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has been shown in figure 4.1. Much more extreme wind profiles in lower atmosphere
have been recorded; some data from actual measurements in lower atmosphere can
be found in ref.[1]. A very dangerous type of windshear is encountered in so-called
microbursts: large pockets of air moving rapidly downwards to the ground in thunderstorms.
An aircraft flying through a microburst can be faced with a sudden increase
in headwind, followed by a severe downdraft that is immediately followed
by a sudden increase in tailwind, all within a matter of seconds. Such conditions
1In some textbooks the term ‘windshear’ is used to denote the local variations of the wind and
turbulence with respect to the ground. In this report turbulence will be considered separately.
44 Chapter 4. External atmospheric disturbances
0 0.5 1 1.5 2 2.5 3
0
50
100
150
200
250
300
350
400
450
500
V
w
[ m / s ]
H [ m ]
Figure 4.1: Wind profile for l = −0.0065 Km−1 and Vw9.15 = 1 ms−1
may exceed the aerodynamic and propulsive performance of airplanes, causing the
aircraft to loose lift and altitude, which can be very hazardous at low altitudes.
One of the best researched accidents involving a microburst was the June 24, 1975
crash of Eastern Air Lines Flight 66 during final approach to John F. Kennedy airport
in New York. Figure 4.2 shows the reconstructed wind profile and the recorded flightpath
of this airplane. Based on this data, numerical models of two-dimensional flowpatterns
for thunderstorms have been developed [11]; such models are often used for
flight crew training in flightsimulators. Although this subject will not be explored in
further detail in this report, it is useful to acknowledge the hazards of such extreme
weather conditions, and to realize that the idealized wind model that will be presented
next will not always be sufficient; for some purposes, it may be necessary
to apply additional models, or even measurements of actual wind velocities during
extreme weather conditions. However, that goes beyond the current scope of this
report.
The atmosphere model used in section 3.5 was based on the ICAO standard atmosphere
model, which is characterized by a standard temperature lapse-rate l = dT/dH =
−0.0065 Km−1; see for instance ref.[30] for more details. The following equations represent
a typical idealized windspeed profile that is valid for this particular value of
the temperature lapse-rate [1]:
Vw = Vw9.15
H0.2545 − 0.4097
1.3470
(0 < h < 300m)
Vw = 2.86585Vw9.15 (h 300m)
(4.1)
Vw9.15 is the windspeed at an altitude of 9.15 m (approximately 30 ft, which is a commonly
used reference height for meteorological experiments). The wind profile in
4.1. Deterministic disturbances 45
Downburst
Outburst
Runway
25 sec
30
35
40
50
20:05 UTC
00 sec
10
11.4 sec: first
ground contact
05
55
Sea wind front
Glideslope
250
200
150
100
50
0
-3000 -2000 -1000
Height [ ]
Distance from threshold [ ]
m
m
Figure 4.2: Microburst wind pattern that caused the crash of Eastern flight 66
figure 4.1 is based upon a value Vw9.15 = 1 ms−1. Ref.[1] presents some alternative
wind profiles, which are typical for other values of the temperature lapse rate.
In sections 2.3 and 3.3.4, we described how the influence of the wind on the motions
of the airplane can be expressed in terms of correction terms for the external force
components in the body-fixed reference frame. If we know the wind velocity relative
to the Earth, we can obtain the components of the wind along the aircraft’s body-axes
using the following axes transformation:
VBw
= TE!B · VEw
(4.2)
where Vw represents the wind vector, the superscript B represents the aircraft’s body
axes, and the superscript E represents the Earth axes. TE!B is the transformation
matrix from Earth to body axes, which involves the three consecutive Euler rotations
shown in figure A.2 in appendix A:
TE!B TV!B = TF · TQ · TY (4.3)
This transformation has been written out in more detail in equation (A.4) of appendix
A.
In practice, wind is usually not given in terms of velocity component along the Earth
axes, but rather in terms of windspeed and wind direction. The first represents the
magnitude of the windspeed vector, and the latter represents the direction on the
compass rose from where the wind emanates; for instance, ‘northerly wind’ means
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