The "pendulum" effect

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 and paragliders

Steve Seibel
www.aeroexperiments.org

This page was last modified on September 15, 2006

 

Some aircraft have a "parasol" configuration --see for example this free-flight model airplane. This configuration has a dihedral-like effect and tends to create a "downwind roll torque" in the presence of a sideways component in the relative wind. In other words this configuration tends to create a "positive coupling between slip (yaw) and roll". This will help make it possible to use the rudder as a roll control (if a rudder is present.) This will also tend to reduce spiral instability or enhance roll stability.

It is often imagined that gravity simply tends to move the aircraft's CG into a position directly under the wing's center of lift, much as gravity tends to pull a pendulum into a position where it is hanging straight down from it's point of attachment. This really doesn't make sense. Gravity acts at the aircraft's CG and so cannot create a roll torque. Or to put it another way, an aircraft does not "feel" the direction of gravity.

Since the wing is located high above the CG, and since the wing's drag vector acts parallel to the relative wind, whenever there is a sideways component in the relative wind the wing's drag vector will create a roll torque that tends to roll the aircraft in the "downwind" direction. This is how the "parasol" geometry creates the dihedral-like effect or "downwind roll torque" or "positive coupling between yaw (slip) and roll". To understand why this would tend to enhance roll stability or reduce roll instability, bear in mind that an aircraft tends to sideslip when it banks, which creates a sideways component in the relative wind, unless the pilot uses a rudder to prevent the sideslip and keep the nose of the aircraft pointing directly into the relative wind. The direction of the sideways airflow from the sideslip is such that if the aircraft rolls in the "downwind" direction, it will roll toward wings-level. To better understand exactly why an aircraft tends to sideslip when it banks, see "A 'holistic' view of how dihedral contributes to roll stability and anhedral contributes to roll instability".

As long as the wing is fairly high above the top of the fuselage, the more slender the fuselage, the stronger these effects must be. Since the center of the fuselage area is usually below the CG, the impact of a sideways airflow against a broad, slab-sided fuselage will contribute a destabilizing "upwind" roll torque that will tend to create a "negative coupling between yaw (slip) and roll". This is an anhedral-like effect, which reduces the net dihedral-like effect of the parasol configuration. In an aircraft shaped like this Fokker D-8, it seems likely that the dihedral-like effect of the parasol configuration is smaller than it would be if the fuselage were more slender and streamlined.

More "conventional" high-winged aircraft where the wing is attached to the top of the fuselage experience another dihedral-like effect due to the way that the fuselage affects the airflow around the wing. We'll explore this in more detail elsewhere in these exploration pages. In this case a large slab-sided fuselage may enhance the dihedral-like effect of the high wing configuration.

The fact that full-scale piloted aircraft with "conventional" high-winged configurations or with "parasol" configurations usually are designed with very modest amounts of dihedral or no dihedral is an indicator that both of these configurations create a significant dihedral-like effect (i.e. a "downwind" roll torque or "positive coupling between yaw (slip) and roll"). Of course unpiloted free-flight models are often designed with ample dihedral even when they have parasol or conventional high-wing configurations, since they must be truly stable in roll and able to recover from disturbances without help from a pilot.

Paragliders have an extreme amount of anhedral in their wings, yet possess strong roll stability. This is due to the "parasol" effect. Note that the paraglider pilot is essentially fixed in place in relation to the wing surface by the tension in the lines and is not free to swing from side to side in relation to the wing surface. (To take a more complete approach, since the fabric wing is not completely rigid, the pilot does have some amount of freedom of sideways movement and will not necessarily always hang directly in line with the centerline of the wing, but any such sideways movement in relation to the wing surface will tension the lines in a way that creates an asymmetrical distortion in the shape of the wing, which may create other stabilizing dihedral-like effects.)

A hang-glider-like aircraft with a heavy mass that is fixed in place in relation to the wing can be viewed as having a "parasol" configuration which will contribute a dihedral-like effect--see for example this RC Rogallo aircraft. The trike "car" is rigidly fixed to the wing and moves from side to side only in response to control inputs that move the servos. This glider can easily be trimmed for prolonged wings-level flight without pilot control inputs. (The high degree of sweep in the wing undoubtedly also contributes a strong dihedral-like effect.)

However, on a conventional hang glider or trike the pilot's body or the trike car is free to swing from side to side. Assuming that the pilot's body has not swung so far that it is pressed against a downtube (or assuming that the trike car has not reached the limit of its side-to-side travel), no roll torque can be exerted by the pilot's body (or by the trike car) on the wing, except for the roll torque that pilot exerts with his own muscles. To take the simplified case where the pilot is attached to the glider via a flexible hang strap that attaches exactly at the CG of the glider, and assuming for the moment that the pilot is not holding on to the control bar, any sideways displacement of the pilot's body or sideways load on the pilot's body cannot transmit a roll torque to the glider, nor can it place an asymmetrical load on the structure of the glider. In other words to a first approximation when the pilot is not holding on to the control bar, the pilot's mass will not affect the aircraft's roll dynamics. Here, the flexible connection between the pilot and the wing is such that the dynamics of the pilot and the wing are de-coupled and there is no dihedral-like "parasol" effect. As far as roll torques are concerned, the only coupling between the pilot's mass (or the mass of the trike car) and the wing is through the pilot's muscles. This coupling disappears when the pilot is not holding onto the control bar.

When the pilot is holding on to the control bar things are more complex. If we want to analyze stability in terms of whether or not the glider will tend to enter a turn when the pilot is using his muscles to hold himself firmly at the centerline of the control bar, then we should view the glider as having a "parasol" configuration. If we want to analyze stability in terms of whether or not the glider will tend to enter a turn when the pilot is not exerting a muscular force on the control bar, then we should not view the glider as having a "parasol" configuration. The latter is really a better way of looking at things--for example, if a pilot must use his muscles to create a roll torque toward the high side of a turn just to keep the bank angle constant, he will view the glider as being spirally unstable at that particular bank angle, even if his body happens to be aligned with the centerline of the control bar.

Note that these two ways of looking at things are really only different to the extent to which a pilot needs to exert a muscle force to keep his body at the centerline of the control bar. In my own hang gliding experience it seems that the muscle forces I exert on the control bar are very strongly correlated to my actual body position, and I never find myself exerting a strong muscle force just to stay at the centerline of the control bar.

The sideloads acting on a pilot's body are really a reflection of the real, tangible aerodynamic sideloads generated by the airflow around the aircraft. If we observe that the apparent sideloads on a hang glider pilot's body are usually small, we are also observing that the real tangible aerodynamic sideforces generated by the sideways airflow around the wing are small. Aerodynamic sideforces acting high above the CG are what create the "parasol effect". If the "parasol effect" is playing a role in the roll dynamics of a hang glider, a pilot will feel this in his muscles and will need to exert a force just to remain on the centerline of the glider. As we've already suggested, since the pilot must create the roll torque involved in the "parasol effect" with his own muscles, it really makes more sense not consider it to be an inherent part of the aircraft's inherent stability dynamics. In other words, it makes more sense to consider the pilot and glider as independent free bodies, and not include roll torques generated by the pilot's muscles as contributors to the "parasol effect" or other aspects of the glider's inherent stability dynamics. But as we've also already noted, it also seems to be the case that a hang glider pilot generally needs to exert only very small muscle forces to keep himself near the centerline of the control bar, which suggests that the "parasol effect" might make only a fairly modest contribution to the glider's roll dynamics even if the pilot were rigidly fixed to the centerline of the base bar.

(Note that in this particular instance, since we are talking about roll dynamics, we do need to define the aerodynamic sideforce in relation to the aircraft's longitudinal axis, not in relation to the actual direction of the flight path and relative wind, which means that the sideways component of the wing's drag vector is included as a sideforce. This is a little bit awkward, as this is not a true sideforce in relation to the actual direction of the flight path and airflow.)

If the pilot's body is connected to the glider at a point on the kingpost that is high above the CG of the glider, then when the pilot lets go of the control bar, any sideforces transmitted through the hang strap to the kingpost will tend to create a destabilizing, anhedral-like, "upwind" roll torque. In the case where we are analyzing the glider's dynamics in terms of the muscle forces that the pilot must exert on the bar, rather than assuming that the pilot will want to clamp himself to the centerline of the control bar at all times (in other words, in the case where we are viewing the pilot and the glider as independent free bodies), we have to view a hang glider with a high kingpost hang point as having an "anti-parasol" configuration rather than a parasol configuration. If a slip creates strong enough aerodynamic sideforces that the pilot's body tends to move significantly toward the low side of the control bar, this will exert a force on the kingpost that creates an "upwind" roll torque, which is a destabilizing effect.

Parts of this analysis can be extended to hang glider tow dynamics. If the towline is connected only to the pilot's body, and the pilot's flexible hang strap is connected to the glider exactly at the glider's CG, then as long the pilot exerts no muscle force on the control bar (and assuming that the pilot has not been pulled against one of the down tubes), the tow line cannot exert a direct roll torque on the glider. The roll torque created by the tow line is cannot be treated as something separate from the roll torque created by the pilot's muscles. The situation is more complex when the pilot is attached to the glider via a high kingpost hang point. And of course, by pulling the glider sideways through the air, the towline can indirectly create roll torques, due to the interaction between the sideways airflow and the glider's anhedral geometry.

In the experiments with flex-wing hang gliders involving controllable rudders and other yaw devices described in "Interesting experiments: adding a controllable rudder and other yaw devices to 4 flex-wing hang gliders", I monitored the gliders' tendency to roll toward a steeper or shallower bank angle primarily by noticing the muscle force I had to exert on the control bar, and secondarily by noting the position of my body on the control bar, and never encountered a situation where these two indicators were noticeably "out of synch" or where I had to exert a noticeable muscle force just to keep my body centered on the control bar. Also, during experiments where the glider was kept flying though the air in a non-turning (straight-line) slip, the displacement of the slip-skid bubbles was very small. All of this suggests that the aerodynamic sideforces were small and that the "pendulum effect" would not have created very much roll torque even if my body mass had been rigidly fixed to the centerline of the control bar.

The only aircraft with true "pendulum" stability in the purest sense are balloons and other lighter-than-air aircraft. While a wing always lifts "upwards" in the aircraft's own reference frame, the buoyant gas always lifts "upwards" in relation to the external world. This means that if the lighter-than-air aircraft is tipped to the side, it will immediately tend to right itself, i.e. the center of buoyancy will tend to end up positioned directly over the CG, via a dynamic that is in no way dependent on the presence of a sideways airflow.

We'll introduce the concept of sideforces more thoroughly in a later Aerophysics Exploration page entitled "Aerodynamic sideforce during slips and skids".

 

At this point in the Aerophysics Exploration Pages we'll relax our focus on flex-wing hang gliders, at least for now. We'll also move on from stability and control issues, and look at some more general aspects of slips and skids.

 

Advance to "More detailed definitions of 'slips' and 'skids'"

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