Magnetic Compass Errors
Turning errors, acceleration and deceleration errors, dip and hemisphere behaviour, variation versus deviation.
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The magnetic compass is accurate only in straight, steady, wings-level flight. Its card is a float hanging below a pivot: when you bank or change speed it tilts, and the downward-dipping part of the Earth's field pulls it round. Press Start turn and compare the compass with the heading indicator: turning away from north the compass first shows a turn the OTHER way (it lags); near south it runs ahead (it leads). Roll out to see both agree again.
That is why you undershoot north and overshoot south when you turn by the compass (UNOS), by roughly the latitude in a 15–18° bank (IFH ch. 7: lead north by the latitude plus your normal roll-out lead, pass south by the latitude minus it). On east or west headings speed changes swing the card instead: Accelerate → North, Decelerate → South (ANDS). The error grows toward the magnetic poles and reverses in the southern magnetic hemisphere, where the dip points up — try Sydney, or Singapore, which is north of the equator but already south of the magnetic equator.
Practice covers the heading indicator: turn at 15° bank, press Roll out when the compass shows the reading you choose, and the result is judged from the heading you actually end on. Variation and deviation, the corrections that apply even in steady flight, are in True / Magnetic / Compass Heading.
Assumption: a simplified physical model — the card settles instantly perpendicular to the apparent vertical (gravity plus the reaction to the aircraft's acceleration) and its magnets follow the part of the Earth's field in the card plane; no fluid swirl, card inertia, oscillation or deviation, and no limit on the tilt (a real float tilts only about 18°; beyond that the page warns). Dip comes from a centred-dipole model of latitude unless a WMM2025 airport or a hand-set value is chosen. The FAA rules of thumb are shown beside the model; they differ from each other and from the model. Roll-out: the bank and turn rate decrease linearly, carrying the heading on by half the bank. Practice pass mark ±5° and the score are platform conventions.
Compass reading: the field (cos I north, sin I down) is expressed in the card's axes after the card is rolled by the bank (coordinated turn: the apparent vertical is the aircraft's normal axis) or tilted by atan(a/g) with its aft end up (acceleration a along the flight path); the reading is the direction of the field's in-plane component relative to the lubber line: reading = atan2(sin ψ cos φ − tan I sin φ, cos ψ) in a turn and atan2(sin ψ, cos ψ cos θ + tan I sin θ) with θ = atan(a/g) when accelerating. Checked against an independent vector-projection construction. Turn rate = g·tan(bank)/V (as in the IFR Trainer).
Dip: centred axial dipole, tan I = 2 tan(latitude) — a model; or WMM2025 (NOAA NCEI / BGS) evaluated at sample airports for 2026.8 at sea level. The model is too low over the contiguous US (Washington: 58.2° model vs 64.7° WMM2025) and slightly high at Anchorage.
Rules of thumb, quoted as rules: IFH FAA-H-8083-15B ch. 7 “Compass Turns” p. 7-22 (lead or lag ≈ latitude at 15–18° bank; example at 30°: roll out at 037 / 203 from the east, 323 / 157 from the west; east or west: 10–12° early from northerly headings, 5° from southerly ones; others interpolated); PHAK FAA-H-8083-25C ch. 8 p. 8-26 (stop the turn 15° plus half the latitude before north and after south). The FAA texts describe the northern hemisphere; their mirror for the south is a derivation from the dip direction (PHAK: the dip points up toward the magnetic South Pole). Other sources: PHAK ch. 8 pp. 8-23 to 8-27 (card, 18° tilt, variation, deviation, dip, ANDS, oscillation, lags or leads); IFH ch. 5 pp. 5-11 to 5-14.
- FAA Pilot’s Handbook of Aeronautical Knowledge, FAA-H-8083-25C (2023), ch. 8 Flight Instruments, Magnetic Compass pp. 8-23 to 8-27: card and lubber line (card read from behind), float tilt about 18° (erratic beyond), variation, deviation, dip errors (dip down toward the magnetic North Pole, up toward the South Pole), northerly and southerly turning errors with the rule of thumb 15° plus half the latitude, acceleration error ANDS, oscillation, lags or leads
- FAA Instrument Flying Handbook, FAA-H-8083-15B (2012), ch. 5 Flight Instruments pp. 5-11 to 5-14 (compass construction, errors, ANDS) and ch. 7 Airplane Basic Flight Maneuvers, Compass Turns p. 7-22 (points 1-5; lead or lag about the latitude at 15-18° bank; worked example at 30° latitude: 037 / 203 / 323 / 157; east / west 10-12° and 5°)
- World Magnetic Model WMM2025 (NOAA NCEI / British Geological Survey) - dip at sample airports for epoch 2026.8 at sea level (evaluator verified against the official WMM2025 test values)
- Model of this tool (stated on the page): a static tilted-card compass (a simplification, checked against an independent vector construction), a centred-dipole dip model, the IFH and PHAK rules shown as rules; the rate of turn as in the IFR Trainer