Spiral instability in flex-wing hang gliders: VG on versus VG off
This page was last modified on October 10, 2006
This article is exploratory in nature and is not meant to be an authoritative, comprehensive expose on all the dynamics that play a role in the spiral stability characteristics of flex-wing hang gliders.
In "The flexible hang-glider wing: how billow contributes to anhedral" and "Looking at anhedral in flex-wing hang gliders: VG off versus VG on", we saw that sail billow creates anhedral, and we saw that a flex-wing hang glider appears to have more anhedral with the VG off than with the VG on, based on visual observations of the wing.
In "Interesting experiments: adding a controllable rudder and other yaw devices to 4 flex-wing hang gliders", "Interpreting in-flight observations: roll torque created by the combined effects of anhedral and sweep in flex-wing hang gliders, VG off versus VG on, high airspeed versus low airspeed", and "In-flight observations supporting the idea that a flex-wing hang glider has more anhedral with the VG off than with the VG on, with notes on yaw-roll oscillations and tow dynamics", we gave several other lines of evidence that a typical flex-wing glider has more anhedral with the VG off than with the VG on, including the results of experiments with the controllable rudder and wingtip drag devices, and notes on yaw-roll oscillations during free-flight and during aerotow.
However, most flex-wing gliders are more spirally unstable with the VG on than with the VG off. For example, this is true of the Airborne Blade, even though this glider displayed other flight characteristics during the tests with the controllable rudder and the wingtip drag devices that indicated the glider had more anhedral with the VG off than with the VG on.
This naturally leads to the question "Why are most flex-wing hang gliders--at least with conventional pulley VG systems--more spirally unstable with the VG tight than with the VG loose"?
I'm not completely satisfied with my understanding of this situation. It does seem that there is a fundamental conflict between the observation that a glider shows a stronger anhedral-like "upwind" roll torque or "negative coupling between yaw (slip) and roll" when the VG is loose, and the observation that the glider is more spirally unstable and requires the pilot to high-side less or low-side more when the VG is tight. What follows is my best shot at a resolution to this conflict.
* An aircraft's dihedral / anhedral geometry plays an important role in the aircraft's spiral stability/ instability characteristics, but so do several other factors. Washout appears to be one of these factors.
* In very crude terms, when an aircraft is engaged in a constant-banked turn, if we increase the wing's washout, this is a little bit like giving an aileron input toward the high side or outside of the turn. In other words, when an aircraft is engaged in a constant-banked turn, if we increase the wing's washout, this is a little bit like giving a rolling-out control input. Here is the reason for this: even though we are decreasing the angle-of-attack of both wingtips, the outside wingtip is moving at a faster airspeed than the inside wingtip. Since lift varies according to the square of airspeed (for a given aerodynamic shape flying at a given angle-of-attack), the change in the geometry of the wing is likely to have a more pronounced effect (in terms of pounds of lift lost) on the outside wingtip than it does on the inside wingtip. Of course a more subtle understanding of these dynamics would need to consider the slope of the lift coefficient curve for the wingtip airfoil, the exact angle-of-attack of each wingtip, etc, but the above description is a good starting point, especially for the higher-airspeed part of the flight envelope when no part of the wing is likely to be stalling. In the lower-airspeed part of the flight envelope where the inside wingtip may actually be stalling, increasing the washout may actually boost the lift generated by the inside wingtip, which again will create a rolling-out torque.
* Another way to look at these dynamics is to recognize that when we decrease washout, we make the wingtip areas "work harder". In other words, the tip areas become more important in terms of the total lift distribution of the wing. In other words, the "effective span" of the wing is increased. An aircraft's wingspan is very important to its spiral instability characteristics, especially at low airspeeds, where the turn radius for a given bank angle is small. The longer an aircraft's "effective span" and the slower it flies, the more the pilot typically needs to maintain a rolling-out control input to hold the bank angle constant. This is because the faster-moving outside wingtip tends to develop more lift than the slower-moving inside wingtip.
* It seems to be the case that because of these relationships, when we tighten the VG of a flex-wing hang glider, the resulting decrease in washout increases the "effective span" enough to create a net increase in the aircraft's spiral instability, despite the fact that the anhedral has decreased. Likewise it seems to be the case that because of these relationships, when we loosen the VG of a flex-wing hang glider, the resulting increase in washout decreases the "effective span" enough to create a net decrease in the aircraft's spiral instability, despite the fact that the anhedral has increased.
At this juncture we've covered the most important points; now let's look at a few more details (or click here to jump to the final summary.)
* For the purposes of this article, when we talk about an "increase in spiral instability" or a "decrease in roll stability", we mean that for any given angle-of-attack, the pilot most maintain a stronger rolling-out control input (or in some cases a weaker rolling-in control input) to keep the bank angle constant during a turn. In other words, we mean that the glider "wants" to come to equilibrium at a steeper bank angle. Likewise when we talk about a "decrease in spiral instability" or an "increase in roll stability", we mean that the pilot most maintain a weaker rolling-out control input (or in some cases a stronger rolling-in control input) to keep the bank angle constant during a turn. In other words, we mean that the glider "wants" to come to equilibrium at a shallower bank angle. These are things that are easy to observe in flight; I haven't attempted to experimentally measure changes in other parameters such as the time it takes to reach a certain bank angle when the pilot goes neutral on the controls during wings-level flight.
* Spiral instability is not caused solely by anhedral or limited to aircraft with anhedral. Many aircraft with dihedral also exhibit spiral instability. Most light airplanes have mild amounts of dihedral, yet will slowly wind up into a banked descending spiral (helix) if the pilot releases all the flight controls. In a long-spanned aircraft like a sailplane this tendency is especially pronounced, even though nearly all sailplanes have substantial dihedral. In a thermalling turn in a typical sailplane, a pilot must continually maintain a fairly substantial roll input toward the high wing, i.e. toward the outside of the turn, or the bank angle will increase. A primary factor here is the roll torque arising from the difference in the airspeed between the wingtips as the aircraft turns, as we noted in "Roll and yaw torques due to the difference in the airspeed of the left and right wingtips".
* Dihedral reduces spiral instability in a turn only if the pilot is not using a rudder to keep the nose of the aircraft pointing directly into the airflow. In other words, dihedral reduces spiral instability in a turn only if the pilot is not using a rudder to keep the turn perfectly "coordinated". Or to put it yet another way, dihedral reduces spiral instability in a turn only if the aircraft tends to sideslip as it turns, and the pilot doesn't eliminate this sideslip via rudder inputs. The amount of sideslip that is present will determine the amount of rolling-out torque that is created by the dihedral.
* Similarly, anhedral contributes to spiral instability in a turn only if the aircraft is slipping as it turns. The amount of sideslip that is present will determine the amount of rolling-in torque that is created by the anhedral.
* We explored these ideas in more detail in "Misconceptions: the 'simple' view of how dihedral contributes to roll stability" and "A 'holistic' view of how dihedral contributes to roll stability and anhedral contributes to roll instability".
* We don't mean to suggest that an aircraft's dihedral or anhedral geometry will typically have little effect on its spiral instability characteristics. As we noted in "A 'holistic' view of how dihedral contributes to roll stability and anhedral contributes to roll instability", most aircraft do in fact show at least a slight amount of sideslip in a turn if the pilot does not apply an "inside" rudder input. This is especially true of long-spanned, slow-flying aircraft where the outside wingtip must move significantly faster--and therefore tends to experience more drag--than the inside wingtip. All the flex-wing hang gliders that I've flown with centrally-mounted (e.g. easily visible) yaw strings have in fact shown several degrees of sideslip in constant-banked turns at all airspeeds and bank angles, at least as measured at a location a few feet in front of the base bar. Also, the hang gliding community's collective experience with a wide variety of glider types, from old "Rogallo" standards to modern topless gliders, shows that tuning adjustments to a flex-wing hang glider that increase anhedral will increase spiral instability, and tuning adjustments to a flex-wing hang glider that decrease anhedral or increase dihedral will decrease spiral instability, just as is the case with all or nearly all other aircraft (including the variable-geometry Zagi that we discussed earlier in these tutorial pages).
* However it seems clear that some other effect--such as the increase in "effective span" that takes place as the VG is tightened--must be overpowering the decrease in anhedral that takes place as the VG is tightened, so that the net result is an increased demand for high siding (or a decreased demand for low-siding) during a constant-banked turn.
* We've argued that sail billow creates an anhedral geometry. We've argued that due to this effect, a flex-wing hang glider has more anhedral with the VG off than with the VG on. Even if a person were reluctant to accept our argument that these effects are much more important than the change in airframe anhedral (the "droop" in the leading edge tubes in relation to the line of the keel) that occurs as a pulley VG system is tightened or loosened, he or she would be hard pressed to offer objections in the case of a glider with a cam VG system, where the sail billow and washout are really the only significant factors that change as the VG is tightened or loosened, so the sail billow and the associated anhedral must both increase as the VG is loosened. If anhedral were the only important factor creating spiral instability in flex-wing hang gliders, a glider with a cam VG system would need markedly more high-siding with the VG loose than with the VG tight. But this is not the case. Instead the amount of high-siding that is required to hold a constant bank angle tends to remain very roughly constant as the setting of the cam VG system is changed. This suggests that as the cam VG system is tensioned, the decrease in roll instability due to the decreased anhedral is counterbalanced by an increase in roll instability from some other cause--such as the increased "effective span" of the wing. In a glider with a pulley VG system, there is slightly less decrease in anhedral as the VG is tensioned than in a glider with a cam VG system, so the various competing effects are no longer in balance, and we experience an increase in spiral instability as we tension the VG system.
* This is all a bit complicated. We're arguing that loosening the VG increases sail billow enough to increase the overall anhedral geometry of the wing, but also increases wingtip washout enough to create a net decrease in the glider's spiral instability. An interesting point is that the increase in washout in and of itself will actually tend to reduce the amount of anhedral that would otherwise be created by the billow (see the "Aerophysics Exploration Pages images gallery" for more on this). We have made a strong case that loosening the VG does in fact increase the wing's overall anhedral geometry. And there's no doubt that loosening the VG does in fact increase wingtip washout. It's just not completely clear that the way that the increased washout decreases the "effective span" is the decisive factor that gives the wing less spiral instability when the VG is loose and more spiral instability when the VG is tight, in spite of the fact that the wing has more anhedral when the VG is loose. No doubt there are also some other contributing factors, and some other competing factors, at play.
* Another factor that could play a significant role in reducing the need for high-siding with the VG loose is that when the sail is looser and more free to flex and billow-shift, any asymmetries in aerodynamic loading will tend to be reduced, as we described in more detail in "The main cause of adverse yaw during rolling motions: the "twist" in the relative wind". However, as I see it, this reduction in asymmetric loading when the VG is loose cannot explain instances where the wing actually needs more low-siding (not just less high-siding) at a given bank angle and angle-of-attack (airspeed) when the VG is loose rather than tight. Perhaps I'm overlooking something in this regard.
* Here are some links to outside sources that support the idea that an increase in washout tends to decrease an aircraft's spiral instability, independent of any changes to the rest of the wing. In some ways the examples involving "rigid" aircraft rather than flex-wing aircraft are the most valuable, because with the rigid aircraft the variables are much more independent, while with the flex-wing aircraft an increase in washout tends to decrease the anhedral that would otherwise be created by sail billow. Note that these links are all specific to swept-wing flying-wing aircraft.
"On the importance of the correct C.G. location in flying wings" by Dr. Karl Nickel
Basic notes on hang glider "washout struts" from an on-line encyclopedia
"The Hang Glider's Bible" by Michael A. Markowski. 1977. TAB Books. This is one of the best of the myriad of books from the "old days" of hang gliding, and it explores the stability and control of full-Rogallo wings and modified Rogallo wings in some depth. There are repeated references to how sail billow creates twist, and how the combined effects of billow and twist contribute to spiral stability or reduce spiral instability. (My own best interpretation of these relationships is that billow creates an anhedral geometry which contributes to a negative coupling between yaw (slip) and roll, and helps the glider respond quicker to the pilot's control inputs, and also tends to contribute to spiral instability, yet billow also creates aerodynamic twist which contributes to spiral stability via some other mechanism.) For example in the chapter entitled "Hang Glider Design and Stability and Control", "Wingtip washout" appears on the list of items that "increase spiral stability", though again we are left wondering whether this is just due to the decrease in sail billow and anhedral that takes place when we increase the upward deflection of a defined washout strut or tip tube.
(more links to be inserted)
* The literature pertaining to the dynamics of spiral instability makes it abundantly clear that in any case where the slow-flying inside wingtip is beginning to stall during a turn, increasing washout will decrease spiral instability. See for example many of the links given in the "Links" section of the Aeroexperiments website, especially from the "Nurflugel pages" link on down through the "On the Wing #1" link. I'm not sure whether or not is appropriate to view the spiral instability dynamics of flex-wing hang gliders in such simple terms--I don't know whether the inboard wing tip is anywhere near the stall in a typical low-airspeed turn with the VG full on. Also, my impression is that for a given bank angle and a given airspeed or angle-of-attack, a flex-wing hang glider requires more high-siding (i.e. is more spirally unstable) when the VG is on than when the VG is off even when the airspeed in question is quite high, though further testing would be appropriate before asserting this too strongly.
* Here is another line of thought that complements the "effective span" idea. The ideas expressed in the following paragraph are highly conjectural and may or may not play an important roll in the dynamics of spiral instability. The ideas expressed in the following paragraph relate only to descending (e.g. gliding) turns, and not to turns where the aircraft's altitude with respect to the surrounding airmass is constant or increasing. The ideas expressed in the following paragraph relate to the slope of the lift curve of a wing section at various angles-of-attack, and are probably of very minor importance when we keep in mind the more fundamental idea that the outboard wing is moving faster than the inboard wing, and lift varies according to the square of the airspeed, and therefore changes in angle of attack will tend to create a larger change in lift on the outboard wing than on the inboard wing, regardless of the exact shape of the lift curve, assuming that the wing section hasn't actually stalled. Nonetheless in the spirit of exploration let's dig a bit deeper.
* Recall that the rolling motion inherent in a constant-banked descending turn increases the angle-of-attack of the inside wingtip and decreases the angle-of-attack of the outside wingtip, which leads to a stabilizing rolling-out torque component, as we explored in "A constant-banked climbing or descending turn involves a continual rolling motion". Assuming that the wing section in question is not operating near the stall angle-of-attack, in general a given increase or decrease in angle-of-attack creates a slightly larger increase or decrease in lift when a wing section is operating at a low angle-of-attack (where the slope of the lift curve is steeper) than when a wing section is operating at high angle-of-attack (where the slope of the lift curve is shallower). (This dynamic is largely responsible for an aircraft's pitch stability, see for example this link for an elementary treatment of this idea.) Therefore it seems that decreasing the incidence of the wingtips (i.e. increasing the washout) might actually increase the amount of rolling-out torque created by the difference in angle-of-attack between the wingtips that arises from the rolling motion inherent in a descending turn. To the extent that this effect is significant, increasing the washout will tend to reduce the aircraft's spiral instability.
* I have no idea whether the effect described immediately above is significant. One caution here is that anything that increases the wingtips' "sensitivity" to a difference in angle-of-attack also ought to increase the roll torque created by the wing's anhedral geometry in the presence of sideways component in the relative wind, which ought to increase the "upwind roll torque" or "negative coupling between slip (yaw) and roll" that arises during any sideslip, including a non-turning (straight-line) sideslip, assuming for the moment that the anhedral geometry is kept constant. Superficially, this seems inconsistent with what we observed in "Interesting experiments: adding a controllable rudder and other yaw devices to 4 flex-wing hang gliders", where we found a stronger "upwind roll torque" or "negative coupling between slip (yaw)" during a non-turning sideslip when the VG was loose than when the VG was tight. However the most important variable in determining the nature of the aircraft's "coupling between slip (yaw) and roll" in straight-line (non-turning) flight is surely the fact that the outer parts of the wing have significantly more anhedral when the VG is loose than when the VG is tight, as we saw in "Looking at anhedral in flex-wing hang gliders: VG off versus VG on"
* The explanation offered 2 paragraphs above assumes that the inside wingtip is in fact experiencing a higher angle-of-attack than the outside wingtip during a descending turn. Since the wing has anhedral, at some large sideslip angle this will no longer be true, especially when the sink rate is low. However, sideslip angles during constant-banked turns in hang gliders are modest. (Hang glider pilots should disabuse themselves of the notion that slips are caused by a high descent rate and that high-airspeed turns are likely to involve a great deal more sideslip than low-airspeed turns; observations of a yaw string in flight will show that constant-banked high-airspeed turns have less slip than constant-banked low-airspeed turns.)
* Some thoughts on possible experimental tests: to the extent that the effect described 3 paragraphs above is significant, it should be most pronounced at low angles-of-attack and high sink rates. In other words, to the extent that this effect is important, changing the VG setting should have more effect on the degree of high-siding or low-siding needed during flight at low-angles-of-attack (high airspeeds), than during flight at high-angles-of-attack (low airspeeds). The opposite will be true of the "effective span" effect since the difference in wingtip airspeeds is most pronounced when the airspeed is low. Note also that the effect described 3 paragraphs above would be reversed if the aircraft were climbing with respect to the airmass--e.g. while a powered climbing turn always tends to need more high-siding than a gliding turn, tightening the VG during a powered climbing turn might create less increase in the need for high-siding than it does during a gliding turn, or if this effect is strong enough, tightening the VG might even decrease the need for high-siding during a rapidly ascending powered climbing turn. In contrast, the "effective span" effect will contribute the same increase in the glider's spiral instability when the VG is tightened, regardless of whether the flight path is climbing or descending with respect to the airmass.
* My intuition is that it's not likely that tightening the VG creates much less increase in spiral instability during a powered climbing turn than it does during a gliding turn. I suspect that the way that decreasing the washout increases the "effective span" of the wing is the main reason why tightening the VG increases an aircraft's spiral instability.
* Regardless of the detailed mechanisms at play, we're being drawn toward the suggestion that an increase in washout tends to decrease an aircraft's spiral instability, across a wide range of angles-of-attack or airspeed, and independent of any changes in anhedral, which will have their own effects on spiral instability.
Let's close by bringing a bit of order to this "can of worms"!
* In summary, I propose that there is some general mechanism by which an increase in washout creates a decrease in spiral instability or an increase in roll stability in a swept-wing flying-wing aircraft, over a wide range of angles-of-attack (airspeeds). I suggest that this general mechanism probably consists primarily of the way that the wing's "effective span" is decreased when the washout is increased. We're using the idea of a "decrease in 'effective span'" as shorthand for the way that the wingtips wash out more, and operate at a lower lift coefficient, when the VG is loose, which will decrease the amount of destabilizing roll torque created by the difference in airspeed between the two wingtips during turning flight. Loosening the VG of a flex-wing hang glider clearly does increase the washout. We've also shown that when a flex-wing hang glider's VG is loosened, the wing's overall anhedral (and especially the anhedral in the outer parts of the wing) increases due to the increased sail billow. I've observed that the sideslip angle during a stabilized (constant-speed, constant-bank) turn at any airspeed or VG setting or bank angle in a flex-wing hang glider is quite modest, and I bring our attention again to the point that the amount of destabilizing roll torque created by anhedral in the presence of a slipping airflow is very strongly dependent on the sideslip angle. I propose that when a flex-wing glider's VG system is loosened, the increased washout, not the increased anhedral, typically turns out to have the most influence on the amount of high-siding required during a constant-banked turn. This is quite different from what we saw in the experiments with the controllable rudder and the wingtip drag devices, many of which involved holding the glider on a constant heading, which allowed us to examine the glider's coupling between sideslip and roll in a "pure" sense that involved no difference in the airspeed between the two wingtips, and was therefore fundamentally different from a study of the glider's spiral instability characteristics. In the constant-heading experiments, tensioning the VG always created a clear decrease in the glider's "negative coupling between slip (yaw) and roll", while in the experiments that examined the amount of high-siding required in a constant-banked turn, tensioning the VG always created an increased demand for high-siding.
Let me know if you have some interesting thoughts or data to contribute, either to support or refute any of the ideas in this article!
Advance to "The 'parasol' or 'pendulum' effect: location of the wing above or below the aircraft CG: influence on yaw (slip) roll coupling and spiral stability or instability, with notes on flex-wing hang gliders
Skip to "More detailed definitions of 'slips' and 'skids'"
Up to the Aerophysics Exploration Pages index
Up to the Aeroexperiments site map