Pilots memorise ANDS and UNOS long before they understand why the compass lies. The rules work — but a pilot who only remembers the mnemonic has nothing to fall back on when the hemisphere flips, the heading isn't exactly E or W, or the examiner asks for the physics. This page walks through the geometry: one tilted magnet, pendulously suspended, doing exactly what Newton says it should.
Magnetic dip — the root cause of everything
"Except near the magnetic equator, where the lines of force are parallel to the surface, one end of the freely-suspended magnet will dip below the horizontal, pointing to the nearer pole... The angle, measured in the vertical plane, between the axis of the magnet and the horizontal is called the angle of dip." — Oxford Instrumentation, ch. 9, "Magnetic Dip"
In plain terms: the earth's field is not horizontal except over the magnetic equator. At mid-latitudes (UK, ~54°N) the field already dips ~66° into the ground; over the magnetic poles it dips 90°. A magnet that is free to rotate in three dimensions would stand almost vertical.
A compass has to give a horizontal heading, so the magnet is held roughly level by being pendulously suspended — the centre of gravity hangs below the pivot:
"To achieve horizontality, the magnet assembly is pendulously suspended, the centre of gravity of this assembly being lower than its supporting pivot... equilibrium being achieved at the cost of only a very slight residual tilt of the magnets (north-seeking ends down) — by about 2° in mid-latitudes — in the northern hemisphere." — Oxford Instrumentation, ch. 10, "Horizontality"
That small residual tilt is the knife-edge on which every compass error balances. Once the CG sits offset from directly beneath the pivot, any horizontal force applied at the pivot becomes a torque about the vertical axis — and the card rotates when it shouldn't.
Turning error — why the compass lags through N and leads through S
Oxford sets out the mechanism directly: in a turn, the aircraft accelerates toward the centre of the turn. That centripetal force acts on the pivot. The magnet's inertia, however, acts at the CG — which sits south of the pivot in the northern hemisphere.
"This results in the magnet assembly tending to swing out from the turn, rotating the magnet assembly around the pivot point and producing a turning error." — Oxford Instrumentation, ch. 10, "Turning Errors"
The consequence depends on whether the turn takes you through the nearer or further pole.
Turning through North (NH)
- Aircraft rolls into a (say, right) turn on a heading near 360°.
- Centripetal force pulls the pivot inward; CG swings outward under inertia.
- Because CG is south of the pivot, the magnet rotates in the same direction as the aircraft.
- Result: the card does not move across the lubber line as fast as the aircraft is turning — Oxford calls this sluggish.
- The pilot who wants to roll out on 045° indicated must roll out early (undershoot) — otherwise he ends up numerically past it.
Turning through South (NH)
- Aircraft rolls into a turn near heading 180°.
- CG still sits south of the pivot, but south is now behind the aircraft, so it swings in the opposite rotational sense.
- Magnet rotates opposite to the aircraft: the card sweeps past the lubber line faster than the aircraft is turning — Oxford calls this lively.
- The pilot must roll out late (overshoot) to stop on the intended heading.
The UNOS rule (NH only)
- Undershoot North — roll out before the indicated heading.
- Overshoot South — roll out after the indicated heading.
In the southern hemisphere the CG sits north of the pivot, so the same physics produces the mirror image — overshoot north, undershoot south. The rule flips entirely.
How much to lead or lag
Oxford gives a specific numerical example at UK latitudes: rolling out at 335° indicated to stop on 315° actual when turning through north — i.e. a 20° lead at ~54°N with a standard-rate turn.
Technique note: many training organisations teach "lead by latitude/3 + half the bank angle" or similar rules of thumb as a field estimate. These approximations are not in Oxford. Use them as guidance only — the magnitude depends on rate of turn, duration of turn, speed, headings involved, and compass design (Oxford Instrumentation, ch. 10, "Magnitude of Turning Errors").
Turning errors are zero at the magnetic equator (where the vertical component Z is zero, so the CG is directly beneath the pivot and no torque arises). They grow with latitude and are largest near the magnetic poles.
Acceleration error — a pendulous-mass story
A straight-line acceleration doesn't rotate the aircraft — but it does swing the pendulously-suspended magnet. Oxford:
"Acceleration errors are zero on N/S magnetic headings (in both hemispheres), increasing to maximum on headings 090°M and 270°M. Acceleration causes an apparent turn towards the nearer pole." — Oxford Instrumentation, ch. 10, "Summary of Acceleration Errors"
The physics is identical to a pendulum in a train carriage. When the aircraft accelerates, the magnet's CG — which is offset from the pivot because of magnetic dip — lags behind the pivot. That lag becomes a rotation about the vertical axis because the CG is offset from the vertical line through the pivot.
Why E/W headings and not N/S
On a north or south heading, the CG offset is aligned in the plane of the acceleration. The magnet tilts fore-and-aft but doesn't rotate in azimuth, so there is no error:
"If the manoeuvre displaces the centre of gravity north or south of its usual position so that CG and pivot are still in the plane of the magnetic meridian, the magnet assembly merely changes its north-south tilt angle, with no rotation in azimuth and consequently no error." — Oxford Instrumentation, ch. 10, "Acceleration and Turning Errors"
On an east or west heading, the offset is perpendicular to the acceleration — so inertia produces a torque about the vertical and the card rotates.
What the pilot sees (NH)
- Accelerate on 090°: compass under-reads (e.g. shows 080° while actual is 090°) — an apparent turn toward North.
- Accelerate on 270°: compass over-reads (e.g. shows 280° while actual is 270°) — also an apparent turn toward North.
- Decelerate on 090°: compass over-reads — apparent turn toward South.
- Decelerate on 270°: compass under-reads — apparent turn toward South.
The ANDS rule (NH only)
- Accelerate → apparent turn toward North.
- Decelerate → apparent turn toward South.
Again, the southern hemisphere reverses the rule — accelerate toward south, decelerate toward north. The CG now sits on the opposite side of the pivot.
Putting ANDS and UNOS together
- ANDS covers speed changes on E/W headings.
- UNOS covers turns through N/S headings.
- Both arise from the same root cause — a tilted magnet whose CG sits offset from the pivot because the earth's field has a vertical component pulling the red end toward the nearer pole.
- Both rules flip sign in the southern hemisphere.
- Both errors vanish at the magnetic equator (where there is no vertical component) and grow with latitude.
Common mistakes
- Applying NH rules below the equator. In Australia or South America both mnemonics reverse — overshoot north, undershoot south; accelerate south, decelerate north. Check hemisphere first.
- Expecting acceleration error on N/S headings. The CG offset is aligned with the acceleration on those headings, so no torque about the vertical axis is generated. Error magnitude is zero.
- Expecting turning error through E/W. Oxford is explicit: "Turning errors are zero when passing through east or west" — the tilt is in the N-S plane, no rotational couple exists around the pivot.
- Forgetting the latitude dependence. Over the magnetic equator the only turning error is a small liquid-swirl effect. Near the poles, H is so weak and Z so strong that the compass is nearly useless — this is why IRS, not magnetic compasses, is used in polar operations.
Why it matters
Standby magnetic compasses are the last line of heading information when both IRS units and the DG fail. The DGCA ATPL and type-rating syllabi include set-piece questions on ANDS / UNOS with numerical expected-heading answers — the traps are almost always hemisphere reversal or applying the wrong mnemonic to the wrong manoeuvre. In the sim, partial-panel exercises routinely require a 180° turn using the standby compass alone: knowing why you roll out at 335° indicated for a target of 315° — rather than just remembering the number — is what keeps you on heading when the workload spikes.