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If Aircraft One is maintaining a low rate of climb/ descent, is there a minimum descent or climb rate threshold below which the up/down arrow will not show up on the TCAS of the Aircraft Two?

I have heard figures of 400 fpm and 500 fpm.

Is there an industry standard, do standards depend on aircraft performance / weight class?

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    $\begingroup$ Got the answer. It's 500 fpm. Below this vertical speed of the target aircraft, V/S arrow is not displayed. $\endgroup$ – Salamanderpress Dec 26 '17 at 15:18
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    $\begingroup$ Feel free to post the answer, explaining how you figured it out, we encourage that. $\endgroup$ – ymb1 Dec 26 '17 at 15:28
  • $\begingroup$ It is also manufacture dependent. For example, I just read in an aviation article that some airplane glass cockpits such as the Cyrus use a 6 second future event timeline and other aircraft such as Boeing use 10 seconds. Emergency and warning criteria does not seem to be standardize or regulated. $\endgroup$ – jwzumwalt Dec 26 '17 at 23:59
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    $\begingroup$ @jwzumwalt it is NOT manufacturer dependant.The TCAS II implementation is very mich standardised and regulated. The TCAS II algorithm logic is prescribed in RTCA DO185B / EUROCAE ED14 Minimum Operational Performance Specifications for TCAS II. $\endgroup$ – DeltaLima Dec 28 '17 at 0:13
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    $\begingroup$ The RTCA DO185B does not necessarily provide limits. It uses terms like, ..." If the intruder gets within 15 to 35s..." and "nominally between 1,500 and 2,000 fpm.", but these are suggestions and not regulations. Referencing a document such as RTCA DO185B without a applicable quote is meaningless to a discussion such as this. RTCA DO185B sets a standard for the audio/visual WARNING MESSAGES but does not set a criteria for what triggers the warning. $\endgroup$ – jwzumwalt Dec 28 '17 at 2:01
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The Minimum Operational Performance Specifications (MOPS) for TCAS II (RTCA DO185B / EUROCAE ED143) specify the requirements for TCAS II.

It states that the arrow must appear when the vertical speed of the intruder is 500 feet per minute or more:

2.2.6.1.2.1.6

Intruder Vertical Speed Arrow

A vertical arrow shall be placed to the immediate right of the traffic symbol if the vertical speed of the intruder (as determined by the TCAS tracker) is equal to or greater than 500 fpm, with the arrow pointing up for climbing traffic and down for descending traffic. The color of the arrow shall be the same as the traffic symbol.

Source: RTCA DO185B / EUROCAE ED14 Minimum Operational Performance Specifications for TCAS II, volume I.

Whilst the MOPS are not regulations themselves, the aviation authorities put them into regulations such that TCAS II needs to be according to the MOPS.

In the US, the FAA has published Advisory_Circular AC 20-151A which states:

The FAA ACO approving the initial installation of the TCAS II equipment must verify that the TCAS II processor design does not differ from the criteria specified in RTCA/DO-185A or RTCA/DO-185B as applicable.

This means it is not up to the manufacturer to decide when to show the arrow symbol. It is required by the MOPS, so it has to be designed that way.

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