Gyroscopes — Page 148, Lesson 172

We're now looking at how the Earth's rotation itself disturbs a gyro — this is the source of what we call apparent wander. Let me set the scene. A gyro holds its axis fixed in space. But the Earth is spinning beneath it, and the local definition of "north" — the meridian — is rotating with the Earth. So, relative to the local meridian, the gyro axis appears to move, even though it hasn't actually moved in space. Let's start at the pole, because that's the cleanest case. At the pole, the gyro stays aligned in space, but the meridian direction — that is, the direction of local true north — changes as the Earth rotates. So we get the full Earth rate of 15 degrees per hour. Why 15? Because the Earth rotates one full revolution, 360 degrees, in one day, 24 hours. 360 divided by 24 is 15. So the Earth's spin rate is 15 degrees per hour. Now, for anywhere between the equator and the pole, the apparent Earth rate is reduced. The formula is: Earth Rate = 15 × sine latitude, in degrees per hour. Let's unpack that. Latitude at the pole is 90 degrees, and sine of 90 degrees is 1. So at the pole you get 15 × 1, which is the full 15 degrees per hour. At the equator, latitude is 0 degrees, and sine of 0 is 0. So at the equator, the apparent Earth rate is zero — the gyro shows no wander from Earth rotation at all. Between those extremes, you scale by the sine of your latitude. Now, whether this Earth rate is positive or negative depends on which hemisphere you're in. Let's look at the northern hemisphere first. Picture the Earth viewed from above the North Pole, looking down — the rotation is anticlockwise. In Figure 11.11, at position 1, the aircraft and the gyro are both pointing north. Now the Earth rotates. At position 2, the gyro remains orientated to the original "gyro north" — it hasn't moved in space. But the local Earth direction of the parked aircraft is up the local meridian, which is true north. So if we take the gyro as the datum, the aircraft is now on a heading of about 280 degrees. The gyro heading has appeared to decrease. We call this a negative Earth rate, and it has a value of -15 × sine latitude, degrees per hour. Now let's flip to the southern hemisphere, as in Figure 11.12. The Earth still rotates eastwards, but seen from above the South Pole, looking upwards, that rotation appears clockwise — the opposite sense. If the aircraft is parked pointing northwards — that's 12 o'clock in position 1 — when the Earth rotates, the aircraft is now still pointing in a direction of true north, which is outwards from the South Pole, pointing at about 3 o'clock in the diagram. But if the gyro is taken as the datum, the gyro heading is about 080 degrees. The gyro heading has appeared to increase. So we get the rule: Earth rate is negative in the northern hemisphere, and Earth rate is positive in the southern hemisphere. That sign convention matters because it tells you which way the gyro heading appears to drift on the ground, purely from the planet's rotation — before you even add any aircraft motion or friction effects. So the key takeaway: the magnitude of apparent wander from Earth rate is 15 × sine latitude, and the sign — negative in the north, positive in the south — tells you the direction of that apparent heading change.