Acceleration Error

A second way to tilt the compass card out the horizontal plane is to accelerate or decelerate the airplane. With the card mounted with its CG below the pivot, acceleration causes the card to tip forward. In the Northern Hemisphere where the magnetic field has a downward component, this causes the north-seeking tip of the compass needle to swing downward.

Figure 6: Compass response to airspeed changes on an East heading

This is illustrated in Figure 6 for an airplane heading East. It shows that acceleration swings the compass toward the North, and deceleration towards the South. The same mnemonic ANDS can be used to remember this.

For completeness, one can derive the relation between the compass and magnetic headings for a given acceleration. Call the acceleration $a$, measured in g's. Then:

$$\lambda = \rm {atan}(a)$$ (3)

$$H_C = {\rm atan2}(\sin(H_M), \cos(M_H) \cos(\lambda)+ \tan(\mu) \sin(\lambda))$$ (4)

where, as before, $\mu$ is the dip angle and $H_C$ and $H_M$ are the compass and magnetic headings, respectively.

Figure 7: Compass error vs. magnetic heading while accelerating

In Figure 7 we plot the compass error vs. magnetic heading for the case of a 55 degree dip angle and accelerations of 0.1g and 0.2g. There is no error on North and South headings, the error is negative for Easterly headings and positive for Westerly ones. As expected these are errors towards the North.

It's hard to imagine attempting to compensate for these errors. If you want the compass to read accurately, keep your airspeed constant!