Not 100% sure, but I guess the time-to-go to the CPA (called TAU) = Slant range between the 2 AC / Closure rate
Example:
2 AC with 1Nm separation.
Closure rate = 1Nm/min
TAU = 1 min
If you take the distance to the CPA with an aircraft speed of 6Nm/min, this would be 6Nm to go before reaching the CPA.
If you divide this range by the closure rate you get 6Nm/(1Nm/min) = 6 min
Which is incorrect. You would need to divide range to CPA by speed of AC, but because closure rate is used, this calculation is not being made by the TCAS.
Concerning the closure rate, does it take into account both aircraft velocities, is it only the own aircraft velocity?
It takes both AC into account, but it's a relative speed between those 2 AC.
E.g. if both AC are flying parallel, with only a few degrees difference in heading and are slowly converging, it doesn't matter which speed they are flying. The TCAS will calculate both AC trajectories and their closure rate.
A320 FCOM:
http://www.smartcockpit.com/site/pdf...Navigation.pdf TCAS: p188-p224 (P195 explains briefly the principle)