# What causes magnetic compass turning errors?

What exactly causes magnetic compass turning errors? I found two completely different and contrasting explanations online and I'm confused as to which one is correct.

Explanation 1: Reference:

(Starting from 4:10)

Summary: The compass’s North end dips down due to magnetic dip. Then CoG of the compass swings to the other side (South side) so the other half ends up heavier and with more inertia.

So when turning, particularly from a North or South heading, the centrifugal force pulls on the compass’s CoG on the South side and makes the South side swing outward (toward the outside of the turn). This causes compass to lag when turning away from a North heading and to lead when turning away from a South heading.

Explanation 2: Reference: https://drive.google.com/file/d/1sgfdgSFPfw0jtNaH2kUkIgy1aOtDl_tn/view (Page 4)

Summary: Turning errors fundamentally occur because the aircraft is in a banked position, and the compass card is also banked relative to the horizon. The magnetic dip then makes the North end of the compass want to dip downward. In that banked position, dipping downward means the compass turning so that the North end of the magnet points closer to the direction of bank (the side with the aircraft's lowered wing). This causes compass to lag when turning away from a North heading and to lead when turning away from a South heading.

In this image Fv is the vertical component of the total magnetic force, aka the force representing magnetic dip and causing the North end of the magnet to dip downward. F error is the vector present in a bank that makes the compass turn erroneously (the component of Fv that makes the North end of the magnet point closer to the direction of bank).

The difference I noticed between the two explanations is: the first explanation attributes turning errors to centrifugal force pulling on the compass’s CoG, which the second explanation attributes it to the aircraft being in a banked position and the magnetic dip pulling the north end of the compass down.

My question is, which explanation is correct? Could they both be correct and both plays a factor? If you’re in a slip where you’re banked (matches condion in Explanation 2) but not turning (no centrifugal force, no Explanation 1), would magnetic compass turning errors still be a thing? And if you're in a rudder-only severely skidding turn with no bank (centrifugal force/Explanation 1 only and no factors from Explanation 2), would there still be compass turning errors?

(Note: for convenience, this explanation is phrased for the northern hemisphere only.)

The second explanation is the one I was previously familiar with. It always made sense to me, and is undoubtedly a major factor in compass "lead" and "lag" in turning flight.

Note the following-- regardless of whether the aircraft is slipping ("overbanked" for the turn rate) or skidding ("underbanked" for the turn rate), the compass is free to tilt as needed to align itself with the apparent "felt" direction of down, as indicated by the slip-skid ball. This suggests that for any given turn rate, on any given heading, we'll see the same tendency for the compass to "lag" or "lead" regardless of whether we are slipping, skidding, or fully coordinated.1

On the other hand, if the compass were designed differently, so that it pivoted on a fixed axle and was not free to tilt side to side in the aircraft's reference frame, then an unbanked skidding turn would create no compass errors, because the compass card would be perfectly horizontal. A coordinated turn would create the same errors we see with the normal design, and a slipping turn would create greater errors than we see with the normal design. Also, flying on a constant heading in even a slight wing-down slip would create a compass error, which would be objectionable.2,3

"Explanation 1" seems problematic. Essentially it is saying that due to magnetic dip, the compass is tilted relative to the "felt" direction of apparent "down" in the aircraft's own reference frame, which on a northerly or southerly heading causes a fore-and-aft mis-alignment between the pivot point (which is the only point where the airplane can actually apply a force to the compass) and the CG of the compass. Therefore on northerly or southerly headings, in turning flight the centripetal force exerted by the aircraft on the compass is acting at a point located fore or aft of the CG of compass card. This causes an inertial swing of the compass card which causes it to "lag" on northerly headings and "lead" on southerly headings.

This seems plausible on first read-through. But how much "tilt" in the compass card do we see when flying due west or east with the wings level in linear, non-turning flight? Very little. This suggests that aviation compasses are designed so that the CG of the compass card is low enough, relative to the pivot point, that the compass card tends to stay oriented rather close to the "felt" up-down direction in the aircraft's reference frame (which in linear wings-level flight is also the actual up-down direction relative to the earth), regardless of the effect of magnetic dip. So the compass card tends not to react to magnetic dip by tilting to any significant degree. It mainly reacts to magnetic dip by rotating about the pivot point, when the aircraft is on a magnetic heading with a southerly or northerly component in turning flight.

This isn't to say that the effect of "Explanation 1" is completely negligible, but it undoubtedly makes much less of a contribution to compass "lead" and "lag" than "Explanation 2". See also footnote 2 below, in relation to the fourth paragraph of this answer-- this seems to be a strong argument that "Explanation 1" is not the dominant cause of compass error.

Footnotes:

1. This paragraph would seem to be true regardless of whether the second explanation or the first explanation is the dominant cause of compass errors, or whether they both contribute about equally.

2. This paragraph would seem to be true only if the "Explanation 2" is the dominant cause of compass errors. If "Explanation 1" were the dominant cause of compass errors, then (at least in coordinated flight) they could be mostly eliminated simply by mounting the compass card on a fixed axle so that the compass card was not allowed the compass to tilt at all as seen in the aircraft's own reference frame. If it were possible to eliminate the compass errors in turning flight this way, it might be worth putting up with the drawbacks posed by such an arrangement in non-turning flight. (Or there could be two compasses, one optimized for turning flight and one optimized for linear flight!) The fact that this is not done in actual practice would seem to be a strong argument that "Explanation 1" is not the dominant cause of compass errors.

3. These issues no doubt need to be considered in the design of electronic heading sensors with no moving parts. The simplest possible design would be analogous to a mechanical compass that was modified so that it pivoted on a fixed axle and was not free to tilt side to side in the aircraft's reference frame, but the results would be problematic.

• Elaborating further on last sentence before footnotes, and Footnotes 2 and 3-- if "Explanation 1" were the only significant cause of compass error, and "Explanation 2" were insignificant, then a simple 1-axis magnetic sensor such as we find on many hand-held GPS receivers for hiking etc would work fine and be free of turning errors when rigidly mounted in the appropriate orientation in an aircraft. It does not! Commented Dec 29, 2023 at 20:18
• (ctd) Just as a physical compass rotates to a wrong heading due to magnetic dip in turning flight, so to does the "virtual" needle in the magnetic sensor "rotate" to a wrong heading due to magnetic dip whenever the aircraft is banked. In actual practice these devices are harder not easier to use in turning flight in an actual aircraft, than a traditional physical magnetic compass. This suggests that inertia-related issues are really not the primary problem. Commented Dec 29, 2023 at 20:18
• Would I be correct to understand that turning errors are essentially present entirely dependant upon whether the "felt" direction of down is misaligned with the actual direction of down relative to the Earth? (As that causes the compass to be tilted relative to the Earth). Therefore with the current freely-tilting compass design, if you had an unbanked skidding turn, you would still experience errors because the "felt" direction of down is tilted toward the outside of the turn due to centrifugal force, and the compass card would also be tilted to match the "felt" direction of down. Commented Jan 1 at 18:11
• Would I also be correct to understand that whether the "felt" direction of down is misaligned with the actual direction of down is dependent upon whether a turn rate is present? Therefore regardless of whether you are unbanked, underbanked, or overbanked, if in all three situations you have the same rate of turn at the same airspeed, then a) the felt direction of down would all be misaligned to the same degree with the actual direction of down, b) the compass card in all three situations would be tilted to the same degree, and c) the same degree of compass errors would be experienced? Commented Jan 1 at 18:18
• The one thing I do wonder about is still the situation of being in a side/forward slip with no change of heading at all/zero turn rate. I'm under the assumption that because during a slip there is no continuous acceleration in any direction (other than the initial change of track in the case of a sideslip), you would experience exactly 1 G, pointed straight down. (So the "felt" direction of down is aligned with the actual direction of down.) As such, with a normal compass design, the compass card wouldn't be tilted relative to the earth and during a slip thus no errors are present. Commented Jan 1 at 18:25