geoprimsField-grade geospatial math

DME arc lead points

Where to start the turn onto a arc from a radial, and how many radials early to turn off the arc onto an inbound course, from the arc's DME and your standard-rate turn.

Planning and education aid. Not for primary navigation. Full disclaimer

Experimental: not yet fully verified. How results are checked

0.64NM

Turn onto the arc 0.64 NM before it, and off it 3.9° before the inbound course.

Lead onto the arc
Lead off the arc
Lead by the rule
Provenance
Computed by
aviation.ifr.dme-arc-lead 1.0.0, core 0.1.0
Model
A standard-rate turn (3°/s) at groundspeed GS has radius GS ÷ (60π) NM. Turning 90° from a radial onto the arc, start one turn radius r short of the arc. Turning 90° from the arc onto an inbound radial, the turn circle sits inside the arc, tangent to it and to the radial, so the lead is asin(r ÷ (R − r)); the rule of thumb is 60 × r ÷ R radials (Instrument Flying Handbook, ch. 9)
Accuracy
Exact for a steady turn in still air; wind moves the lead points
Notes
1 shown with the answer
Cites
Federal Aviation Administration, Instrument Flying Handbook, FAA-H-8083-15B

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How we got thisFormula, worked example, sources, and proof

Model: A standard-rate turn (3°/s) at groundspeed GS has radius GS ÷ (60π) NM. Turning 90° from a radial onto the arc, start one turn radius r short of the arc. Turning 90° from the arc onto an inbound radial, the turn circle sits inside the arc, tangent to it and to the radial, so the lead is asin(r ÷ (R − r)); the rule of thumb is 60 × r ÷ R radials (Instrument Flying Handbook, ch. 9)

Accuracy: Exact for a steady turn in still air; wind moves the lead points

Worked example: A 10 DME arc at 120 kt. Source: Hand check: radius 120 ÷ (60π) = 0.64 NM; lead asin(0.64 ÷ 9.36) = 3.9°, rule 3.8°. It is golden test vector v001, and every build checks the tool still gives its answer within its tolerance.

You enter

Arc
10 NM
Groundspeed
120 kt

You get

Turn radius
0.64 NM
Lead onto the arc
0.64 NM
Lead off the arc
3.9°
Lead by the rule
3.8°

Review: Not yet independently reviewed by a flight instructor (CFI).

Last verified: 2026-09-18, when a maintainer last confirmed this tool's sources at the issuer. See the sources ledger.

Status: version 1.0.0, core 0.1.0. See this tool in the verification report.

Checked against: 7 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources

Terms

DME: distance measuring equipment
A radio aid that shows the straight-line distance from the aircraft to a ground station, in nautical miles. Up high and close in, that slant distance is longer than the distance over the ground. Source: Instrument Flying Handbook

Experimental means this tool has not yet met the stable bar: at least 20 golden vectors, differential tests, and an independent worked example.

DME — distance measuring equipment

A radio aid that shows the straight-line distance from the aircraft to a ground station, in nautical miles. Up high and close in, that slant distance is longer than the distance over the ground.

Source: Instrument Flying Handbook