Single engine Cessna tailplane lift

[guy]

Just to clarify:

Given the continuum of designs, this clearly depends to some extent on the size of the tail plane

No. The size of the tail plane will only influence the required angle of attack necessary for this tailplane the generate the correct amount of lift/downforce created. It will however not change the requirement to either need a lift or a downforce.

A larger tailplane offers a larger range of vertical force which in turn offers a greater possible CG range. If the designer chooses to take advantage of this increase (i.e. a greater permissible range), this affects the "correct" amount of lift/downforce which may be required and can indeed "change the requirement to either need a lift or a downforce". Consider enlarging the taiplane progressively until it becomes a Delanne tandem, and observe the progressive changes in rearmost permissible CG position and lift/downforce required of the rear surface.

Also:

Conversely, we also know that many conventional tailplanes spend a lot of time pushing down (and causing trim drag).

As stated many times in the previous posts, the feeling of "pushing down" is completely irrelevant. You can not derive whether your are generating lift or not by just feeling the stick.

I described the tailplane pushing down aerodynamically, not the stick force or subjective feeling. My apologies if this was not wholly obvious.

[digits_]

Just to clarify:

Given the continuum of designs, this clearly depends to some extent on the size of the tail plane

No. The size of the tail plane will only influence the required angle of attack necessary for this tailplane the generate the correct amount of lift/downforce created. It will however not change the requirement to either need a lift or a downforce.

A larger tailplane offers a larger range of vertical force which in turn offers a greater possible CG range. If the designer chooses to take advantage of this increase (i.e. a greater permissible range), this affects the "correct" amount of lift/downforce which may be required and can indeed "change the requirement to either need a lift or a downforce". Consider enlarging the taiplane progressively until it becomes a Delanne tandem, and observe the progressive changes in rearmost permissible CG position and lift/downforce required of the rear surface.

I agree that it might increase the range in which the CoG may fall to have a stable aircraft, however, a lager tailplane does not change the requirement to switch from a down force to a lift. Never.

The lift generated by the tailplane can be written as L = x * S, with S the surface area of the tailplane ( always > 0 ) and x the other components of the lift formulae. The sign of L can only be changed by changing the sign of x, for example by changing the angle of attack of the tailplane, moving the elevator, modifying the lift coefficient of the surface etc.