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I was trying to find out what exactly causes magnetic compass acceleration errors, and I found two completely different and contrasting explanations online (both are supported by an equal amount of reliable sources).

Explanation 1: Reference:

(starting at 3:28). Summary: when on a east or west heading (in the northern hemisphere), 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. enter image description here

This image represents the compass mounted on a pivot point, with the magnet shown.

So when you change speed, that heavier end (the South end), having more inertia thus more resistance to speed change, swings forwards/backwards depending on deceleration or acceleration, and compass will indicate turn to the North/South. enter image description here Acceleration enter image description here Deceleration

Explanation 2: Reference: https://drive.google.com/file/d/1sgfdgSFPfw0jtNaH2kUkIgy1aOtDl_tn/view (page 4-6: page 6 in particular but pages 4-5 provide a backgrounder)

Summary: I’ve also seen some people say that the compass card’s center of gravity is below its pivot point, thus acceleration causes the bottom-heavy compass card to tilt forward (bottom swings back), and deceleration causes the compass card to tilt backward (bottom swings forward).

The magnetic dip then makes the North end of the compass want to dip downward. At that forward/backward tilted angle, dipping downward means the compass turning so that the North end of the magnet is at a lower point. Hence the compass will indicate turn to the North when accelerating and South when decelerating. enter image description here

The difference I noticed between the two explanations is that as seen from the pics, the first explanation thinks the compass card is tilted sideways as viewed by pilot (North end down) due to magnetic dip. While the second explanation thinks the compass card is tilted forward/back due to compass card CoG being at the bottom (and magnetic dip comes in after to make the compass card turn). So my question is: which explanation is correct? Could they both be correct?

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  • $\begingroup$ Hi Katrina, I posted an answer, but then found this: does it answer your question: aviation.stackexchange.com/a/78871/42636 $\endgroup$
    – Jpe61
    Commented Dec 28, 2023 at 20:28
  • $\begingroup$ @Jpe61 and Katrina -- I'd suggest that that answer is a little unclear. I'd suggest that aviation compasses are typically not counterweighted in the sense of having a one side of the compass card heavier than the other side, but are weighted in the sense of having the CG of the compass card as low as possible relative to the pivot point to prevent the compass card from tilting in reponse to magnetic dip. Some hand-held compasses (Silva etc) are counterweighted in the former sense and do have different versions for N and S hemispheres. $\endgroup$
    – quiet flyer
    Commented Dec 30, 2023 at 13:32
  • $\begingroup$ ( Note also that as long the compass is undergoing neither linear acceleration nor centripetal acceleration, allowing the needle to dip does not actually introduce a systematic error in reading, but in a Silva-type compass it would tend to make the needle rub on the housing, essentially increasing the apparent friction of the pivot point.) $\endgroup$
    – quiet flyer
    Commented Dec 30, 2023 at 13:35
  • $\begingroup$ Actually Jpe61's linked question raises a third possible source of acceleration error-- an off-center counterweight. Note also that an off-center counterweight that was "correct" for a given dip angle in a 1-G situation would be "wrong" if we changed either the dip angle or the G-loading. (But, aviation compasses aren't expected to work well at G-loadings significantly above or below 1 G anyway so -- that doesn't prove much.) $\endgroup$
    – quiet flyer
    Commented Dec 30, 2023 at 13:44
  • $\begingroup$ @quietflyer an off-center counterweight is exactly what I'm describing in my answer. Or at least it's what I'm trying to describe😃 An off-center counterweight balancing the needle against the dip will produce acceleration errors. As for the hand held compasses, it seems weird for them to be counter weighed. The dip can be overcome simply by slightly tilting the compass. That is actually very intuitive, since you instinctively try to level the needle inside the casing. $\endgroup$
    – Jpe61
    Commented Dec 30, 2023 at 22:50

2 Answers 2

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Much the same logic applies here as in this related answer to a related question. How much tilt of the compass card due to dip do you see when flying east or west on a linear course with no acceleration? 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 non-accelerating 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. This suggests that "explanation 1" plays only a minor role.

However, just like a "plumb bob" weight hanging from a string, the low CG of the compass card will cause it to tilt during linear acceleration or deceleration. Once the card is tilted, if the magnetic field lines have non-zero dip in the region where the aircraft is flying, and the aircraft is not flying due magnetic south or magnetic north, the card can better align itself with the magnetic field lines by rotating about the pivot point. "Explanation 2" accounts for most of the observed error during linear acceleration and deceleration.

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As it was taught to me, the acceleration errors of the magnetic compass are caused by the counterweight on the compass needle. This counterweight is installed on the needle (or dial) to keep it level despite the magnetic dip you mentioned.

While the small counterweight keeps the needle/dial level, it also shifts the center of gravity of the needle/dial from the axle, making it react to horizontal acceleration in certain directions.

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