airfoil shaped stabilizers

[sailplaneguy]

I notice that most model gliders use a flat stabilizer, while
most real airplanes use an inverted airfoil (curved side on the bottom).
In real airplanes this is done to provide dynamic pitch stability.
Since the cg is slightly forward of the center of lift, when the
airspeed increases because the nose is lowered, the stab produces more
downward lift thus raising the nose. This is why too forward a cg can be
dangerous on landing because the elevator may not be able to offset
the forward cg, and too aft a cg the airplane becomes unstable and
hard to control, although it flies more efficiently.

Why don't we see many models with an airfoil shape on the horizontal
tail? Is it because we depend on the decalage (I think
that's the right term - the angle between the stab. and the
wing chords?) to compensate for the cg - cl difference? Does
this cause greater upset and drag due to extra trimming?

[Ollie]

One difference between a symmetrical airfoil or flat plate and an inverted airfoil with mean line camber is that the zero lift angle of attack is shifted to a slightly more positive angle of attack for the cambered airfoil. The coefficient of lift vs. angle of attack line has the same slope for both. Therefore, if the decalage is adjusted to allow for the difference in zero lift, the effect on stability will be nearly identical in both cases. The reason that some tails are given inverted cambered airfoils is that the tail can then reach a lower angle of attack and produce more downward lift before it stalls and therefore can be a bit smaller, saving a little parasitic drag. How much lift the tail produces and in which direction depends on the CG location and pitch trim. Planes with flaps produce a larger nose-down pitching moments when the flaps are deployed. To stay in pitch trim, the nose down pitching moment must be balanced by a large down load on the tail and that's where the inverted cambered airfoil is an advantage. In the flaps-down mode the stab doesn't have to be as big if it is cambered and inverted. In the flaps- up mode the smaller stab improves range and fuel economy some compared to a larger symmetrical stab that would be required for the flaps-down mode.

[Sparky Paul]

You should also note that inverted horizontals are usually seen, full-scale, on short fuselaged airplanes.. C-130, L-1011.. that gives the longitudinal stability desired when there is a "situation" with the length.
OTOH, on models, such things are frequently seen on special designs. Typcially the SAE lifter airplanes will use the inverted horizontal.
Why, I don't know, but it works.