How billow contributes to anhedral

The flexible hang-glider wing: how billow contributes to anhedral

Steve Seibel
www.aeroexperiments.org

October 13, 2006 edition

 

In "Oblique and side views of 'M'-shaped wings", we examined some wings that had dihedral on their inboard panels and anhedral on their outboard panels. We explored how from the right viewing angle, we could see the top surface of the outboard wing panel nearest the camera, and we could see the bottom surface of the outboard wing panel furthest from the camera, and we could see the bottom surface of the inboard wing panel nearest the camera, and we could see the top surface of the inboard wing panel furthest from the camera. We noted that whenever the nose of an aircraft with an "M"-shaped wing is pointing in a different direction than the aircraft is actually travelling through the airmass, i.e. whenever there is a sideways component in the relative wind, the dihedral geometry of the inboard panels will interact with the sideways airflow to create a "downwind" roll torque, and the anhedral geometry of the outboard wing panels will interact with the sideways airflow to create an "upwind" roll torque. We noted that the "upwind" roll torque created by the anhedral geometry of the outer wing panels will be more important than the "downwind" roll torque created by the dihedral geometry of the inboard wing panels, because the outboard wing panels are so much further from the CG of the aircraft.

All of these same geometries can actually be present in a wing with completely straight leading edges. In a flex-wing hang glider, the trailing edge billows into an "M" shape that creates anhedral in the outboard wing panels and dihedral in the inboard wing panels, even though the leading edges of the wing are straight.

To see this, look closely at this interesting video. Note that at certain times, especially as the glider is being "launched", we can clearly see the top surface of the outboard part of the wing nearest the camera, and we can clearly see the bottom surface of the outboard part of the wing furthest from the camera. At the same time, we can clearly see the bottom surface of the inboard part of the wing nearest the camera, and we can clearly see the top surface of the inboard part of the wing furthest from the camera.

Even though this wing has straight leading edges, if we take a "holistic" look at the wing's 3-dimensional shape we see that the inboard wing panels do have dihedral and the outboard wing panels do have anhedral. Whenever the nose of the glider is pointing in a different direction than the glider is actually travelling through the airmass, the sideways airflow will interact the with the anhedral geometry of the outboard parts of the wing to create a roll torque in the "upwind" direction. Because the inboard parts of the wing have dihedral rather than anhedral, they will interact with a sideways airflow to contribute a roll torque in the "downwind" direction, but as noted above, this will be much smaller than the "upwind" roll torque created by the outboard panels.

In general, the less billow a flex-wing hang glider has, the more "droop" the designer will incorporate into the leading edges. This makes sense when we understand that both the billow in the sail, and the "droop" in the leading edges, contribute to the overall anhedral geometry of the glider, and increase the glider's tendency to roll in the "upwind" direction whenever there is a sideways component in the relative wind, i.e. whenever the nose of the glider is not pointing in exactly the same direction as the glider is actually travelling through the airmass. Anhedral, whether due to billow or due to "droop" in the leading edges, helps a glider "harness" adverse yaw and convert it into a helpful roll torque. Of course, sail billow also contributes favorably to a flex-wing glider's handling characteristics in other ways, which involve actual changes in the shape of the wing in response to asymmetrical aerodynamic loading. We'll explore this briefly in "The main cause of adverse yaw during rolling motions: the 'twist' in the relative wind".

Many more photos will be added to this page in the future to further illustrate how sail billow creates anhedral in the outboard parts of the wing of a flex-wing hang glider. For now, peruse the "Pool of images for the Aerophysics Exploration Pages" for more illustrations of this geometry.

 

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