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It 'appears' that in most flights the horizontal stabilizer is set for positive angle of attack.
So does this produce an 'up force' (lifting force) on tail thus making the aircraft nose-heavy?
Or does the horizontal stablizer presents itself to the relative air at a different angle of attack than the wing does (which creates down force on tail)?
You are right, the horizontal tail of a conventional airplane appears to have a higher incidence, but the actual angle of attack is smaller than that of the wing.
The wing, flying ahead of the tail, produces downwash, so the flow at the tail location has a distinct downward component. The downwash angle can be calculated from the lift coefficient and the geometry of the aircraft: To simplify things, let's assume the wing is just acting on the air with the density $\rho$ flowing with the speed $v$ through a circle with a diameter equal to the span $b$ of the wing. If we just look at this stream tube, the mass flow is $$\frac{dm}{dt} = \frac{b^2}{4}\cdot\pi\cdot\rho\cdot v$$
Lift $L$ is then the impulse change which is caused by the wing and equal to weight. With the downward air speed $v_z$ imparted by the wing, lift is: $$L = \frac{b^2}{4}\cdot\pi\cdot\rho\cdot v\cdot v_z = S\cdot c_L\cdot\frac{v^2}{2}\cdot\rho$$
$S$ is the wing area and $c_L$ the overall lift coefficient. If we now solve for the vertical air speed, we get $$v_z = \frac{S\cdot c_L\cdot\frac{v^2}{2}\cdot\rho}{\frac{b^2}{4}\cdot\pi\cdot\rho\cdot v} = \frac{2\cdot c_L\cdot v}{\pi\cdot AR}$$ with $AR = \frac{b^2}{S}$ the aspect ratio of the wing. Now we can divide the vertical speed by the air speed to calculate the angle by which the air has been deflected by the wing. Let's call it $\alpha_w$: $$\alpha_w = arctan\left(\frac{v_z}{v}\right) = arctan \left(\frac{2\cdot c_L}{\pi\cdot AR}\right)$$ A typical airliner cruise lift coefficient is 0.4, and a typical aspect ratio is around 8: This results in a downwash angle of nearly 2° if the lift distribution over span is elliptical. In reality, it is more triangular-shaped, so the downwash angle is larger near the center of the aircraft. Note that the engine nacelles of the DC-9 and the MD-80 range are tilted 3° up to align them with the local flow.
The resulting angle of attack is lower by those 3°, and if the angle of attack difference between wing and tail is less than that, the tail surface will appear angled upward. To achieve static stability, the tail will have to fly at a slightly lower angle of attack than the wing.
