Roll and yaw torques due to the difference in the airspeed of the left and right wingtips
This page was last modified on September 14, 2006
In a turn, the outside or high wingtip must move forward faster than the inside or low wingtip. This effect is especially pronounced in long-spanned, slow-flying aircraft.
If we set aside the complications created by a descending or climbing turn and focus on the simplified case of a (powered) turn that is neither climbing nor descending with respect to the airmass, we can see that the faster-moving outside wingtip will tend to experience more lift, which will create a rolling-in torque.
However, the faster-moving outside wingtip will also experience more drag, which will tend to yaw the nose of the aircraft to point toward the outside or high side of the turn. In other words the aircraft will tend to slip. If the aircraft has dihedral or sweep, the slipping (sideways) component in the relative wind will tend to create a rolling-out torque, which will promote roll stability or reduce roll instability. If the aircraft has anhedral, the slipping (sideways) component in the relative wind will create a rolling-in torque, which will reduce roll stability or increase spiral instability.
One reason many aircraft have dihedral is to mitigate some of the rolling-in torque caused by the difference in wingtip airspeeds, and reduce the aircraft's tendency to enter a spiral dive. However, at any time that the pilot applies some inside rudder to keep the nose (or more precisely the wing) aligned with the direction of the relative wind, the dihedral will not experience a sideways component in the airflow, which means the dihedral will not create a stabilizing rolling-out torque.
The difference in airspeed between the two wingtips will be greatest when the airspeed is low and the bank angle is moderate. At very steep bank angles, the difference in airspeed between the two wingtips becomes less important, not only because steep bank angles are always associated with high airspeeds, but also because at very steep bank angles a turn involves a great deal of rotation around an aircraft's pitch axis and only a little rotation about the aircraft's yaw axis.
Here are some outside sources that make note of the way that a turn creates a difference in airspeed between the inside and outside wingtips:
"Differential Wingtip Speed; Overbanking
" from John S. Denker's superb "See How it Flies" website.
Advance to Curvature in the relative wind about the yaw axis
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