Tcas Resolution Advisory

TCAS II Resolution Advisory (avionics/surveillance/tcas-resolution-advisory)

Use when the task is evaluating a TCAS II traffic alert and collision avoidance resolution advisory for an own aircraft against one intruder, starting from already-measured range, range rate and altitude state: pick the sensitivity level from the own altitude band, compute the modified tau closing-time metric with the distance-modified DMOD term, apply the horizontal threat test and the altitude test, and choose the climb or descend RA sense. This leaf is the first of the avionics/surveillance pack, which frames airborne surveillance logic; future siblings may add ADS-B or transponder functions. It pairs with avionics/flight-management/rnp-anp-containment for separation assurance in the flight management system, avionics/flight-management/lateral-navigation for the route guidance an RA overrides, and avionics/flight-management/radio-navigation-aids for the navaid sensors.

The boundary matters: this leaf is the threat and sense logic on measured state, not the transponder waveform, not the FMS route, not a datalink transport. The MOPS parameters below are paraphrased DO-185B summary values, never a reproduction of the proprietary tables. Pure Python stdlib, deterministic and offline. Units follow the avionics standard: range in nautical miles, range rate in nautical miles per second, altitude in feet, closing speed in knots, time in seconds.

Domain quick reference

• Sensitivity level selection: the own altitude band index, lower bound inclusive and upper bound exclusive, with boundaries at 1000, 2350, 5000, 10000 and 20000 ft selecting sensitivity levels 2 through 7 above sea level. Level 1 exists only as an inhibited low-altitude state below the model; the table used here starts at level 2.
• Per-level thresholds (paraphrased values, exact numbers live in the SENSITIVITY_TABLE module constant in the logic file): tau (the horizontal tau threshold) grows from 20 s at level 2 to 48 s at level 7, DMOD grows from 0.30 to 1.10 nmi, and ALIM (the altitude test limit) grows from 300 to 600 ft.
• Modified tau: tau_mod = -(range^2 - DMOD^2) / (range * range_rate), where range is in nmi and range_rate is negative for a closing encounter. When the range already lies at or inside the DMOD cylinder the modified tau collapses to 0.0 and the encounter is an immediate horizontal threat. The DMOD term removes the singularity at small range, so tau_mod stays finite down to the cylinder.
• Horizontal threat test: tau_mod <= tau for the active sensitivity level, a closing-time check that keeps long, slow encounters out of the advisory.
• Altitude test: the vertical separation |dh| between the intruder and the own aircraft must stay within ALIM for the advisory to fire.
• RA sense: descend when the intruder sits above the own aircraft and climb when it sits at or below it, so the advisory always moves the own aircraft away from the intruder. A tie at equal altitude resolves to climb.
• Threat verdict: a closing encounter that passes the horizontal test and the altitude test is a threat; otherwise the verdict carries the failing gate as the reason, "tau-exceeded" or "altitude-exceeded", and a non-closing encounter reports "not-closing" with no modified tau.

Workflow

1. Fix the encounter state: range in nmi, closing range rate in nmi/s (negative when closing), own altitude in ft, intruder altitude in ft. Convert a closing speed in knots to nmi/s by dividing by 3600 before calling the functions.
2. Select the sensitivity level with sensitivity_level(own_altitude_ft); the returned level keys the SENSITIVITY_TABLE thresholds (tau, DMOD, ALIM).
3. For a closing encounter, compute the modified tau with modified_tau(range_nmi, range_rate_nmi_s, dmod_nmi). A range at or inside DMOD returns 0.0, which is an immediate horizontal threat.
4. Run threat_verdict(range_nmi, range_rate_nmi_s, own_altitude_ft, intruder_altitude_ft) for the full verdict dict: sensitivity level, tau threshold, DMOD, ALIM, modified tau, the threat flag and either the sense or the reason. Non-closing encounters are gated here before the modified tau is called.
5. Read the sense with ra_sense(intruder_altitude_ft, own_altitude_ft), or take the whole chain from evaluate_encounter(range_nmi, range_rate_nmi_s, own_altitude_ft, intruder_altitude_ft), which returns sensitivity_level, modified_tau, threat, the reason or the sense, the resolution_advisory ("climb", "descend" or "none") and the active parameters.
6. Confirm the deterministic checks with the contract test scripts/test_tcas_resolution_advisory.py.

Worked example

Own aircraft at 8000 ft, which selects sensitivity level 5 (tau 40 s, DMOD 0.75 nmi, ALIM 350 ft), closing at 300 kt (range rate -0.08333 nmi/s).

• Case 1: range 3.0 nmi, intruder at 8200 ft (200 ft above). Modified tau: -(9 - 0.5625) / (3 * -0.08333) = 33.75 s, within the 40 s tau gate, and |dh| 200 ft within ALIM 350 ft: threat True, sense "descend", resolution_advisory "descend".
• Case 2: range 8.0 nmi, intruder at 8200 ft. Modified tau 95.16 s exceeds 40 s: threat False with reason "tau-exceeded" and resolution_advisory "none"; the closing time is still too long for an advisory.
• Case 3: range 2.0 nmi, intruder at 7800 ft (200 ft below). Modified tau 20.63 s passes the tau gate: threat True, sense "climb".
• Case 4 (high altitude): own aircraft at 30000 ft (sensitivity level 7, tau 48 s, DMOD 1.10 nmi, ALIM 600 ft), range 5.0 nmi closing at 180 kt (range rate -0.05 nmi/s), intruder 500 ft below. Modified tau 95.16 s exceeds 48 s: threat False with reason "tau-exceeded" even though the 500 ft separation sits inside ALIM 600 ft. The tau gate protects the own aircraft at long range.
• Case 5: own aircraft at 5000 ft (level 5), range 1.0 nmi closing at 300 kt, intruder 100 ft above. The range hugs the DMOD influence, modified tau 5.25 s passes the tau gate: threat True, sense "descend".
• ValueErrors: a negative altitude, a non-positive range or DMOD, and a non-negative range rate passed directly to modified_tau all raise ValueError; evaluate_encounter propagates them unchanged.

Verification

• sensitivity_level(8000) returns 5, sensitivity_level(500) returns 2 and sensitivity_level(30000) returns 7.
• The band edges sit at 999/1000, 2349/2350, 4999/5000, 9999/10000 and 19999/20000 ft, with the upper boundary belonging to the higher band.
• The five worked cases reproduce the anchors: modified tau 33.75, 95.16, 20.63, 95.16 and 5.25 s within 0.01 s, with the stated threat flags, reasons and senses.
• A non-closing or opening range rate produces reason "not-closing" with modified_tau None and never reaches the modified tau function.
• Range at or inside DMOD returns modified tau 0.0.
• Sense selection: intruder above gives descend, intruder below gives climb, and an equal-altitude tie resolves to climb.
• Every non-physical input raises ValueError: negative altitude, non-positive range, non-positive DMOD, non-negative range rate.
• Run the contract test offline: python3 scripts/test_tcas_resolution_advisory.py (31 tests, deterministic).

Related leaves

• avionics/flight-management/rnp-anp-containment: separation assurance against the RNP containment bound in the FMS context.
• avionics/flight-management/lateral-navigation: the route guidance a resolution advisory overrides during the maneuver.
• avionics/flight-management/radio-navigation-aids: VOR, DME and ILS geometry, the surveillance and navigation context around the TCAS logic.
• avionics/data-bus/arinc429-protocol: the data bus transport that can carry the measured state, distinct from the threat logic itself.

Pitfalls

• Flipping the range-rate sign: range rate is negative for a closing encounter and tau_mod = -(range^2 - DMOD^2) / (range * range_rate) needs that closing sign - a closing speed in knots must be divided by 3600 before calling, and a non-negative (opening) rate is the "not-closing" gate, which never reaches the modified tau function and raises ValueError if passed to it directly.
• Assigning the sensitivity band edges to the wrong side: each own altitude band is lower-inclusive and upper-exclusive (boundaries at 1000, 2350, 5000, 10000 and 20000 ft), so 8000 ft selects level 5 and 500 ft selects level 2 while the low-altitude level 1 is an inhibited state outside the model - a 1000 ft aircraft belongs to the level 3 band, not level 2.
• Dividing by range rate inside the DMOD cylinder: once the range sits at or inside DMOD the modified tau collapses to 0.0 and the encounter is an immediate horizontal threat - the DMOD term exists to remove the small-range singularity, so never evaluate the raw quotient inside the cylinder.
• Reading a False threat as a clean bill: the verdict always carries the failing gate, "tau-exceeded" or "altitude-exceeded", and a closing encounter that fails the tau test can still sit inside ALIM - case 4's 95.16 s against the 48 s tau at level 7 fails even with 500 ft of vertical separation inside the 600 ft ALIM, and long, slow encounters are exactly what the tau gate is for.
• Reversing the advisory sense: the own aircraft descends when the intruder sits above it and climbs when the intruder is at or below it (equal altitude resolves to climb) - the sense always moves the own aircraft away from the intruder, so swapping the comparison commands a climb into a higher intruder.
• Using one threshold set for every altitude: tau (20 to 48 s), DMOD (0.30 to 1.10 nmi) and ALIM (300 to 600 ft) grow with the sensitivity level selected from own altitude - level 5 at 8000 ft runs tau 40 s, DMOD 0.75 nmi, ALIM 350 ft, and the values in SENSITIVITY_TABLE are paraphrased teaching values, never the MOPS tables of rtca-do-185b.

Behavior contract (gate 3)

Run the deterministic contract test (stdlib unittest, offline):

python3 scripts/test_tcas_resolution_advisory.py

The test covers the sensitivity level band edges and worked anchors, the five spec cases with their modified tau values, threat verdicts and climb or descend senses, the not-closing gate, the tau-exceeded versus altitude-exceeded reasons, sense selection in both directions with ties to climb, the full evaluate_encounter chain with its parameters dict, and ValueError rejection of negative altitude, non-positive range and DMOD, and non-closing range rate.

Compliance

• RTCA DO-185B (Minimum Operational Performance Standards for TCAS II Airborne Equipment, EUROCAE twin ED-143) is referenced, not reproduced: it is a proprietary RTCA document, and the sensitivity level parameters shown here are paraphrased summary values for teaching, never the MOPS tables. The modified tau and threat test relations are the standard engineering method in summary form.
• compliance: STANDARDS-REF, gated: false.