An aircraft is flying directly toward a VOR/DME station and is currently 5,280 feet (1 NM) above the station's elevation. The DME readout indicates 3.16 NM. Approximately how far is the aircraft from the point on the ground directly below it to the station (ground track distance)?
- A3.16 NM
- B3.0 NM
- C1.0 NM
- D4.16 NM
Show answer & explanationAnswer & explanation
Correct answer: B. 3.0 NM
DME measures slant-range distance, the straight-line distance between the aircraft and the station, not actual ground distance. Using the Pythagorean theorem: slant range² = altitude² + ground distance², so 3.16² = 1² + ground distance², giving ground distance² = 10 − 1 = 9, so ground distance = 3.0 NM. This slant-range error becomes most significant at high altitudes and short distances from the station.
Why the other options are wrong
- A. 3.16 NM is the DME slant-range reading itself, not the corrected ground distance.
- C. 1.0 NM is the altitude component, not the ground distance.
- D. 4.16 NM incorrectly adds altitude and slant range rather than using the Pythagorean relationship.
DME Slant-Range Error
DME measures the direct line-of-sight (slant) distance to the station rather than the actual horizontal ground distance, causing a small overstatement of distance that is most significant when close to and high above the station.
- Slant range = √(altitude² + ground distance²)
- Error is negligible at typical en route distances
- Error becomes largest when directly over a high-altitude station
Memory trick: DME cuts the corner—it measures the diagonal, not the straight ground line