# Is the amount of dihedral on low wing aircraft based more on landing considerations than on aerodynamic benefits?

During a recent discussion on glider design, a quandary arose over what the aerodynamic effects of moving an otherwise unchanged wing from the top of an aircraft to the bottom would be.

One claim was that it would reduce "self righting" characteristics due to a change in the interaction of the relative wind to the upwind wing/fuselage root and reduced effect on the lift of the downwind wing. This would be the equivalent of increased "anhedral effect".

Another point of view was that lowering the wing lowers CG, increasing area above the CG, which (as an upright tail fin or fuselage component) would increase tendency to roll away from a side wind, or increased "dihedral effect".

In the mean time, high wings and low wings continue to fly on in abundance, with passionate arguments supporting the virtues of each.

With so much ambiguity, even after more than 120 years of aviation to sort things out, is it possible that both designs still exist because one really does not have a significant aerodynamic advantage over the other?

Landing considerations of long winged aircraft are obvious considering the dangers of catching a wing tip and "cartwheeling". Increased dihedral and a high wing position help prevent this. Others state low wings are easier maintenance.

In the air, are they really closer than we think?

• The two models pictured where thrown from a 25 foot hill in a mild crosswind. They landed so close to each other they nearly collided. Jun 5 at 10:46
• Many related questions could be linked, including those referencing the "pendulum effect", which most of us understand isn't actually very analogous to the physics at play in a real pendulum, yet the vertical placement of the CG relative to various surfaces of the aircraft clearly does have some effect on roll stability, due to effects of surface area above/below CG in a sideslip... anyway to start that list of linked questions-- aviation.stackexchange.com/q/12099/34686, aviation.stackexchange.com/q/26396/34686, aviation.stackexchange.com/a/703/34686, Jun 5 at 12:19
• Here's a point which may often go under-appreciated in such discussions-- imagine a wing with no dihedral or anhedral, and imagine that we can consider that the wing has no "side area". It still makes a contribution to the total drag of the aircraft. If the wing is above or below the CG, then during a sideslip, the orientation of that drag vector is such that it does create a rolling moment around the aircraft's longitudinal axis, even if no actual "sideforce" is generated (i.e. no force perpendicular to the flight path in the direction perpendicular to the lift vector), only L and D. Jun 5 at 12:39
• (ctd) So even in a pure "flying wing" design w/ no fuselage/wing interaction, or fuselage side area, or actual anhedral or dihedral, if we mount a heavy weight on a long skinny pole protruding high above or below the wing, we'd still create some anhedral-like or dihedral-like effect. The point being, just because a wing has minimal "side area", and no actual dihedral or anhedral, doesn't mean that it's only contribution to the balance of roll torques during a sideslip is its influence on the vertical location of the CG, by virtue of its mass. Jun 5 at 12:39
• A possible related new ASE question could be posed as to whether, in case of fuel tanks positioned well below or above aircraft CG (think typical high-wing or low-wing GA planes with fuel tanks in the inboard portions of the wings), status of tanks full versus empty has a noticeable effect on aircraft's roll stability... Jun 5 at 13:01

Dihedral cannot be chosen in isolation. For good flying characteristics the parameter it controls, namely $$\text{c}_{l\beta}$$, must have a certain relation to weathervane stability $$\text{c}_{n\beta}$$. While $$\text{c}_{n\beta}$$ is positive, $$\text{c}_{l\beta}$$ is negative, so if you plot both as in the figure below (taken shamelessly from Ray Whitford's Fundamentals of Fighter Design), the ratio can be found in the second quadrant of a coordinate system.

If weathervane stability is high, dihedral must also be higher than usual so the ratio of both coefficients falls into the "satisfactory" area. If the engine-out case drives tail size up, the wing dihedral has to follow so that flying characteristics do not suffer.

The hasty development of the Heinkel 162 resulted in too much dihedral and adverse flying qualities. The quick fix was to add Lippischohren (Lippisch ears), named after the person who used them first, Alexander Lippisch.

He-162 front view (picture source). No, these are not inverted winglets but Lippischohren to correct excessive dihedral.

• That's probably where Canadair got the idea for the CL415 tips, for precisely the opposite purpose. Jun 6 at 12:50
• See Grumman F9F Panther as a follow-on. Jun 6 at 15:25
• @JohnK Same for the horizontal tail of the MPP version of the Diamond DA42. Jun 7 at 10:12

Some points to consider:

1. Dihedral effect requires sideslip to work. When an airplane banks due to a disturbance, you must have some sideslip develop to create the self-righting differential lift in the first place. The vertical tail volume must be low enough to allow some sideslip to develop. If the fin/rudder is too large, sideslip instantly generates a weathervaning yaw and you get a spiral diving tendency instead of an automatic return to wings level tendency. So there is a whole balancing act on fin sizing you have to deal with first.
2. Pendulum effect to the extent that it exists, isn't a pendulum so much, rather than a form of static stability in a vertical plane (you're floating in a gas - a pendulum requires a fixed attachment). If the aerodynamic center of the body in the vertical axis, the vertical Neutral Point, is offset from the roll rotation axis, the vertical C of G, then when a lateral movement is present the Neutral Point will seek to trail, or weathervane, behind the center of mass so to speak, just as in the yaw and pitch axis. If the Neutral Point is above the vertical C of G, a restorative moment is created similar to dihedral effect because the body with the wind acting on it wants to "trail" the vertical C of G. Take a Cessna 172, and add a heavy weight on the end of a long rigid pole below the fuselage, and skid the plane, and it will roll away from the skid from static stability forces acting in the vertical axis (it's not the "pendulum effect" of the weight down below, it's the body of the plane trying to weathervane behind the lowered center of mass, about which the airplane is rolling, and in fact the same effect will work in weightlessness). I would say that although this effect is present to some degree in most airplanes, slightly positive in high wing airplanes and close to neutral in low wing ones, it's too subtle to notice because the vertical Neutral Point and center of mass are too close together in most cases. However this effect can be observed on float planes due to the mass of the floats moving the vertical C of G down more than they move the aerodynamic center down, and in my experience airplanes have somewhat noticeably better roll stability when on floats than when on wheels.
3. Then there's dihedral effect from actual geometric dihedral of the wings, and dihedral effect that high wing airplanes enjoy from the T configuration, where sideslip generates a righting force just from the lack of side surface area above the wing. A low wing airplane will need more wing physical dihedral than a high wing one to have the same righting effect during sideslip. Lots of high wing airplanes do fine with no wing dihedral at all, just relying on the T junction of wing-to-fuselage. The Wittman Tailwind homebuilt and the CL215/415 water bomber come to mind, designs where mild dihedral effect was all that was wanted, so the wings have zero geometric dihedral. In fact, when the CL415 was developed from the 215, one of the nasty surprises was that the flat PW120 engine nacelles sticking up above the wing killed off some of the T junction effect, as if it had become a mid-wing airplane, and roll stability was insufficient. The odd turned up wingtips of the CL415 are there to create some geometric dihedral effect to compensate, without having to redesign the entire wing (one of the ultimate aerodynamic bandaids).

So in the end, a low wing airplane with a dihedral angle of, say 3 degrees, might have the same roll stability, that is, righting force from sideslip, as a high wing airplane with a T configuration plus 1.5 degrees of geometric dihedral. In the end it's what do you have to do to achieve a given righting tendency from sideslip with whatever configuration you're using, and if you moved a wing from the top to the bottom, you would expect to have to increase (or introduce) dihedral angle to maintain the same righting tendency due to sideslip.

As far as landing conditions go, not really. The best example is the Corsair, where anhedral is used to shorten the gear legs, but must be offset by major dihedral outboard to achieve the desired roll stability. If the Corsair's wings were made straight with longer gear legs, the overall dihedral angle would be way less than the outboard gull wing's has to be.

• I'm also wondering if: back in the pre-FADEC days was "snaking" from variations in engine thrust adding to the design woes more than today? Jun 5 at 16:40
• @RobertDiGiovanni Yeah you look at a C172 there is a bit of dihedral, looking to be between 1 and 2 deg, but less than a low wing Piper which is upwards of 4 or 5 or something. On engines, once an engine is set it's pretty constant FADEC or no, so I've never heard of that being a problem. What FADEC gets you is the ability to operate much closer to the margins and limits, which is where most of the efficiency and responsiveness benefits come from, plus a bit ease of use benefit by automating some of the of power setting, etc. Note that pre FADEC engines are still electronically trimmed. Jun 5 at 17:30
• Fun experiment. Make the vertical tail surface of your glider massively oversize and see what it does. It should develop a tendency to turn on its own a lot more, maybe entering a spiral every time you throw it. Jun 5 at 17:33
• Done that with paper airplanes (BB before balsa). Absolutely, and excessive anhedral makes it worse. I had high hopes for upright big fins at first (yawing into the wind and accelerating the leeward wing), but found that what happened in a crosswind (with dihedral) was the plane would roll away from the wind, sink, and turn downwind, especially when I went from 30 cm wings to 1 meter wings (these were free flight, no controls allowed). Getting it to roll into the wind really helps it turn into the wind, hence a (Predator-like) downward facing fin. Jun 5 at 19:23
• For some configurations (significantly swept wing with tail-mounted engines) anhedral absolutely can be a design concern for takeoff/landing. For example, on Tu-134 you can have wingtips strike before you get tailstrike. And with minimum roll, on Tu-154.
– Zeus
Jun 6 at 8:09