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I am in the process of designing a small wing (Re ~ 50-100k) and am wondering if given (a) the Cm on the main wing is relatively small at low aoas, (b) the horizontal stabilizer will produce lift as long as it is not at 0° aoa and (c) it has some amount of leverage over the main wing, will trimming the horizontal stabilizer to some aoa result the same amount of aoa in the main wing?

There will probably be some discrepancy introduced by Cm on the main wing not being zero, but I feel like that might be small enough to neglect?

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    $\begingroup$ Depending on the Reynolds number and the general dynamics over the history of the flow, the wing will produce a wake that will generally change the angle of attack (AoA) observed by the horizontal stabilizer (compared to the AOA of the wing from the freestream). This is quite case-dependent depending on the airfoil shape, as larger camber implies larger downwash of the flow in the wake, and is difficult to predict. The point of the horizontal tail is to stabilize the aircraft with elevator deflection, and the drag generated by it is usually negligible compared to drag from other components. $\endgroup$ Oct 13, 2021 at 15:40
  • $\begingroup$ The question is in the Vote To Close queue. It has been flagged as Needs Details Or Clarity. Yet when I read the question, I fully understand it. Voting to keep open. $\endgroup$
    – Koyovis
    Oct 15, 2021 at 0:17

2 Answers 2

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If the wing center of pressure is perfectly positioned over the center of gravity, the tail will rotate around the center of gravity until it is in a zero lift condition. Normally, CG is set slightly forward of wing CP, requiring some tail downforce.

Therefore the tail is doing two jobs in straight and level flight, maintaining wing AOA and keeping the net sum of all pitch torque forces (including any off-set thrust vectors) at 0. This is generally accomplished on an as needed basis with trim tabs once proper elevator deflection is established by the pilot.

What makes it a bit more complicated is that wing CP can change with AoA, generally moving forward and increasing with higher AoA. This is can partially compensated by deliberately placing the horizontal stabilizer in the downwash zone of the wing, providing additional counter balancing tail force. The Cessna 172 is an excellent example of this subtly brilliant design feature, allowing for use of a strong lifting cambered wing.

But downwash effects should not be "assumed" or "neglected", they should be carefully studied (wind tunnels), tested, and quantified; at high angles of attack control authority of the aircraft can be most important. Downwash can result in a significantly different AoA on the tail than one might expect from the free stream. One can modify or eliminate these effects by changing the vertical placement of the horizontal stabilizer on the tail.

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  • $\begingroup$ "wing CP can change with AoA", "placing the horizontal stabilizer in the downwash zone of the wing" ... uh ... I think I have some homework to do :-) $\endgroup$
    – fho
    Oct 14, 2021 at 10:18
  • $\begingroup$ @fho Not to worry. Because of much lower wing loading, classic airplane designs scale down to models well. Just remember tail must control the wing. With models, a few crashes along the way will help build your knowledge (in a much safer way). Regarding wing loading, lower speed of models plus Reynolds number effects need to be considered. The more experience you get building and flying the better you will be. You may wish to start with a similar sized model from a hobby store that flies within your planned speed envelope. $\endgroup$ Oct 14, 2021 at 10:26
  • $\begingroup$ I guess "iterate until perfection" is something that is really daunting as a newcomer. Actually this is already Mk2. Mk1 was basically build without any knowledge of aerodynamics and works ... ok. Now it's time to get a somewhat solid grasp on the theory before startin Mk2. $\endgroup$
    – fho
    Oct 14, 2021 at 12:26
  • $\begingroup$ After, oh, a million years, given the same set of conditions, intelligent design and trial/error will arrive at the same solution, with one faster and the other well tested. Sometimes it is a little bit of both. $\endgroup$ Oct 14, 2021 at 12:55
  • $\begingroup$ I will note that one of the reasons behind the T-tail was to get the hstab out of the wings downwash-affected area and into the free stream because it simplifies the analysis considerably. The downside is that in a deep stall the hstab can move into the roiling air behind the stalled wing reducing elevator effectiveness in some cases making recovery impossible. $\endgroup$
    – Jim
    Oct 14, 2021 at 14:19
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The short answer is "No" the AoA of the horizontal stabilizer is not the same as the AoA of the wing. For the aircraft to remain in the air the AoA of the wing must be positive. if a positive AoA were seen by the Hstab, positive lift would also be produced by the tail, but a downforce is required from the tail in order to stabilize the aicraft. Therefore the AoA of the stab must be negative.

This, by the way, leads to the idea of the canard where the forward stabilizer needs to produce a lifting force rather than a downforce to stabilize the aircraft.

Even if the pitching moment in level flight from the wing/body were zero, then there stabilizing force from the tail would need to be zero as well. So, again, positive AoA on the wing, zero AoA on the stab.

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    $\begingroup$ Welcome to Av.SE! $\endgroup$
    – Ralph J
    Oct 14, 2021 at 2:45
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    $\begingroup$ @RalphJ - Thanks. I’ve resisted joining for years (‘cuz I really don’t need another time sink :-) but here I am… $\endgroup$
    – Jim
    Oct 14, 2021 at 2:51
  • $\begingroup$ Related: Does static longitudinal stability require download on the tail? $\endgroup$
    – ymb1
    Oct 15, 2021 at 3:02

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