DME Slant Range Visualizer
Ground distance versus slant range with altitude and position controls.
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DME measures the straight line from the aircraft to the station — the slant range — not the distance over the ground. The side view draws the right triangle: height above the station (purple), horizontal distance (green) and the DME reading (amber). Drag the aircraft up, down, in or out and watch the three sides; the coral bar on the ground is the error you make if you treat the DME reading as a horizontal distance.
The error is large only when you are high and close. The IFH rule: it is negligible when you are at least 1 NM from the station for every 1,000 ft above it — at the boundary it is about 1.3 % of the reading. Over the station the DME cannot go to zero: it shows your height in NM (6,076 ft ≈ 1.0 NM). Press Fly over to watch the reading flatten out at that value while the DME groundspeed drops to zero.
Switch to “DME reading → position” to go the other way: enter what the DME shows and the height above the station gives the horizontal distance. A reading shorter than the height is impossible and is rejected. The plan view shows both circles: green where you are, amber dashed where you would plot yourself from the raw reading.
Assumption: flat earth and straight-line propagation (no Earth curvature or refraction, negligible at these distances); the DME reading is exact (the AIM accuracy figure — ½ NM or 3 % — is shown for comparison, not added); height = altitude MSL − station elevation; the DME groundspeed shown is the rate of change of the slant range with no receiver averaging. The IFH rule is applied to the horizontal distance.
Slant range = √(horizontal² + height²) with the height in NM (÷ 6,076.12 ft). The reading is the slant range of the IFR Trainer’s receiver; the inverse uses its DME-fix method (horizontal = √(DME² − height²), rejected when the DME is shorter than the height). Error = slant − horizontal, also as a percentage of the reading; at the IFH boundary (horizontal = height in thousands of feet, in NM) the ratio is constant: 1 − 1/√(1 + (1,000/6,076.12)²) ≈ 1.33 %.
DME groundspeed while flying over = groundspeed × (component of the position along the track) ÷ slant range: low close to the station, 0 overhead (PHAK ch. 16: groundspeed and time-to-station are accurate only when tracking directly to or from the station, and the receiver needs stabilised flight). Time to station = DME ÷ DME groundspeed.
AIM 1-1-7 b: “Distance information received from DME equipment is SLANT RANGE distance and not actual horizontal distance”; accuracy “better than 1/2 mile or 3 percent of the distance, whichever is greater”. IFH ch. 9 “DME Errors”: “Slant range error is negligible if the aircraft is one mile or more from the ground facility for each 1,000 feet of altitude above the elevation of the facility”; close in “the DME receiver displays altitude (in NM) above the facility”. The same IFH paragraph says that at 3,000 ft and 0.5 NM the DME “would read 0.6 NM”; the geometry gives 0.70 NM — the page shows the computed value (scenario 2) and records the discrepancy. The 1 NM per 1,000 ft rule is IFH text, not AIM text (AIM 1-1-7 states only that DME is slant range).
- FAA Aeronautical Information Manual, para. 1-1-7 b Distance Measuring Equipment (faa.gov HTML, read 2026-10-14): DME is SLANT RANGE distance, not horizontal; accuracy better than 1/2 NM or 3 % of the distance, whichever is greater; reliable to 199 NM at line-of-sight altitude
- FAA Instrument Flying Handbook, FAA-H-8083-15B (2012), ch. 9 Navigation Systems, "DME Errors" p. 9-19: slant range error negligible at one mile or more from the facility per 1,000 ft above its elevation; overhead the DME displays the height in NM (the printed 3,000 ft / 0.5 NM -> 0.6 NM example is inconsistent with the geometry, 0.70 NM - recorded)
- FAA Pilot’s Handbook of Aeronautical Knowledge, FAA-H-8083-25C (2023), ch. 16 Navigation, Distance Measuring Equipment p. 16-27/28: station passage over a VORTAC at 6,076 ft AGL shows about 1.0 NM; groundspeed and time-to-station accurate only when tracking directly to or from the station
- Cross-tool: the slant range and the DME-fix method of the IFR Trainer’s VOR module, unchanged