Saturday, September 25, 2021
HomeGyroscopeEarth's EffectEffect of Earth Rotation on Gyro - At Equator and Pole

Effect of Earth Rotation on Gyro – At Equator and Pole

Effect of Earth rotation on Gyro must be understood by us to evolve our free gyro into a Gyroscope. It needs no explanation that our Earth has its own magnetic field. Every object on/ at Earth is influenced by its magnetic force. So does our free Gyro. This post will discuss the effect of Earth rotation on Gyro at different locations on Earth viz. equator and pole when observed from space and Earth.

Effect of Earth Rotation on Gyro at Equator

The Effect of Earth rotation on Gyro needs to be understood before understanding how it settles to the meridian. Take a case in which the Gyro has been placed at equator with its axis indicating in the direction of east west. At this location, the gyro will achieve its highest tilt rate. The tilt rate in this will be 360 degrees in one day. Or you can say 15 degree with every hour passing by.

Effect of earth rotation on Gyro 1

Fig. 1 – Effect of Earth Rotation of Gyro at Equator

On completion of twelve hours by a gyro at equator, We will get a delusion as if the gyro has altered its initial direction. However, in actual, this condition does not occurs. The only thing that has changed is the direction of the Earth (due to Earth’s rotation). This phenomena is often known as Gyro’s Apparent Effect.

Effect of Earth Rotation on Gyro at Equator Observed from Space

Imagine yourself in a space ship which is somewhere out in space and looking at the Earth’s South Pole. If you see the Earth with the South Pole in the center, the Earth’s rotation will appear to be in clockwise direction. Now change your ship’s position so that it is in line with the south pole and the south pole appears on the perimeter. You can now observe that the earth is completing its one rotation in 24 hours. We can observe it by making a big post (visible from space) on the equator also. Fig. 2 below refers to that.

Effect of Earth rotation on gyro A

Fig. 2 – Post on the Equator Viewed from Space

Now, assume a case in which the post is at 12 o’clock position, then due to Earth’s rotation, it will be at the right side to you at 18 o’clock (6 o’clock) position, behind you at 24 o’clock (12 o’clock), at left side to you at 6 o’clock position, and finally back to its initial place i.e. 12 o’clock position the next day. It should be noted here that we have observed here that this post acquires a lot of locations. And it is just because it does not have rigidity in space.

Now keep a Gyroscope in place of the post. This time you will observe some dissimilar action. Assume a condition in which the Gyro is placed in equator keeping the Gyro’s spinning axis in line with the Earth’s axis of east west. Now, in this case, the Gyroscope has both the properties which the post was not having i.e. it contains a spinning motion as well as the rigidity in space. Now, if you observe Fig. 3 below, the spin axis of Gyro is parallel (horizontal) w.r.t. the Earth’s axis in 12 o’clock position.

Effect of Earth rotation on gyro B

Fig. 3 – A Gyro on Equator Viewed from Space.

Similarly, spin axis of Gyro will be perpendicular w.r.t. the Earth’s axis in 18 o’clock (6 o’clock) position. Did you notice, the gyro has not changed its position w.r.t. earth. Till now, it is rotating in line with the initial axis in which it was placed. The spin axis of Gyro has the same plane as before. In the same way, the spin axis of Gyro will be parallel (horizontal) w.r.t. the Earth’s axis in 24 o’clock (12 o’clock) position and perpendicular in 6 o’clock position.

In this case study, we observed that as the Earth rotated, the direction of spin axis (Gyroscope) has not changed with it. Instead, it maintained its direction of spin axis. This could be possible due to the rigidity of Gyro in space.

Effect of Earth Rotation on Gyro at Equator Observed from Earth

Its time to return to the Earth. lol. This time, imagine yourself just beside the Gyroscope. If you observe from your position (refer Fig. 4 below), the spinning axis will appear to carry out one absolute rotation within 24 hour. You already know that Gyroscope has rigidity in space and the things which have rotation are yourself and the Gyroscope.

Effect of Earth rotation on gyro C

Fig. 4 – A Gyro on Equator Viewed from Earth

This is why this effect of the Earth’s rotation on a gyroscope is also called as Apparent Drift, Apparent Precession or Apparent Rotation.

Effect of Earth Rotation on Gyro at Pole

Similar to the Effect of rotation of the Earth in equator, if the Gyro is placed at pole keeping the Gyro’s spinning axis in line with the Earth’s axis, the gyro will achieve its highest drift rate of 360 degree in one day. Or you can say 15 degree of drift in an hour.

Effect of earth rotation on Gyro 2

Fig. 5 – Effect of Earth Rotation on Gyro at Pole

Conclusion

  1. The Gyro will have highest tilt rate and lowest (nearly Zero) drift rate at equator.
  2. The Gyro will have highest drift rate and lowest (nearly Zero) tilt rate at poles.
  3. Tilt is created by HER*.
  4. Drift is created by VER**.

Effect of Earth Rotation on Gyro III

Fig. 6 – Vector Representation of HER and VER

Abbreviations used Above

*HER – Horizontal Earth Rate

**VER – Vertical earth Rate.

Also Read: 
Path traced by Gyroscope 
Undamped Oscillation of Gyro 
Settling Period of Gyro
Sahil Mishra
Sahil is a BTech in Marine Electrical. He is also a Reliability Analyst and has specializations in Russian Control Systems, Machinery Control System and Automated Power Management. He has work experience of 18 years. He is an Author, Editor and Partner at Electricalfundablog.
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  19. What would happen to a gyroscope that only had freedom to move parallel to earth’s surface? That is, if it was restricted from tilting and could only drift? You would not, I think, see only the drift component: you induce a kind of precession when you force the axis of a gyroscope to change its pitch or yaw. So the forced movement of the disk outside of its inertial path will induce a change in the apparent drift. Can you characterize that movement?

    • Bob, Can you elaborate your question a bit more. A gyroscope settles at the meridian only when it has three degrees of freedom. That’s the basic concept and fundamental rule. And in another words, it is this three degrees of freedom which make it a Gyroscope. So, its quite obvious that if you restrict its any one degree of freedom, it will not settle at the meridian. If you are not satisfied with the answer then get back to me.

      Regards
      Sahil

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