If one were to design an aircraft to have neutral longitudinal stability would this reduce the required horizontal stabiliser surface and hence trim drag?
Terminology first: Trim drag is the drag component added by adjusting the incidence of the horizontal tail rsp. the deflection angle of the elevator for trim. The increased parasitic drag of a larger tail surface itself is already part of the aircraft's zero-lift drag.
Sizing criteria for tail surfaces
The horizontal stabilizer surface must be dimensioned with these criteria in mind:
Sufficient static longitudinal stability. To achieve this, the tail volume (tail area times lever arm) must be high enough. Use similar aircraft and copy what has been found to work well.
Sufficient pitch damping. This is driven by tail size times the square of the tail lever arm.
Sufficient control power at the most forward cg location over the whole speed range.
- Sufficient control power at the most forward cg location over all load factors (including pitch damping effects).
- Sufficient control power when flaring in ground effect (which reduces elevator effectivity)
- For T-tail configurations: Sufficient control power over all sideslip angles. Sideslip produces a strong pitch-down moment in T-tail configurations.
- For gliders: Sufficient compensation for the force of the tow line, both at the beginning of a winch launch (tow line horizontal) and at the end (tow line vertical).
The other criteria (upper and lower limits on stick force gradients over speed and load factor) can be tailored with elevator chord, so the horizontal tail surface is not directly affected.
In the end your horizontal tail will be as large as you want your cg range to be wide. Operators like wide cg ranges, so the small drag penalty of a bigger tail surface might be worth it.
Also, wing airfoils with a high pitching moment (think rear loading, i.e. high camber in the rear part) will need a bigger tail surface due to the larger shift of the center of pressure over speed, but have less drag and a higher maximum lift than comparable, old-fashioned airfoils (think NACA 4-digit range), so the wing can be smaller and has less drag, which easily compensates for the increased tail surface.
Do not optimize each surface separately
If your wing has already an optimized lift distribution, adding more lift in the same Treffz plane will spoil the end result. In the end, it does not make much of a difference at which position in streamwise direction lift is created, only the sum of it counts. Therefore, it might be better to have as little tail loading as possible in the design point.
If you take the mass of the wing structure in consideration, your optimum lift distribution over the wingspan will change to a more triangular shape, and now it might even make sense to create a small downforce on the tail to reduce the downwash angle in the center section. A lighter wing will require less lift and help to reduce drag.
Think of it this way: The triangular lift distribution produces a higher downwash angle at the tail, and any downforce there would actually point slightly forward, creating induced thrust. Effectively, it helps to equalize downwash over span in the Treffz plane of wing and tail.