Parameter Estimation Methods for Spins

The use of rotary balances of ever-increasing complexity for measuring aero­dynamic forces and moments in spins is avoided if aerodynamic forces and moments can be inferred directly from free-spinning model or airplane tests. Two promising approaches to this application of parameter estimation have been reported.

The first approach (Fremaux, 1995) extends the Gates-Bryant equilibrium or steady-state spin analysis to include the nonequilibrium angular acceleration terms p, q, and r and the spin acceleration term f2. Calculated aerodynamic moments by this method vary with time if the spin is oscillatory. The calculated moments oscillate about the Gates-Bryant values, which also can be measured independently on a rotary balance. This method requires the investigator to record rapid angular motions in a spin, feasible now with the advent of modern data-acquisition techniques.

A second parameter estimation approach for spins (Jaramillo and Nagati, 1995) appears to have been inspired by the finite-element methods used in structural analysis. A set of control points are established. Aerodynamic force coefficients at these points are correlated with local angles of attack and sideslip during spinning motions. These aerodynamic force (and moment) coefficientsare in effect influence coefficients. The influence coefficientsare found by minimizing cost functions based on the errors between measured vehicle accelerations and those calculated using forces and moments derived from the influence coefficients. Once the dimensionless influence coefficients are found, the method appears to have predictive capabilities. An improved version (Lee and Nagati, 1999) of the original method reduces the number of unknown parameters to be solved for by using static wind-tunnel test data.