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25 November 2024 05:55
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Welcome to the gyroscope forum. If you have a question about gyroscopes in general,
want to know how they work, or what they can be used for then you can leave your question here for others to answer.
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Question |
| Asked by: |
Chetan Kulkarni |
| Subject: |
Gyroscope precession |
| Question: |
Hi, I am the Master student and i m doing my research on Gyroscope. In my research in the center there is a sphere instead of disc, and there is outer and inner gimbals. I would like to ask 2 questions.
1) I wanna give the rotation to both outer and inner gimbals. For inner gimbal rotation is there any solution,as if we are mounting the motor to rotate the inner gimbal it will also rotate along with the outer gymbal so i need solution to this problem.
2) Is it necessary to consider the Moment of inertia of the gimbals? I mean to ask both inner as well as outer gimbals. Please try to answer me as i stuck with these two questions.
Regards,
Chetan Kulkarni. |
| Date: |
15 January 2009
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Answers (Ordered by Date)
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| Answer: |
Paul LaRocca - 10/03/2009 18:17:30
| | | Hi,
I would be happy to talk to you about why a gryoscope works.
I would ask you sign a NDA.
What you have learned is all wrong!
But I like your questions so I see there is a possibility you will catch on quick.
The answer to Your question would be found through magnetics.
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| Answer: |
Subramanian K - 17/05/2009 17:26:30
| | | One of the Answers for your Question, Indirectly, is that our earth, which is a Sphere , is Itself is like a Gyro--Spinning Mass. The Axis of Rotation ie the North -- South Axis is wobbling . Probably the Article Pasted Below may give you some Details to see Earth ,An Approx Spherical Mass Rotating (Spinning.
)
Precession of the Earth's Axis
When ancient people looked at the stars at night, they saw a different "Pole Star" than the Polaris that we have today as our Pole Star. Even the ancient Greeks (specifically Hipparchus) had noticed this slowly changing effect. It was such a slow effect that he didn't SEE it, but rather, he noticed that drawings of star locations which were made generations before him showed clearly different positions of the stars! Of course, at that time they didn't realize that the Earth moved or that it went around the Sun, so they didn't have any analysis or explanation for what they were recording.
Eventually, (after it was accepted around 1500 AD that the Earth rotates and moves around the Sun!) it was realized that the fact that the Earth's spin axis is significantly TILTED (which causes our Seasons), caused a situation where the Earth's motion
represented an effect apparently resembling that of a child's top or gyroscope. The CAUSE of this effect is not quite the same as for a toy gyroscope on the Earth's
surface. The premise is that the earth is a giant gyroscope which is affected by each of
the Sun and Moon, and which therefore has a period for the precessional "wobble" of (currently) about 25,800 years.
_____________________________________________________________________
Thanks.
Since the motion of the Earth seems so similar to that of a gyroscope, it seems that it has been assumed that the same mechanism is at work. That is only a partially correct assumption! It is certainly another application of Euler's equations, and very closely related, but different. I think that using the same term, precession, to describe the action of a gyroscope and the Earth's motion, may be technically incorrect, and definitely somewhat misleading. Even though they LOOK to be the same, they are actually somewhat OPPOSITE!
A child's gyroscope is affected by the outside effect (gravity) where the gyroscope tries to fall over. The Earth is affected by the outside effect(s) (the separate gravitation of the Sun and Moon) where the Earth tries to stand up straighter!
If the Earth were perfectly spherical and uniform, there would be no precession at all! It only occurs BECAUSE the Earth has an equatorial bulge, that is, the Earth is deformed due to its rapid spinning.
It is pretty accurately known that the entire Earth has a moment of inertia of about 8.070 * 1037 kg-m2. But this number has no direct value in analyzing the precessional movement of the Earth! Because the Earth spins fairly fast on its axis, once every day, where locations on the Equator are rotating at over 1,000 miles per hour, the actual shape of the Earth is not precisely a sphere but it is slightly deformed. We sometimes say that the Earth is "flattened" at the Poles. There are a lot of complex ways of describing and explaining this flattening (officially called Oblateness) but we will just accept it as a fact here. Effectively, for our purposes here, we can look at the Earth as being a composite of two different (spinning) objects. The first is a perfectly spherical planet, with a diameter of the Polar diameter (around 7899 miles [12,713 km]). This object, being spherical, has NO significance regarding any precession effects. The second component is an extra 'belt' of material, with a maximum thickness of around 13 miles (21.4 km), around its middle, that accounts for the Equatorial diameter of 7926 miles (12,756 km). This "belt" somewhat resembles a very distorted "donut" of material has its maximum thickness at the Equator, and tapers off in thickness both to the north and south. The significant fact here is that ONLY THE BELT represents an equivalent to our toy gyroscope. That belt of material is estimated to have an effective moment of inertia (I) of about 3.3 * 1035 kg-m2, about 1/250 that of the whole Earth.
This all makes excellent sense. The next part gets a little more complicated. Imagine JUST the Sun for a moment (and forget the effects of the Moon). On March 21 or September 21, on an Equinox, the Sun is directly above the Equator. At this time, there is NO Precession effect! The Earth does NOT Precess at all on those days! Now consider June 21, the Summer Solstice, where the Sun is as far north of the Earth's Equator as it can ever get. Try to ONLY think about that belt now, from the Sun's point of view. The belt would look tilted downward, 23.45° toward the Sun. (Someone on the Sun would sort of think they were looking at the 'top' of the oval-looking belt.)
Now just think about the NEAREST part of the belt to the Sun (on that day). The Sun's gravity would be pulling it, of course. The important part here is that part of that pull of the Sun on the Earth would be pulling THAT PART of the belt, not only TOWARD the Sun as we expect, but ALSO UPWARD. This would have the effect TOWARD flattening the tilt position of the belt out (or of causing the Earth's rotational axis to stand up more vertically). Now, if we consider the farthest part of the belt from the Sun, the effect would be to also pull it UPWARD, but that would act to make the belt tilt even more (or of causing the Earth's rotational axis to tilt over farther). These two effects are opposite of each other, the first trying to level out the belt and the second trying to tilt it more. It might seem that these two effects would exactly cancel and nothing would happen. Almost! The NEARER part of the belt is nearer the Sun, and the effect of gravity depends on distance (the inverse-square law). The result of this is that the effect on the front portion is stronger than the similar effect on the rear section. So the "flattening" effect is stronger/greater than the "increased tilting" effect. When they are combined, the TOTAL EFFECT is to act to try to flatten out the belt of material, or equivalently, to stand the Earth's spin axis up more vertically.
The effect is therefore actually a SECOND-ORDER effect, where the main (larger) effect tends to cancel out amd only a smaller effect remains to have any effect.
In case this was too confusing, the important part is that Sun's gravitational effect on the belt (on that day) would have the effect of creating a Moment (or torque) that would be trying to tilt the Earth's belt axis toward being more upright. The fact that the belt is rigidly attached to the rest of the Earth means this same effect occurs to the entire Earth. The technical name for the tilt of the Earth's axis is the Obliquity of the Ecliptic.
If you followed this, you might want to think through what happens at December 21, the Winter Solstice. You should find that, again, the net effect is to try to cause the Earth's axis to become more vertical. This (differential) effect of the Sun is therefore the same whether the Sun is looking at the top or the bottom of the equatorial belt.
Even though Summer and Winter have the Sun looking at opposite sides of our Equatorial belt, the effect turns out to be the same, where both have the effect of trying to cause the Earth's axis to become more vertical. So we have NO precession around March 21, a MAXIMUM around June 21, NONE again around September 21 and MAXIMUM again around December 21! It is NOT a constant effect like everyone has always told you!
OK. This is SOMEWHAT like a child's gyroscope, but with two major differences. (1) Where gravity on a toy gyroscope is trying to INCREASE the tilt angle of the axis with vertical (make it fall over), the situation with the Sun and the belt of the Earth is trying to do the opposite, to stand the Earth up straighter! (But both are applying a Moment (torque) to try to tilt the axis, which is actually the important part!) And (2), the precession effect of the Sun is NOT CONSTANT! Every year, it completely stops at March 21 and September 21 (when the Sun is directly over the Equator and the belt) and becomes maximum on June 21 and December 21.
When people speak of the precession of the Earth, they usually ASSUME that it is a CONSTANT process! They probably don't realize that they are actually talking about an AVERAGE rate, because it is constantly changing like crazy!
We have been discussing the effect of the Sun, but the Moon also has essentially identical effects. The Moon's motion is extremely complex and there are other (small) variations in the rate of precession due to the Moon. The Moon revolves around the Earth each month, and it is much closer to us than the Sun is. Even though the Moon is far less massive than the Sun, the gravitational effects regarding Precession are actually greater due to the Moon than due to the Sun (as calculated below). AND they change even faster, with the two maxima and two minima every 29.5 days!
The analysis of the Precession due to the Moon is more complicated, for several reasons. The Moon's orbit is tilted several degrees from the Ecliptic, its orbit is rather elliptic (the Moon coming nearer and going farther from us every single month, and worse!) and the plane of that orbit constantly Regresses in an action similar to precession, in a period of around 19 years. This variation on the orientation of the Moon's orbit sometimes enhances the Sun's Precessional effect and sometimes fights it, so there is a prominent variation of precession in around a 19-year period, one of the effects which are collectively called Nutation.
I hope you can see why I am a little bothered by using the same word, Precession, to describe a gyroscope's (constant, fall-over) motion and the Earth's (herky-jerky, stand-up) motion. But, yes, they certainly have many similarities, especially the end effect of the wobble!
Because the Moon has so many other effects involved, our calculations here will focus on the Sun and its precessional effects. The Moon is analyzed in the same way, but the mathematics is far more involved, and we feel it would be distracting here.
The magnitude of the Sun-sourced force vector (and Moment) must be calculated in the same manner as for the gyroscope. The Earth's total moment of inertia (I) is 8.07 * 1037. We have also discussed above that the estimated moment of inertia of the Earth's equatorial belt (Ib) is about 3.3 * 1035. Any torque (or Moment) applied to the (belt or whole) Earth has to act on the whole solid Earth. The Earth's daily rotation rate w is 7.292 * 10-5 radians per second, so the magnitude of the Earth's angular momentum vector (H) is the product of the TOTAL Moment of Inertia of the Earth times that rotation rate, or 5.866 * 1033 kg-m2/sec or nt-m-sec.
The mass and distance of the Sun are known, and so is the 23.45° angle of the tilt of the Earth's axis. It is possible to calculate the Moment/torque effect of the gravitational attraction of the Sun on the Equatorial BELT at any instant, since it is basically only dependent on the distance involved and the angle of the tilt at that instant. We know that it is ZERO around March 21 or September 21!
It is pretty easy to calculate the instantaneous Torque on June 21 for the tiny part of the equatorial belt directly under the Sun and that part exactly opposite. It represents about 5.73 * 1022 nt-m. One must mathematically Integrate the Moment effect over the entire belt and over an entire year (fairly easy Calculus) to get the net annual average torque effect due to the Sun as being 1.44 * 1022 nt-m.
We then have an (average) Moment (torque) applied of 1.44 * 1022 nt-m. This is the dH/dt of far above! H is the 5.866 * 1033 nt-m-sec we just calculated. In the same was as we did with the toy gyroscope, we can now determine how great the effect is. The quotient of this is 2.45 * 10-12 radians/second. This is the same as a Precession rate of 15.94" arc-seconds per year. Note that we have ONLY considered the Sun, and resulted in a precession effect on the Earth, completely due to the Earth's non-spherical shape (due to the Earth spinning on its axis) and its effect of creating a belt around the Equator. The Moon does NOT even need to exist for this Precession to occur! However, this precession due to only the Sun (the 15.94 arc-seconds per year) would mean that the Earth would precess entirely around in (360 degrees divided by 15.94 arc-seconds or) 81,300 years, much more slowly than we know that it actually does!
By the way, we have simplified these calculations here to not include the effects of the varying distance of the Earth to the Sun due to its elliptical orbit, or that that ellipticity is even slowly changing!
It turns out that if we ONLY consider the Moon, using entirely different numbers but essentially the same logic, we get another precessional effect on the Earth. The Moon's orbit is tilted from the Earth's equator (and also has another 5° of orbital inclination from the Ecliptic) and so all the same stuff applies. The Moon is much less massive than the Sun, but it is also much closer. The calculations (like above) give us an average monthly average torque as 3.1 * 1022 nt-m, slightly more than double the effect of the Sun. With all the exact same calculations as above, we get a result that if only the Moon were causing precession, the Earth would precess entirely around in (360 degrees divided by 34.45 arc-seconds or) 37,600 years, or alternately, we can say that the Moon causes an annual precession of 34.45 arc-seconds.
The Moon's orbit is not very circular (it has eccentricity, and that eccentricity has constant changes of its own!) and so the calculations depend on where the Moon is in its orbit, so the math is much more complicated, but otherwise the same.
. By the way, the fact that the Moon has these effects far more rapidly than the Sun does, every few days, and it is also of around twice the net effect, our associated presentation regarding the Violation of the Conservation of Angular Momentum includes the calculations which show that an average of around 63 million kiloWatts of power is being transferred into or out of the Earth's Lunar-driven Precessional motion! This 63,000 Megawatts is comparable to ALL the electrical power generated by ALL of the US Nuclear-powered electric powerplants. I do not see any possible way that we humans could ever accomplish where we might ever capture any of that power, but it is certainly an intriguing thought!
Scientists generally refer to a Luni-solar Precession, which is the total effect of these two, the 15.94 arc-seconds per year due to the Sun and the 34.45 arc-seconds per year due to the Moon, or a net effect of 50.39 arc-seconds per year.
All this has been presented to remind you that the ACTUAL precessing effect at any instant is dependent on a huge number of variables, and that the normal reference to "precession" is really just a long-term average of a lot of complex effects!
The Earth's precessional movement is actually an effect almost identical to a phenomenon called the Regression of the Nodes of the orbit of the Moon. If you are familiar with that phenomenon, hopefully you see the many similarities. If not, never mind! (Or consult a good textbook on Regression of the Nodes.)
We just noted that when the (annual) precession of the Earth due to the Sun and that due to the Moon are combined, the calculated effect is a (lunisolar) precession of around 50.39" of arc per year. (This would indicate that precession would take around 25,700 years.) However, because the Earth's axis is tilted, even the other planets are able to cause the same sort of precessional effect! And the other planets' gravity act to distort the orbit of the Earth, too, (Regression of the Nodes) slightly changing its shape and angle and orientation. Each planet causes its own effect, but the greatest is due to the massive Jupiter. Since we "pass" Jupiter in our smaller orbit, its precessional effect is actually in the reverse direction of that due to the Sun or Moon. When all the planets are combined, their combined precessional effect (Planetary Precession) on the Earth is (currently) around -0.106" of arc per year. SOOO! The TOTAL of all precessional effects on the Earth is slightly reduced from the lunisolar precession and is (currently) around 50.29" per year (and slowly but temporarily increasing, due to a variety of causes). This results in a full precession cycle as being (currently) very close to 25,800 years. (For clarification, all the way around means 360 degrees, which is 1,296,000 seconds of arc. Divide 1,296,000 / 50.29 to find out how many years that precession rate would take to go all the way around, which is about the 25,800 years.)
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| Answer: |
Glenn Hawkins - 18/05/2009 23:09:51
| | | Hello Chetan, I learned that anything to do with a gyroscope is hard to explain and that once explained it is even harder to understand. Your English is fine. That’s not a problem.
You say your flywheel is spherical and that you want to rotate not the sphere, but rather the two right angled frames that are called rings. ----- That’s not what you mean to say.
I suppose you want a motor with a gear to rotate the sphere. I suppose you wish to attach the motor housing to an enter gimbals ring to provide stability against the equal and opposite torque your motor produces. The sphere and ring however, would then rotate oppositely with equal momentum. Again I suppose -- that’s not what you want to happen. If you next attached with bearings the enter ring to the outer ring again nothing much will change motion wise. If you were to however, still seeking stability, remove the bearings and weld the rings together it too would -- -- -- --. I believe from what you wrote you already understand all this.
My friend what I think, at least in regards to my mind, is what you should do first is design a question much better, and as I said at the beginning, I think that is hard to do concerning gyroscopes. Be sure to try again. The next time will be better.
Luck with your project.
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| Answer: |
Ed Bargy - 17/08/2009 23:39:21
| | | Just from a mechanical design view
Use compressed air to drive the inner sphere and to develop a reaction jet nozzle to keep the inner gimble from counter rotating to the sphere. The gimbles and there bearings can be hollow to duct the air flow.
You''l won't any heavy electric motors to mount and spin on the gimbles.
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