Model illustrating the "hinge lines" on a wing with billow
This page last updated September 3 2005
When thinking about dihedral and anhedral, it's useful to start with the image of a flat wing, and then conceptualize "bending" or "folding" panels or sections of the wing around "hinge lines".
Of course, when we have a fore-and-aft-running hinge line located along the inboard edge of a wing panel, then if we lift the wing panel we create a dihedral effect, and if we lower the wing panel we create an anhedral effect. For example if we have a hinge line running along the centerline of the aircraft, and we bend the left and right wing panels downward, we create anhedral.
We can also think about hinge lines that have a large spanwise component, rather than running solely fore-and-aft. These hinge lines may be swept forward or swept aft. When we lift a wing panel in a way that involves a rotation around an aft-swept hinge line, we create an anhedral effect. When we lift a wing panel in a way that involves a rotation around a forward-swept hinge line, we create a dihedral effect. When we lower a wing panel in a way that involves a rotation around an aft-swept hinge line (e.g. lowering the flaps on a Swift or an ATOS) we create a dihedral effect. When we lower a wing panel in a way that involves a rotation around a forward-swept hinge line we create a anhedral effect. (In all cases we're assuming that the hinge line is located at the front, not the rear, of the wing panel in question.)
For more detailed illustrations of the way that raising a discrete wing panel using an aft-swept hinge line creates an anhedral effect, and the way that lowering a discrete wing panel using an aft-swept hinge line creates a dihedral effect, see this page.
How do this "hinge line" idea apply to a continuous, billowed wing surface?
In the case of a full-Rogallo "standard" hang glider, where the sail is attached to the full length of the keel (or behaves almost as if it is attached to the full length of the keel) and the keel is long and the nose angle is small, we can envision the keel itself as being a hinge line. As the sail rises from the keel it creates a V-shaped dihedral geometry in the inboard part of the sail. The aft-swept leading edge tubes are also hinge lines. Rather than streaming straight back from the leading edge tubes, the wings panels rise upwards behind the aft-swept leading edge tubes. Since the aft-swept leading edge tubes are serving as hinge lines for the outboard parts of the sail as the outboard parts of the sail billow upwards, this creates an anhedral geometry in the outboard parts of the sail. This picture gives a good illustration of this geometry (if we ignore the strange wrinkle lines). We can see the bottom surface of the inboard portion of the wing nearest the camera (look especially at the extreme rear of the glider), which illustrates the dihedral geometry of the inboard portions of the wing. We can see the top surface of the outboard portion of the wing nearest the camera, which illustrates the anhedral geometry of the outboard portions of the wing. In general the outboard portions will create more roll torque in the presence of a sideways airflow than the inboard portions, because the outboard portions are further from the CG. So we could say that this glider has a net anhedral geometry. Of course old Rogallo gliders such as this one also have an extreme amount of sweep which will create a powerful dihedral-like effect. Because of the dihedral-like effect created by sweep, most of the old Rogallo gliders tended to remain wings-level in smooth air without any help from the pilot. Here are some more photos showing similar geometry on old Rogallo hang gliders: #1, #2, #3 (left), #4 (upper right). (In some of the photos the crossbar is long enough, and has been given enough dihedral, that the outboard anhedral portions of the wing have become rather small and the inboard dihedral portions of the wing have become rather large; it's possible that these gliders may have a "net dihedral geometry" even though they have a lot of billow, apart from the dihedral-like effects created by sweep. Also in the glider with the extreme forward sweep in the trailing edge, the outboard anhedral portions of the wing are again quite small.)
Modern flex-wing gliders have a much more complex shape. The forward part of the wing surface is held in a well-defined airfoil shape by the battens and the mylar stiffeners. Only the aft part of the sail is free to billow to some extent. Also, the wing root chord has become much smaller in relation to the leading edges. Also, the wing surface no longer is attached to the full length of a nearly-linear keel in a way that pulls inboard part of the sail down into a strong "V" shape, with the keel at the bottom of the "V". As a result of all these changes, the sail has much less billow and the billow is distributed in a more complex manner. This photo is a good one for illustrating the complex way that the wing of a modern flex-wing hang glider billows in flight. Very loosely speaking, the inboard parts of the aft portion of the sail are billowing upward in a way that involves a forward-swept hinge line, creating a dihedral effect, while the outboard parts of the aft portion of the sail are billowing upward in a way that involves an aft-swept hinge line, creating an anhedral effect. On this model, we've sketched very rough representations of these forward-swept and aft-swept hinge lines that are involved in creating sail billow on the wing of a modern flex-wing hang glider. Again, the outboard portions of the wing will create more roll torque in the presence of a sideways airflow than the inboard portions, because the outboard portions are further from the CG. So again, we could say that billow contributes to the net anhedral geometry of a modern flex-wing hang glider.
For more illustrations of the way that billow creates an anhedral geometry on the outer portions of the wing of a modern flex-wing hang glider, see the rest of the photos on this page.
On this model, the "hinge lines" on the wing on the viewer's right are drawn in a way that includes wing-tip washout as well as billow. The lines on wing on the viewer's left only show the effects of billow; the wingtip has not been allowed to wash out. It appears that washing out the wingtip ends up decreasing the angle of sweep of the hinge line for the outer part of the wing which tends to decrease the amount of anhedral that would otherwise be created by the billow. (It's hard to say this with absolute certainty; washing out the tip does increase the total sail area involved in the "billow" effect.) On the other hand, in a case where we were dealing only with washout (twist) and no billow, as long as the wing had enough sweep that we could model the washout as a twist around an aft-swept hinge line, the washout would create some amount of anhedral effect.
Up to "Photos of hang gliders and models to illustrate how billow contributes to the net geometric anhedral of a swept wing"