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For a reference of direct and indirect attitude indicator, see How is a confusion possible between Western and Russian Attitude Indicators?, and https://www.skybrary.aero/index.php/Western_and_Russian_Artificial_Horizon_Formats.

Direct (Western) attitude indicators can be made to work without tumbling, or even made into a "Navball" that also displays directional information:

F-4 Phantom's instruments See the attitude indicator at the center, Source, and Source. Or alternatively, look at Kerbal Space Program's navball.

Is the same thing possible with the indirect style indicator? If one plays DCS, he or she should know that this style of indicator would always tumble when maneuvering pass 90 degrees above horizon, even though the gyro has no gimbal limit.

This is understandable, because otherwise the indicator must display the horizon upside down... or am I missing something? Is there another way I missed which can get around this issue, or is indirect attitude indicators not capable of representing full 3D orientation, like a navball can?

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Yes. It's actually easier.

Just consider the fact that an indirect indicator consists of two separate moving parts with one degree of freedom each, rather than one with two (or even three for navball) DoF. Instead of a ball, the pitch indicator can be a ring with continuous rotation, like so:

AGD-1

Note that most modern attitude indicators have a remote (separate) sensor, with the indicator driven mechanically by little servos (like the pictured AGD-1) or, of course, rendered digitally. This makes things even easier: the gimbal lock is a separate problem of the sensor (avoided with a tracking mechanism, pictured on the left here), while indication can be made however we want. You can easily have continuous pitch as well as continuous roll.

However, this is usually not done (on either type of indication), and this is a matter of convention rather than technical limitations. If we allow unrestrained angles, attitude becomes ambiguous: pitch ±180° with zero roll is the same as pitch 0 with ±180° roll. For this reason, the convention is that pitch is limited to ±90°, so only the second of these indications is valid. The necessary consequence is that roll "tumbles" when going past ±90° pitch. At the same time, the pitch indicator just inverts direction (and so mechanically it can be a semi-circle).

As a result, you will consistently see 180° roll, zero pitch no matter how you arrive to it: by a semi-loop or by rolling. This is reasonable given that continuous rolling is much more common.

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  • $\begingroup$ I see. So, does this mean indirect indicators are not good for, say, space flight? $\endgroup$
    – Carl Dong
    Nov 27, 2020 at 23:08
  • $\begingroup$ @Carl, "good" is what is most clear for the pilot. This is not a trivial matter, even for pilots themselves (objective tests may show different results to what pilots believe intuitively). In fact, indirect indication was shown to be significantly better (in terms of error rate), esp. in unusual attitudes. So I'm not sure navbal is better for anything. In aviation, splitting pitch/roll (AI) and yaw (HSI/compass) makes perfect sense: one is "flying", the other is "navigating". Similarly, it can be argued that pitch and roll control are substantially different... $\endgroup$
    – Zeus
    Nov 29, 2020 at 23:37
  • $\begingroup$ ...for the pilot and should be treated (and thus indicated) differently/separately. But in space, the whole mental picture may be different, and the indication should reflect that. $\endgroup$
    – Zeus
    Nov 29, 2020 at 23:40
  • $\begingroup$ I was thinking that navball can represent an inertial reference frame, while an indirect style assumes that there is a "ground plane" to reference from, and thus is not useful in space. Obviously, I agree that this is true for aviation. $\endgroup$
    – Carl Dong
    Nov 30, 2020 at 2:31

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