Why does the Neutral Point not vary with Tail incidence angle?

The neutral point is the position where if the CG were present, the aircraft would be statically neutral, ie., the moment about the CG would be constant with varying AoA.

Now, consider an aircraft with a wing and tail only. In this case, the moment generating sources would be the wing lift, wing moment about its AC, tail lift, and tail moment about its AC. We know that both the AC moments will be constant with AoA, so it will only be the lifts that vary with AoA. Thus for the aircraft to be neutral the moments at the neutral point from the lifts of the tail and wing would have to cancel out.

Now, if we change the angle of incidence of the tail, the tail lift would change over the whole range of aircraft AoA (not just one AoA value) thus requiring the neutral point to shift so that the lift from the wing can continue to be cancelled out.

I know how in the equations the angle of tail incidence doesn't factor in in the neutral point or Cm slope equations, but I am unable to intuitively understand the fact, as you can see.

• Well, in practical terms I've found that with some radio-controlled model sailplanes, it seems that the stability does vary with the tail incidence angle. At my current CG, my "Radian" r.c. sailplane is positively pitch stable enough to recover from mild disturbances when trimmed for low-speed flight, but when trimmed for high-speed flight, the least disturbance leads to a very steep dive. (And naturally, the trim position for high-speed flight involves a lower elevator position than for low-speed flight, and a lower el. position is like a less pos. or more neg tail incidence angle.) Commented Jun 19 at 17:45
• (Likely many confounding factors here but... ) Commented Jun 19 at 17:46

All your reasoning is perfect until here:

Now, if we change the angle of incidence of the tail, the tail lift would change thus requiring the neutral point to shift so that the lift from the wing can continue to be cancelled out.

There you've forgotten that what is important for the stability is not the lift itself rather the change of lift with AoA i.e. the slope of $$C_L$$. This is exactly why you've correctly written that the wing's and tail's moment don't enter in the stability calculation since

both the AC moments will be constant with AoA

and their contribution to the stability is zero (they're constant i.e. their change with AoA is zero).

The slope of $$C_L$$ is basically constant for all the AoAs of interest and therefore neither the neutral point nor the stability characteristics of the airplane change with tail setting (but the trim does).

• Understood, Thanks! Commented Jun 20 at 18:53

requiring the neutral point to shift so the wing can continue to be canceled out.

Remember, the tail controls pitch. Incidence change is is exactly what one does with an "all moving surface", such as a stabilator. Tail trim is used to cancel out all other torques around the center of gravity for a stable pitch to the horizon.

Neutral point is based on the longitudinal stability of the aircraft. If one made the tail area smaller, or with a lower coefficient of lift, the neutral point would move forward.

This is why delta designs became more popular when (jet) engines were placed more to the rear.