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Dihedral on the wings and tailplane of a Boeing 737 of Ryanair

Dihedral is the upward angle from horizontal in a fixed-wing aircraft or bird wing from root to tip, as viewed from directly in front or behind the aircraft. The aerodynamic stabilising qualities of the dihedral were first described by Sir George Cayley in 1808/09. Downward angled wings have negative dihedral, or anhedral. Wings with local dihedral angles that change along the span are polyhedral.

The purpose of positive dihedral is to confer stability in the roll axis. Most aircraft in the civilian or transport sector use dihedral for roll stability. The dihedral angle is usually greater on low-wing aircraft, compared to an otherwise similar high-wing aircraft.

Fig. 1: Uncompensated weight component produces a side force F_y, which causes the aircraft to sideslip.

Fig. 2: Non-zero sideslip sets the lower, upwind wing to a higher angle of attack, resulting in stabilising roll moment P. The aircraft is shown flying towards the viewer.

If a disturbance causes an aircraft to roll away from its normal wings-level position, the aircraft will sideslip in the direction of the down-going wing (see Fig. 1). This creates an airflow component along the length of the wing from tip to root called the relative wind. The dihedral angle can be seen as presenting a positive angle of attack to this lateral flow, hence generating some additional lift. It is this lift which restores the aircraft to its normal attitude (Fig. 2).

Anhedral on the wings and tailplane of an RAF Harrier GR7A

Military fighter aircraft often have near zero dihedral, or anhedral. This reduces inherent stability, but increases maneuverability. Many modern military aircraft have relaxed stability, and require continuous small corrections made by on-board computers.

Pronounced anhedral is also often seen on aircraft with a high mounted wing, such as the BAe 146, Lockheed Galaxy and others. In such designs, the high mounted wing is above the center of mass which confers roll stability due to the pendulum effect also called the Keel effect, so additional dihedral is not required. In fact, such designs can be excessively stable, so the anhedral is added to cancel out some of the roll stability to ensure that the aircraft can be easily maneuvered.

A side effect of dihedral can be roll-coupling, a tendency for an aircraft to dutch roll. This is unpleasant to experience, and can lead to loss of control or can overstress an aircraft. A certain amount of anhedral can combat this effect.

Wing sweepback also increases roll stability. This is another reason for anhedral configuration on military aircraft with high sweep angle, as well as on some airliners, even on low-wing aircraft such as Tu-134 and Tu-154.

McDonnell Douglas F-4 Phantom II showing polyhedral wing

Most aircraft have been designed with planar wings with simple dihedral (or anhedral). Some pre-World War II aircraft had gull wings bent near the root. Modern polyhedral wing designs generally cant upwards near the wingtips, increasing effective dihedral angle. Winglets are a special case of polyhedral.

Polyhedral is commonly seen on gliders, and some other aircraft. The McDonnell Douglas F-4 Phantom II is one such example, unique among fighters for having dihedral wingtips. This was added after prototype flight testing (the original prototype of the F-4 had a flat wing) showed the need to correct some unanticipated roll instability - angling the wingtips, which were already designed to fold up for carrier operations, was a far more practical solution than re-engineering the entire wing.

A popular but erroneous explanation for how dihedral works, "explained" in many books, is as follows:

If the aircraft is perturbed such that one wing is lowered relative to the other, dihedral causes the lower wing to increase its surface area relative to the airflow, thus increasing its lift. This acts to oppose the original roll motion. An alternative way to visualize this is to imagine that the aircraft is sitting in the bottom of a shallow V-shaped "slot" in the air, thanks to the angle of the wings. This position is naturally stable.^{[citation needed]}

The apparent increase in surface area is in fact an illusion and contributes no additional lift. No respectable textbook on aerodynamics will seriously propose this explanation.^{[citation needed]}

http://www.aeroexperiments.org/washoutbillow.shtml

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