FAA Instrument Rating Airplane (IRA)Navigation SystemsMedium
An aircraft's DME indicates a slant-range distance of 5.0 NM from a VOR/DME station while the aircraft is flying at 30,000 feet MSL directly over terrain at the station's elevation (sea level). What is the approximate actual horizontal (ground) distance from the station?
- A3.0 NM
- B5.0 NM
- C0.8 NM
- D4.9 NM
Show answer & explanationAnswer & explanation
Correct answer: C. 0.8 NM
Convert altitude to NM: 30,000 ft ÷ 6,076 ft/NM ≈ 4.94 NM. Using the slant-range formula, ground distance = √(slant²−altitude²) = √(5.0²−4.94²) = √(25−24.4) = √0.6 ≈ 0.8 NM. This illustrates that DME slant-range error is greatest when the aircraft is close to the station at high altitude.
Why the other options are wrong
- A. 3.0 NM does not match the geometry of the given altitude and slant range.
- B. 5.0 NM ignores the significant slant-range error at this altitude/distance combination.
- D. 4.9 NM would only be correct if altitude were negligible relative to distance.
DME Slant-Range Error
DME measures line-of-sight (slant-range) distance, not true ground distance; the error is greatest when close to the station at high altitude and negligible at greater distances.
- Slant range² = ground distance² + altitude²
- Error is most significant when near the station at high altitude
- Error becomes negligible beyond about 5–10 NM at typical altitudes
Memory trick: 'Close and high means DME lies.'