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scenario consisting of two aircraft under air traffic control: a blunderer (an aircraft
deviating from a safe trajectory to one that crosses the path of another aircraft) and an
evader (the threatened aircraft). Both aircraft are assumed to fly in a constant direction
and at a constant speed during the blunder, unless an evasion maneuver is executed. The
evasion, if completed in time, is assumed to be successful. (The possibility of an evasion
resulting in a collision exists, but is relatively unlikely and can be handled in a separate
analysis.)
Definitions
The following definitions are made to facilitate the discussion:
A blunder is an air traffic situation in which two aircraft are on courses which cause, or
will cause (unless corrected), a simultaneous violation of minimum separation
requirements (in the horizontal plane and the vertical plane), i.e., a conflict. A blunder
could be caused by an inappropriate change in direction, speed, and/or climb/descent angle
on the part of one of the aircraft (the blunderer), or it could be caused by a pending
conflict going undetected beyond the latest time at which corrective action should have
been taken. In the later case, this time could be taken to be the moment the blunder
occurred.
A collision is the result of a blunder which causes horizontal separation to be less than the
average diameter of the two aircraft and vertical separation to be less than the average
heights of the two aircraft (considered as discs).
Air traffic control (ATC) reaction (or response) time is the time between when a blunder
occurs and the time required for an air traffic controller to observe the threat, decide on a
corrective action, obtain a clear radio channel, and convey instructions to the flight crew.
It depends on the number of aircraft being monitored by the controller, the skill level of
the controller, the scan rate and display capability of the ATC equipment, the nature of the
threat, random factors, etc.
Flight crew reaction time is the time required between the moment that instructions are
conveyed by the controller and the moment that controls in the cockpit are moved
1 The model was created by Ken Geisinger (ATX-400) with the assistance of several George Washington
University students over a number of years.
SEPARATION SAFETY MODELING
6-2
appropriately. This time depends on the type of aircraft, the skill level of the pilots, the
time required to disengage automatic controls (if necessary), the interference of other
flight control activities, random factors, etc.
Airframe reaction time is the time required between the moment that controls are adjusted
and the moment that the aircraft responds with a suitable change in direction, speed, or
rate of climb/descent. This is a function of the type of aircraft; the current trajectory,
speed, altitude, throttle setting, atmospheric conditions; and random factors.
Blunder duration is the time between the moment that the blunder occurs and the moment
that either aircraft executes an avoidance maneuver without the assistance of ATC (e.g.,
through visual or Traffic Alert and Collision Avoidance System (TCAS) detection of the
threat). Note that by this definition, a blunder can continue to endure indefinitely, but the
model is only concerned with whether or not it endures when the blunderer crosses (or
would have crossed) the evader’s path.
Required Input Data
The following are required input data:
ALPHA1 = Climb (if positive) or descent (if negative) angle of the blunderer (degrees).
ALPHA2 = Climb (if positive) or descent (if negative) angle of the evader (degrees).
PHI = Crossing angle of the blunderer and evader paths in the horizontal plane (degrees).
Note: it is required that 0 < PHI < 180 degrees.
SPEED1 = Speed of blunderer along the flight path (knots).
SPEED2 = Speed of evader along the flight path (knots).
INSEPH = Initial distance from blunderer to closest point on the evader path in the
horizontal plane, in nm.
INSEPV = Initial vertical separation between the blunderer and the closest point on the
evader path in feet (negative if evader path is above blunderer).
HEIGHT1 = Height of blunderer aircraft, in feet.
HEIGHT2 = Height of evader aircraft, in feet.
WSPAN1 = Diameter of blunderer, in feet.
WSPAN2 = Diameter of evader, in feet.
TRFDTY = Number of aircraft per hour on evader path.
Initial distances refer to distances at time zero, which is taken to be the time that the
blunder occurs. Seven response time distributions are required, as discussed below.
Methodology
Given that a blunder occurs, the probability of a collision can be approximated by:
Pc = (Pn)x (Pb)x(Pe)x(Ps)
　
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