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EXISTING MODELS AND MODELING TOOLS
6-3
where,
Pn is the probability that both aircraft will arrive at the crossing point close enough in time
and space to result in a collision, assuming that no intervention occurs. Pn is a function of
PHI, ALPHA, SPEED, HEIGHT, WSPAN, TRFDNTY, and H, the vertical separation (in
feet) between paths at the crossing point, which is computed.
The function Pn is derived in “Airspace Conflict Equations” [R6.1]. This function is a
three-dimensional model that assumes that the aircraft fly at constant speed, direction and
climb angle through the intersection and that a specified number of evaders per hour are
randomly distributed according to the uniform probability distribution on the evader
course.
Pb is the probability that ATC intervention will not cause the blunderer to modify its
course in time to avoid a collision.
Pe is the probability that ATC intervention will not cause the evader to modify its course
in time to avoid a collision.
Ps is the probability that neither modifies its course in time to avoid a collision without
ATC intervention.
The probability that an ATC-assisted avoidance maneuver on the part of the blunderer
does not occur in time is given by:
Pb = Prob(Tbe > Tc)
Where,
Tbe = time required for the blunderer to evade (probability distribution), and
Tc = time (in seconds) between the moment of initiation of the blunder to the moment that
the blunderer would cross the evader’s path, assuming that no evasion occurs.
The probability that a successful ATC-assisted evader correction does not occur in time is:
Pe = Prob(Tee > Tc)
Where,
Tee = time required for the evader to evade (probability distribution).
Both Tbe and Tee are computed through numerical convolution of user-specified
probability distributions for the three reaction times described above (air traffic control,
flight crew, and airframe).
SEPARATION SAFETY MODELING
6-4
Ps is given by:
Ps = Prob(Tsc > Tc)
Tsc is the time, in the absence of ATC intervention, from the initiation of the blunder until
either aircraft flight crew detects and reacts to the threat, and their aircraft executes an
avoidance maneuver. If both aircraft execute avoidance maneuvers, the shorter reaction
time is used. (Future versions of the ABRM will explicitly consider visual detection and
TCAS alerts.)
Figure 6-1 is a flow diagram of the basic logic in the ABRM, showing input data and the
steps leading to the computation of Pc for a given collision risk scenario. Probably, the
best way to illustrate the operation of the ABRM is through a hypothetical example.
Analytic Blunder Risk Model
Simplified Overall Logic
Compute time, Tc
f r o m s t a r t u n t i l B
crosses E’s path
G i v e n P . D . A T C
reaction time for
blunderer, Tba
C o m p u t e P s =
P r o b . t h a t T s > T c
G i v e n P . D . p i l o t
reaction time for
blunderer, Pbp
G i v e n P . D . A / C
reaction time for
blunderer, Tbf
G i v e n P . D . A T C
reaction time for
evader, Tea
G i v e n P . D . p i l o t
reaction time for
evader, Tep
G i v e n P . D . A / C
reaction time for
evader, Tea
Compute P.D. total
reaction time for
blunderer, Tbe
G i v e n P . D . o f s e l f
correction time for
either, Ts
C o m p u t e P b =
p r o b . t h a t T b e > T c
Compute P.D. total
reaction time for
evader , Tee
C o m p u t e P e =
p r o b . t h a t T e e > T c
Prob. of Collision
PC=Pn*Pb*Pe*Ps
Compute Prob. of
Blind Flying Colli
s i o n = P n
Given trajectories
of Blunderer, B
and Evader, E
Note: P.D. = probability distribution
ATC = air traffic control
A/C = aircraft
Blunderer = deviating A/C
Evader = potentially threatened A/C
Figure 6-1. Analytic Blunder Risk Model Logic
Hypothetical example
As a hypothetical example, consider the following problem which is based on an actual
operational error in which an aircraft was vectored and cleared to descend in the face of
oncoming traffic 2,000 feet below:
Aircraft data: Evader Blunderer
Wingspan 125 108 feet
Height 40 30 feet
Speed 502 398 knots
Climb angle 0 -4 degrees
EXISTING MODELS AND MODELING TOOLS
6-5
Blunder data
Crossing angle (PHI) = 120 degrees
Initial separation INSEPH = 4 nm , INSEPV = 2000 feet
Evader traffic density (TRFDTY) = 1 aircraft/hour
A set of hypothetical reaction time distributions were used to obtain the overall reaction
　
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