What is the purpose of a flying stab vs a conventional stab and elevator? What does it do that a conventional stab will not do? Do the same things apply in a model? Thank you very much.

Its main advantage is that it allows you to change the pitch rigging (longitudinal dihedral, sometimes called decalage) without changing either the wing mount or the horizontal tail mount. It does not have less drag or more control authority than a well designed and built articulated elevator. It is more sensitive to slop and elasticity in the linkages.The necessary hardware for a strong and rigid support of an all moving tail adds weight.

Some airliners have both so that they can adjust the tail angle relative to the wing and also have superior control authority.

Thank you Ollie. The reason I asked is that I had a chance to fly a plane with the flying stab and at high speed it seemed to react normally. At low speeds however it seemed to be extremely sensitive. Would this be expected or perhaps it is something else? Thanks Mel.

I'd say it's something else. None of the models with all flying stabs that I've flown have had that sort of Jekyll and Hyde behaviour. I'm not sure what sort of setup would cause that kind of difference either.

Normally control response increases as the square of the airspeed. For example, if you double the airspeed the control response should be four times greater.

The placement of the pivot line of an all moving stab is of critical importance. When the pivot line is through the aerodynamic center of the stab surface, the torque required to deflect the surface is theoretically zero at any airspeed. (An advantage I forgot to mention in my previous post) If the pivot axis is forward of the aerodynamic center, the deflected surface will produce a torque reaction that will tend to reduce the deflection. If the axis location is way off and the servo strength is too small and the linkage not stiff enough, then it might explain your experience. However, such a situation would usually result in serious flutter at high speed.