# Radio Navigation Aids > Use when you must compute the radio navigation geometry of conventional navaids for the aircraft navigation solution: derive the VOR radial and the bearing from the aircraft to the station from the planar station and aircraft coordinates, compute the DME slant range from the ground distance and the aircraft altitude, compute the ILS localizer deviation angle from the lateral offset and the distance to the runway threshold, and compute the ILS glideslope deviation from the height above the threshold and the distance to the threshold against the nominal glideslope angle. Produces the VOR bearing and radial, the slant range, and the localizer and glideslope deviation angles that gate radio navigation geometry checks. Trigger: VOR radial, DME slant range, ILS localizer deviation, glideslope deviation, radio navigation geometry, bearing to the navaid station, approach course offset. - Skill: `ashfordeou/radio-navigation-aids` (Agent Skill, multi-file: 3 files) - Install (CLI): `npx skillmds@latest add ashfordeou/radio-navigation-aids` - Raw SKILL.md: https://api.skillmd.com/api/skills/ashfordeou/radio-navigation-aids/raw - Safety review: pending - Works with: Claude Code, Claude.ai, OpenAI Codex - Category: Coding & Dev Tools - License: Apache-2.0 - Author: ashfordeOU (https://skillmd.com/u/ashfordeou) - Updated: 2026-09-17 - Page: https://skillmd.com/skills/ashfordeou/radio-navigation-aids --- # Radio Navigation Aids (avionics/flight-management/radio-navigation-aids) Use when the task is the receiver level geometry of conventional radio navigation aids for the aircraft navigation solution: turning the planar station and aircraft coordinates into the VOR bearing and reciprocal radial, the DME slant range that the distance measuring equipment reports, and the ILS localizer and glideslope deviation angles that the approach receivers display against the runway centerline and the nominal glidepath. This leaf implements that geometry in pure Python, stdlib only, on the local tangent plane with x east, y north and z up. It pairs with the sibling lateral-navigation leaf, the FMS downstream consumer of the nav geometry, with flight-planning for the route context, and with the gnc navigation leaf that owns the position fix feeding the coordinates. ## Domain quick reference - Coordinate convention: local tangent plane, x east (m), y north (m), z up (m). The VOR/DME station sits at the origin; the aircraft is at (x_ac, y_ac, altitude_m). Planar geometry is a documented simplification for short ranges; great-circle corrections are out of scope. - Bearing from the station to the aircraft, clockwise from north: bearing = deg(atan2(x_ac, y_ac)) normalized to [0, 360). Due east gives 90 deg, due north 0 deg. - VOR radial FROM the station: radial = (bearing + 180) mod 360, the reciprocal of the bearing the aircraft flies toward the station. - DME slant range: d = sqrt(x_ac^2 + y_ac^2 + altitude_m^2). The DME measures the straight line from the station at ground level to the aircraft at altitude, so the slant range always exceeds the ground distance once the altitude is above zero. - Localizer deviation: dev_loc = deg(atan(lateral_offset_m / distance_to_threshold_m)), positive when the aircraft is right of the localizer centerline (lateral offset to the right of the approach course is positive). - Glideslope deviation: actual = deg(atan(height_agl_m / distance_to_threshold_m)); dev_gs = actual - gs_angle_deg, with the nominal glideslope default 3.0 deg and the deviation positive above the glidepath. - Units are SI throughout: m, deg. - DO-178C frames the software context of the nav receivers; the relations above are standard planar trigonometry, summary-only. ## Workflow 1. Take the aircraft position (x_ac, y_ac, altitude_m) in the local tangent frame with the VOR/DME station at the origin; flight- planning and the gnc position fix leaves provide the coordinates. 2. Get the bearing from the station with bearing_deg and the radial FROM the station with radial_deg of that bearing. 3. Get the DME answer with dme_slant_range_m; compare it against the ground distance to confirm the altitude contribution. 4. For the ILS localizer, feed the lateral offset and the distance to the runway threshold to loc_deviation_deg; a positive result means the aircraft is right of the centerline. 5. For the glideslope, feed the height above the threshold, the distance to the threshold and the nominal path angle to gs_deviation_deg; positive means above the glidepath. 6. For a full solution call analyze once with all inputs and read the dict of bearing, radial, slant range and both deviation angles. 7. Confirm the deterministic checks with the contract test scripts/test_radio_navigation_aids.py. ## Worked example Aircraft 10 km east and 17.32 km north of the VOR/DME at 1000 m. - Bearing: atan2(10000, 17320) = 30.0007 deg, within 0.01 of 30.0 deg. - Radial: 30.0007 + 180 = 210.0007 deg, within 0.01 of 210.0 deg. - Slant range: sqrt(1e8 + 2.999824e8 + 1e6) = sqrt(4.009824e8) = 20024.5 m, within 1.0 m. The summary figure 20022.5 m in the wave-27 spec came from rounding 17320^2 to 2.999e8 before summing; the exact value for the stated inputs is 20024.5 m (recorded assumption). - Localizer: aircraft 100 m right of the centerline at 5000 m to the threshold gives dev = atan(100 / 5000) = 1.1458 deg. - Glideslope against the 3 deg path at 5724 m to the threshold: at 300 m height the actual angle is 3.0002 deg and the deviation 0.0002 deg; at 400 m the actual is 3.9974 deg and the deviation 0.9974 deg, about 1 deg high. ## Verification - Confirm bearing_deg(10000, 17320) is within 0.01 of 30.0 deg and radial_deg of it within 0.01 of 210.0 deg. - Confirm dme_slant_range_m(10000, 17320, 1000) returns 20024.5 m and that a 3-4-5 triangle at zero altitude returns 5000.0 m exactly. - Confirm loc_deviation_deg(100, 5000) returns 1.1458 deg and the zero-offset case returns 0.0 deg. - Confirm gs_deviation_deg(300, 5724) is within 0.001 of 0.0002 deg, gs_deviation_deg(400, 5724) within 0.01 of 0.9974 deg, and the height on the nominal path returns near-zero deviation. - Confirm the radial round trip: radial_deg applied twice returns the original bearing. - Confirm ValueError rejection of negative altitude, non-positive distance to threshold, glideslope angle outside (0, 90) deg, negative height above ground, and non-finite inputs. - Run the contract test offline: python3 scripts/test_radio_navigation_aids.py (38 tests, deterministic). ## Related leaves - avionics/flight-management/lateral-navigation: the FMS lateral guidance downstream of this nav geometry. - avionics/flight-management/flight-planning: the route and leg context for the navaid geometry checks. - avionics/flight-management/vertical-navigation: the FMS vertical profile that the glideslope intercept supports. - gnc-autonomy/navigation/gnss-pseudorange-positioning: the position fix boundary feeding the aircraft coordinates. ## Pitfalls - Confusing the bearing with the radial: bearing_deg is the direction FROM the station to the aircraft, while the VOR radial is the reciprocal (bearing + 180) mod 360 - a 030 bearing from the station puts the aircraft on the 210 radial, and applying radial_deg twice returns the original bearing. - Using ground distance for the DME readout: the DME measures the slant range sqrt(x^2 + y^2 + altitude^2), which always exceeds the ground distance once the altitude is above zero (20024.5 m versus 20000.0 m at 1000 m over the worked example) - altitude is not a second-order term in the DME answer. - Reversing the deviation signs: localizer deviation is positive when the aircraft is RIGHT of the centerline and glideslope deviation is positive ABOVE the path - an aircraft below the glidepath carries a negative deviation and must correct up, not down. - Comparing height to the path instead of angle: gs_deviation_deg computes the actual angle atan(height / distance) and subtracts the nominal 3.0 deg path, so 300 m at 5724 m is on-path (0.0002 deg) while 400 m is about 1 deg high - a fixed height error shrinks as the aircraft nears the threshold. - Applying the planar model at long range: the local tangent plane with x east / y north is a documented simplification for short ranges and great-circle corrections are out of scope - do not stretch these station-local formulas across oceanic distances. - Feeding non-physical geometry: negative altitude, non-positive distance to the threshold, glideslope angle outside (0, 90) deg, negative height above ground, and non-finite inputs raise ValueError in every entry point. ## Behavior contract (gate 3) Run the deterministic contract test (stdlib unittest, offline): python3 scripts/test_radio_navigation_aids.py The test covers the worked-example contract (bearing 30 deg, radial 210 deg, slant range 20024.5 m, localizer deviation 1.1458 deg, glideslope deviations 0.0002 deg and 0.9974 deg), the cardinal bearings and the [0, 360) normalization, the radial reciprocal round trip, the DME slant versus ground distance behavior, zero and symmetric deviation cases, and ValueError rejection of negative altitude, non-positive distance, out-of-range glideslope angle, negative height and non-finite inputs. ## Compliance - Standards referenced, not reproduced: DO-178C frames the software life cycle of the nav receivers; the planar geometry above is standard engineering methodology, summary-only per standards-map. - compliance: STANDARDS-REF, gated: false.