Notes on sail billow, dihedral, and anhedral in flex-wing hang gliders

This page is currently under construction, last updated April 21 2014. Stay tuned for more! Some of these ideas could be conveyed by sketches and captions better than by words and photos, so I hope to add those items in the future.

When an aircraft is "slipping" or moving sideways through the air, with the nose not exactly aligned with the actual direction of the flight path and airflow, we can say that there is a sideways component in the flight path. We can also say that there is a sideways component in the "relative wind" or apparent wind created by the aircraft's motion through the air. We can also say that there is a sideways component in the real, actual airflow over most of the portions of the aircraft.

If a wing has dihedral or anhedral, then whenever there is a sideways component in the flight path and airflow, the "upwind" wing will meet the air at a different angle-of-attack than the "downwind" wing. Nearly all the interesting properties of a wing with dihedral or anhedral are a direct result of this fact.

During a sideslip, the relative wind or airflow "sees" the wings in the same way as a camera looking at the aircraft from the side sees the wings. For example consider this picture of a "Superfloater" ultralight sailplane-- we can see the bottom of the "near" wing-- the wing nearest the camera-- while we see the "far" wing directly edge-on. If the aircraft were moving directly toward the camera-- which would be an example of a very extreme sideslip-- the "near" wing or "upwind" wing would have a positive angle-of-attack, as the airflow struck its bottom side. The "far" wing or "downwind" wing would have zero angle-of-attack, as the airflow struck it edge-on. The "upwind" wing would create more lift than the "downwind" wing, and the aircraft would roll away from the camera, toward the "far" or "downwind" wing.

Dihedral creates a "downwind" roll torque during a sideslip.

Similarly, anhedral creates an "upwind" roll torque during a sideslip.

Consider this picture of an Aerianne Swift ultralight sailpane-- we can see the bottom of the "far" wing-- the wing furthest from the camera-- while we see the "near" wing directly edge-on. If aircraft were moving directly toward the camera-- which again would be an example of an extreme sideslip-- the "far" wing or "downwind" wing would have a positive angle-of-attack, as the airflow struck its bottom side. The "near" wing or "upwind" wing would have zero angle-of-attack, as the airflow struck it edge-on. The "downwind" wing would create more lift than the "upwind" wing, and the aircraft would roll toward the camera, toward the "near" or "upwind" wing.

Let's practice "seeing" dihedral and anhedral geometries.

All these pictures show a dihedral geometry. In all these pictures, we can see one of the following combinations--

* The bottom side of the "near" wing and the top side of the "far" wing:

MX Quicksilver ultralight airplane, Turkey Vulture (bird)

* The bottom side of "near" wing and an edge-on view of the "far" wing

Superfloater ultralight sailplane, Ercoupe 1, Ercoupe 2, Ercoupe 3, Stinson, Schweizer TG-3 sailplane, Piper airplane

* An edge-on view of the "near" wing and the top side of the "far" wing:

Free-flight model airplane

All these pictures show an anhedral geometry. In all these pictures, we can see one of the following combinations--

* The bottom side of the "far" wing and the top side of the "near" wing:

metal model, Moyes Lightsport hang glider, Moyes Sonic hang glider

* The bottom side of "far" wing and an edge-on view of the "near" wing:

Aerianne Swift ultralight sailplane, Aerianne Swift #2, Odyssey lightsport airplane, Ilyushin Il-76 transport

* An edge-on view of the "far" wing and the top side of the "near" wing:

Harrier 1, Harrier 2

Flex-wing hang gliders have a complex geometry. In later editions of this web page, we'll explore in more detail why it's not sufficient to simply measure the "airframe geometry"-- the "droop" of the leading-edge tubes relative to the keel tube-- to quantity the real anhedral geometry contained in the three-dimensional shape of the wing.

For now we'll just focus on the fact that when we look at the wing from the side, we can see that the billowed shape of the sail creates a dihedral geometry in the inboard parts of the wing and an anhedral geometry in the outboard parts of the wing.

Look at the dihedral geometry of the inboard parts of the wings in these photos. In all these pictures, we can see one of the following combinations--

* The bottom side of the inboard part of the "near" wing and the top side of the inboard part of the "far" wing:

Moyes Sonic, Wills Wing Falcon #1, Wills Wing Falcon #2

* The bottom side of the inboard part of the "near" wing and an edge-on view of the inboard part of the "far" wing:

Osprey (bird) (source: Raptors of Western North America, text and photos by Brian K. Wheeler, Princeton University Press, 2003), Cloudman standard hang glider

* An edge-on view of the inboard part of the "near" wing and the top side of the inboard part of the "far" wing:

Wills Wing Falcon

Look at the anhedral geometry of the outboard parts of the wings in these photos. In all these pictures, we can see one of the following combinations--

* The bottom side of the outboard part of the "far" wing and the top side of the outboard part of the "near" wing:

"Skysailor" RC trike, Cloudman standard hang glider, Moyes Sonic, Falcon #1, Wills Wing Falcon #2, Wills wing topless hang glider, Wills Wing Falcon #3, Wills Wing Falcon #4, Northwing Freedom, Wills Wing Falcon #5, Wills wing topless hang glider #2, Wills wing topless hang glider #3

* The bottom side of the outboard part of the "far" wing and an edge-on view of the outboard part of the "near" wing:

Wills Wing Falcon, Osprey (bird) (source: Raptors of Western North America, text and photos by Brian K. Wheeler, Princeton University Press, 2003), Red-shouldered hawk (bird) (source: Raptors of Western North America, text and photos by Brian K. Wheeler, Princeton University Press, 2003)

* An edge-on view of the outboard part of the "far" wing and the top side of the outboard part of the "near" wing:

(no photos here yet)

Note--re the bird photos above-- of course in these cases the dihedral-inboard, anhedral-outboard geometry is achieved not through billow, but simply through bending the wing parallel to the bird's longitudinal axis! Yet the end result is the same whether the geometry is created by billow or by simple folding-- as "seen" by the camera, and the wind, the wing has dihedral inboard and anhedral outboard. During a sideslip, the inboard panels will contribute a "downwind" roll torque and the outboard panels will contribute an "upwind" roll torque.

Video clips of flex-wing hang gliders illustrating how the combined effects of airframe geometry and sail billow create washout, and also create dihedral on the inboard parts of the wing and anhedral on the outboard parts of the wing:

You tube video of a flex-wing hang glider landing in a wheelbarrow at Fort Funston showing how sail billow creates dihedral in the inboard portions of the wing and anhedral in the outboard portions of the wing. Note also the modest but clearly visible yaw oscillations that take place as the glider launches, and the lack of any apparent strong roll torques arising from these yawing motions.

You tube video of flex-wing hang glider winch-launching --the segment from 0:20 to 0:40 of this short clip gives us a good rear view of the way that sail billow creates washout: as the glider climbs away from us, we can see the top surface of the inboard parts of the wing and the undersurface of the outboard parts of the wing. The same segment also shows how sail billow creates dihedral on the inboard parts of the wings and anhedral on the outboard parts of the wings. Note that when the glider is briefly pointing strongly to the right of our sight line around 0:25, we can see the bottom surface of the outboard part of the far wing but not the bottom surface of the outboard part of the near wing, due to the way that sail billow creates an anhedral geometry in the outboard parts of the wings.

You tube video of flex-wing hang glider launching --skip past the extensive para footage to see the segment between 1:30 and 1:40 of this clip for another rear view of the way that sail billow creates washout: as the glider climbs away from us, we can see the top surface of the inboard parts of the wing and the undersurface of the outboard parts of the wing. The same segment also shows how sail billow creates dihedral on the inboard parts of the wings and anhedral on the outboard parts of the wings.

You tube video of a flex-wing hang glider landing --in this 37-second clip, the segment from 0:11 to 0:17 emphasizes how sail billow creates washout: we can see the undersurface of the inboard parts of the wing but not the outboard parts of the wing. Then the segment from 0:17 to 0:27 emphasizes anhedral: we have an edge-on view of the central and outboard parts of the near wing, and we can see the bottom surface of the central and outboard part of the far wing.

You tube video of a flex-wing hang glider landing --in this 1-minute clip, in the segment from 0:39 to 0:45 we have an edge-on view of the central and outboard parts of the near wing, and we can see the bottom surface of the central and outboard part of the far wing, showing the wing's anhedral geometry.

You tube video of flex-wing hang gliders ridge-soaring --in this 5-minute clip, the segment from 0:50 to 1:10 gives a great view of the top surface of the tip area of the near wing and the bottom surface of the tip area of the far wing. This is primarily due to the way that sail billow creates an anhedral geometry in the outboard parts of the wing, not due to asymmetries in the shape of the left and right wings. Around 0:55, and then again around 1:02, we see the tip area of the near wing in a nearly edge-on manner, and we see the bottom of the tip area of the far wing, again illustrating the anhedral geometry of the outboard parts of the wings. At 1:20 we have a great view of washout on the launching glider--looking at the glider tail-on, we can see the top surface of the inboard part of the wing and the bottom surface of the outboard part of the wing--and then from 1:28 to 1:31 we again see the top surface of the tip area of the near wing and the bottom surface of the tip area of the far wing, due to the way that sail billow creates anhedral in the outboard parts of the wings. Then from 1:55 to 2:05, we are looking at the outboard part of the near wing in a nearly edge-on manner, while we can see the bottom surface of the outboard part of the far wing, again showing the anhedral geometry of the outboard parts of the wings.

You tube video of a landing that didn't come out quite like it was supposed to! Included here to show that the geometry of the trailing edge stays relatively fixed, even as the pilot shifts his weight. The changes in perspective that we are seeing in the above videos are mostly not due to actual changes in the wing shape as the pilot weight-shifts, though this does happen to some extent.

One more clip from you tube: from the Annecy valley in the Rhone-Alpes region of France-- spectacular cliff launches and more. The segment from 2:50 to 3:00 gives a great view of anhedral (we can see the bottom surface of the far wing, while we see the near wing in an edge-on manner). The segment from 3:00 to 3:15 shows how sail billow creates both washout and anhedral (sometimes we can see the bottom surface of the inboard parts of the wings but not the bottom surface of the outboard parts of the wings, and sometimes we can see the bottom surface of the outboard part of the far wing and the top surface of the outboard part of the near wing.)

So sail billow creates a dihedral geometry inboard and a dihedral geometry outboard. The more the billow, the more pronounced this geometry.

When we increase the sail billow, which change is more important-- the increase in the inboard dihedral, or the increase in the outboard anhedral? If we increase sail billow, will the wing act like we are giving it more anhedral or less dihedral, so that it creates more "upwind" roll torque or less "downwind" roll torque in a sideslip than it did when the wing was flatter? Or will the wing act like we are giving it more dihedral or less anhedral, so that it creates more "downwind" roll torque or less "upwind" roll torque in a sideslip than it did when the wing was flatter?

The outboard portions of the wing are much further from the CG, and contribute much more roll torque per unit area in a sideslip. (This is completely independent of how heavily these portions are loaded in non-slipping flight.) On the other hand, due to the tapered or delta shape of the sail, the inboard portions of the wing are bigger than the outboard portions.

In this antique hang glider with a giant root chord and tiny tips, the inboard dihedral surely dominated over the outboard dihedral. If we changed the sail to have less billow, the glider would behave as if it had less dihedral. This is in accordance with what we read in Markowski's "The Hang Glider's Bible" (1977, TAB Books).

In a modern glider, even including a docile "trainer" like a Wills Wing "Falcon", the outboard portions are large enough that increasing the sail billow effectively gives the glider more anhedral, and decreasing the sail billow effectively gives the glider less anhedral. We'll give some calculations in support of this statement in future editions of this web page. When we understand the role of sail billow in creating an anhedral geometry, we can see why a glider like a Falcon doesn't exhibit extreme positive "effective dihedral" in flight, despite the substantial sweep built into the planform, and despite the fact that the leading-edge tubes have very little downward droop in relation to the keel tubes.

When we understand the relationship between billow and anhedral, we're better prepared to understand the observed effects of a cam VG system. When we tension the cam VG system, we remove sail billow and washout without changing the “airframe anhedral”. This decreases the “aerodynamic anhedral”. This decrease in “aerodynamic anhedral” is evidently exactly what is needed to offset the rolling-in tendency that would otherwise be created by these two factors: the increase in the glider’s “effective span" due to decreased washout, and the slight decrease in sweep. This balance is an accident of glider design and evolution.

As we tension a pulley VG system, it is less obvious how the “aerodynamic anhedral” is changing. We are adding “airframe anhedral” at the same time as we are removing billow and washout, so the “aerodynamic anhedral” may only be decreasing slightly, or may even be increasing. Sweep is also slightly decreasing, just as in the glider with the cam VG system. The practical outcome is the same in either case-- if a given glider fitted with a cam VG system shows little change in roll trim as we tension the VG, we can be sure that the same glider fitted with a pulley VG system will need progressively less low-siding or more high-siding as we tension the VG, at any given airspeed and bank angle.

We've been focussing on the effect of changes in sail shape due to changes in billow. We've barely touched on the question of whether the "effective dihedral"-- the net roll torque created by sideslip-- is positive or negative. Few modern gliders have any "airframe dihedral"-- the leading edges are either in plane with the keel tube, or they have some downward droop relative to the keel tube. When we start with such an airframe and then add a sail that has some billow, and a reasonably low taper ratio (so that the tip portions are not tiny compared to the root portions as in an old Rogallo "standard"), we're sure to end up with a net anhedral geometry. In a sideslip, the net roll torque due to the difference in angle-of-attack between the various parts of the left and right wings is sure to be an "upwind" roll torque, just like we would see in a simple, unswept, rigid, unbillowed wing with some anhedral. But "effective dihedral" is a larger concept that encompasses the effects of sweep as well as the difference in angle-of-attack between the various parts of the wings. Sweep generates a dihedral-like "downwind" roll torque, and much more so when the angle-of-attack is high than when the angle-of-attack is low. When we have both sweep and anhedral, it seems reasonable that the overall "effective dihedral" might be zero at some part of the flight envelope, meaning that a sideslip will generate neither an upwind roll torque nor a downwind roll torque. In the future we'll explore this more deeply on this website. For now we'll simply note that simple ground-handling experiments, and in-flight experiments with controllable rudders and other yaw devices, suggest that many flex-wing hang gliders have mildly positive "effective dihedral" at high angles-of-attack such as near the min.- sink angle-of-attack, but the bar doesn't have to be pulled in very much to cause the "effective dihedral" to become neutral. At even lower angles-of-attack the "effective dihedral" is markedly negative. This is very useful during ground-handling-- pulling in the bar will drive the "upwind" wingtip to the ground which is a safe, stable configuration. The bar doesn't have to pulled in so far that the wing is actually making net negative lift-- the "effective dihedral" becomes negative even when the wing is still lifting a substantial part of its own weight. These observations lead to some interesting questions, such as-- "if the 'effective dihedral' is strongly negative at low angles-of-attack, why do I need to low-side the bar to hold the glider in a constant-banked turn when I'm flying very fast?" The answer has to do with the very important role that "effective span" plays in the glider's roll balance-- at high airspeeds and low angles-of-attack, the "effective span" is very small, or even can be thought of as being "negative", meaning that the outboard portions of the wing are generating a great deal of downward lift. In turning flight, this generates a powerful rolling-out torque, because the wingtip on the outside of the turn is flying faster and generating more downward lift than the wingtip on the inside of the turn. This effect has nothing do to with sideslip and therefore isn't considered when we're talking about "effective dihedral"-- "effective dihedral" simply deals with the aircraft's roll response to sideslip. Also, this effect is absent during ground-handling, because when we are standing still on the ground with the glider on a fixed heading, both wingtips are moving through the air at the same airspeed. We'll explore "effective dihedral" and "effective span" in more detail on this website in the future.

Exactly why does sail billow create dihedral in the inboard portions of a wing and anhedral in the outboard portions of the wing? The most satisfactory way to conceptualize is this is via a "theory of swept hinge lines". Click here for more on this. A less satisfactory way to conceptualize these relationships is by looking at the downward droop in the leading-edge tubes, or the quarter-chord line of the wing, relative to the mean chord line of the wing.

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