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Planes are more stable if the center of mass is ahead of the center of lift. But this means that the tail must provide downforce to keep the nose up, which is inefficient.

Are there any designs where all horizontal surfaces support the craft in the air? The three-surface craft wiki article makes it unclear whether all three surfaces provide upward lift.

In terms of stability, there are several ways this could be maintained. One is to enlarge the rear stabilizer and/or adding wingtips on the rear-most wing. Both of these would weathercock to reverse yaw. In terms of pitch, the nonlinear angle-of-attack-lift coefficient relationship could potentially be used to keep pitch stable. Another possibility is an active control systems, which is used in some fighter jets and birds (more unstable means more maneuverable).

Edit: Birds gain extra lift from their tails.

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Are there any designs where all horizontal surfaces support the craft in the air?

Absolutely.

Canards, as per the designs of Burt Rutan, for one. Not to mention the Wright brothers!

Also, many "free-flight" model airplanes (which operate with no pilot guidance of any kind) have been designed with lifting tails (horizontal stabilizers), with tail airfoils with a concave top surface, and the bottom surface more or less flat. Models of this nature have been flown regularly from the 1930's or the 1940's, up to the present day. In these designs, the horizontal tails typically are rather large.

Re the free-flight model airplanes, it has been argued that the prevalence of these designs is an artifact of certain provisions in the contest rules (e.g. the model is limited in wing area, but tail area is not counted), and that a neutrally-lifting or down-lifting (and also smaller?) horizontal tail would actually be more efficient, but nonetheless these designs do exist.

Furthermore, evidence exists that even in many general aviation aircraft such as the Cessna 172, the horizontal tail provides upward lift in cruising flight when the aircraft is operated near the aft edge of the allowable CG envelope.1

Last but not least, consider tandem-wing aircraft designs, many examples of which may be seen here.

(As an aside-- soaring hawks typically spread their tail to the maximum possible extent when circling in thermal updrafts, to maximize lifting area. In many cases the wings are visibly swept forward, which would help balance the uplift from the tail. It appears that the anatomy is such that sweeping the wing forward also increases wing camber, and thus lift coefficient. When gliding between thermals--when the optimum airspeed in still air would be the speed that maximizes the L/D and Cl/Cd ratios, and the optimum airspeed against a headwind would be higher than that--the tail is typically folded, and the wings are no longer swept forward. The faster the bird wants to fly in the glide, the more the wings will be folded (by sweeping back) to optimize the glide ratio for that particular airspeed. In the simple case of an aircraft of fixed shape, the optimum speed for minimizing the sink rate, and thus for maximizing the climb rate in a thermal updraft, is the speed that optimizes (Cl ^3 ) / (Cd ^2) -- this will be significantly slower than the speed for max L/D ratio (which is also the speed for max ratio of Cl / Cd). So you want to fly slower when circling in a thermal than when gliding between thermals-- and even more so if you have the added advantage of variable-area (foldable) wings and tail.)

Footnotes:

  1. See this section of John Denker's excellent "See How It Flies" website. Scroll down to the sentence beginning "Here’s an explicit example. I’ve actually done the following experiment:"
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  • $\begingroup$ Someone could google up some suitable images of free-flight model airplanes showing the conformation I'm describing-- I don't have time to do it right now but might make an addition a bit later-- $\endgroup$ Oct 7, 2021 at 17:13
  • $\begingroup$ I don't buy that article about the 172 where he validates his theory looking at tufts on tail tips. To be in trim with the tail making up lift, the net pitching moment from the main wing has to be nose up to provide a counter force for the tail to work with to balance at given AOA. The CG would have to be much farter aft, probably aft of the NP and the airplane would be quite unpleasant to fly. To work, you would have to make the tail much larger and shrink the main wing to move the NP aft of the CG, and voila! you now have a tandem wing a/c, like a Q2 or Flea. $\endgroup$
    – John K
    Oct 7, 2021 at 17:54
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    $\begingroup$ Nose-up pitch with velocity increase is not incompatible with positive lift by a conventional stabilizer. All that's actually required is that the forward surface must always have a higher coefficient than the after surface; this is the same for canards, tandems, three-surface aircraft, and conventionals with either positive or negative lift at the tail. $\endgroup$
    – Zeiss Ikon
    Oct 7, 2021 at 18:16
  • $\begingroup$ @ZeissIkon but you don't actually see that with conventional a/c.Main surface net pitching moment is always ND, to one degree or another, and the tail has to produce a NU pitching moment to balance it to be able to trim the main wing to a given AOA. Therefore its lift has to be downward FOR TRIM (not static stability). If the tail is lifting for trim, the net pitching moment forward has to be NU. This only occurs with canards and tandems. The entire point of tandems and canards is elimination of drag losses from the stabilizing surface having to work against the main surface to trim to an AOA $\endgroup$
    – John K
    Oct 7, 2021 at 23:02
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Yes, there are designs using forward canards, for example the Rutan VariEze, Long-EZ and Beechcraft Starship are excellent examples. There is also the Eurofighter Typhoon.

enter image description here

But perhaps the best example is the first powered airplane, the Wright Flyer, which used a forward canard.

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All that's required for any layout -- convention, canard, or three-surface -- to fly with static stability is that the more forward surface(s) must fly at a higher coefficient of lift than the rearward, so that any increase in speed produces a nose-up moment, or a decrease produces nose-down.

With canards, all I've seen fly with positive lift on the canard stabilizer. As noted in another answer, it's also been relatively common for free-flight model airplanes intended for competition to glide with positive lift on the (conventional layout) stabilizer (free-flight competition often involves a relatively short power run followed by an optimized glide).

For a three-surface layout, it would be less common for the rearmost surface and canard to both operate in positive lift -- if the center of mass is rearward enough to fly the rear stabilizer as a lifting surface, the front might need to be in negative lift, and vice versa -- but there's nothing that would prevent careful weight trimming from allowing this.

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