Details: yaw oscillations during roll inputs in flex-wing hang gliders
August 8, 2007 edition
In Aerial experiments: Looking for the "slipping"
turn while hang gliding--overview, we describe how a hang glider typically shows a significant sideslip, due to adverse yaw, as it rolls from wings-level into a steep turn.
In reality, a hang glider can be seen to go through several yaw oscillations when we give a sudden hard roll input to initiate a roll from wings-level into a steep turn. For example, as we watch the yaw string while we give a hard left roll input, we might see the yaw string first swing 10 degrees to the right of the glider centerline, and then swing back to 2 degrees to the left of the glider centerline, and then swing back to 8 degrees right of the glider centerline, and then swing back to 2 degrees right of the glider centerline, and then swing back to 6 degrees right of centerline and then -- as we allow the bank angle to stop increasing-- settle down to just a few degrees to the right of the glider centerline as the glider settles into a steady, constant-banked left turn with only a slight amount of sideslip.
These oscillations in the degree of sideslip will not be evident just from watching the nose of the glider. If we watch the nose of the glider we will just see the nose initially swing to the right, and then start tracking around the horizon from right to left. We will see some variation in the yaw rotation rate but we will not realize the full extent of the oscillations in sideslip that are taking place.
These oscillations in sideslip show that the glider has a significant amount of rotational inertia in the yaw axis. Oscillations in physical systems nearly always involve some sort of inertial lag. We can see a similar dynamic in an aircraft with a rudder, when we apply a sudden rudder input, or when we gradually apply some rudder and then suddenly release the rudder. The nose of the aircraft will oscillate from side to side through several visible yaw oscillation cycles.
For an overall analysis of the glider's dynamics it is probably adequate to look at the average position of the yaw string and not worry about each yaw oscillation. The average position of the yaw string as we give a hard left roll input is a significant displacement to the right, followed by a movement back closer to the glider centerline as we allow the bank angle to stop increasing and the glider settles down into a steady, constant-banked left turn with only a slight amount of sideslip. The oscillation is superimposed on top of this average movement.
Here is another piece of evidence that yaw rotational inertia is not negligible: with a series of alternating roll inputs, we can "pump up" a series of roll reversals that involve much more sideslip than would a single roll input starting from wings-level flight. We can see a similar dynamic in an aircraft with a rudder, where a series of alternating rudder inputs will "pump up" a series of yaw oscillations than involves much more sideslip than we could create with any one single rudder input.