Zagi experiments

Interesting experiments: Zagi RC glider with variable anhedral/dihedral geometry, and rudder

Steve Seibel
www.aeroexperiments.org

October 13, 2006 edition

 

Variable-geometry Zagi RC glider with controllable rudder -- in this configuration, this glider was successfully flown using "wrong-way" rudder inputs as the sole means of roll control: a right rudder input created a left roll torque.

Variable-geometry Zagi with dihedral. In this configuration this glider could easily be flown with "normal" rudder inputs serving as the sole means of roll control, as per a Gentle Lady or other similar "floater" sailplane: a right rudder input created a right roll torque.

Planform view of same aircraft (with wings adjusted to a flatter configuration).

More about the variable-geometry Zagi's construction:

The Zagi's wing sweep angle was slightly increased from the original planform, so that the sweep angle, as measured at the quarter-chord position, was approximately the same as that of the 4 flex-wing hang gliders described in "Interesting experiments: adding a controllable rudder and other yaw devices to 4 flex-wing hang gliders".

To allow the Zagi's anhedral or dihedral angle to be changed from one flight to the next, I inserted a spar in each wing. The spars were offset slightly in the fore-and-aft sense, so that a single bolt could be passed through both spars. This bolt acted as a hinge: when this bolt was loosened, the Zagi's anhedral or dihedral angle could be changed. (Photo of offset spars and pivot bolt.)

More notes on the flight characteristics of the variable-geometry Zagi in the anhedral configuration:

When I gave the Zagi enough anhedral, the Zagi exhibited a "backwards" roll response to rudder inputs, i.e. a "negative coupling between yaw (slip) and roll". This negative coupling between yaw (slip) and roll was always strongest in the high-airspeed, low-angle-of-attack part of the flight envelope. This negative coupling between yaw (slip) and roll was always weakest in the low-airspeed, high-angle-of-attack part of the flight envelope.

With just the right amount of anhedral, the Zagi could be made to exhibit a "backwards" or negative coupling between yaw (slip) and roll in the high-airspeed, low angle-of-attack part of the flight envelope and a "normal" or positive coupling between yaw (slip) and roll in the low-airspeed, high-angle-of-attack corner of the flight envelope. When the Zagi was configured in this way the coupling between yaw (slip) and roll was slight throughout the flight envelope and an unusually large rudder was used to allow unusually large yaw (slip) angles to be created so that the coupling between yaw (slip) and roll could be detected.

All of these relationships are consistent with our understanding of the interplay between the aerodynamic effects of sweep and anhedral as described in "Competing effects of sweep and anhedral".

With substantially more anhedral (see the photo link near the top of this page), the glider showed a "backwards" roll response to rudder inputs (i.e. a negative coupling between yaw (slip) and roll) throughout the entire flight envelope, and this "backward" roll response or negative coupling between yaw (slip) and roll was strong enough to allow the glider to be successfully flown using "wrong-way" rudder inputs as the sole means of roll control. The Zagi was very unstable in this configuration and I had to be careful not to allow the bank angle to get too large, or else I would need to use the elevons to assist in the recovery to wings-level flight.

Since for a given trim setting, an aircraft will fly at a lower angle-of-attack in a turn than in wings-level flight, the following interesting phenomenon was observed: the Zagi was given just the right amount of anhedral so that the coupling between yaw (slip) and roll was negative at low angles-of-attack and positive at high angles-of-attack. The Zagi was then trimmed to fly at a high angle-of-attack in wings-level flight. As long as the wings were level, a right rudder input created a right roll torque, but once a substantial bank angle developed, the resulting decrease in angle-of-attack reversed the coupling between yaw (slip) and roll, so that a right rudder input created a left roll torque. Again, when the Zagi was configured in this way the coupling between yaw (slip) and roll was slight, and an unusually large rudder was needed to allow these interesting effects to be discerned.

When the Zagi was configured and trimmed so that the sideways airflow over the wing arising from a gradual rudder input created a "backwards" roll response to the rudder, i.e. a "negative coupling between yaw (slip) and roll", I was interested to see whether a rapid rudder input might create a "normal" roll response to the rudder, i.e. a "positive coupling between yaw and roll", due to the difference in airspeed between the two wings that temporarily existed as the Zagi rapidly yawed to a new heading with respect to the external world. In actual practice it never was the case that a fast rudder input created a roll response in the opposite direction as did a slow rudder input, except in a few cases where the Zagi was trimmed very near the stall angle-of-attack and a rapid rudder input appeared to produce a temporary tip stall of one wingtip.

In other words, in all configurations where the Zagi exhibited a discernable "backwards" roll response to slow rudder inputs, i.e. a "negative coupling between yaw (slip) and roll", it appeared that the roll torque arising from the difference in wingtip airspeeds resulting from a rapid yawing motion was smaller than the roll torque resulting from the interaction between the sideways (slipping) component in the relative wind and the anhedral geometry of the wing, so that the difference in airspeed between the two wingtips during a yawing motion was a relatively unimportant factor in the Zagi's response to rudder inputs. This might not be true in an aircraft with a slower "scale speed", i.e. a slower airspeed / wingspan ratio.

When exploring the Zagi's behavior at various angles-of-attack, I relied heavily on the pitch trim lever and generally kept my hands off the elevon stick as much as possible, taking care to leave the elevon stick in the neutral pitch detent when the elevons were needed for roll inputs.

I experimented with different rudder positions: sometimes the rudder was positioned so that almost all its area projected above the wing root chord line, and sometimes the rudder was positioned so that it had equal area above and below the wing root chord line. These changes had relatively little effect--equivalent to a very slight change in the dihedral/anhedral angle or a very slight change in the position of the pitch trim level-- on the direction and magnitude of the observed "coupling between yaw (slip) and roll". In other words, the flight characteristics when the rudder's center of area was located high above the wing root chord line were almost the same as the flight characteristics when the rudder's center of area was at the same height as the wing root chord line. This isn't surprising, since the height of the rudder was quite small in relation to the wingspan. In an aircraft where the height of the rudder was larger in relation to the wingspan, the position of the rudder in the vertical sense would have much more influence on the aircraft's flight characteristics.

More content to be added to this page in the future: notes on the anhedral angle that allowed the rudder to serve as a "wrong-way" roll control throughout the flight envelope. Notes on the anhedral angle at which the rudder created a "normal" roll torque at low airspeeds (high angles-of-attack) and created a "wrong-way" roll torque at high airspeeds (low angles-of-attack). Notes on the anhedral angle at which the rudder created a "normal" roll torque at all airspeeds. General notes on the aircraft's stability characteristics and control response characteristics in various anhedral and dihedral configurations. Notes on the usefulness of normal "coordinated" rudder inputs automatically coupled to elevon roll inputs, with various anhedral or dihedral configurations. Notes on effects of adding or removing a fixed vertical tail when the wing is in various anhedral or dihedral configurations. Description of how yaw oscillations provoked by the adverse yaw from a series of aggressive alternating roll inputs could lead to full-blown tumbles involving yaw, pitch, roll, in cases where yaw stability was marginal. Description of tumble provoked by the installation of wingtip weights to increase the rotational inertia in the yaw and roll axes.

 

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