The identification of coupled flapping/inflow models for hovering flight

The validation of coupled flapping/inflow rotor models has received much recent attention. The present paper concentrates on the analysis of flight conditions close to hover in order to resolve some of the difficulties encountered in earlier studies. New light is shed on the fundamental problems of identifiability by designing optimal experiments for the parameters of a variety of coupled flapping/inflow models. The models include the Pitt and Peters formulation of the induced flow equations and both first and second order flapping is considered. From the design of optimal experiments it is possible to determine theoretically the minimum possible variance of parameter estimates for a given set of experimental conditions. It is thus possible to determine if the available instrumentation can provide estimates of a specific quality. Using this approach careful attention is given both to the question of whether flapping measurements alone are sufficient for the reliable identification of coupled flapping/inflow models and to the suitability of test inputs currently employed. It is concluded for the models considered, in the absence of direct measurements of inflow, and despite the relatively short time constants of the models, it is important to retain low frequency information in the system identification process. Finally, it is shown that within the limitations of the flight data available, a simple flapping model with no induced flow dynamics cannot be bettered and gives a good fit to measured data for all frequencies up to that of the rotor