Competing effects of sweep and anhedral

Competing effects of sweep and anhedral

Steve Seibel
www.aeroexperiments.org

This page was last modified on August 29, 2006

 

In "The roll torque created by dihedral or anhedral is not strongly dependent on the angle-of-attack of the wing as a whole", we saw that for a given yaw (slip) angle between the aircraft's heading and the actual direction of the flight path and relative wind, and a given airspeed, the roll torque created by dihedral or anhedral is not strongly dependent on the angle-of-attack of the wing as a whole. We also saw that for a given yaw (slip) angle and a given G-loading (e.g. 1-G flight), the roll torque created by dihedral or anhedral tends to be greater at high airspeeds than at low airspeeds.

In "The dihedral-like effect of sweep depends strongly upon angle-of-attack", we saw that for a given yaw (slip) angle between the aircraft's heading and the actual direction of the flight path and relative wind, and a given airspeed, the "downwind" roll torque created by sweep is strongly dependent on the angle-of-attack of the wing as a whole. We also saw that for a given yaw (slip) angle and a given G-loading (e.g. 1-G flight), the roll torque created by sweep tends to be greater at low airspeeds than at high airspeeds.

If a wing has both sweep and anhedral, then for a given yaw (slip) angle, the "downwind" roll torque generated by sweep will depend strongly on the angle-of-attack of the wing as a whole, and the "upwind" roll torque generated by anhedral will not depend strongly on the angle-of-attack of the wing as a whole. This means that if the sweep and the anhedral create equal and opposite roll torques in the presence of a sideways airflow when the wing as a whole is at some intermediate angle-of-attack, then the dihedral-like effect of sweep will tend to dominate when the wing as a whole is flying at a higher angle-of-attack, and the anhedral will tend to dominate when the wing as a whole is flying at a lower angle-of-attack.

Depending on how much sweep or anhedral are present, one or the other of these effects may end up dominating across most of the flight envelope.

In an aircraft with dihedral and sweep, if the anhedral exactly balances the dihedral-like effects of sweep during 1-G flight at some given airspeed, then the following will be true:

During 1-G flight at a lower airspeed (higher angle-of-attack), sweep will dominate, creating a net "downwind" roll torque in the presence of a sideways component in the relative wind.

During 1-G flight at a higher airspeed (lower lift angle-of-attack), anhedral will dominate, creating a net "upwind" roll torque in the presence of a sideways component in the relative wind.

During flight at some given airspeed, if the G-load is high enough (i.e. if the angle-of-attack is high enough), the sweep will dominate and the wing will create a net "downwind" roll torque in the presence of a sideways component in the relative wind. (In some cases where the sweep angle is low in relation to the amount of anhedral, we might not see these dynamics because we might reach the stall angle-of-attack first.)

During flight at the same airspeed, if the G-load is low enough (i.e. if the angle-of-attack is low enough), the anhedral will dominate and the wing will create a net "upwind" roll torque in the presence of a sideways component in the relative wind.

During 0-G flight (i.e. when the wing as a whole is at the zero-lift angle-of-attack so that the lift coefficient of the wing as a whole is zero), sweep will not create any roll torque even if there is a sideways component in the relative wind. In this case the anhedral will dominate and the wing will create a net "upwind" roll torque in the presence of a sideways component in the relative wind, for any non-zero airspeed.

During negative-G flight (i.e. when the wing as a whole is at a negative-lift angle-of-attack), then the sweep will actually contribute an anhedral-like effect, so the wing will generate a very strong anhedral-like "upwind" roll torque or "negative coupling between yaw (slip) and roll" in the presence of a sideways component in the relative wind.

(These dynamics were explored experimentally with the variable-geometry Zagi with the controllable rudder and ground-adjustable anhedral/dihedral. (Photo 1, photo 2.) For certain anhedral angles, applying the rudder created a "backwards" roll torque at high airspeeds and a "normal" roll torque at low airspeeds.)

Swept-wing aircraft are often given anhedral to partially counterbalance the dihedal-like effects of sweep. (In such cases the primary purpose of the sweep is not to provide a dihedral-like effect, but rather to provide good high-speed flight characteristics as the airflow nears the speed of sound, or in the case of a tail-less aircraft, to provide yaw stability.) In many of these aircraft, the anhedral angle is mild enough that the dihedral-like effect of sweep still dominates to some degree across most of the flight envelope, particularly at the high angle-of-attack (low airspeed) end of the flight envelope, while the anhedral may dominate (causing a rudder input to create a "backwards" roll torque) at very low angles-of-attack, e.g. during very high-speed flight or during reduced-G "pushover" manuevers. During 0-G or negative-G maneuvering the anhedral characteristics of the wing will be even more pronounced, as we've noted above.

The "other side of this coin" is that it is common for aircraft with both sweep and dihedral to suffer from an excessive dihedral-like "downwind" roll torque when there is a sideways component in the relative wind, or "positive coupling between slip (yaw) and roll, in the low-airspeed high-angle-of-attack part of the flight envelope. This is a factor in the "Dutch Roll" oscillations that some swept-wing aircraft experience in this part of the flight envelope. (These dynamics were also explored with the variable-geometry Zagi.)

 

Here is an excellent link that addresses the combined effects of sweep and dihedral or anhedral at various airspeeds, as well as many other topics of great interest: "Swept Wings and Effective Dihedral" by Bill and Bunny Kuhlman. From RC Soaring Digest, January-March 2000.

Here is a good link from a good Q-and-A site for model aviation that addresses the combined effects of sweep and dihedral at various airspeeds: www.djaerotech.com/dj_askjd/dj_questions/sweepdihedral.html

 

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