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I’ve read many places (such as the FAA’s Instrument Flying Handbook) that a turn coordinator can sense both roll rate and turn rate due to the gyro being tilted 30 degrees.

However, why does tilting it do this, vs a turn and bank indicator without the tilt? I’m looking for an explanation of the applied physics and how the mechanisms inside the instrument turn that into a useful indication.

I do understand the principles of rigidity and precession, or at least how they apply to the attitude indicator and directional gyro, so no need to rehash those unless my question indicates I don’t actually understand them as well as I think.

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The turn coordinator is a rate gyro. Unlike attitude and heading gyros that are free to rotate and the instrument senses the orientation of their axis, the turn coordinator (and the turn indicator one) has the axis mounted fixed and the instrument measures the torque forces as the gyroscope tries to resist the rotational motion.

With the axis mounted along the longitudinal axis in a turn rate indicator, banking the aircraft does not apply any torque to the axis, so it is not reflected by the indication. Only turning does.

But with the axis mounted tilted 30° in the turn coordinator banking also causes change in the orientation of the axis, so it is also detected.

The benefits of a rate gyro are that it cannot tumble in unusual attitude, because there are no gimbals, and that it does not accumulate any drift. Those are especially useful in a spin where the attitude indicator will likely have large error, but the turn coordinator still indicates correctly so you can reliably tell which way you are spinning to correct it.

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  • $\begingroup$ I was unaware of the lack of gimbals in the TC; that plus the axis explains exactly what I was missing! $\endgroup$
    – StephenS
    Sep 4, 2021 at 15:22
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    $\begingroup$ @StephenS note that in modern “glass cockpit” avionic suites all the gyros are rate ones (either vibrating or laser ring), one for each axis, and the attitude is integrated in software. That is mechanically simpler, so more reliable, and if the math is done correctly, cannot tumble. $\endgroup$
    – Jan Hudec
    Sep 4, 2021 at 16:02
  • $\begingroup$ They kind of work in two stages; you get an initial bank indication from the roll axis movement, plus the yaw action coming in as heading starts to change, but roll stops as you get to the bank angle and hold it and from that point the indication is from the yaw motion. You get a more instantaneous indication, and yaw motions without bank are inhibited, helped further by an internal hydraulic motion damper. Regular TBs have no damping. If you fly with a regular T&B in an airplane that wags its tail in bumps, it can be pretty challenging on partial panel, the needle going like a metronome. $\endgroup$
    – John K
    Sep 4, 2021 at 16:59
  • $\begingroup$ @JanHudec, pedantically, we like to call those gyrometers in my field (autonomous flight). It is a bit of any oxymoron to call them rate gyroscopes as the definition of a gyroscope is "a device used for measuring orientation", which the solid-state device clearly does not do. $\endgroup$ Sep 6, 2021 at 23:02

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