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"Dihedral goes hand in hand with low wing aircraft, and anhedral goes with high wing". This is what I assumed till now.

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But when I see a Cessna 172, the wings are a little dihedral. So why does it need more lateral stability? Or is the lateral stability more pronounced with the weight of the aircraft (comparing with Antonov An-225 Mriya)?

Do high-wingers have dihedral? only talks about whether they have or not, or what dihedral does, which I knew already. Thanks to John K, now I understand the relation of swept wings and dihedral effect better.

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    $\begingroup$ Does this answer your question? Do high-wingers have dihedral? $\endgroup$
    – user12873
    Jul 3, 2021 at 16:24
  • $\begingroup$ @DigitalDracula thank you for the link, but it did not. $\endgroup$
    – Noorul Quamar
    Jul 3, 2021 at 17:42
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    $\begingroup$ Congratulations on writing a post which manages to meaningfully put the Mriya and the Cessna-172 in a single post :D $\endgroup$
    – chx
    Jul 4, 2021 at 0:31
  • $\begingroup$ The vast majority -- perhaps 100%- of high-wing light airplanes do not have anhedral! $\endgroup$
    – quiet flyer
    Jul 5, 2021 at 13:53

2 Answers 2

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The dihedral effect is an opposing rolling moment induced by a sideslip. When an airplane is disturbed from wings level, it immediately starts to slip "downhill", slide sideways toward the low wing, in effect. The vertical fin starts to react to this after a certain amount of slip has developed, to realign the airplane with the airstream, weathervaning it more or less, and the airplane turns (while going downhill, unless you increase angle-of-attack.

The fin needs to be small enough to allow this slip to develop a small amount for dihedral effect to work. The slip generates the rolling moment to restore level flight, and there's your lateral stability. If the fin is too big, it will start to weathervane the plane too soon, and dihedral effect can't develop strongly enough to roll the wings level, and the plane instead wants to spiral right away.

Anyway, you get dihedral effect from three configurations that can generate rolling moments from sideslip: geometric dihedral (wings angled up), the T intersection of a high wing configuration (where diagonal flow is unhindered across the roof, but is blocked by the fuselage below, increasing the lift on the low wing), and wing sweep. High wing airplanes may get enough dihedral effect just from the T configuration, and the wing can be straight, especially if maneuvering is a higher priority than cruising.

The Canadair CL-215 has no geometric dihedral; the T junction is sufficient for a water bomber that makes maneuvering a higher priority than cruising (when the CL-415 was tested, the flat engine nacelles sticking up were like fences that inhibited lateral flow, as if there was fuselage extending above the wings, and resulted in killing off much of the dihedral effect of the T junction; the odd turned up wingtips of the 415 are "dihedral plates" a band-aid designed to restore dihedral effect for the desired lateral stability).

In the 172, (and probably most high wing unswept aircraft designed for cruising), Cessna wanted to supplement the dihedral effect of the T configuration with a bit of geometric dihedral to get the total effect they wanted. The geometric dihedral is probably about half the angle of a low wing airplane, since no more is necessary thanks to the high wing placement. High wing transports with unswept wings, like the Dash 8 family, have a small amount of geometric dihedral as well, maybe a degree or so outboard of the engines, to supplement the dihedral effect of the T configuration.

This brings us to wing sweep. Wing sweep generates really strong roll due to sideslip (something you find out pretty fast when you take a jet initial type rating), so there is strong dihedral effect from sweep. When the wing is at the top, you have the dihedral effect of the T configuration, plus the dihedral effect of the wing sweep, and you get way too much roll due to sideslip for desirable lateral stability and dutch roll characteristics. To reduce the excessive dihedral effect, they use anhedral to reduce the total roll/yaw coupling effects to a desirable level.

That's why almost all high wing aircraft with swept wings have anhedral (to basically cancel out some of the effect of the sweep), whereas high wing airplanes with unswept wings have zero or mildly positive geometric dihedral. Likewise, a low wing swept wing jet will have less dihedral than it would have if the wings were unswept.

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  • $\begingroup$ in doing research with uncontrolled high aspect free flight monowing models, it was found that a side wind gust actually rolled the plane away from the wind faster than the tail fin could turn it into the wind. One solution was to keep the wing dihedral, but put more "anhedral effect" area under the CG. Amazingly, dihedralled biplanes of similar wing area performed better in crosswinds. $\endgroup$
    – Robert DiGiovanni
    Jul 4, 2021 at 7:36
  • $\begingroup$ "When an airplane is disturbed from wings level, it immediately starts to slip "downhill", slide sideways toward the low wing, in effect. " -- in my opinion the cause of sideslip when an aircraft banks is complex, and intimately related to the fact that banking causes turning, and is best not viewed as being driven by the gravity vector or tending to involve a loss of altitude. The idea that gravity tends to pull a banked aircraft sideways through the air toward the low wingtip, thus causing a sideslip, is a fundamentally an Aristotelian perspective. $\endgroup$
    – quiet flyer
    Jul 5, 2021 at 14:04
  • $\begingroup$ Btw, this viewpoint has become widespread in hang gliding training, and the error has been further compounded via an additional faulty leap of logic, which claims that the way to prevent or minimize sideslip while turning (in a rudderless aircraft) is to adequately "load up" the wing during the turn entry by increasing the angle-of-attack (moving the control bar forward). In reality I've found that an accelerating (airspeed-increasing), diving, low-G style of rolling in to a turn, while rather exciting, actually involves no more sideslip than a more "correct" ("coordinated") turn entry. $\endgroup$
    – quiet flyer
    Jul 5, 2021 at 14:04
  • $\begingroup$ In many cases (including the hang gliding case, and most light aircraft when being flown w/o use of the rudder), roll rate is by far the dominant driver of sideslip. In some light aircraft and especially sailplanes, aileron position can also be a strong driver of sideslip, thus allowing constant-heading constant-bank sideslips w/ pilots feet off rudder pedals. Obviously, for dihedral or high-wing position to have the effect that it does, bank angle can also be a driver of sideslip, but the point of these comments is that the mechanism for this is not as obvious as it may first appear. $\endgroup$
    – quiet flyer
    Jul 5, 2021 at 14:11
  • $\begingroup$ When you tilt the lift vector by banking, a horizontal component is added to the lift. This is more or less perpendicular to the direction of travel, so the airplane slews sideways. It's no different than when hovering a helicopter and you tilt the rotor left with left cyclic. It moves sideways, and if also going forward, it's moving ahead and sideways. The fin's weathervaning effect is what induces the actual heading change. The hang glider also slips sideways when it banks, but the weathervaning effect is still there to create the heading change, built into the wing sweep. $\endgroup$
    – John K
    Jul 5, 2021 at 14:31
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From your examples, the Cessna 172 is "in between".

One key to understanding this is vertical Center of Gravity and how the plane behaves in a slip. Dihedral can be added to help roll away from the relative wind, as can a tall vertical tail fin or any area above the CG.

But the main function of dihedral is for roll stability in straight line, unaccelerated flight, ie. cruising. A little nudge from a gust or turbulence will be damped by the momentary offset of the center of vertical lift and the center of gravity. That, and any ensuing side slip, will tend to roll the plane back upright.

Any plane that has to build in anhedral, such as a massive cargo carrier, does so because it is excessively sluggish in roll. In smaller aircraft, aerodynamic effects, rather than inertia, dictate roll rates. Anhedralled wings are rare in aircraft the size of a 172, or any aircraft where cruising comfort is desired.

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  • $\begingroup$ @RobertGiovianni, Thank you. Isn't lateral stability an Inherent property of High wing? So considering not anhedral to avoid instability and discomfort, yet 0 dihedral on highwing still will give stability right? The point of including An-225 was to compare whether keel affect is more pronounced in heavy aircraft? Or it's anhedral is just about increasing manoeuvrability? SIMPLY: If there is no dihedral on C172, will the aircraft be laterally stable? $\endgroup$
    – Noorul Quamar
    Jul 3, 2021 at 17:39
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    $\begingroup$ Vertical position centre of gravity is totally irrelevant. It is centre of lateral drag that matters! $\endgroup$
    – Jan Hudec
    Jul 3, 2021 at 20:48
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    $\begingroup$ Anhedral is not done due to sluggish roll characteristics. It's done because the effects of wing sweep plus the high wing T junction of wing to fuse, creates excessive dihedral effect, which aggravates dutch roll tendencies. The anhedral is to cancel some of that out. This is why you see anhedral only on swept wing high wing transports, not straight wing ones. $\endgroup$
    – John K
    Jul 3, 2021 at 23:13
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    $\begingroup$ @JanHudec surprised you would say vertical CG is irrelevant, after all, what will the center of lateral drag rotate about? I found this out by putting a paperclip on the front/bottom of a paper airplane and found it flew worse. When I put it nearer the wings, it flew much better. $\endgroup$
    – Robert DiGiovanni
    Jul 3, 2021 at 23:23
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    $\begingroup$ @JanHudec I am sorry but what is centre of Lateral Drag? $\endgroup$
    – Noorul Quamar
    Jul 4, 2021 at 7:34

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