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Altitude DMOD (ft) (NM) 0-1000
1000-2350 0.20 2350-5000 0.35 5000-10000 0.55
10000-20000 0.80 more than 20000 1.1
R **ON A/C 106-149, 201-209, 211-299, 301-399, 401-499,
(2) Time to intercept (TAU) The TCAS does not need to locate the CPA in space, but rather it needs to know the time to intercept for two aircraft. For example, if two aircraft are approaching on the same axis on a collision course, this time is the ratio of distance between them to the sum of their speeds.
D
T = ---------
V1 + V2
More generally, the TCAS uses range and range rate measurement to
compute this time:
RANGE R(NM) TAU = ------------ i.e. TAU(s) = 3600 --------
RANGE RATE RR (Kts) With the risk of collision being in inverse proportion to this time, trajectory correction orders are initiated by crossing predetermined time thresholds whose values depend on the altitude layer in which the aircraft is located. 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 will not be 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
R 1EFF : 051-099, 106-149, 201-209, 211-299, 1 34-43-00Page 73 1301-399, 401-499, 1Aug 01/05 1 1 1CES 1
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 1000-2350ft, to 1.1 NM above 20,000 ft as shown below:
Altitude DMOD
(ft) (NM)
0-1000
1000-2350 0.20
2350-5000 0.35
5000-10000 0.55
10000-20000 0.80
more than 20000 1.10
**ON A/C 201-207, 210-210,
Post SB 34-1179 For A/C 201-207,
Post SB 34-1238 For A/C 201-207,
(2) Time to intercept (TAU)
The TCAS does not need to locate the CPA in space, but rather it needs to know the time to intercept for two aircraft. For example, if two aircraft are approaching on the same axis on a collision course, this time is the ratio of distance between them to the sum of their speeds.
D T = ---------
V1 + V2 More generally, the TCAS uses range and range rate measurement to compute this time:
RANGE R(NM) TAU = ------------ i.e. TAU(s) = 3600 --------
RANGE RATE RR (Kts) With the risk of collision being in inverse proportion to this time, trajectory correction orders are initiated by crossing predetermined time thresholds whose values depend on the altitude layer in which the aircraft is located. 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
R 1EFF : 106-149, 201-299, 301-399, 401-499, 1 34-43-00Page 74 1 1 Aug 01/05 1 1 1CES 1 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 will not be 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:
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