Investigation of a non-uniform helicopter rotor downwash model

Abstract: This master thesis was carried out at the Department of Aerodynamics and Flight Mechanics at Saab Aerosystems, Linköping, Sweden. It makes up the author’s final work prior to graduation in the field Applied Physics and Electrical Engineering at the Department of Electrical Engineering at The Linköping Institute of Technology (LiTH), Linköping, Sweden.   The objective of the paper was to study a non-uniform helicopter rotor downwash model in forward flight for the unmanned helicopter Skeldar, which is under development at Saab. The main task was to compare the mentioned model with today’s uniform downwash model in order to find differences and similarities. This was done both from a modeling and a controlling perspective. To start with, an introduction is given which is followed by a helicopter theory chapter. The following three chapters deal with the theory of induced velocity, the helicopter model and the Linear Quadratic Regulator (LQR). Finally, the results are presented and discussed.   The downwash models were derived using Momentum Theory (MT) and Blade Element Theory (BET). These two theories were combined in order to find a connection between the induced velocity and the rotor thrust coefficient. The non-uniform downwash model that was studied is proposed by Pitt & Peters and describes a linear variation of the induced velocity in the longitudinal plane.   For the control, a LQ-regulator was chosen since it is easily implemented in MATLAB and it stabilizes the plant model by feedback and consequently creates a robust system. Before the controller could be implemented, the models had to be reduced and the states had to be divided into longitudinal and lateral ones.   The comparison between the open systems clearly shows that differences in the inflow models propagate to all states and consequently the helicopter behaves differently in all planes. Great discrepancies are apparent for the angular velocities p and q. For Pitt & Peters’ model those states are believed to be strongly affected by the system’s positive real pole, causing a rather unstable behavior. When the systems were closed by feedback, the differences were reduced dramatically. Pitt & Peters’ model resulted in greater overshoots than the uniform model, but the overall behavior of all states was rather similar for the two models.   It is concluded, that the adaption of Pitt & Peters’ inflow model does not make any substantial difference when a controller is implemented. The differences between the open systems, however, are reason enough to question Pitt & Peters’ model. In order to evaluate the non-uniform model properly, it has to be compared to suitable flight data which is still lacking up to this date.