The state feedback velocity that minimizes the Direct Operating Cost (DOC) of a cruising aircraft is the solution to a Partial Differential Equation (PDE) called the Hamilton-Jacobi-Bellman (HJB) equation. Though Turbojet and Turboprop aircraft possess different dynamics, a comparison of their resulting HJB equations illustrates the relationship between their optimal cruising speeds. The main contribution of this work is to propose a state-feedback velocity that minimizes the DOC of a cruising Turbojet, a sub-optimal approximation of the optimal cruising speed of a Turboprop, and a transformation of parameters that maps solutions of the turboprop HJB that do not depend explicitly on position to solutions of the Turbojet HJB. Numerical examples for the airbus A320 and Beechcraft 99 will be presented to illustrate the methodology.
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