A magnetic compass has various sources of error that must be taken into account when taking a reading from it. Because magnets are magical and confusing, the errors and corresponding corrections aren’t always intuitive, so let’s walk through them.
Variation and Deviation
These are the two simplest sources of error to consider.
Variation is caused by the difference between magnetic north, and true north. Isogonic lines (lines of equivalent variation) are typically indicated on a sectional chart. To adjust for variation, either °E or °W, subtract or add from true course, respectively.
East is least, west is best
Deviation is caused by the various magnetic fields contained in the aircraft. It can be reduced through airplane-specific calibration of the compass, and accounted for by using a compass card which shows deviation corrections for various headings.
Magnetic Dip
The Earth’s magnetic field is only parallel to the surface at the magnetic equator. As you move towards the poles, the magnetic field lines have an increased vertical component. This causes the north side of the compass to point down in the northern hemisphere, and up in the southern hemisphere.
Magnetic dip is responsible for two types of compass errors: turning errors, and acceleration errors.
Turning Errors
When turning from a northernly heading, the compass tends to lag the turn, sometimes even showing a turn in the opposite direction. Turning from a southernly heading shows the opposite behavior, and the compass will lead the turn.
Undershoot North, Overshoot South
Acceleration Errors
During acceleration and deceleration, the compass has a tendency to erroneously indicate a turn. This is most pronounced when on on east/west heading, and is absent when on a north/south heading. When accelerating, the compass will show a turn to the north, and when decelerating, the compass will show a turn to the south. This behavior is reversed in the southern hemisphere.
Accelerate North, Decelerate South
To understand why we see the magnetic compass shift during acceleration, we have to understand a little bit about how the compass is assembled. The magnetic portion of the compass is suspended inside its enclosure such that the magnetic portion remains aligned with the Earth’s magnetic field while the housing and the rest of the airplane rotates around it. Because the vertical component of the magnetic field is not useful for purposes of navigation, the compass is constrained to only rotate in the horizontal plane. This is done by dropping the compass’ center of gravity below the pivot point it’s mounted on, and results in only the horizontal component of the magnetic field affecting the compass indication when the assembly is level.
During acceleration and deceleration, the pendulous nature of the mounting means the compass will lean nose-down or nose-up, respectively. This causes the vertical component of the magnetic field to have an effect on the compass indication, causing the errors described above.
References
The material this is based on can be found in The Pilot’s Handbook of Aeronautical Knowledge, Chapter 8, under the section Compass Systems.