SP...
"TAU" is a protective area around an aircraft which is defined not purely as a distance between your aircraft and an intruder aircraft, but one based on time to impact (or closest point of passing).
If you think of a simple area, x nautical miles all around an aircraft, the area defined would be a perfect circle. However, with Tau, you are considering the relative closure rates of two aircraft. The protective "circle" is distorted by this effect.
If you have two aircraft converging at high speed, say head on, the circle would have to extend far in front of the aircraft (distance-wise) to ensure protection for these aircraft (detection, reaction and manoeuvre times have to be considered at these greater speeds). TCAS warnings are given when the aircraft are quite far apart.
If you have an intruder aircraft coming up behind your aircraft, the closure rate should be a lot less, so TCAS will allow the intruder aircraft to get much closer to you before it sounds a warning (The protection zone is squashed at the rear (distance-wise).
In the latter case, there are additional safeguards built into the TCAS circuits for very slow closure rates (Absolute distance between aircraft must also be considered).
Hope this helps.
Rgds.
Q.