Gyroscopes — Page 139, Lesson 166

Let’s pick this up right where the gyro’s two basic properties left off, because now we’re going to put those properties to work inside an aircraft. I want you to picture the aircraft flying left to right across the page, so its longitudinal axis—that’s the nose-to-tail line—is also the gyro axis XX. Now, be careful here: that XX axis is not the spin axis. The spin axis is the one the rotor spins around. XX is the axis we’re using as a reference for the aircraft’s motion. With the gyro’s spin axis horizontal and fixed in direction, the aircraft is free to bank—to roll about its longitudinal axis—without disturbing the gyro. It’s also free to pitch, again without affecting the gyro. But here’s the catch: if the aircraft yaws, the gyro and its gimbal get forced out of their original orientation. So we have a system where the aircraft can pitch or bank freely, but it cannot yaw without dragging the gyro along. Now, how we describe this depends on the convention in use. Some references will call this a two-degrees-of-freedom system. But the convention used by EASA—the European Aviation Safety Agency—does not count the spin axis as a degree of freedom, because no measurement can be made in pitch. That’s a subtle but important point: a degree of freedom only counts if you can actually measure something along it. Since the spin axis gives you no pitch measurement, EASA doesn’t credit it as a degree of freedom. Now let’s move to Figure 11.3, which shows a two-gimbal system. Here, with that second gimbal added, the aircraft is free to pitch and bank as before, but now it’s also free to yaw without disturbing the gyro. So the second gimbal buys you that yaw freedom. This brings us to the definition of rigidity, which is also called gyroscopic inertia. The definition includes the words “fixed direction in space.” And that phrase is loaded. Rigidity is subject to Newton’s Laws of Motion, which apply to all of space, not just the earth. So in theory, if there were no other errors and the gimballing system allowed complete freedom, the gyro’s axis would point to a fixed point in space—for instance, a distant star—irrespective of the rotation of the earth or the motion of the aircraft over the earth. Now, over short periods of time, this difference between earth orientation and space orientation may not matter much, particularly 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 key contrast: short-term, earth reference is fine; long-term, space reference matters. Finally, let’s look at Figure 11.4. On simple aircraft, gyros don’t normally have more than two gimbals. Here we have an inner gimbal and an outer gimbal, but there’s a third structure on the outside of the outer gimbal—that’s the frame. The frame is attached to the aircraft and moves with the aircraft. So the frame is your mounting structure; the gimbals are what give the gyro its freedom. So to tie it together: the spin axis is not a degree of freedom under EASA convention, rigidity means fixed direction in space governed by Newton’s laws, and the frame is the part that moves with the aircraft while the gimbals isolate the gyro from the aircraft’s motion. That’s the foundation we’ll build on as we look at how gyros actually drive your attitude and heading instruments.