Published Report (DOT/FAA/CT-94-36)

2.0 BASIC RISK COMPUTATION
2.1 DEFINITION OF A TCV
Although the definition of a collision of two aircraft is
obvious, a definition which can be used in mathematical analysis
is not as obvious and could be considered by some to be
subjective. Since aircraft are basically long tubular structures
with various protuberances, it is possible that two aircraft
could pass very close to one another without touching. On the
other hand, the aircraft could simply touch wing tips with the
centers of gravity far removed. For this reason it was decided
to simply place the evading aircraft in the center of a
hypothetical sphere and determine whether or not the center of
gravity of the blundering aircraft penetrates that sphere. It
will be assumed that such a penetration would result in a
collision. Obviously not all such penetrations would result in
collisions, but in mathematical analysis some simplifying
assumptions must be made. The choice of the radius of this
sphere is somewhat subjective. It must be at least as large as
the wingspan of the largest aircraft which will be involved in
parallel approach operations, and it must be at least as large as
the wingspan of aircraft in the foreseeable future. For these
reasons the radius of the sphere was chosen to be 500 feet.
Since an incursion of the blundering aircraft into the 500 foot
sphere of the evader aircraft does not guarantee a collision, it
will be called a Test Criterion Violation or TCV.
2.2 DEFINITION OF WORST CASE BLUNDER
Previous studies as well as the current study indicate that
blunders in the 30' range are the most likely to result in a TCV.
The probability of a TCV during a 20' or less blunder is
considered to be remote. Not all 30' blunders will result in a
flight by the blundering aircraft through the NTZ into the path
of the evading aircraft just as not all swerves by automobiles
toward the center median result in a crossing of the median.
Simulations have shown that if the pilot of the blundering
aircraft is able to return the aircraft to the course centerline
because of controller intervention or personal initiative, the
risk of collision is negligible. Therefore, a worst case blunder
(WCB) is defined to be a 30' blunder in which the pilot of the
blundering aircraft is unable to respond to a controller
direction to return to course. The reason why the pilot may not
respond could be a communications failure, a mechanical failure,
a severe weather problem such as a thunderstorm, or a
physiological problem of some member of the crew. For the
purposes of this study, the reason will be simply referred to as
no response.
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