Complete yaw-roll coupling in flex-wing hang gliders

A more "complete" consideration of adverse yaw in flex-wing hang gliders, with notes on fixed vertical fins: does adverse yaw create a helpful roll torque or an unfavorable roll torque?

Steve Seibel
www.aeroexperiments.org

October 13, 2006 edition

 

In "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", we noted the following:

Many flex-wing hang gliders with no VG, and many flex-wing hang gliders with the VG full off, have enough anhedral to create a net "upwind" roll torque or net "negative coupling between yaw (slip) and roll" at all angles-of-attack, except perhaps in some cases at angles-of-attack very close to the stall. Because of the way that the competing effect of sweep is most pronounced at high angles-of-attack, this net "upwind" roll torque or net "negative coupling between yaw (slip) and roll" is much stronger at low angles of attack than at high angles-of-attack. In other words, this net "upwind" roll torque or net "negative coupling between yaw (slip) and roll" is much stronger at high airspeed than at low airspeed. In other words, the flight characteristics arising from the wing's anhedral geometry are most pronounced at high airspeeds, but dominate across most or all of the flight envelope when the VG is off or absent.

This net "upwind" roll torque or net "negative coupling between yaw (slip) and roll" allows a flex-wing hang glider to harness the sideways airflow arising from adverse yaw, to create a helpful roll torque. This effect will be most pronounced at low angles-of-attack (high airspeed).

The above analysis is accurate, but not complete. When we say that the glider is "harnessing the sideways airflow arising from adverse yaw to create a helpful roll torque", this is not exactly the same as saying that an adverse-yaw motion will create a net helpful roll torque. An adverse-yaw motion has an additional aspect, apart from the resulting sideways airflow, that we have not yet considered. An adverse-yaw motion will likely create a helpful roll torque over a large part of the flight envelope, but perhaps not over quite as much of the flight envelope as we might have concluded from a quick reading above analysis.

A complete analysis of the effect of adverse yaw also needs to consider the difference in airspeed between the two wingtips that arises as a glider adverse-yaws. The roll torque created by this difference in wingtip airspeed is completely separate from the roll torque created by the interaction between the sideways airflow and the anhedral wing. This difference in wingtip airspeed will contribute an unfavorable roll torque during the time interval where the nose of the glider is actively yawing in the "wrong" direction in relation to the external world. My experience is that this time interval is usually brief and that adverse yaw in a flex-wing hang glider is primarily evidenced by the nose of the glider "lagging" behind the actual (changing) direction of the flight path at any given moment, so that the nose of the aircraft points toward the outside or high side of the developing turn in relation to the actual direction of the flight path and relative wind at any given moment, but is not actively swinging in the "wrong" direction in relation to the outside world. Even if the "complete" adverse yawing motion, including the difference in airspeed between the two wingtips, does actually end up creating a mild net unfavorable roll torque during the initial part of the entry into a turn, this net unfavorable roll torque will be much weaker than it would be if the interaction between the sideways component in the relative wind and the overall 3-dimensional geometry of the wing were not contributing a helpful "upwind" roll torque.

A glider will experience less adverse yaw if it has a fixed vertical fin than if it does not. Therefore we can get some insights into the complete effect of adverse yaw by thinking about fixed vertical fins. When we speak of the "complete" effect of adverse yaw, we are emphasizing that we are including the unfavorable roll torque resulting from the difference in airspeed in the two wingtips as the aircraft adverse-yaws.

If the complete effect of adverse yaw creates a strong unfavorable roll torque across most of the flight envelope, then installing a fixed vertical fin will create an increase in roll responsiveness across most of the flight envelope. Similarly, if the complete effect of adverse yaw creates a strong unfavorable roll torque in the low-speed part of the flight envelope, then installing a fixed vertical fin will create a clear increase in roll responsiveness across the low-speed part of the flight envelope. Yet most flex-wing hang glider pilots do not perceive a fixed vertical fin to create any noticeable increase in a glider's responsiveness in the roll axis. My own perception is that a fixed vertical fin has little or no perceptible effect on the roll handling of the flex-wing hang gliders that I've flown with and without fins. I do suspect that even when wingtip airspeed differences are considered, adverse yaw generally does create some net helpful roll torque across most of the flight envelope with flex-wing hang gliders with no VG or with the VG full off, so that a fixed vertical fin does create some reduction in the glider's roll responsiveness in these parts of the flight envelope. I have no doubt that this must be the case in the high-speed part of the flight envelope when the VG is only partially on, or is fully off, or when there is no VG. Note that the difference in airspeed between the two wingtips created by a yawing motion is much less important when an aircraft is flying at a high airspeed than when an aircraft is flying at a low airspeed.

(In the interest of collecting more data, if you are a flex-wing hang glider pilot who has made careful observations on the roll handling of various gliders when flown with a fixed vertical fin versus when flown without a fixed vertical fin, at specific parts of the airspeed envelope, I would be interested in hearing these observations.)

Here's some food for thought that tends to suggest that the differential tip speed effect can be rather important at times: a very experienced dune pilot has suggested to me that the way that dune pilots use yaw inputs in various situations--for example during a decelerating ground run after a dunetop landing--suggests that a strong yaw input (made with the pilot's feet on the ground) can indeed create a net roll torque in the same direction as the yaw input (i.e. a "positive coupling between yaw and roll") over a wide range of angles-of-attack. To the extent that this is true, it does suggest that the difference in wingtip airspeed is important, assuming that we've convinced ourselves that a sideways component in the relative wind will interact with the 3-dimensional shape of the wing to contribute a net anhedral-like "upwind" roll torque or "negative coupling between yaw (slip) and roll" over most of the flight envelope with most flex-wing gliders with the VG loose or absent. I'm not quite sure what to make of all this because many different confounding variables (wind gradient etc) may be present in the dune environment. Also, this situation may involve lower forward airspeeds, in conjunction with higher yaw rotation rates, than would normally occur in actual flight. This would make the roll torque created by the differential wingtip airspeed effect relatively more important, and the roll torque created by the sideways (slipping) airflow around the glider relatively less important, than they would be when the glider adverse-yawed in normal flight. Also, this technique may be most effective at relatively high angles-of-attack--after all, a pilot will not be pulling in the bar very much if he is trying to decelerate. I have a hard time imagining that the "upwind" roll torque created by the interaction between the sideways airflow and the anhedral geometry of the wing would not be the dominant factor at low angles-of-attack (high airspeeds), even with fairly substantial yaw rotation rates.

Along the same lines, many expert hang glider pilots do report using yaw inputs (which in the absence of a rudder, can only be made by taking advantage of their body's yaw rotational inertia by quickly and forcefully "levering" the control bar in a twisting manner) in the intended direction of turn in certain situations while thermalling. To the extent that this technique works when the VG is loose as well as when the VG is tight, and assuming that one of the effects of this maneuver is to roll the glider in the intended direction of turn, and assuming that the sideways component in the relative wind will interact with the 3-dimensional shape of the wing to contribute a net anhedral-like "upwind" roll torque or "negative coupling between slip (yaw) and roll" over most or all of flight envelope when the VG is loose or absent, the difference in airspeed between the left and right wingtips would appear to be playing quite a significant role in the dynamics of the glider in this maneuver.

As we consider the relative importance of the "negative coupling between yaw (slip) and roll" created by the interaction between the sideways component in the relative wind and the 3-dimensional shape of the wing, and the "positive coupling between yaw and roll" arising from the difference in airspeed between the two wingtips during a rapid yawing motion, it's worth keeping this in mind: the "upwind roll torque" or "negative coupling between yaw (slip) and roll" created by the interaction between the sideways component in the relative wind and the 3-dimensional shape of the wing that we observed in the experiments with the flex-wing hang gliders was quite modest in the low-airspeed (high angle-of-attack) corner of the flight envelope. After all, all the gliders were comfortably controllable in the low-speed corner of the flight envelope at all VG settings even with the rudder fully deflected, or with a fairly sizeable drogue chute deployed from a wingtip (ruler is 18 inches). (At higher airspeeds, with the VG (if present) fully loose, the "negative coupling between yaw (slip) and roll" was much stronger and the gliders were NOT comfortably controllable when a chute of this size was deployed from a wingtip!)

But as more food for thought, it's also worth noting that during the experiments that we described in "Interesting experiments: Zagi RC glider with variable anhedral/dihedral geometry, and rudder", which were well suited to exploring the consequences of abrupt yaw inputs, it never was the case that a rapid, abrupt yawing motion made the glider roll in the direction of the yaw input, if the glider was configured with enough anhedral (in relation to the airspeed trim setting) so that the interaction between the sideways component in the relative wind and the 3-dimensional shape of the wing created an "upwind" roll torque or "negative coupling between slip (yaw) and roll" during a non-turning straight-line sideslip. However a hang glider does fly at a slower "scale speed" (wingspans per time) than a Zagi so wingtip airspeed effects will likely be generally more pronounced in the case of the hang glider than in the case of the Zagi.

Regardless of the relative importance of a difference in airspeeds between the wingtips and regardless of whether the "complete" effects of a typical adverse-yaw motion end up creating a mild dihedral-like "downwind" roll torque or an anhedral-like "upwind" roll torque in the lower-speed part of the flight envelope, it's clear enough that if the wing had no anhedral, adverse yaw would create a much stronger, unfavorable, "downwind" roll torque in every part of the flight envelope, especially in the low-speed high-angle-of-attack part of the flight envelope where the dihedral-like effects of sweep are most pronounced. This would greatly slow the glider's response to the pilot's roll inputs.

In "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", we also noted the following:

The results expressed in "Interesting experiments: adding a controllable rudder and other yaw devices to 4 flex-wing hang gliders" strongly suggest that most flex-wing hang gliders have more anhedral with the VG off than with the VG on. After all, the Airborne Blade exhibited a net anhedral-like "upwind" roll torque or a net "negative coupling between yaw (slip) and roll" even in the low-speed portion of the flight envelope with the VG fully off, but exhibited a net dihedral-like "downwind" roll torque or net "positive coupling between yaw (slip) and roll" in the low-speed portion of the flight envelope with the VG fully on. This relationship is one of the reasons why flex-wing hang gliders respond more slowly to pilot roll inputs when the VG is fully on. In the low-speed, high angle-of-attack portion of the flight envelope with the VG fully on, when the pilot begins to roll the glider from wings-level into a turn and the glider adverse-yaws and this creates a sideways airflow over the aircraft, the sideways airflow will create a net "downwind" or unfavorable roll torque that will slow the glider's roll response to the pilot's roll control input.

In the low-speed, high angle-of-attack portion of the flight envelope with the VG fully on, and any other part of the flight envelope where a glider exhibits a net dihedral-like "downwind" roll torque or net "positive coupling between yaw (slip) and roll" in response to a sideways airflow, we can also make the following observation: whenever the aircraft's nose is actually swinging in the "wrong" direction in relation to the external world as well as in relation to the direction of the flight path and airflow at any given moment, the resulting difference in airspeed between the two wingtips will contribute an additional unfavorable roll torque that adds to the unfavorable roll torque created by the interaction between the sideways airflow from the adverse yaw and the glider's net "positive coupling between yaw (slip) and roll". In this part of the flight envelope, the complete effects of adverse yaw definitely create an unfavorable roll torque. In this part of the flight envelope, minimizing adverse yaw by installing a fixed vertical fin must create some degree of improvement in the glider's responsiveness to the pilot's roll control inputs.

By the way, this is exactly the situation with most "conventional" aircraft with dihedral or sweep, and no anhedral, that use ailerons for roll control. If the pilot isn't applying the rudder as needed to keep the nose of the aircraft aligned with the actual direction of the flight path, i.e. if the pilot isn't making whatever rudder inputs are needed to keep the nose of the aircraft pointing directly into the relative wind, then adverse yaw will create an unfavorable roll torque both due to the interaction between the sideways airflow and the dihedral or sweep, and due to the difference in airspeed between the two wingtips. (With fast-flying aircraft the first of these will be the most important effect and the difference in airspeed between the two wingtips will not create a very significant roll torque.) If the pilot isn't applying the rudder as needed to keep the nose of the aircraft aligned with the actual direction of the flight path, i.e. pointing directly into the relative wind, then a large fixed vertical fin will enhance the aircraft's responsiveness to the pilot's roll control inputs, by reducing adverse yaw. For a good example of this principle, remove the tip fins from a Zagi RC glider or any other rudderless swept-wing aircraft, do some aileron rolls, and note how the roll responsiveness has decreased! The idea that by reducing adverse yaw, a fixed vertical fin will enhance the roll rate of a rudderless aircraft or a "conventional" aircraft where the pilot is not using the rudder, is a natural extension of ideas we discussed in the tutorial page entitled "Conventional use of the rudder".

At some future point, this tutorial will include a page that describes in detail how an adverse yaw motion in a flex-wing hang glider is actually more complex than a simple swing of the nose in the "wrong" direction. If a pilot watches a centrally-mounted yaw string while making a strong left roll input to roll quickly from wings-level into a left bank, he or she will see the yaw string first deflect strongly toward the right. Then the yaw string will go through several oscillations where it moves to the left and then back to the right. (In some cases, the first of these oscillations will actually bring the yaw string to left of the aircraft centerline, showing that the aircraft is briefly skidding rather than slipping!) When the (left) bank angle becomes constant, the yaw string will end up streaming slightly to the right of the aircraft centerline. The point in a nutshell is that when a pilot makes a strong roll input, the resulting adverse yaw motion is actually a dynamic series of yaw oscillations. Only at the very beginning of these oscillations is the nose likely to be swinging in the "wrong" direction in relation to the external world, as well as in relation to the actual direction of the flight path and airflow at any given moment. In other words, only at the very beginning of these oscillations is aircraft's compass heading likely to be changing in a "backwards" fashion. This means that only at the beginning of these oscillations will we see the descending wingtip actually moving forward with a higher airspeed than the rising airspeed. In the future we'll depict this more clearly with a matched set of graphs showing the direction of the aircraft's flight path versus time, and the aircraft's compass heading versus time, and the change in the aircraft's compass heading versus time (which is what creates a difference in airspeed between the two wingtips), and the yaw (slip) angle in relation to the actual direction of the flight path and airflow versus time (as illustrated by the yaw string), and the change in the yaw (slip) angle in relation to the actual direction of the flight path and airflow versus time.

 

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