Dihedral (aeronautics)

In analysis of aircraft stability, the dihedral effect is also a stability derivative called C_{l${\displaystyle \beta }$}[note 1] meaning the change in rolling moment coefficient (the "C_l")[note 2] per degree (or radian) of change in sideslip angle (the "${\displaystyle \beta }$").

The purpose of dihedral effect is to contribute to stability in the roll axis. It is an important factor in the stability of the spiral mode which is sometimes called "roll stability".[note 3] The dihedral effect does not contribute directly to the restoring of "wings level", but it indirectly helps restore "wings level" through its effect on the spiral mode of motion described below.

Aircraft designers may increase dihedral angle to provide greater clearance between the wing tips and the runway. This is of particular concern with swept-wing aircraft, whose wingtips could hit the runway on rotation/touchdown. In military aircraft dihedral angle space may be used for mounting materiel and drop-tanks on wing hard points, especially in aircraft with low wings. The increased dihedral effect caused by this design choice may need to be compensated for, perhaps by decreasing the dihedral angle on the horizontal tail.

In Figure 2, the sideslip conditions produce greater angle of attack on the forward-yawed wing and smaller angle of attack on the rearward-yawed wing. This alteration of angle of attack by sideslip is visible in Figure 2. As greater angle of attack produces more lift (in the usual case, when the wing is not near stalling), the forward wing will have more lift and the rearward wing will have less lift. This difference in lift between the wings is a rolling moment, and it's caused by the sideslip. It's a contribution to the total dihedral effect of the aircraft.

The rolling moment created by the sideslip (labeled as "P") tends to roll the aircraft back to wings level. More dihedral effect tries to roll the wings in the "leveling" direction more strongly, and less dihedral effect tries to roll the wings in the "leveling" direction less strongly. Dihedral effect helps stabilize the spiral mode by tending to roll the wings toward level in proportion to the amount of sideslip that builds up. It's not the whole picture however. At the same time that angle of sideslip is building up, the vertical fin is trying to turn the nose back into the wind, much like a weathervane, minimizing the amount of sideslip that can be present. If there is no sideslip, there can be no restoring rolling moment. If there is less sideslip, there is less restoring rolling moment. Yaw stability created by the vertical fin opposes the tendency for dihedral effect to roll the wings back level by limiting sideslip.

The spiral mode is the tendency to slowly diverge from, or the tendency to slowly return to wings level. If the spiral mode is stable, the aircraft will slowly return to wings-level, if it is unstable, the aircraft will slowly diverge from wings-level. Dihedral effect and yaw stability are the two primary factors that affect the stability of the spiral mode, although there are other factors that affect it less strongly.

Wing sweepback also increases dihedral effect. This is one reason for anhedral configuration on aircraft with high sweep angle, as well as on some airliners, even on low-wing aircraft such as the Tu-134 and Tu-154, with the small German 1930s – 1945 biplanes of the Bücker Flugzeugbau, the Bucker Jungmann two-seat trainer and more famous Bücker Jungmeister aerobatic competition biplane, both having approximately 11° of wing sweepback giving both designs a degree of dihedral effect, beyond the small amount of dihedral both biplanes' designs also featured.

The center of mass, usually called the center of gravity or "CG", is the balance point of an aircraft. If suspended at this point and allowed to rotate, a body (aircraft) will be balanced. The front-to-back location of the CG is of primary importance for the general stability of the aircraft, but the vertical location has important effects as well.

The vertical location of the CG changes the amount of dihedral effect. As the "vertical CG" moves lower, dihedral effect increases. This is caused by the center of lift and drag being further above the CG and having a longer moment arm. So, the same forces that change as sideslip changes (primarily sideforce, but also lift and drag) produce a larger moment about the CG of the aircraft. This is sometimes referred to as the pendulum effect.[note 5]

An extreme example of the effect of vertical CG on dihedral effect is a paraglider. The dihedral effect created by the very low vertical CG more than compensates for the negative dihedral effect created by the strong anhedral[note 6] of the necessarily strongly downward curving wing.

Anhedral on the wings and tailplane of an RAF Harrier GR7A.

Front view of an Antonov An-124. The anhedral wings are clearly seen.

Military fighter aircraft often have near zero or even anhedral angle reducing dihedral effect and hence reducing the stability of the spiral mode. This increases maneuverability which is desirable in fighter-type aircraft.

Anhedral angles are also seen on aircraft with a high mounted wing, such as the very large Antonov An-124 and Lockheed Galaxy cargo aircraft. In such designs, the high mounted wing is above the aircraft's center of gravity which confers extra dihedral effect due to the pendulum effect (also called the keel effect) and so additional dihedral angle is often not required. Such designs can have excessive dihedral effect and so be excessively stable in the spiral mode, so anhedral angle on the wing is added to cancel out some of the dihedral effect so that the aircraft can be more easily maneuvered.

McDonnell Douglas F-4 Phantom II showing polyhedral wing and anhedral tail

Most aircraft have been designed with planar wings with simple dihedral (or anhedral). Some older aircraft such as the Vought F4U Corsair and the Beriev Be-12 were designed with gull wings bent near the root. Modern polyhedral wing designs generally bend upwards near the wingtips (also known as tip dihedral), increasing dihedral effect without increasing the angle the wings meet at the root, which may be restricted to meet other design criteria.

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