Optimum 4D guidance for long flights

For long flights of commercial aircraft, the minimum cost flight profile produced by a flight management system (FMS) is significantly affected by the cost index used. In a 4D guidance system the FMS seeks to adjust the cost index to achieve a required time of arrival, but the flight time versus cost index relation for long flight contains discontinuities due to changes in the optimum step climb points. This is especially significant if winds are included in the optimization function. Such discontinuities prevent convergence to some RTA values unless special provisions are made to remove them. An example of a flight case shows a 17-min interval to which no cost index corresponds. The author identifies two types of discontinuities and presents methods for removing them. Removal of discontinuities is absolutely necessary to achieve optimum 4D guidance