Analytical prediction of height-velocity diagram of a helicopter using optimal control theory

The autorotative landing of a single-engine helicopter following power failure is analyzed using optimal control theory. The optimization problems are formulated to minimize the unsafe region in the height-velocity diagram under the condition that the touchdown speed is within the capability of the landing gear. Nonlinear equations of motion are described using a rigid-body dynamic model with longitudinal three degrees of freedom. The aerodynamic model of the rotor takes account of the effects of blade stall during descent and increased induced flow in the vortex ring state. The present method gives a good estimation of the height-velocity boundary in comparison with the existing flight test data. It is pointed out that the test pilot started the collective flare earlier than that occurred in the optimal solution.