Predictability of top of descent location for operational idle-thrust descent

To enable arriving aircraft to fly optimized descents computed by the flight management system (FMS) in congested airspace, ground automation must accurately predict descent trajectories. To support development of the trajectory predictor and its uncertainty mod-els, commercial flights executed idle-thrust descents at a specified descent speed, and the recorded data included the specified descent speed profile, aircraft weight, and the winds entered into the FMS as well as the radar data. The FMS computed the intended descent path assuming idle thrust after top of descent (TOD), and the controllers and pilots then endeavored to allow the FMS to fly the descent to the meter fix with minimal human intervention. The horizontal flight path, cruise and meter fix altitudes, and actual TOD location were extracted from the radar data. Using approximately 70 descents each in Boeing 757 and Airbus 319/320 aircraft, multiple regression estimated TOD location as a linear function of the available predictive factors. The cruise and meter fix altitudes, descent speed, and wind clearly improve goodness of fit. The aircraft weight improves fit for the Airbus descents but not for the B757. Except for a few statistical outliers, the residuals have absolute value less than 5 nmi. Thus, these predictive factors adequately explain the TOD location, which indicates the data do not include excessive noise. Nomenclature b Least squares estimate of β IW,FMS Integral with respect to time of the along-track component of the wind forecast entered into the FMS descent winds page N Number of observations p Number of terms in regression model, including the constant r Least squares residual S0 Path distance of TOD location if winds were zero STOD Path distance relative to the meter fix of TOD location Vh Vertical speed Wv Along-track component of wind, positive for a tailwind x = (x0, x1,..., xp−1)T Predictive factors in regression model Z Observed values of STO