How sweep creates an aerodynamic coupling between yaw and roll

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.

**Here's how sweep 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 sweep angle of each wing in relation to the airflow will have a large effect on each wing's lift coefficient, while at low angles-of-attack this relationship will be less pronounced.

**If a swept wing is flying at a negative angle-of-attack, creating a negative lift force, then the direction of the roll torque will reversed. If a swept wing is flying at a negative angle-of-attack, then when the aircraft yaws to the left in relation to the actual direction of the flight path and airflow (relative wind), creating a right-to-left sideways component in the airflow over the wing, and the right wing becomes "less swept" in relation to the airflow, and the left wing becomes "more swept" in relation to the airflow, as shown in the illustration, then the right wing creates more (negative) lift and the left wing creates less (negative) lift, and this creates a roll torque toward the right. A wing with anhedral--not dihedral--would behave the same way in the same airflow. Unlike the roll torque created by dihedral or anhedral--which always acts in the same direction regardless of whether the wing as a whole is flying at a positive angle-of-attack, at a negative angle-of-attack, or at the zero-lift angle-of-attack--the direction of the roll torque created by sweep reverses in direction when the wing goes from a positive angle-of-attack to a negative angle-of-attack.