Do flex wing-wing hang gliders have effective dihedral or effective anhedral?
August 8, 2007 edition
* Here are some notes on the competing effects of sweep and anhedral:
1) Sweep creates a dihedral-like effect. Flex-wing hang gliders have both sweep and anhedral. Therefore the roll torque that arises when we yaw a flex-wing hang glider will be determined by the competing effects of sweep and anhedral.
2) The dihedral-like roll torque created by sweep is known to be strongest at high angles-of-attack.
3) The roll torque created by anhedral is known to be relatively independent of angle-of-attack.
4) Therefore the competing effects of sweep and anhedral will create a stronger anhedral effect or a weaker dihedral effect at low angles-of-attack (high airspeeds), and a weaker anhedral effect or stronger dihedral-like effect at high angles-of-attack (low airspeeds).
* The results given in "Experimental results and interpretation: yaw experiments with a controllable rudder and wingtip-mounted drogue chutes on flex-wing hang gliders" suggest that many flex-wing hang gliders have effective anhedral over nearly all of the flight envelope, including angles-of-attack near min. sink.
* The results given in "Experimental results and interpretation: using yaw inputs for roll control while ground-handling flex-wing hang gliders" suggest that many flex-wing hang gliders have effective dihedral over a good part of the flight envelope, especially at high to moderate angles-of-attack.
* At present I don't know how to resolve this contradiction. At high angles-of-attack, might gliders exhibit effective anhedral when bearing the pilot's full weight and effective dihedral when some significant part of the pilot's weight is borne by his feet? Possibly because the wing has more billow when heavily loaded than when lightly loaded?
* Now let's focus on the high-angle-of-attack part of the flight envelope, e.g. typical thermalling flight.
* All rudderless aircraft (except perhaps those using spoilerons for roll control) exhibit adverse-yaw while rolling from wings-level into a bank. The sideways airflow from the slip interacts with dihedral to create a rolling-out torque and interacts with anhedral to create a rolling-in torque. In an aircraft with effective anhedral, adverse yaw will create a helpful roll torque, and dampening the adverse yaw will diminish the helpful roll torque which will decrease the glider's responsiveness to roll inputs. Conversely, in an aircraft with effective dihedral, adverse yaw will create an unfavorable roll torque, and dampening the adverse yaw will diminish the unfavorable roll torque which will increase the glider's responsiveness to roll inputs. The fact that many hang glider pilots have reported that a fixed vertical fin decreases roll responsiveness in many hang gliders seems to suggest that these gliders have effective anhedral. However, an alternative explanation is that as the glider adverse-yaws, the fin pushes the keel in relation to the rest of the airframe in the direction that creates an unfavorable billow-shift, or at least decreases the favorable billow-shift that would normally take place.
* All rudderless aircraft tend to show at least a small amount of sideslip during a constant-bank turn. The sideways airflow from a slip interacts with dihedral to create a rolling-out torque and interacts with anhedral to create a rolling-in torque. The fact that many hang glider pilots have reported that a fixed vertical fin increases the need for low-siding, or diminishes the need for high-siding, in a constant-banked turn in many hang gliders seems to suggest that these gliders have effective anhedral. If when we decrease sideslip by adding a fin, we seem to have removed some rolling-in torque, this suggests that the glider has effective anhedral. However, an alternative explanation is that as the glider slips a bit while turning, the fin pushes the keel in relation to the rest of the airframe in the direction that creates a rolling-out torque.
* What other evidence do we have, apart from the effects of a keel-mounted fin, that suggests that adverse yaw creates either a helpful roll torque or a harmful roll torque? This would suggest that we were dealing with effective anhedral or effective dihedral, respectively. The relationships would likely be strongly dependent on angle-of-attack. What happens to the roll rate when we dampen adverse yaw with wingtip fins, or by changes in the wing shape?
* What kind of roll response, if any, do we see when we make an "impulse" yaw input by yawing our body sharply to one side to induce a small, temporary, opposite, yawing motion in the wing?
* If a glider requires low-siding during a turn, is this evidence that the glider has effective dihedral, especially if we are talking about a low-airspeed turn with a low sink rate with respect to the airmass? What other factor could create a need for low-siding? The difference in airspeed between the two wingtips tends to create a rolling-in torque. The glider is slipping a bit as it turns. It seems that the interaction between the slipping airflow and a wing geometry that creates effective dihedral is the only significant factor that could create a rolling-out torque, at least at low airspeeds. This line of thought suggests that any hang glider that needs low-siding has substantial effective dihedral at that angle-of-attack. Are we over-looking some other important factor here, perhaps something involving the glider's aeroelasticity? See below where we discuss one other factor that could create a need for low-siding.
* Some of the gliders that seemed to exhibit effective anhedral during the in-flight experiments with the wingtip-deployed drogue chutes as well as with the controllable rudder, needed low-siding during normal thermalling turns. How is this possible? Was there some flaw in the rudder and drogue-chute experiments that made the gliders seem as if they had more effective anhedral than was actually present? Or are we over-looking some other significant factor?
* As the angle-of-attack is decreased by pulling in the control bar, a flex-wing hang glider typically needs less and less high-siding, or more and more low-siding, in order to maintain a constant bank angle. Since decreasing the angle-of-attack increases the effective anhedral (or decreases the effective dihedral) in the wing, as noted at the start of this article, why is a great deal of low-siding usually required at very low angles-of-attack (i.e. with the bar well pulled in)? There seems to be a contradiction here. Here is the explanation: when the sink rate with respect to the airmass is high, the glider's flight path is a descending helix. The extreme example of this would be a vertically descending rolling dive. All constant-banked descending turns involve some degree of rolling motion in the direction of the turn. If this rolling motion stops, the bank angle decreases. The glider has some resistance to rolling-- this is the "aerodynamic damping in the roll axis". When the sink rate with respect to the airmass is high, the glider's rotation in the roll axis becomes significant, and the pilot has to low-side the bar to overcome the aerodynamic damping effect and keep the rolling-in motion going, just to hold the bank angle constant. The bank angle has a strong tendency to decrease during a high-speed diving turn where the glider has a high sink rate with respect to the surrounding airmass. This effect can create the need for low-siding even in a glider with effective anhedral. Is this effect sometimes significant even during high angle-of-attack, low-airspeed turns? Could this explain why we need to low-side the bar during normal thermalling flight even in a glider that appears to have effective anhedral rather than effective dihedral?
* The dynamic described above, that creates a strong need for low-siding during a high-airspeed, low angle-of-attack turn, is really a function of the sink rate with respect to the airmass, not the angle-of-attack. If we add power to the aircraft to create a climb with respect to the airmass, everything changes, even if we keep the angle-of-attack low (but more so if we allow the angle-of-attack to increase!). During a powered climbing turn the glider again has a rolling motion, but now the rolling motion is against the direction of the turn. The extreme case of a powered climbing turn would be a vertical rolling climb, with the direction of roll opposite the original direction of turn. All constant-banked climbing turns involve a rolling motion opposite the direction of the turn. If this rolling motion stops, the bank angle increases. The glider has some resistance to rolling-- this is the "aerodynamic damping in the roll axis". When the climb rate with respect to the airmass is high, the glider's rotation in the roll axis becomes significant, and the pilot has to high-side the bar to overcome the aerodynamic damping effect and keep the rolling-out motion going, just to hold the bank angle constant. The bank angle has a strong tendency to increase during a powered climbing turn.
* The fact that a high-airspeed (low angle-of-attack) gliding turn typically needs more low-siding or less high-siding than a low-airspeed (high angle-of-attack) gliding turn, even though a swept anhedral wing actually has more effective anhedral at low angles-of-attack than at high angles-of-attack, reminds us that a glider's degree of effective dihedral or anhedral is not the only important factor that determines how much high-siding or low-siding is required in a turn. The amount of sideslip that we expect in a steady, constant-banked turn is small, and dihedral or anhedral geometries only create roll torque in proportion to the amount of sideslip that is present. Therefore it's not surprising that an aircraft's anhedral or dihedral geometry will only be one of many important factors that determine whether high-siding or low-siding are required in a constant-banked turn. A direct yaw experiment seems the best way to quantify an aircraft's degree of effective anhedral or dihedral.