The Direct Indicating Compass — Page 129, Lesson 148

Let’s pick this up right where the compass’s own behaviour starts to matter in the air. We’re looking at the errors caused by linear acceleration — that is, the errors you get when the aircraft speeds up or slows down in a straight line, not turning. First, the headline fact you must carry with you: the size of the acceleration error depends on a number of factors, and one of the most important is the aircraft’s heading. The acceleration and deceleration errors are maximum on East and West magnetic headings, and they are zero on North and South magnetic headings. So if you’re flying due north or due south magnetically, linear acceleration gives you no error at all. The worst case is when you’re on an easterly or westerly heading. Now, why does this happen at all? The error is caused by inertia acting on a magnet which has residual dip. Let me unpack that. The magnet in a direct indicating compass is not perfectly horizontal — because of the vertical component of the Earth’s magnetic field, which we call Z, the magnet has a slight tilt, a residual dip. So the magnet isn’t lying flat; it’s slightly nose-down or nose-up in the vertical sense. That residual dip is the key, because it means the magnet’s centre of gravity is not in line with its pivot. Let’s take the first case: acceleration on 270°M in the northern hemisphere — that’s a magnetic heading of 270, i.e. due west, such as during take-off on runway 27. The magnet assembly is pendulously suspended — that means it hangs from a pivot like a pendulum, free to swing. When the aircraft accelerates forward, the inertia of that hanging magnet assembly makes it swing back behind the pivot point. Now, the pivot point is offset to the north of the magnet’s centre of gravity. That displacement — the magnet swinging back — creates a turning couple produced by the Earth’s vertical component Z, and that couple rotates the magnet assembly anticlockwise round the pivot. Here’s the effect on the reading. The compass reading is the angle measured clockwise from the north-seeking end of the magnet round to the aircraft’s nose. Because the magnet has rotated anticlockwise, that clockwise angle from the north-seeking end to the nose increases. So the compass reading increases, and it indicates an apparent turn towards north. In other words, the compass says the aircraft is now heading, say, 280°, when its real heading is still 270°. The compass is over-reading — it shows a heading greater than the true heading. Now the opposite case: acceleration on 090°M in the northern hemisphere — that’s due east. Same setup: the magnet assembly is pendulously suspended, and its inertia again makes it swing back behind the pivot point. That displacement again enables a turning couple, but this time it rotates the magnet assembly clockwise round the pivot. Now the angle measured clockwise from the north-seeking end to the aircraft’s nose reduces. So the compass reading decreases, again indicating an apparent turn towards north. The compass now says, say, 080°, when the real heading is still 090°. The compass is under-reading — it shows a heading less than the true heading. So the pattern in the northern hemisphere: on a westerly heading, acceleration makes the compass over-read; on an easterly heading, acceleration makes it under-read. And in both cases the compass falsely suggests a turn towards north. That’s the linear acceleration error — inertia on a pendulously suspended, residual-dip magnet, with the vertical component Z doing the rotating.