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/2
, , ( )
1
, , ( )
t Twndw
t Twndw
Vwx y z d
Twndw
Vwx y z t
The turbulent kinetic energy TKE is then computed from
2 2 2
2
1
TKE u v w (13)
The “window” time interval Twndw is specified by the program user. The calculation of EDR is a more complicated
process, which will be described in chapter 3.
2.6.2 Wake vortex encounter event
In fact the program WINDSTURB can do a lot more. The core of the program was programmed to be able to
detect from the QAR data whether or not the aircraft had flown through a wake vortex encounter. Such an event is
detected using the magnitude and signal-to-noise ratio of the computed vorticity (a vector quantity), which is the
rotation in the airflow surrounding the aircraft. In order to be able to compute this parameter, an extensive list of
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( )] 2 [ , , ( ) , ,
1
2 ( )
, ,
t Twndw
t Twndw
Vwx y z Vwx y z d
Twndw
u v w t
8
additional parameters had to be recorded, e.g. aileron and spoiler deflections, angular rates, etc. Details of the
algorithm are beyond the scope of this paper, and the reader is referred to Ref. 1. The vorticity vector can eventually
be expressed in earth axes as:
x
V
x
V
z
V
z
V
y
V
y
V
y x
x z
z y
w w
w w
w w
z
y
x
γ (14)
As a case in point, such an event was detected on one flight approaching HKIA. This flight was flown by an
A320 on July 24th, 2005. A plot of runway cross -track versus runway along-t rack distance (km) from touchdown is
given in Figure 2.
HDA 761; July 24t h, 2005
0 5 10 15 20 25 30 35
RWY ALONG-TRACK DISTANCE[KM]
70
60
50
40
30
20
10
0
-10
RWY CROSS-TRACK DISTANCE [KM]
WVE
Figure 2 Flight path where WVE occurred
It shows a segmented flight towards the airport, with interception of the computed final approach course of
251º true (253º magnetic) at about 25 km or 13 NMfrom the airport. The program corrected for the small track error
that was present by introducing a bias of about 1 degree. The location where the wake vortex encounter (WVE)
occurred is marked by the diamond symbol. The altitude at the moment of encounter was 1374 m (4507 ft).
The angle of attack profile during this flight is shown in Figure 3.
DISTANCE TO TOUCHDOWN [NM]
ANGLE OF ATTACK [DEG]
0
2
4
6
8
10
20 18 16 14 12 10 8 6 4 2 0
Figure 3 Angle of attack versus distance to touchdown
9
As the figure shows, there is a spike in angle of attack at about 16 NM from touchdown, with a total AOA (Angle Of
Attack) change of about 4º, which is due to the wake vortex encounter.
The fact that it was indeed a WVE is obvious when looking at the roll angle. The roll angle is shown in Figure 4.
DISTANCETO TOUCHDOWN [NM]
BANKANGLE[DEG]
-25
-20
-15
-10
-5
0
20 19 18 17 16 15 14 13 12
Figure 4 Roll vs distance to touchdown during wake vortex encounter
At the same distance of 16 NM from touchdown, there is what looks like a roll reversal of about 10º magnitude, first
in the sense of rolling back and then back to the bank angle in the turn it was supposed to have (i.e. -25º). The
“ correction” back to -25º is due to the autopilot, the upset from -25º to -11º was due to the ai rplane ent ering a wake
vortex generated by a preceding aircraft. This roll angle upset of 10º is subjectively rated as “moderate” by all
accounts, depending also on the altitude (above 2000 feet AGL) at which it occurs and the duration of the event.
A plot of the magnitude and signal-noise ratio of the vorticity in non-dimensional form (in the runway reference
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