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a conflict between two aircraft, "... given a predicted pair of
trajectories and their levels of uncertainty." ["A conflict is
defined here as having two or more aircraft come within some
minimum allowed separation distance from each other."]
The trajectory prediction errors (along-track, cross-track,
vertical) are modeled as normally distributed, independent random
variables. For computational efficiency, transformations of
coordinates are made and the two distributions [i.e., prediction
error covariance matrices] are combined, in effect assuming one
aircraft has no predicted position error, and assigning all of the
error to the other aircraft. Numerical integration is then used,
employing a 3-dimensional grid, with the probability of an
aircraft being within a grid element approximated by the
probability density at the center of the element and the volume of
the element. Inputs to the computation are the path crossing
angle, the predicted minimum separation, and the predicted time of
minimum separation. Numerical and graphical examples are given.
COMMENTS:
Is the normality assumption reasonable? The authors quote a
reference for this assumption, but the papers I've seen usually
assume a double exponential or double-double exponential
distribution for horizontal errors, or at least for cross-track
errors.
Is the assumption of independent prediction errors justified, as
potentially conflicting aircraft would both be affected by "the
same" winds?
FP. Parker, I. G., "A Review of Work on Deriving a Target Level of Safety
(TLS) for En-route Collision Risk," RGCSP WG/A, WP/8, Brussels, May
1995.
1. Topic: Risk Tolerability, Target Levels of Safety
2. Very readable
FQ. Peterkofsky, Roy I., "Knowledge-Based Relative Prioritization of
SEPARATION SAFETY MODELING
B-28
Aircraft for Air Traffic Flow Control," Berkeley, CA: University of
California, Institute of Transportation Studies, (UCB-ITS-WP-86-4)
46p. $10.00.
FR. Polhemus, N.W. and D. Livingston, "Characterizing Cross-Track Error
Distributions for Continental Jet Routes," Journal of Navigation,
Vol.34, No.1, 1981
FS. Polhemus, N.W., "Collision Risk Modeling for Continental Jet Routes,"
Unpublished
FT. Pool, A, "Historical Development of Collision Risk Models for
En-Route Air Traffic"
1. Topic: Mathematical models for collision risk
FU. Popp, (Captain) Peter T., USAF, "The Physical Limitations of the 'See
and Avoid' Concept for Separation of Air Traffic," ISASI Forum,
September 1995
1. This paper concludes that the use of "see and avoid" in preventing
en route midair collisions is of extremely limited usefulness.
This conclusion is reached based on compelling arguments and
research about the limitations of normal human vision. These
limitations include the following:
The very narrow area in which the eye has its best visual
acuity - only about 2 degrees of the total visual field.
The scanning motion of the eye when looking for something.,
which results in large gaps in the visual field when
scanning for distant objects.
Empty-field myopia, the natural tendency of the eye to focus at
a distance of 12" to 36" when scanning a clear sky.
The fact "... that an object must cover approximately 12
minutes of arc to be reasonably recognizable as another
aircraft (NTSB, 1993)." Furthermore, this limitation is
when the eye is directly looking at the object. Objects
outside the 2 degree area of best vision are less likely to
be recognized.
A simulator study concludes that the point where avoiding a midair
collision becomes pure chance is approximately 160 knots closing
APPENDIX B
BIBLIOGRAPHY
B-29
speed. [Naturally, this depends on the size of the intruding
aircraft]
[This study does not take into account other visual difficulties,
including the difficulty a pilot may have in determining if a
distant, intruding aircraft is at, above, or below his/her
aircraft's altitude and in estimating both the distance of an
intruding aircraft and its distance at closest approach.]
FV. Porter, David B., "A Numerical Study of Airplanes Flying in
Proximity," (Master's thesis), MONTEREY CA: NAVAL POSTGRADUATE
SCHOOL, September 1993, 140 pages. (ADNUMBER: ADA273373.)
1. During an emergency such as an unsafe landing gear indication, a
second aircraft is often used to perform an airborne visual
inspection of the landing gear. The chase airplane may be quite
dissimilar in size and wing loading and consequently experience
　
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