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Reading this question and answers, I was wondering if modern airliners with cruciform tail have some noticalbe washout or negative twist along the horizontal stabilizer's span.

During cruise, if wing's downwash angle is larger near the center of the aircraft, shouldn't horizontal stabiliser be slightly twisted according to this particular value, in order to reduce induced drag?

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  • $\begingroup$ It's important to note that wing washout is not to improve efficiency, it's to delay tip stall. The tail, which is "lifting" downward, doesn't really have to worry about tip stall because it never gets close to its stalling AOA anyway. If you put washout in it, you would have it twist leading edge up going inboard to outboard so that the tip is always at a lower AOA than the inboard (remember, it's lifting downward - many airliners have cambered tail airfoils which operate "inverted"). The washout partially unloads the washed out span, requiring a larger surface for no real benefit. $\endgroup$ – John K Mar 26 at 19:26
  • $\begingroup$ @JohnK I was referring to this statement in the related accepted answer: "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" $\endgroup$ – qq jkztd Mar 27 at 8:56
  • $\begingroup$ Well I think the answer there (not totally sure so I won't post it) is that the DW variation within the span of the stab span itself is too small to matter in the larger scheme of things. I've never heard of tail washout on any airplane, but perhaps someone has done it. $\endgroup$ – John K Mar 27 at 13:19
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There is little to be gained by twisting the horizontal stabilizer in terms of efficiency.

First, the span of a typical horizontal tail is much smaller than the wing (see A320 illustration below for example). Apart from the small outboard portions, the downwash behind most of the wing is fairly constant. This makes the simplification of a uniform downwash on horizontal tail valid.

A320 3-view

Second, the lift and drag contribution of the horizontal tail on the overall aircraft at cruise, during which aerodynamic efficiency is paramount, is fairly small. Even assuming a large static margin of 30% (smaller static margin equates to smaller tail contribution), improving the tail span efficiency from 0.8 (typical) to 1 (elliptical) only reduced the total induced drag by half a drag count using some typical aircraft parameters.

These are the parameters I used if you want to verify yourself:

  • $C_{L_{trim}} = 0.4$
  • $\alpha_{wb} = 4.8$
  • $\frac{\partial\epsilon}{\partial\alpha} = 0.43$
  • $\epsilon_0 = 2.8$
  • $C_{m_{ac_{wb}}} = -0.12$
  • $\overline{V_H} = 0.6$
  • $a_t = 4$
  • $\frac{S_t}{S} = 0.25$
  • $h_{n_{wb}} = 0.22$
  • $C_{L_{0_{wb}}} = 0.4$
  • $e_{wb} = 0.85$
  • $e_t = 0.8$ (typical, compared to fully elliptical of unity)
  • $A_{wb} = 8$
  • $A_t = 5$
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