Testing the relationship between VG setting and "effective dihedral"
Last updated June 26, 2014
Q: Do we really give a glider more anhedral when we tension a pulley VG system?
A: Not always! In fall 2013 I made some flights with a Wills Wing Sport 2 equipped with an experimental controllable rudder on the keel. The keel was lashed tightly to the crossbar to prevent the rudder from pushing the keel from side to side. Launches were by aerotow, in smooth air. The keel lashings could be de-tensioned in flight, to increase safety for landing. One flight was made with the VG full on, and one flight was made with the VG full off.
With the VG full on, at trim, the glider's "effective dihedral" was mildly positive. When the rudder was locked down deflected to the left, the glider wanted to roll to the left-- toward the "downwind" or "trailing" wing. I had to keep my weight shifted to the right to prevent the glider from rolling and keep the glider flying in a straight line. At some higher airspeed about 5 mph above trim speed, the glider's "effective dihedral" was neutral-- when the rudder was locked down deflected to the left, it created no roll torque. The glider would keep flying in a straight line with my weight centered, even though the glider was flying in a slightly yawed attitude, with the right wing "leading" and the left wing "following" and the yaw strings or slip strings streaming off toward the left. At progressively higher airspeeds, the glider's "effective dihedral" became progressively more negative. When the rudder was locked down deflected toward the left, the glider wanted to roll toward the right--toward the "leading" or "upwind" wing-- and I had to keep my weight shifted toward the left to prevent the glider from rolling and keep the glider flying in a straight line.
With the VG full off, the trim speed was almost the same, but the glider's "effective dihedral" at trim was neutral. When the rudder was locked down deflected to the left, it created no roll torque. When I accelerated to the airspeed that yielded "neutral" coupling with VG on, the glider's "effective dihedral" was clearly mildly negative with VG off-- with the rudder deflected toward the left, I had to keep my weight shifted toward the left to prevent the glider from rolling and keep the glider flying in a straight line. At progressively higher airspeeds, the glider's "effective dihedral" became progressively more negative-- the glider showed a progressively stronger tendency to roll against the direction of the deflected rudder, and I had to shift my weight progressively further toward the direction of the deflected rudder to stop the glider from rolling and make the glider fly in a straight line.
In essence, the glider basically behaved the same with VG off and with VG on-- the "effective dihedral" became progressively less positive or more negative as the bar was pulled in and the angle-of-attack was decreased, as expected for any swept-wing aircraft with anhedral. (For more, see the related article on this website entitled "Notes on theory--"effective dihedral" in flex-wing hang gliders".) But the "neutral point" where "effective dihedral" was zero occurred at a noticeably higher airspeed with VG on than with VG off. For any given airspeed or angle-of-attack, the glider's "effective dihedral" was noticeably more positive or less negative with VG full on than with VG full off.
With VG full off, at very high airspeed the glider's "effective dihedral" was so powerfully negative that I had to keep my weight shifted full to the side to keep the glider from rolling away from the deflected rudder. At the same airspeed with VG full on, the roll tendency was noticeably less and the glider was more manageable.
Alternative tests where the rudder was replaced with a small drogue chute attached to a line connected well outboard on one of the lower side wires yielded generally similar results, though the chute didn't always fly level behind the glider, which made it harder to make careful observations.
Why would tightening the pulley VG system shift the glider's "effective dihedral" in the more positive or less negative direction? Tightening the pulley VG increases "airframe anhedral"-- the leading edges are pulled lower in relation to the keel tube. But tightening the pulley VG system also takes away sail billow. A simple look at the three-dimensional geometry of a hang glider sail shows us that sail billow contributes strongly to a wing's anhedral geometry, as "seen" by the airflow or relative wind. For more on this, visit the related article on this website entitled "Notes on sail billow, dihedral, and anhedral in flex-wing hang gliders".
In the particular case of the Sport 2, as we tightened the VG, the loss of sail billow was evidently more important than the increase in "airframe anhedral", in terms of the net change in the glider's "effective dihedral".
If we changed the same glider over to a cam VG system, "airframe anhedral" would stay roughly constant as we tightened the VG system, and the resulting positive shift in "effective dihedral" would be much more pronounced. In gliders with cam VG systems, the positive shift in "effective dihedral" as we tighten the VG is often strong that the glider's roll trim while circling remains more or less unchanged, despite the increase in "effective span" which contributes a rolling-in tendency. Not so with the Sport 2-- the glider needs more high-siding while circling with the VG tight than with the VG loose. The small positive shift in "effective dihedral" with the VG tight is not enough to offset the increased rolling-in torque generated by the increased "effective span".
A few more details in closing:
Every make of glider has a different shape and geometry. It wouldn't be particularly surprising if similar tests carried out in some other gliders with pulley VG systems showed that the "effective dihedral" was essentially unchanged as the VG was tensioned, or shifted mildly in the negative direction. But the shift would be much less than we would predict if we only considered the change in "airframe anhedral" Also, bear in mind that sail billow only creates an anhedral geometry in the outboard portions of the wings. A given amount of sail billow will make the greatest negative contribution to a glider's "effective dihedral" if the glider has a high-aspect ratio wing with minimal taper and a reasonably high ratio of outboard wing area to inboard wing area. Therefore even though higher-performance gliders have less sail billow than lower-performance gliders, it seems still likely that tensioning a high-performance glider's pulley VG system might shift the glider's "effective dihedral" in the more positive or less negative direction. Only an in-flight test with a rudder or other yaw device can give the final answer here.
Keep in mind that a glider is less effective at creating lift with the VG full off, so the average angle-of-attack as measured at the mean chord line of the whole wing must be higher to sustain the glider at any given airspeed with VG off than with VG full on. If the "effective dihedral" were strictly a function of angle-of-attack and otherwise independent of VG setting, we'd expect the "effective dihedral" to be more positive or less negative at any given airspeed with the VG full off than with the VG full on. But we saw the opposite. This supports the conclusions above regarding the importance of sail billow.
Another factor at play is that when we increase washout, we decrease the dihedral-like effect created by sweep in the outer portions of the wing, since these portions are now flying at a lower angle-of-attack, and the dihedral-like contribution from sweep is strongly dependent on angle-of-attack. At very low angles-of-attack when the tips are making negative lift, these portions could easily contribute a net anhedral-like effect. This must have contributed to the positive shift in "effective dihedral" as the VG was tightened, and the negative shift in "effective dihedral" as the VG was loosened, that we observed in these tests. But this alone can't explain how a flex-wing hang glider's "effective dihedral" can be nearly neutral even at high angles-of-attack, where the tips are surely making some positive lift. Consider for example a glider like the Wills Wing Falcon 1, with plenty of sweep and essentially zero "airframe anhedral", i.e. essentially no droop in the leading-edge tubes relative to the keel tube. Yet the same type of rudder tests carried out on this glider showed essentially zero "effective dihedral" near the min. sink angle-of-attack, and negative "effective dihedral" at lower angles-of-attack. Again, this supports the idea that sail billow is contributing a strong anhedral geometry to the three-dimensional shape of the sail.
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