Analytical Determination of a Helicopter Height-Velocity Curve

A helicopter height velocity (HV) diagram was analytically constructed using optimal control techniques. A three degree of freedom, point-mass, dynamic model was developed and validated with flight test data. An induced velocity calculation was incorporated which addressed the affects of vortex ring state. The problem was posed as an open final time, constrained initial state, constrained final state problem, with the objective function as a weighted sum of the initial altitude and quadratic controls. This formulation was solved using direct pseudo-spectral collocation and adaptive mesh refinement as implemented by the GPOPS-II® software suite. Proper adjustment of path constraints was crucial in achieving solutions which were comparable with flight test data. Results compare favorably with flight test data and previous analytical HV diagrams.