geoprimsField-grade geospatial math

Holding pattern entry

Which holding entry to fly (direct, teardrop, or parallel) from your heading to the fix, the inbound course, and the turn direction, per AIM 5-3-8, with the headings for each entry.

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

direct

Fly a direct entry. Cross the fix and turn right to the outbound course, 180°.

Arrival angle
Outbound course
Teardrop outbound heading
Parallel outbound heading
What to do
Provenance
Computed by
aviation.ifr.hold-entry 1.1.0, core 0.1.0
Model
AIM 5-3-8 sectors relative to the inbound course, split by the 70° line on the holding side: direct 180°, teardrop 70°, parallel 110°; mirrored for left turns; within 5° of a boundary either entry is acceptable (ICAO PANS-OPS and TC AIM zone of flexibility)
Accuracy
Exact sector geometry, using your heading as you reach the fix. ATC instructions and the published procedure govern.
Notes
None
Cites
Federal Aviation Administration, Aeronautical Information Manual; Federal Aviation Administration, Instrument Flying Handbook, FAA-H-8083-15B; International Civil Aviation Organization, Procedures for Air Navigation Services, Aircraft Operations (PANS-OPS), Doc 8168; Transport Canada, Transport Canada Aeronautical Information Manual (TC AIM), TP 14371E

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TeardropParallelDirectInbound 0°Arriving 90°Direct entry, right turns
How we got thisFormula, worked example, sources, and proof

Model: AIM 5-3-8 sectors relative to the inbound course, split by the 70° line on the holding side: direct 180°, teardrop 70°, parallel 110°; mirrored for left turns; within 5° of a boundary either entry is acceptable (ICAO PANS-OPS and TC AIM zone of flexibility)

Show your work

  1. Angle onto the inbound course

    the heading measured against the inbound course

    heading 090° against inbound 360° = 90°

  2. Sector

    the entry sector that angle falls in, measured toward the holding side, for a hold with turns to the right

    90° toward the holding side = direct

The same steps an agent gets from the MCP server with explain: true.

Accuracy: Exact sector geometry, using your heading as you reach the fix. ATC instructions and the published procedure govern.

When to use this: Use this when you are cleared to hold, or a hold is published at your clearance limit, and you want to know before you reach the fix which entry to fly: direct, teardrop, or parallel. Give the inbound course, the turn direction, and your heading to the fix, and it names the entry, the headings to fly, and whether you are close enough to a sector line that the next entry is also fine.

Limitations: The sectors are read from your heading as you reach the fix. In a strong crosswind your heading and your track differ, and the FAA draws the sectors by where you come from, so near a boundary work from the course you are flying to the fix. It does not know the holding fix type: at a VOR intersection or a DME fix, ICAO and Transport Canada limit the entry to the radials or arc that form the fix. It says nothing about wind correction or timing on the legs, the maximum holding speed, or an RNAV system that flies the entry for you with a fly-by turn. ATC instructions and the published procedure come first.

Worked example: Inbound 360°, right turns, arriving on heading 090°. Source: AIM 5-3-8 FIG 5-3-4: an arrival 90° right of the inbound course is in the direct sector.

You enter

Heading to the fix
90 deg
Inbound course
360 deg

You get

Entry
direct
Arrival angle
90°
Outbound course
180°
Teardrop outbound heading
150°
Parallel outbound heading
180°
What to do
Cross the fix and turn right to the outbound course, 180°.

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 1.1.0, core 0.1.0. See this tool in the verification report.

Changes

Checked against: 35 golden test vectors (download the test vectors, each with its source and tolerance). See how results are checked and every source.

Sources