Some thoughts on sail billow, anhedral, and VG setting in flex-wing hang gliders
August 8, 2007 edition
* It is difficult to quantify anhedral in a flex-wing hang glider.
* The "airframe anhedral" is the droop in the leading edges in relation to the root chord or keel tube. However the keel tube is essentially an arbitrary piece of metal that does not serve as a good reference line in any aerodynamic sense. There is no fixed relationship between the mean chord line of the wing, and the keel tube.
* When we tighten the VG, the leading edges have slightly more droop with respect to the keel tube. However, the whole trailing edge is pulled down, which creates a rotation in the mean chord line of the wing. Essentially, when we tighten the VG we rotate the keel tube upward, in relation to the mean chord line of the wing. Assuming that the glider will fly with the mean chord line of the wing at some roughly constant angle, we'll expect the aft end of the keel tube to ride higher when the VG is tight than when the VG is loose. We can feel this in flight--the bar moves aft when we tighten the VG.
* With any swept-wing aircraft with anhedral, lowering the nose reduces the droop in the leading edges with respect to the horizon, and raising the nose increases the droop in the leading edges with respect to the horizon.
* If we keep the mean chord line of the wing horizontal, it appears that tightening the VG actually reduces the downward droop in the leading edges (measured with respect to the horizon, i.e. measured with respect to the mean chord line of the wing.)
* Here is an illustration. On this glider we are keeping the mid-span chord line horizontal (i.e. we are positioning the glider so that the trailing edge disappears behind the leading edge at a point that is in the middle of the span of each of the two wings). The position of the keel tube is not being kept constant. With respect to the mid-span chord line (not with respect to the keel tube), the glider appears to have more anhedral with VG off than with VG on. The glider has a pulley VG system. This relationship would be even more pronounced with a cam VG system, because tightening the VG would no longer create any airframe anhedral.
* The above photos are a bit exaggerated. The intent was to keep the wing as a whole at the same average angle-of-attack, i.e. to keep the mean chord line horizontal, as the VG setting was changed. The mid-span point was probably not the most representative point, because more than half of the wing's area lies inboard from this point. However we get the same general results if we use the quarter-span chord line as our reference. More photos will be added to show this in the future.
* The front views given above really are not a very holistic way of looking at anhedral, especially when we are dealing with a complex wing shape that includes both twist and billow.
* When we take an oblique look at a wing, anywhere that we can see the bottom surface of a section of the far wing and the top surface of the corresponding section of the near wing, we are looking at an anhedral geometry. Anywhere that we can see the top surface of a section of the far wing and the bottom surface of the corresponding section of the near wing, we are looking at a dihedral geometry. When we are interested in aerodynamic dihedral effects or anhedral effects, it is the upward or downward slope of the surfaces that matter, not the height of the surfaces above the aircraft CG or any other reference point.
* When we take an oblique view of the wing of a hang glider, we can see how the trailing edge rises, and then falls. This creates dihedral in the inboard part of the wing and anhedral in the outboard part of the wing. Again, anywhere that we can see the bottom surface of a section of the far wing and the top surface of the corresponding section of the near wing, we are looking at an anhedral geometry. This is true of the outboard parts of the wing in this photo. And anywhere that we can see the top surface of a section of the far wing and the bottom surface of the corresponding section of the near wing, we are looking at a dihedral geometry. This is true of the inboard parts of the wing in this photo.
* When we tighten the VG we reduce the sail billow, which reduces the rise and fall of the trailing edge of the wing, so we end up with less dihedral in the inboard part of the wing and less anhedral in the outboard part of the wing. Oblique photos of gliders with VG on and VG off will be included in future editions of this article to show this.
* Aerodynamically, the anhedral on the outboard part of the wing is probably more important than the dihedral on the inboard part of the wing, because the outboard part of the wing acts at a greater distance from the CG. (This would not be true on gliders with a very low nose angle, i.e. with very highly swept leading edges, where most of the wing area is concentrated on the inboard part of the wing span. In such a glider, the more the sail billow, the more the dihedral effect we might expect.) In any glider with a reasonably high (wide) nose angle, when we tighten the VG and reduce the sail billow and reduce the anhedral in the outer part of the wing, it seems likely that the glider ends up with less overall anhedral in an aerodynamic sense. This is consistent with what I saw in the experiments with the experimental yaw devices (see "Experimental results and interpretation: yaw experiments with a controllable rudder and wingtip-mounted drogue chutes on flex-wing hang gliders"). On a glider with a cam VG system rather than a pulley VG system, we would expect these relationships to be even more pronounced, because when we tighten the VG we no longer have any increase in airframe anhedral (i.e. in the droop in the leading edge tubes in relation to the keel tubes).
* Flex-wing hang gliders with pulley VG systems are generally more spirally unstable (e.g. require more high siding) with the VG loose than with the VG tight. This appears to contradict our thesis that tightening the VG reduces the effective aerodynamic anhedral in the wing. However tightening the VG also makes the outboard parts of the wing work "harder", increasing the glider's "effective span". This likely contributes to the decrease in spiral stability that we see when we tighten the VG. (Recall that many airplanes and sailplanes with dihedral rather than anhedral are spirally unstable, especially if they have long wingspans.) On a glider with a pulley VG the decrease in aerodynamic anhedral is evidently not enough to offset this effect, so tightening the pulley VG makes the glider more spirally unstable, while on a glider with a cam VG the greater decrease in aerodynamic anhedral evidently is enough to offset this effect, so changes in the cam VG setting have little effect on the glider's spiral stability.
* To sum up our thesis: increasing sail billow increases a glider's effective aerodynamic anhedral. Tightening the VG decreases sail billow and decreases a glider's effective aerodynamic anhedral, more so on a glider with a cam VG system than with a pulley VG system. Two of the factors that strongly influence a glider's spiral stability are the "effective span" and the anhedral geometry. In a glider with a cam VG these factors appear to roughly balance each other so that tightening the VG has no strong influence on the glider's spiral stability. In a glider with a pulley VG, when the VG is tightened, the anhedral does not decrease enough to counterbalance the increase in "effective span" and the glider becomes more spirally unstable.
* Other factors such as aeroelasticity also vary with VG setting and undoubtedly also influence a flex-wing hang glider's spiral instability.
* This thesis is best regarded as still being in the "experimental" stage! It represents a synthesis of what I see when I look at a hang glider wing while changing the VG setting, and what I observed while flying with the experimental yaw control devices, and the spiral stability characteristics that can be observed in normal flight in many different hang gliders.
*It appears to me that effective aerodynamic anhedral may contribute to yaw-roll oscillations in hang gliders. On a glider with both anhedral and sweep, anhedral effects are strongest at low angles-of-attack. Yaw-roll oscillations tend to be most pronounced at low angles-of-attack, and with the VG loose. This is consistent with the idea that flex-wing hang gliders have more anhedral with the VG loose than with the VG tight. However other factors such as aeroelasticity also vary with VG setting and may play a key role in determining a glider's susceptibility to yaw-roll oscillations.