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 design problems that every compass has to solve: 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 nearly as possible in the horizontal plane during normal straight and level flight. But here's the catch: if you just hung a magnet assembly freely, it would align itself with the Earth's total magnetic field. And the Earth's total field is only horizontal at the magnetic equator. Everywhere else, the field dips down into the ground — that's the vertical component we call Z. So a freely suspended magnet would tilt, and it would only be truly horizontal at the equator. That's useless for measuring horizontal direction. So how do we force the magnets to stay horizontal? The answer is pendulous suspension. The magnet assembly is hung so that its centre of gravity is lower than its supporting pivot. Think of it like a pendulum — the weight hangs below the pivot point. That's exactly what Figure 29.3 shows: equilibrium in the Northern hemisphere, viewed from the west. Now, why does that work? Because the tilting effect caused by the vertical component Z of the Earth's field is opposed by the weight of the magnet assembly. Z is trying to pull the magnet down into the ground, but the weight of the assembly resists that. The equilibrium is achieved at the cost of 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. And in the Southern hemisphere, it's the South-seeking ends that dip down instead. Let me break down the two turning couples involved, because that's the heart of Figure 29.3. A couple is a pair of equal and opposite forces that produces rotation. The first couple is produced by Z. 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 is produced by 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. So you've got W pushing down at the centre of gravity and R pushing up at the pivot, and that pair of forces also produces a rotation. For equilibrium, the magnet takes up the amount of tilt necessary to make these two couples balance. The magnet tilts just enough that the couple from Z is exactly cancelled by the couple from the weight. There's actually a third couple — a very weak one — produced by the horizontal component H of the Earth's field, which opposes the tilt. But that one is omitted for simplicity in the figure. Now let's move to the second problem: 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: near the poles, H is too weak for the compass to work properly. 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 the magnet's own strength — how strongly it wants to align. Now, the weak external field H at any given place cannot be changed. You can't make the Earth's horizontal field stronger. So the only thing you can do to improve sensitivity is to increase the magnetic moment of the magnet itself. That's the design lever you have. So to summarise where we are: horizontality is achieved by pendulous suspension, with the centre of gravity below the pivot, giving a small residual tilt of about 2° in mid-latitudes. And sensitivity — the ability to seek H — depends on the external field strength and the magnet's magnetic moment, and since you can't change H, you improve sensitivity by increasing the magnetic moment.