The Role of Rotary Derivatives in Spins
The rotary derivatives are the force and moment coefficient derivatives with respect to dimensionless angular velocity The rotary derivatives appear in the airplane equations of motion for normal unstalled flight, as well as for spinning flight. However, at the relatively low airspeeds and high angular velocities for spinning flight, the rotary derivatives are much more important than they are for unstalled flight. Physically, under spinning conditions there will be large differences in local flow angles of attack at different parts of the airplane, and possibly local separated flows.
Stated otherwise, the rotary derivatives are generally of secondary importance to flight simulation and flight control design for normal unstalled flight. If the airplane has stability augmentation systems that drive the control surfaces to provide artificial damping, this is even more true; artificial damping swamps out the rotary derivatives that supply natural aerodynamic damping. Thus it is that, at least in modern times, the drive to refine analytic and measurement techniques for the rotary derivatives has come from spinning studies.
The early 1950s saw a rush of 5- and 6-degree-of-freedom inertial coupling computer simulations, as told in Chapter 8, “The Discovery of Inertial Coupling.” It is interesting that some of the same investigators, such as Cecil V Carter, John H. Wykes, and Leo Celniker, who helped crack inertial coupling with their simulations moved on to spin simulation using analog or digital computers. The motivation was there, because the same airplane loading characteristics that lead to inertial coupling also lead to post-stall gyrations and departures, motions not easily studied in free-spinning wind tunnels.
The problem was that this period coincided with a shutdown of rotary balance testing at NACA. The NACA rotary balance was updated in the late 1950s, but it was not used for analytical studies until several years had passed. Thus, the spin computer analysis results reported at the 1957 Wright Air Development Center Airplane Spin Symposium (Westbrook and Doetsch, 1957), made without the benefit of current rotary balance data, came under criticism for using inadequate rotary derivatives by knowledgeable people such as Dr. Irving C. Statler and Ronald F. Sohn.