4.3.3 Omnidirectional Wind
The plane is inevitably affected by the wind. However, a certain wind direction cannot
be specified when estimating the track. Therefore, ICAO defines a wind direction that is
the most unfavorable to the aircraft—omnidirectional wind. The omnidirectional wind
direction is always perpendicular to the current heading of the aircraft and points in the
opposite direction of the turn. Assuming that the omnidirectional wind speed is w, the
real-time turning radius can be expressed as
R
0
1 ¼ R 1 þ
w
a
ð12Þ
where a is the number of angles that the aircraft turns when it turns to a heading parallel
to the airspace boundary. At this time, the military aircraft is closest to the civil aircraft.
Therefore, the minimum lateral distance for defining a military and civil aircraft is
DL ¼ y
0
À x 1 þ R
0
1
ð13Þ
where y
0 is the abscissa of the actual position of the civil aircraft.
5 Simulation of Military and Civil Aviation Lateral
Deviation
There are nonlinear terms in the lateral deviation expression of military and civil
aircraft, so it is difficult to obtain an analytical expression of the probability density
function of the lateral spacing. Assume that each military airport has 24 fighters, each
of which requires 200 h of flight training per year. There are five training airspaces in
the airport area of responsibility. For each training flight, the duration of the military
aircraft’s activity in the airspace is half of the total flight duration. Then, the average
frequency of training flights in each hourly airspace is
b ¼
24 Â 200
365 Â 24
Â
1
2
Â
1
5
¼ 0:054
ð14Þ
Assume that the starting point of the hover training flight is S 2 À
ffiffi
2
p
2 R 0 ;
ffiffi
2
p
2 R 0
.
Other parameters involved in the simulation are as follows in Table 1.
Among the above parameters, the military civil aircraft size uses the public data of
the F16 and A380 passenger aircraft [4]. The vertical safety interval uses a safety
interval of 10 km from our radar. The Monte Carlo method is used to select the random
number corresponding to the probability density function of speed and slope, and the
simulation of the lateral deviation of military aircraft and civil aviation aircraft with
n = 1,000,000 times is carried out. The results are shown in Figs. 3 and 4.
It is assumed that the training airspace boundary is tangent to the circling path, that
is, no interval margin is left in the training airspace. The lateral deviation value of the
civil aircraft obtained from the simulation is subtracted from the lateral deviation of the
military aircraft. Calculate the number of simulations where the difference is less than
82
G. Zhao et al.
The plane is inevitably affected by the wind. However, a certain wind direction cannot
be specified when estimating the track. Therefore, ICAO defines a wind direction that is
the most unfavorable to the aircraft—omnidirectional wind. The omnidirectional wind
direction is always perpendicular to the current heading of the aircraft and points in the
opposite direction of the turn. Assuming that the omnidirectional wind speed is w, the
real-time turning radius can be expressed as
R
0
1 ¼ R 1 þ
w
a
ð12Þ
where a is the number of angles that the aircraft turns when it turns to a heading parallel
to the airspace boundary. At this time, the military aircraft is closest to the civil aircraft.
Therefore, the minimum lateral distance for defining a military and civil aircraft is
DL ¼ y
0
À x 1 þ R
0
1
ð13Þ
where y
0 is the abscissa of the actual position of the civil aircraft.
5 Simulation of Military and Civil Aviation Lateral
Deviation
There are nonlinear terms in the lateral deviation expression of military and civil
aircraft, so it is difficult to obtain an analytical expression of the probability density
function of the lateral spacing. Assume that each military airport has 24 fighters, each
of which requires 200 h of flight training per year. There are five training airspaces in
the airport area of responsibility. For each training flight, the duration of the military
aircraft’s activity in the airspace is half of the total flight duration. Then, the average
frequency of training flights in each hourly airspace is
b ¼
24 Â 200
365 Â 24
Â
1
2
Â
1
5
¼ 0:054
ð14Þ
Assume that the starting point of the hover training flight is S 2 À
ffiffi
2
p
2 R 0 ;
ffiffi
2
p
2 R 0
.
Other parameters involved in the simulation are as follows in Table 1.
Among the above parameters, the military civil aircraft size uses the public data of
the F16 and A380 passenger aircraft [4]. The vertical safety interval uses a safety
interval of 10 km from our radar. The Monte Carlo method is used to select the random
number corresponding to the probability density function of speed and slope, and the
simulation of the lateral deviation of military aircraft and civil aviation aircraft with
n = 1,000,000 times is carried out. The results are shown in Figs. 3 and 4.
It is assumed that the training airspace boundary is tangent to the circling path, that
is, no interval margin is left in the training airspace. The lateral deviation value of the
civil aircraft obtained from the simulation is subtracted from the lateral deviation of the
military aircraft. Calculate the number of simulations where the difference is less than
82
G. Zhao et al.