TCAS - Threat Evaluation Figure 019
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This method of calculation avoids the initiation of corrections if, from a certain distance, the TAU trend is inverted even though the distance separating the two aircraft decreases. For example, in the case of two aircraft moving on parallel axes but in the opposite direction. (Ref. Fig. 020, 021) The curve represents the TAU variation before the closest point of approach. (Ref. Fig. 021) This time decreases as the range decreases, reaches a minimum when the intruder's relative bearing is 45 deg. and then increases rapidly. If the time corresponding to a predetermined threshold has not been reached before the minimum TAU value, a trajectory correction is not initiated. Certain conditions exist, however, in which this formula may prove insufficient. This may arise for example when two aircraft fly in the same direction with a very low closure rate. In this case, the range/range rate ratio gives a high TAU value whereas in fact, the two aircraft could be very near. The TCAS uses a slightly different formula to preclude this situation:
range - X (DMOD) to the power two TAU = ----------with X = ---------
range rate range This formula represents an estimate of the time the aircraft would take to penetrate a sphere around the intruder with a radius equal to (DMOD)expnt2/range. The DMOD coefficients are in function of altitude, ranging from 0.20 NM for 1000-2350 ft, to 1.1 NM above 30,000 ft as shown below (for the RA DMOD):
Altitude DMOD TA DMOD RA (ft) (NM) (NM)
0-1000 0.30 -1000-2350 0.33 0.20 2350-5000 0.48 0.35 5000-10000 0.75 0.55
10,000-20,000 1.0 0.80 >20,000 1.3 1.1
R **ON A/C 051-099,
R (2) Time to intercept (TAU)
R The TCAS does not need to locate the CPA in space, but rather it
R needs to know the time to intercept for two aircraft. For example, if
R two aircraft are approaching on the same axis on a collision course,
R this time is the ratio of distance between them to the sum of their
R speeds.
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TCAS - TAU Minimum Configuration Figure 020
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TCAS - TAU Curve Figure 021
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R D
R T = ---------
R V1 + V2
R More generally, the TCAS uses range and range rate measurement to
R compute this time:
R RANGE R(NM)
R TAU = ------------ i.e. TAU(s) = 3600 --------
R RANGE RATE RR (Kts)
R With the risk of collision being in inverse proportion to this time,
R trajectory correction orders are initiated by crossing predetermined
R time thresholds whose values depend on the altitude layer in which
R the aircraft is located.
R This method of calculation avoids the initiation of corrections if,
R from a certain distance, the TAU trend is inverted even though the
R distance separating the two aircraft decreases. For example, in the
R case of two aircraft moving on parallel axes but in the opposite
R direction.
R (Ref. Fig. 020, 021)
R The curve represents the TAU variation before the closest point of
R approach.
R (Ref. Fig. 021)
R This time decreases as the range decreases, reaches a minimum when
R the intruder's relative bearing is 45 deg. and then increases
R rapidly. If the time corresponding to a predetermined threshold has
R not been reached before the minimum TAU value, a trajectory
R correction is not initiated.
R Certain conditions exist, however, in which this formula may prove
R insufficient. This may arise for example when two aircraft fly in the
R same direction with a very low closure rate. In this case, the
R range/range rate ratio gives a high TAU value whereas in fact, the
R two aircraft could be very near.
R The TCAS uses a slightly different formula to preclude this
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