Sub-optimal and optimal periodic solutions for hypersonic transport

It has been known that periodic cruise control can save fuels for many aircraft and engine models. Applying the periodic operation to hypersonic transports with a scramjet engine is particularly interesting since fuel saving is critical to achieve maximum range of the transports. In this paper, the authors construct an analytic model of hypersonic transport and engines by using data from available literature in the area of the space plane and by using some theory deduction. A sub-optimal solution for periodic cruise of the hypersonic transport model has been determined by assuming the shape of altitude as a sinusoidal function of range and by adopting a bang-bang type throttle control. The numerical results show this sub-optimal solution has a fuel saving of 3.5% over the steady-state cruise. More importantly, this sub-optimal solution gives a good estimate for initial values of the two-point boundary-value problem related to the optimal solution. The sub-optimal solution is modified to the family solutions of the optimal solution. The minimizing-boundary-condition method (MBCM) is then used to converge the optimal solution. The optimal solution shows fuel savings of 8% over the steady state cruise