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Most of the information I've seen about TCAS talks about only two aircraft being involved.

It's pretty unlikely, although far from impossible that situations involving three or more aircraft may arise.

In such situations is TCAS expected to detect the situation and offer sensible advice still? Or are all bets off and a series of confusing and conflicting advice the most likely outcome?

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TCAS can deal with conflicts with multiple aircraft, a so called Multiple Threat Encounter. It will attempt to resolve the conflict but it will be limited in its options.

Examples of a MTE are rare, one case I can point to is this incident involving an aircraft turning into the approach stream between two aircraft instead of following the last in line.

MIT Lincoln lab has reported on MTEs and the TCAS algorithm performance in 2009. They report the majority of MTEs involved three aircraft, but mention one TCAS MTE involving seven aircraft.

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    $\begingroup$ Holy carp, the TCAS engineers definitely earned their money that day... $\endgroup$ – Sean Oct 22 '18 at 2:59
  • $\begingroup$ The link to the Lincoln Lab is now broken. The title of the report is "TCAS Multiple Threat Encounter Analysis", and it's still available at web.archive.org/web/20100614005807/http://www.ll.mit.edu/…. $\endgroup$ – Terran Swett Oct 22 '18 at 14:04

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