Misconceptions: the "simple" view of dihedral

Misconceptions: the "simple" view of how dihedral contributes to roll stability

Steve Seibel
www.aeroexperiments.org

This page is still under construction!
This page was last modified on September 13, 2006

 

One version of the "simple" view of how dihedral contributes to roll stability goes something like this: when an aircraft with dihedral tips into a bank, the lift vector from the low wing becomes "more vertical" than the lift vector from the high wing. This creates a roll torque that acts to bring the aircraft toward wings-level.

Another version of the "simple" view of how dihedral contributes to roll stability goes something like this: when an aircraft with dihedral tips into a bank, the low wing has a greater "projected area" than the high wing. This creates a roll torque that acts to bring the aircraft toward wings-level.

The "simple" view of dihedral makes no sense. In a head-on view of the aircraft, the lift vector generated by each wing acts perpendicular to the respective wing, not perpendicular to the horizon. This is true regardless of the bank angle. As long as the lift vectors from each of the two wings are equal in size or magnitude, the fact that one of the lift vectors happens to be "more vertical" than the other lift vector with respect to the horizon will do nothing at all to create a roll torque about the aircraft's CG.

The magnitude of the lift vector generated by each wing will be determined by the airspeed and by the angle-of-attack. The aircraft's pitch stability mechanisms that control the angle-of-attack of the wings operate around the aircraft's own pitch axis, not around an axis that is horizontal with respect to the outside world. Therefore, as long as there is no sideways component in the airflow over the aircraft, there is no reason that the wing that is "more horizontal" should have a greater angle-of-attack than the wing that is "less horizontal". In other words, as long as there is no sideways component in the airflow over the aircraft, there is no reason that the lift vector that is "more vertical" should be any larger than the lift vector that is "less vertical".

Note that the "simple view" of how dihedral contributes to roll stability gives us no insight at all as to how the rudder can be used as a roll control on an aircraft with dihedral.

Here are some sources that advocate the "simple" view of dihedral:

(To be inserted)

Here are some sources that critique the "simple" view of dihedral:

"Model Aircraft Aerodynamics" by Martin Simons. 2d edition 1987. Argus Books. See pp. 166-167, especially figure 12-17.

The "Roll-Wise Stability" section in John S. Denker's superb "See How It Flies" website.

 

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