This thesis studies optimal category-A helicopter flight operations in the event of one engine failure. Both Continued Takeoff (CTO) and Rejected Takeoff (RTO) operations are studied.; A two-dimensional point mass model has been used to study CTO and RTO from an elevated heliport. In this model, the main rotor and tail rotor dynamics are modeled to better predict the power required during flight. A first order dynamic of the One Engine Inoperative (OEI) contingency power is considered.; Flights after engine failure are formulated as nonlinear optimal control problems. For studying optimal strategies, the performance index is selected in a way that reflects the main parameters to be optimized. Problems are formulated to minimize heliport size, subject to helicopter equations. In addition to the equations of motion, state and control constraints, FAA regulations are enforced. FAA regulations are enforced during CTO, while safety considerations are enforced during RTO.; These optimal control problems are solved numerically using a direct approach. States, controls, and helicopter constant parameters are parameterized, and a collocation method is employed. The cost function and path constraints are enforced as algebraic equations at the nodes, while the differential constraints are enforced by integrating the equations of motion in between nodes using Simpson's one third rule. The problem is then fed to a nonlinear programming routine to solve for all parameters.; Extensive optimization of CTO and RTO problems are conducted, and results are computed, plotted, and interpreted physically. A balanced weight concept is concluded. The balanced weight concept is similar to the balanced field-length concept in field takeoff.
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