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Fundamentals of Stability - 2004/08

Author: Dave Harding


Edition: Model Aviation - 2004/08
Page Numbers: 36,37,38,39,40

“YOU SHOULD USE a ‘flat-bottomed’
airfoil on a trainer because it is more
stable.”
How many times have you read that
often-quoted statement? Well, as is so much
folklore, it is untrue, and I will explain why
and what does make a stable model (or fullscale
airplane).
To begin with, I have to square away a few
terms. I should first explain what we mean
when we say an airplane is “stable.”
Second, we should add “about ... axis,”
because an airplane is free to rotate and
move in all three directions and rotations.
See Figure 1.
We call something “stable” when it
returns to its original state following a
disturbance. When something is “unstable,”
it continues to diverge from its original state
when it’s disturbed. “Neutrally stable” items
simply stay in the disturbed condition. See
Figure 2.
The axis of primary concern to us is the
“pitch” axis. If you don’t get this right you
won’t get a chance to find out about the
others, so I’ll examine the forces involved.
See Figure 3. However, before I launch into
stability, I have one more concept to add
which you will likely understand: trim.
Trim involves balancing the forces so
the airplane does not climb or dive at the
chosen speed. So examining the forces
depicted in Figure 3, trim requires that the
sum of the lift forces—wing and tail—equal
the weight, and the sum of their moments is
zero. The latter means that the airplane will
not pitch up or down.
The sum of the moments is what we do
on a teeter-totter; the force multiplied by the
moment arm, or distance, must equal the
other forces multiplied by their moment
arms. You can do this calculation about any
point as a fulcrum—the nose, the CG, or
36 MODEL AVIATION
of STABILITY
Fundamentals by Dave Harding
Figure 1
Figure 2
Figure 3
Drawings by the author
even the tail if you want. I’ll use the CG.
When we fly our (stable) airplanes, we
adjust the elevator such that we balance
these forces by watching the pitch motion
and rate of climb. The airplane is considered
“in trim” when it holds level flight at the
chosen speed.
What actually happens when we move
the elevator is that the lift changes on the
stabilizer such that the airplane pitching
08sig2.QXD 5/24/04 8:43 am Page 36
moment changes. This, in turn, causes the
airplane to pitch or rotate nose-up or nosedown
until the desired balance is achieved.
Airplane stability is not theoretically a
necessary condition to achieve such trim or
balance, although in practice it is. You can
balance a pin, but it is difficult. See Figure
4.
Let’s examine the pitch stability. Our
airplane is said to be stable if, following a
pitch disturbance, it returns to its original
attitude. The upset from trim can be from
any cause, but let’s consider the effects from
a gust-induced pitch up. See Figure 5.
In the situation shown, the airplane is
stable if the additional moments caused by
wing- and tail-lift changes cause the airplane
to pitch back down. You can see in Figure 5
that if the CG is ahead of the wing center of
lift (more about this later), the airplane is
stable regardless of tail area, tail moment
arm, or wing section; the wing will produce
more lift with more pitch as long as it is not
stalled.
But CG ahead of the wing-lift center is
not a necessary condition for a stable
airplane. Consider the case where the CG is
behind the wing center of lift, or
aerodynamic center. See Figure 6. In this
case, the unstable moment from the wing
(acting in the direction to increase the pitch
upset) must be counteracted by the
stabilizing effect of the tail-lift increase.
In a simple world, we might assume that
a square inch of wing and tail would
produce the same increment of lift for an
incremental change in pitch. Then we could
calculate the size of tail required to balance
the destabilizing effect of the wing.
The condition would be for the wing area
multiplied by the distance ahead of the CG
to equal the tail area multiplied by the tail
distance from the CG. This is known as the
“neutral point,” and is indeed a fundamental
element of real airplane design definition.
See Figure 7.
In this simple model, the neutral point is
a distance aft of the wing aerodynamic
center “a,” where AT divided by AW is the
ratio of the tail-to-wing area. The distance
“a” is expressed as a percentage of mean
wing chord. See Figure 8.
However, the real world is more
complicated than that, and wings and tails
do not produce lift as a pure function of
their area. The rate at which a wing
produces lift with changes in angle of attack
varies with aspect ratio. A low-aspect-ratio
wing builds lift more slowly than a highaspect-
ratio wing. (This is one of the
noticeable aspects of delta-wing flight.) All
wing sections produce roughly the same
amount of lift per increment of pitch. There
is no difference in “flat-bottom” and
“symmetrical” sections.
The aspect-ratio factor also applies to the
tail, which experiences two additional
modifiers involving the fact that the tail
operates in the wake of the wing. The first,
and usually most powerful, effect is that the
wing, in producing lift, generates a
downwash. This downwash is proportional
to the lift on the wing, so as the wing
increases in angle of attack, the downwash
angle increases. This is “seen” by the tail as
a reduction in effective angle of attack; it
could be as much as 75% reduction.
The second effect is that the tail
operating in the wake of the wing
experiences a loss of dynamic pressure.
(The airflow is not as strong as free stream.)
On airplanes with high-drag fuselages, this
loss can be as much as 50%. So high T-tails
operating above the downwash and wake are
much more effective than low tails in the
wake of fuselage excrescences.
August 2004 37
Figure 4
Figure 5
Figure 6
Figure 8
08sig2.QXD 5/24/04 8:43 am Page 37
Tails usually have lower aspect ratios
than wings, further reducing the tail
effectiveness. This reduction must be
accounted for in calculating the neutral
point. It can be considered an effective
reduction in area. Of course, in a
comprehensive calculation of neutral point,
you must also consider the fuselage and all
other wetted surfaces and features. See
Figure 9.
All these factors mean that calculating
the neutral point is quite difficult, but never
mind; we deal with this by fudging! Let’s
try it with an example.
Tail area is 25% of wing area, but it is
low—lower aspect ratio than the wing and
behind the blunt fuselage and landing gear.
Let’s assume its effectiveness is 50%, so the
effective tail area is .5 x .25 = .125.
So, AT/AW effective = .125.
Tail moment is four wing chords, so LT/c
= 4.
From the equation aerodynamic center,
or AC, = (4 x .125 / 1 + .125) x 100.
Or AC = (.5/1.25) x 100.
So, AC = 40% of Mean Aerodynamic
Chord (MAC).
If we had not decremented the tail
effectiveness, we would have calculated the
neutral point at 80% chord!
We never design and test airplanes with
the CG on the calculated neutral point.
Experience shows that various levels of
positive stability are achieved by
positioning the CG within specific ranges
ahead of the estimated neutral point. The
typical range is from 5% to 25%, so a good
38 MODEL AVIATION
Figure 7
Figure 9
Figure 10
Phugoid
08sig2.QXD 5/24/04 8:43 am Page 38
starting point might be 15%. If we apply this
to the preceding example, we would start
with the CG at 25% chord. Wow, that’s
scary! It might even be right!
At this point we have to ask what level of
stability we want and what the associated
effects are. There are various answers,
depending on application, and it is a
fundamental that stability and control must
be in harmony. High stability means more
difficult to control.
The fundamental relationships involved
with longitudinal stability are a coupling
between pitch attitude, lift, flight path, and
speed. An upset in pitch causes the stable
airplane to climb and lose speed, whereupon
it pitches down and gains speed until it
pitches up and repeats the process. This
motion is known as a “phugoid.” The
motion can be quite severe in airplanes with
high stability, although it damps out quickly
with good design. See Figure 10.
The other behavior of high longitudinal
stability is the strong coupling between
speed and pitch trim. This is because with
high stability there is a larger offset between
August 2004 39
Figure 11
Figure 12
The Longitudinal Stability Dive Test
Setup of a Trainer With Various Airfoils
08sig2.QXD 5/24/04 9:36 am Page 39
the CG, where the airplane weight acts, and
the neutral point, where the aerodynamic
forces act. As speed increases, the
aerodynamic forces increase but the weight
does not. This requires a large aerodynamic
trim change to rebalance.
To fly a straight flight profile with large
speed variation, you must input large pitchtrim
control inputs that are well coordinated
with speed. This is undesirable in an
aerobatic airplane where you really want to
point it and have it stay pointed without
further input. This is no problem for a
trainer, where you want the airplane to
overcome the inadvertent upset by the novice
pilot.
Sailplanes are designed to have the most
efficient aerodynamics; this means the
lowest drag. If we examine the effects of
greater stability, it involves reduced lift on
the tail or, frequently, a down force which
counteracts the primary wing lift. The wing
must lift more, and this means more drag
too. This is known as trim drag.
High-performance sailplanes have small
tails and aft CG locations to minimize this
trim drag while exhibiting the minimum
stability necessary to achieve controlled
flight. Indeed, there is a widely discussed—
but perhaps not so widely practiced—flighttrimming
technique known as the “dive test.”
The process is to take the airplane to
altitude, put it in a dive, and then let go of
the stick. If the glider pulls out strongly, the
CG is too far forward or the airplane is too
stable. You then move the CG aft and repeat
the test.
At some point when you put the airplane
in the dive, it will pitch down and steepen
the dive without further input. If you can
save it, you have controlled an unstable
airplane, and I am sure there is some kind of
award for that (in addition to getting your
airplane back). See Figure 11. Actually, this
is not too unlike the maneuvers that are
performed in the certification of full-scale
airplanes.
The Lockheed L-1011 airliner was
retrofitted with a fuel tank built into the
horizontal tail. It is empty on takeoff and
landing, but fuel is pumped into it in cruise
flight so that the CG is moved aft and the
trim drag is reduced. This had a significant
effect in reduced fuel consumption. Pumping
the fuel back forward allowed for the
increased stability necessary at low-altitude
flight in turbulence and in landing.
So how much stability should you
provide, or where should you start with the
CG location?
In practice, the stability margin—
expressed as the distance between the CG
and the neutral point—is 5% to 25% of the
MAC, with trainers and sport/Scale airplanes
favoring the forward location and aerobats
and gliders favoring the aft. But beware; the
actual calculation with the full suit of effects
is complicated and a minefield in which
mistakes can be made. For instance, the
calculation of the MAC and AC of complex
wing shapes can be tricky, so start
conservatively and move toward the “dive
test.”
Notice that the effects of specific wing
airfoils (and tail airfoils, if it comes to that)
do not feature markedly here. You have
probably even forgotten that I already stated
that the airfoil has little or no effect on
longitudinal stability.
Let’s examine this a bit more. In defining
the stability model, we assumed that the AC
of the wing and tail do not move over the
pitch range of interest. This is generally true
because most airfoils operating in the
Reynolds number region of our RC models
do produce their aerodynamic forces at a
relatively fixed location: the quarter chord.
Some airfoils—actually, cambered ones
(say flat-bottomed or semisymmetrical if you
will)—do have a small change in this
40 MODEL AVIATION
location, which results in a pitch up with
increased angle of attack. This means
slightly destabilizing!
Symmetrical NACA airfoils have
practically no pitching moment with angle of
attack. That is the primary reason why the
airfoil of choice in most early helicopters
was the symmetrical NACA 0012. The early
helicopters had mechanical controls, and the
pilot would have to physically hold the
controls against the blade control forces.
The advent of hydraulically boosted
controls and the aerodynamic efficiency
advantages of cambered airfoils meant that
the later helicopters no longer used the 0012.
But I digress.
Flat-Bottomed Airfoils for Trainers? So
why is it said that you must use a “flatbottomed”
airfoil on a trainer?
Although they are no more stable than
symmetrical airfoils, they do have a higher
lift capability, so they allow for lower takeoff
and landing speed, or more maneuver margin
to accommodate inadvertent control inputs or
recovery from poor flight-path control.
Another factor is in setting up the initial
trim condition. Extremely stable airplanes
have downward lifting empennages while
the wing lifts upward. To satisfy this
condition, the decalage—the difference
between the wing and tail incidence—has to
be large. (See Figure 12.)
The wing must have, say, +4°, and the
tail must have 0° to –3°. If we build the
conventional “trainer” fuselage with a flat
top and bottom and then use a flat-bottomed
airfoil and a low-slab tail, we automatically
have 4° of decalage. This is because the
zero-lift line on the flat-bottomed airfoil,
such as the Clark Y, is at roughly +4°. A nobrainer!
On the other hand, if we want to use a
symmetrical airfoil, we must make a more
complicated upper fuselage to mount the
wing accommodating the lower surface
curvature and the necessary 4° of real
incidence. Much harder! Yeah, right!
Could it really be this simple? Tell me if
you know the right answer—please! MA
Dave Harding
4948 Jefferson Dr.
Brookhaven PA 19015
BRODAK
Brodak
Manufacturing &
Distributing Co., Inc.
The largest supplier of control-line airplanes
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E-Mail: [email protected] • Web Site: www.brodak.com
08sig2.QXD 5/24/04 8:43 am Page 40

Author: Dave Harding


Edition: Model Aviation - 2004/08
Page Numbers: 36,37,38,39,40

“YOU SHOULD USE a ‘flat-bottomed’
airfoil on a trainer because it is more
stable.”
How many times have you read that
often-quoted statement? Well, as is so much
folklore, it is untrue, and I will explain why
and what does make a stable model (or fullscale
airplane).
To begin with, I have to square away a few
terms. I should first explain what we mean
when we say an airplane is “stable.”
Second, we should add “about ... axis,”
because an airplane is free to rotate and
move in all three directions and rotations.
See Figure 1.
We call something “stable” when it
returns to its original state following a
disturbance. When something is “unstable,”
it continues to diverge from its original state
when it’s disturbed. “Neutrally stable” items
simply stay in the disturbed condition. See
Figure 2.
The axis of primary concern to us is the
“pitch” axis. If you don’t get this right you
won’t get a chance to find out about the
others, so I’ll examine the forces involved.
See Figure 3. However, before I launch into
stability, I have one more concept to add
which you will likely understand: trim.
Trim involves balancing the forces so
the airplane does not climb or dive at the
chosen speed. So examining the forces
depicted in Figure 3, trim requires that the
sum of the lift forces—wing and tail—equal
the weight, and the sum of their moments is
zero. The latter means that the airplane will
not pitch up or down.
The sum of the moments is what we do
on a teeter-totter; the force multiplied by the
moment arm, or distance, must equal the
other forces multiplied by their moment
arms. You can do this calculation about any
point as a fulcrum—the nose, the CG, or
36 MODEL AVIATION
of STABILITY
Fundamentals by Dave Harding
Figure 1
Figure 2
Figure 3
Drawings by the author
even the tail if you want. I’ll use the CG.
When we fly our (stable) airplanes, we
adjust the elevator such that we balance
these forces by watching the pitch motion
and rate of climb. The airplane is considered
“in trim” when it holds level flight at the
chosen speed.
What actually happens when we move
the elevator is that the lift changes on the
stabilizer such that the airplane pitching
08sig2.QXD 5/24/04 8:43 am Page 36
moment changes. This, in turn, causes the
airplane to pitch or rotate nose-up or nosedown
until the desired balance is achieved.
Airplane stability is not theoretically a
necessary condition to achieve such trim or
balance, although in practice it is. You can
balance a pin, but it is difficult. See Figure
4.
Let’s examine the pitch stability. Our
airplane is said to be stable if, following a
pitch disturbance, it returns to its original
attitude. The upset from trim can be from
any cause, but let’s consider the effects from
a gust-induced pitch up. See Figure 5.
In the situation shown, the airplane is
stable if the additional moments caused by
wing- and tail-lift changes cause the airplane
to pitch back down. You can see in Figure 5
that if the CG is ahead of the wing center of
lift (more about this later), the airplane is
stable regardless of tail area, tail moment
arm, or wing section; the wing will produce
more lift with more pitch as long as it is not
stalled.
But CG ahead of the wing-lift center is
not a necessary condition for a stable
airplane. Consider the case where the CG is
behind the wing center of lift, or
aerodynamic center. See Figure 6. In this
case, the unstable moment from the wing
(acting in the direction to increase the pitch
upset) must be counteracted by the
stabilizing effect of the tail-lift increase.
In a simple world, we might assume that
a square inch of wing and tail would
produce the same increment of lift for an
incremental change in pitch. Then we could
calculate the size of tail required to balance
the destabilizing effect of the wing.
The condition would be for the wing area
multiplied by the distance ahead of the CG
to equal the tail area multiplied by the tail
distance from the CG. This is known as the
“neutral point,” and is indeed a fundamental
element of real airplane design definition.
See Figure 7.
In this simple model, the neutral point is
a distance aft of the wing aerodynamic
center “a,” where AT divided by AW is the
ratio of the tail-to-wing area. The distance
“a” is expressed as a percentage of mean
wing chord. See Figure 8.
However, the real world is more
complicated than that, and wings and tails
do not produce lift as a pure function of
their area. The rate at which a wing
produces lift with changes in angle of attack
varies with aspect ratio. A low-aspect-ratio
wing builds lift more slowly than a highaspect-
ratio wing. (This is one of the
noticeable aspects of delta-wing flight.) All
wing sections produce roughly the same
amount of lift per increment of pitch. There
is no difference in “flat-bottom” and
“symmetrical” sections.
The aspect-ratio factor also applies to the
tail, which experiences two additional
modifiers involving the fact that the tail
operates in the wake of the wing. The first,
and usually most powerful, effect is that the
wing, in producing lift, generates a
downwash. This downwash is proportional
to the lift on the wing, so as the wing
increases in angle of attack, the downwash
angle increases. This is “seen” by the tail as
a reduction in effective angle of attack; it
could be as much as 75% reduction.
The second effect is that the tail
operating in the wake of the wing
experiences a loss of dynamic pressure.
(The airflow is not as strong as free stream.)
On airplanes with high-drag fuselages, this
loss can be as much as 50%. So high T-tails
operating above the downwash and wake are
much more effective than low tails in the
wake of fuselage excrescences.
August 2004 37
Figure 4
Figure 5
Figure 6
Figure 8
08sig2.QXD 5/24/04 8:43 am Page 37
Tails usually have lower aspect ratios
than wings, further reducing the tail
effectiveness. This reduction must be
accounted for in calculating the neutral
point. It can be considered an effective
reduction in area. Of course, in a
comprehensive calculation of neutral point,
you must also consider the fuselage and all
other wetted surfaces and features. See
Figure 9.
All these factors mean that calculating
the neutral point is quite difficult, but never
mind; we deal with this by fudging! Let’s
try it with an example.
Tail area is 25% of wing area, but it is
low—lower aspect ratio than the wing and
behind the blunt fuselage and landing gear.
Let’s assume its effectiveness is 50%, so the
effective tail area is .5 x .25 = .125.
So, AT/AW effective = .125.
Tail moment is four wing chords, so LT/c
= 4.
From the equation aerodynamic center,
or AC, = (4 x .125 / 1 + .125) x 100.
Or AC = (.5/1.25) x 100.
So, AC = 40% of Mean Aerodynamic
Chord (MAC).
If we had not decremented the tail
effectiveness, we would have calculated the
neutral point at 80% chord!
We never design and test airplanes with
the CG on the calculated neutral point.
Experience shows that various levels of
positive stability are achieved by
positioning the CG within specific ranges
ahead of the estimated neutral point. The
typical range is from 5% to 25%, so a good
38 MODEL AVIATION
Figure 7
Figure 9
Figure 10
Phugoid
08sig2.QXD 5/24/04 8:43 am Page 38
starting point might be 15%. If we apply this
to the preceding example, we would start
with the CG at 25% chord. Wow, that’s
scary! It might even be right!
At this point we have to ask what level of
stability we want and what the associated
effects are. There are various answers,
depending on application, and it is a
fundamental that stability and control must
be in harmony. High stability means more
difficult to control.
The fundamental relationships involved
with longitudinal stability are a coupling
between pitch attitude, lift, flight path, and
speed. An upset in pitch causes the stable
airplane to climb and lose speed, whereupon
it pitches down and gains speed until it
pitches up and repeats the process. This
motion is known as a “phugoid.” The
motion can be quite severe in airplanes with
high stability, although it damps out quickly
with good design. See Figure 10.
The other behavior of high longitudinal
stability is the strong coupling between
speed and pitch trim. This is because with
high stability there is a larger offset between
August 2004 39
Figure 11
Figure 12
The Longitudinal Stability Dive Test
Setup of a Trainer With Various Airfoils
08sig2.QXD 5/24/04 9:36 am Page 39
the CG, where the airplane weight acts, and
the neutral point, where the aerodynamic
forces act. As speed increases, the
aerodynamic forces increase but the weight
does not. This requires a large aerodynamic
trim change to rebalance.
To fly a straight flight profile with large
speed variation, you must input large pitchtrim
control inputs that are well coordinated
with speed. This is undesirable in an
aerobatic airplane where you really want to
point it and have it stay pointed without
further input. This is no problem for a
trainer, where you want the airplane to
overcome the inadvertent upset by the novice
pilot.
Sailplanes are designed to have the most
efficient aerodynamics; this means the
lowest drag. If we examine the effects of
greater stability, it involves reduced lift on
the tail or, frequently, a down force which
counteracts the primary wing lift. The wing
must lift more, and this means more drag
too. This is known as trim drag.
High-performance sailplanes have small
tails and aft CG locations to minimize this
trim drag while exhibiting the minimum
stability necessary to achieve controlled
flight. Indeed, there is a widely discussed—
but perhaps not so widely practiced—flighttrimming
technique known as the “dive test.”
The process is to take the airplane to
altitude, put it in a dive, and then let go of
the stick. If the glider pulls out strongly, the
CG is too far forward or the airplane is too
stable. You then move the CG aft and repeat
the test.
At some point when you put the airplane
in the dive, it will pitch down and steepen
the dive without further input. If you can
save it, you have controlled an unstable
airplane, and I am sure there is some kind of
award for that (in addition to getting your
airplane back). See Figure 11. Actually, this
is not too unlike the maneuvers that are
performed in the certification of full-scale
airplanes.
The Lockheed L-1011 airliner was
retrofitted with a fuel tank built into the
horizontal tail. It is empty on takeoff and
landing, but fuel is pumped into it in cruise
flight so that the CG is moved aft and the
trim drag is reduced. This had a significant
effect in reduced fuel consumption. Pumping
the fuel back forward allowed for the
increased stability necessary at low-altitude
flight in turbulence and in landing.
So how much stability should you
provide, or where should you start with the
CG location?
In practice, the stability margin—
expressed as the distance between the CG
and the neutral point—is 5% to 25% of the
MAC, with trainers and sport/Scale airplanes
favoring the forward location and aerobats
and gliders favoring the aft. But beware; the
actual calculation with the full suit of effects
is complicated and a minefield in which
mistakes can be made. For instance, the
calculation of the MAC and AC of complex
wing shapes can be tricky, so start
conservatively and move toward the “dive
test.”
Notice that the effects of specific wing
airfoils (and tail airfoils, if it comes to that)
do not feature markedly here. You have
probably even forgotten that I already stated
that the airfoil has little or no effect on
longitudinal stability.
Let’s examine this a bit more. In defining
the stability model, we assumed that the AC
of the wing and tail do not move over the
pitch range of interest. This is generally true
because most airfoils operating in the
Reynolds number region of our RC models
do produce their aerodynamic forces at a
relatively fixed location: the quarter chord.
Some airfoils—actually, cambered ones
(say flat-bottomed or semisymmetrical if you
will)—do have a small change in this
40 MODEL AVIATION
location, which results in a pitch up with
increased angle of attack. This means
slightly destabilizing!
Symmetrical NACA airfoils have
practically no pitching moment with angle of
attack. That is the primary reason why the
airfoil of choice in most early helicopters
was the symmetrical NACA 0012. The early
helicopters had mechanical controls, and the
pilot would have to physically hold the
controls against the blade control forces.
The advent of hydraulically boosted
controls and the aerodynamic efficiency
advantages of cambered airfoils meant that
the later helicopters no longer used the 0012.
But I digress.
Flat-Bottomed Airfoils for Trainers? So
why is it said that you must use a “flatbottomed”
airfoil on a trainer?
Although they are no more stable than
symmetrical airfoils, they do have a higher
lift capability, so they allow for lower takeoff
and landing speed, or more maneuver margin
to accommodate inadvertent control inputs or
recovery from poor flight-path control.
Another factor is in setting up the initial
trim condition. Extremely stable airplanes
have downward lifting empennages while
the wing lifts upward. To satisfy this
condition, the decalage—the difference
between the wing and tail incidence—has to
be large. (See Figure 12.)
The wing must have, say, +4°, and the
tail must have 0° to –3°. If we build the
conventional “trainer” fuselage with a flat
top and bottom and then use a flat-bottomed
airfoil and a low-slab tail, we automatically
have 4° of decalage. This is because the
zero-lift line on the flat-bottomed airfoil,
such as the Clark Y, is at roughly +4°. A nobrainer!
On the other hand, if we want to use a
symmetrical airfoil, we must make a more
complicated upper fuselage to mount the
wing accommodating the lower surface
curvature and the necessary 4° of real
incidence. Much harder! Yeah, right!
Could it really be this simple? Tell me if
you know the right answer—please! MA
Dave Harding
4948 Jefferson Dr.
Brookhaven PA 19015
BRODAK
Brodak
Manufacturing &
Distributing Co., Inc.
The largest supplier of control-line airplanes
METAL FUEL TANKS
1/4 ounce to 7 ounce
Brodak Metal Fuel Tanks are individually
constructed, using high quality tinplated
steel and copper fill, vent & feed tubes.
also available Catalogue #12
Send $5.00 to Brodak’s
100 Park Avenue • Carmichaels, PA 15320
Phone: 724-966-2726 • Fax: 724-966-5670
E-Mail: [email protected] • Web Site: www.brodak.com
08sig2.QXD 5/24/04 8:43 am Page 40

Author: Dave Harding


Edition: Model Aviation - 2004/08
Page Numbers: 36,37,38,39,40

“YOU SHOULD USE a ‘flat-bottomed’
airfoil on a trainer because it is more
stable.”
How many times have you read that
often-quoted statement? Well, as is so much
folklore, it is untrue, and I will explain why
and what does make a stable model (or fullscale
airplane).
To begin with, I have to square away a few
terms. I should first explain what we mean
when we say an airplane is “stable.”
Second, we should add “about ... axis,”
because an airplane is free to rotate and
move in all three directions and rotations.
See Figure 1.
We call something “stable” when it
returns to its original state following a
disturbance. When something is “unstable,”
it continues to diverge from its original state
when it’s disturbed. “Neutrally stable” items
simply stay in the disturbed condition. See
Figure 2.
The axis of primary concern to us is the
“pitch” axis. If you don’t get this right you
won’t get a chance to find out about the
others, so I’ll examine the forces involved.
See Figure 3. However, before I launch into
stability, I have one more concept to add
which you will likely understand: trim.
Trim involves balancing the forces so
the airplane does not climb or dive at the
chosen speed. So examining the forces
depicted in Figure 3, trim requires that the
sum of the lift forces—wing and tail—equal
the weight, and the sum of their moments is
zero. The latter means that the airplane will
not pitch up or down.
The sum of the moments is what we do
on a teeter-totter; the force multiplied by the
moment arm, or distance, must equal the
other forces multiplied by their moment
arms. You can do this calculation about any
point as a fulcrum—the nose, the CG, or
36 MODEL AVIATION
of STABILITY
Fundamentals by Dave Harding
Figure 1
Figure 2
Figure 3
Drawings by the author
even the tail if you want. I’ll use the CG.
When we fly our (stable) airplanes, we
adjust the elevator such that we balance
these forces by watching the pitch motion
and rate of climb. The airplane is considered
“in trim” when it holds level flight at the
chosen speed.
What actually happens when we move
the elevator is that the lift changes on the
stabilizer such that the airplane pitching
08sig2.QXD 5/24/04 8:43 am Page 36
moment changes. This, in turn, causes the
airplane to pitch or rotate nose-up or nosedown
until the desired balance is achieved.
Airplane stability is not theoretically a
necessary condition to achieve such trim or
balance, although in practice it is. You can
balance a pin, but it is difficult. See Figure
4.
Let’s examine the pitch stability. Our
airplane is said to be stable if, following a
pitch disturbance, it returns to its original
attitude. The upset from trim can be from
any cause, but let’s consider the effects from
a gust-induced pitch up. See Figure 5.
In the situation shown, the airplane is
stable if the additional moments caused by
wing- and tail-lift changes cause the airplane
to pitch back down. You can see in Figure 5
that if the CG is ahead of the wing center of
lift (more about this later), the airplane is
stable regardless of tail area, tail moment
arm, or wing section; the wing will produce
more lift with more pitch as long as it is not
stalled.
But CG ahead of the wing-lift center is
not a necessary condition for a stable
airplane. Consider the case where the CG is
behind the wing center of lift, or
aerodynamic center. See Figure 6. In this
case, the unstable moment from the wing
(acting in the direction to increase the pitch
upset) must be counteracted by the
stabilizing effect of the tail-lift increase.
In a simple world, we might assume that
a square inch of wing and tail would
produce the same increment of lift for an
incremental change in pitch. Then we could
calculate the size of tail required to balance
the destabilizing effect of the wing.
The condition would be for the wing area
multiplied by the distance ahead of the CG
to equal the tail area multiplied by the tail
distance from the CG. This is known as the
“neutral point,” and is indeed a fundamental
element of real airplane design definition.
See Figure 7.
In this simple model, the neutral point is
a distance aft of the wing aerodynamic
center “a,” where AT divided by AW is the
ratio of the tail-to-wing area. The distance
“a” is expressed as a percentage of mean
wing chord. See Figure 8.
However, the real world is more
complicated than that, and wings and tails
do not produce lift as a pure function of
their area. The rate at which a wing
produces lift with changes in angle of attack
varies with aspect ratio. A low-aspect-ratio
wing builds lift more slowly than a highaspect-
ratio wing. (This is one of the
noticeable aspects of delta-wing flight.) All
wing sections produce roughly the same
amount of lift per increment of pitch. There
is no difference in “flat-bottom” and
“symmetrical” sections.
The aspect-ratio factor also applies to the
tail, which experiences two additional
modifiers involving the fact that the tail
operates in the wake of the wing. The first,
and usually most powerful, effect is that the
wing, in producing lift, generates a
downwash. This downwash is proportional
to the lift on the wing, so as the wing
increases in angle of attack, the downwash
angle increases. This is “seen” by the tail as
a reduction in effective angle of attack; it
could be as much as 75% reduction.
The second effect is that the tail
operating in the wake of the wing
experiences a loss of dynamic pressure.
(The airflow is not as strong as free stream.)
On airplanes with high-drag fuselages, this
loss can be as much as 50%. So high T-tails
operating above the downwash and wake are
much more effective than low tails in the
wake of fuselage excrescences.
August 2004 37
Figure 4
Figure 5
Figure 6
Figure 8
08sig2.QXD 5/24/04 8:43 am Page 37
Tails usually have lower aspect ratios
than wings, further reducing the tail
effectiveness. This reduction must be
accounted for in calculating the neutral
point. It can be considered an effective
reduction in area. Of course, in a
comprehensive calculation of neutral point,
you must also consider the fuselage and all
other wetted surfaces and features. See
Figure 9.
All these factors mean that calculating
the neutral point is quite difficult, but never
mind; we deal with this by fudging! Let’s
try it with an example.
Tail area is 25% of wing area, but it is
low—lower aspect ratio than the wing and
behind the blunt fuselage and landing gear.
Let’s assume its effectiveness is 50%, so the
effective tail area is .5 x .25 = .125.
So, AT/AW effective = .125.
Tail moment is four wing chords, so LT/c
= 4.
From the equation aerodynamic center,
or AC, = (4 x .125 / 1 + .125) x 100.
Or AC = (.5/1.25) x 100.
So, AC = 40% of Mean Aerodynamic
Chord (MAC).
If we had not decremented the tail
effectiveness, we would have calculated the
neutral point at 80% chord!
We never design and test airplanes with
the CG on the calculated neutral point.
Experience shows that various levels of
positive stability are achieved by
positioning the CG within specific ranges
ahead of the estimated neutral point. The
typical range is from 5% to 25%, so a good
38 MODEL AVIATION
Figure 7
Figure 9
Figure 10
Phugoid
08sig2.QXD 5/24/04 8:43 am Page 38
starting point might be 15%. If we apply this
to the preceding example, we would start
with the CG at 25% chord. Wow, that’s
scary! It might even be right!
At this point we have to ask what level of
stability we want and what the associated
effects are. There are various answers,
depending on application, and it is a
fundamental that stability and control must
be in harmony. High stability means more
difficult to control.
The fundamental relationships involved
with longitudinal stability are a coupling
between pitch attitude, lift, flight path, and
speed. An upset in pitch causes the stable
airplane to climb and lose speed, whereupon
it pitches down and gains speed until it
pitches up and repeats the process. This
motion is known as a “phugoid.” The
motion can be quite severe in airplanes with
high stability, although it damps out quickly
with good design. See Figure 10.
The other behavior of high longitudinal
stability is the strong coupling between
speed and pitch trim. This is because with
high stability there is a larger offset between
August 2004 39
Figure 11
Figure 12
The Longitudinal Stability Dive Test
Setup of a Trainer With Various Airfoils
08sig2.QXD 5/24/04 9:36 am Page 39
the CG, where the airplane weight acts, and
the neutral point, where the aerodynamic
forces act. As speed increases, the
aerodynamic forces increase but the weight
does not. This requires a large aerodynamic
trim change to rebalance.
To fly a straight flight profile with large
speed variation, you must input large pitchtrim
control inputs that are well coordinated
with speed. This is undesirable in an
aerobatic airplane where you really want to
point it and have it stay pointed without
further input. This is no problem for a
trainer, where you want the airplane to
overcome the inadvertent upset by the novice
pilot.
Sailplanes are designed to have the most
efficient aerodynamics; this means the
lowest drag. If we examine the effects of
greater stability, it involves reduced lift on
the tail or, frequently, a down force which
counteracts the primary wing lift. The wing
must lift more, and this means more drag
too. This is known as trim drag.
High-performance sailplanes have small
tails and aft CG locations to minimize this
trim drag while exhibiting the minimum
stability necessary to achieve controlled
flight. Indeed, there is a widely discussed—
but perhaps not so widely practiced—flighttrimming
technique known as the “dive test.”
The process is to take the airplane to
altitude, put it in a dive, and then let go of
the stick. If the glider pulls out strongly, the
CG is too far forward or the airplane is too
stable. You then move the CG aft and repeat
the test.
At some point when you put the airplane
in the dive, it will pitch down and steepen
the dive without further input. If you can
save it, you have controlled an unstable
airplane, and I am sure there is some kind of
award for that (in addition to getting your
airplane back). See Figure 11. Actually, this
is not too unlike the maneuvers that are
performed in the certification of full-scale
airplanes.
The Lockheed L-1011 airliner was
retrofitted with a fuel tank built into the
horizontal tail. It is empty on takeoff and
landing, but fuel is pumped into it in cruise
flight so that the CG is moved aft and the
trim drag is reduced. This had a significant
effect in reduced fuel consumption. Pumping
the fuel back forward allowed for the
increased stability necessary at low-altitude
flight in turbulence and in landing.
So how much stability should you
provide, or where should you start with the
CG location?
In practice, the stability margin—
expressed as the distance between the CG
and the neutral point—is 5% to 25% of the
MAC, with trainers and sport/Scale airplanes
favoring the forward location and aerobats
and gliders favoring the aft. But beware; the
actual calculation with the full suit of effects
is complicated and a minefield in which
mistakes can be made. For instance, the
calculation of the MAC and AC of complex
wing shapes can be tricky, so start
conservatively and move toward the “dive
test.”
Notice that the effects of specific wing
airfoils (and tail airfoils, if it comes to that)
do not feature markedly here. You have
probably even forgotten that I already stated
that the airfoil has little or no effect on
longitudinal stability.
Let’s examine this a bit more. In defining
the stability model, we assumed that the AC
of the wing and tail do not move over the
pitch range of interest. This is generally true
because most airfoils operating in the
Reynolds number region of our RC models
do produce their aerodynamic forces at a
relatively fixed location: the quarter chord.
Some airfoils—actually, cambered ones
(say flat-bottomed or semisymmetrical if you
will)—do have a small change in this
40 MODEL AVIATION
location, which results in a pitch up with
increased angle of attack. This means
slightly destabilizing!
Symmetrical NACA airfoils have
practically no pitching moment with angle of
attack. That is the primary reason why the
airfoil of choice in most early helicopters
was the symmetrical NACA 0012. The early
helicopters had mechanical controls, and the
pilot would have to physically hold the
controls against the blade control forces.
The advent of hydraulically boosted
controls and the aerodynamic efficiency
advantages of cambered airfoils meant that
the later helicopters no longer used the 0012.
But I digress.
Flat-Bottomed Airfoils for Trainers? So
why is it said that you must use a “flatbottomed”
airfoil on a trainer?
Although they are no more stable than
symmetrical airfoils, they do have a higher
lift capability, so they allow for lower takeoff
and landing speed, or more maneuver margin
to accommodate inadvertent control inputs or
recovery from poor flight-path control.
Another factor is in setting up the initial
trim condition. Extremely stable airplanes
have downward lifting empennages while
the wing lifts upward. To satisfy this
condition, the decalage—the difference
between the wing and tail incidence—has to
be large. (See Figure 12.)
The wing must have, say, +4°, and the
tail must have 0° to –3°. If we build the
conventional “trainer” fuselage with a flat
top and bottom and then use a flat-bottomed
airfoil and a low-slab tail, we automatically
have 4° of decalage. This is because the
zero-lift line on the flat-bottomed airfoil,
such as the Clark Y, is at roughly +4°. A nobrainer!
On the other hand, if we want to use a
symmetrical airfoil, we must make a more
complicated upper fuselage to mount the
wing accommodating the lower surface
curvature and the necessary 4° of real
incidence. Much harder! Yeah, right!
Could it really be this simple? Tell me if
you know the right answer—please! MA
Dave Harding
4948 Jefferson Dr.
Brookhaven PA 19015
BRODAK
Brodak
Manufacturing &
Distributing Co., Inc.
The largest supplier of control-line airplanes
METAL FUEL TANKS
1/4 ounce to 7 ounce
Brodak Metal Fuel Tanks are individually
constructed, using high quality tinplated
steel and copper fill, vent & feed tubes.
also available Catalogue #12
Send $5.00 to Brodak’s
100 Park Avenue • Carmichaels, PA 15320
Phone: 724-966-2726 • Fax: 724-966-5670
E-Mail: [email protected] • Web Site: www.brodak.com
08sig2.QXD 5/24/04 8:43 am Page 40

Author: Dave Harding


Edition: Model Aviation - 2004/08
Page Numbers: 36,37,38,39,40

“YOU SHOULD USE a ‘flat-bottomed’
airfoil on a trainer because it is more
stable.”
How many times have you read that
often-quoted statement? Well, as is so much
folklore, it is untrue, and I will explain why
and what does make a stable model (or fullscale
airplane).
To begin with, I have to square away a few
terms. I should first explain what we mean
when we say an airplane is “stable.”
Second, we should add “about ... axis,”
because an airplane is free to rotate and
move in all three directions and rotations.
See Figure 1.
We call something “stable” when it
returns to its original state following a
disturbance. When something is “unstable,”
it continues to diverge from its original state
when it’s disturbed. “Neutrally stable” items
simply stay in the disturbed condition. See
Figure 2.
The axis of primary concern to us is the
“pitch” axis. If you don’t get this right you
won’t get a chance to find out about the
others, so I’ll examine the forces involved.
See Figure 3. However, before I launch into
stability, I have one more concept to add
which you will likely understand: trim.
Trim involves balancing the forces so
the airplane does not climb or dive at the
chosen speed. So examining the forces
depicted in Figure 3, trim requires that the
sum of the lift forces—wing and tail—equal
the weight, and the sum of their moments is
zero. The latter means that the airplane will
not pitch up or down.
The sum of the moments is what we do
on a teeter-totter; the force multiplied by the
moment arm, or distance, must equal the
other forces multiplied by their moment
arms. You can do this calculation about any
point as a fulcrum—the nose, the CG, or
36 MODEL AVIATION
of STABILITY
Fundamentals by Dave Harding
Figure 1
Figure 2
Figure 3
Drawings by the author
even the tail if you want. I’ll use the CG.
When we fly our (stable) airplanes, we
adjust the elevator such that we balance
these forces by watching the pitch motion
and rate of climb. The airplane is considered
“in trim” when it holds level flight at the
chosen speed.
What actually happens when we move
the elevator is that the lift changes on the
stabilizer such that the airplane pitching
08sig2.QXD 5/24/04 8:43 am Page 36
moment changes. This, in turn, causes the
airplane to pitch or rotate nose-up or nosedown
until the desired balance is achieved.
Airplane stability is not theoretically a
necessary condition to achieve such trim or
balance, although in practice it is. You can
balance a pin, but it is difficult. See Figure
4.
Let’s examine the pitch stability. Our
airplane is said to be stable if, following a
pitch disturbance, it returns to its original
attitude. The upset from trim can be from
any cause, but let’s consider the effects from
a gust-induced pitch up. See Figure 5.
In the situation shown, the airplane is
stable if the additional moments caused by
wing- and tail-lift changes cause the airplane
to pitch back down. You can see in Figure 5
that if the CG is ahead of the wing center of
lift (more about this later), the airplane is
stable regardless of tail area, tail moment
arm, or wing section; the wing will produce
more lift with more pitch as long as it is not
stalled.
But CG ahead of the wing-lift center is
not a necessary condition for a stable
airplane. Consider the case where the CG is
behind the wing center of lift, or
aerodynamic center. See Figure 6. In this
case, the unstable moment from the wing
(acting in the direction to increase the pitch
upset) must be counteracted by the
stabilizing effect of the tail-lift increase.
In a simple world, we might assume that
a square inch of wing and tail would
produce the same increment of lift for an
incremental change in pitch. Then we could
calculate the size of tail required to balance
the destabilizing effect of the wing.
The condition would be for the wing area
multiplied by the distance ahead of the CG
to equal the tail area multiplied by the tail
distance from the CG. This is known as the
“neutral point,” and is indeed a fundamental
element of real airplane design definition.
See Figure 7.
In this simple model, the neutral point is
a distance aft of the wing aerodynamic
center “a,” where AT divided by AW is the
ratio of the tail-to-wing area. The distance
“a” is expressed as a percentage of mean
wing chord. See Figure 8.
However, the real world is more
complicated than that, and wings and tails
do not produce lift as a pure function of
their area. The rate at which a wing
produces lift with changes in angle of attack
varies with aspect ratio. A low-aspect-ratio
wing builds lift more slowly than a highaspect-
ratio wing. (This is one of the
noticeable aspects of delta-wing flight.) All
wing sections produce roughly the same
amount of lift per increment of pitch. There
is no difference in “flat-bottom” and
“symmetrical” sections.
The aspect-ratio factor also applies to the
tail, which experiences two additional
modifiers involving the fact that the tail
operates in the wake of the wing. The first,
and usually most powerful, effect is that the
wing, in producing lift, generates a
downwash. This downwash is proportional
to the lift on the wing, so as the wing
increases in angle of attack, the downwash
angle increases. This is “seen” by the tail as
a reduction in effective angle of attack; it
could be as much as 75% reduction.
The second effect is that the tail
operating in the wake of the wing
experiences a loss of dynamic pressure.
(The airflow is not as strong as free stream.)
On airplanes with high-drag fuselages, this
loss can be as much as 50%. So high T-tails
operating above the downwash and wake are
much more effective than low tails in the
wake of fuselage excrescences.
August 2004 37
Figure 4
Figure 5
Figure 6
Figure 8
08sig2.QXD 5/24/04 8:43 am Page 37
Tails usually have lower aspect ratios
than wings, further reducing the tail
effectiveness. This reduction must be
accounted for in calculating the neutral
point. It can be considered an effective
reduction in area. Of course, in a
comprehensive calculation of neutral point,
you must also consider the fuselage and all
other wetted surfaces and features. See
Figure 9.
All these factors mean that calculating
the neutral point is quite difficult, but never
mind; we deal with this by fudging! Let’s
try it with an example.
Tail area is 25% of wing area, but it is
low—lower aspect ratio than the wing and
behind the blunt fuselage and landing gear.
Let’s assume its effectiveness is 50%, so the
effective tail area is .5 x .25 = .125.
So, AT/AW effective = .125.
Tail moment is four wing chords, so LT/c
= 4.
From the equation aerodynamic center,
or AC, = (4 x .125 / 1 + .125) x 100.
Or AC = (.5/1.25) x 100.
So, AC = 40% of Mean Aerodynamic
Chord (MAC).
If we had not decremented the tail
effectiveness, we would have calculated the
neutral point at 80% chord!
We never design and test airplanes with
the CG on the calculated neutral point.
Experience shows that various levels of
positive stability are achieved by
positioning the CG within specific ranges
ahead of the estimated neutral point. The
typical range is from 5% to 25%, so a good
38 MODEL AVIATION
Figure 7
Figure 9
Figure 10
Phugoid
08sig2.QXD 5/24/04 8:43 am Page 38
starting point might be 15%. If we apply this
to the preceding example, we would start
with the CG at 25% chord. Wow, that’s
scary! It might even be right!
At this point we have to ask what level of
stability we want and what the associated
effects are. There are various answers,
depending on application, and it is a
fundamental that stability and control must
be in harmony. High stability means more
difficult to control.
The fundamental relationships involved
with longitudinal stability are a coupling
between pitch attitude, lift, flight path, and
speed. An upset in pitch causes the stable
airplane to climb and lose speed, whereupon
it pitches down and gains speed until it
pitches up and repeats the process. This
motion is known as a “phugoid.” The
motion can be quite severe in airplanes with
high stability, although it damps out quickly
with good design. See Figure 10.
The other behavior of high longitudinal
stability is the strong coupling between
speed and pitch trim. This is because with
high stability there is a larger offset between
August 2004 39
Figure 11
Figure 12
The Longitudinal Stability Dive Test
Setup of a Trainer With Various Airfoils
08sig2.QXD 5/24/04 9:36 am Page 39
the CG, where the airplane weight acts, and
the neutral point, where the aerodynamic
forces act. As speed increases, the
aerodynamic forces increase but the weight
does not. This requires a large aerodynamic
trim change to rebalance.
To fly a straight flight profile with large
speed variation, you must input large pitchtrim
control inputs that are well coordinated
with speed. This is undesirable in an
aerobatic airplane where you really want to
point it and have it stay pointed without
further input. This is no problem for a
trainer, where you want the airplane to
overcome the inadvertent upset by the novice
pilot.
Sailplanes are designed to have the most
efficient aerodynamics; this means the
lowest drag. If we examine the effects of
greater stability, it involves reduced lift on
the tail or, frequently, a down force which
counteracts the primary wing lift. The wing
must lift more, and this means more drag
too. This is known as trim drag.
High-performance sailplanes have small
tails and aft CG locations to minimize this
trim drag while exhibiting the minimum
stability necessary to achieve controlled
flight. Indeed, there is a widely discussed—
but perhaps not so widely practiced—flighttrimming
technique known as the “dive test.”
The process is to take the airplane to
altitude, put it in a dive, and then let go of
the stick. If the glider pulls out strongly, the
CG is too far forward or the airplane is too
stable. You then move the CG aft and repeat
the test.
At some point when you put the airplane
in the dive, it will pitch down and steepen
the dive without further input. If you can
save it, you have controlled an unstable
airplane, and I am sure there is some kind of
award for that (in addition to getting your
airplane back). See Figure 11. Actually, this
is not too unlike the maneuvers that are
performed in the certification of full-scale
airplanes.
The Lockheed L-1011 airliner was
retrofitted with a fuel tank built into the
horizontal tail. It is empty on takeoff and
landing, but fuel is pumped into it in cruise
flight so that the CG is moved aft and the
trim drag is reduced. This had a significant
effect in reduced fuel consumption. Pumping
the fuel back forward allowed for the
increased stability necessary at low-altitude
flight in turbulence and in landing.
So how much stability should you
provide, or where should you start with the
CG location?
In practice, the stability margin—
expressed as the distance between the CG
and the neutral point—is 5% to 25% of the
MAC, with trainers and sport/Scale airplanes
favoring the forward location and aerobats
and gliders favoring the aft. But beware; the
actual calculation with the full suit of effects
is complicated and a minefield in which
mistakes can be made. For instance, the
calculation of the MAC and AC of complex
wing shapes can be tricky, so start
conservatively and move toward the “dive
test.”
Notice that the effects of specific wing
airfoils (and tail airfoils, if it comes to that)
do not feature markedly here. You have
probably even forgotten that I already stated
that the airfoil has little or no effect on
longitudinal stability.
Let’s examine this a bit more. In defining
the stability model, we assumed that the AC
of the wing and tail do not move over the
pitch range of interest. This is generally true
because most airfoils operating in the
Reynolds number region of our RC models
do produce their aerodynamic forces at a
relatively fixed location: the quarter chord.
Some airfoils—actually, cambered ones
(say flat-bottomed or semisymmetrical if you
will)—do have a small change in this
40 MODEL AVIATION
location, which results in a pitch up with
increased angle of attack. This means
slightly destabilizing!
Symmetrical NACA airfoils have
practically no pitching moment with angle of
attack. That is the primary reason why the
airfoil of choice in most early helicopters
was the symmetrical NACA 0012. The early
helicopters had mechanical controls, and the
pilot would have to physically hold the
controls against the blade control forces.
The advent of hydraulically boosted
controls and the aerodynamic efficiency
advantages of cambered airfoils meant that
the later helicopters no longer used the 0012.
But I digress.
Flat-Bottomed Airfoils for Trainers? So
why is it said that you must use a “flatbottomed”
airfoil on a trainer?
Although they are no more stable than
symmetrical airfoils, they do have a higher
lift capability, so they allow for lower takeoff
and landing speed, or more maneuver margin
to accommodate inadvertent control inputs or
recovery from poor flight-path control.
Another factor is in setting up the initial
trim condition. Extremely stable airplanes
have downward lifting empennages while
the wing lifts upward. To satisfy this
condition, the decalage—the difference
between the wing and tail incidence—has to
be large. (See Figure 12.)
The wing must have, say, +4°, and the
tail must have 0° to –3°. If we build the
conventional “trainer” fuselage with a flat
top and bottom and then use a flat-bottomed
airfoil and a low-slab tail, we automatically
have 4° of decalage. This is because the
zero-lift line on the flat-bottomed airfoil,
such as the Clark Y, is at roughly +4°. A nobrainer!
On the other hand, if we want to use a
symmetrical airfoil, we must make a more
complicated upper fuselage to mount the
wing accommodating the lower surface
curvature and the necessary 4° of real
incidence. Much harder! Yeah, right!
Could it really be this simple? Tell me if
you know the right answer—please! MA
Dave Harding
4948 Jefferson Dr.
Brookhaven PA 19015
BRODAK
Brodak
Manufacturing &
Distributing Co., Inc.
The largest supplier of control-line airplanes
METAL FUEL TANKS
1/4 ounce to 7 ounce
Brodak Metal Fuel Tanks are individually
constructed, using high quality tinplated
steel and copper fill, vent & feed tubes.
also available Catalogue #12
Send $5.00 to Brodak’s
100 Park Avenue • Carmichaels, PA 15320
Phone: 724-966-2726 • Fax: 724-966-5670
E-Mail: [email protected] • Web Site: www.brodak.com
08sig2.QXD 5/24/04 8:43 am Page 40

Author: Dave Harding


Edition: Model Aviation - 2004/08
Page Numbers: 36,37,38,39,40

“YOU SHOULD USE a ‘flat-bottomed’
airfoil on a trainer because it is more
stable.”
How many times have you read that
often-quoted statement? Well, as is so much
folklore, it is untrue, and I will explain why
and what does make a stable model (or fullscale
airplane).
To begin with, I have to square away a few
terms. I should first explain what we mean
when we say an airplane is “stable.”
Second, we should add “about ... axis,”
because an airplane is free to rotate and
move in all three directions and rotations.
See Figure 1.
We call something “stable” when it
returns to its original state following a
disturbance. When something is “unstable,”
it continues to diverge from its original state
when it’s disturbed. “Neutrally stable” items
simply stay in the disturbed condition. See
Figure 2.
The axis of primary concern to us is the
“pitch” axis. If you don’t get this right you
won’t get a chance to find out about the
others, so I’ll examine the forces involved.
See Figure 3. However, before I launch into
stability, I have one more concept to add
which you will likely understand: trim.
Trim involves balancing the forces so
the airplane does not climb or dive at the
chosen speed. So examining the forces
depicted in Figure 3, trim requires that the
sum of the lift forces—wing and tail—equal
the weight, and the sum of their moments is
zero. The latter means that the airplane will
not pitch up or down.
The sum of the moments is what we do
on a teeter-totter; the force multiplied by the
moment arm, or distance, must equal the
other forces multiplied by their moment
arms. You can do this calculation about any
point as a fulcrum—the nose, the CG, or
36 MODEL AVIATION
of STABILITY
Fundamentals by Dave Harding
Figure 1
Figure 2
Figure 3
Drawings by the author
even the tail if you want. I’ll use the CG.
When we fly our (stable) airplanes, we
adjust the elevator such that we balance
these forces by watching the pitch motion
and rate of climb. The airplane is considered
“in trim” when it holds level flight at the
chosen speed.
What actually happens when we move
the elevator is that the lift changes on the
stabilizer such that the airplane pitching
08sig2.QXD 5/24/04 8:43 am Page 36
moment changes. This, in turn, causes the
airplane to pitch or rotate nose-up or nosedown
until the desired balance is achieved.
Airplane stability is not theoretically a
necessary condition to achieve such trim or
balance, although in practice it is. You can
balance a pin, but it is difficult. See Figure
4.
Let’s examine the pitch stability. Our
airplane is said to be stable if, following a
pitch disturbance, it returns to its original
attitude. The upset from trim can be from
any cause, but let’s consider the effects from
a gust-induced pitch up. See Figure 5.
In the situation shown, the airplane is
stable if the additional moments caused by
wing- and tail-lift changes cause the airplane
to pitch back down. You can see in Figure 5
that if the CG is ahead of the wing center of
lift (more about this later), the airplane is
stable regardless of tail area, tail moment
arm, or wing section; the wing will produce
more lift with more pitch as long as it is not
stalled.
But CG ahead of the wing-lift center is
not a necessary condition for a stable
airplane. Consider the case where the CG is
behind the wing center of lift, or
aerodynamic center. See Figure 6. In this
case, the unstable moment from the wing
(acting in the direction to increase the pitch
upset) must be counteracted by the
stabilizing effect of the tail-lift increase.
In a simple world, we might assume that
a square inch of wing and tail would
produce the same increment of lift for an
incremental change in pitch. Then we could
calculate the size of tail required to balance
the destabilizing effect of the wing.
The condition would be for the wing area
multiplied by the distance ahead of the CG
to equal the tail area multiplied by the tail
distance from the CG. This is known as the
“neutral point,” and is indeed a fundamental
element of real airplane design definition.
See Figure 7.
In this simple model, the neutral point is
a distance aft of the wing aerodynamic
center “a,” where AT divided by AW is the
ratio of the tail-to-wing area. The distance
“a” is expressed as a percentage of mean
wing chord. See Figure 8.
However, the real world is more
complicated than that, and wings and tails
do not produce lift as a pure function of
their area. The rate at which a wing
produces lift with changes in angle of attack
varies with aspect ratio. A low-aspect-ratio
wing builds lift more slowly than a highaspect-
ratio wing. (This is one of the
noticeable aspects of delta-wing flight.) All
wing sections produce roughly the same
amount of lift per increment of pitch. There
is no difference in “flat-bottom” and
“symmetrical” sections.
The aspect-ratio factor also applies to the
tail, which experiences two additional
modifiers involving the fact that the tail
operates in the wake of the wing. The first,
and usually most powerful, effect is that the
wing, in producing lift, generates a
downwash. This downwash is proportional
to the lift on the wing, so as the wing
increases in angle of attack, the downwash
angle increases. This is “seen” by the tail as
a reduction in effective angle of attack; it
could be as much as 75% reduction.
The second effect is that the tail
operating in the wake of the wing
experiences a loss of dynamic pressure.
(The airflow is not as strong as free stream.)
On airplanes with high-drag fuselages, this
loss can be as much as 50%. So high T-tails
operating above the downwash and wake are
much more effective than low tails in the
wake of fuselage excrescences.
August 2004 37
Figure 4
Figure 5
Figure 6
Figure 8
08sig2.QXD 5/24/04 8:43 am Page 37
Tails usually have lower aspect ratios
than wings, further reducing the tail
effectiveness. This reduction must be
accounted for in calculating the neutral
point. It can be considered an effective
reduction in area. Of course, in a
comprehensive calculation of neutral point,
you must also consider the fuselage and all
other wetted surfaces and features. See
Figure 9.
All these factors mean that calculating
the neutral point is quite difficult, but never
mind; we deal with this by fudging! Let’s
try it with an example.
Tail area is 25% of wing area, but it is
low—lower aspect ratio than the wing and
behind the blunt fuselage and landing gear.
Let’s assume its effectiveness is 50%, so the
effective tail area is .5 x .25 = .125.
So, AT/AW effective = .125.
Tail moment is four wing chords, so LT/c
= 4.
From the equation aerodynamic center,
or AC, = (4 x .125 / 1 + .125) x 100.
Or AC = (.5/1.25) x 100.
So, AC = 40% of Mean Aerodynamic
Chord (MAC).
If we had not decremented the tail
effectiveness, we would have calculated the
neutral point at 80% chord!
We never design and test airplanes with
the CG on the calculated neutral point.
Experience shows that various levels of
positive stability are achieved by
positioning the CG within specific ranges
ahead of the estimated neutral point. The
typical range is from 5% to 25%, so a good
38 MODEL AVIATION
Figure 7
Figure 9
Figure 10
Phugoid
08sig2.QXD 5/24/04 8:43 am Page 38
starting point might be 15%. If we apply this
to the preceding example, we would start
with the CG at 25% chord. Wow, that’s
scary! It might even be right!
At this point we have to ask what level of
stability we want and what the associated
effects are. There are various answers,
depending on application, and it is a
fundamental that stability and control must
be in harmony. High stability means more
difficult to control.
The fundamental relationships involved
with longitudinal stability are a coupling
between pitch attitude, lift, flight path, and
speed. An upset in pitch causes the stable
airplane to climb and lose speed, whereupon
it pitches down and gains speed until it
pitches up and repeats the process. This
motion is known as a “phugoid.” The
motion can be quite severe in airplanes with
high stability, although it damps out quickly
with good design. See Figure 10.
The other behavior of high longitudinal
stability is the strong coupling between
speed and pitch trim. This is because with
high stability there is a larger offset between
August 2004 39
Figure 11
Figure 12
The Longitudinal Stability Dive Test
Setup of a Trainer With Various Airfoils
08sig2.QXD 5/24/04 9:36 am Page 39
the CG, where the airplane weight acts, and
the neutral point, where the aerodynamic
forces act. As speed increases, the
aerodynamic forces increase but the weight
does not. This requires a large aerodynamic
trim change to rebalance.
To fly a straight flight profile with large
speed variation, you must input large pitchtrim
control inputs that are well coordinated
with speed. This is undesirable in an
aerobatic airplane where you really want to
point it and have it stay pointed without
further input. This is no problem for a
trainer, where you want the airplane to
overcome the inadvertent upset by the novice
pilot.
Sailplanes are designed to have the most
efficient aerodynamics; this means the
lowest drag. If we examine the effects of
greater stability, it involves reduced lift on
the tail or, frequently, a down force which
counteracts the primary wing lift. The wing
must lift more, and this means more drag
too. This is known as trim drag.
High-performance sailplanes have small
tails and aft CG locations to minimize this
trim drag while exhibiting the minimum
stability necessary to achieve controlled
flight. Indeed, there is a widely discussed—
but perhaps not so widely practiced—flighttrimming
technique known as the “dive test.”
The process is to take the airplane to
altitude, put it in a dive, and then let go of
the stick. If the glider pulls out strongly, the
CG is too far forward or the airplane is too
stable. You then move the CG aft and repeat
the test.
At some point when you put the airplane
in the dive, it will pitch down and steepen
the dive without further input. If you can
save it, you have controlled an unstable
airplane, and I am sure there is some kind of
award for that (in addition to getting your
airplane back). See Figure 11. Actually, this
is not too unlike the maneuvers that are
performed in the certification of full-scale
airplanes.
The Lockheed L-1011 airliner was
retrofitted with a fuel tank built into the
horizontal tail. It is empty on takeoff and
landing, but fuel is pumped into it in cruise
flight so that the CG is moved aft and the
trim drag is reduced. This had a significant
effect in reduced fuel consumption. Pumping
the fuel back forward allowed for the
increased stability necessary at low-altitude
flight in turbulence and in landing.
So how much stability should you
provide, or where should you start with the
CG location?
In practice, the stability margin—
expressed as the distance between the CG
and the neutral point—is 5% to 25% of the
MAC, with trainers and sport/Scale airplanes
favoring the forward location and aerobats
and gliders favoring the aft. But beware; the
actual calculation with the full suit of effects
is complicated and a minefield in which
mistakes can be made. For instance, the
calculation of the MAC and AC of complex
wing shapes can be tricky, so start
conservatively and move toward the “dive
test.”
Notice that the effects of specific wing
airfoils (and tail airfoils, if it comes to that)
do not feature markedly here. You have
probably even forgotten that I already stated
that the airfoil has little or no effect on
longitudinal stability.
Let’s examine this a bit more. In defining
the stability model, we assumed that the AC
of the wing and tail do not move over the
pitch range of interest. This is generally true
because most airfoils operating in the
Reynolds number region of our RC models
do produce their aerodynamic forces at a
relatively fixed location: the quarter chord.
Some airfoils—actually, cambered ones
(say flat-bottomed or semisymmetrical if you
will)—do have a small change in this
40 MODEL AVIATION
location, which results in a pitch up with
increased angle of attack. This means
slightly destabilizing!
Symmetrical NACA airfoils have
practically no pitching moment with angle of
attack. That is the primary reason why the
airfoil of choice in most early helicopters
was the symmetrical NACA 0012. The early
helicopters had mechanical controls, and the
pilot would have to physically hold the
controls against the blade control forces.
The advent of hydraulically boosted
controls and the aerodynamic efficiency
advantages of cambered airfoils meant that
the later helicopters no longer used the 0012.
But I digress.
Flat-Bottomed Airfoils for Trainers? So
why is it said that you must use a “flatbottomed”
airfoil on a trainer?
Although they are no more stable than
symmetrical airfoils, they do have a higher
lift capability, so they allow for lower takeoff
and landing speed, or more maneuver margin
to accommodate inadvertent control inputs or
recovery from poor flight-path control.
Another factor is in setting up the initial
trim condition. Extremely stable airplanes
have downward lifting empennages while
the wing lifts upward. To satisfy this
condition, the decalage—the difference
between the wing and tail incidence—has to
be large. (See Figure 12.)
The wing must have, say, +4°, and the
tail must have 0° to –3°. If we build the
conventional “trainer” fuselage with a flat
top and bottom and then use a flat-bottomed
airfoil and a low-slab tail, we automatically
have 4° of decalage. This is because the
zero-lift line on the flat-bottomed airfoil,
such as the Clark Y, is at roughly +4°. A nobrainer!
On the other hand, if we want to use a
symmetrical airfoil, we must make a more
complicated upper fuselage to mount the
wing accommodating the lower surface
curvature and the necessary 4° of real
incidence. Much harder! Yeah, right!
Could it really be this simple? Tell me if
you know the right answer—please! MA
Dave Harding
4948 Jefferson Dr.
Brookhaven PA 19015
BRODAK
Brodak
Manufacturing &
Distributing Co., Inc.
The largest supplier of control-line airplanes
METAL FUEL TANKS
1/4 ounce to 7 ounce
Brodak Metal Fuel Tanks are individually
constructed, using high quality tinplated
steel and copper fill, vent & feed tubes.
also available Catalogue #12
Send $5.00 to Brodak’s
100 Park Avenue • Carmichaels, PA 15320
Phone: 724-966-2726 • Fax: 724-966-5670
E-Mail: [email protected] • Web Site: www.brodak.com
08sig2.QXD 5/24/04 8:43 am Page 40

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