Here's what Mark Drela had to say about the movement of the
neutral point with changes in pitch attitude:
"
I find the Cm curve is more typically S-shaped,
with a positive slope at small and large Cl's,
and a larger negative slope at intermediate Cl's.
-Cm
^
|
| ..
. | . .
.| . .
| ..
|
----+----------------> alpha
|
The nonzero slopes of the curve cause the stability margin to
vary
considerably with Cl, or equivalently, the aerodynamic center
to shift with Cl.
The shift in the AC, as a fraction of chord, is
delta( x_AC / chord ) = (-dCm/dAlpha) / (dCl/dAlpha)
At small and large Cl's the shift is forward (destabilizing),
while at intermediate Cl's the shift is rearward (stabilizing).
The positive and negative slopes of the curve increase as Re
decreases,
as Ollie mentioned. On small gliders the more troublesome
forward
AC shifts are 10% of the chord or more. On large gliders, shifts
of less than 5% are more typical.
These predicted shifts closely match the differences I observe
between
the AC position as computed by theory, and the AC position
observed
by incrementally moving the CG backwards on the glider until
instability is reached. "Theory" here refers to the vortex-lattice
method, with correction to account for the nonlinear Cm curve.
So it is possible to pick a stability margin and very closely nail
the correct CG location and decalage before the first flight, but
this requires doing the vortex lattice and Xfoil polar calculations.
The AC shifting has practical implications to the more casual RC
glider pilot.
A glider which is stable in cruise (stable intermediate-Cl region),
can become unstable and tuck into a dive if the speed is
increased
until the positive-slope left part of the Cm curve is entered
Having the CG below the wing, like on a poly glider, also
contributes
to the tuck-in behavior, as does a flexible wing and/or tailboom.
In any case, one needs sufficient stability margin to overpower
the combined destabilizing effects of the nonlinear Cm curve,
poly/dihedral, and elasticity. The "dive test" is useful in that
it represents the worst-case situation where all these
destabilizing
effects gang up, and hence it reveals the farthest-forward
AC position that the glider will ever see.
The existence of the "stable" middle part of the curve can be
demonstrated with a small flat plank of balsa with ballast on
the leading edge. This plank can be made to glide slowly at
moderate Cl
even though it has no reflex camber (not possible with a flat Cm
curve).
Free-flight HLG's and some paper airplanes make use of this
phenomenon.
A FFHLG has nearly zero decalage to allow a high non-looping
launch.
If there was no stabilizing Cm curve, such a glider would not be
able
to glide slowly after launch.
>What is the cause?
The culprit is the variation of the boundary layer thickness
and the movement of the separation bubble with Cl.
The boundary layer and bubble changes the effective camber
shape
of the airfoil, which then causes the Cm to change. The effective
shape of the airfoil is plotted in Xfoil under the Cp vs x/c plot.
As you increase the Reynolds number the boundary layer and
the
bubble get thinner, so the modifications to the camber line
get smaller. Hence the Cm variations get smaller as well.
- Mark"
My take is that it is unrealistic to assume that stability depends
only on the CG location and that criticism of the dive test is
based directl or indirectly on the assumption of constant stability.
Once hte concept of stability varying with airspeed is accepted
the dive test can be judged in the proper context.
Regards, Ollie
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