Dihedral
In geometry, the dihedral is the angle between two planes. See dihedral angle.Dihedral is the upward angle of an
aircraft's (or
bird's)
wings from root to tip, as viewed from directly in front of or behind the aircraft. Downward angled wings are said to have
anhedral.
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Dihedral on the wings and tailplane of a Boeing 737 |
The purpose of dihedral is to confer
stability in the roll axis. The explanation for the action of dihedral is this: If a disturbance causes an aircraft to roll away from its normal 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).
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Fig. 1: Uncompensated weight component produces a side force Fy, which causes the aircraft to sideslip. |
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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. |
Most aircraft in the civilian or transport sector use dihedral for stability. Military combat aircraft, in contrast, often have flat wings or anhedral. This reduces inherent stability but increases manoeuvrability. Many modern military aircraft are inherently unstable (see
relaxed stability), and require millions of tiny corrections every second by on-board computers.
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Anhedral on a Harrier GR7 |
A side effect of dihedral can be roll-coupling, a tendency for an aircraft to "corkscrew" through the air under certain conditions. This rolling motion, called a
dutch roll, 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. 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 itself confers roll stability (due to the pendulum effect of the fuselage, engines, etc), 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 manoeuvred.
Sweptback wing 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.
An alternative to dihedral for the wing as a whole is to cant the wingtips or outer section of the wing upwards instead. This is called polyhedral and has the same effect. It 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 that 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. 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.
