Competing effects of sweep and anhedral at various angles-of-attack

April 16 2005 edition
Steve Seibel
www.aeroexperiments.org
steve at aeroexperiments.org

 

NOTE August 2006: all the content in this section has now received a fresher treatment in the "Semi- Unconventional Aerophysics Tutorial" pages. Many items that are not yet covered in the main text pages of the SUAT section are covered briefly on the page entitled "Pool of images for Semi-Unconventional Aerophysics Tutorial Pages." This older material is still accurate to the best of my knowledge except for one point: I now feel that the suggestion that increasing wingtip washout (as opposed to increasing sail billow) will tend to create an anhedral geometry was unwarranted.

 

This article consists primarily of some excerpts from the longer article entitled "How billow and washout increase the net geometric anhedral of a swept wing, and other related topics". The passages marked "*" are excerpts from this longer article and the passages marked "**" are additional notes.

**When the nose of an aircraft is not exactly aligned with the actual direction of the flight path through the airmass, this creates a sideways component in the airflow (relative wind) over the aircraft. This situation is called a "slip" or a "skid". If the aircraft's wing has dihedral, anhedral, or sweep, then the sideways airflow will interact with the wing's 3-dimensional geometry to create a roll torque.

*The roll torque created by dihedral or anhedral during a sideslip or skid is caused by the fact that the left wing is experiencing a higher or lower angle-of-attack than the right wing, due to the sideways component in the airflow (relative wind).

*To understand this, look at these photographs of wings and models of wings, taken from the side. (Photo 1: Superfloater ultralight sailplane with dihedral.) (Photo 2: model of wing with dihedral) (Photo 3: model of wing with anhedral). In many of them, you can see the underside of the left wing and the top side of the right wing, or vs. vs.. If the aircraft were moving directly toward the camera, which would involve an extreme angle of sideways motion through the airmass, i.e. an extreme sideslip angle, then clearly there would be a very large difference in angle-of-attack between the left and right wings: one wing would be generating a positive lift force and the other side of the wing would be generating a negative lift force. In real-life situations, involving much smaller angles of sideways motion (sideslip), neither wing will be flying at a negative angle-of-attack, but the difference in angle-of-attack between the left and right wings will still exist to a smaller degree. This will create a roll torque. Use your imagination and visualize what kind of roll torque will be created as a small sideways airflow component flows over these wings. You will see that the left wing will be developing more lift than the right wing, or vs. vs., due to the difference in angle-of-attack between the left and right wings.

*Just as dihedral tends to return an aircraft to wings-level whenever a wing drops in turbulence and the aircraft starts sliding sideways, so too does dihedral tend to make an aircraft respond sluggishly to a pilot's roll inputs (unless a rudder or spoilerons are being used to overcome adverse yaw and/or yaw rotational inertia and avoid a sideslip).

*Just as anhedral tends to make an aircraft roll into a tighter bank whenever a wing drops in turbulence and the aircraft starts sliding sideways, so too does anhedral tend to make an aircraft respond more quickly to a pilot's roll inputs (at least in cases where a rudder or spoilerons are not being used to overcome adverse yaw and/or yaw rotational inertia and avoid a sideslip.)

*The roll torque created when a wing with anhedral or dihedral experiences a sideways airflow leads to a "coupling between yaw and roll". What does this mean? If a pilot applies heavy right rudder to yaw the nose of the aircraft toward the right, or if adverse yaw or any other phenomenon yaws the nose of the aircraft toward the right, then the aircraft will be moving sideways through the air. The nose will not be pointing the same direction that the aircraft is actually moving through the airmass. There will be a sideways component in the airflow (relative wind) over the aircraft, blowing from the left wingtip toward the right wingtip. Then dihedral or anhedral will create a roll torque:

*If the wing has dihedral, then when the pilot's rudder input (or adverse yaw or any other factor) yaws the nose of the aircraft toward the right (in relation to the actual direction of the flight path and airflow) as described above, the resulting left-to-right sideways component in the airflow will cause the left wing to experience a higher angle-of-attack than the right wing, and this will create a roll torque toward the right. So an initial yaw toward the right ends up creating a roll torque toward the right. This is a "positive coupling" between yaw and roll.

*In the same situation, if the wing has anhedral rather than dihedral, the left-to right sideways component in the airflow will cause the right wing to experience a higher angle-of-attack than the left wing, and this will create a roll torque toward the left. So an initial yaw toward the right ends up creating a roll torque toward the left. This is a "negative coupling between yaw and roll.

*Therefore, over-enthusiastic use of a rudder or wingtip drag device to "skid" the nose in the direction of the intended turn (as opposed to using the "right" amount of rudder to overcome adverse yaw and keep the nose aligned with the flight path and airflow (relative wind), or using no rudder and allowing the nose to swing the "wrong" way due to adverse yaw) will create a helpful roll torque in the case of a wing with dihedral--this is why many aircraft such as Gentle Lady RC sailplanes, Dragonfly tugs and even Cessna 152's can be controlled with the rudder alone, without use of the ailerons. (Granted this technique is not always very efficient, and in some cases can be an invitation to a spin).

*By the same logic, over-enthusiastic use of a rudder to "skid" the nose in the direction of the intended turn (as opposed to using the "right" amount of rudder to overcome adverse yaw and keep the nose aligned with the flight path and airflow (relative wind), or using no rudder and allowing the nose to swing the "wrong" way due to adverse yaw) will create an unfavorable roll torque in the case of a wing with anhedral. In an aircraft with anhedral, it is very possible for a left rudder input to cause a right bank followed by a right turn--this vividly demonstrates that "yawing" (i.e. swinging the nose to one side in relation to the direction of the flight path and relative wind) and "turning" (i.e. creating a curvature of the flight path) are not at all the same thing! And by the same logic, on an aircraft with anhedral, adverse yaw will actually create a helpful roll torque! All this will be discussed in much more detail in the areas of this website that deal with experiments with rudders on flex-wing hang gliders with anhedral.

*Sweep is very similar to dihedral: it creates a "positive coupling between yaw and roll". When a swept-wing aircraft yaws to the left in relation to the actual direction of the flight path and airflow (relative wind), this creates a right-to-left sideways component in the airflow over the aircraft. The right wing becomes "less swept" in relation to the airflow, and the left wing becomes "more swept" in relation to the airflow. (Illustration, center right of page). The right wing creates more lift and the left wing creates less lift, and this creates a roll torque toward the left, just as would a wing with dihedral in the same airflow.

*Swept-wing aircraft often have a mild amount of anhedral to reduce the excessive "positive coupling between yaw and roll" that would otherwise be created by the sweep.

*The roll torque created by a swept wing in a sideways airflow is highly dependent on the magnitude of the G-load or lift force that the wing is generating. If the wing is "unloaded" to the zero-lift angle-of-attack, then the left and right wings will create the same amount of lift (none), and there will be no roll torque. In a maneuver where the aircraft is creating multiple G's, the aircraft will create more roll torque in the presence of a sideways airflow than it would in ordinary 1-G flight.

*In ordinary 1-G flight, the roll torque created by a swept wing in a sideways airflow is still highly dependent on the wing's angle-of-attack. This illustration (top of page) shows that at high angles-of-attack, changing the wing's sweep angle in relation to the airflow will have a large effect on the wing's lift coefficient, while at low angles-of-attack this relationship will be less pronounced.

*The roll torque created by dihedral or anhedral is more pronounced when the wing is generating a large G-loading. But in ordinary 1-G flight, the roll torque created by dihedral or anhedral is relatively independent of the wing's angle-of-attack.

*Therefore if an aircraft has both sweep and anhedral, it's quite possible for the anhedral to dominate at high airspeeds (low angles-of-attack), and for the sweep to dominate--creating a dihedral-like effect--at low airspeeds (high angles-of-attack). The aircraft's roll stability characteristics--and its response to rudder inputs--would be very different at low airspeeds than at high airspeeds. I've seen this effect while experimenting with a rudder on a hang glider with sweep and anhedral, and also while experimenting with a rudder on a modified variable-geometry Zagi RC glider with sweep and anhedral. In these aircraft, at low airspeeds a left rudder input created a left bank and a left turn, while at high airspeeds, a left rudder input created a right bank and a right turn.

**For more on the competing effects of sweep and anhedral, browse this collection of "djaerotech" links from the "links" page of the Aeroexperiments website. (These links are from a model airplane q-and-a webpage and contain some insightful comments on sweep, dihedral, anhedral, fins, yaw and roll stability, etc.—though I wish the authors wouldn’t make so many references to "centrifugal force"!)

www.djaerotech.com/dj_askjd/dj_questions/sweepback.html
www.djaerotech.com/dj_askjd/dj_questions/sweepdihedral.html
www.djaerotech.com/dj_askjd/dj_questions/fwingdihedral.html
www.djaerotech.com/dj_askjd/dj_questions/sweepdihedral2.html
www.djaerotech.com/dj_askjd/dj_questions/flywingfly.html

(If you liked these links, see the "links" page of the Aeroexperiments website for a few more.)