Evaluation of Aerodynamic Derivatives from a Magnetic Balance System
When it comes into operation, the University of Virginia (three component) magnetic balance wind-tunnel facility will support a magnetic sphere in a Mach 3 wind tunnel. A model, built around the magnetic sphere, is essentially rotationally free at all frequencies and is free in translation at frequencies above some adjustable "balance frequency" (of the order of 10-15 Hz). The system, by responding to translation at frequencies below the balance frequency, holds the model in the test section. It is straightforward to arrange a passive, static magnetic restoring moment on the model so that it oscillates in rotation and translation at a frequency well above the balance frequency. Thus stable motion of an aerodynamically unstable model can be arranged. The study of the dynamic stability (or the evaluation of the dynamic derivatives) of a model corresponds to measuring the balance forces and moments, observing the model motion, and inverting the equations of motion to obtain both static and dynamic derivatives of the model. The motion of the model cannot be restricted to simple one or two-degree-of-freedom oscillations. Consequently, it was considered important to study the character of the problem of extracting aerodynamic derivatives from six-degree-of-freedom motion data. The analysis proceeded by calculating the motion of a 15° cone, the anticipated first model, in a reasonably realistic approximation of the model in the tunnel and using the full sixdegree-of-freedom equations of motion. The z force (in body frame) and pitching moment derivatives (and, of course, the corresponding lateral derivatives which follow from symmetry of the body)' which have nonzero values are the following: CKw = dCK/d(W/VT), CKq = dCK/d(Q d/VT) K = z,m