Consider the general aviation aircraft carrying out a sequence of longitudinal coordinated flight maneuvers defined by a sequence of waypoints described below. The specified waypoints are defined with respect to a ground-fixed frame: the x and y axes are in a horizontal plane located at an altitude of 1,000 ft with the x-axis pointing due east and the y-axis pointing due north; the z-axis defines the altitude above this horizontal plane.
Waypoint Name Coordinates (x, y, z) in ft 1 climb (0, 0, 0) 2 cruise (120000, 0, 12000) 3 descend (2280000, 0, 12000) 4 (2400000, 0, 0) The general aviation aircraft should be in steady climbing flight between waypoints 1 and 2; it should be in steady level flight between waypoints 2 and 3, and it should be in steady descending flight between waypoints 3 and 4. Assume the aircraft takes off with a full fuel tank at waypoint 1; ignore the mass of fuel burned during the climbing flight segment and during the descending flight segment but not during the cruising flight segment.
(a) Develop a flight plan that specifies the airspeed and the flight path angle for each of the three steady flight segments that satisfy the waypoint specifications. Select a flight plan that is fuel efficient.
(b) For the climbing flight segment and the descending flight segment constructed in part (a), determine the elevator deflection and the throttle setting that guarantee the desired steady flight conditions along that flight segment; these expressions should be in terms of the air density. For the cruising flight segment determine the the elevator deflection and the throttle as functions of the aircraft weight. Check that all flight constraints are satisfied for all steady flight segments.
(c) What amount of fuel is required to complete the flight? What is the elapsed flight time from waypoint 1 to waypoint 4.
(d) On the basis of your flight plan in part (a), give plot(s) that describe the 3D path of the general aviation aircraft.