DME arc distance
A DME arc keeps the aircraft at approximately a constant slant-range distance from a DME facility while the bearing to the station changes. The path is part of a circle, so arc distance depends on both the radius and the number of degrees flown around that circle.
Arc length formula
Arc distance = radius × angle in radians. Because pilots normally think in degrees, convert degrees to radians by multiplying degrees by π ÷ 180.
60° along a 10 DME arc
For a 10 DME arc covering 60 degrees, the distance is 10 × (60 × π ÷ 180), which is about 10.47 NM. A larger arc angle or larger radius creates a longer path.
A full circle check
A 360-degree arc at 10 NM radius would be the circumference of the circle: 2 × π × 10, or about 62.8 NM. A 90-degree arc is one quarter of that distance.
DME shows slant range
DME measures line-of-sight slant range rather than pure horizontal ground distance. Close to the station and high above it, the difference can be noticeable. The simple arc-length calculation treats the stated radius geometrically.
Arc distance is not the same as radial change
Changing from one radial to another tells you the angle swept around the station. The distance flown depends on the radius at which that angle is flown.
Procedure use
When a DME arc is part of an instrument procedure, the published procedure and current navigation data control. The formula is a training aid for understanding geometry, not a substitute for procedure guidance.
Related PilotDesk tools
Reciprocal heading · Great-circle distance · Holding leg distance