Magnetic Compass Errors: UNOS, ANDS, Variation and Deviation

The direct-reading magnetic compass is the only heading reference in a light aeroplane that needs no electrical power, no vacuum and no alignment — and it is also the only one that will lie to you at exactly the moment you most want to believe it. The magnetic compass errors examined here all trace back to a single fact: the Earth's magnetic field does not run horizontally. This article works through variation and deviation, then magnetic dip, then the two errors that dip produces — turning error and acceleration error — and it is careful about the part most student notes get wrong: which hemisphere the mnemonics apply in.

Three Norths, and the Two Angles Between Them

Before the dynamic errors make sense, the static bookkeeping has to be straight. There are three norths, and every navigation calculation moves between them — the conversion chain is Navigation-paper bread and butter, and how that paper divides from the rest is set out in EASA PPL theory exams explained. Strictly, only deviation is an error of the instrument: variation is a property of the Earth and would exist with no compass fitted at all. Both must be applied before the compass gives you a heading you can steer.

True north is geographic north, the direction of the meridian. Charts are drawn on it and the underlying survey is published against it. But almost everything published for the pilot to fly is magnetic: airway and ATS route tracks, VOR radials, ATC headings and runway designators are all in degrees magnetic. Runway 27 is a magnetic approach heading of 265–274° — the designator is the whole number nearest one tenth of the magnetic heading — which is exactly why a runway centreline makes a usable check on your compass. Only in designated high-latitude areas are published bearings referenced to true or grid north.

Magnetic north is the direction in which the horizontal component of the Earth's field points at your position — not a fixed spot you can stand on, but a local direction that drifts year on year and is deflected by the geology beneath you. Compass north is where your compass, in your aeroplane, on your heading, actually points: the only one you can read directly, and the least trustworthy.

The angle between true and magnetic north is variation. It is a property of where you are, not of your aeroplane. Charts show it with isogonals — lines of equal variation — and the line of zero variation is the agonic line, which swept across the British Isles around 2019 after decades in which UK variation had been several degrees west. Variation changes slowly and continuously — one concrete reason to fly current charts.

The angle between magnetic north and compass north is deviation. It is a property of your aeroplane, and it changes with heading, with what is switched on, and with what is stowed near the instrument.

Worked example, run as the whole chain. True track 090°. The wind gives 5° of drift to the right, so to make that track good the nose must point 5° to the left of it: true heading 085°. Variation 3°W: magnetic heading = 085 + 3 = 088°M. The deviation card shows 2°E on that heading, so steer 088 − 2 = 086°C.

The order is load-bearing, and it is where marks are lost: true track → apply drift → true heading → apply variation → magnetic heading → apply deviation → compass heading. Drift goes on before variation and deviation because a track is not something you can steer, and because the deviation card is entered with the heading you will actually fly.

The Compass Swing and the Deviation Card

An aeroplane is a flying collection of magnets. Hard iron is permanent magnetism retained by ferrous structure, engine mounts and welded joints. That field is fixed in the airframe and turns with it, so the deviation it causes still swings as a sine or cosine of heading — but it does not care where on Earth you are. Soft iron carries no field of its own; it is magnetised by the Earth's field, so its contribution changes with heading and with magnetic latitude, and reverses with hemisphere. That latitude dependence is the reason a large change of magnetic latitude invalidates a swing. On top of both sits the field from current in the electrical system.

A compass swing measures the resulting deviation on a series of known magnetic headings, removes what the correctors can, and records the rest. It is done on a magnetically clean site, aeroplane levelled in the flight attitude, engine running and electrical services on as they will be in flight — a swing with everything off certifies a configuration you will never fly in.

The measurements resolve into coefficients. Treat easterly deviation as positive and westerly as negative throughout, or the arithmetic is ambiguous:

• Coefficient A — constant on every heading, normally a misalignment between the lubber line and the fore-and-aft axis. It is the mean of all the deviations swung, and is corrected by rotating the instrument in its mounting.
• Coefficient B — varies with the sine of the heading, so it is largest on east and west and zero on north and south. Its permanent part comes from hard iron along the longitudinal axis. B = (dev 090 − dev 270) ÷ 2 — so with 3°E on 090 and 1°W on 270, B = (+3 − −1) ÷ 2 = +2, that is 2°E.
• Coefficient C — varies with the cosine of the heading, so it is largest on north and south and zero on east and west. Its permanent part comes from hard iron along the lateral axis. C = (dev 360 − dev 180) ÷ 2.

B and C each carry an induced contribution as well as a permanent one, which is the formal reason a swing is only good for the magnetic latitude it was flown at.

B and C are removed with corrector magnets, adjusted on the headings where each peaks. What cannot be removed goes on the deviation card beside the compass, usually in 30° steps, as “For 060, steer 062”. Certification puts a hard ceiling on what may be left: the classic CS-23 and FAR-23 requirement at 23.1327 is that the compensated installation must show no more than 10° of deviation in level flight on any heading, and the card must record a calibration made in level flight with the engines running, in steps of not more than 30°. Ten degrees is the limit, not the target — a properly swung light aeroplane shows a degree or two on most headings.

A swing is called for after work on the compass or nearby equipment, after a lightning strike, after carrying ferrous loads, after a large change of magnetic latitude — the induced part of the deviation has genuinely changed — whenever deviation is suspected, and at whatever interval the maintenance programme specifies, set by the programme and not by folklore.

Magnetic Dip: The Root of Both Magnetic Compass Errors

Dip is the reason the compass has dynamic errors at all, and how big they are is set by how far you are from the magnetic equator. The field lines emerge from the ground, arch over the planet and re-enter it, so a freely suspended magnet does not lie flat — it tips. The angle between the field and the horizontal is the dip, or inclination.

Dip is zero at the magnetic equator and increases towards the magnetic poles, where the field is vertical and a freely suspended magnet would stand on end. Across Europe it runs from roughly 50–55° over the southern Mediterranean, through the mid-60s over the UK, France and Germany, to the mid-70s and beyond in northern Scandinavia and Iceland. Everywhere in the EASA area, then, the field the compass works in is predominantly vertical.

That matters twice over. First, the only part of the field a compass can use for direction is the horizontal component — the total field multiplied by the cosine of the dip angle. At high magnetic latitudes that component is small, so the directive force pulling the card back towards north is weak: the card becomes sluggish, slow to settle, easily disturbed by turbulence and acceleration, and eventually useless — which is why polar operations use grid or inertial references. The damping is done by the liquid in the bowl and does not change with latitude; what weakens is the force doing the pointing. An instrument that misleads in a predictable, calculable way is a recurring theme in this syllabus — the altimeter does the same thing in cold air, worked through in cold weather altimetry.

Second, the designer must fight the vertical component to keep the magnet system level, and the way that fight ends is the source of every dynamic error. The assembly is pendulously suspended: the pivot sits above its centre of gravity, so gravity acts as a restoring force keeping the card level. In the northern hemisphere the vertical component pulls the north-seeking end down; the suspension pulls it back. Equilibrium is a compromise — a small residual tilt, north end low. And because the assembly hangs from a pivot, tilting it north-end-low swings the centre of gravity, which is below the pivot, the other way: slightly to the south of it.

Two consequences, one error each. The card is free to rotate only about the axis perpendicular to its own face, so as soon as a bank tilts that axis away from the vertical, the vertical component of the Earth's field gains a torque about it — turning error. And the residual tilt leaves the centre of gravity offset from the pivot along the north–south line, an offset that inertia can twist — acceleration error. Take the dip away and there is no vertical component to twist a banked card and no offset for inertia to work on: no errors.

Turning Error and the UNOS Mnemonic

In a balanced turn the compass card banks with the aeroplane. It hangs along the apparent vertical, which in a balanced turn is perpendicular to the wings, so the card tilts by the bank angle — twenty or thirty degrees, not the fraction of a degree that the residual dip tilt amounts to.

Now the mechanism, because this is the step that is usually skipped. The card can rotate only about the axis perpendicular to its own face. Wings level, that axis is vertical, the vertical component Z of the Earth's field acts straight along it, and a force acting along an axis exerts no moment about it — no turning error. Bank the aeroplane and the card's axis tilts away from the vertical, while Z goes on acting straight down exactly as it always did. Z now has a moment about that tilted axis, and the card rotates.

One sentence then predicts every northern-hemisphere case: the north-seeking end of the magnet migrates towards the low side of the tilted card. Work the four cardinal headings with that and no table is needed.

Rolling into a left turn from north (360). On a northerly heading the left wing points west, so the west side of the card goes low. The north-seeking end drifts west, rotating the card the same way the aeroplane is turning. The indication therefore increases: the compass momentarily shows a turn to the right while you roll left. That is the classic northerly turning error. As the turn continues the card keeps being dragged round with it, under-reading the turn achieved: the compass lags on northerly headings.

Rolling into a left turn from south (180). Now the left wing points east, so the east side is low. The north-seeking end drifts east, rotating the card against the turn. The indication runs ahead of the aeroplane: the compass leads on southerly headings.

Turning from east or west. Bank on 090 or 270 puts the low wing pointing north or south — straight along the magnet. Nothing rotates the card about its own axis, so turning error is effectively nil on easterly and westerly headings.

That gives the roll-out technique and the mnemonic UNOS — Undershoot North, Overshoot South, which applies in the northern hemisphere:

• Rolling out on a northerly heading, the compass is lagging and will still be catching up after you stop the turn. Stop the turn before the indication reaches your target, and let it settle onto the number.
• Rolling out on a southerly heading, the compass is leading and has already gone past. Keep turning after the indication passes your target, and let it fall back.

How much? The error grows with dip, so with magnetic latitude. A widely taught rule of thumb puts the lead or lag at roughly the local magnetic latitude in degrees, plus about half the bank angle for the roll-out — strictly magnetic latitude, since it is dip and not geography that drives the error. Treat it as an approximation for practical flying, not a figure to be examined on: different schools quote noticeably different approximations, which is itself the clue that the number is not what is being tested. At European latitudes the error is large enough that a timed turn is the better technique, and EASA questions test the direction of the error far more than its size.

One refinement. In a prolonged turn the damping fluid is dragged round by the bowl and, once moving, drags the card with it — always in the direction of turn. This liquid swirl therefore adds to the lag on northerly headings and subtracts from the lead on southerly ones. It comes from fluid friction rather than from dip, so unlike everything else in this section it does not disappear near the magnetic equator.

Acceleration Error and the ANDS Mnemonic

Turning error needs bank. Acceleration error needs none — it appears wings-level, in the cruise, which is what makes it insidious.

Recall the offset: in the northern hemisphere the magnet assembly hangs slightly north-end-low, leaving its centre of gravity displaced a little to the south of the pivot. When the aeroplane accelerates, the pivot is hauled forward with the airframe while the mass of the assembly resists through inertia, and that inertial reaction acts at the offset centre of gravity. An off-centre force about a pivot is a torque, and the card rotates.

The geometry then decides everything:

• The offset lies along the magnetic north–south line. An acceleration along that same line — on a heading of north or south — has no moment about the card's vertical axis. The centre of gravity also hangs below the pivot, so such an acceleration may tilt the card slightly, but nothing rotates it in azimuth and the reading does not change: acceleration error is nil on northerly and southerly headings.
• An acceleration across the offset — on a heading of east or west — acts with the full moment arm about the vertical axis. Acceleration error is greatest on easterly and westerly headings.

The result in the northern hemisphere is ANDS — Accelerate North, Decelerate South. On an easterly or westerly heading, acceleration makes the compass indicate a turn towards north and deceleration a turn towards south. Nothing has moved but the airspeed.

Note what “towards north” does to the number, because this is where students come unstuck. On 090, accelerating drives the indication towards 000, so the reading decreases: 090 becomes 080. On 270 it also drives towards north, but north is the other way round the card, so the reading increases: 270 becomes 280. The mnemonic gives the direction the indication moves on the rose, not whether the number grows.

The everyday triggers are precisely the moments you want a heading: the take-off roll; levelling off at cruise, where the aeroplane accelerates for a minute or more; entering a climb, where it decelerates; any deliberate speed change; and turbulence.

The symmetry is a favourite exam hook: turning error is greatest on north and south and nil on east and west; acceleration error is greatest on east and west and nil on north and south. No heading is immune to both — only flight conditions are.

South of the Magnetic Equator, Both Mnemonics Reverse

Most student notes quote UNOS and ANDS without ever saying which hemisphere they belong to. Both are northern hemisphere rules, and both invert.

Only one thing has changed: the sign of the dip. In the southern magnetic hemisphere the field lines run the other way and the south-seeking end of the magnet is pulled down. The assembly hangs slightly south-end-low, and its centre of gravity sits north of the pivot instead of south. Every torque in the previous two sections changes sign, and so does every conclusion.

Turning error. The heuristic becomes “the south-seeking end migrates towards the low side of the tilted card”. The compass now leads on northerly headings and lags on southerly ones, and the roll-out rule inverts with it: ONUS — Overshoot North, Undershoot South, which is UNOS with the verbs swapped.

Acceleration error. On easterly and westerly headings, acceleration now drives the indication towards south and deceleration towards north. It is still greatest on east and west and nil on north and south, because the offset is still aligned north–south; only its direction has flipped. Which headings each error is worst on never changes with hemisphere — only the direction the needle goes.

Two further points matter. First, the boundary is the magnetic equator — the aclinic line of zero dip — not the geographic one. The two lines cross at some longitudes and diverge at others by as much as ten to fifteen degrees of latitude, so there are places well north of the geographic equator that are magnetically southern, and vice versa.

Second, the errors do not switch abruptly: they fade as dip approaches zero, reverse sign, then grow again. At zero dip there is no dip-induced turning error and no acceleration error at all — in a turn, liquid swirl, which does not depend on dip, is all that is left — and the horizontal component is at its maximum, so the compass is at its steadiest and most accurate. Every dip-induced compass error is ultimately a measure of distance from the magnetic equator.

The Practical Consequence: Straight, Level and Unaccelerated

Strip out the theory and one operating rule survives. The magnetic compass tells the truth only in straight and level unaccelerated flight — wings level, constant speed, settled, out of turbulence. In any other condition it shows a blend of your heading and your recent flight path, and you cannot separate the two by looking at it.

That rule is why the heading indicator exists and why it is aligned the way it is. The DI has no magnetic errors, but as a gyroscopic instrument it wanders — apparent wander from the Earth's rotation and from movement over the surface, plus real wander from bearing friction — so it must be re-referenced to the compass. Conventional practice is every ten to fifteen minutes and always before a phase of flight where heading accuracy matters, but the timing is secondary to the condition. Align the DI only wings level, on a steady heading, at constant speed: not in a turn, not while rolling out, not while the card is still swinging, not in turbulence, and above all not just after levelling off from a climb or descent, when the aeroplane is still accelerating and an easterly or westerly heading will put the DI several degrees out.

If the DI fails, the technique that sidesteps every error in this article is the timed turn: establish a known rate of turn on the turn and slip indicator or turn coordinator, hold it for the calculated time, roll out, then let the aeroplane settle wings-level at a steady speed and only then read the compass, allowing a few seconds for the card to stop oscillating. Know the numbers: rate one is 3° per second, so 180° in a minute and a 90° turn in 30 seconds, at a bank angle of roughly (TAS ÷ 10) + 7 degrees. If you must turn onto a heading on the compass alone, apply UNOS and expect the roll-out to need a second look. This sits alongside the perceptual traps in spatial disorientation and visual illusions; the wider syllabus is in the EASA Instrument Rating theory guide.

On the ground, check the deviation card is present, legible and for the right aeroplane, that the fluid is free of bubbles — a bubble degrades the damping and can let the card stick — and that the card swings freely in the taxi turns.

What the PPL papers ask. Expect the direction of correction between true, magnetic and compass; which headings each dynamic error is greatest and least on; how the indication moves for a given turn or acceleration; the causes of deviation and what invalidates a swing; and why the DI is aligned in straight and level unaccelerated flight. The topic straddles Navigation and Aircraft General Knowledge, so it can surface in either paper.