Optimization of Unpowered Descents of Commercial Aircraft in Altitude-Dependent Winds

Abstract

Unpowered descents of commercial transport aircraft are optimized in tbe presence of altitude-dependent winds witb tbe objective of maximizing range. Tbe optimal problem and an optimized constant calibrated-airspeed procedure are analyzed. Tbe optimal problem is studied using tbe tbeory of singular optimal control. Tbe optimal control is of tbe bang-singular-bang type, and tbe optimal trajectories are formed by a singular arc and two minimum/maximum-patb-angle arcs joining tbe singular arc witb tbe given initial and final points. Tbe constant calibrated-airspeed procedure is optimized using parametric optimization tbeory. Results are presented for a model of a Boeing 767-300ER and for linear wind profiles. Tbe effects of botb tbe average wind and tbe wind sbear on tbe optimal results, as well as tbe effects of the aircraft weigbt, are analyzed. Tbe wind sbear is sbown to have a clear effect on tbe maximum range. Tbe comparison between tbe two sets of results sbows tbat tbe optimized constant calibratedairspeed descent is very close to optimal. From the operational point of view, the optimum descent calibrated airspeed is defined in terms of tbe wind profile and tbe aircraft weigbt. a CASJ Co Ci. D 8 H h, h L M m P S Sw t,tf V W w, w X max Aw 0 k p Nomenclature = speed of sound = optimum descent calibrated airspeed = drag coefficient = lift coefficient = drag = gravity acceleration = Hamiltonian = altitude, average altitude = lift = Mach number = aircraft mass = pressure = switching function = reference wing surface = time, flight time = aerodynamic speed = aircraft weight = wind speed, average wind speed = horizontal distance = maximum range = aerodynamic path angle, ground path angle = wind-shear parameter = temperature = adjoint variable = density

Contingency path planning for hybrid-electric UAS

“…Though it is beyond the scope of this study, one might consider using a more sophisticated glide performance model, such as described in [16] which also includes the effects of turn performance on the achievable range, and consider [17] and [18] which describe an optimization method for the in-flight performance in variable (and altitude dependent) winds.…”

Vertical Trajectory Optimization to Minimize Environmental Impact in the Presence of Wind

“…To check if these parts are satisfied the necessary conditions, the sign of H γ should be known. In this paper, H γ is checked by the similar way in [14]. From the necessary condition, the adjoint variables λ V and λ h are continuous at the junction point.…”

“…Wu and Zhao [13] assumed descent trajectory with several segments and converted optimal control problem to parameter optimization problems with fuel and emission costs. Few papers used CDA trajectory structure assuming idle thrust descent [14,5,15]. Franco et al [14] solved maximum descent range problem by singular arc analysis in the presence of the along track wind.…”

“…Few papers used CDA trajectory structure assuming idle thrust descent [14,5,15]. Franco et al [14] solved maximum descent range problem by singular arc analysis in the presence of the along track wind. However, they did not consider the cross wind and the flight envelope which is modeled as a pure state inequality constraint.…”

An Analysis of Altitude Wind and Humidity based on Long-term Radiosonde Data

“…According to a study, the effect of wind (combined with temperature) on fuel consumption can be as high as +1.4% and +2.3% for the westbound (east to west) and +1% for the southbound flights, for a B747-400 [7]. While, many studies have been dedicated to mapping a ground wind profile for wind energy purposes [8][9][10], there have also been a number of studies focusing on wind effect estimations for various situations, such as the descent phase [11][12][13] or for flight range [14]. These studies help to minimize uncertainties encountered particularly during trajectory prediction investigations.…”