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2 related questions: may a turn rate indicator be calibrated to be accurate at all airspeeds, or only for one? Likewise for a turn "coordinator".

The meaning of "accurate" intended in this question is this: -- if the instrument is labelled "2 minute turn" and we fly for 2 minutes with the needle at the calibrated index, we accomplish 360 degrees of heading change, not more or less.

Some added context: note that if the bank angle is very steep, a turn involves mostly pitch rotation, not yaw rotation. Consider the related question What is the formula for the bank angle required for a turn in line-abreast formation? -- several answers indicate that an aircraft flying at a higher airspeed and larger turn radius needs more bank angle to complete a turn in the same time than an aircraft flying at a lower airspeed and smaller turn radius. Therefore the faster aircraft will be turning with more pitch rotation and less yaw rotation, and a given turn rate indicator could not read exactly the same in both aircraft, IF the instrument only measured yaw rotation.

So the essence of this question is-- can a turn rate indicator accurately measure the rotation component of a turn that involves pitch rotation rather than yaw rotation? Is this true at all airspeeds, or only in a limited range? Is any shortcoming in this regard significant in actual instrument flying? Is the same true of a turn coordinator, or will it tend to be accurate only in a narrower range of airspeeds than a turn rate indicator?

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  • $\begingroup$ There is a highly related question out there already aviation.stackexchange.com/questions/27666/… , but it is not clear to me that it has any good answers. Also, my question is asking specifically about both turn rate indicators and turn coordinators. Basically, it seems that both instruments are usually calibrated on the assumption that the turn involves 100% yaw and zero % pitch, which does introduce some small speed-related inaccuracies. $\endgroup$ Jun 18, 2019 at 0:22
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    $\begingroup$ What do you mean by "accurate"? To my knowledge, what a turn-and-slip indicator or a turn coordinator does is completely unrelated to airspeed, so if it reads accurately at one airspeed, it will read accurately at all airspeeds. For that matter, it'll read accurately under the sea or in outer space. But I think you have a different idea than me about how a turn coordinator is supposed to read. $\endgroup$ Jun 18, 2019 at 3:55
  • $\begingroup$ @TannerSwett-- did that clarification help? $\endgroup$ Jun 18, 2019 at 11:22
  • $\begingroup$ Yes, it did, thank you! $\endgroup$ Jun 18, 2019 at 12:11
  • $\begingroup$ Really a duplicate of aviation.stackexchange.com/questions/27666/… $\endgroup$ Oct 27, 2020 at 11:56

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Turn rate indicators are calibrated to Rate 1, 2 and 3 turns at a specific TAS. A rate 1 turn is 180° a minute or 3° a second. A rate 2 turn is twice that, 360° a minute or 6° a second. A rate 3 turn is three times as much, 540° a minute or 9° a second. The angle of bank required to achieve a given rate of turn increases with the TAS.

It is inherent in the design of the instrument that in any yaw condition the gyro axis will tilt. and the gyro will become sensitive to pitch rate.

If the aircraft is then rapidly pitched nose up (in a loop or recovery from a spiral dive) this pitch input can deflect the gyro to read maximum turn rate. This is called looping error. This pitch rate error also affects the instrument readings in normal turns.

To compensate for this and for the difference between yaw and turn rates the indicators are calibrated to show rates of turn correctly in balanced turns for Rate 1, 2 and 3 turns at specific angles of bank and TAS.

Although the indicated rate of turn will be incorrect at speeds away from these datums the errors are not significant in normal operation.

Source

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  • $\begingroup$ Turn coordinators are considered less useful than turn rate indicators because the gyro on a TC is at a 30 degree angle and turning in the reverse direction. This makes the instrument sensitive to G force, and it under reads as you pull G's in a turn. The only way I know of to counteract this is to push the yoke/stick forward to bring the G's back to 1. That said, different pilots have different opinions about all this so your mileage may vary depending on who you talk to. $\endgroup$ Jun 18, 2019 at 11:40
  • $\begingroup$ "It is inherent in the design of the instrument that in any yaw condition the gyro axis will tilt. and the gyro will become sensitive to pitch rate." Is this saying that the gyro axis will tilt relative to the aircraft, and it will become sensitive to rotation about the aircraft's lateral axis? Or is it saying that the gyro axis will tilt along with the aircraft and it will be sensitive to changes in the aircraft's pitch (the amount by which the nose is pointing above or below the horizon)? $\endgroup$ Jun 18, 2019 at 12:10
  • $\begingroup$ The theory is explained here: en.wikipedia.org/wiki/Turn_and_slip_indicator#Turn_indicator $\endgroup$ Jun 18, 2019 at 13:26
  • $\begingroup$ @JuanJimenez -- this is really a better question -- aviation.stackexchange.com/questions/27666/… -- consider posting your answer there too -- I'm considering deleting the present question. $\endgroup$ Oct 27, 2020 at 8:16
  • $\begingroup$ @JuanJimenez -- the url attached to your link "Source" is now behind a paywall. This answer would benefit greatly from saying what the actual source is. It goes to an airline pilot's forum, but did the quote on the forum cite a specific published source? Thanks. $\endgroup$ Oct 29, 2020 at 11:11
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A turn rate indicator measures only the angular rate of heading change. A turn coordinator measures both the angular rate of heading change and the angular rate of bank change. They are not effected by airspeed.

Your line abreast question should be asked separately. But the outside plane must travel faster and have more bank than the inside plane.

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Based on the related answer What is the formula for the bank angle required for a turn in line-abreast formation? , it appears that aircraft flying at different airspeeds will require different bank angles to carry out 360 degrees of heading change in a set time period. At a steep bank angle, 360 degrees of heading change requires more pitch rotation, and less yaw rotation, than at a shallow bank angle. If a "turn rate indicator" only detected the rate of yaw rotation, it could only be calibrated to read correctly at one particular airspeed.

A "turn coordinator" is similar to a "turn rate indicator", but the axis of rotation of the gyro is canted to sense roll as well as yaw. However, in a constant-altitude turn, the roll rotation rate must be zero, and thus the situation is fundamentally no different than is the case with the "turn rate indicator".

The shallow bank angle involved in standard-rate turns in most aircraft minimizes these errors, in most aircraft. An obvious exception would be an aircraft flying at very high airspeed, where a standard-rate turn would involve a rather high bank angle, and this would involve a higher percentage of pitch rotation and a lower percentage of yaw rotation than would be would be the case at a shallower bank angle, causing a turn rate indicator to tend to read abnormally low, if only yaw rotation were detected.

Some related outside reading -- https://www.pprune.org/tech-log/528255-turn-rate-indicator-turn-coordinator-looping-error.html , https://www.pprune.org/tech-log/82721-turn-gyro-axis.html , During "partial panel" flying, in what ways is a turn rate indicator more useful than a turn coordinator? . The long and short of it seems to be that the design of these instruments is complex and somewhat varied. In actual practice, any slight error in a stabilized turn due to the calibration being only valid for one airspeed is the least of a pilot's worries when flying blind. Furthermore it appears that in most turn rate indicators, the gyro cants during a turn in such a way that it is closer to vertical and so does measure something closer to the actual turn rate, than just yaw rate alone. It appears that this is never perfectly true at all airspeeds, and so the calibration of the instrument may only be perfectly accurate at one airspeed. It appears that instruments designed with weaker centering springs will more accurately read the true turn rate in a stabilized turn, yet will also severely over-read when excess "G" is applied. It appears that turn coordinators are generally accurate over a narrower range of airspeeds than turn rate indicators are, due to the differences in design-- it appears that there is little or no sensing of pitch rotation, or possibly even a wrong-way sensing of pitch rotation even in a stabilized turn, in the case of a turn coordinator.

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  • $\begingroup$ Doesn’t the turn rate indicator scale stop at something like 30°? Maybe up to that bank angle, error is below x% with x being generally accepted, and above that the concept becomes less relevant anyway? $\endgroup$ Jun 18, 2019 at 6:44
  • $\begingroup$ Far from a perfect answer yet, but a start $\endgroup$ Jun 18, 2019 at 12:43
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    $\begingroup$ If you are concerned about the accuracy at differing airspeeds I would suggest you gather empirical data. Next time you go flying drop the flaps and stabilize at some comfortable minimum airspeed and perform a standard rate turn, timing yourself to see how long it takes to perform a 360. Then accelerate to a max airspeed and perform the same test. I would wager that the accuracy of the instrument at different airspeeds exceeds your (and mine) ability to nail the turn. $\endgroup$ Jun 18, 2019 at 19:31
  • $\begingroup$ A more refined version of this answer may now be found here -- aviation.stackexchange.com/a/81919/34686 $\endgroup$ Oct 27, 2020 at 11:41

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