En-route aircraft wake vortex encounter analysis in a high density air traffic region Ulrich Schumann 1) and Robert Sharman 2) 1) Institut für Physik der Atmosphäre, DLR, Oberpfaffenhofen 2) Research Applications Laboratory, National Center for Atmospheric Research, Boulder, Colorado
Wake vortex encounters are potential hazards not only near airports but also at cruise altitudes Wake vortex encounters have been observed at upper levels Rossow and James (2000) & Nelson (2006) point out: the frequency of en-route encounters may increase for growing air traffic density, reduced vertical separation minimum, increased disparity of the size of aircraft flying at cruise altitudes Hoogstraten et al. (2013) find severe wake vortex encounters could be expected approximately once every 38 days over Europe Holzäpfel (2014) identifies wind, stratification, turbulence, position, mass, span load factor as critical parameters. Open: how often, for which aircraft sizes, during which flight phases, how dependent on traffic density? 2
Here: Wake Vortex Program (WAVOP) with traffic data (ASDI form FAA) and Weather data (WRF-RAP of NOAA) WAVOP: new efficient method to test for possible encounters for all aircraft pairs in high traffic regions. Encounter definition: when the encounter aircraft E comes close to the wake vortex V from a generator aircraft G and when E experiences lift forces L or roll moments RM exceeding given critical limits. Wake vortex model: assumes age-dependent vortex circulation Γ(t), constant descent speed w 0, maximum descent distance z max. Γ(t)/Γ 0, z max, age 1, age 2 from two-phase model of Holzäpfel (2003). Traffic data: waypoints (x, y, z, t) and aircraft type for all movements over the US (12 GByte for 46 days) Aircraft data: span s, mass M, speed U, FL-> wake b 0, Γ 0, t 0, w 0 Meteorology NWP data: Wind, Brunt Vaisaila frequency N, dissipation rate (ε or EDR=ε 1/3 ) from WRF-RAP of NOAA 3
Determination of encounter between E (encounter ac) and vortex line (V) behind G (generator ac) For given flight paths, wake descent, and ambient wind fields, the positions are linear functions of time t and vortex age a The distance D between E and any point on V is a function of t and a t and a at encounter are determined by D 2 (a,t) = min This implies a linear system of equations, solved by WAVOP exactly and efficiently 4
Wake Vortex decay: Two-Phase model (Holzäpfel (2003) Γ(t)/Γ 0, z max, age 1, age 2 from two-phase model of Holzäpfel (2003) and z max parameterization (Schumann, 2012). for given Brunt Vaisaila frequency N BV, dissipation rate (EDR=ε 1/3 ), and wake scales b 0, w 0, t 0, Γ 0 age 1 age 2 z max N*=N BV t 0 ε * =(ε b 0 ) 1/3 /w 0 5
The model approximates observed wake conditions as identified from in-situ trace gas measurements A380 A319 From DLR-Falcon Cockpit-Camera (see Schumann et al., GRL; 2013 ->discussion)
Loads Roll moment coefficient RM C and lift moment coefficient L C are computed for given relative position of E and V behind G, Hallock-Burnham vortex flow model, core radius for G span, R C =0.03 s G versus time t 7
Encounter Assessment for encounter assessment we use the maximum values occurring during encounter of the magnitude values of RM C and L C for given encounter angles and distances in vertical and horizontal directions. An encounter is assumed to be critical when RM C > 0.03 or L C > 0.1 8
For test and validation, we compare WAVOP results with 1) turbulence peaks derived from automated in-situ EDR measurements. and 2) wake vortex encounters reported by pilots for 1): Automated in-situ turbulence energy dissipation rate (EDR) measurements are obtained from vertical wind measured on Delta Air Lines (DAL) commercial B737 aircraft. The data are recorded routinely every 60 s for a large set of flights (Sharman et al., 2012, 2014). DAL EDR counts over North America in the year 2012 9
An EDR peak was reported from in-situ data of a DAL flight E, e.g. 19 Nov 2010 WAVOP finds time t and vortex age a of minimum approach between encounter E and wake vortex V at a time which coincides with the time of observed EDR peak up to 70 s 10
The exact position and encounter time is sensitive to the variations in position data, aircraft mass, and wind speed But the fact that an encounter occurs is robust, at least for this case with nearly parallel flights of two descending aircraft 11
Coincidences between in-situ observed EDR peaks and WAVOP-analyzed encounters - found for 17 cases 12
The observed positions agree with computed wake descent properties, both for the 17 EDR cases and for 3 PIREPs mean descent speed: 1.5 m/s, both from the model and the observations, with some deviations in single cases GLF4 GCN UUA /OV PGS079045/TM 1902/FL300/TP GLF4/TB SEV/RM DESCENDING TO FL240. (CONTROLLER SUSPECTS WAKE TURBULENCE). AWC-WEB:KZLA D83 SPS UUA /OV SPS/TM 1350/FL310/TP MD83/TB MOD-SEV FL310-FL290/RM ACFT HAD UNCOMMANDED ROLL OF 45 DEGREES. 15 MILES IN TRAIL OF B757 POSSIBLE WAKE TURB AWC-WEB:KZFW B757 LNS UUA /OV LRP180020/TM 1849/FL380/TP B757/TB MOD-SEV SEV/RM POSSIBLE WAKE TURBULENCE 13
Traffic from Aircraft Situation Display to Industry (ASDI) and examples of encounters during one hour (full) or one day (open symbols) 14
Number of encounters identified in upper air space during 46 days Flights all constant level (10 hft vertical separation) encounters per day with D/s G <1 280 1 critical encounters per day 26 0.07 age a/s and standard deviation 104±26 131±27 separation/km 21.2±7.5 30.0±9.0 angle α 20.3 ±32 90 ±55 upper air space in the US: above FL 180 analysis restricted to cases with horizontal separation > 5 nautical miles 15
Number of encounters identified in upper air space during 46 days Flights all constant level (10 hft vertical separation) encounters per day with D/s G <1 280 1 critical encounters per day 26 0.07 age a/s and standard deviation 104±26 131±27 separation/km 21.2±7.5 30.0±9.0 angle α 20.3 ±32 90 ±55 Sensitivity studies show: 4 times more encounters for zero ambient wind 20 % fewer encounters for doubled vortex wake core radius R C 13 times less encounters for doubled threshold values 16
Number of encounters identified in upper air space during 46 days Flights all constant level (10 hft vertical separation) encounters per day with D/s G <1 280 1 critical encounters per day 26 0.07 age a/s and standard deviation 104±26 131±27 separation/km 21.2±7.5 30.0±9.0 angle α 20.3 ±32 90 ±55 critical wake vortex encounters may occur up to 26 per day over USA mainly between medium sized ac 17
Encounters with distance D<120 m occur typically at 20 km (> 12 nautical miles) horizontal separation between G and E at small relative angle α between flight path E and wake vortex V, at cruise and during ascent/ descent at all flight levels (FL), many with very small wake distance D many with small, but a few with large lift and/or roll moment (magnitude) coefficients The number of critical encounters decreases exponentially with the threshold loads 18
Frequency histograms for all encounters identified with distance D<120 m mostly at small vertical separation in wakes from medium and heavy aircraft for N and EDR values typical for tropospheric weather A separate study has been performed for 1000 feet vertical separation See: Schumann and Sharman, paper submitted to J. Aircraft (2014) 19
The encounter frequency increases with the square of traffic density 20
Conclusions WAVOP, a new method to identify potential wake vortex encounters from given airtraffic and meteorological data, has been applied to radar-observed traffic over North America on 46 days in 2010/11, and validated against PIREPs and automated in-situ turbulence reports. Most upper-level encounters are found for medium-sized aircraft on nearly parallel flight routes during descent. The daily frequency of wake vortex encounters increases with the square of air traffic density. Limitations: mainly from uncertainties in data for traffic, weather, aircraft mass. Further studies should address: traffic at low levels, traffic over Europe, traffic with a larger fraction of heavy aircraft, random traffic, mitigation strategies, etc. The algorithm may be applicable to onboard wake-vortex-encounter detection and avoidance systems 21
Thanks to colleagues at NCAR and DLR 22
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Wake vortex depth versus plume age t in wake scales for 4 aircraft with different mass M, speed V, and span s small/large circles: c/c wake >0.1 c/c wake >0.5 c = measured NOy mass mixing ratio c wake= m F EI NOx /(ρ A p ) z = z FL z Falcon z = min(w 0 t, z max ), with w 0 = 8 g M /(π 3 s 2 ρ V) z max = (π/4)s [7.68(1-4.07 ε * +5.67ε *2 )(0.79-N * )+1.88] with N * = N BV t 0, ε * = (ε b 0 ) 1/3 /w 0 t max = w 0 / z max, Schumann, Jeßberger, Voigt (GRL, 2013) 24
Contrail ice particle formation in the wakes of airliners Ice particles are formed from at least 10 15 /kg soot particles per burnt fuel mass, ice particle sublimate in sinking and adiabatically heating wake vortex Schumann, Jeßberger, Voigt (GRL, 2013) 25