Prediction of Top of Descent Location for Idle-thrust Descents

Abstract

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent tra- jectories. Development and assessment of the trajectory predictor and the concept of operations requires models of the prediction error due to various error sources. Polynomial approximations of the along-track distance of the top of descent (TOD) from the meter fix are given in terms of the inputs to the equations of mo- tion. Polynomials with three different levels of complexity are pre- sented, with the simplest being linear. These approximations were obtained by analyzing output from one predictor. While this pre- dictor's thrust and drag models do not seem to agree well with those used by the FMS, both laboratory and operational data us- ing commercial FMSs support the conclusion that, for given mod- els of thrust and drag, the TOD location is roughly a linear combi- nation of cruise altitude, descent CAS, aircraft weight, wind, and altitude and speed at the meter fix. The laboratory data include 14 descents each in a Boeing 737-700 simulator and a Boeing 777- 200 simulator, using a test matrix that varied aircraft weight and descent speed. The operational data include approximately 70 de- scents each in commercial Boeing 757 and Airbus 319/320 aircraft. enabling continuous descents is being pursued by several re- search groups. Most of the previous research has focused on prediction of arrival time at a waypoint. While this helps with lateral separation, accurate prediction of the vertical profile is also essential to ensure vertical separation from aircraft at dif- ferent altitudes, including crossing traffic. In fact, error in pre- diction of the vertical profile is likely to have more impact than along-track prediction error on procedures and data exchange necessary to enable more fuel-efficient descents in congested airspace. Only the TOD location is analyzed in this paper, which is the first step in understanding the entire vertical pro- file. Once prediction of TOD location is sufficiently accurate, analysis will be expanded to the rest of the vertical profile. The purpose of this paper is to identify the factors that af- fect the TOD location and how they affect it. This is done by developing several approximations, with varying accuracy, of the distance between TOD and the meter fix. After presenting the background, related literature, and equations of motion in Sec. II and Sec. III, this paper presents results from three dif- ferent types of analysis. Sec. IV describes analysis of the equa- tions of motion to obtain polynomial approximations of TOD location. These approximations give insight into how factors affect TOD location. They must, however, be validated with FMS data. Use of a laboratory environment makes it possible to use a test matrix, which simplifies analyzing and visualizing the effects of individual factors. On the other hand, an impor- tant concern is the amount of randomness that will occur under operational conditions. This can only be determined by ana- lyzing operational data. Therefore, Sec. V presents analysis of data from both FMS test bench experiments and commercial operations.