Figure 10.4 Acceleration on 270° M — Page 129, Lesson 150

Let’s pick this up with the acceleration error on a heading of 270°M in the northern hemisphere, because that’s the case shown in Figure 10.4. Here’s the setup. The magnet assembly inside the compass is pendulously suspended — that means it hangs from a pivot, like a pendulum. When the aircraft accelerates, the inertia of that hanging magnet assembly makes it swing backwards, behind the pivot point. In the northern hemisphere, on a heading of 270°M, that backward swing displaces the magnet assembly in such a way that a turning couple is created, and that couple rotates the magnet assembly anticlockwise around the pivot. Now, here’s the key relationship you need to lock in. When the magnet assembly is displaced anticlockwise, the compass reading increases — the compass over-reads. So on 270°M in the northern hemisphere, accelerating makes the compass indicate an apparent turn towards south. The compass might show, say, 280° while the aircraft’s real heading is still 270°. That’s the over-reading. Now let’s contrast that with the southern hemisphere case, Figure 10.7 — acceleration on 270°M in the southern hemisphere. Same acceleration, same heading, but now the pivot point is offset to the south of the magnet’s centre of gravity. The inertia still swings the magnet assembly back behind the pivot, but because of that offset, the turning couple now rotates the magnet assembly clockwise around the pivot. And here’s the opposite relationship: when the magnet assembly is displaced clockwise, the readings decrease — the compass under-reads. So in the southern hemisphere, accelerating on 270°M makes the compass indicate an apparent turn towards south as well, but now it under-reads — it might show 260° while the real heading is still 270°. So you see, in both hemispheres, acceleration on 270°M gives an apparent turn towards south — but in the north it over-reads, in the south it under-reads. The direction of the apparent turn is the same; the over/under-reading is what flips. Now let’s look at the deceleration case, Figure 10.6 — deceleration on 090°M in the northern hemisphere. Deceleration means the aircraft is slowing down, so the inertia of the pendulously suspended magnet assembly causes it to swing forwards, ahead of the pivot point. That forward displacement creates a turning couple that rotates the magnet assembly anticlockwise around the pivot. Anticlockwise again — so the reading increases, and the compass over-reads. The compass indicates an apparent turn towards south. It might show 100° while the real heading is still 090°. So deceleration on 090°M in the northern hemisphere gives an apparent turn towards south, and it over-reads. Now, here’s the important special case — acceleration on a northerly heading in the northern hemisphere, Figure 10.8. When you accelerate on 360°M, the centre of gravity lags, and the north-south tilt of the magnet assembly changes. But here’s the crucial point: the magnets are tilting in the vertical plane of the magnetic meridian through the pivot. Because the tilt happens in that vertical plane, no error occurs. The same applies to deceleration on north/south headings — again no error, only a reduced north-south tilt due to the inertial forward swing of the magnet assembly. So let me give you the summary of acceleration errors, because this is the part you need to remember precisely. Acceleration errors are zero on north/south magnetic headings — in both hemispheres. They increase to a maximum on headings of 090°M and 270°M. Acceleration causes an apparent turn towards the nearer pole. In the northern hemisphere, that’s an apparent turn north. In the southern hemisphere, that’s an apparent turn south. Deceleration causes an apparent turn towards the further pole. In the northern hemisphere, that’s an apparent turn south. In the southern hemisphere, that’s an apparent turn north. And the over/under-reading rule is simple and absolute: whenever the magnet assembly is displaced clockwise, the readings decrease and the compass under-reads. Whenever the magnet assembly is displaced anticlockwise, the readings increase and the compass over-reads. Finally, the size of a linear acceleration error depends on four things: the heading, the magnitude of the acceleration, the design of the magnet system, and the magnetic latitude — which affects the relative strengths of H and Z. H is the horizontal component of the Earth’s magnetic field, Z is the vertical component. The errors are maximum near the magnetic poles, and they decrease to zero at the magnetic equator. So the whole picture is: the error is a function of heading, acceleration magnitude, magnet system design, and latitude — and it vanishes on north/south headings and at the magnetic equator.