Let’s decipher this. Every airfoil has what
is called a zero-lift AOA. For the popular flatplate
airfoil and for symmetrical airfoils, this
zero-lift angle is the same as the chord line
for the airfoil. That makes sense, doesn’t it?
For semisymmetrical airfoils, flat-bottom
airfoils, and undercambered airfoils, the zerolift
angle happens when the chord line is at a
small nose-down angle compared to the
oncoming air. It is simple to estimate the
zero-lift angle for a large variety of airfoils,
and we will revisit this someday (probably
when I write about propeller pitch angles).
Starting from the zero-lift angle, the lift
that an airfoil produces increases as the AOA
increases. If you were to graph that change in
lift versus AOA, you would get a straight
sloping line, as in the diagram, until the AOA
becomes large enough that the airflow no
longer “sticks to” the top of the airfoil, and it
stalls and the lift dies off. I’ll limit these
discussions to the range of moderate AOA,
where the slope is basically a straight line.
When any airfoil, including a flat plate, is
driven through the air with a positive AOA,
the oncoming air stagnates and “splits” at a
point below (and maybe slightly behind) the
front of the airfoil, and the air that flows
around the top of the LE speeds up a great
deal. In fact, the fastest airflow over an airfoil
is directly behind the LE on the top side.
Remember Bernoulli? The principle says
that the air pressure on that part of the airfoil
will be the lowest, and gradually increase
toward the TE. Also, the highest pressure is
immediately behind the LE on the bottom
side, quickly decreasing as the air flows
toward the TE.
Take a moment to play with the FoilSim
Java program on the NASA (National
Aeronautics and Space Administration) Web
site. (See the “Sources” listing for the
address.) Select the “Shape/Angle” menu
button and watch the pressure distribution plot
change as you fiddle with the AOA slider.
The trick to reading the pressure profile
diagram is that the bottom line corresponds to
the pressure on the top side of the airfoil, and
the upper line, showing higher pressures,
corresponds to the bottom of the airfoil. In the
simulator, the lines are shown as yellow and
white, and it takes awhile to pick them apart.
Maybe I’m weird, but I find it more
entertaining than Guitar Hero.
Have you played with the simulator long
enough? Good.
The result of the shifting shape of this
pressure distribution is that if you can pick a
point close to one-quarter of the way back on
the chord line, something fascinating happens.
The difference between top and bottom
pressures all along the chord line, multiplied
86 MODEL AVIATION
by the lever arm away from that one-quarter
chord point, would add up to a nose-down
torque around the fulcrum at the one-quarter
chord point.
The fascinating thing is that if you pick the
one-quarter chord point as the fulcrum for this
seesaw, the torque does not change with AOA
until close to stall. It is almost natural, at this
point, to say that the wing’s lift acts upward
through this AC. This is because as you look
at changes in lift as the AOA is increased, you
don’t have to worry about changes in the
pitching torque exerted by the wing. It
simplifies the way we think about the wing’s
lifting characteristics.
This is what the definition of the AC really
means. In the case of flat plates and
symmetrical airfoils, that near-constant torque
is zero. For semisymmetrical wings, there is a
slight nose-down torque, and for flatbottomed
and undercambered wings, the
torque is even stronger.
That’s why the pivot point for the
stabilator on the Warlock was placed onequarter
of the way back on the average chord
of a symmetrical airfoil. The control forces on
the elevator servo would be at a minimum.
If you don’t think that the control forces
needed to move a model airplane’s control
surfaces could be all that large, look at “The
Great Rudder Experiment” that was
performed quite some time ago by my friends,
Ron Ellis and Mike Whaley. You can find this
excellent piece described epic-style on the
Internet. (See the “Sources” list for the
address.) I highly recommend it.
Again, for most airfoils used on our
models, the AC is right at the one-quarter
chord point; that is, one-quarter of the way
back from the LE. This is easy to figure out
with a constant-chord, or “Hershey’s-bar,”
wing. How do you figure out where it is on a
swept wing? How about tapered? What about
elliptical and other complicated wing shapes?
I’ll start on that topic, but I won’t finish it
until the next time we get together. To begin
with, instead of referring to the one-quarter
point of the wing chord, we should start
referring to one-quarter of the mean
aerodynamic chord. The word “mean” in this
instance is used in the same way as it is in
statistics; it means average, not nasty. It is hard
to prove this next statement, but here goes.
If you’re looking top-down at a wing’s
planform, as long as it has straight LEs, and
straight TEs, no matter how much sweep or
taper it has, the mean aerodynamic chord is
the line on either side of the airplane where
exactly half of the wing area lies inboard of
it and exactly half of the wing area lies
outboard.
As soon as there are “cranks” in the LEs,
as on a P-51, or in the TEs, as with a Katana,
or “steps” in the LE, as on an F-4 Phantom,
the rule does not apply. Don’t worry; next
month I will write about how to figure out
the mean aerodynamic chord and the AC for
such planforms.
This half-area inboard rule also works for
elliptical planforms such as the Spitfire’s,
even if it’s a bit difficult to figure out the
areas.
I’ll leave you with a simple graphic method
for figuring the mean aerodynamic chord for
all of those planforms that follow the
preceding.
Draw the planform accurately. You can
do the drawing scaled down if you like.
Draw a line onto the front and back of the
wingtip chord that is the same length as the
root chord. Draw a similar line onto the
front and back of the root, but make it as
long as the chord at the wingtip.
Draw two long diagonals from the
corners of these lines, and they will cross on
the mean aerodynamic chord line. Now
draw the chord line onto your drawing,
taking care to make it parallel to the root.
The AC is one-quarter of the way back from
the LE on that line. This is also a good
starting point for the CG before any test
flight.
We know where to pick up next time.
Until we get together again, have fun and
take care of yourself. MA
Sources:
FoilSim Java program:
www.grc.nasa.gov/WWW/K-12/airplane/
foil4.html
The Great Rudder Experiment:
www.mindspring.com/~rellis2/rcpattrn/
rudder.htm
Edition: Model Aviation - 2009/04
Page Numbers: 83,84,86
Edition: Model Aviation - 2009/04
Page Numbers: 83,84,86
BACK WHEN I
was maybe 17 years
old, there was a
construction article
in the old American
Aircraft Modeler
(AAM) magazine for
an RC Aerobatics
(Pattern) model
called the
“Warlock.” Hello
out there, Jim
Wilmot. If you are
reading this, it may
please you to know
that your novel
design and amusing
article are
remembered.
It was a radical
design (even today
the Warlock would
be viewed as
radical), with
tandem retractable
landing gear and
wing outriggers, as on a U-2 spyplane; aggressive angular lines; and,
most intriguingly to me, an all-flying horizontal tail or stabilator.
This was cool, not only because all of the latest supersonic fighter
jets were being designed with all-flying tails, but also because all the
talk I’d ever heard at the local flying field about stabilators was that
they were tricky. Put the pivot in the wrong spot, and they would either
flutter off the airplane at speed or overload the servo and cause a crash.
Wonder of wonders, here were shrunk-down plans in the magazine
that showed a working stabilator design, complete with the correct pivot
tube location and construction details. I would appropriate this design
element and use it in an airplane I had been contemplating for a while.
The wing was swept an inch or 2 at the TE (please forgive the fuzzy
memory), with a tip chord something near 70% of the root chord, and
the symmetric airfoil was borrowed from the late Pappy deBolt’s Live
Wire Sonic Cruiser design.
My dad had built and flown the daylights out of one of these when I
was 8 or 9 years old. After its demise, I had made a CL flying wing
from the surviving outer one-third of both wing panels. It flew pretty
well as I remember. The airfoil was an NACA 64012, and further
homage had been paid to Pappy when Art Schroeder (long-time editor
of Model Airplane News magazine) used it in his popular and
successful Eyeball design series.
The fuselage moment arms (the length from propeller to wing
aerodynamic center and from the wing’s aerodynamic center to the
stabilator pivot) were lifted from yet another popular Pattern aircraft of
the day, and the fuselage had the popular, at the time, fishlike profile.
The triangular fin and rudder had a dorsal fin that ran all the way up to
the canopy in a stylish curve, because I liked how Dennis Donohue’s El
Tigre looked. The airplane was never properly named and oh, how I
wish I had a picture of it.
It was more an exercise in styling than aerodynamics, painted in
gold and bright-red automotive lacquer. An O.S. .60 Blackhead
provided the go, a World Engines Expert-series radio made it behave,
and on the ground it sat on Rhom-Air retracts.
It flew great, as I remember, and even through the rose-colored
lenses of nostalgia for my youth, I can accurately say that it was another
10 years before I was successful in designing anything that flew better.
What is the aerodynamic center, and what does it mean?
April 2009 83
If It Flies ... Dean Pappas | [email protected]
Lift Vs. AOA for Several Different Airfoils
An airfoil’s lift increases as the AOA increases. The diagram shows the relative shape of three airfoils. The symmetrical airfoil
produces no lift at zero AOA, while the undercambered airfoil produces lift at negative AOA. The straight slope in the
diagram represents an “ideal” condition of infinite aspect ratio (or wingspan divided by wing chord). This is similar to what is
measured in a wind tunnel when the test wing touches its sides. For realistic wing planforms, the slope is somewhat less.
Very low-aspect-ratio wings show a slope roughly half that shown.
Coefficient of Lift (unitless)
AOA (degrees)
Undercambered
Semisymmetrical
Symmetrical
Find the Mean Aerodynamic Chord and CG
Straight Wing
The mean aerodynamic chord
is the chord everywhere. The
AC is 25% of the way back on
the chord line.
Any Tapered or Swept Wing,
With Straight LE and TE
The mean aerodynamic chord
splits the wing into an outer
50% of the area and an inner
50% of the area. That line is
the mean aerodynamic chord.
This simple graphic method is
described in the text. The
aerodynamic center is 25% of
the way back on the chord
line.
It Even Works on Delta
Wings
Even though the tip chord has
zero length, the same
technique works. The mean
aerodynamic chord of a
“pure” delta is one-third of
the way from root to tip.
Again, the AC is 25% of the
way back on the mean
aerodynamic chord line.
04sig3.QXD 2/24/09 2:01 PM Page 83
Fast-forward to just a few months ago,
when I was thinking back to the unnamed
red-and-gold beast. In what can only be
described as one of those serendipitous
connections, I remembered that the Warlock
construction article was published in the same
issue of AAM as the CL Stunt (Precision
Aerobatics) Sweet-Pea that my buddy,
Dennis Adamisin, designed. (AAM was the
predecessor to MA as the AMA’s house
organ.)
Surely Dennis would have an old copy of
the issue with his design in it. One enjoyable
phone call later, a scanned version of the old
article showed up in my e-mail. Thanks,
compadre.
There it was: the stabilator design that got
the ball rolling in the first place. Armed with
just a bit more understanding than I had as a
teenager, I carefully measured the stabilator
plan, reproduced it in CAD, and did the
calculations to see if the Warlock conformed
to the usual rule for stabilator pivot
placement.
Sure enough, it did; the pivot was right on
the stabilator’s Aerodynamic Center (AC).
Maybe that’s why I never had a bit of trouble
with the elevator control on the old beast,
despite the earth-moving 45 ounce-inches of
torque that the World S-4 servo provided.
The airplane eventually died, when I
forgot to extend the transmitter antenna
before takeoff. (It’s always pilot error.) I lost
control of the model immediately after doing
the prettiest 8-point roll I had ever done.
It crashed through a thicket of saplings
that strained the mechanical and radio bits
from the lighter balsa bits like water from
spaghetti in a colander. It took a lot of help
from friends to find the crash site, too.
What is the AC, and what does it mean?
That is this month’s subject, and it is a lead-in
to a discussion about why moving the CG
(also called the balance point) forward or aft
changes an airplane’s flying characteristics,
making it more or less stable.
The textbook definition is simple enough,
but, as with most technical language, very
few words say a lot. The AC of an airfoil,
moving through the air, is the point at which
the pitching moment for the airfoil does not
vary with lift coefficient or angle of attack
(AOA). Remember that “moment” is another
word for “torque.”
Let’s decipher this. Every airfoil has what
is called a zero-lift AOA. For the popular flatplate
airfoil and for symmetrical airfoils, this
zero-lift angle is the same as the chord line
for the airfoil. That makes sense, doesn’t it?
For semisymmetrical airfoils, flat-bottom
airfoils, and undercambered airfoils, the zerolift
angle happens when the chord line is at a
small nose-down angle compared to the
oncoming air. It is simple to estimate the
zero-lift angle for a large variety of airfoils,
and we will revisit this someday (probably
when I write about propeller pitch angles).
Starting from the zero-lift angle, the lift
that an airfoil produces increases as the AOA
increases. If you were to graph that change in
lift versus AOA, you would get a straight
sloping line, as in the diagram, until the AOA
becomes large enough that the airflow no
longer “sticks to” the top of the airfoil, and it
stalls and the lift dies off. I’ll limit these
discussions to the range of moderate AOA,
where the slope is basically a straight line.
When any airfoil, including a flat plate, is
driven through the air with a positive AOA,
the oncoming air stagnates and “splits” at a
point below (and maybe slightly behind) the
front of the airfoil, and the air that flows
around the top of the LE speeds up a great
deal. In fact, the fastest airflow over an airfoil
is directly behind the LE on the top side.
Remember Bernoulli? The principle says
that the air pressure on that part of the airfoil
will be the lowest, and gradually increase
toward the TE. Also, the highest pressure is
immediately behind the LE on the bottom
side, quickly decreasing as the air flows
toward the TE.
Take a moment to play with the FoilSim
Java program on the NASA (National
Aeronautics and Space Administration) Web
site. (See the “Sources” listing for the
address.) Select the “Shape/Angle” menu
button and watch the pressure distribution plot
change as you fiddle with the AOA slider.
The trick to reading the pressure profile
diagram is that the bottom line corresponds to
the pressure on the top side of the airfoil, and
the upper line, showing higher pressures,
corresponds to the bottom of the airfoil. In the
simulator, the lines are shown as yellow and
white, and it takes awhile to pick them apart.
Maybe I’m weird, but I find it more
entertaining than Guitar Hero.
Have you played with the simulator long
enough? Good.
The result of the shifting shape of this
pressure distribution is that if you can pick a
point close to one-quarter of the way back on
the chord line, something fascinating happens.
The difference between top and bottom
pressures all along the chord line, multiplied
86 MODEL AVIATION
by the lever arm away from that one-quarter
chord point, would add up to a nose-down
torque around the fulcrum at the one-quarter
chord point.
The fascinating thing is that if you pick the
one-quarter chord point as the fulcrum for this
seesaw, the torque does not change with AOA
until close to stall. It is almost natural, at this
point, to say that the wing’s lift acts upward
through this AC. This is because as you look
at changes in lift as the AOA is increased, you
don’t have to worry about changes in the
pitching torque exerted by the wing. It
simplifies the way we think about the wing’s
lifting characteristics.
This is what the definition of the AC really
means. In the case of flat plates and
symmetrical airfoils, that near-constant torque
is zero. For semisymmetrical wings, there is a
slight nose-down torque, and for flatbottomed
and undercambered wings, the
torque is even stronger.
That’s why the pivot point for the
stabilator on the Warlock was placed onequarter
of the way back on the average chord
of a symmetrical airfoil. The control forces on
the elevator servo would be at a minimum.
If you don’t think that the control forces
needed to move a model airplane’s control
surfaces could be all that large, look at “The
Great Rudder Experiment” that was
performed quite some time ago by my friends,
Ron Ellis and Mike Whaley. You can find this
excellent piece described epic-style on the
Internet. (See the “Sources” list for the
address.) I highly recommend it.
Again, for most airfoils used on our
models, the AC is right at the one-quarter
chord point; that is, one-quarter of the way
back from the LE. This is easy to figure out
with a constant-chord, or “Hershey’s-bar,”
wing. How do you figure out where it is on a
swept wing? How about tapered? What about
elliptical and other complicated wing shapes?
I’ll start on that topic, but I won’t finish it
until the next time we get together. To begin
with, instead of referring to the one-quarter
point of the wing chord, we should start
referring to one-quarter of the mean
aerodynamic chord. The word “mean” in this
instance is used in the same way as it is in
statistics; it means average, not nasty. It is hard
to prove this next statement, but here goes.
If you’re looking top-down at a wing’s
planform, as long as it has straight LEs, and
straight TEs, no matter how much sweep or
taper it has, the mean aerodynamic chord is
the line on either side of the airplane where
exactly half of the wing area lies inboard of
it and exactly half of the wing area lies
outboard.
As soon as there are “cranks” in the LEs,
as on a P-51, or in the TEs, as with a Katana,
or “steps” in the LE, as on an F-4 Phantom,
the rule does not apply. Don’t worry; next
month I will write about how to figure out
the mean aerodynamic chord and the AC for
such planforms.
This half-area inboard rule also works for
elliptical planforms such as the Spitfire’s,
even if it’s a bit difficult to figure out the
areas.
I’ll leave you with a simple graphic method
for figuring the mean aerodynamic chord for
all of those planforms that follow the
preceding.
Draw the planform accurately. You can
do the drawing scaled down if you like.
Draw a line onto the front and back of the
wingtip chord that is the same length as the
root chord. Draw a similar line onto the
front and back of the root, but make it as
long as the chord at the wingtip.
Draw two long diagonals from the
corners of these lines, and they will cross on
the mean aerodynamic chord line. Now
draw the chord line onto your drawing,
taking care to make it parallel to the root.
The AC is one-quarter of the way back from
the LE on that line. This is also a good
starting point for the CG before any test
flight.
We know where to pick up next time.
Until we get together again, have fun and
take care of yourself. MA
Sources:
FoilSim Java program:
www.grc.nasa.gov/WWW/K-12/airplane/
foil4.html
The Great Rudder Experiment:
www.mindspring.com/~rellis2/rcpattrn/
rudder.htm
Edition: Model Aviation - 2009/04
Page Numbers: 83,84,86
BACK WHEN I
was maybe 17 years
old, there was a
construction article
in the old American
Aircraft Modeler
(AAM) magazine for
an RC Aerobatics
(Pattern) model
called the
“Warlock.” Hello
out there, Jim
Wilmot. If you are
reading this, it may
please you to know
that your novel
design and amusing
article are
remembered.
It was a radical
design (even today
the Warlock would
be viewed as
radical), with
tandem retractable
landing gear and
wing outriggers, as on a U-2 spyplane; aggressive angular lines; and,
most intriguingly to me, an all-flying horizontal tail or stabilator.
This was cool, not only because all of the latest supersonic fighter
jets were being designed with all-flying tails, but also because all the
talk I’d ever heard at the local flying field about stabilators was that
they were tricky. Put the pivot in the wrong spot, and they would either
flutter off the airplane at speed or overload the servo and cause a crash.
Wonder of wonders, here were shrunk-down plans in the magazine
that showed a working stabilator design, complete with the correct pivot
tube location and construction details. I would appropriate this design
element and use it in an airplane I had been contemplating for a while.
The wing was swept an inch or 2 at the TE (please forgive the fuzzy
memory), with a tip chord something near 70% of the root chord, and
the symmetric airfoil was borrowed from the late Pappy deBolt’s Live
Wire Sonic Cruiser design.
My dad had built and flown the daylights out of one of these when I
was 8 or 9 years old. After its demise, I had made a CL flying wing
from the surviving outer one-third of both wing panels. It flew pretty
well as I remember. The airfoil was an NACA 64012, and further
homage had been paid to Pappy when Art Schroeder (long-time editor
of Model Airplane News magazine) used it in his popular and
successful Eyeball design series.
The fuselage moment arms (the length from propeller to wing
aerodynamic center and from the wing’s aerodynamic center to the
stabilator pivot) were lifted from yet another popular Pattern aircraft of
the day, and the fuselage had the popular, at the time, fishlike profile.
The triangular fin and rudder had a dorsal fin that ran all the way up to
the canopy in a stylish curve, because I liked how Dennis Donohue’s El
Tigre looked. The airplane was never properly named and oh, how I
wish I had a picture of it.
It was more an exercise in styling than aerodynamics, painted in
gold and bright-red automotive lacquer. An O.S. .60 Blackhead
provided the go, a World Engines Expert-series radio made it behave,
and on the ground it sat on Rhom-Air retracts.
It flew great, as I remember, and even through the rose-colored
lenses of nostalgia for my youth, I can accurately say that it was another
10 years before I was successful in designing anything that flew better.
What is the aerodynamic center, and what does it mean?
April 2009 83
If It Flies ... Dean Pappas | [email protected]
Lift Vs. AOA for Several Different Airfoils
An airfoil’s lift increases as the AOA increases. The diagram shows the relative shape of three airfoils. The symmetrical airfoil
produces no lift at zero AOA, while the undercambered airfoil produces lift at negative AOA. The straight slope in the
diagram represents an “ideal” condition of infinite aspect ratio (or wingspan divided by wing chord). This is similar to what is
measured in a wind tunnel when the test wing touches its sides. For realistic wing planforms, the slope is somewhat less.
Very low-aspect-ratio wings show a slope roughly half that shown.
Coefficient of Lift (unitless)
AOA (degrees)
Undercambered
Semisymmetrical
Symmetrical
Find the Mean Aerodynamic Chord and CG
Straight Wing
The mean aerodynamic chord
is the chord everywhere. The
AC is 25% of the way back on
the chord line.
Any Tapered or Swept Wing,
With Straight LE and TE
The mean aerodynamic chord
splits the wing into an outer
50% of the area and an inner
50% of the area. That line is
the mean aerodynamic chord.
This simple graphic method is
described in the text. The
aerodynamic center is 25% of
the way back on the chord
line.
It Even Works on Delta
Wings
Even though the tip chord has
zero length, the same
technique works. The mean
aerodynamic chord of a
“pure” delta is one-third of
the way from root to tip.
Again, the AC is 25% of the
way back on the mean
aerodynamic chord line.
04sig3.QXD 2/24/09 2:01 PM Page 83
Fast-forward to just a few months ago,
when I was thinking back to the unnamed
red-and-gold beast. In what can only be
described as one of those serendipitous
connections, I remembered that the Warlock
construction article was published in the same
issue of AAM as the CL Stunt (Precision
Aerobatics) Sweet-Pea that my buddy,
Dennis Adamisin, designed. (AAM was the
predecessor to MA as the AMA’s house
organ.)
Surely Dennis would have an old copy of
the issue with his design in it. One enjoyable
phone call later, a scanned version of the old
article showed up in my e-mail. Thanks,
compadre.
There it was: the stabilator design that got
the ball rolling in the first place. Armed with
just a bit more understanding than I had as a
teenager, I carefully measured the stabilator
plan, reproduced it in CAD, and did the
calculations to see if the Warlock conformed
to the usual rule for stabilator pivot
placement.
Sure enough, it did; the pivot was right on
the stabilator’s Aerodynamic Center (AC).
Maybe that’s why I never had a bit of trouble
with the elevator control on the old beast,
despite the earth-moving 45 ounce-inches of
torque that the World S-4 servo provided.
The airplane eventually died, when I
forgot to extend the transmitter antenna
before takeoff. (It’s always pilot error.) I lost
control of the model immediately after doing
the prettiest 8-point roll I had ever done.
It crashed through a thicket of saplings
that strained the mechanical and radio bits
from the lighter balsa bits like water from
spaghetti in a colander. It took a lot of help
from friends to find the crash site, too.
What is the AC, and what does it mean?
That is this month’s subject, and it is a lead-in
to a discussion about why moving the CG
(also called the balance point) forward or aft
changes an airplane’s flying characteristics,
making it more or less stable.
The textbook definition is simple enough,
but, as with most technical language, very
few words say a lot. The AC of an airfoil,
moving through the air, is the point at which
the pitching moment for the airfoil does not
vary with lift coefficient or angle of attack
(AOA). Remember that “moment” is another
word for “torque.”
Let’s decipher this. Every airfoil has what
is called a zero-lift AOA. For the popular flatplate
airfoil and for symmetrical airfoils, this
zero-lift angle is the same as the chord line
for the airfoil. That makes sense, doesn’t it?
For semisymmetrical airfoils, flat-bottom
airfoils, and undercambered airfoils, the zerolift
angle happens when the chord line is at a
small nose-down angle compared to the
oncoming air. It is simple to estimate the
zero-lift angle for a large variety of airfoils,
and we will revisit this someday (probably
when I write about propeller pitch angles).
Starting from the zero-lift angle, the lift
that an airfoil produces increases as the AOA
increases. If you were to graph that change in
lift versus AOA, you would get a straight
sloping line, as in the diagram, until the AOA
becomes large enough that the airflow no
longer “sticks to” the top of the airfoil, and it
stalls and the lift dies off. I’ll limit these
discussions to the range of moderate AOA,
where the slope is basically a straight line.
When any airfoil, including a flat plate, is
driven through the air with a positive AOA,
the oncoming air stagnates and “splits” at a
point below (and maybe slightly behind) the
front of the airfoil, and the air that flows
around the top of the LE speeds up a great
deal. In fact, the fastest airflow over an airfoil
is directly behind the LE on the top side.
Remember Bernoulli? The principle says
that the air pressure on that part of the airfoil
will be the lowest, and gradually increase
toward the TE. Also, the highest pressure is
immediately behind the LE on the bottom
side, quickly decreasing as the air flows
toward the TE.
Take a moment to play with the FoilSim
Java program on the NASA (National
Aeronautics and Space Administration) Web
site. (See the “Sources” listing for the
address.) Select the “Shape/Angle” menu
button and watch the pressure distribution plot
change as you fiddle with the AOA slider.
The trick to reading the pressure profile
diagram is that the bottom line corresponds to
the pressure on the top side of the airfoil, and
the upper line, showing higher pressures,
corresponds to the bottom of the airfoil. In the
simulator, the lines are shown as yellow and
white, and it takes awhile to pick them apart.
Maybe I’m weird, but I find it more
entertaining than Guitar Hero.
Have you played with the simulator long
enough? Good.
The result of the shifting shape of this
pressure distribution is that if you can pick a
point close to one-quarter of the way back on
the chord line, something fascinating happens.
The difference between top and bottom
pressures all along the chord line, multiplied
86 MODEL AVIATION
by the lever arm away from that one-quarter
chord point, would add up to a nose-down
torque around the fulcrum at the one-quarter
chord point.
The fascinating thing is that if you pick the
one-quarter chord point as the fulcrum for this
seesaw, the torque does not change with AOA
until close to stall. It is almost natural, at this
point, to say that the wing’s lift acts upward
through this AC. This is because as you look
at changes in lift as the AOA is increased, you
don’t have to worry about changes in the
pitching torque exerted by the wing. It
simplifies the way we think about the wing’s
lifting characteristics.
This is what the definition of the AC really
means. In the case of flat plates and
symmetrical airfoils, that near-constant torque
is zero. For semisymmetrical wings, there is a
slight nose-down torque, and for flatbottomed
and undercambered wings, the
torque is even stronger.
That’s why the pivot point for the
stabilator on the Warlock was placed onequarter
of the way back on the average chord
of a symmetrical airfoil. The control forces on
the elevator servo would be at a minimum.
If you don’t think that the control forces
needed to move a model airplane’s control
surfaces could be all that large, look at “The
Great Rudder Experiment” that was
performed quite some time ago by my friends,
Ron Ellis and Mike Whaley. You can find this
excellent piece described epic-style on the
Internet. (See the “Sources” list for the
address.) I highly recommend it.
Again, for most airfoils used on our
models, the AC is right at the one-quarter
chord point; that is, one-quarter of the way
back from the LE. This is easy to figure out
with a constant-chord, or “Hershey’s-bar,”
wing. How do you figure out where it is on a
swept wing? How about tapered? What about
elliptical and other complicated wing shapes?
I’ll start on that topic, but I won’t finish it
until the next time we get together. To begin
with, instead of referring to the one-quarter
point of the wing chord, we should start
referring to one-quarter of the mean
aerodynamic chord. The word “mean” in this
instance is used in the same way as it is in
statistics; it means average, not nasty. It is hard
to prove this next statement, but here goes.
If you’re looking top-down at a wing’s
planform, as long as it has straight LEs, and
straight TEs, no matter how much sweep or
taper it has, the mean aerodynamic chord is
the line on either side of the airplane where
exactly half of the wing area lies inboard of
it and exactly half of the wing area lies
outboard.
As soon as there are “cranks” in the LEs,
as on a P-51, or in the TEs, as with a Katana,
or “steps” in the LE, as on an F-4 Phantom,
the rule does not apply. Don’t worry; next
month I will write about how to figure out
the mean aerodynamic chord and the AC for
such planforms.
This half-area inboard rule also works for
elliptical planforms such as the Spitfire’s,
even if it’s a bit difficult to figure out the
areas.
I’ll leave you with a simple graphic method
for figuring the mean aerodynamic chord for
all of those planforms that follow the
preceding.
Draw the planform accurately. You can
do the drawing scaled down if you like.
Draw a line onto the front and back of the
wingtip chord that is the same length as the
root chord. Draw a similar line onto the
front and back of the root, but make it as
long as the chord at the wingtip.
Draw two long diagonals from the
corners of these lines, and they will cross on
the mean aerodynamic chord line. Now
draw the chord line onto your drawing,
taking care to make it parallel to the root.
The AC is one-quarter of the way back from
the LE on that line. This is also a good
starting point for the CG before any test
flight.
We know where to pick up next time.
Until we get together again, have fun and
take care of yourself. MA
Sources:
FoilSim Java program:
www.grc.nasa.gov/WWW/K-12/airplane/
foil4.html
The Great Rudder Experiment:
www.mindspring.com/~rellis2/rcpattrn/
rudder.htm