Gyroscopic Rigidity & Precession

Rigidity is the tendency of a spinning mass to hold its axis pointing at the same place in space no matter what the case around it does. It comes from angular momentum, H = Iω, so it grows with the mass and how far that mass sits from the axis, and with the speed of rotation. This is why instrument rotors are made heavy at the rim and spun fast, and why an attitude indicator takes a few minutes to become usable after start: until the rotor is up to speed it has too little rigidity to be trusted.

Precession is what happens when you do apply a force. The gyro does not move where you pushed it. The response appears 90° further round in the direction of rotation, and its rate is Ω = T / H. Two consequences follow directly. A larger torque precesses faster, and a faster rotor precesses more slowly, because the same torque is working against more angular momentum. That second point is why a run-down gyro not only loses rigidity but wanders faster.

Every gyroscopic instrument exploits one or both. The attitude indicator uses a vertical-axis gyro for rigidity, with an erection system that applies tiny torques to keep it upright against drift. The directional gyro uses a horizontal-axis rotor and must be reset against the compass, because it is rigid in space rather than to the earth, which rotates beneath it. The turn indicator is the exception: it is built to precess deliberately, so the amount of precession against a calibrated spring reads directly as rate of turn.

• Try this: In the rigidity demonstration, tilt the case right over. Where does the rotor axis point, and what does that tell you about what an instrument is really measuring?
• Try this: In the precession demonstration, apply a force at the top. Which way does the axis actually move, and by how many degrees round is that from where you pushed?
• Try this: Hold the force steady and reduce rotor speed. Why does the same push produce a faster precession, and what does that mean for an instrument whose gyro is running down?