If It Flies - 2009/08

HI, FRIENDS. There is nothing new under
the sun! At least that’s what the old saying
tells us. You want proof?
Remember how this whole discussion was
started, when I was reminiscing about the
airplane I “designed” as a teenager? Shortly
after the April issue was mailed to the
members (that would be you!), I received an
e-mail from James Wilmot: the designer of
the aircraft from which I lifted the stabilator
design for my second airplane design.
“The flying stab was copied from a CIM-
10 Bomarc missile that was near the Air Force
Academy here in Colorado,” wrote James.
Yes, I thought I was copying from the
original source, but I only borrowed
secondhand.
I also need to correct something that I
wrote. In that same column, I presented a
graphical method for finding the Mean
Aerodynamic Chord (MAC) for any flying
surface with a trapezoidal planform (parallel
root and tip with straight lines for the LE and
TE). The method is fine, and it finds the MAC
line exactly.
I went on to claim that when you find the
MAC, you will see that half of the area lies
inboard of that chord line and half lies
outboard. It is true, but not exactly. This
statement is an approximation only.
It is a good approximation for “normal”
wing tapers and aspect ratios (the ratio of
wingspan to average chord), but thanks to my
new friend, Cal Malinka, and his careful math,
I saw that the rule I had been taught ages ago
was not precise—only an estimate that
worked in most cases.
That’s what happens when you don’t
question what you’ve been taught; maybe
that’s a good principle to remember in
general. The equal area inboard versus
outboard approximation falls apart with
highly tapered planforms such as deltas.
Thanks again, Cal.
Back to calculating an airplane’s neutral
point (NP) and then selecting a starting CG
location based on the static stability margin. In
the June column, I ran the numbers for my
Tiger 60. It’s a sweet-flying airplane with a
rather long tail-moment arm.
The Tiger’s wing has 900 square inches of
area, and the stabilizer has 195 square inches.
The quarter-chord point of the wing is 133/8
inches behind the propeller face, and the
quarter-chord point of the stabilizer is 473/8
inches behind the propeller.
Restating the calculation of the NP’s
distance behind the propeller face, NP
location from propeller face = [(Wing Area x
Distance of Wing AC Behind Propeller) +
(Stabilizer Area x Distance of Stabilizer AC
Behind Propeller)] ÷ (Total Flying Surface
Area).
Selecting a starting CG location based on static stability margin
August 2009 75
If It Flies ... Dean Pappas | [email protected]
Plug in the numbers and you get: [(900 x
133/8) + (195 x 473/8)] ÷ (900 + 195), which
equals 197/16 inches behind the propeller face.
When I measured back that distance, I
learned that the NP was 93/16 inches behind
the LE, or 72% of the wing chord, which is
123/4 inches. So if you balanced the Tiger at
93/16 inches behind the LE, it would be
borderline unflyable. How far forward do you
need to move it?
Because the Tiger has a relatively long tail
moment and a large “tail volume coefficient,”
the rule of thumb is that if the static stability
margin, or distance the CG is in front of the
NP, is 10% of the average wing chord, the
airplane will be flyable but twitchy and
sensitive in pitch.
This means moving the CG forward
roughly 11/4 inches, to less than 8 inches from
the LE. At 20% margin, the Tiger will be
sensitive but comfortable to fly. That works
out to 63/4 inches back from the LE. At 40%
margin, or 41/4 inches back from the LE, the
model will fly smoothly but may not be
maneuverable enough for some pilots’ taste.
Mine is balanced at 43/4 inches.
At the other extreme, flying wings such as
Zagis and deltas are sensitive but flyable at
5% margin of stability, and they exhibit their
best glide performance when balanced
dangerously close to the NP. The danger is an
interesting subject for another day.
Tailless airplanes are happy at 10%
margin, and they become sluggish and lose
substantial glide performance at 15%-20%.
Both flying wings and the tail-volume
coefficient are subjects for another day—so
many things to write about!
At the close of the last column, I wrote that
we would explore how to find the NP of
something complicated, such as an F-16. The
F-16 and F-22 have what is often called a
Blended Wing Body.
I decided to work the numbers for an F-22
while I was looking at a great in-flight picture
of the aircraft. How do you make tough
decisions?
I obtained a picture of the F-22 that I
found online and a copy of its basic
specifications, such as wingspan and length. I
performed the exercise that any Scale modeler
would go through if he or she were trying to
draw plans for a model’s photographic
documentation.
After carefully measuring a printout of the
picture, I scaled it to 1-inch-to-the-foot and
drew the top view in CAD, yielding an
airplane with a 62-inch length and a 441/2-inch
wingspan. The total flying area at that size is
close to 1,300 square inches, which would
yield a sweet-flying airplane, even with the
weight of a healthy electric-ducted-fan power
plant. It’s yet another project I’ll never get to.
Then I reduced the drawing to straight
lines that closely approximate the shape.
That’s what you see with this column.
On the right, I cut that shape into deltas,
trapezoids, and swept-wing-shaped sections,
because those are the shapes for which we
know how to calculate the mean aerodynamic
centers. I fudged the right stabilator a bit, to
make it into two neat trapezoids with the
centerline parallel to the airplane centerline.
The F-22’s vertical fins are angled, so
when viewed directly from the top, you don’t
just see the tip but you see surface area. I
fudged that outline a bit and made it into a
delta shape. That “projected” area counts as a
horizontal flying surface.
The same is true with V-tails and any other
angled flying surfaces. (The same is true when
looking at side area; when you look at the
airplane from the side, wing dihedral and
horizontal stabilizer dihedral or anhedral
contribute to the side area.) I calculated the
area of each one; the areas for left and right
halves together is listed in the diagram next to
the appropriate part. Then I plugged the areas
and their distances from the nose into the
same formula, as I did with the Tiger.
However, this time there were seven
pieces, or terms, in the sum instead of just two
for the wing and stabilizer. It’s the same
simple formula—just more of it. The total
area includes all seven pieces too.
The math is written out in the diagram,
and the NP ends up only 11/4 inches behind
the wing’s aerodynamic center. So if you had
built an F-22 and balanced it at 25% of the
wing’s MAC for starters, you would have had
a tiger by the tail. Many pilots would unlikely
complete the test flight successfully.
How much margin do we need? The F-22
is neither a flying wing, nor does it have a
long tail moment. The tail moment is only
roughly one wing chord, so the rule for
stability margin represents an average of the
two I discussed in the preceding—maybe a
little closer to the case of the flying wing.
I would start with a CG that is close to
20% of the wing chord in front of the NP. The
average wing chord is 22 inches, and I think
I’d shoot for a starting balance point that is 27
or 28 inches back from the nose. That’s only 8
inches forward of the classic one-quarter of
the way back on the wing that I’ve told you.
That rule is still good, but only for
airplanes with “normal” tails. Sometimes you
have to question things you were taught long
ago.
I think I am out of space for now. Until we
get together again, have fun and do take care
of yourself. MA