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This question may sound like a duplicate of these two, but it is not (in my estimation):

My question is about the explanation some give for why a gyroscope stays upright while a plane travels around the Earth. The answers given in the other StackExchange posts claim that gyroscopes correct for the curvature over time. I accept this as true, however some other people (like the person in this YouTube video ) claim that gyroscopes would stay upright relative to gravity even if they were perfect gyroscopes without friction. In other words, that an ideal gyroscope would maintain an orientation with the gravitational field that it is in.

So, my questions are, specifically:

  • Does an "ideal" gyroscope tend to stay fixed relative to the gravitational field that it is spun up in, or does it tend to stay fixed independent of that?

  • What would I expect an "ideal" gyroscope to do while in a plane going large distances (assuming no turning of the plane except for maintaining the same distance from the center of the Earth, and assuming the gyroscope does not perform any "correction")?

Qmechanic
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Greg Schmit
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  • The Apollo spacecraft used gyros throughout their missions, irrespective of the different gravitational fields they encountered.... https://en.wikipedia.org/wiki/Apollo_PGNCS –  Mar 11 '17 at 01:13

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A gyroscope tends to stay fixed relative to it's original direction of spin (angular momentum vector direction).
If a torque is applied it will show some resistance. In some scenarios that torque can be applied by the force of gravity. There are countless scenarios in which other forces can be involved.

JMLCarter
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    I think you answered my question, but I want to be clear. If I take an ideal gyroscope on a plane, spin it up, and suspend it from a string, as the plane circumnavigates the Earth, I should expect the ideal gyroscope to turn and when we have gone to the opposite side of the Earth, it should be inverted? (ignoring the problem of it getting tangled in it's own string) – Greg Schmit Mar 11 '17 at 01:38
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    Yes, in principle. This is a widely used mechanism for inertial navigation. In practice gyroscopes tend to drift and need to be reset after a while to maintain accuracy; it depends on the device. – JMLCarter Mar 11 '17 at 01:51
  • Application of a force tends to cause precesion. – JMLCarter Mar 11 '17 at 01:55
  • precession (two 's') – JMLCarter Mar 11 '17 at 02:02
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    I get that it would precess, however I just wanted to know if it would stay fixed relative to the gravitational field, which I didn't think it would based on my Physics instruction (no reason a gravitational field would change the angular momentum vector), and you've clarified that for me. Thanks! – Greg Schmit Mar 11 '17 at 02:04
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    It will only precess if you apply a torque to it. The weight of the gyro (i.e. the force produced by a gravitational field) acting through its center of mass does not create a torque on its own, but only in conjunction with some reaction forces depending on how the gyro is supported. An inertial navigation gyro is mounted in a gimbal so that the combination of the reaction forces and the weight of the gyro do not create a torque. – alephzero Mar 11 '17 at 04:32
  • @JMLCarter, keep in mind that there's an additional process going on regarding the drag that the gyroscope's housing has on the gyroscope itself. A lower quality gyro might actually stay relative to ground the entire way. An analogue of this would be looking at a round chunk of ice floating in a glass of water. Rotating the glass (on axis with its height) CW and CCW will result in very little motion of the ice. Move it s.u.p.e.r s.l.o.w.l.y and it'll drag it around. A fast move will allow the ice & water to "slip". A plane gyro is similarly dragged because of it's slow curve reorientation. – tgm1024--Monica was mistreated Apr 28 '21 at 18:01
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Question 1: "Independent" that is, it stays fixed relative to the stars. Question 2: It keeps its orientation relative to the stars, that is, it would rotate slowly as the plane curved around the earth.

Both of these answers rely on this idea: That ideal means that the gyroscope is free from all torques. Thus its angular momentum is conserved and always points in the same direction.

All this talk about airplanes has confused the issue, because gyros in airplanes are carefully designed to get just the torque necessary to keep them aligned with the horizon. That is, an external mechanism applies torque to the gyro in order to align it with the horizon. It is non-ideal by design.

Andrew
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    I totally agree that the gyros in planes are non-ideal by design. I just wanted to know if (in principle) a gyro would stay aligned to a gravitational field (like the YT video said, wrongly). I was under the impression that gyro-based systems must correct themselves for Earth's curvature (using an external torque), and it seems that is the consensus. – Greg Schmit Mar 11 '17 at 02:09
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The torque is applied by gravity through the use of pendulous veins in the gyro. These allow gravity to pull the Y axis into a proper orientation as the plane travels around earth's curve. I think these pendulous veins are something unique to attitude indicator gyros and gyros with similar functions.

Many hobby gyros do not have frictionless gimbals though, and may not pick up motion under a certain speed (ex. less than 15° per hour may not register). There is aprox. 1.43° of curve in 100 miles. If a plane's moving at 500mph, it will be going through about 7.15° of curve per hour, far too little for most hobby gyros to register. Little to no precession of this type of gyro could be expected since the friction will likely resist it.

Check out the channel Wolfie2060 on YT. He is a commercial pilot and has posted several videos on gyros, artificial horizons, flight times, flight routes, etc. He could tell you far more about gyros than I can.

Hoodoo
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A gyroscope, when spinning and functioning correctly, is not affected by anything at all. If the gyroscope slows down it will still maintain its level unless it is tilted by another force such as something hitting it or bumping into it. A gyroscope is similar in principle to a spinning top. If you spun up a top on a surface that was not fixed, and tilted the surface, the top would remain vertical as the surface beneath it yawed and pitched. The only reason the top would deviate from its vertical position is if it slowed down and was then susceptible to wobbling if it were even slightly off balance. A gyro is practically mechanically perfect and balanced so as to not wobble. A perfect gyro has the centre centrifuge disc surrounded by at least 2 additional rings to ensure the gyroscope is completely suspended and not affected by any movement from outside forces, including gravity. The 2 outer rings absorb any movement leaving the central disc to spin unimpeded. If this weren't the case, then at no point could you rely on a gyro to give a complete, and accurate reading of a level surface by which to navigate by. A gyro in an aircraft is not a computer generated image and it doesn't rely on any complicated mechanics for it to work. It is a basic piece of equipment which uses a perfectly balanced, spinning mechanism to operate.

Alex
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the spinning part of gyroscope is not affected by gravitational force. Something heavy is tied on it to pull the spinning part down to keep it facing the direction of earth center.

gyroscope work by when plane or the part surrounding it move and the spinning part doesn't. the difference between the spinning and not is calculated

hahalol
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The earth itself is a gyroscope and if it slowed down the gravity effect of the sun would bring it closer to the sun. Gyroscopes are affected by gravity, as they have mass, but the faster they spin the less gravity has an effect. Ultimately if the spin was fast enough, then the gyroscope would drift into space.

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Ted Boogie
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