For computer simulations of unsteady spins, incipient spins, and the quasi-spin conditions called post-stall gyrations and departures, data from coning rotary balance tests are helpful but are not sufficient. Thus far, three approaches have been identified to create aerodynamic data bases for calculating unsteady spinning motions, as follows:
1. rotary balance oscillatory coning tests, in which the axis of rotation is misaligned with the tunnel flow, creating a periodic variation in angles of attack and sideslip;
2. combined rotary balance coning or oscillatory coning data and data from forced oscillation tests;
3. orbital or two-axis rotary balance tests.
As an example of the first category, the rotary balance rig at the French ONERA-IMFL 4-meter vertical spin tunnel can be arranged to produce oscillatory coning tests. A remotely controlled mechanism can misalign the spin axis to the tunnel wind direction as much as 20 degrees. This of course makes angle of attack and sideslip periodic instead of constant.
Balance reading time histories under oscillatory coning show results consistent with one’s expectations of flow hysteresis. Normal force coefficient variations with angle of attack above the stall of a delta wing form a typical hysteresis loop (Tristrant and Renier, 1985). This means the force coefficient at a given angle of attack is different during angle of attack increases than during decreases. The hysteresis loop shrinks to a normal lift curve for oscillatory coning below the stall angle of attack.
In the second category, the combination of rotary balance coning data with data from forced oscillation tests, a number of investigators have been busy in this challenging work. The well-known theoreticians Murray Tobak and L. B. Schiff at the NASA Ames Research Center propose a set of aerodynamic coordinates that are consistent with data from rotary balances (Tobak and Schiff, 1976). The normal angle of attack of body axes a is replaced by a “total” angle of attack a of the longitudinal axis to the velocity vector. A sideslip angle is defined by the airplane’s roll angle with respect to the plane in which a is measured. Force and moment coefficients are expanded into series in which each term is identified with a characteristic rotary balance coning motion or ordinary forced oscillation.
Similar schemes have been devised by Juri Kalviste (1978) at Northrop Aircraft and by Martin E. Byers (1995) in Canada. Kalviste projects the airplane’s total angular velocity vector onto the coning axis, about which rotary balance data are taken, and the three body axes, for which oscillatory data or estimations are available. A special algorithm is used to reduce the number of components from four to three. The algorithm selects components that are close angularly to the total angular velocity vector. This is intended to avoid using aerodynamic data formed by the differences of large numbers.
The third category of data base formation for computer simulation of unsteady spins, the use of orbital or two-axis rotary balances, is at the time of writing only a concept. In orbital rotary balance testing, coning motions would be superimposed on circular pitching and yawing at a different rate. This would yield small-amplitude angle of attack and sideslip perturbations about large fixed mean values of angle of attack and sideslip in a rotary flow. Practical difficulties appear to be formidable. Two-axis rotary rigs would have to be small enough for wind-tunnel installations and yet have good rigidity.