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27 November 2024 10:17
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Welcome to the gyroscope forum. If you have a question about gyroscopes in general,
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Question |
| Asked by: |
George |
| Subject: |
gyroscopes |
| Question: |
Ok. We know that gyroscopes do what they do, but WHY do they do it?
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| Date: |
31 December 2008
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Answers (Ordered by Date)
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| Answer: |
glenn - 01/01/2009 20:52:56
| | | http://www.gyroscopes.org/forum/questions.asp?id=1005
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| Answer: |
Malcolm - 20/02/2009 15:13:57
| | | Q: What causes gyroscopic precession?
A: Momentum of the gyro being forced to deflect (in the direction of rotation) away from an externally applied force, which creates a diametrically opposed (nearly equal) counteractive force, which (seemingly) restricts movement to (only) right angles from the applied force.
If you are not well versed on the effects of gyroscopic precession I recommend you watch some of the plethora of movies available on the net first. You may find this explanation easier to grasp if you draw what I describe on a piece of paper or have a gyro to look at. First some basics.
The quantity of momentum in every moving object is a direct function of its velocity and mass. Gyroscopes travel at high velocity (rotational speed) and have large masses at he rim and have a lot of momentum for a seemingly small object (a four inch diameter gyro at 5000 rpm will out run any sprinter down a long corridor and leave a large dent it the wall when it gets there). When gyroscopic forces are demonstrated it is mostly overlooked that the force used by the demonstrator is only a small fraction of the energy within the system.
The Gimballed Gyro.
Imagine you are standing at a round table looking down at it from above. On it are marked North, East, South and West, in their respective compass positions. You are standing at South (there is a chair behind you and a chair at the East, keep them, you’ll need them later). In the centre of the table is a gimballed gyroscope, the outer gimbal rings and the (clockwise rotating) gyro are all horizontal. The axis of the gimbals line up with the compass points. You now sit down in the South chair so your eye line is level with the gyro. You now press down on the Southern gimbal axis (nearest to you). The North, South line you are pressing on will remain seemingly stationary (there will be a very slight downward movement for what seems to be a lot of pressure) and the gyro will tilt down at the West and tilt up at the East until you stop pressing. Nothing new there.
Well, this is what causes it to happen…
With your finger still pressing down on the Southern gimbal axis (Southern point), imagine a ball (with a diameter equal to the gyro rim thickness) being fired horizontally from East to West so that it just touches the bottom of your finger as it passes. When the ball touches your finger physics now demands that your finger is pushed upwards and the ball is deflected downwards (no matter how slightly) as it finishes it’s journey.
Now imagine another ball is fired as before, but when it touches your finger, though still visible, it becomes part of the gyro rim at the point of contact. The embedded ball will still travel downwards as it (rotationally) travels westward (clockwise from above). This downward change in direction to the momentum of the atoms in the gyro rim (after the point of contact and following the direction of rotation) is what causes the gyro to tilt down at the West.
Now sit in the chair at the East, eyes still level with the gyro (told you you’d need two chairs). When it reaches the Western point the ball cannot travel downward any further because the Northern point of the gyro cannot move downwards as it is being held up by you pushing down the Southern point. Therefore the ball can only travel back upward to the Northern point. In going upwards the ball now exerts a downward pull on the Northern point, again as physics demands when a moving object is forced to change its path. This downward pull on the Northern point counteracts the downward push you are giving the Southern point and therefore the gyro seems to be stationary at the Northern and Southern points. Although this is never a complete counteraction due to losses, it is enough to make the relative amounts of gyro movements between the East, West and the North, South seem inexplicably large.
As it passes the Northern point the ball is still travelling in an upward direction which, now obviously I hope, causes the Eastern side of the gyro to rise. As the ball passes the Eastern point it has to travels back downward toward the Southern point (as your downward push on the Southern point stops it from rising to meet the ball), and in doing so it exerts an upward pull on the Southern point. This completes the counteracting force cycle. As long as finger pressure is maintained this process will keep repeating itself, increasing the angle of gyro tilt. When the finger is removed the gyro will immediately stop moving as there is now no external force to deflect the momentum of the gyro.
In summary: The basic tenet that every action must have an equal and opposite reaction demands a deflection of the momentum (of the atoms) of the gyro after the point of contact and in the direction of rotation. Because the gyro is a ridged structure this deflection is very small and only uses a small amount of the energy applied. The rest of the energy applied (minus losses) is transferred to the opposite side of the gyro (from the point of contact) and acts as a counteracting force against the original external force (your finger). The effect of this is to effectively lock those two points (though not completely) and therefore force any movement of the gyro to be at right angles to the original applied force. Therefore the seemingly anomalous reactions of gimballed gyros are simply momentum following the rules the only way it can within the physical constraints forced on it.
The gyro supported on a pedestal or on a string.
Imagine you are standing at the South of the round table looking down at it from above, the compass points and the chairs are still the same positions. On the table is a gyro with its axel running horizontally from North to South, the North facing axel end is at the centre of the table (imagine a clock face at 6:30). The axel end at the table centre is resting on either a pedestal or suspended by string (makes no difference). If you now sit down and look North you will see the clockwise rotating gyro facing you. Now imagine that the gyro face has its own compass points, with North at the top, obviously. Now allow the hypothetical gyro to move freely. It will precess around the table centre to the left (West, clockwise as viewed from above), and will gradually spiral downward until it falls off the pedestal or the string. Those of you with the string will notice that the innermost axel end is now itself rotating about (not at) the centre of the table, concentrically with the outer axel end (both ends on the same side of the table). If you now push the outermost axel end so as it increase the speed of precession around the table, you will see the gyro raise itself upward until you stop pushing. If you pull the outermost axel end so as it decreases the speed of precession around the table, you will see that it drops downward until you stop pulling. In both cases the gyro will then carry on as before, but from the new axel angle.
And this happens because…
Sitting in the East chair you see the gyro sideways on (it should look like a crucifix (without anyone nailed to it) rotated 90 degrees to the left), on it’s pedestal or string. Gravity is obviously the only external force being applied to the gyro. Gravity causes the gyro and the axel to move downward (duh), but as the innermost axel end (centre of table) is fixed in position by a pedestal or string, the axel (and gyro) will have to rotate anticlockwise as it goes down.
This is the very crux of the matter and therefore warrants a separate paragraph. Any movement of the gyro (up or down), no matter how miniscule, is causing it to rotate (because one end of the axel is always fixed). As explained in the above summary, whenever you rotate (tilt) a gyro about its axis you create a (nearly equal) counteracting force diametrically opposite the applied force causing the rotation (tilt) to all but cease along that plane. This causes the gyro to (seemingly) only rotate at right angles to the applied force. This still applies even if the gyro movement is 1 thousandth of a millimetre.
Looking from the South chair the downward movement causes the gyro North to come towards you and the gyro South to go away. This rotation of the gyro as it moves downward causes the counteracting forces described above and consequently makes the gyro precess to the left (West, or clockwise as seen from above) around the table centre for the pedestal people. For the people using the string, the gyro does actually rotate clockwise (as seen from above) about its centre of mass because the string cannot prevent it, but the pedestal can. This swings the innermost axel end away from the centre of the table and causes the ends of the axel to become out of line with the table centre. Check this for yourself by hanging a gyro from a string while you look down from above, then use a finger to point at the centre of the circle the gyro follows or place a piece of paper with a large x on it underneath. You will easily see that the angle of the gyro axel is offset from the radial line of your finger or x. It will always be offset in the same direction as the precession e.g. clockwise offset for clockwise gyro precession.
For those of you who think that gravity’s effects on the gyro have been removed (wholly or partially) because the gyro seems to ‘hang’ in the air, I will say this. Just because the gyro has transferred (most of) the gravitational pull (externally applied force) back on itself (only within the gyro), the same as it did to your finger in the gimballed example, THIS IN NO WAY REMOVES THE FORCE(S) OF GRAVITY. All that is happening is that most (not all) of the force applied by gravity is being transferred 180 degrees as a counteractive force that greatly slows down (but does not stop. No seriously, that’s NEVER gonna happen, EVER!) the ability of gravity to ROTATE the gyro, which is what is needed to make it move downward. The mass of the gyro is still the same and therefore so is its weight. The weight of the gyro, caused by gravity, is now being transferred down the axel to the pedestal or string (congratulations, your gyro axel is now acting as an A frame). Place the gyro on a scale and the weight measured will not change when it precesses.
Because the energy transfer within any system is never perfect the gyro will always be brought down by gravity. How quickly this happens is down to the efficiency of the gyro. This property will ONLY work if the gyro is allowed to rotate freely around the axis of its base (pedestal or string). If it is stopped from precessing (say by a pencil) then there is no deflection of the gyro’s momentum as it does not rotate (tilt) to the left and therefore no counteracting forces are created (the precessing force does not disappear, it is absorbed by the pencil through the axel end instead of deflecting the gyro’s momentum). Want proof? Hold a pencil vertically in the path of a horizontally precessing gyro, when it stops against the pencil the gyro can no longer precess and will fall as if dropped (harder to do with the string as it tends to wobble out of the way of the pencil before it falls).
When you pull the outermost axel end so as it decreases the speed of precession around the table centre (pedestal), you are absorbing some of the energy used to deflect the gyro’s momentum and therefore proportionally reducing the counteractive force along the gyro’s North, South points that supports it. Obviously any reduction to the counteractive force will cause the gyro to be forced downward faster by gravity. This downward movement causes the gyro to (as seen from the East chair) rotate in an anticlockwise direction which, as physics still demands, will cause the innermost axel end (pedestal end) to become proportionally lighter during this process. If the gyro was being weighted during this the scales would show a proportional loss in weight but only because the gyro is trying to lift up that end of the axel while the other end of the axel is being pushed down (equal and opposite actions again). There is no change to the overall weight of the system as there is no change in mass or gravity, all that has changed is the weight distribution from the supported to the unsupported axel end, causing the unsupported end to drop. When you then let go the balance of the gyro system will be restored and it will precess as before, but from the new (lower) axis angle.
When you push the outermost axel end so as it increases the speed of precession around the table centre (pedestal), you are adding some energy to the system. You are now (relatively speaking as if you are following the gyro’s precession from above) effectively rotating the gyro in a clockwise direction over and above what it is doing on it’s own. This is the same as applying a force to the gyro’s Eastern point which will cause the gyro North to move away from you and the gyro South to come towards you, which because of the pedestal causes it to rise. This does create it’s own counteractive force along the gyro’s East, West line (all existing forces are still working) which some might think will reduce the gyro’s ability to precess and therefore weaken it’s original North, South counteractive force, causing it to drop. Because counteractive forces are not perfect they will allow movement if enough force is applied. The reality is that the force you input to increase the gyro’s speed of precession (with a finger lets say) is much larger that the counteractive forces created by this input and will therefore override it (the force of your finger actually includes your whole arm, they are attached). The upshot is that because the speed of precession will always be greater than needed to maintain the North, South counteraction and the East, West counteraction is overcome by the external force you applied the gyro can only go upward. The upward movement (gyro rotation) now causes the innermost axel end to press down on the pedestal which will cause a set of scale to register a proportional increase in measured weight during this process. As before this is just a change in the weight distribution and when you let go the balance of the gyro system will be restored and it will precess as before, but from the new (higher) axis angle.
Nuations.
These are merely caused by the forces explained in the last two paragraphs when the user introduces a directional force (knowingly or not) when the gyro is released. This imparted directional force acts as an external force (which it is) which causes temporary imbalances in the gyro’s otherwise balanced system, causing it to move as a misshapen sine wave when it precesses. The amplitude of the nuations keeps decreasing as internal losses cause the eventual elimination of the imparted directional force.
If you don’t understand it by now keep banging them rocks together, you’ll get that fire lit eventually.
Don’t copy and paste! It’s called homework because it involves work. You know who you are.
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| Answer: |
Luis Gonzalez - 21/02/2009 19:10:28
| | | This forum is a great place to find valuable rare information (alongside many errors).
The best explanation for precession is viewed in strictly angular terms.
A) Applying torque to an object causes it to spin (a rule for rotation).
B) Applying a tilting torque “crossway” to a spinning object changes the direction of the spin, until the object ends up spinning in the same direction as the torque (a thought provoking rule).
Precession results from purely angular causes and the 2 simple rules above explain precession well (in an unencumbered object). These rules also extend to explain precession when spinning objects are attached to distant pivot points.
Confusion happens when people use linear terms to explain precession.
The linear perspective requires ignoring spin at moments, which lulls the explanation to say that precession moves the object at 90 degrees to the torque.
(Wrong or right this is only a perception.)
The object appears to move at 90 degrees when we consider only the “crossway” new motion, without taking into account the motion of spin (which is occurring simultaneously).
This explanation is helpful only when we are willing to think purely in angular terms, without ignoring the overall dynamics and without complicating the explanation with linear factors and visualizations.
I hope you find use for this simple explanation of precession (in angular terms).
Best Regards,
Luis G.
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