Plain English Meaning
DME tells you how far you are from a ground station in a straight line, but what you usually want to know is how far you are along the ground. When you are high up and near the station, those two distances are noticeably different, and that difference is the slant-range error.
Full Definition
The discrepancy between the distance shown by DME (Distance Measuring Equipment) and the actual horizontal distance to the station, caused by DME measuring the straight-line distance from the aircraft to the ground station rather than the distance along the ground. The error is greatest when the aircraft is high and close to the station, and smallest when the aircraft is far from the station relative to its altitude.
Context Anchor
Seen when using DME distance close to a station, especially when flying at higher altitudes.
Derivation
‘Slant’ comes from the Middle English ‘slenten,’ meaning to slope or angle. ‘’ here means distance. Together, ‘’ describes a distance measured along a sloped line — from the aircraft down to the station — rather than along the ground. Once you picture the slope, the error becomes obvious.