Suppose the expected flight speed is V = 900 km/h, the actual speed is V′, the
expected turning slope is c = 45°, and the actual turning slope is c′, both of which are
affected by the pilot’s motion error. Then, the turning radius under the influence of
speed error and turning slope error is:
R 1 ¼
V
0
ð Þ
2
g tan c 0
ð Þ
ð6Þ
The actual speed and the actual turning slope obey the following probability
distribution.
f c c
0
ð Þ ¼
1
ffiffiffiffiffi ffi
2p
p r c
exp À
45 À c
0
ð
Þ
2
2r 2
c
!
f V V
0
ð Þ ¼
1
ffiffiffiffiffi ffi
2p
p r V
exp À
250 À V
0
ð
Þ
2
2r 2
V
!
ð7Þ
4.3.2 Center of the Circling Path
Suppose the aircraft starts to turn from the S x s ; y s
ð
Þ point in the heading h, then the
actual center O 1 x 1 ; y 1
ð
Þ is
x 1 ¼ x s þ R 1 cos h
y 1 ¼ y s À R 1 sin h
ð8Þ
It is assumed that the heading error is affected by navigation accuracy, airborne
navigation equipment error, and pilots’ operation error. All of them obey the Gauss
distribution in angle. Therefore, the joint probability distribution function of heading
error also follows the Gauss distribution.
f h h
0
ð Þ ¼
1
ffiffiffiffiffi ffi
2p
p r h
exp À
# À h
0
ð
Þ
2
2r 2
h
!
ð10Þ
According to the conservative values given in ICAO 8168 document, the standard
deviation is theta = 2.6°, where theta is the heading angle in the ideal state and the
expression is:
# ¼
p À arctan
y S
x S
x S [ 0; y s 6 ¼ 0
2p À arctan
y S
x S
x S \0; y s 6 ¼ 0
p
2
x S ¼ 0; y S ¼ R 0
À
p
2
x S ¼ 0; y S ¼ ÀR 0
p
x S ¼ R 0 ; y S ¼ 0
0
x S ¼ ÀR 0 ; y s ¼ 0
8
> > > > > > > > <
> > > > > > > > :
ð11Þ
Risk Analysis of Lateral Collision of Military and Civil …
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