Evaluation of Fast-Time Wake Vortex Models using Wake Encounter Flight Test Data

Abstract

This paper describes a methodology for the integration and evaluation of fast-time wake models with flight data. The National Aeronautics and Space Administration conducted detailed flight tests in 1995 and 1997 under the Aircraft Vortex Spacing System Program to characterize wake vortex decay and wake encounter dynamics. In this study, data collected during Flight 705 were used to evaluate NASA's fast-time wake transport and decay models. Deterministic and Monte-Carlo simulations were conducted to define wake hazard bounds behind the wake generator. The methodology described in this paper can be used for further validation of fast-time wake models using en-route flight data, and for determining wake turbulence constraints in the design of air traffic management concepts. Γ = vortex circulation (ft 2 /s) 0 Γ = initial vortex circulation (ft 2 /s) V 0 = initial vortex descent velocity (ft/s) b 0 = initial vortex pair separation (ft) y 0 = initial vortex pair lateral offset from a reference point (ft) z 0 = initial vortex pair vertical offset from a reference point (ft) N = dimensional Brunt-Väisälä frequency (s -1 ) N* = non-dimensional Brunt-Väisälä frequency = 1 0 0 − V Nb ε = dimensional eddy dissipation rate (ft 2 /s 3 ) ε * = non-dimensional eddy dissipation rate = ( ) 1 0 3 / 1 0 − V b ε θ = potential temperature/theta (K) 2 T = temperature (°F) T L = Sarpkaya time-to-link u = east-west velocity component (ft/s) v = north-south velocity component (ft/s) ρ = air density (sl/ft 3 ) ∆t e = vortex encounter time (s) ∆x = distance between generator and follower at time of encounter (nmi) g = acceleration due to gravity (ft/s 2 ) W G = weight of the generator (lb) b F = follower wing span (ft) b G = generator wing span (ft) F Y = y-coordinate of follower's center of gravity normalized by b G F Z = z-coordinate of follower's center of gravity normalized by b G s = half of vortex pair separation (b 0 ) normalized by b G c r = vortex core radius size normalized by b G I xx = roll moment of inertia (sl·ft 2 ) F λ = wing taper ratio of the follower V F = follower airspeed (ft/s) V G = generator airspeed (ft/s) q = free-stream dynamic pressure (lb/ft 2 ) v l C = vortex-induced rolling moment coefficient F L C α = three-dimensional lift curve slope of the follower c l C = pilot input roll control corresponding to maximum aileron deflection p l C = roll damping coefficient φ = bank angle (deg) ∞ φ = maximum bank angle of the aircraft without control input (deg) max φ = maximum vortex-induced bank angle (deg)

Simulation of Runway Operations with Application of Dynamic Wake Separations to Study Runway Limitations

“…This model is a semi-empirical wake behavior model developed by NASA that predicts wake decay as a function of atmospheric turbulence and stratification. Typical NASA evaluations of fast-time models using field data measured with light detection and ranging (LIDAR) demonstrated the TDAWP model to be more accurate than other wake behavior models (5). First, aircraft input parameters such as an identifier (ID), wingspan, MTOW, maximum allowable landing weight (MALW), and performance characteristics are loaded into the simulation.…”

“…The analysis applied a Monte Carlo simulation approach, in conjunction with the NASA AVOSS TDAWP 2.1 model, to derive combinations of wake behavior parameters to obtain wake behavior under different conditions. NASA evaluations of fast-time models using field data measured with light detection and ranging (LIDAR) demonstrated the TDAWP model to be more accurate than other wake behavior models (5).…”