In-flight observations supporting the idea that a flex-wing hang glider has more anhedral with the VG off than with the VG on, including notes on yaw-roll oscillations and tow dynamics
October 16, 2006 edition
In the previous tutorial page, "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?", we noted that a yawing motion (with respect to the external world) creates a difference in airspeed between the left and right wingtips, which creates a roll torque. This dynamic will be less important in the discussion that follows below. We'll begin by discussing results from the experiments with rudders and wingtip drag devices where the glider's heading was held constant, so there was no difference in airspeed between the two wingtips. Then we'll discuss dynamics that take place in the high-speed part of the flight envelope, where the difference in airspeed between the wingtips arising from a yawing motion is less important than it is at lower airspeeds.
In "Interesting experiments: adding a controllable rudder and other yaw devices to 4 flex-wing hang gliders" and "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 explored what happened when we made experimental yaw inputs while flying flex-wing hang gliders. We noted that for any given airspeed, in the presence of a sideways airflow, the flex-wing hang glider with VG showed a much stronger anhedral-like "upwind" roll torque (or "negative coupling between yaw (slip) and roll") when the VG was off than when the VG was on. We argued that the underlying reason for this was that the glider actually did have more anhedral with the VG off than with the VG on.
This is consistent with the observations that we made while looking at 3-dimensional shape of the same flex-wing hang glider with the VG off and with the VG on in "Looking at anhedral in flex-wing hang gliders: VG off versus VG on". In several different kinds of observations, we noted more anhedral in the 3-dimensional shape of the wing when the VG was off than when the VG was on.
Bear in mind that the geometry of the outboard parts of the wings will be more important than the geometry of the inboard parts of the wings as far as the glider's roll characteristics are concerned, because the outboard parts of the wings are so much further from the glider's CG, and thus tend to create more roll torque than the inboard parts of the wings. For the purposes of our discussion here, if we decrease the anhedral on the inboard parts of the wing and we increase the anhedral on the outboard parts of the wing, and this causes the glider to exhibit a stronger "upwind" roll torque in the presence of a sideways component in the relative wind, we'll say that we've increased the glider's overall anhedral geometry.
Of course, it is the case that a flex-wing hang glider has slightly more sweep with the VG off than with the VG on. This would tend to create a slightly stronger dihedral-like effect or weaker anhedral-like effect with the VG off than with the VG on. The fact that we actually see the opposite flight characteristics further supports the idea that the glider in question must have more anhedral with the VG off than with the VG on.
Note that our test glider--an Airborne Blade--has a conventional pulley VG system. In a glider with a cam VG system, the leading edge tubes will stay "in plane" with the keel tube, rather than dropping downward with respect to the keel tube, as the VG is system tensioned. This means that when the VG system is tensioned, a glider with a "cam" VG system will see an even greater decrease in the anhedral geometry of the outboard parts of the wings than will a glider with a conventional pulley VG system. In light of this, it seems valid to conclude that most flex-wing gliders with VG systems of any kind will have more anhedral in the outboard parts of the wings when the VG is loose than when the VG is tight.
We'll take a moment here to point out that a cam VG system makes a lot of sense from a performance standpoint. The whole point of tensioning a VG cord is to improve the glider's performance, even if this comes at the expense of ease of handling. Anhedral is good for handling, but it doesn't do anything for performance, so the more of it we can remove by tensioning the VG cord, the better. Some pilots who like to use VG as a way to modify the glider's rolling-in or rolling-out characteristics during thermalling prefer pulley VG systems to cam VG systems. We'll take up the issue of VG systems and roll instability later in the Aerophysics Exploration Pages.
Here's another line of evidence in support of the idea that most flex-wing gliders have more anhedral in the outboard parts of the wings when the VG is loose than when the VG is tight: while flying at a low angle-of-attack (high airspeed), most flex-wing hang gliders are much more prone to yaw-roll oscillations in free flight, and also on tow, when the VG is fully loose than when the VG is partly or fully tight. For a given VG setting, these oscillations are much more pronounced when the glider is flying at a low angle-of-attack (high airspeed) than when the glider is flying at a high angle-of-attack (low airspeed).
We noted in "Competing effects of sweep and anhedral" that in a swept-wing aircraft with anhedral, the dihedral-like effects of sweep tend to dominate at low airspeeds (high angles-of-attack), and the anhedral tends to dominate at high airspeeds (low angles-of-attack). So the increased prevalence and intensity of these yaw-roll oscillations at high airspeeds (low angles-of-attack) suggests that they are being driven in part by the negative coupling between yaw (slip) and roll that arises from the wing's anhedral geometry. And the increased prevalence and intensity of these yaw-roll oscillations when the VG is tight suggests that the glider has more anhedral when the VG is tight than when the VG is loose.
Let's explore these yaw-roll oscillations a bit further.
In contrast to what many flex-wing hang glider pilots believe, I've found that these yaw-roll oscillations are not always pilot-induced. During free flight, if I pull the bar well aft on my Airborne Blade with the VG full loose and make no further roll inputs, the glider will settle into a series of oscillations involving yaw, roll, and pitch, where the nose describes a sideways "8" across the horizon. During a fast aerotow with the VG loose, with no fixed vertical fin installed on the glider, the same glider is highly prone to entering a series of marked yaw-roll oscillations even in the complete absence of any pilot roll inputs, and even when the pilot uses the proper "limp" grip on the control bar to avoid transmitting yaw torques through the towline to the glider. (Of course, well-timed roll inputs can stop these oscillations).
I prefer to tow the Airborne Blade with the VG one-third to one-half on to help avoid these yaw-roll oscillations (while still affording some margin of responsiveness to actual pilot roll inputs), and many other flex-wing hang glider pilots follow a similar practice with their gliders.
I'm convinced that all these yaw-roll oscillations are caused by the glider's anhedral geometry and net "negative coupling between slip (yaw) and roll". That's one reason that they are absent in rigid-wing hang gliders with dihedral. The looser the VG, the more the anhedral, especially in the outer parts of the wings, and the more the glider will show a tendency toward these yaw-roll oscillations.
The yaw-roll oscillations seen during flight at high speeds on tow and in free flight in flex-wing hang gliders appear to be quite different from the true "Dutch Roll" yaw-roll oscillations seen during free flight in some "conventional" aircraft with dihedral and/or sweep, and no anhedral. True "Dutch Roll" oscillations can be thought of being caused in part by an "excessive" positive coupling between yaw (slip) and roll, due to an "excessive" amount of dihedral and/or sweep. Anhedral is often designed into "conventional" swept-wing aircraft in order to reduce or eliminate these true "Dutch Roll" oscillations. In contrast, the yaw-roll oscillations that occur in flex-wing hang gliders during flight at high airspeeds on tow and in free flight appear to be caused in part by the negative coupling between yaw (slip) and roll that is created by the large amount of anhedral that exists in the geometry of the wing, in relation to the amount of sweep. (In the interest of not oversimplifying the "Dutch Roll" phenomenon, we'll give some additional notes on true "Dutch Roll" at the end of this article).
The forcing mechanisms during behind true "Dutch Roll" oscillations are well understood. I don't fully understand the forcing mechanisms behind the yaw-roll oscillations seen during flight at high speeds on tow and in free flight in flex-wing hang gliders. On tow, the towline undoubtedly plays a significant role in forcing these oscillations.
In the interest of not oversimplifying our discussion of true "Dutch roll", here are a few more notes on this phenomenon. Like most oscillations, Dutch roll oscillations are most likely to arise and amplify at high density altitudes, and thus they are often particularly problematic for high-flying aircraft. Also, while Dutch roll oscillations can be described as resulting from "too much dihedral-like positive coupling between yaw (slip) and roll, in relation to the amount of yaw stability or 'weathervane effect'", i.e. "too much sweep or dihedral in relation to the size of the vertical fin", it's not really accurate to say that they are most likely to occur at the low-speed end of the flight envelope because this is where the dihedral-like effects of sweep are most pronounced. Since Dutch roll is a complex oscillation rather than a simple roll response to a single yaw input, it seems that it can be excited over a large part of the flight envelope, and as far as I'm aware, increasing the airspeed or decreasing the angle-of-attack is not one of the recommended strategies for ending a Dutch roll oscillation. This is different than what we see with yaw-roll oscillations in flex-wing hang gliders, where a decrease in airspeed (when possible, i.e. during free flight) always makes the oscillations stop. Here are a few links that briefly address "Dutch roll" oscillations:
"Free Directional Oscillations (Dutch Roll)"
"Basics of Roll Control and Stability"
Note that as described in the last of the above links, in a "Dutch Roll" oscillation the roll torque generated by dihedral is one of the restoring forces that drives the oscillation. What is the restoring force that drives a high-airspeed yaw-roll oscillation in a flex-wing hang glider, particularly in the free-flight case where there is no towline? One important factor may be the "roll damping" effect that creates a stabilizing roll torque (toward wings-level) whenever the flight path is steeply descending with respect to the airmass. Note that the yaw-roll oscillation that develops in free flight (i.e. not on tow) in the case where the pilot holds the bar in a constant, well pulled-in position in pitch and truly avoids making roll inputs (as opposed to the case where the pilot is "chasing" the glider with out-of-synch roll inputs) is a slow, long-period oscillation where the nose slowly describes a sideways figure-8 on the horizon, and the glider slowly goes through large changes in pitch attitude (and airspeed) as well as in bank angle. At times in this oscillation, the flight path is indeed steeply descending.
The main point of this discussion has been to advance the idea that flex-wing hang gliders have more anhedral with the VG off then with the VG on. At this juncture, a logical question is "why are most flex-wing hang gliders more spirally unstable with VG on than with VG off"? Some readers may want to jump directly to the Aerophysics Exploration page that explores this question, entitled "Spiral instability in flex-wing hang gliders: VG on versus VG off". However, we'll first explore some of the causes of adverse yaw, and then we'll explore the basic reasons why dihedral tends to create a stabilizing roll torque when an aircraft tips into a bank, and why anhedral tends to create a destabilizing roll torque when an aircraft tips into a bank.
Advance to "The main cause of adverse yaw during rolling motions: the 'twist' in the relative wind"
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