# Does using a reverse high Cm horizontal tail airfoil coupled with a low Cm wing increase horizontal tail effectiveness?

Does using a high Cm reverse horizontal tail airfoil coupled with a low Cm wing increase horizontal tail effectiveness?

Just noticed that the Zenith 701 wing uses a NACA650-18 which is low $$C_m$$, while their inverted horizontal stabilizer uses a NACA4412 foil which is a high $$C_m$$ foil. They could just as easily have used a low cm NACA0018 or NACA2415 foil with a slotted elevator to get the same $$C_L$$, but they chose a high $$C_m$$ foil instead

I'm assuming using a low $$C_m$$ wing and a high $$C_m$$ horizontal tail adds to the effective moment produced by the area of the horizontal tail, allowing for a smaller horizontal tail area.

Is this correct?

• maybe it's been designed like it is for another purpose, where low cm wing allows smaller horizontal tail surface, thus reducing drag when cruising, and some slatted elevator would produce a lot of drag while cruising.There's this nice paper about horizontal stabilizer behaviour when engine is out, adding VG to elevator. (this does not answer your question that's why it's a comment) – qq jkztd Jul 22 '19 at 21:34

They could just as easily used a low Cm NACA0018 or NACA2415 foil with a slotted elevator to get the same CL, but they chose a high Cm foil instead.

For an elevator, we want to maximize the lift coefficient at the maximum effective control deflection, while maintaining a high degree of linearity with respect to the deflection. There is a maximum effective deflection because any higher control deflection will no longer increase the lift.

A well-designed slotted elevator is theoretically supposed to help with that. But the size of the slot, and any spoiling elements along the hinge would need to be carefully tested in the wind tunnel. Otherwise, they may end up reducing your maximum effective deflection instead. The mechanism required to achieve a good slot may also be complicated for an elevator (slotted flaps don't move like an elevator).

I'm assuming using a low Cm wing and a high Cm horizontal tail adds to the effective moment produced by the area of the horizontal tail, allowing for a smaller horizontal tail area.

That's a good question. I did some quick math using a variation of usual airplane parameters, and here's the summary of the results:

1. The static margin is unaffected by the camber. For NACA4412, there may even be a forward shift in AC (for the same tail planform), so there may be a slight reduction in static margin.

2. Having a negatively cambered tail offloads the tail lift, exacting a small saving in trim drag (a few counts at cruise CL of 0.4). Since it offloads the tail, it may also be beneficial to preventing tail stall, but the effect is fairly small.

3. A negatively cambered tail also produces negative zero-incidence lift. The amount of negative lift can be tailored depending on the overall configuration (CG range, flaps, thrust lines) to minimize form drag.

We can derive the following trimmed lift and pitching moment equations assuming a cambered tail and zero thrust:

(1) $$C_{L}=C_{L_{wb_0}}+a\alpha+\frac{S_t}{S}[C_{L_{t_0}}+a_t(i_t-\epsilon_0)]$$

(2) $$C_m=C_{m_{ac_{wb}}}+C_{m_\alpha}\alpha-V_H[C_{L_{t_0}}+a_t(i_t-\epsilon_0)]+(h-h_{ac_{wb}})C_{L_{wb_0}}+\frac{S_t}{S}C_{m_{ac_t}}=0$$

where,

• $$C_{m_\alpha}=a(h-h_{ac_{wb}})-a_t\overline{V_H}(1-\frac{\partial \epsilon}{\partial \alpha})$$

• $$a=a_{wb}+a_t\frac{S_t}{S}(1-\frac{\partial \epsilon}{\partial \alpha})$$

• $$a_t$$ is the lift slope of the tail, $$a_{wb}$$ is the lift slope of the wingbody, $$\overline{V_H}$$ is the tail volume from the wingbody AC, $$V_H$$ is the tail volume from the CG, $$\epsilon$$ is the downwash on the tail

• Perhaps a better description would be a slotted flap which would increase the cL max from 2.2 to about 2.8!! – Fred Jul 27 '19 at 16:16
• @Fred tail stall occurs at negative tail incidence angle. Why do you think a slotted flap on tail helps? – JZYL Jul 27 '19 at 16:19
• Zenith uses a slotted elevator to generate as much downforce as possible, so they can ascend or descend at an AOA of 30 deg for STOL purposes with elevator deflections of 40 deg!! – Fred Jul 27 '19 at 16:32
• @Fred Where do you see they use a slotted elevator? On their design page, I only see slotted LE on the wing. – JZYL Jul 27 '19 at 16:51
• See zenithair.com/stolch801/design/design.html. for their venturi/slotted elevator, near zero drag slats, low speed flaps, etc. – Fred Jul 29 '19 at 15:55