The Direct Indicating Compass — Page 500, Lesson 497

I want to walk you through the direct indicating compass, and we're starting with the two big ideas that make it work: horizontality and sensitivity. First, horizontality. The whole point of a compass is to measure direction in the horizontal plane. So the magnets inside it must lie as close to horizontal as possible during normal straight and level flight. But here's the problem: if you just hung a magnet freely, it would align itself with the Earth's total magnetic field. That total field isn't horizontal — it dips down into the ground at most latitudes. So a freely suspended magnet would only actually be horizontal at the magnetic equator. Everywhere else it would tilt. To fix that, the magnet assembly is what we call pendulously suspended. That means the centre of gravity of the whole assembly is deliberately placed lower than its supporting pivot. Look at Figure 29.3 — that's the equilibrium state in the Northern hemisphere, viewed from the west. Now, why does that help? The Earth's field has a vertical component, which we label Z. That vertical component Z tries to tilt the magnet. But because the centre of gravity hangs below the pivot, the weight of the assembly opposes that tilting. The two effects balance out, and the result is only a very slight residual tilt of the magnets — the North-seeking ends dip down by about 2° in mid-latitudes in the Northern hemisphere. In the Southern hemisphere it's the opposite: the South-seeking ends dip down instead. Let me be precise about the two turning couples involved, because that's the heart of the equilibrium. A couple is a pair of equal and opposite forces that produces rotation. The first couple comes from Z, the vertical component. Z exerts a downward force on the red end of the compass magnet — that's the North-seeking end — and an upward force on the blue end, the South-seeking end. So Z is trying to rotate the magnet. The second couple comes from the weight W acting downwards through the centre of gravity, which is displaced because of the tilt, and the reaction R acting upwards through the pivot. Those two forces, W down and R up, are offset from each other, so they form the opposing couple. For equilibrium, the magnet takes up exactly the amount of tilt needed to make these two couples balance. There's actually a third couple, but it's very weak, so we omit it for simplicity: that's the couple produced by the horizontal component H of the Earth's field, which opposes the tilt. Now let's move to sensitivity. The magnet system is required to seek the horizontal component H of the Earth's field in all areas — except near the magnetic poles, where the horizontal component is inadequate. That's a key limitation: close to the poles, H is too weak for the compass to do its job. From the notes on magnetism, the ability of a pivoted magnet to align itself with an external field — that's its sensitivity — depends on two things: the strength of the external field, and the magnetic moment of the magnet. The magnetic moment is essentially a measure of how strong the magnet itself is, its tendency to align. Now here's the practical catch: the weak external field H at a given place cannot be changed. You can't make the Earth's horizontal field stronger. So the only thing the designer can control is the magnetic moment of the magnet itself — and that's what determines how sensitive the compass will be in a weak field. So to tie it together: horizontality is achieved by pendulous suspension, balancing the vertical component Z against the weight, leaving only a small residual tilt. And sensitivity, the ability to find H, is governed by the magnet's magnetic moment, since H itself is fixed by where you are on Earth.