Gyroscope precession compensation questions

[leech10]

Hello

I was watching some videos about gyroscopes and inertial guidance.
In one of the videos lecturer said that rotating gyroscope set in one direction on gimbal will be pointing one direction and stay like this virtually forever, so we can use it for guidance system.



However I read more articles about and it is not actually true as gyroscope will be moving according to Earth rotation.

http://fer3.com/arc/m2.aspx/Coriolis-gyros-second-attempttyposcorrected-LaPook-aug-2009-g9606

So if it is moving depending on where actually it is, and how it is set(orientation),how the drift is compensated. Despite electronics for example on V2 rocket or V1 flying bomb during WWII. They had Gyroscope guidance but they had to compensate Earth rotation and keep correct flight position during flight.

Do you know how it is done in the mechanical way?

And maybe one more. When I see boards with gyros there are 3 of them. X,Y and Z axis. Why one gyro with 3 dimension gimbal is not used? or is it one gyroscope but with 3 outputs for each axis?

Regards
Piotr

 

[FactChecker]

However I read more articles about and it is not actually true as gyroscope will be moving according to Earth rotation.

Yes. That has to be take into account if the flight is long enough for the Earth to rotate significantly. For a long distance flight, there are other issues due to coriolis forces.

They had Gyroscope guidance but they had to compensate Earth rotation and keep correct flight position during flight.

The gyro is attached to a computer (digital or old-fashioned analog) that figures it out. The Earth's rotation is constant, so that is relatively easy to deal with. When the system is turned on, there is an initialization step when it needs to remain still and determine which direction is North. That is the "alignment" process.

Do you know how it is done in the mechanical way?

I'm not sure that there ever was a totally mechanical inertial reference system. Current systems all have a fairly complicated computer algorithm. Others may have better information about the old systems.

And maybe one more. When I see boards with gyros there are 3 of them. X,Y and Z axis. Why one gyro with 3 dimension gimbal is not used? or is it one gyroscope but with 3 outputs for each axis?

The first thing to notice is that a gyro will not precess due to vehicle rotations around the gyro's axis. So you would need at least one more gyro which is oriented to detect that. It's not immediately clear to me why a third one is needed.

 

[leech10]

Hi

Thanks a lot for the reply

The first thing to notice is that a gyro will not precess due to vehicle rotations around the gyro's axis. So you would need at least one more gyro which is oriented to detect that. It's not immediately clear to me why a third one is needed.

Yep you are right one gyro will miss this axis. I did not thing about it, and this is quite simple. V2 had 2 gyros so everything is clear now.

The Earth's rotation is constant, so that is relatively easy to deal with.

But we need to take the actual lattitude into account and then count it during flight, but as you said it is not an issue for a computer with GPS. But without GPS... i don't think it's so easy

BTW do MEMS or Laser gyros have the same drift due to Earths rotation signal from the board is already compensated?

 

[FactChecker]

Yep you are right one gyro will miss this axis. I did not thing about it, and this is quite simple. V2 had 2 gyros

Aha!

so everything is clear now.

But we need to take the actual lattitude into account and then count it during flight, but as you said it is not an issue for a computer with GPS. But without GPS... i don't think it's so easy

That is an issue for tracking position. But the rotation rate and orientation are not directly affected by latitude.

BTW do MEMS or Laser gyros have the same drift due to Earths rotation signal from the board is already compensated?

The physical unit itself has the same problems as the old mechanical gyros, but they are much more stable, reliable, and accurate. Where I worked, we just got an Inertial Reference System box to mount and the signals from it had everything figured out. I do not know where within the box the Earth rotation rate was compensated for.

PS. A long time ago, in a prior lifetime, I did a simulation where I tracked airplane position in non-rotating space using its linear and rotational velocities and then just rotated the Earth beneath it to get longitude. I must have gotten something wrong because the answers were not correct.

 

[leech10]

That is an issue for tracking position. But the rotation rate and orientation are not directly affected by latitude.

Hi

Lattitude actually has an influence on it, as per article, but as you said, when you worked with Inertial Reference System systems they are already compensated.

"Precession Variation. Earth rate precession varies between 15.04o/hr at the poles and 0o/hr at
the equator. It is computed for any latitude by multiplying 15.04o times the sine of the latitude. For
example, at 30o N, the sine of latitude is 0.5. The horizontal component of Earth rate is, therefore,
15o/hour right x 0.5 or 7.5o/hour right at 30o N as shown in Figure 14.12."

 

[FactChecker]

The effect of latitude depends on how the gyros are oriented. Two gyros at different latitudes that are oriented the same way in inertial space will be affected the same way by the rotation of the Earth. On the other hand, two gyros at different latitudes that are oriented the same way in the locally level coordinate system will, in general, be affected differently by the rotation of the Earth. But the latter two are not, in general, oriented the same way in inertial space because locally level is not the same at different latitudes.

If you want to allow that the gyros are not oriented the same way in inertial space, then you have the issue that the orientation of the vehicle may always be changing (whether due to latitude or vehicle motion).

 

[leech10]

Two gyros at different latitudes that are oriented the same way in inertial space will be affected the same way by the rotation of the Earth.

You mean if Gyro on the pole is placed horizontally and is turning approx 15 deg. per hour and gyro on the equator is placed vertically and will be flipping with the same angle yes?

 

[FactChecker]

You mean if Gyro on the pole is placed horizontally and is turning approx 15 deg. per hour and gyro on the equator is placed vertically and will be flipping with the same angle yes?

Yes.

 

[FactChecker]

The systems that I have experience with were in a box mounted to the vehicle. So the orientation of the vehicle always had to be accounted for, whether it was due to latitude or any other rotation. But I do not know how the gyros inside the box were affected by the orientation of the vehicle.

 

[leech10]

Hi

Thanks a lot, now I got the idea