Glossary term
Dihedral Effect
Rolling-moment response to sideslip, commonly represented by the lateral stability derivative C_l_beta in aircraft flight dynamics.
Definition
phenomenonDihedral effect is the aircraft rolling-moment response to sideslip, usually represented by the derivative C_l_beta.
Dihedral effect describes how sideslip creates rolling moment. It is influenced by wing dihedral angle, wing sweep, vertical placement of the wing and mass, fuselage side force, tail surfaces, angle of attack, Mach number, configuration, stores and aeroelastic deformation. It is not the same as wing dihedral angle: the angle is geometry, while dihedral effect is an aerodynamic response derivative. The sign of C_l_beta must be interpreted with the stated sideslip and rolling-moment convention.
Dihedral effect is the rolling-moment response caused by sideslip. In a linearized lateral-directional model it is commonly represented by:
where C_l is rolling-moment coefficient, \beta is sideslip angle in radians and C_{l_\beta} is the derivative of rolling moment with respect to sideslip. The derivative sign depends on the chosen axes, beta definition and rolling-moment convention.
Engineering Role
Dihedral effect helps determine spiral tendency, Dutch-roll coupling, roll response after yaw disturbances, rudder-roll coupling, sideslip limits and lateral handling qualities. It is one of the reasons yaw and roll cannot be treated as independent axes in real aircraft.
The name can be misleading. Wing dihedral angle often contributes to dihedral effect, but it is not the whole phenomenon. Wing sweep, high-wing or low-wing placement, fuselage side force, vertical tail side force, nacelles, stores, angle of attack, Mach number, flap setting, landing gear, ice, damage and aeroelastic deformation can all change the effective derivative.
Worked Example: Sideslip Rolling Moment and Aileron Equivalent
A lateral-directional model uses the following convention: the listed C_{l_\beta} sign creates a rolling moment that tends to reduce the stated sideslip disturbance.
| Parameter | Value |
|---|---|
| Sideslip angle, \beta | 3.5^\circ |
| Dihedral-effect derivative, C_{l_\beta} | -0.060\ \text{rad}^{-1} |
| Dynamic pressure, \bar{q} | 3600\ \text{N/m}^2 |
| Reference area, S | 18.0\ \text{m}^2 |
| Wing span, b | 11.0\ \text{m} |
| Aileron derivative magnitude, $ | C_{l_{\delta_a}} |
Convert sideslip to radians:
Estimate the rolling-moment coefficient increment:
The dimensional rolling moment is:
A simple aileron-equivalent comparison asks what aileron deflection magnitude would create the same rolling-moment coefficient magnitude:
Convert to degrees:
Engineering comment: this comparison does not say that sideslip is equivalent to an aileron command. It only gives a first-pass scale for the rolling moment at one flight condition and sign convention. A real assessment must include yawing moment, roll damping, yaw damping, rudder response, aileron limits, sensor validity, configuration effects and uncertainty.
Distinction from Related Terms
Dihedral effect is not wing dihedral angle. Wing dihedral angle is a geometric angle. Dihedral effect is an aerodynamic rolling-moment response to sideslip.
Dihedral effect is not directional stability. Directional stability is mainly a yawing-moment response to sideslip, represented by C_{n_\beta}. Dihedral effect is a rolling-moment response to sideslip, represented by C_{l_\beta}.
Dihedral effect is not roll damping. Roll damping is rolling moment due to roll rate. Dihedral effect is rolling moment due to sideslip.
Dihedral effect is not aileron control effectiveness. Aileron effectiveness is rolling moment due to aileron deflection. Dihedral effect occurs even with fixed controls if sideslip is present.
Dihedral effect is not Dutch roll or spiral mode. Those are coupled dynamic modes. Dihedral effect is one derivative that influences them together with directional stability, roll damping, yaw damping, inertia and control laws.
Validation and Common Mistakes
Dihedral effect can be estimated from wind-tunnel sideslip sweeps, CFD, handbook stability methods, flight-test sideslip maneuvers, system identification or validated aerodynamic databases. A defensible value states the coordinate system, beta sign convention, rolling-moment sign convention, flight condition, configuration, Mach number, Reynolds number, angle-of-attack range, sideslip range, control-surface positions, reference area, reference span and uncertainty.
Common mistakes include:
- treating wing dihedral angle as if it were the complete dihedral effect;
- reporting C_{l_\beta} without sign convention;
- comparing derivatives from models that use different body, stability or wind axes;
- ignoring wing sweep, vertical placement, fuselage side force or tail contribution;
- assuming stronger dihedral effect always improves handling qualities;
- checking spiral mode without the balance of directional stability, roll damping and yaw damping;
- using clean-cruise derivatives for approach, high angle of attack, icing, stores or damaged configurations.