Tilt compensation: what to expect

In order to help in the calibration of a tilt-compensated compass, I have pre-calculated what are the uncorrected compass readings, for different heading and heel angles.

At my northern location, the horizontal and vertical components of the magnetic field are respectively 17.686 and 51.676 microteslas, meaning that the inclination of the field in the ground is 71.107°.

The results of these calculations are summarized in the following two figures, for positive and negative heel angles (with a zero pitch angle). Heel angle is considered positive when the mast leans to starboard.

It is interesting to note that there is one heading where the non-compensated compass will give a correct result, independantly of the heel angle: 270° for positive heel, and 90° for negative heel.

To reproduce these results for other locations, here are the equations to use.