| This is a long
awaited moment. I can’t wait any longer, as I still don’t
understand longitudinal stability, and don’t think I ever will.
So I have here stolen
David Fraser’ work from Soartech 6, p100, March 1987. Better
talk to the elephant now, so what do we mean by “longitudinal
stability”?
Best to take an example. Being the worlds laziest and slowest
builder, and finding myself in need of a Scramble model for my
Mills 0.75, I had a rummage thru my bits and came up with the
following: a Dixielander (Fuller) wing, an FAI Viking (Goldberg)
fuselage and a Skystreak tailplane. Now the Skystreak tailplane
(Sal Taibi, Falling Models} is off a 40 ship, and it’s pretty
darn big: I figured it would make the model be hugely stable in
pitch, which would possibly help any lateral instability
(wrong!).
Actually, wrong on both counts! Bolting everything together, the
C/G came out at about 6” behind the wing TE. Otherwise, it all
looked pretty good. So down to the green sward at Rosalie Park
and a few hand glides. Very promising, nice and slow: just right
for Scramble. Thus, the model was in trim for its glide speed,
given the elements it was concocted from. Unfortunately, “trim”
is not stability.
Looking to have some fun, I banked it over and gave a hurl as
though I was flying a chuckie. Yikes, it dived straight into the
ground! Now this was as unexpected as it was disappointing. I
was expecting the extra speed would make it climb, but it dived
instead!
This behaviour in pitch relates to “longitudinal stability”.
Diving into the ground above trim speed is “longitudinal
instability”. We don’t want that!
According to Fraser, there is a magical place on the model
called the “neutral point”. It is related to the wing and tail
moments, and the area of the wing and tail.
If the C/G is ahead of the neutral point, a diving model will
pull its nose up out of the dive: if the C/G is behind the
neutral point, it will continue to dive, or even steepen the
dive.
Now how you figure out the neutral point position, I don’t know.
Perhaps if one were to keep pushing the C/G back until the model
dived into the ground, then that point would be the “neutral
point”. Actually, after looking at a formula for neutral point,
that might be as good a way as any!
Now right at the back of Soartech 6, p152, there is a formula
for neutral point.
The credit for this formula goes to Canadian Ernie Currington.
It looks rather weird, has various unexplained constants, and is
really a mystery to me. Despite this, it was possible to code it
up in Quick Basic and have a look at the variables.
For my Dixielander, my trim position for the C/G is 105%. That
is to say, the C/G is behind the trailing edge by 5% of the wing
chord. This was obtained by moving the C/G to give the power
spiral I wanted, not too many turns, not chasing its tail, but
still to transition into the glide OK. In other words, by test
flying.
So I ran the code, noting that the formula would not like the
Dixie’s aspect ratio of 7 (not being in the range 10 to 20), and
came up with the neutral point at 120% of the wing chord: ie,
20% of the chord behind the TE. The “static margin”, which is
the difference between the C/G and the neutral point, as a
fraction of the wing chord, was 14.7%
So what is all that about? Well, the C/G was in front of the
neutral point, which is good. The static margin was greater than
0, which is good. But at 14.7% the static margin was not
markedly greater than 0%. A figure of 20% is better. There is a
possibility that my Dixie will be slow to pull out of a dive,
but it will pull out sooner or later. State Champs for Slow Open
Power next week; this weakness should show up then!
That about covers the idea of longitudinal stability and neutral
point. But there is more to think about.
I have seen some enormous tailplanes on free-flight models, up
to 60% of the wing area. Also, people building F/F scale models
seem always to increase the size of the tailplane. So evidently,
big tailplanes are good. But this is not what Fraser says. I
quote from Soartech 6:
‘One of the interesting outcomes from the neutral point equation
is that is clearly shows any configuration can be made stable
simply by properly locating the C/G, no matter what the relative
sizes of the wing and tail’
This ties in with the C/G location I have seen on more modern,
high-powered, F/F contest designs. Some have the C/G at 70%
(fixed surface, no VIT), yet have even smaller tailplanes! Sweet
Daddy Pearl (Chenault) fits this bill nicely. Stoke in as much
power as you like, it will not loop or dive (but it will
spiral), it will rocket up, and then drop back to glide speed,
no VIT, no autorudder!
The only saving grace I can think of for rearward C/G and large
tailplane, is that it makes tail-tilt work well for the glide
turn. Did you know MacCready patented this idea, after modellers
using it for many years?
Makes you think. If one ignores certain confounding factors, the
position of the neutral point depends only on the areas of wing
and stab, and the distance between their respective ¼ chord
lines. Amazing. Oh, I forgot a factor for tailplane efficiency,
which can be taken as about unity or a little less.
Here is the equation for neutral point from Fraser, p110.
Where:
This formula ignores the effect of other surfaces, such as the
fuselage, prop disc etc.
This formula seems too good to be true. No airfoil section
details, no lift or drag coefficients, nothing nasty or too
unknowable. But there it is. Sometimes you win.
So next time your chuckie climbs straight, turns around and
dives straight back down again, you might care to reflect on the
above!
Addendum: Just for fun, I ran the numbers for Bob Stalick’s
B-QUELL, from Model Builder, p 62, November 1982. The B-QUELL is
an A-B class free-flight model for K&B 21 power, and very
pretty, too.
Published C/G was at 75% of wing root chord, but was incorrectly
placed on the drawing.
Neutral point came in at 95% of the wing root chord, giving a
static margin of 20%.
To my way of thinking, these numbers suggest a tendency toward
loopiness on the climb, requiring plenty of roll. Also, tail
tilt for glide turn would be a little inadequate with the C/G so
far forward.
If the roll is induced by washin on the right inner panel, then
a secondary problem may arise if the transition is bad.
A stall off the top leads to a dive and increase in airspeed.
The model may then tend to roll left, climb again and stall
again: this can be repeated, forming the infamous “Zoom to Doom”
syndrome.
Right auto rudder may not help. The right rudder is effective in
the first part of the dive, but as the nose comes up, the left
roll due to washin can dominate.
The only cure I know is wing wiggler. At engine shutoff, the
right wing moves up to eliminate the climb washin and replace it
with slight amount of washout for the glide. This small amount
of washout has a magical effect in killing the secondary stall. |
