Gyroscopes — Page 148, Lesson 174

Let’s pick up with the second of the two big wander effects: transport wander. I want you to picture the earth stopped in space, not rotating at all. We’re deliberately ignoring earth rate for a moment, even though in reality both happen at the same time — we separate them just to make each one clear. So, imagine an aircraft flying from Los Angeles to London. At Los Angeles, the gyro is aligned with the local meridian — that means it’s pointing at local true north. That’s the solid white line in the figure. Now the aircraft flies across to London. When it arrives, the gyro is still pointing along the exact same direction in space — that’s the dotted white line. But here’s the key: the actual direction of true north from London is the line connecting London to the North Pole. And that line is not parallel to the one at Los Angeles, because meridians converge as you move toward the pole. The difference between those two directions — the direction the gyro is still holding in space versus the true north direction at London — that difference is the transport wander. In fact, it’s precisely the difference in the alignment of the meridians at Los Angeles and London. So transport wander is caused by the aircraft physically moving across the curved surface of the earth, carrying the gyro’s fixed-in-space axis to a new location where the local reference direction has changed. Now let’s move on to a completely different way of classifying gyros: by function. Some gyros measure angles — for example, 10° of pitch, 5° of bank, 30° of heading change. These are called displacement gyros. Others measure angular rate — for example, a turn rate of 3° per second. These are called rate gyros. The construction difference is important. Displacement gyros have 2 gimbals and 2 degrees of freedom. Examples are the Directional Gyro Indicator (DGI) and the Artificial Horizon. Rate gyros, on the other hand, have one gimbal and one degree of freedom, and they’re used in the Rate of Turn Indicator and in yaw dampers. Now, displacement gyros can be subdivided further into space gyros and tied gyros. A space gyro has gyroscopic inertia with reference to a point in space. It is free to wander, and if it does wander, nothing corrects it back to its original datum. That means it must have a rate of real wander so low that it can be considered negligible for practical purposes. Because of that requirement, space gyros need to be very accurate indeed — and they are correspondingly expensive. They are used in Inertial Navigation Systems. A tied gyro, by contrast, is one that, if it wanders, is restored back to some orientation by an external force. Tied gyros are maintained in some particular attitude or direction rather than in space. The classic example: the directional gyro of a gyro-magnetic compass is slaved to remain oriented to magnetic north. So an external force — the magnetic reference — keeps pulling it back to that heading whenever it drifts off. So the whole picture is: displacement gyros measure angles and have two gimbals and two degrees of freedom; rate gyros measure angular rate and have one gimbal and one degree of freedom. And among displacement gyros, space gyros are free and uncorrected, needing extreme accuracy and cost, while tied gyros are continuously restored by an external force to a reference like magnetic north.