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frame) is given in Figure 5.
20 18 16 14 1 2 10 8 6 4 2 0
DISTANCE TO TOUCHDOWN [NM]
0
1
2
3
4
5
MAGNITUDE OF VORTICITY [-]
0
2
4
6
8
10
SIGNAL-NOISE RATIO[- ]
MAGNITUDE
SIGNAL-NOISE RATIO
Figure 5 Vorticity vs distance to touchdown during wake vortex encounter
The signal-noise ratio peaks to well above 8.0 at 16 NM, where the vorticity magnitude itself peaks to just above
1.0. The signal-noise ratio turned out to be a good indicator to tell whether or not aWVE event occurred.
3 Calculation of eddy dissipation rate for turbulence study
A couple of methods are available in the literature for the computation of the eddy dissipation rate EDR, as
discussed in a review in Ref. 4. They include the “ vertical accel eration”-based method and the “wind”-based
method. Between these two methods, the wind-based method is preferred (Ref. 4) since it is less sensitive to aircraftspeci
fic parameters. Its accuracy depends on the accuracy with which the vertical wind component can be derived.
Moreover, it is a time-domain method, requiring assumptions as to the low and high cut-off frequencies ω1 and ω2 as
well as the size of the time window under consideration. To allow flexibility in processing the QAR data, these
frequencies and the size of the moving time window are kept as input variabl es to be selected by the program user.
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A set of recommended values of these paramet ers has been determined based on selected turbulence events at
HKIA.
The wind-based EDR calculation method is implemented as follows. asAs derived from the first principle o f
turbulence, the cal culation of EDR requires the solution of the power spectrum of the vertical wind component over
a selected time window with a certain vertical mean velocity. A more practical method is to employ a running-mean
standard deviation (sigma) calculation of the bandwidth-filtered vertical wind (Ref. 5):
2/3)
2
2/3
( 1 1.05 2/3
1/3
Va
w
(15)
The vertical wind component Vwz is to be filtered with a digital band-pass filter with cut-off frequencies f1 and f2
(with ω=2πf). Airspeed Va is passed through a low-pass filter in order to represent the average flying speed for the
running time interval, and w
is computed as the running standard deviation (on the sliding time-window) of the
band-pass-filtered vertical wind variations.
A sensitivity study of EDR computation with respect to the input parameter values has been conducted (Ref. 5).
It was found that, based on inspection of vertical wind spect ra over the selected cases, there seems to be no need to
employ a low-pass filter to the vertical wind signal. Only high-pass filtering would be required. The influence of the
high-pass frequency on the evaluated EDR values appeared to be rather small. It is suggested to use f1 = 0.1-0.2 Hz
and f2 = 2 Hz (the effective maximum detectable frequency in a 4 Hz sampled signal) in Eq.(15.The moving time
window size of 10-20 seconds also appears to be a proper value.
Other parameters that could be important for meteorological purposes are the static (or potential) air temperature,
the temperature lapse rate, air density and the Richardson number, to name a few. If more speci fic parameters are
required by the user then accommodations can be made to the software to output these quantities as well.
4 Application examples
The first case is a signi ficant windshear event that has been analyzed in Ref. 6. An aircraft (B747-400) landed at
HKIA from the west on 29 March 2005 and the pilot reported encountering windshear of +40 knots headwind gain
during landing. From the wind speed computed from the QAR data, there is a wind change (increase) of ~12 m/s (24
knots) at about 2 nautical miles (NM) from touchdown (Figure 6).
Figure 6 Wind variation along the approach
This wind change is smaller than the magnitude of windshear reported by the pilot. In order to reveal what has
happened, the airspeed and ground speed of the aircraft are plotted together in Figure 7.
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Figure 7 Airspeed and ground speed versus distance to touchdown for theB747 flight
At 3 NM from touchdown, both the airspeed and the ground speed are almost the same. From 3 NM, the airspeed
increas es by about 20 m/s (40 knots). However, the ground speed increases also, but by about 10 m/s (20 knots)
only. The raw data file indicated that at this point the aircraft was under control of autopilot C in COMMAND
mode, but the Auto-throttles (AT) apparently had not been engaged (they were OFF for the entire duration of this
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Quick Access Recorder (QAR) Data Analysis Software(7)
