The dihedral-like effect of sweep depends strongly upon angle-of-attack

The dihedral-like effect of sweep depends strongly upon angle-of-attack

Steve Seibel
www.aeroexperiments.org

This page was last modified on September 13, 2006

 

The dihedral-like effect of sweep depends strongly upon the angle-of-attack of the wing as a whole.

For any given airspeed, and for a given yaw (slip) angle between the aircraft's heading and the actual direction of the flight path and relative wind, the "downwind" roll torque created by sweep will be much stronger when the wing as a whole is flying at a high angle-of-attack, than when the wing as a whole is flying at a low angle-of-attack. This means that for any given airspeed, the dihedral-like effect of sweep will be much more pronounced when the wing is generating a large amount of lift (i.e. when the G-loading is high) than when the wing is generating a small amount of lift (i.e. when the G-loading is low).

When the wing as is made to fly at the zero-lift angle-of-attack (i.e. when the G-loading is zero), then the wing's swept geometry will not create any roll torque even if there is a sideways component in the relative wind.

When the wing as a whole is made to fly at a negative angle-of-attack (or more precisely for non-symmetrical airfoils, a negative lift coefficient or a negative-lift angle-of-attack), then a sideways component in the relative wind will create an anhedral-like "upwind" roll torque rather than a dihedral-like "downwind" roll torque.

The above 2 points will make it rather tricky to use the rudder as the sole means of roll control in a swept-wing aircraft with no dihedral, if 0-G and negative-G (e.g. sustained inverted) maneuvers are contemplated! The rudder will create no roll torque at the zero-lift angle-of-attack, and the rudder will create a "backwards" roll torque at negative-lift angles-of-attack! These dynamics were explored experimentally with the variable-geometry Zagi with the controllable rudder and ground-adjustable anhedral/dihedral. (Photo 1, photo 2.)

When the G-loading is kept constant (e.g. during normal 1-G flight), a high angle-of-attack will correspond to low-speed flight and a low angle-of-attack will correspond to high-speed flight. Therefore, for a given yaw (slip) angle between the aircraft's heading and the actual direction of the flight path and relative wind, the "downwind" roll torque created by sweep will generally be stronger when the aircraft is flying at a low airspeed than when the aircraft is flying at a high airspeed.

This diagram (see the uppermost diagram) illustrates the reduction of lift coefficient due to sweep, and the way that this is most pronounced at high angles-of-attack. We saw in the previous tutorial page that when there is a sideways component in the relative wind, the "upwind" wing of a swept-wing aircraft meets the airflow in a less swept manner and the "downwind" wing of a swept-wing aircraft meets the air in a more swept manner. When we keep this in mind, this diagram becomes the key to understanding why the dihedral-like roll torque created by a swept wing in the presence of a sideways component in the relative wind is most pronounced when the wing as a whole is flying at a high angle-of-attack, and is least pronounced when the wing as a whole is flying at a low angle-of-attack.

For example, if the yaw (slip) angle between the aircraft's heading and the actual direction of the flight path and relative wind happens to be such that the "upwind" wing has zero sweep in relation to the relative wind and the "downwind" wing has the same sweep in the relation to the relative wind as is depicted by the lower ("swept") line on the diagram, then the roll torque generated by the swept planform will be determined by the vertical distance between the two lines on the diagram. Clearly, this distance is greater when the wing as a whole is flying at a high angle-of-attack than when the wing as a whole is flying at a low angle-of-attack. At the zero-lift angle-of-attack, the two lines meet, and the interaction between a sideways component in the relative wind and the swept planform of the wing will generate no roll torque at all.

It's interesting to note the following: sweep is fundamentally similar to dihedral or anhedral in that that all of these geometries create a roll torque in the presence of a sideways airflow by creating a difference in lift coefficient between the left and right wings. However, this difference in lift coefficients is based on a difference in angle-of-attack between the left and right wings in the case of a wing with dihedral or anhedral. This difference in lift coefficients is not based on a difference in angle-of-attack between the left and right wings in the case of a wing with sweep. If a swept wing has no dihedral or anhedral, then the left wing will always be at the same angle-of-attack as the right wing, regardless of any sideways component in the airflow.

(Source of diagrams: "Aerodynamics for naval aviators (NAVWEPS 00-80T-80)" by Hugh H. Hurt (1965, Office of the Chief of Naval Operations, Aviation Training Division, for sale by the Supt. of Documents, US Govt. Printing Office))

See these sources for more notes on how the dihedral-like effects of sweep are strongly dependent on angle-of-attack or lift coefficient:

"Swept Wings and Effective Dihedral" by Bill and Bunny Kuhlman. From RC Soaring Digest, January-March 2000.

 

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