Fuel-efficient optimized profile descents with time control

4-D (3-dimensional position plus time) trajectory is an essential building block for both FAA's Next Generation Air Transportation Modernization (NextGen) program and the European Single European Sky ATM Research (SESAR) program. Under this 4-D trajectory concept, Flight Management Systems (FMSs) not only need to predict the 4-D trajectory of the aircraft but also to coordinate with the flight control system to track the planned 4-D trajectory within required positioning and timing thresholds. This 4-D trajectory architecture requires the FMS to ensure the aircraft arrive at a metering waypoint within 6 seconds or 30 seconds of its Required Time of Arrival (RTA), for waypoints on descent or in cruise, respectively. Most FMSs currently in production can comply with the RTA accuracy of 30 seconds at the 95% probability. However, most FMSs encounter significant difficulty in complying with the RTA accuracy of 6 seconds at the 95% probability for metering waypoints on descent due to technical challenges, such as much tighter timing threshold requirements, the true airspeed is continuously changing during descent, wind velocity varies over altitude, and standard descent speed profiles should be used. This paper presents a time control design that enables the FMS to not only comply with the RTA accuracy of 6 seconds but also execute a fuel-efficient 4-D trajectory. The proposed time control design is also cost-effective since it does not require any changes in existing auto pilot/auto-throttle systems. The Optimized Profile Descent (OPD) procedures are used in this paper to illustrate the performance of the proposed time control design. However, the applications of the proposed time control design are not limited to the Optimized Profile Descent flight procedure.