According to the TCAS user manuals it should be correct, but maybe the system does have distance calculations included in the algorithm. Would someone care to elaborate on this? (good question!)
TCAS warns you at a distance further away when you are head on, as opposed to when you are catching up with someone. I think distance is also considered, otherwise you could get quite close if you are catching up to someone very close to your own speed, but TCAS manuals always speak of time.
From the PDF document
http://www.honeywelltcas.com/product...pilotguide.pdf :
The TCAS II system monitors the airspace sur rounding
your aircraft by interrogating the transponder of
intruding aircraft.The interrogation reply enables
TCAS II to compute the following information about
the intruder:
1) Range between your aircraft and the intruder.
2) Relative bearing to the intruder.
3) Altitude and vertical speed of the intruder, if
reporting altitude.
4) Closing rate between the intruder and your
aircraft.
Using this data TCAS II predicts the time to,and the
separation at,the intruders closest point of approach
(CPA).Should TCAS II predict that certain safe
boundaries may be violated,it will issue a Traffic
Advisory (TA) to alert the crew that closing traffic is
in the vicinity.
If the intruder continues to close,TCAS II will issue a
Resolution Advisory (RA) to obtain or maintain safe
vertical separation between your aircraft and the
intruder.TCAS II bases the alarms on a five second
crew reaction time to begin the separation maneuver.
Increase or reversal of an RA requires a reaction in
two and one half seconds
...
A symbol change to a filled yellow circle indicates
that the intruding aircraft is considered to be potentially
hazardous.Depending on your altitude TCAS II
will display a TA when the time to CPA is between 20
and 48 seconds.
...
Under normal conditions a TA will precede an RA by
10 to 15 seconds.