I don't think this is true. Without Mode C (Altitude Reporting) all that can ever be displayed is a TA. The TCAS equipment can't work out a vertical closure rate since it will not know the intruders height, and the horizontal closure rate will be the same whether the intruder aircraft is physically above or below the TCAS equipped aircraft. Won't it ??
Correct all that can ever be displayed is a TA without C. I did not say this was the case. However TCAS works on closure rates as well as altitude. It just measures the change in time taken for successive interrogations to be replied to. Its all to do with slant range.
Like the old railway analogy of stuff you can see out the window appears to pass you at different speeds depending on range. Thus something a few hundred feet away but missing will have a different rate to something a 1000 ft away and missing to something that will hit. TCAS can crudely decide if a non C is a threat BUT crucially can not give an RA because because it can not give an accurate miss manouvre without height readout.
Tracking:
Using surveillance reports each second, the CAS logic tracks the slant range and closing speed of each target aircraft, to determine the time in seconds to the CPA. If the target is equipped with an altitude-coding transponder, the CAS logic also tracks the altitude reports to project the altitude of the target at the CPA. The CAS logic determines the vertical rate of the target by measuring the time it takes to traverse successive 100-foot increments of altitude.
The CAS logic uses the data from its own aircraft pressure altimeter either directly from the altitude encoder or as processed by an air data computer, to determine own aircraft altitude, vertical rate, and the relative altitude of each target. The Outputs from the tracking algorithm (target range and range-rate, relative altitude and vertical rate) from the inputs for the traffic advisory and threat detection algorithms.
Below 1700 feet AGL, the CAS logic uses the difference between its own aircraft pressure altitude and radar altitude to determine the approximate elevation of the ground above sea level. It then subtracts the latter value from the pressure altitude value received from the target, to determine the approximate altitude of the target above the ground. If this altitude is less than 180 feet. TCAS considers the target to be on the ground, so the CAS logic does not generate a TA.
Traffic Advisory:
Range and altitude tests are performed on each altitude-reporting target. A proximity target is displayed if the target does not quality for a TA but is currently within 6 NM and 1200 feet of the TCAS aircraft.
A non-altitude reporting target is declared an intruder it the range test alone shows that the calculated tau is within the RA tau threshold associated with the current SL being used. This varies from 20 seconds for SL 4 to 35 seconds for SL 7. When TCAS is in SL 2 the tau threshold used is 15 seconds.
and
A non-altitude reporting target will trigger the
generation of a TA if the range test is satisfied, on
the basis of the same tau values associated with the
RA.
see
http://www.eurocontrol.int/ra-downli...ning_ver20.pdf