The aerodynamic forces acting on a delta wing, mounted on a free-to-roll sting-balance apparatus, were measured. Two wing planforms having leading edge sweeps of 76 and 80 deg were tested, but only the wing with the 80 deg sweep would undergo periodic self-induced roll oscillation. The time dependent forces and roll angles for this wing were then recorded for various test conditions. In these tests a considerable drop in the average normal force of the free-to-roll wing was measured, relative to the normal force obtained in the static tests. Also, the helium-bubble flow visualization technique was used to gain some insight into the periodic motion of the separated leading edge vortices.

Dynamic load measurements with delta wings undergoing self-induced roll-oscillations

A theory is developed for predicting wing rock characteristics. From available data, it can be concluded that wing rock is triggered by flow asymmetries, developed by negative or weakly positive roll damping, and sustained by nonlinear aerodynamic roll damping. A new nonlinear aerodynamic model that includes all essential aerodynamic nonlinearities is developed. The Beecham-Titchener method is applied to obtain approximate analytic solutions for the amplitude and frequency of the limit cycle based on the three degree-of-freedom equations of motion. An iterative scheme is developed to calculate the average aerodynamic derivatives and dynamic characteristics at limit cycle conditions. Good agreement between theoretical and experimental results is obtained.

Theory of wing rock

Wing/vortex interactions and wing rock

The phenomenon of wing rock was investigated using flow visualization in a water tunnel. Models with 70deg, 75-deg, 80-deg, and 85-deg sweeps were tested in a free-to-roll rig and a forced oscillation rig. Wing rock was observed to occur on various wings in the absence of asymmetric vortex liftoff, vortex breakdown, and static hysteresis. These phenomena are therefore not the necessary ingredients for wing rock. The presence of these phenomena, however, can have strong influence on characteristics such as the amplitude and frequency of wing rock.

Experimental Study of Vortex Flows over Delta Wings in Wing-Rock Motion

An experimental investigation into the fluid mechanisms responsible for wing rock on a slender delta wing with 80 deg leading edge sweep has been conducted. Time history and flow visualization data are presented for a wide angle-of-attack range. The use of an air bearing spindle has allowed the motion of the wing to be free from bearing friction or mechanical hysteresis. A bistable static condition has been found in vortex breakdown at an angle of attack of 40 deg which causes an overshoot of the steady state rocking amplitude. Flow visualization experiments also reveal a difference in static and dynamic breakdown locations on the wing. A hysteresis loop in dynamic breakdown location similar to that seen on pitching delta wings was observed as the wing was undergoing the limit cycle oscillation.

The effect of asymmetric vortex wake characteristics on a slender delta wing undergoing wing rock motion

An analysis is presented using control theory concepts to show that aerodynamic hysteresis of the form of relay action can lead to lateral-directional limit cycle motions. These limit cycle motions are usually described in a colloquial sense as airframe wing rock. The aerodynamic details leading to wing-rock oscillations will vary with airframe configuration, and usually the exact description of the aerodynamic nonlinearity is difficult to obtain or predict. The purpose of the studies described herein is to promulgate a flight mechanics analysis technique which by virtue of its simplicity offers the analyst an insight into potential candidate aerodynamic mechanisms.

L. V. Schmidt

Papers

Wing Rock Due to Aerodynamic Hysteresis