The low-speed height-velocity (HV) diagram of a helicopter is analytically predicted based on the idea of minimizing the unsafe region of the HV diagram under the condition of realistic autorotation landing. The autorotation landing of the helicopter is formulated as a nonlinear optimal control problem. The state equations are described by an augmented longitudinal three-dimensional rigid body flight dynamic model. The nonlinear optimal control problem is solved by using direct transcription and nonlinear programming. For UH60 helicopter, the analytical methodology is used to develop a reasonable estimation of the one engine inoperative (OEI) low-speed HV diagram with 1 s pilot delay. The OEI autorotation landing procedures from the high hover point, knee point and low hover point are presented. The results show that the autorotation landings can be made by using normal pilot procedures.