88 MODEL AVIATION
THE LAST TWO
months have been
hectic around here.
The day job,
actually a
consulting gig, has
had me working
seven days a week
all but one Sunday
since I last sat at
the keyboard to
write to you all, and that has put a crimp in everything, not just
flying. (My 16-year-old, the one with the wicked sense of humor
asked, “Mommy who is that strange man?”)
Alas, we do what we have to do. That’s not to say that my
aeromodeling skills went completely unused these last few weeks.
The widget I’ve been working on, these long days, is roughly
the size of a two-stroke .40 engine. It has four densely populated
circuit boards and fiber-optic equipment packed so tightly that the
tall and short parts on one circuit board dovetail with short and
tall parts on the next circuit board.
Who got to assemble the first one? My longtime workmate,
Bob, turned to me as we admired the first one finished (Look, Ma,
no parts left!) and said, “It sure will be a good thing to have the
assembly directions written by the guy who builds model
airplanes.” I learned all about that by building model airplanes
too!
Contemplate, for a moment, the directions and plans for kits,
ARFs, and even home appliances that require assembly that you
have seen. Some of them are pretty darned good, while others
stink to high heaven.
Good plans and assembly instructions are a thing of beauty,
producing a meeting of the minds between designer and builder
without their ever having to physically meet. I’ll bet you never
heard anyone wax poetic about assembly directions, but there is a
first time for everything!
A well-designed model with a good set of plans sticks in your
mind. As a preteen, I remember building an airplane from a
Graupner kit. I think it was a Taxi trainer. I couldn’t read a single
word of German, yet the directions were as clear as a bell, not to
mention that I still remember the names of most of the parts of an
airplane in German as a result of building that kit.
The last two times we got together, I wrote about the notion of an
airplane’s neutral point (NP) and how the relationship between it
and the CG dictates whether the model is unstable, marginally
stable, or nice and stable in pitch.
Retracing my steps, I examined the flying surfaces themselves
and how the aerodynamic center (AC) of a flying surface
represents the place where it can be said that both a constant nosedown
torque and the lift of that flying surface act. The AC, as it
turns out, is usually one-quarter of the way back from the LE on
the mean aerodynamic chord (MAC).
Then I wrote about how to find the MAC on a variety of wing
shapes with a simple graphical method. I used the straightforward
seesaw analogy to figure the “balance point” of the wing’s area
and the stabilizer’s area.
By doing that, I extended the idea of finding a wing’s or
stabilizer’s AC to finding the entire aircraft’s AC. We call this the
airframe’s NP; it’s the point through which you could say that all
of the model’s lift acts. If the CG is in front of the NP, the
airplane will be stable in pitch and will become unflyable as the
CG moves behind the NP.
Model airplanes build character
If It Flies ... Dean Pappas | [email protected]
Also included in this column:
• How wingspan and tail size
affect stability
In the August issue I wrote about how to find the NP for an
airframe that has a blended wing/body, such as an F-22. It turns
out that I have a buddy who wanted to know just that, and the
timing was perfect.
The payoff after finding the NP is that you now know the place
10sig3.QXD 8/21/09 12:53 PM Page 88
the CG has to be forward of to make the
aircraft stable in pitch. I laid out a few
rules of thumb for how much farther
forward the CG has to be. With that,
you’d think I would be finished with the
subject.
As it turns out, we are close to the
finish line but we’re not there yet. The
problem is a little more complicated than I
described several months ago.
The problem when explaining
something such as this subject is how to
introduce the complications. If I had
described them up front, the prospect of
trying to grapple with a complicated
description would discourage the same
readers I wanted to reach. So I started
with the simple model of a seesaw.
Remember that seesaw calculation that
used the wing and stabilizer areas? I used
it to find a Goldberg Tiger 60’s NP. The
NP location I calculated with that method
was a bit aft of the actual NP.
The reason is that several complicating
factors were ignored. I will continue to
ignore the smaller effects, such as the
propeller and the vertical location of the
wing and stabilizer compared to the
airplane’s thrustline.
On the other hand, it is time to add the
two most important complicating factors.
As it turns out, both move the eventual NP
location forward, and that does matter,
because the NP represents the farthest aft
that you dare push the CG.
They are the effect of low aspect ratio
on the effective area of the tail and the
effect of wing downwash on the tail. Let’s
deal with them in that order.
The Tiger uses a symmetrical airfoil on
the wing and a flat-plate airfoil on the
stabilizer. I made the statement, back
then, that the different airfoils didn’t
matter, because the lift per square inch of
wing area changes by the same amount for
each degree change in angle of attack
(AOA).
In proper math-aero speak, the slope of
the coefficient of lift (Cl) vs. AOA is the
same for a wide variety of airfoils. I
illustrated this with a diagram in the April
issue. I know, it’s tough to remember that
far back.
It turns out that while airfoil choice has
little to do with finding the NP, the aspect
ratio (AR) of the flying surfaces does have
a meaningful effect. Not all square inches
are created equal!
The Cl vs. AOA for a flying surface is
only the same as what aerodynamicists
measure in a wind tunnel if the wing has a
very high aspect ratio. Low ARs reduce
the lift slope, as shown in the diagram.
The AR is the surface span divided by
its average chord. The higher the AR, or
the skinnier the wing, the farther apart the
wingtip vortices will be from each other,
when the distance between them is
measured in average wing chords. The
wingtip vortices represent a loss of lift
and additional drag, and the farther apart
they are, the less wing efficiency is lost.
After rooting around in the old
textbook pile, I found this approximation
in Theory of Flight by von Mises, Prager,
and Kuerti; it reads:
Cl (corrected for AR) = Cl (wind tunnel) x 1 ÷ (1
+ 2 ÷ AR)
In English, this means that the lift vs.
AOA slope is reduced by a factor that
depends on the AR.
That is only an approximation (it tends
to overestimate the degradation with ARs
less than 4), but it means that the wing on
my Tiger 60 has an AR of 5.65, while the
stabilizer has a much lower AR of 3.25.
Therefore, every square inch of stabilizer
area will be less effective than a square
inch of wing area. Let’s figure out how
much that effect has.
The wing has 900 square inches, and
the correction factor for an AR of 5.6 is
74%. We could say that the wing behaves
as if it had 665 square inches of windtunnel
area. The 195 square inches of
stabilizer take a beating, with its low AR.
The AR of 3.25 gives a multiplier of 62%.
The stabilizer works as if it has 121 square
inches.
Yes, I am rounding the arithmetic. Now
the seesaw formula for the NP gets the
corrected wing and stabilizer areas.
NP location from propeller face = ([wing area
x wing AC location from propeller face] +
[stabilizer area x stabilizer AC location from
propeller face]) ÷ (wing area + stabilizer area)
Plugging in the corrected areas looks as
follows.
NP location from propeller face = ([665 x
133/8] + [121 x 473/8]) ÷ (665 + 121), or
185/8 inches behind the propeller face
That moved the NP 13/16 forward, to
83/8 inches behind the LE. That’s now 65%
of the wing chord behind the LE, and we
still have to add the other big factor.
Downwash: it’s not hogwash!
The original seesaw problem assumed
that as the airplane changes AOA, both the
wing and stabilizer “see” air coming at
them from the same direction. I am
assuming that the wing and stabilizer
incidence are zero compared to each other,
but this does not change the basic
relationships; it simplifies the explanation.
That just ain’t true, because the
stabilizer sees air that has been rotated
downward as a byproduct of making lift.
(See the diagram.) There is a small effect
from the upwash in front of the stabilizer
changing the air that the wing sees, but I
am going to ignore that small complication
too.
The downwash angle has to be
subtracted from the AOA, and that means
that the stabilizer makes less lift as the
entire airplane’s AOA changes. If the
downwash angle is one-third of the AOA,
the stabilizer is working only with the
remaining two-thirds compared to the
wing.
Again, this behaves as if the stabilizer
area has been reduced. The amount of
downwash from the wing, for a given
AOA, is most strongly affected by the
wing’s aspect ratio. The lower the AR, the
greater the downwash. But the downwash
angle won’t exceed the AOA, no matter
how low the AR is.
That factor (I’m asking you to trust me
on this) is approximately 1 - (3.24 ÷
ARwing), where the 3.24 is based on a few
important assumptions. One is that the AR
is more than 4 or 5. If the AR is less than
that, the 3.24 shrinks too.
For the Tiger, with a wing AR of 5.65,
this downwash correction factor works out
to 43%. Remember that 195 square inches
of stabilizer? It was effectively reduced to
121 by its low AR, and now we are going
to apply the 43% multiplier for the
downwash it sees. That makes the
stabilizer like it has a mere 52 square
inches of area.
Now the seesaw equation looks like the
following.
NP location from prop face = ([665 x 133/8]
+ [52 x 473/8]) ÷ (665 + 52 ), or 1513/16
inches behind the propeller face. Now the
NP is 59/16 inches behind the wing LE, or
just 44% of the wing chord.
That’s fairly far forward of my original
estimate of 72%, and this represents a
proper estimate for the farthest aft the CG
should ever go. Move the CG forward 10%
of a wing chord for an acceptable margin
of stability, and you have an airplane
balanced one-third of the way back on the
wing. Hey, that’s where I fly mine!
This month’s column got a bit theoretical
and had a bit more math than I’d really
like to subject you all to. But if you
wanted to go through all the steps as in the
preceding now, you could nail the CG’s
“exact” aft limit.
Next time, I’ll write about something
you actually encounter while flying.
Until then, have fun, check out some kit
instructions, and do take care of
yourself. MA
Edition: Model Aviation - 2009/10
Page Numbers: 88,89
Edition: Model Aviation - 2009/10
Page Numbers: 88,89
88 MODEL AVIATION
THE LAST TWO
months have been
hectic around here.
The day job,
actually a
consulting gig, has
had me working
seven days a week
all but one Sunday
since I last sat at
the keyboard to
write to you all, and that has put a crimp in everything, not just
flying. (My 16-year-old, the one with the wicked sense of humor
asked, “Mommy who is that strange man?”)
Alas, we do what we have to do. That’s not to say that my
aeromodeling skills went completely unused these last few weeks.
The widget I’ve been working on, these long days, is roughly
the size of a two-stroke .40 engine. It has four densely populated
circuit boards and fiber-optic equipment packed so tightly that the
tall and short parts on one circuit board dovetail with short and
tall parts on the next circuit board.
Who got to assemble the first one? My longtime workmate,
Bob, turned to me as we admired the first one finished (Look, Ma,
no parts left!) and said, “It sure will be a good thing to have the
assembly directions written by the guy who builds model
airplanes.” I learned all about that by building model airplanes
too!
Contemplate, for a moment, the directions and plans for kits,
ARFs, and even home appliances that require assembly that you
have seen. Some of them are pretty darned good, while others
stink to high heaven.
Good plans and assembly instructions are a thing of beauty,
producing a meeting of the minds between designer and builder
without their ever having to physically meet. I’ll bet you never
heard anyone wax poetic about assembly directions, but there is a
first time for everything!
A well-designed model with a good set of plans sticks in your
mind. As a preteen, I remember building an airplane from a
Graupner kit. I think it was a Taxi trainer. I couldn’t read a single
word of German, yet the directions were as clear as a bell, not to
mention that I still remember the names of most of the parts of an
airplane in German as a result of building that kit.
The last two times we got together, I wrote about the notion of an
airplane’s neutral point (NP) and how the relationship between it
and the CG dictates whether the model is unstable, marginally
stable, or nice and stable in pitch.
Retracing my steps, I examined the flying surfaces themselves
and how the aerodynamic center (AC) of a flying surface
represents the place where it can be said that both a constant nosedown
torque and the lift of that flying surface act. The AC, as it
turns out, is usually one-quarter of the way back from the LE on
the mean aerodynamic chord (MAC).
Then I wrote about how to find the MAC on a variety of wing
shapes with a simple graphical method. I used the straightforward
seesaw analogy to figure the “balance point” of the wing’s area
and the stabilizer’s area.
By doing that, I extended the idea of finding a wing’s or
stabilizer’s AC to finding the entire aircraft’s AC. We call this the
airframe’s NP; it’s the point through which you could say that all
of the model’s lift acts. If the CG is in front of the NP, the
airplane will be stable in pitch and will become unflyable as the
CG moves behind the NP.
Model airplanes build character
If It Flies ... Dean Pappas | [email protected]
Also included in this column:
• How wingspan and tail size
affect stability
In the August issue I wrote about how to find the NP for an
airframe that has a blended wing/body, such as an F-22. It turns
out that I have a buddy who wanted to know just that, and the
timing was perfect.
The payoff after finding the NP is that you now know the place
10sig3.QXD 8/21/09 12:53 PM Page 88
the CG has to be forward of to make the
aircraft stable in pitch. I laid out a few
rules of thumb for how much farther
forward the CG has to be. With that,
you’d think I would be finished with the
subject.
As it turns out, we are close to the
finish line but we’re not there yet. The
problem is a little more complicated than I
described several months ago.
The problem when explaining
something such as this subject is how to
introduce the complications. If I had
described them up front, the prospect of
trying to grapple with a complicated
description would discourage the same
readers I wanted to reach. So I started
with the simple model of a seesaw.
Remember that seesaw calculation that
used the wing and stabilizer areas? I used
it to find a Goldberg Tiger 60’s NP. The
NP location I calculated with that method
was a bit aft of the actual NP.
The reason is that several complicating
factors were ignored. I will continue to
ignore the smaller effects, such as the
propeller and the vertical location of the
wing and stabilizer compared to the
airplane’s thrustline.
On the other hand, it is time to add the
two most important complicating factors.
As it turns out, both move the eventual NP
location forward, and that does matter,
because the NP represents the farthest aft
that you dare push the CG.
They are the effect of low aspect ratio
on the effective area of the tail and the
effect of wing downwash on the tail. Let’s
deal with them in that order.
The Tiger uses a symmetrical airfoil on
the wing and a flat-plate airfoil on the
stabilizer. I made the statement, back
then, that the different airfoils didn’t
matter, because the lift per square inch of
wing area changes by the same amount for
each degree change in angle of attack
(AOA).
In proper math-aero speak, the slope of
the coefficient of lift (Cl) vs. AOA is the
same for a wide variety of airfoils. I
illustrated this with a diagram in the April
issue. I know, it’s tough to remember that
far back.
It turns out that while airfoil choice has
little to do with finding the NP, the aspect
ratio (AR) of the flying surfaces does have
a meaningful effect. Not all square inches
are created equal!
The Cl vs. AOA for a flying surface is
only the same as what aerodynamicists
measure in a wind tunnel if the wing has a
very high aspect ratio. Low ARs reduce
the lift slope, as shown in the diagram.
The AR is the surface span divided by
its average chord. The higher the AR, or
the skinnier the wing, the farther apart the
wingtip vortices will be from each other,
when the distance between them is
measured in average wing chords. The
wingtip vortices represent a loss of lift
and additional drag, and the farther apart
they are, the less wing efficiency is lost.
After rooting around in the old
textbook pile, I found this approximation
in Theory of Flight by von Mises, Prager,
and Kuerti; it reads:
Cl (corrected for AR) = Cl (wind tunnel) x 1 ÷ (1
+ 2 ÷ AR)
In English, this means that the lift vs.
AOA slope is reduced by a factor that
depends on the AR.
That is only an approximation (it tends
to overestimate the degradation with ARs
less than 4), but it means that the wing on
my Tiger 60 has an AR of 5.65, while the
stabilizer has a much lower AR of 3.25.
Therefore, every square inch of stabilizer
area will be less effective than a square
inch of wing area. Let’s figure out how
much that effect has.
The wing has 900 square inches, and
the correction factor for an AR of 5.6 is
74%. We could say that the wing behaves
as if it had 665 square inches of windtunnel
area. The 195 square inches of
stabilizer take a beating, with its low AR.
The AR of 3.25 gives a multiplier of 62%.
The stabilizer works as if it has 121 square
inches.
Yes, I am rounding the arithmetic. Now
the seesaw formula for the NP gets the
corrected wing and stabilizer areas.
NP location from propeller face = ([wing area
x wing AC location from propeller face] +
[stabilizer area x stabilizer AC location from
propeller face]) ÷ (wing area + stabilizer area)
Plugging in the corrected areas looks as
follows.
NP location from propeller face = ([665 x
133/8] + [121 x 473/8]) ÷ (665 + 121), or
185/8 inches behind the propeller face
That moved the NP 13/16 forward, to
83/8 inches behind the LE. That’s now 65%
of the wing chord behind the LE, and we
still have to add the other big factor.
Downwash: it’s not hogwash!
The original seesaw problem assumed
that as the airplane changes AOA, both the
wing and stabilizer “see” air coming at
them from the same direction. I am
assuming that the wing and stabilizer
incidence are zero compared to each other,
but this does not change the basic
relationships; it simplifies the explanation.
That just ain’t true, because the
stabilizer sees air that has been rotated
downward as a byproduct of making lift.
(See the diagram.) There is a small effect
from the upwash in front of the stabilizer
changing the air that the wing sees, but I
am going to ignore that small complication
too.
The downwash angle has to be
subtracted from the AOA, and that means
that the stabilizer makes less lift as the
entire airplane’s AOA changes. If the
downwash angle is one-third of the AOA,
the stabilizer is working only with the
remaining two-thirds compared to the
wing.
Again, this behaves as if the stabilizer
area has been reduced. The amount of
downwash from the wing, for a given
AOA, is most strongly affected by the
wing’s aspect ratio. The lower the AR, the
greater the downwash. But the downwash
angle won’t exceed the AOA, no matter
how low the AR is.
That factor (I’m asking you to trust me
on this) is approximately 1 - (3.24 ÷
ARwing), where the 3.24 is based on a few
important assumptions. One is that the AR
is more than 4 or 5. If the AR is less than
that, the 3.24 shrinks too.
For the Tiger, with a wing AR of 5.65,
this downwash correction factor works out
to 43%. Remember that 195 square inches
of stabilizer? It was effectively reduced to
121 by its low AR, and now we are going
to apply the 43% multiplier for the
downwash it sees. That makes the
stabilizer like it has a mere 52 square
inches of area.
Now the seesaw equation looks like the
following.
NP location from prop face = ([665 x 133/8]
+ [52 x 473/8]) ÷ (665 + 52 ), or 1513/16
inches behind the propeller face. Now the
NP is 59/16 inches behind the wing LE, or
just 44% of the wing chord.
That’s fairly far forward of my original
estimate of 72%, and this represents a
proper estimate for the farthest aft the CG
should ever go. Move the CG forward 10%
of a wing chord for an acceptable margin
of stability, and you have an airplane
balanced one-third of the way back on the
wing. Hey, that’s where I fly mine!
This month’s column got a bit theoretical
and had a bit more math than I’d really
like to subject you all to. But if you
wanted to go through all the steps as in the
preceding now, you could nail the CG’s
“exact” aft limit.
Next time, I’ll write about something
you actually encounter while flying.
Until then, have fun, check out some kit
instructions, and do take care of
yourself. MA