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practical or necessary to draw the volume in the shape of an aircraft. It is only necessary
that the probability of the point being in the volume approximates the probability of two
aircraft being close enough to cause a collision.
A variety of volumes are used in various models, depending on the mathematical
formulation and whether the model is two dimensional or three dimensional. Usually, the
simplest form mathematically is a circle or sphere. Some models use boxes or rectangles.
The Sector Design and Analysis Tool (SDAT) and the Analytic Risk Blunder Model
(ARBM) models use a disc shape, which was derived to approximate the en route
separation minima rules. Because aircraft wingspan and length are usually approximately
equal and much larger than aircraft height, the disc shape is a reasonable approximation,
but other approximations would be quite satisfactory. The same model can use different
dimensions for analyzing conflicts or collisions.
The dimensions are very important, as the probability of a point being within the volume is
directly proportional to the size of the volume. Doubling the radius of a disc or both
horizontal dimensions of a rectangular box, results in a fourfold increase in the probability
of a point randomly placed in space being within the solid. Doubling the radius of a
sphere or all dimensions of a box or disc, increases the risk estimate by a factor of eight.
For a disc or spherical representation, the average of the two aircraft wingspans1 is a
reasonable estimate for the horizontal radius, for this corresponds to the two aircraft
centers being at a distance that would result in wingtips touching, or at least the aircraft
possibly interfering in the flight dynamics of each other. Some studies have used a sphere
with a radius of 500 feet, which is somewhat generous when one considers that a C-5
Galaxy has a wingspan of 223 feet and a length of 248 feet.
A special problem arises when working with step simulations. In order to determine if a
collision occurs, the distance between aircraft centers is computed at each time step.
1 Wingspan measured from wingtip to wingtip.
SEPARATION SAFETY MODELING
3-2
These steps must be made very close, or the aircraft could step through each other
undetected. This analysis approach requires an extremely large number of computations
to move the aircraft through space. Some form of continuous simulation or
supplementary analytic computations would be needed to ensure that a time step
simulation would not miss some collisions or conflicts.
Due to aircraft wake, it is not always necessary to have physical contact to have an
accident, or at least to encounter turbulence sufficient to cause passenger injury or worse.
Recent experience with reduced vertical separations in the North Atlantic suggest that
some aircraft are experiencing significant turbulence problems caused by the wakes of
aircraft flying many miles ahead and 1,000 ft. above them. At this time, it is uncertain how
best to incorporate aircraft wake into a collision risk model. The strength and location of
a wake and its effects on other aircraft are highly dependent on the sizes and weights of
the aircraft and on atmospheric conditions. Thus, incorporating wake vortices into a
collision risk model can introduce a significant, additional complexity into an already
complex model.
3.2 RISK METRICS - WHAT IS AN APPROPRIATE METRIC FOR
DEFINING THE RISK OF COLLISION?
Generally speaking, risk can be measured in terms of the chance of an adverse event per
unit of some activity. In aviation, there are a number of metrics which may conceivably be
used to describe risk. These include the following:
Number of Accidents
Number of Fatal Accidents
Number of Fatalities
PER
Year
Aircraft Flying Hour
Aircraft Mile
Passenger
Passenger Hour
Passenger Mile
Flight Stage
Passenger Journey
At any moment, the same level of risk could, given sufficient data, be expressed by a
variety of metrics, such as fatal accidents per flight hour, expected number of accidents
per calendar year, and fatalities per en route passenger hour. It is stressed “at any
moment” because, of course, some metrics will be affected by changes in traffic levels or
average passenger loads.
Tables 3-1 and 3-2 illustrate that different metrics can be equated to the same level of risk
only when done at a given point in time. Neither table is meant to imply anything about
the actual level of collision risk in these areas, which may, of course, differ from the
figures shown.
COLLISION MODELING DEFINITIONS AND RISK METRICS
3-3
Table 3-1 shows how an assumed risk level of 1.5x10-8 fatal accidents per flight hour
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a concept paper for separation safety modeling(11)
