Directional Gyro Indicator (DGI) — Page 162, Lesson 194

Let's start with the Directional Gyro Indicator — the DGI. This is the instrument that gives you a stable heading reference, and the whole reason it works is gyroscopic rigidity. But here's the catch: the earth rotates, and that rotation plays tricks on your gyro. That's what I want to walk you through now. First, the key idea. A gyro rotor axis, once spinning, stays aligned with a fixed direction in space. That's rigidity. But your aircraft, and the meridian you're trying to measure heading against, are rotating with the earth. So the gyro stays put in space while the earth — and your instrument case — rotates underneath it. The result is that the DGI reading appears to drift, even though the gyro hasn't actually moved in space. We call this apparent wander. Let me make that concrete with the figures. At the North Pole, Figure 12.7 shows the apparent wander over time — at 0 hours and at 6 hours. At the Equator, Figure 12.8 shows the same thing. And Figures 12.9 and 12.10 show apparent wander at intermediate latitudes, in the northern and southern hemispheres respectively. Now, Figure 12.9 demonstrates something specific: how the apparent drift due to the earth's rotation causes the reading of a DI — that's the Direction Indicator, another name for the DGI — to decrease in the northern hemisphere. Let's walk through it. At point A, an observer looking north at the DGI reads 360°. As the observer and his gyro rotate with the earth to point B, the observer will see a value some degrees west of north — a DGI reading of less than 360°. Why? Because gyroscopic rigidity is keeping the gyro rotor axis aligned with a fixed direction in space, while the earth has turned. Here's the crucial point: the rotor axis cannot remain aligned north-south with the meridian, because the meridian — except at the equator — is continually changing its direction in space. That changing spatial orientation is exactly what causes the apparent drift. As the observer and gyro continue to rotate with the earth, the readings will decrease further. Now contrast that with the southern hemisphere. If an observer and gyro located there rotate with the earth from point E, the readings of the DGI will increase. So: northern hemisphere, readings decrease; southern hemisphere, readings increase. That's the direction of the effect. Now let's quantify it. Figure 12.11 shows graphically the variation of apparent drift with latitude. The drift rate is proportional to the sine of the latitude. So, assuming there is zero random drift and no compensation has been made, the apparent drift rate is: Apparent drift rate = 15 × sin lat, in degrees per hour. Let me unpack that. The 15 comes from the earth's rotation — 360° in 24 hours is 15° per hour. Multiply that by the sine of your latitude, and you get the drift rate in degrees per hour. At the pole, sin 90° is 1, so you get the full 15° per hour. At the equator, sin 0° is 0, so there's no apparent drift at all — which matches what Figure 12.8 shows. At intermediate latitudes, you get something in between. But there's a critical limitation I need you to remember. This formula is only correct if the gyro is stationary — meaning it is not being moved or transported from one place to another. The moment you fly the aircraft, you're transporting the gyro, and that introduces additional errors beyond this simple earth-rotation drift. So this 15 × sin lat relationship is the baseline apparent wander on an uncorrected gyro, assuming it's sitting still on the ground. So to tie it together: the DGI gives you a heading reference through gyroscopic rigidity, but the earth's rotation makes that reference appear to drift. The drift rate depends on latitude through the sine function, it decreases readings in the northern hemisphere and increases them in the southern, and the simple formula only holds for a stationary gyro. That's the foundation for understanding why the DGI needs periodic resetting and why it's not a self-contained heading source.