Singular trajectories in airplane cruise-dash optimization

Optimal cruise-dash trajectories are obtained for the case of time-fuel optimization using a linear combination of time and fuel as the performance index. For the case of the steady-state arc being flown at full throttle, the skeletal transient trajectories are also flown at full throttle and the transients approach the cruise-dash points monotonically in an asymptotic fashion. When the steady-state arc is flown at an intermediate throttle, the transient trajectories follow a singular control law and exhibit a complex structure that differs from that of the full-throttle transients. With respect to optimality of the steady-state arc, it is found that although steady-state cruise fails a Jacobi-type condition, steady-state cruise-dash can satisfy this condition if the emphasis on time is sufficiently large.