Glossary term
Wing Dihedral Angle
Wing geometry angle describing the upward or downward inclination of a wing panel relative to the aircraft lateral reference plane.
Definition
quantityWing dihedral angle is the angle by which a wing panel inclines upward or downward from the aircraft lateral reference plane when viewed in the front plane.
Positive dihedral usually means the wing tip is higher than the wing root. Negative dihedral is often called anhedral. A wing with multiple panel angles may be described as polyhedral. The angle is a geometric quantity, not the same as dihedral effect. Dihedral effect is the rolling-moment response to sideslip and is influenced by wing dihedral, sweep, vertical placement, fuselage shape, tail surfaces, angle of attack, Mach number and configuration.
Wing dihedral angle is the inclination of a wing panel relative to the aircraft lateral reference plane when viewed from the front or rear. A conventional positive dihedral has the wing tip higher than the root. A negative value is commonly called anhedral.
For a straight panel measured between two span stations:
where \Delta z is the vertical change between the two stations and \Delta y is the spanwise distance between them. The sign convention must state which direction is positive and which structural or aerodynamic reference line is being measured.
Engineering Role
Wing dihedral angle is used to shape lateral-directional stability, sideslip response, roll-yaw coupling, handling qualities, ground-clearance geometry, fuel and landing-gear packaging, structural load paths and aeroelastic behavior. It is also part of aircraft configuration definition, because a stability model, wind-tunnel model, CFD geometry and production drawing must use the same reference geometry if their results are to be compared.
Dihedral angle is not equal to dihedral effect. Dihedral angle is geometry. Dihedral effect is the rolling-moment tendency created by sideslip and is often represented in a linear model by a derivative such as C_{l_\beta}. The derivative can be influenced by wing dihedral, but also by sweep, vertical wing location, fuselage side force, tail geometry, angle of attack, high-lift devices, Mach number, stores and aeroelastic deformation.
Worked Example: Geometry and Sideslip Screening
A wing panel is measured from the aircraft centerline reference station to the tip reference station:
| Parameter | Value |
|---|---|
| Spanwise distance, \Delta y | 5.50\ \text{m} |
| Tip vertical rise, \Delta z | 0.42\ \text{m} |
| Dynamic pressure, \bar{q} | 3200\ \text{N/m}^2 |
| Reference area, S | 16.2\ \text{m}^2 |
| Wing span, b | 10.8\ \text{m} |
| Sideslip angle, \beta | 4.0^\circ |
| Rolling-moment derivative, C_{l_\beta} | -0.075\ \text{rad}^{-1} |
The geometric dihedral angle is:
Convert to degrees:
If a layout review targets:
the required tip rise over the same span station is:
The drawing would therefore need about:
additional tip rise if the same measurement stations and reference line are used.
Now use the separate lateral-directional derivative only as a first screen. Convert sideslip to radians:
The rolling-moment coefficient increment is:
The dimensional rolling moment is:
Engineering comment: the 4.37^\circ result is a geometry measurement. The -2930\ \text{N m} result is a stability-derivative screen at one flight condition and sign convention. Changing the dihedral angle may change C_{l_\beta}, but the derivative must be obtained from an aerodynamic model, wind-tunnel result, CFD, flight test or validated handbook method. It should not be inferred from geometry alone.
Distinction from Related Terms
Wing dihedral angle is not wing sweep angle. Sweep is a planform fore-aft angle; dihedral is an out-of-plane vertical inclination.
Wing dihedral angle is not wing twist. Twist changes local incidence along the span; dihedral changes vertical panel inclination. A wing can have both twist and dihedral, and each must be measured with its own reference line.
Wing dihedral angle is not sideslip angle. Sideslip describes the aerodynamic flow direction relative to the aircraft body. Dihedral can influence the rolling moment produced by sideslip, but it is not itself a flow angle.
Wing dihedral angle is not Dutch roll, spiral mode or roll subsidence. Those are lateral-directional dynamic modes. Dihedral can influence the derivatives that shape those modes, but the modes also depend on directional stability, roll damping, yaw damping, inertia, control laws, sensors, actuators and flight condition.
Wing dihedral angle is not aileron or rudder control effectiveness. Control effectiveness describes rolling or yawing moment generated by control-surface deflection. Dihedral geometry can change the coupled response, but it is not a control derivative.
Validation and Common Mistakes
A defensible dihedral-angle value states the coordinate system, sign convention, measured span stations, vertical datum, reference line, whether the measurement is geometric or effective, whether the wing is unloaded or loaded, and whether the wing has a single panel, breaks, cranks, winglets or polyhedral segments.
Common mistakes include:
- reporting a dihedral angle without stating whether positive tip-up or tip-down is used;
- mixing front-view dihedral with planform sweep or local twist;
- measuring from different span stations in drawing, CFD, wind-tunnel and flight-test geometry;
- treating anhedral as a separate variable instead of negative dihedral under the stated convention;
- assuming a larger dihedral angle automatically improves handling qualities;
- using a static ground geometry after aeroelastic deflection has changed the loaded wing shape;
- inferring C_{l_\beta} directly from dihedral angle without validated aerodynamic data;
- mixing degrees and radians in stability-derivative calculations.