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On the probability of collision for crossing aircraft

L.M.B.C. Campos (Instituto Superior Técnico (IST), Lisboa, Portugal)
J.M.G. Marques (Universidade Lusófona de Humanidades e Tecnologias (ULHT), Lisboa, Portugal)

Aircraft Engineering and Aerospace Technology

ISSN: 0002-2667

Article publication date: 6 September 2011




The purpose of this paper is to calculate the probability of collision of flying aircraft crossing on straight paths in any direction.


The probability of deviations from the intended flight paths is used to calculate the probability of collision that is integrated over time to cover whole events.


The probabilities of collision are calculated in terms of the r.m.s. position errors and encounter geometry, that is aircraft velocities and flight path angles and crossing angles.

Research limitations/implications

The method does not apply to aircraft flying in parallel tracks at the same velocity in air corridors: that case has been covered elsewhere, as well as the case of climbing or descending aircraft.

Practical implications

International Civil Aviation Organization (ICAO) specifies as target level of safety (TLS) a probability of collision not exceeding 5×10−9 per hour. To meet the ICAO TLS standard, it is necessary to calculate collision probabilities for all stages of flight.

Social implications

A low collision probability is a safety metric; the value does depend on a realist choice of probability distribution.


Calculates the probability of collision for crossing flights, corresponding to a common scenario on air traffic management.



Campos, L.M.B.C. and Marques, J.M.G. (2011), "On the probability of collision for crossing aircraft", Aircraft Engineering and Aerospace Technology, Vol. 83 No. 5, pp. 306-314.



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Copyright © 2011, Emerald Group Publishing Limited

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