Application of the calculus of variations in determining optimum flight profiles for commercial short haul aircraft

Abstract

The method of steepest descent of the calculus of variations is used to determine the optimal flight profile of a hypothetical tilt wing aircraft travelling a distance of 50 miles. Direct operating cost, (as derived from the ATA formulation) is minimized using aircraft lift coefficient and power as control variables each with upper and lower limits. Only the portion of the flight from the end of transition to the beginning of retransition was considered, with both initial and final values of velocity, flight path angle, and altitude specified. The results show that full power is used to accelerate and to climb at a speed about twice the value for maximum rate of climb. At 12000 feet, power is reduced to flight idle and a high speed, power off glide is made to destination. A rapid deceleration is made at low altitude to achieve the specified conditions for retransition. While the optimal profiles for velocity, altitude, and power are greatly different from the nominal profiles chosen to design the aircraft (Ref. 5), the optimal trip cost of $30.54 is only slightly less than the nominal trip cost of $31.60.