Magnetic Compass Errors — Turning (UNOS) & Acceleration (ANDS) Explained

You roll into a steady standard-rate turn from 270° toward 360°. The needle sweeps lazily, then almost stops near the target — and when you roll out on the indicated 360°, you've actually only turned to about 340°. Twenty degrees short. The compass didn't break; it lied, and it lied in a predictable way. UNOS and ANDS are the two mnemonics that describe the lie. They come from a single root cause: the compass magnet doesn't sit perfectly horizontal.

Why the compass lies — the root cause

Magnetic dip

The earth's magnetic field is not parallel to the surface. Field lines come straight up out of the ground at the magnetic poles and lie flat at the magnetic equator; in between, they slope into the ground at an angle called the magnetic dip (also called the angle of dip). In the UK the dip is about 66°; in mid-latitudes roughly 50–60°; at the magnetic poles 90°.

The dip is described by two parts of the magnetic field at any point:

• H (horizontal component) — the part that lies along the surface; this is what a compass needle uses to point north.
• Z (vertical component) — the part that pulls the needle downward (NH) or upward (SH); this is the troublemaker.

At the equator Z is zero. Toward the poles H weakens and Z grows, which is why all compass errors get worse with latitude.

"Pendulously suspended" — what it actually means

If you let a bar magnet swing freely, it doesn't sit horizontal — it tilts to align with the sloped field, north end down in the NH. A useful compass has to read a level heading, so the magnet is pendulously suspended: imagine a chandelier hanging from a single point in the ceiling. The pivot is the ceiling hook, and the magnet's mass — its centre of gravity (CG, the average point where its weight acts) — hangs below the hook like the chandelier's body. Gravity pulls the heavy bit downward and that keeps the magnet nearly horizontal.

"Nearly" is the key word. A small residual dip of about 2° at mid-latitudes is left over — enough that the magnet's north end still droops slightly down (NH). That tiny residual tilt is the geometric defect every compass error grows out of.

Why a tilted magnet rotates when you push it sideways

Because the assembly is tilted, the vertical line going down through the pivot no longer passes through the CG. In the NH the CG ends up slightly south of the pivot (in the SH, slightly north). Now imagine pushing the pivot sideways — say, kicking the chandelier's ceiling hook. The chandelier body, hanging off-centre, doesn't just swing back and forth; it also twists because the push is offset from where the weight is.

That twist is a couple — engineering language for "two equal and opposite forces acting at different points, producing rotation." It's the same idea as a torque (a turning force). Any horizontal push on the pivot — the centripetal force that pulls the aircraft around in a turn, or the longitudinal force during a speed change — produces a couple about the vertical axis through the pivot. The compass card rotates when the heading isn't actually changing.

Two things follow immediately:

1. No tilt → no error. At the magnetic equator the field is horizontal, the CG sits under the pivot, and the compass is accurate during turns and accelerations (apart from a small liquid swirl effect, see below).
2. Hemisphere flips the geometry. In the SH the CG offset is on the north side of the pivot, so every error reverses sign.

Quick glossary — Pivot: the point the magnet pivots around, like the bearing of a spinning top. Lubber line: the painted reference mark on the compass bowl that you read the heading against. Inertia: a body's tendency to keep moving in a straight line until a force pushes it. Centripetal force: the inward pull needed to keep something moving in a circle (the rope tension when you whirl a stone overhead). Centrifugal force: in the rotating-aircraft frame, the apparent outward push that throws things to the outside of a turn (really just inertia trying to carry the mass straight on while the aircraft curves away). Torque: a turning force — what you apply to a wrench to undo a bolt. Equal in this context to a couple. Couple: a pair of equal-and-opposite forces acting at different points; the net effect is pure rotation, no straight-line push. A torque applied at an offset point is a couple about the pivot. Azimuth: the compass-bearing direction (rotation about the vertical axis), as opposed to pitch or roll.

UNOS — turning errors

In a turn the airframe pulls the compass pivot around an arc; the centripetal force needed to do so is supplied by the pivot (it's bolted to the aircraft). The magnet's CG, however, is connected to the pivot only through the suspension, and its inertia tries to keep it moving in a straight line. The result is that the CG is "thrown outward" relative to the pivot — out of the turn — and that displacement, combined with the pre-existing N-S offset, rotates the card around the vertical axis.

The direction of that rotation depends on which cardinal heading the aircraft is passing through, because the aircraft heading determines how the existing N-S offset of the CG is oriented in the aircraft's frame.

Turning through North (NH) — sluggish, undershoot

Heading north, the south-of-pivot CG offset lies behind the aircraft. As the aircraft turns (say, left), the centrifugal throw sends the CG outward — to the right of the turn — and the resulting couple rotates the card in the same direction the aircraft is turning (anticlockwise for a left turn). The magnet rotates the same way the aircraft does, but more slowly than the aircraft itself. The lubber line therefore sweeps past the painted numbers slower than the heading actually changes — the compass is sluggish, and reads less than the actual heading change.

• Pilot rule: roll out before the indicated target heading.
• Rough rule of thumb (NH, ~30° bank, std rate): lead ≈ latitude in degrees. About 20° at 50°N, 10° at 25°N, 0° at the magnetic equator.
• The error grows with latitude (stronger Z), rate of turn, and bank angle, and depends on compass design — the "lead = latitude" rule is a useful starting point, not a precise number.

Worked example. Heading 270°, latitude ≈ 30°N, standard-rate right turn to 360°. Estimated lead ≈ 30°. Start the rollout when the compass shows 330°, and once wings are level the card will "catch up" and settle on 360°.

Turning through South (NH) — lively, overshoot

Now heading south, the CG offset (still south in the earth frame) is ahead of the pivot in the aircraft's frame. The same centrifugal throw now produces a couple in the opposite direction to the aircraft turn. The aircraft turns clockwise; the magnet rotates anticlockwise (and vice-versa). The lubber line sweeps past the numbers faster than the heading is actually changing — the compass is lively.

• Pilot rule: roll out after the indicated target heading.
• Same magnitude as turning through north (≈ latitude), opposite sense.

Worked example. Heading 090°, ≈ 30°N, standard-rate left turn to 180°. Estimated lag ≈ 30°. Continue the turn until the compass shows 210°, then roll out — the card will settle back on 180°.

UNOS — the mnemonic

• Undershoot North (roll out early)
• Overshoot South (roll out late)

Turns through East and West produce no turning error: the residual tilt is in the N-S plane, so the centripetal force at the pivot acts along the same axis as the CG offset and there is no couple about the vertical axis.

In the southern hemisphere every sign flips: overshoot N, undershoot S.

One subtle extra: liquid swirl

The compass card floats in damping liquid. During a sustained turn the liquid is dragged along with the bowl and tries to push the magnet in the same direction as the aircraft turn. This effect is called liquid swirl. It's small, but:

• Through north (NH), the magnet is already rotating with the aircraft, so swirl adds to the turning error.
• Through south (NH), the magnet is rotating opposite to the aircraft, so swirl reduces it.
• At the magnetic equator, swirl is the only turning error, and it's small.

Liquid swirl is also one reason a southerly heading is easier to steer accurately than a northerly one in the NH — the indications are lively and self-correcting rather than sluggish and ambiguous.

ANDS — acceleration errors

Acceleration error has nothing to do with turning. It comes from straight-line speed changes — push the throttles up and the compass briefly indicates a turn that isn't happening.

The mechanism is again inertia acting on the offset CG. Picture a plumb-bob hanging in a train carriage: when the train accelerates forward, the bob swings backward. Now offset the bob slightly to one side of the suspension line — the backward swing becomes partly a rotation about the vertical axis through the pivot. That rotation is the acceleration error.

The geometry, heading by heading

• N or S headings. The CG offset (south of the pivot) is aligned with the aircraft's longitudinal axis. A fore-aft acceleration acts along the same line — the magnet only changes its N-S tilt, with no rotation about the vertical. No error.
• E or W headings. The CG offset is now perpendicular to the longitudinal axis. The fore-aft acceleration applied at the pivot, with the CG offset to the side, produces a couple about the vertical axis. Maximum error.

ANDS — the mnemonic

• Accelerate → apparent turn toward North (NH, on E/W)
• Decelerate → apparent turn toward South

The error is transient: as soon as airspeed is steady, the pendulum settles and the card returns to the correct heading. There is nothing to "correct" — the lesson is to not chase the apparent turn during a level acceleration. A common trap on a westerly take-off in the NH is to "correct" the apparent northward swing by banking slightly south (left from heading 270°), which puts you genuinely off heading.

In the southern hemisphere the rule reverses: accelerate → south, decelerate → north. The size of the error depends on heading, acceleration magnitude, magnetic latitude (Z component), and compass design. Errors are maximum near the magnetic poles and vanish at the magnetic equator.

One-page summary

| Situation | NH rule | SH rule | Magnitude | | --- | --- | --- | --- | | Turning through N | Undershoot (roll out early) | Overshoot | ≈ latitude° (rule of thumb) | | Turning through S | Overshoot (roll out late) | Undershoot | ≈ latitude° (rule of thumb) | | Turning through E or W | No error (only small swirl) | Same | ≈ 0 | | Accel on E or W | Apparent turn to N | Apparent turn to S | Largest at high latitude | | Decel on E or W | Apparent turn to S | Apparent turn to N | Largest at high latitude | | Accel/decel on N or S | No error | No error | 0 | | At the magnetic equator | Zero (turning + accel) | Zero | ≈ 0 |

Common mistakes

1. Applying NH rules below the equator. Both UNOS and ANDS reverse in the southern hemisphere. Always check hemisphere first.
2. Expecting acceleration error on N or S headings. The CG offset is aligned with the acceleration on those headings — torque about the vertical axis is zero.
3. Expecting turning error through E or W. The tilt is in the N-S plane; the centripetal force at the pivot acts along that line, so no rotational couple (apart from a small liquid-swirl effect).
4. Forgetting that error scales with dip. A 20° lead at 50°N is closer to 10° at 25°N and zero at the magnetic equator. Don't apply a textbook NH number to a flight in Singapore.
5. Treating acceleration error like turning error. Acceleration error is transient and self-corrects when speed stabilises — there is no rollout to plan.
6. Chasing the compass on take-off. Westerly take-offs in the NH show an apparent turn toward north as you accelerate. Hold the wings level and let the card settle.

Why it matters

The standby (direct-reading) magnetic compass is the last source of heading information when both IRS units fail and the standby attitude/heading instruments are degraded. Partial-panel exercises in the simulator regularly require a 180° turn using the standby compass alone, and ATPL/CPL written papers include set-piece questions of the form: "At 50°N, what indicated heading do you roll out on for a target of 360°?" Knowing why the compass lies — and not just chanting UNOS — is what keeps the answer (and the actual heading) correct under workload.