In some "turn coordinators", does the gyro spin opposite to the direction it spins in a "turn rate indicator"?

Question

A "turn coordinator" has a symbolic airplane on the display face that tilts (banks) to indicate the direction of yaw or roll. The gimbal axis of the gyro is tilted up about 30 degrees to allow sensing of roll as well as yaw. A "turn rate indicator" uses a needle on the display face to indicate the direction of yaw. The gimbal axis of the gyro is parallel to the aircraft's longitudinal axis rather than tilted upwards, and only yaw is sensed.

In both instruments, the spin axis of the gyro wheel is oriented laterally, i.e. parallel to the aircraft's wingspan, when the aircraft is not moving. We know that in all "turn rate indicators", and in at least some "turn coordinators", the gyro wheel spins clockwise as viewed from the right, so that the top of the gyro wheel spins away from the pilot.

In some "turn coordinators", does the gyro wheel spin in the reverse direction-- i.e. counterclockwise as viewed from the right, so that the top of the gyro wheel spins toward the pilot?

What is the advantage of having the gyro in a "turn coordinator" spin counterclockwise as viewed from the right, if any are in fact configured this way?

Or is it just an aviation "myth" that in some turn coordinators, the top of the gyro spins toward the pilot rather than away from the pilot?

The ideal answer would include video evidence or a manufacturer's diagram, etc.

This question is only about instruments using actual physical rotating gyros.

The gyro is angled at 45 degrees so that it's sensitive to both yaw and bank.Pure yawing motions have a limited effect, and pure banking motions have a limited effect, with the strongest effect from when the two movements are combined as in an actual turn.To help, the gyro has a hydraulic damper, like those tiny dampers for turntable tone arms, to help filter out small yaw and roll movements.The damper on mine crapped out once and the thing bounced around wildly, unusable.They are electric, running off fixed frequency ac created by a teeny tiny static inverter in the unit. Dunno the direction. — John K, Oct 30 '20 at 02:49
@JohnK do you happen to know if the needle-style turn rate indicator has the same kind of damper, or if it doesn't need it, why not? Maybe grounds for another ASE question... — quiet flyer, Nov 02 '20 at 17:07
I had a turn and bank apart once and there was no damping device in it. On the DVs, I think some of the members on here think of questions posted as a method to post a prepared response by the poster as underhanded somehow, when it's actually fine to do. — John K, Nov 02 '20 at 22:10
@JohnK thanks for the info; would be interesting to learn someday why it is not needed — quiet flyer, Nov 02 '20 at 22:13
@quietflyer Unless this post made up said myth (which doesn't seem to be the case) I don't see why this is a poor question. — Chris, Dec 15 '23 at 21:06
@Chris -- look through my (admittedly overly long) answer to see the links to three sources (including 1 ASE answer) repeating the wrong-way spin idea re turn coordinators. Look for the stand-alone sentence "Here are three such sources:" about 2/3 of the way down through the answer. — quiet flyer, Dec 19 '23 at 14:39

score 1 · Answer 1 · answered Dec 18 '23 at 20:16

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Neither instrument works properly unless it turns clockwise as viewed from the right.

If a turn coordinator is made to rotate counterclockwise as viewed from the right, the gyro will rotate counterclockwise as viewed by the pilot when the aircraft is yawed or rolled to the left. If it is spinning the other way, it will rotate clockwise. Since the symbolic airplane could be made to rotate with or against the gyro, it doesn't really matter for yawing or rolling motions which way the gyroscope rotates.

The response to pitch is different- if the gyroscope rotates counterclockwise as viewed from the right then pitching up during a turn will cause the indicated turn rate will decrease. This is a big problem! In a 30° banked level turn, the yaw rate (that is, intrinsic rotation about the vertical axis) of is only 87% of the turn rate (that is, the change in heading). The rest is pitching up.

When the turn coordinator is calibrated to show a proper standard rate turn in a 30° bank, the pitching response makes up for the other 13%. If it rotated the other way, it would instead show 13% less and indicate a turn rate 26% too low!

answered Dec 18 '23 at 20:16

Chris

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@quietflyer For sure. I also discuss the pitching response of a turn indicator here. I appreciate your question- it made me think through the topics and I feel I understand the instruments a lot better now. – Chris Dec 18 '23 at 20:44
@quietflyer No, a CCW gyro causes the pitch to indicate in the wrong direction. Sure you could still calibrate it for one specific bank angle, but it would read grossly wrong at any other bank angle. Fundamentally a level turn always pitch up with the yaw so you need "more pitch" to indicate as "more turn" not "less turn" and you only get that with a CW gyro. – Chris Dec 18 '23 at 20:45
@quietflyer Also, the percentages I refer to are just referring to the motion. The yaw rate in a bank angle of $\theta$ is equal to the turn rate times $\cos\theta$. So you set the stiffness of the spring so that its pitch response is enough to make up for that $1-\cos\theta$ deficit in the yaw response. This only works exactly at one specific bank angle but with a CW gyro it's pretty close for a wide range of angles since the cosine function doesn't change very fast at small angles. – Chris Dec 18 '23 at 20:56
In short, in a 30 degree banked level turn your yaw rate is 87% of the turn rate ($\cos30^\circ$) and your pitch rate is 50% of your turn rate ($\sin30^\circ$). If you want to calibrate your instrument for a 30 degree bank then you make the stiffness of the spring whatever it needs to be so that in a standard turn in the neighborhood of 30 degrees is about enough to make up for the change in yaw rate. E.g. in a 29 degree bank you'll have more yaw and less pitch. If you calibrated the spring properly the loss in pitch response will be about equal to the gain in yaw response so it will be right. – Chris Dec 18 '23 at 21:08
In a standard rate turn the torque (and thus the deflection of the instrument) due to pitching and yawing motions combined is proportional to $\cos(\theta-\phi)$, where $\theta$ is the bank angle and $\phi$ is the angle the gyroscope makes with the vertical axis of the airplane in a standard turn. By setting $\phi$ to be a specific angle you make the turn coordinator most accurate in the vicinity of that angle, since the cosine function varies slowly around 0. – Chris Dec 18 '23 at 21:40
The same instrument with CCW spin has torque proportional to $\cos(\theta+\phi)$. There is no way you can calibrate this to have a similar "plateau" like $\cos(\theta-\phi)$ has when $\theta\approx\phi$. – Chris Dec 18 '23 at 21:46
@JuanJimenez -- care to comment on this answer, considering your opposing answer https://aviation.stackexchange.com/a/56126/34686 ? – quiet flyer Dec 19 '23 at 14:41
(Some responses to above answer / comments now added in chat https://chat.stackexchange.com/rooms/150416/discussion-between-quiet-flyer-and-chris ) – quiet flyer Dec 19 '23 at 16:15
I'm going to go ahead and delete most of my comments above to help keep mods happy, see the chat instead-- – quiet flyer Dec 19 '23 at 16:44

quiet flyer · Answer 2 · 2023-12-19T16:34:26.900

On all turn rate indicators-- the instrument with the needle indicator and no tilt to the gyro's gimbal axis-- the gyro spins clockwise as seen from the right, with the top of the gyro spinning away from the pilot. On several diagrams and videos of turn coordinators-- the instrument with the moving symbolic airplane on the face of the instrument and the tilted axis for the gyro gimble-- the gyro wheel is clearly set up to spin in the same direction. At present the author of this answer has been able to find no diagrams or videos of a turn coordinator whose gyro wheel spins in the opposite direction.

In this image from Wikipedia, the gyro on a turn coordinator is illustrated as spinning clockwise as seen from the right, just like the gyro on the turn rate indicator in the diagram.

In this AOPA article, the gyro on a turn coordinator is illustrated as spinning clockwise as seen from the right. The reverse gearing is illustrated that makes the symbolic airplane tilt to the right when the gyro spin axis tilts to the left, exactly as we see in the video below. If the gyro were spinning the other way, the gyro's spin axis would tilt to the right when the aircraft yawed or rolled to the right, and no reverse gearing would be needed to make the symbolic airplane tilt to the right.

In this video of a Cessna Turn Coordinator, when electrical power is applied at 1:50, we can clearly see the gyro wheel start to spin clockwise as viewed from the right, with the top of the wheel moving away from the pilot. When the instrument is yawed to the left at 3:33, we can see the spin axis of the gyro wheel tilt (bank) to the right-- clearly the symbolic airplane on the front of the instrument is being driven by reverse gearing, so it tilts (banks) the opposite direction as the spin axis of the gyro wheel. This is all exactly as is the case in a Turn Rate Indicator, except for the fact that the gimble axis of the Turn Coordinator's gyro is tilted so that it can sense roll as well as yaw.

Here's another similar video "How a Turn Coordinator Works-- Inner Workings". When the instrument is subjected to a left yaw rotation, the spin axis of the gyro wheel tilts (banks) to the right, and the symbolic airplane on the front of the instrument, driven through reverse gearing, tilts (banks) to the left. We can't clearly see the gyro wheel's direction of spin in this video, but if it were spinning the opposite direction, the spin axis of the gyro wheel would tilt (bank) the opposite direction in response to yaw or roll

Here's another video showing more of the same. The relevant portion start at 7:11. The clockwise direction of rotation of the gyro wheel as viewed from the right is clearly illustrated, as is the direction that the spin axis of the gyro tilts (banks) in response to yaw or roll, and the way that the symbolic airplane on the front of the aircraft is geared to tilt (bank) in the opposite direction.

Here's a video of a Turn Rate Indicator. More of the same, except that the gimbal axis of the gyro wheel is purely longitudinal rather than tilted upwards, and the instrument senses only yaw, not roll. Again, we can't clearly see the gyro wheel's direction of spin in this video, but if it must be clockwise as viewed from the right-- if the gyro wheel were spinning the opposite direction, the spin axis of the gyro wheel would tilt (bank) the opposite direction in response to yaw, and the needle would need to be driven by direct gearing rather than by reverse gearing.

Note with direction of gyro rotation shown in these videos-- where when the spin axis of the gyro wheel tilts (banks) in once direction, the indicator on the face of the instrument tilts (banks) in the opposite direction-- in a normal coordinated turn, as the aircraft banks, the gyro's spin axis will tilt relative to the instrument housing and the airplane in the direction that keeps the gyro wheel's spin axis somewhat close to horizontal relative to the earth's surface. If the gyro wheel were spinning the opposite direction and the gyro's spin axis were tilting (banking) the opposite direction in response to yaw or roll, the gyro wheel's spin axis would be tilting away from horizontal relative to the earth's surface.

Note that the direction of rotation of the gyro wheel that we see in the above videos and illustrations will cause the instrument to over-indicate the turn rate whenever the aircraft is under an unusually high G-load in relation to the bank angle, i.e. whenever the flight path is curving upward. This is true for two different reasons. (This is about to get complicated-- the reader is encouraged to make some sketches, or better yet, to make a simple model of a gyro wheel such as a pencil skewered through a round disk that he or she can hold in different attitudes in space.) One, whenever the gyro's spin axis is banked off level relative to the instrument housing and the airplane, any pitch rotation of the aircraft is transformed by the gyroscopic precession effect into a tendency for the bank angle of the gyro's spin axis relative to the instrument housing and the airplane to increase. (This may be more clear if we imagine the gyro's spin axis to be banked almost vertically, relative to the instrument housing and the airplane, which would never actually happen in reality). This effect is also present in a turn rate indicator, where the gyro's gimbal axis is parallel to the aircraft's longitudinal axis. And two, since the turn coordinator gyro's gimbal axis is not truly aligned with the aircraft's longitudinal axis, but rather is mounted with the forward end raised and the aft end lowered to permit sensing of roll rotation as well as yaw rotation, whenever the gyro's spin axis is banked away from level relative to the instrument housing and the airplane, the lowered end of the gyro's spin axis is moved forward, and the raised end of the gyro's spin axis is moved aft. This re-orientation of the gyro's spin axis causes any nose-up pitch rotation of the aircraft to be transformed by the gyroscopic precession effect into a tendency for the gyro's spin axis to yaw even further away from the aircraft's lateral axis and closer to the aircraft's longitudinal axis. (This may be more clear if we imagine that the gyro's spin axis to be almost parallel to the aircraft's longitudinal axis, which would never actually happen in reality.) Since the gyro's gimbal axis is mounted with the forward end raised and the aft end lowered, this yaw rotation of the gyro's spin axis must also cause the bank angle of the gyro's spin axis relative to the instrument housing and the airplane to increase. This will cause the turn rate indication on the face of the instrument to increase. This second effect is only present in a turn coordinator, and not in a turn rate indicator.

Yet one often comes across sources that say that the gyro wheel in a turn coordinator spins counterclockwise as viewed from the right-- so that the top of the gyro wheel is spinning toward the pilot. The same sources say that in contrast to a turn rate indicator, a turn coordinator tends to under-indicate when the G-loading is excessively high in relation to the bank angle. A common theme of these sources is that this characteristic makes it difficult to use the turn coordinator to recover from unusual attitudes.

Here are three such sources:

A post on an airline pilot's discussion forum (#13)

Another post on the same discussion forum (#2)

An ASE answer to a related question

Or is it just an aviation "myth" that on some turn coordinators, the top of the gyro spins toward the pilot rather than away from the pilot?

It seems unlikely. The idea seems very widespread. Certainly an under-indication of the turn rate when the G-loading is excessively high in relation to the bank angle is indeed what we would expect if the gyro wheel in a turn coordinator were spinning counterclockwise as viewed from the right-- so that the top of the gyro wheel were spinning toward the pilot.

Here's why:

One, whenever the gyro's spin axis is banked off level relative to the instrument housing and the airplane, any pitch rotation of the aircraft is transformed by the gyroscopic precession effect into a tendency for the bank angle of the gyro's spin axis relative to the instrument housing and the airplane to decrease. (Again, this may be more clear if we imagine the gyro's spin axis to be banked almost vertically, relative to the instrument housing and the airplane, which would never actually happen in reality). And two, since the gyro's gimbal axis is not truly aligned with the aircraft's longitudinal axis, but rather is mounted with the forward end raised and the aft end lowered (to permit sensing of roll rotation as well as yaw rotation), whenever the gyro spin axis is banked away from level relative to the instrument housing and the airplane, the lowered end of the gyro spin axis is moved forward, and the raised end of the gyro spin axis is moved aft. This re-orientation of the gyro's spin axis causes any nose-up pitch rotation to be transformed by the gyroscopic precession effect into a tendency for the gyro's spin axis to yaw closer to the aircraft's lateral axis and further away from the aircraft's longitudinal axis. (This may be more clear if we imagine the gyro's spin axis to initially be almost parallel to the aircraft's longitudinal axis, which would never actually happen in reality.) Since the gyro's gimbal axis is mounted with the forward end raised and the aft end lowered, this yaw rotation of the gyro's spin axis must also cause the bank angle of the gyro's spin axis relative to the instrument housing and the airplane to decrease. This will cause the turn rate indication on the face of the instrument to decrease. Again, this second effect is only present in a turn coordinator, and not in a turn rate indicator.

As we've already noted, if the gyro wheel rotates in this direction-- counter-clockwise as seen from the right, so that the top of the gyro wheel spins toward the pilot-- in a normal coordinated turn, as the aircraft banks, the gyro's spin axis will tilt relative to the instrument housing and the airplane in the direction that brings the gyro's spin axis further away from horizontal relative to the earth's surface, not closer to horizontal relative to the earth's surface. This would appear to make the calibration of the instrument at any given turn rate more dependent on the bank angle, which means that the calibration of the instrument at any given turn rate will be more dependent on True airspeed. The reason for this is explored in more detail in this related answer.

What is the advantage of having the gyro in a "turn coordinator" spin counterclockwise as viewed from the right, if any are in fact configured this way?

Lacking a decisive answer to this question, here are a few thoughts. We've already noted that when the gyro wheel rotates clockwise as viewed from the right, with the top of the gyro wheel spinning away from the pilot, two different effects combine to make the instrument over-indicate the turn or roll rate whenever the G-load is excessive for the bank angle. Perhaps in some designs, this might tend to "peg" at the indicator at full deflection too easily. Perhaps rotating the gyro the other direction helps to calm things down. Perhaps superior damping technologies have made it no longer necessary to use this strategy.

Links (also cited in body of answer)--

Wikipedia illustration of Turn and Slip Indicator and Turn Coordinator

"How it works: Turn Coordinator". Jill W. Tallman. Flight Training (AOPA). January 1, 2019.

Video links (also cited in body of answer)--

How Gyroscopic Turn & Slip Indicator Works (You Tube video) -- in the cutaway, note how far the gyro's spin axis tilts to the side (rolls) in response to yaw rotation-- the tilt at full deflection appears to be about 40 degrees. We can see that the tilt is in the direction that would bring the gyro's spin axis closer to horizontal with respect to the earth during a normal coordinated turn. By the fact that the gyro's spin axis rolls to the left when the instrument is yawed to the right, we can see that the gyro must be spinning clockwise as viewed from the right-- i.e. the top of the gyro is moving away from the pilot.

"How a Turn Coordinator Works-- Inner Workings" -- Again we can see that gyro's spin axis rolls in response to yaw, and the roll is in the direction that would bring the gyro's spin axis closer to horizontal with respect to the earth during a normal coordinated turn. Again, by the fact that the gyro's spin axis rolls to the left when the instrument is yawed to the right, we can see that in this particular turn rate coordinator, the gyro must be spinning clockwise as viewed from the right--i.e. the top of the gyro is moving away from the pilot.

Cessna Turn Coordinator (You Tube video) -- when electrical power is applied at 1:50, we can clearly see the gyro wheel start to spin clockwise as viewed from the right, with the top of the wheel moving away from the pilot.

"Gyroscopic instruments" (You Tube video) -- this animation is very well done. The relevant portion starts at 7:11. The clockwise direction of rotation of the gyro wheel as viewed from the right is clearly illustrated, as is the direction that the spin axis of the gyro tilts (banks) in response to yaw or roll, and the way that the symbolic airplane on the front of the aircraft is geared to tilt (bank) in the opposite direction.

In some "turn coordinators", does the gyro spin opposite to the direction it spins in a "turn rate indicator"?

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