Gyroscopes — Page 139, Lesson 166

Let’s start with the heart of this: a gyroscope’s two basic properties. The first is rigidity, which we also call gyroscopic inertia. Rigidity means the spin axis of the gyro wants to stay fixed in direction in space. The second property is precession, which we’ll get to later in the chapter — for now, just know it’s the other half of the story. Now, the key idea I want you to hold onto is what “degrees of freedom” really means in an aircraft gyro. Look at Figure 11.2 — imagine the aircraft flying left to right across the page, so its longitudinal axis is the gyro axis XX. Careful here: the gyro axis XX is not the spin axis. The spin axis is the axis the rotor spins around; the gyro axis is the reference axis we’re measuring against. In this setup, the aircraft is free to bank — roll about its longitudinal axis — and the gyro stays put, spin axis horizontal and fixed in direction. But if the aircraft yaws, the gyro and its gimbal get forced out of their original orientation. So with one gimbal, the aircraft can pitch or bank freely without disturbing the gyro, but it cannot yaw. Now here’s where conventions get tricky. Some references call this a “2-degrees of freedom system.” But the EASA convention does not count the spin axis as a degree of freedom, because no measurement can be made in pitch. So under EASA, that same one-gimbal setup is described differently — the spin axis isn’t a usable degree of freedom. Now move to Figure 11.3 — a two-gimbal system. Here the aircraft is still free to pitch and bank, but with that second gimbal it’s also free to yaw without disturbing the gyro. That’s the full three degrees of freedom in the EASA sense: pitch, bank, and yaw all free. Let me tie this to rigidity. The definition of rigidity includes the words “fixed direction in space.” Rigidity, or gyroscopic inertia, is subject to Newton’s Laws of Motion, which apply to all of space, not just the earth. In theory, if there were no other errors and the gimballing system allowed complete freedom, the gyro axis would point to a fixed point in space — say, a distant star — regardless of the earth’s rotation or the aircraft’s motion over the earth. Now, over short periods, the difference between earth orientation and space orientation may not matter, especially if it’s swamped by mechanical errors, or if the gyro is maintained by mechanical means to some earth reference. But it becomes important when you’re dealing with accurate freely-gimballed gyros over long periods. That’s the drift you’ll see later — the earth rotates under the gyro, and the gyro stays fixed in space. Finally, on simple aircraft, gyros normally don’t have more than two gimbals. Look at Figure 11.4 — you have an inner gimbal and an outer gimbal, but the third structure, on the outside of the outer gimbal, is the frame. The frame is attached to the aircraft and moves with the aircraft. So the frame is not a degree of freedom — it’s just the mounting that ties the gyro to the airframe. So the takeaway: degrees of freedom are about which aircraft motions the gyro can ignore. One gimbal gives you pitch and bank freedom but not yaw. Two gimbals give you all three. And the frame is just the structure that moves with the aircraft — it’s not a gimbal.