PPRuNe Forums - View Single Post - Turn Rate Indicator / Turn Coordinator / Looping Error
Old 22nd Nov 2013, 19:33
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flyer101flyer
 
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Theory of gyros-- turn rate indicators and turn coodinators

* Thinking more generally about turn rate indicators and turn coordinators:

* If the gyro were purely “vertical” in the aircraft’s own reference frame, it would measure yaw rate, not turn rate. A turn is a mix of pitching and yawing-- the steeper the bank angle, the more the pitching. A turn rate indicator with a gyro that stayed nearly “vertical” in the aircraft’s own reference frame could be calibrated to give an accurate turn rate at various bank angles at one specific airspeed or one specific angle-of-attack, but not at all possible airspeeds or all possible angles-of-attack.

* I’ve always assumed that the instrument simply is intended to give a pure yaw indication, with the difference between yaw rate and turn rate being considered negligible at the shallow bank angles typically used in instrument flying. I may be wrong in this assumption.

* Inherent in the design of the turn rate indicator, is that the gyro must be allowed to tilt (precess) in response to yaw. This response is harnessed to drive the movement of the needle or symbolic airplane through a geared mechanism. If the gyro spins clockwise as viewed from the right side of the aircraft, as illustrated here File:Turn indicators.png - Wikipedia, the free encyclopedia, the tilt will be in the direction that tends to keep the gyro somewhat closer to “vertical” relative to the earth, in a coordinated turn. If the gyro spins in the opposite direction, it will tilt in the opposite direction-- further away from “vertical” relative to the earth, in a banked turn.

* If the direction and amount of tilt (precession) in response to yaw is such that the gyro tends to stay rather close to vertical with respect to the earth as the bank angle varies, this will tend to reduce the error in turn rate indication induced by changes in bank angle and airspeed, for any given turn rate. I.e., the errors induced by the fact that a banked turn involves pitching as well as yawing. This may involve designing the gyro in such a way that the amount of tilt (precession) is fairly large. In fact, in the extreme case where the gyro really will stay completely vertical with respect to the earth, the amount of tilt (precession) would need to be equal to the bank angle. Some of the posts in the earlier thread http://www.pprune.org/tech-log/82721...gyro-axis.html seemed to raise this idea-- that the gyro tilts (precesses) so much much that it stays nearly vertical with respect to the earth. Really I’m being completely speculative here-- I have no idea whether turn rate indicators have ever been designed to have large amounts of tilt (precession) for this specific purpose, or not.

* It appears that if the tilting (precession) due to yaw was such that the gyro axis stayed perfectly vertical relative to the earth, the instrument would serve as a perfect turn rate indicator, not a yaw rate indicator. This could never happen perfectly across the whole spectrum of possible airspeeds and bank angles, for any given turn rate. (Because the tilt angle due to precession would need to be equal to the bank angle, and the relationship between bank angle and turn rate varies with airspeed.) The design of the instrument would have to be optimized for some particular target turn rate and bank angle and airspeed. After all, fundamentally, the gyro in a turn rate indicator is not free to float freely in all 3 axis and does not serve as a fixed platform relative to the earth, as does the gyro in an artificial horizon. Still, even if the gyro can't really stay close to vertical with respect to the earth, it seems better that the tilt (precession) of the gyro in response to yaw should be in the direction that keeps the gyro more nearly vertical with respect to the earth, than in the opposite direction, as would be the case if the gyro were spinning the opposite way.

* However, if we design the instrument so that the tilt (precession) in response to yaw is quite large--perhaps in an effort to keep the gyro somewhat close to vertical relative to the earth-- we create some other problems. The more the gyro tilts away from the aircraft’s own “vertical” during a turn, the more that a pitching motion will be sensed as yawing motion. We’ve noted that this pitch sensing may serve a useful purpose in terms of helping to indicate something closer to turn rate than pure yaw rate, in a steady-state turn. However, this pitch sensing will also cause the instrument to show an excessively high turn rate whenever the pilot pulls “extra” G’s, above and beyond the steady-state G-load for the bank angle. If the aircraft is to serve well during a partial-panel recovery from unusual attitudes, this seems like a very poor tradeoff.

* Alternatively, the gyro may be designed in such a way that the tilting (precession) in response to yaw is kept to a minimum--by using stiff centering springs as noted in post #4 in the earlier thread http://www.pprune.org/tech-log/82721...gyro-axis.html. This will keep gyro nearly “vertical” in the aircraft’s reference frame. Now the gyro will be much closer to a pure yaw rate sensor.

* In this case, for any given turn rate, the indicator will tend to read significantly low at a steep bank angle. The calibration marking on the face of the instrument an be arranged to take this into account, but this requires some assumption to be made about what the airspeed will be. A yaw rate sensor can't be calibrated to perfectly indicate turn rate for all possible combinations of airspeed and bank angle. However, this design will also minimize the instrument’s tendency to show an excessively high turn rate when the pilot pulls “extra” G’s, above and beyond the normal steady-state G-load for the bank angle. If the instrument is to serve well in a partial-panel recovery from unusual attitudes, this seems like a very good tradeoff.

* Thinking about the fact that I couldn’t clearly detect a relationship between G-load and gyro sensitivity in my recent tests, while others describe a need to unload the aircraft before reading the gyro-- maybe the design of modern turn rate indicators has evolved to the point where the tilting (precession) of the gyro is fairly small and thus pitching-related errors are minimized. Alternatively, maybe there is an advantage to designing turn rate indicators intended for use in high-speed aircraft to have more tilting (precession) while yawing, for better indication of something close to turn rate (not yaw rate) across a wider range of bank angles, so a test in a high-speed aircraft might yield significantly different results than I observed, even with an instrument of modern design.

* Whether the instrument is a turn rate indicator or turn coordinator, I can’t see any advantage to spinning the gyro the opposite way (counter-clockwise as viewed from the right side of the aircraft). This would cause the gyro to tilt (precess) away from true vertical during yawing, rather than toward true vertical. This would accentuate the error caused by the fact that a turn includes pitch as well as yaw-- if the indicator were calibrated to work well at shallow bank angles, then it would tend to read very much too low at steep bank angles. It’s hard to see why such a design would ever be used. Pitching would be sensed as a reduction in yawing. Pulling “extra” G’s above and beyond the steady-state value for the bank angle, would also result in a reduced indication of turn rate. If some turn coordinators really were designed in this way, it’s not hard to see why they would prove unsuitable for unusual attitude training, as suggested by post # 13 on the earlier thread http://www.pprune.org/tech-log/82721...gyro-axis.html. I don’t see anything inherent in the operation of a turn rate coordinator that requires that the rotor to spin in this way (counterclockwise as viewed from the aircraft’s right side.) This illustration File:Turn indicators.png - Wikipedia, the free encyclopedia suggests that the more common practice is for the rotor to spin the other way (clockwise as viewed from the aircraft’s right side), whether the instrument is a turn rate indicator or turn coordinator. My "research" has been limited to a bit of googling around on the web but I can't find any depiction of a turn coordinator with the gyro spinning counter-clockwise as viewed from the aircraft's right side, so I suspect this is not a common practice.

* One possible advantage to spinning the rotor counter-clockwise (as viewed from the aircraft’s right side) is that the direction of tilt of the needle (turn rate indicator) or symbolic aircraft (turn coordinator) is same as the direction of tilt (precession) of the gyro, rather than opposite as in the design illustrated here File:Turn indicators.png - Wikipedia, the free encyclopedia . This might simplify the operation of the mechanism-- yet it seems simple enough to include a reversal of direction in the gearing.

* As long as the rotor is spinning in the correct direction (clockwise as viewed from the right side of the aircraft), I still think that the combined yaw/roll sensing inherent in a turn coordinator will generally be helpful in partial-panel recoveries from unusual attitudes. The turn coordinator tends to make it easier to stop the roll out of a steep turn right at wings-level without overshooting into a turn in the opposite direction. As noted previously though, the combined roll/yaw sensing does present problems in recovering from an inverted spin.

* One more note-- what is "looping error"? In the older thread http://www.pprune.org/tech-log/82721...gyro-axis.html, post #11 seems to suggest (at least in my reading of it) that looping error is the tendency of the instrument to read too low at steep bank angles because the turn involves pitch as well as yaw, and the gyro is staying near vertical relative to the aircraft (not the earth) and so is sensing yaw, not turn rate. The posts suggests that this is considered when the markings are put on the instrument-- which suggests that the instrument is optimized for some particular airspeed.

On the other hand post # 13 in the same older thread seems to suggest that looping error is the instrument's tendency to over-deflect when the pilot pulls excess G's, because the gyro is significantly tilted relative to the aircraft's own "vertical".

Note that IF the gyro were always tilting (due to precession) exactly as needed to stay perfectly vertical relative to the earth, then the turn rate would be perfectly indicated at all bank angles and airspeeds, so long as there were no upward or downward curvature in the flight path as viewed by an external observer at the same altitude. I.e., as long as the G-loading was not higher or lower than the normal, steady-state value for that bank angle. Letting the gyro tilt relative to the aircraft's axis does NOT introduce an over-sensitivity in the turn rate indication as long as the gyro is not tilted beyond vertical with respect to the earth, and is long as the pilot is not pulling more G's than the normal steady-state value for that bank angle. Rather, the mixing of pitch sensing with yaw sensing is helping the gyro to detect something closer to turn rate, not yaw rate. But, I don't believe it is possible that the gyro behaves this way, consistently tilting to anything close to vertical with respect to the earth over a wide range of airspeeds and bank angles and turn rates.

Note also that as the bank angle is increased beyond 45 degrees, the yaw rate starts to decrease, not increase, so there's no way that precession would continue to drive a further tilt of the gyro. Of course, in the real world the gyro reaches its limit of tilt long before the bank angle reaches 45 degrees...

Last edited by flyer101flyer; 23rd Nov 2013 at 16:54.
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