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29 November 2024 02:58
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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.
You may also be able to help others by answering some of the questions on the site.
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Question |
| Asked by: |
Luis Gonzalez |
| Subject: |
The What, Why, How, and Which of Precession! |
| Question: |
WHAT is Precession?
Precession is the “motion” that occurs as an object realigns its rotation axis, to the rotation axis of the torque applied.
WHY do these 2 axes of rotation have to realign?
Realignment of rotation axis occurs because the aligned position is the position where the sum of all the dynamics requires the least (minimum) energy and is therefore more stable.
HOW does the rotating object determine in which direction to move so it realigns correctly?
The direction of realignment motion (precession) occurs as a result of the encounter of 2 forces in different directions. The aggregation of the force vectors determines the direction toward alignment.
WHICH forces create the vectors that determine precession’s attributes?
An inventory of forces tells us that Centripetal / Centrifugal (CC) forces exist in 2 locations, 1) the gyro-flywheel, and 2) the system.
The direction of Centripetal / Centrifugal (CC) forces is radial in relationship to their respective centers of rotation. Note that each CC force is distinguished from an exact twin that would be created by rotation in the opposite direction.
Therefore the direction of the momentum in rotation gives the forces involved a sense of direction that can be said to be right / left handed or clockwise / counterclockwise, depending on the perspective of observation. The dynamics of each cycle maintain absolute and balanced sets of symmetries.
Opinions on this model theory are welcome.
Please stick to the point, and backup your comments with logic based on acceptable or evident premises.
Thank you, Luis |
| Date: |
13 August 2006
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Answers (Ordered by Date)
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| Answer: |
chris jones - 18/08/2006 19:56:28
| | | hello luis
so to get my machine to fly I have to make it fall upwards
sounds easy now
thanks
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| Answer: |
Luis Gonzalez - 21/08/2006 03:38:22
| | | Chris,
I am guessing you are responding to the content of this thread, but I can’t imagine how you arrived at your conclusion based on it alone.
The content of this thread strives for a better understanding of precession.
I don’t see the connection to flying yet (you may be reading more into what I wrote than I intended).
If you are sticking to the point, please develop your line of thinking so we may all try to understand it.
Thank you, Luis
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chris jones - 22/08/2006 18:38:49
| | | only joking luis
sorry
the gyroscope will not realign itself
It will never ever ever occupy the same space again, even relative to the earth it is just falling over but taking its longest rout..consider the the centre of the gyro, it is relativey motionless compared to the rim, as it topples one the motionless part moves off centre so that the gyro is now out of balance so it changes direction. As it is constantly falling it is constantly changing direction but it will eventually hit the floor.
lots of love chris
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| Answer: |
Luis Gonzalez - 24/08/2006 03:10:21
| | | Chris,
Your comments made me realize the error of taking a portion of a thread and placing it out of its context as I did with my opening statement.
The context I failed to bring to this thread is that I am referring to a gyro in gimbals and the torque is applied by turning the gimbals (using a motor or simply ones hand and wrist), not by gravity.
This changes the nature of the exercise and I should have placed it in the introduction of the thread.
Your response refers to a gyro with an axle of asymmetrical length, where the other end of the axle rests on a tower and the torque is applied by gravity. The physics on your example are much more complicated (even though the device is easier to build).
In your example, the gyro-flywheel still attempts to realign itself to the rotation of the pivot-torque created by gravity and the tower; however the gyro simply chases the “position of balance” but can never achieve re-alignment because the pivot torque changes dynamically; continuously staying exactly ahead on the cycle (it is a remarkable toy).
Strictly speaking the downward motion observed in a gyro on a tower under gravity is not primarily caused by “falling” but rather by secondary precession as tiny frictions produce forces that respond at 90 degrees (downward in this case, per Nitro’s law).
“Falling” would be the motion of mass carried in the direction of the force of gravity, but that is negligible in a fast spinning gyros which sill move downward with each round.
In a very slow spinning gyro “falling” contributes a greater amount to the observation of downward motion.
I don’t expect you to believe or understand this explanation though it is what takes place; read through my previous thread (16 May 2006 by Luis AE Gonzalez http://www.gyroscopes.org/forum/questions.asp?id=571) for a fuller explanation of the dynamics of precession etc.
Thank you, Luis
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chris jones - 25/08/2006 17:33:10
| | | hello luis
If you don't expect me to believe or understand your explanation why don't you write it in a way that I may understand it and then if it makes sense I may well believe it.
chris
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| Answer: |
Luis Gonzalez - 26/08/2006 04:45:53
| | | Forums have audiences that vary in size and attendance over time.
Though we appear to be addressing a single individual, forums offer our writing to a broad audience for an indefinite time span.
Readers who have the right type of training, sufficient time and the will to stretch their minds visualizing the dynamics can understand the challenging concepts explained.
My clarifications are for that category of readers (I know of a group who understands it quite well).
I thank Chris for making me realize that I had left out the context from my initial statement.
If you are really interested in understanding, you can do it by applying some effort and careful reading the right portions of this forum. (I suspect it won’t be easy.) The information is in this forum, but it’s not for everyone.
Cheers, Luis
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chris jones - 26/08/2006 12:42:56
| | | I suspect this is more about how clever you are than abou gyroscopes
thanks for your so obviously wasted time,
best wishes chris
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Nitro MacMad - 26/08/2006 14:25:06
| | | Dear Luis,
The British army (and others) used to use a pseudo Latin motto that was oft quoted thus :- "Nil Iligitimi tu carborundum." Roughly translated it stands for:- Don't let the b**tards grind you down."
I don't always agree with you but then I'm a shed man, myself. I do however think you put some effort into arriving at you views. No one should be castigated for effort.
Perhaps Chris, you might like to put some effort into putting your views in a more pleasant from and express your ways to progress our understanding next time.
Kind regards
NM
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chris jones - 26/08/2006 15:48:24
| | | dear nitro nand luis
I have no wish to cause any offence to anyone here and have read most of the threads in this forum
I apologise unreservedly and withdraw
I wish you well with your endeavours
chris
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Momentus - 05/09/2006 11:03:14
| | | Nitro,
Nicely Phrased response. Gratuitous insults are so easy to make and are usually the weapon of choice of the scientific establishment. As you so rightly say, they have no place in reasoned argument
The apology, Chris, would have had merit if it had addressed the substance of Luis’ argument. Some logic if you do not agree.
Luis
As I have previously posted, velocity has two components, magnitude and direction. Precession is the change in direction; spin speed is the change in magnitude.
Precession can be visualised as the deflection (change in direction) of a small mass circling inside a crystal sphere. Think ball bearing in fish bowl.
As the ball passes the north pole, it is deflected by a force applied at right angles to the plane of rotation. This deflection does not alter the velocity of the ball, (i.e. the spin speed remains constant.)
When the deflected ball reaches the south pole, it is deflected again by a force equal and opposite to the previous one. Repeat the actions and the plane of rotation turns about the north/south axis. This is to say, the spin axis moves around the equator.
The equal and opposite forces, acting at the distance between the poles, constitute a couple. The reaction to the couple is precession, orthogonal to the couple and spin.
Now keep adding balls to the visualisation until it approximates a solid rim.
Luis you say:-
“An object realigns its rotation axis, to the rotation axis of the torque applied. “
This is not so. The axis of spin, torque and precession remain orthogonal at all times.
I agree the downward motion of a tower gyroscope is as you say, caused by “tiny frictions produce forces”
Torque is a vector quantity - adding friction torque to gravity torque gives a resultant torque and a resultant precession which spirals the gyroscope down.
I do not agree with your statement:-
“Precession is the “motion” that occurs as an object realigns its rotation axis, to the rotation axis of the torque applied.”
This is a simple mnemonic designed to assist in determining the direction in which a gyroscope will precess under different spin/torque combinations. It should not be confused with the reality of gyroscope behaviour where at all times and under all conditions spin, torque and precession remain orthogonal.
Simple rule of thumb: - If it rotates that is precession and there is a couple acting orthogonal to the movement, whether or not that is the couple you thought you applied, or the movement you thought you would get.
Centrifugal/petal forces do not cause precession, are not part of the process. Precession is the orthogonal reaction to a couple, pure and simple.
I trust you find this of interest and useful in your pursuit of “THE MYSTERY” of gyroscope behaviour.
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Luis Gonzalez - 11/09/2006 02:36:45
| | | Gentlemen,
Thank you for your responses.
Momentus,
Your explanation of precession is a notch above what is found in text books, in part because of the so well presented, compelling images. Yet it is still not easy to find full explanations of the how and the why (I tend to get into lengthy explanations whenever I try, but we must continue expanding the depth of our understanding).
You are one of few I regard highly in this subject. It is unfortunate that all human beings find occasion to be wrong, if only by the limitations of language.
In the interest of brevity I will address only what I think is the one most important issue.
I do agree that a gyro on a tower (under gravity) always maintains an orthogonal relationship between the torque-axis and the precession-axis (there is a good reason for that). However you may have missed my second response to Chris where I added context to my initial statement (haste makes waste).
Please conduct the following test using a gyro in gimbals with symmetric axis (i.e. axis of same length on both sides therefore no gravity-torque) guided by the steps enumerated below.
1) Spin the gyro flywheel
2) Use your hand, a turn table, or any other mechanical means to apply a consistent torque to the external gimbals cage.
3) Observe that the initial resistance, which is accompanied by temporary precession, soon gives way. Precession stops even though the applied torque is maintained because the system has achieved a position of balance.
4) Maintaining your exact same torque take note the axis of torque.
5) Note that the gyro spin-axis is the same or parallel to the torque-axis.
The correct conclusion is that the 2 axes are no-longer orthogonal.
It is a difficult to discuss a subject with many possible configurations and experiments.
Also, terms may be used I slightly different ways making their use ambiguous at times.
The search is exhilarating but the experience can be humbling; it is the sign of a worthwhile effort.
I will be crossing the pond this Wednesday to join a Mediterranean cruise until the end of the month.
I hope to find more interesting responses when I return. Ciao.
Thank you, Luis
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Momentus - 18/09/2006 13:29:24
| | | Hi Luis
The fully gimballed gyroscope which you describe does follow the orthogonal rule.
It may help you to figure it out for yourself if you think about the instantaneous nature of couple/precession. A batsman may talk of hitting the ball; it is equally valid to say the ball hits the bat. So with precession, the movement and the force are one event.
That being the case, the force you are applying is only part of the resultant force that reacts the orthogonal couple which accompanies the precession.
Torque is a vector quantity. If you examine your particular configuration you will see how the other vector is transmitted through the frame.
If you position the spin axis at 45 degrees to the torque axis, there will be two of the frame rings which can be used to move the spin axis.
I am off to the Mediterranean myself today for a well earned holiday, back in a fortnight.
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Luis Gonzalez - 01/10/2006 16:22:42
| | | To understand what follows one must be able to exclude the existence of gravity from many of the interactions explained.
FACT1 – If two separate axis (around which angular momentum takes place) are parallel, then it is not possible for these 2 exes to be orthogonal (at right angled to each other) at the same time. By definition perpendiculars can not be parallel and visa versa.
FACT 2 – Anyone can verify that applying a torque in the same direction that a gyro is spinning, produces NO precession. This is the position of “stability,” which occurs where the axis of spin’s angular motion is parallel to the axis of angular motion of applied torque.
FACT 3 – When torque is applied to a gyro at any other angle where both axes are not parallel, then precession WILL occur toward the position of “stability.” This precession will stop (shortly after) when the gyro arrives at the position of “stability” which is where both axes of angular motion (spin & torque) are parallel.
You can dispel any doubts about these facts with tests that are relatively easy to conduct by anyone.
Momentus, I hope you enjoyed your Mediterranean trip as much as we did.
Your statement regarding whether a bat strikes a ball or visa versa addresses the relationship between motion and force but is not relevant to the point I am trying to make regarding the basic relationship between “axis” of angular motion of spin, an the “axis” of the angular motion of torque (note that I am only talking about the two axes and nothing more complicated than that).
All statements and arguments regarding torque vectors and other vectors (true or not) are beyond the point being presented (the axes) and are not germane to the 3 facts above. These 3 facts are basic to the foundation upon which a clear explanation of precession may be derived (or built upon).
It is apparent (if not obvious) that current explanations of precession lack clarity, completeness, and many are encumbered by truths bundled together with misconceptions.
At best, the existing landscape of explanations for precession is littered with partial facts connected in questionable and incomplete ways. Further, the best explanations of precession fail to mention important facts, relationship, and rules that are essential attributes of precession, even though these attributes are self evident in gyro interactions.
I believe it is time to build from the ground upwards, a new paradigm of what happens during precession (based on Newtonian facts); hence the need to promote basic, realistic foundation facts upon which to build this paradigm.
Momentus states that, “The axis of spin, torque and precession remain orthogonal at all times.” Note that this indicates all 3 axes must remain perpendicular to each other (orthogonal) at all times; observation indicates otherwise.
Momentus’ statement is only partially true. The axis of torque and the axis of precession are in fact always orthogonal. However this is NOT entirely true for the axis of spin (under any configuration)!
Note that I am not referring to vectors, but simply to the relative positions of the axes (plural for axis in America).
- The rebellious axis of spin can occupy a range of positions from less than 180 degrees to greater than zero degrees in relationship to the precession axis (as in a tower under a gravity torque), XOR in relationship to the torque axis (as when a constant mechanical torque is applied), BUT NOT in relation ship to both!
Not understanding this last set of rules causes tremendous confusion because (to my knowledge) they have never been stated publicly before. (This dynamic relationship among the 3 axes is MOST important when trying to make sense of precession).
It will take keen minds to see how these rules are true facts, and how transition can occur from spin-axis being orthogonal with the precession-axis, to being orthogonal with the torque-axis. It is easy to demonstrate such a transition by hurrying a gyro in precession under gravity, so that it rises as the torque of gravity is replaced by the torque of an angular push, in the direction of the original precession. The difficulty occurs when one tries to recognize all the interactions and what is happening to the relationships among the 3 axes.
My thanks go to Momentus, for stimulating me to write this response.
Regards, Luis
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Luis Gonzalez - 10/10/2006 22:25:11
| | | While you are thinking about the last response, here is another point of interest.
The term “couple” refers to dynamic interaction between angular motions (two or more velocities and/or forces). Spin and torque are the 2 coupling motions that produce precession. Both of these angular motions are inseparable from each of their own Centripetal/Centrifugal (C/C) forces, and can not exist without them. The C/C forces are in fact alternate manifestations of the kinetic energy embodied in the angular motion which provides the energy for the “couple.” A “couple” can not exist without an embodied energy (any one disagrees?).
On the basis of considering the energy requirements necessary for a “couple,” and with all due respect, I disagree with an earlier statement from Momentus that “Centrifugal/petal forces do not cause precession, are not part of the process.” This statement assumes that C/C forces are completely separate from the interaction (i.e. the couple) of the motions involved. It appears to imply that the C/C forces can be removed or should be ignored when considering precession. This is an error; the fact is that Centripetal/Centrifugal (C/C) forces simply provide an alternate view from which to perceive and analyze precession in a deeper and more complete way.
Momentus prefers to simply say that “Precession is the orthogonal reaction to a couple, pure and simple.” In other words, that one need not go any deeper and that the statement sheds sufficient light and brings full understanding to all; but it does not. This statement is a shorthand or mnemonic that is accepted without full explanation; a widely accepted sort of black-box. However saying that precession is an orthogonal reaction to a “couple,” is not any clearer than saying that precession is a gyro’s 90degree response to a torque. Both statements are true but fail to provide further explanation and fuller clarity.
Mnemonics or rules-of-thumb are appropriate and speedy for common engineering purposes, but do more harm than good when the goal is to explore and uncover hidden truths. The otherwise useful shortcuts simply get in the way of drilling down to uncover chains of cause and effect.
The best way to find the secrets of any “MYSTERY” is to pursue cause-and-effect chains and document them in an organized manner. It is a sure way to melt any mystery into simple facts and concepts.
The bottom line is that if C/C forces and angular motions are different perceptions of the same basic energies involved; shouldn’t we try to find ways to further define what occurs during precession? The standard rules-of-thumb have thus far proven insufficient to resolve whether gyro propulsion is possible or not. Maybe we are not allowing ourselves to explore in directions that are correct.
Many incredibly erroneous perceptions are expressed in this forum without opposition from anyone. For example, I have more than once read a statement that “precession results from gravity causing the downward side of the gyro spin to try to move faster than the upward side of the gyro spin.” No one pointed out the error in this kind of thinking.
I may conclude that extraordinary errors are not challenged because they are not worth addressing.
Does that mean that challenges to my model indicate it is worthwhile addressing or at least that it is not perceived to be utterly ridiculous?
Once again, thank you for the space to express my views among intelligent men. Please excuse any hurtful effects of my remarks; remember that I attack the ideas and not the people.
It’s easy to become complacent with stale ideas that interfere with forward progress (isn’t that precisely what we in this forum constantly complain about in regards to academia’s views?
Thank you, Luis
P.S. Naturally you can be sure that the relative positioning of the 3 axis discussed previously lays the foundation upon which the dynamics of C/C forces is used to explain precession in a, hopefully, more clear and intuitive manner.
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Momentus - 14/10/2006 20:53:31
| | | Hi Louis,
"The term “couple” refers to dynamic interaction between angular motions (two or more velocities and/or forces)."
No. In the context of spin, precession couple "ie gyro behaviour, couple means equal and opposite forces applied at a distance. No more. No less."
Torque is a vector quantity.
Your whole concept of aligning spin axis to torque axis is based upon your mis understanding of this fact. It does not happen if the test/experiment is done with full freedom of motion.
I will have another go at explaining this when I am not so pushed for time.
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Luis Gonzalez - 17/10/2006 14:14:34
| | | In this somewhat esoteric subject it’s not easy to gauge levels of understanding with few words.
Momentus, I agree with you that with full degrees of freedom, the 3 axes do remain perpendicular (orthogonal) to each other. You are correct from the standpoint of pure theory; I stand corrected in that my intent has been to develop a robust model theory starting from pure basics.
The issue with pure theory is in its application; in the ability to use it to build practical mechanical devices.
Let me explain. It may be impractical to build devices with mechanically driven torque, and at the same time expecting the axis of the torque motor to move smoothly in order to remain orthogonal with both spin and precession axes, either of which will be in motion. The practical dilemma is that a robust torque motor, capable of producing significant thrust, will need to be carried along with the motion of precession (if it is to remain orthogonal).
Granted, a trivial version of such device is not extraordinarily challenging to build; if one uses a relatively light spring as a torque source, but this device can only operate for short spans of time. The key here is that if one wishes to provide all axes the full freedom of motion required to remain orthogonal, then one must place the torque-agent inside, what may be considered as the inner ring of gimbals, (Let me know if you don’t visualize this, though I believe you already have).
The main problem is that the weight of a robust torque motor adds significantly to the total dead weight inside the inner gimbals ring. As the ratio of deadweight mass to spinning mass increases the gyro bogs down i.e. is more quickly carried along in the direction of the torque. This is the equivalent of a toy gyro falling off the tower too quickly.
Secondly, a configuration that provides complete freedom of motion basically duplicates the configuration of a gyro-on-a-tower-under-gravity, which is not a likely device for conversion to effective linear acceleration.
I recognize that I should have introduced earlier the concepts involving degrees of freedom and how applying a ‘useful’ mechanical torque effectively removes one degree of freedom. I just happened to write things in the order that I presented them.
I still believe that when trying to build practical propulsion machines, the way I explained the principle is more suitable. I do have to preamble my description with the statement that the torque axis is fixed in order for the behaviors I describe to be true.
I also agree that your definition of “couple” is the correct one, which in Physics means, a pair of forces of equal magnitude acting in parallel but opposite directions, capable of causing rotation but not translation.
However I still believe that the statement that “Precession is the orthogonal reaction to a couple, pure and simple” is much too simple to shed the necessary level of clarity needed to understand the interactions taking place in precession.
All in all I appreciate your insightful responses enormously Momentous.
Thank you, Luis
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Sandy Kidd - 23/11/2006 06:55:20
| | | Momentus,
In your posting you stated:
“No. In the context of spin, precession couple "ie gyro behaviour, couple means equal and opposite forces applied at a distance. No more. No less."
I am old, and probably not the sharpest knife in the drawer, but for the life of me would someone, in simple mechanical terms, explain to this old coffin dodger where, why, and how, this alleged gyroscopic couple makes its presence felt.
Sandy Kidd
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Luis Gonzalez - 25/11/2006 19:28:30
| | | Sandy,
Start by thinking about it simply as a “mechanical couple,” NOT as a “gyroscopic couple.” First research the concept of a “couple” from a neutral perspective to get a clean view if what it means without the hubbub and complications of gyroscopes (do a Google search on “mechanical couple.”). Once you have the pure concept of a “mechanical couple” clearly in your mind then apply it to an inanimate object. For example picture a vehicle parked crossways on the middle of a two way road. Then see it getting hit simultaneously by two cars of same mass and speed coming from opposite directions of the road. The two cars hit the badly parked car at exactly the same time, one clips the front bumper and the other one clips the rear bumper (in different directions). The badly parked car is left spinning in the exact same spot it was originally resting. This is a bad though vivid illustration of a mechanical couple. If only one car had clipped one of the bumpers it would illustrate “torque,” and the car would have still spun but would have been moved by the impact to a different location.
In precession (and in all gyro responses at 90 degree to a torque) the motive force is a torque; the radial distance at which the force is applied is significant to the relevant calculations from that external perspective. However, from a perspective internal to the gyro flywheel, the radial distance to the point where the force was applied becomes irrelevant to the nature of the behavior. From this internal perspective it’s not relevant to know whether the magnitude was derived from the strength of the applied force or from the radial distance that leveraged the applied force. While torque and mechanical couple may resemble in many ways there are differences. Torque is a single force applied from a single direction (at any given point in time). “Mechanical couple” is composed of two parallel and opposing forces (at all moments in time) that do not meet at one point but rather at some distance from each other (though both forces interact with the same object). In precession, torque” is the applied external force, and “mechanical couple” is what results internally within the gyro. Though torque may be applied from a single direction at any given moment (as in gravity induced torque), or from all around (as in a motor driven torque), its effects are bifurcated by the shape and the dynamics of the rim in a gyro disk. The spin of the disk dictates that not all the radial segments of the rim receive the exact same effect from the torque. Rather, only opposing sides on the rim of the gyro flywheel receive effects of the exact same magnitude, but in opposite directions; hence the resulting transformation of an external torque into an internal “mechanical couple.”
It’s important to grasp that the internal effect (derived from the external torque) upon the rim of the gyro flywheel are two parallel and opposing forces, of the exact same magnitude, applied at opposing sides of the rim circle (can you see that?). That is why a “mechanical couple” is a better representation than a torque, when analyzing the dynamics involved in precession, from an internal perspective. The “mechanical couple” produces a change in orientation in opposed segments of the gyro flywheel’s rim, without directly changing the spatial position of the gyro. This subtle difference is a key perception toward understanding the cause-and-effect-chain of events that occurs during precession (and all such 90 degree responses of gyros).
To get a broader perspective of why we need to do this, think of it as zooming in to see the internal picture that allows us to perform qualitative or quantitative analysis, and then zooming out, to use externally, the results that we derived during the zoom-in exploration. In precession external forces cause change in the internal workings of a dynamic subsystem, and these results can then cause effects on the external system (there is a translation from the external to the internal dynamics, and the results are re-translate from the internal back to the external system). This translation of perspectives provides a way to ignore irrelevant variables at appropriate segments that these extraneous variables are not needed, and opens ways to apply mathematics in a cleaner way. I like to compare it to how the dynamics of planetary motion were once upon a time calculated from the perspective of earth being at the center, as opposed to conducting the same calculations based on having the sun at the center. The more accurate perspective opens the door for accurate calculations and a much better perception of the problem space.
Following this logic provides a way to apply step by step analysis to the phenomena of precession, in a way that is consistent with and congruent to the existing body of knowledge of science. When applied correctly this method is akin to normalization, de-normalization, and renormalization, processes that are used in highly complex areas of science such as computer software, as well as in the mathematical correlation of fundamental forms of energy (ours is a simpler effort).
Why should we do this? Because it offers a pictorial glimpse at the flow of gyro behavior during precession and may extend to explain why gyros behave as they do in different interactions. Also this analysis promises to yield correct quantitative results when properly applied (it provides guidelines for applying independent quantitative approaches).
In short, viewing the dynamics within the gyro as a “mechanical couple” (i.e. two parallel and opposing forces applied at different point of an object) yields a visual model from which precession can be seen to emerge from illustrations such as those presented by Momentus. The two main illustrations that Momentus presents are, one with a billiard ball bouncing off the banks of a circular billiard table, and the other includes a ball bearing moving on the inner surface of a crystal sphere. I will leave it up to you to re-read the two illustrations that Momentus provided. His illustrations (minus a couple of minor errors) become much clearer when we see how the “mechanical couple” fits in. Beyond this, the concept provides results that are predictably correct.
I am quite sure that I have misstated (or even hijacked) portions of Momentus’ concepts, but I am even more sure that Momentus will correct my inaccuracies.
Please excuse the long answer; I wanted to be sure I covered the landscape, though I am sure I missed important points. Ciao for now.
Thank you, Luis
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Sandy Kidd - 27/11/2006 15:35:47
| | | Good day Luis, and thank you for your reply to my question.
You said:
“It’s important to grasp that the internal effect (derived from the external torque) upon the rim of the gyro flywheel are two parallel and opposing forces, of the exact same magnitude, applied at opposing sides of the rim circle (can you see that?).”
No Luis I am dreadfully sorry but I do not see that at all.
These 2 parallel and opposing forces, where do they come from?
Consider a gyroscope which is rotating counter-clockwise when viewed on its outside or unsupported face, and the gyroscope itself is accelerated in a counter-clockwise direction when viewed from above its path of rotation.
Under any kind of acceleration the lower or advancing sector of the gyroscope will experience an increase in angular momentum whilst the topmost or receding sector of the rim will experience a lesser amount of angular momentum, due to the differential in relative velocity.
How can this produce a gyroscopic couple as so often quoted, a mechanical couple or any other kind of couple?
It will produce a differential across the gyroscope but not a couple.
What is supposed to create this inward rotating and opposite half of the couple?
Sandy Kidd
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Luis Gonzalez - 03/12/2006 00:38:41
| | | Sandy,
Anyone who can calculate momentum from velocity can determine the velocity-differential that would be necessary to produce momentum of sufficient magnitude to induce a 90-degree turn (it needs to be substantial).
This said, it’s a common error to believe that momentum differentials (of the type you explain above) are the cause of precession. This erroneous notion presupposes that the gyro moves continuously in the direction of the torque, preceding the 90-degree motion so precession can take place (otherwise there is no such differential). Simple observation shows that the 90-degree response to torque is direct and requires no initial motion in the direction of the torque. Further, more effective gyros (that have less deadweight) respond more efficiently in the 90-degree direction (larger proportions of deadweight can cause a slight drag in precession allowing for small amounts of motion in the direction of the torque.) Deadweight (the root cause of any such differential) can not contribute to precession. Finally, the velocity differential (in less efficient gyros) is inordinately small compared to the force necessary to produce the 90-degree turn of precession. Sandy and I appear to be looking at the Elephant from different perspectives.
Unfortunately, paradigm shifts are often the most difficult step toward achieving meetings of minds, because they require changing the way we think before we can accept the basis to the proof. It is not possible to make all concepts clear to everybody and that is also true about the concepts of “mechanical couple.” However, I will take a final attempt but must first reconcile the differences in perspective regarding the problem space:
(A) It seems evident that all 90-degree responses, by gyros, result from the portion of a torque that attempts to modify the orientation of the gyro’s axis of rotation. Any one disagrees?
(B) All other force vectors will not yield the 90-degree phenomenon (unless they introduce an element of modifying the orientation of the gyro’s spin-axis). Any one disagrees?
If we move the gyro in straight lines, curving arcs, or even circles (in any or all of the 3 dimensions) the 90-degree phenomenon will NOT occur unless we push (or pull) on one side of the axle more then on the other. Relatively simple experiments will prove these points.
NOTE: Items A and B above indicate that all other factors (other than attempting to change the orientation of the gyro’s axis) have nothing to do (directly) with the 90-degree phenomenon (i.e. precession). If you can accept the reconciling statements made up to this point, then we may be half way towards the necessary paradigm shift. Let’s continue.
(IMPORTANT) Though the length of the off-center axle contributes to the torque-strength, this axle-length only affects the displacement-VELOCITY of the gyro’s 90-degree motion (precession); however it does NOT affect the PERIOD of precession (i.e. the precession RPM remains the same, despite the length of the off-center axis, as long as all other factors remain the same). This is easy to verify through experiments (the math and physics also supports it).
I’m don’t know if I need to spell it out but here it is: If the “PERIOD” of “precession” is unchanged by varying the length of the axle (i.e. system radius), and all other causal factors of precession remain unchanged, this indicates that the ACTUAL DYNAMICS that converts torque to “precession” must also remain the same, despite variations to the length of the system radius (can this be a chance for counterargument). This tells us that ACCURATE analysis of the 90-degree phenomenon need consider ONLY the direct cause and effect factors; such analysis should not take into account other peripheral motions (which can only add confusion) because these other factors have no bearing on the connection between cause and effect of precession.
This is where I make the distinction between what I call an “internal” perspective (that excludes the peripheral dynamics) versus an “external” perspective that includes all the dynamics that we perceive from our normal standpoint when we observe gyro phenomena (Sandy’s momentum-differential is one such external perception).
Those who manage to grasp the concepts up to this point have most likely also made the paradigm shift and are ready to see how the “mechanical couple” fits in. Under the paradigm that “precession results ONLY from changes in orientation of the gyro-axis,” it’s simple to see that the motion of precession (90-degree phenomenon) is SYMMETRIC within the gyro-flywheel (when viewed from the “internal” perspective). It’s also simple to see that that the force received by the gyro-flywheel is also SYMMETRIC within the gyro-flywheel, when viewed from the “internal” perspective.
(IMPORTANT) Therefore precession’s true causal force is symmetric and the 90-degree result is also symmetric. From this internal perspective, the force can not be a torque because torque is NOT symmetric; however a “mechanic COUPLE” is SYMMETRIC! (Please refer again to the explanations of a “mechanic couple” to refresh your memory, see the connection, and achieve clarity.)
Those who have comprehended up to this point, are now at the doorway to once again review Momentus’ “round billiard table” and “bearing in a glass sphere” illustrations of how mechanical couple produces precession. The dynamics of precession have nothing to do with imbalances but have everything to do with symmetries. Though imbalance can cause the external induced torque, the rigorous analysis on the dynamics of precession must leave behind that step (in the sequence of events) and delve into what really occurs at the heart of the phenomenon, inside the symmetry of the gyro-wheel.
I suspect that this explanation may not be sufficient to convince some. Fortunately it’s not my goal to convince everyone. My purpose is to reveal an in-depth look at facts about what takes place during precession.
Thank you, Luis Gonzalez
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Luis Gonzalez - 03/12/2006 14:47:40
| | | To all those who still cling to the erroneous notion that a momentum-differential, in the gyro-flywheel (as explained by Sandy), is the cause of “precession” I say, try the following experiment (this can be a “thought experiment” or a physical experiment depending on your experimental resources):
Spin up a gyro. Then, suppose that instead of placing the gyro on top of its tower, you DROP IT from a very tall location so that you can observe as it travels downward to a safe area below. On the way down the momentum-differential (explained by Sandy) will increase to more substantial magnitudes (the momentum of the upward spinning side of the wheel will reduce substantially while the momentum of the downward spinning side will increase substantially). The “differential” will continue to increase ‘Exponentially!!’
At what point will the gyro begin precession? ... The answer is NEVER… I am sure no one can believe otherwise….
Anyone who has believed this notion, constructed theories based upon it, or built physical models based on this erroneous notion has based it all upon a wrong premise and achieved wrong conclusions (precession is the single most important premise for gyro-propulsion). My sincere suggestion about this notion is that you DROP IT.
If it’s any consolation, this type of error is common in the history of scientific effort. The belief that earth was at the center of revolving planets dominated for a period that still managed to yield some positive results. However under this erroneous paradigm calculating positions of planets required many ad-hock parameters that simply confused the issue.
Thank you, Luis
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Sandy Kidd - 04/12/2006 06:27:40
| | | Luis,
You did not answer my question.
You have gone around the question in every conceivable way without answering what I asked.
I will repeat.
Where does the inward turning portion of this couple come from?
In simple terms this time please, without the smoke.
Better still, as you appear to understand gyroscopic actions much better than I do, how do you explain this away in a non gravity accelerated system?
I await your answer with great interest.
Sandy.
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Sandy Kidd - 04/12/2006 13:31:01
| | | Luis,
In answer to your following posting
Yes you are correct in your falling spinning disc experiment but you have completely missed the point.
Because a disc is spinning does make it a gyroscope, or is this so hard for you to see.
So a Frisbee is a gyroscope, maybe I should give up now.
Where is the radial acceleration, which apparently does seem not matter to you?
Give your falling spinning disc some radial acceleration and make it a gyroscope and when you do, I’ll ask you once more, where is the couple?
Sandy
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Luis Gonzalez - 08/12/2006 02:53:52
| | | Sandy,
Someone has definitely missed the point!
We seem to agree that Momentum-Differentials (M-D) are USELESS without the correct angular force.
Introducing an angular force (intended to change the orientation of the axle) yields precession, but the Momentum-Differential (M-D) becomes UNNECESSARY!
In both cases the Momentum-Differential (M-D) is unnecessary & useless for precession; “is this so hard to see?”
Thank you,
Luis
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Luis Gonzalez - 08/12/2006 02:55:52
| | | Sandy,
Someone has definitely missed the point!
We seem to agree that Momentum-Differentials (M-D) are USELESS without the correct angular force.
Introducing an angular force (intended to change the orientation of the axle) yields precession, but the Momentum-Differential (M-D) becomes UNNECESSARY!
In both cases the Momentum-Differential (M-D) is unnecessary & useless for precession; “is this so hard to see?”
Thank you,
Luis
Sandy.
Dreadfully sorry you can’t understand my explanations. I re-read my response and find it to be clear (to anyone in the right frame of mind). I don’t expect you can agree with me, and suspect we will waste our time and energy beyond this point.
(I do thank you for your original question which provided me with the opportunity to further explore and explain the nature of precession.)
Perhaps Momentus, or someone else, can answer your question in a way that’s more to your liking.
Thank you, Luis
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Sandy Kidd - 11/12/2006 06:29:02
| | | Luis,
Why did you make that stupid statement about the falling disc in the first place.
If you know radial acceleration is required, I am really at a loss to figure out why you used it as an example.
It is obvious I am not going to get a straight answer, just more smoke.
I would agree this is a waste of time.
You are way too sharp for me.
Sandy Kidd
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Sandy Kidd - 11/12/2006 07:30:47
| | | Luis,
For years I have been under the misunderstanding that the gyro/flywheel/disc had to rotate, and now you have enlightened me to the fact that it does not have to rotate at all
All those years wasted making gearboxes, ball joints, gyro bearing shafts etc.
Wish you had come along sooner, it would have saved me a fortune.
No differential required on the gyroscope, and I always believed it was essential.
All those wasted hours! Makes you sick.
Sandy Kidd
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Luis Gonzalez - 16/12/2006 03:55:46
| | | Sandy,
Spin is necessary and Momentum-Differential is not necessary.
To get the real meaning of what others write I often have to read it multiple times.
I suspect this is a common human affliction caused by the limitations of language.
Thank you, Luis
P.S. Why do people do things that look stupid to others in this forum?
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Luis Gonzalez - 16/12/2006 17:13:43
| | | In the spirit of Christmas season I will explain a bit further. (Do keep in mind that seeds can grow to bear fruit only in fertile ground.)
Please first review or find a good description and comparison between torque and mechanical couple as forces.
Here is the short explanation to the request:
From the perspective of a symmetrical environment there is no way to distinguish torque from “mechanical couple.”
Here is a little more help for those who need it:
Torque is applied in an ASYMETRIC way but if the interaction-environment is SYMMETRIC then it is impossible to determine where the lack of symmetry is because opposite sides of the symmetry will respond in exactly the same manner, as if the force was being applied from opposite directions!
In symmetric environments, an applied torque takes on the quality of “a couple” when its force interacts with the existing symmetrical features and motions of that environment (the response is relative to the configuration of the interaction).
The perspective from the off-center system is an ASSYMETRIC force (torque). However, from the perspective of a SYMMETRIC-DISK is that the force interacts SYMMETRICALLY (mechanical couple).
That is it; it’s that simple.
For those who still can’t see it lets bring in some context.
The applied force interacts with the rim of the spinning disk in a symmetrical interaction rather than in an asymmetrical way (some can see this intuitively). From here it becomes easier to visualize Momentus’ illustrations of precession (I hope they are not also considered to be just smoke).
Understanding the dynamics of this symmetrical interaction prepares the ground to explain why precession (the motions that occurs as a 90 degree response) des NOT produce an equal and opposite reaction (I have explained this elsewhere in this forum but would be happy to try it again after the above explanation).
Thank you, Luis
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Sandy Kidd - 19/12/2006 07:33:44
| | | Luis,
You say:-
From the perspective of a symmetrical environment there is no way to distinguish torque from “mechanical couple.”
Who said it was a symmetrical environment, certainly not me.
You are telling us that if there was a couple there, we would not know anyway, but there is a couple because you know there is a couple.
If there is a couple, because you know there is a couple, you must know why it is a couple, so what causes the inward turning part of the couple?
Sandy Kidd
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Luis Gonzalez - 23/12/2006 22:17:05
| | | Sandy,
The main point of your question addresses the core of the confusion.
We all know that “THE SYSTEM” is the environment where the torque is applied and that it may NOT be symmetric.
We also know that gyro-flywheels have symmetric shapes and highly symmetric motion (spin) that cursory observation may not even notice. (For now I will forgo delving into different symmetries of disks.)
Therefore in response to your first sentence, no one needs to tell us that the environment ON a spinning gyro-flywheel is highly symmetric; it is self evident. That is the symmetric-environment perspective that I referred to, and that you quoted me on. I explained it previously in hope of bringing clarity; unfortunately my effort was perceived as smoke.
In short, the disk itself is a symmetric environment. Can anyone disagree with this? (I refer to it as the inner environment).
The explanation about “couple” follows naturally from this (inner) perspective; however, if more explanation is necessary to bring it all together, read what follows:
From the symmetric perspective of the gyro-flywheel (inner environment) there is no way to differentiate between changes in orientation which are caused by torque, as opposed to changes in orientation which are caused by a mechanical couple (please compare the 2 definitions).
The highly symmetric spin of the gyro-flywheel environment interacts with the Force of the torque symmetrically, and the Force is perceived as a mechanical couple!!
This could conclude my answer to clarify the confusion expressed through your three sentence question, except for the end of your last sentence…
In that part of the sentence you asked “what causes the inward turning part of the couple?”
This segment of your question simply reflects a misperception regarding the symmetric (inner) environment of the spinning disk, and how it applies to my relevant explanation. From the perspective of the disk’s inner environment there is no inward (or outward) direction; there is only a change in orientation along symmetric axes of a disk (excluding the spin axis).
This should be the end of the story, but you are probably thinking that even in an environment without inward and outward direction there is still the opposing force that needs to be accounted for!
My answer is “symmetry” and I will explain with an illustration:
Take a playground seesaw (fulcrum) and put a weight on one end. Then apply a downward Torque on the other end of the seesaw (using a motor pulley etc) and notice that the weight rises. Where does the rising Force (in the opposite direction from applied torque) come from? (This is a rhetorical question.)
We all understand how the torque applied downward interacts with the rigid material and configuration of the fulcrum structure; as a result the weight is lifted in the opposite direction that the torque was applied!
I hope this puts that little piece of the puzzle to bead.
A clue to this interesting perspective is in the fact that the precession “period” of a system (under a consistent torque) is the same despite the length of the axle (did you know that?).
Can you make the connection about how that small but significant fact (about the period of precession) can lead toward focusing on the flywheel perspective over the overall system perspective to better understand precession? (Remember that the spinning flywheel is a sub-system of the gyro setup system as a whole.) I hope you don’t perceive this as just smoke.
If you manage to think through this piece of the puzzle, then we can think about tackling how and why precession causes motion that moves the mass of the gyro over a curved distance in space within the overall system (and why that motion does not have an equal and opposite reaction).
Other questions regarding relationships between the overall gyro-system and the spinning-disk sub-system (and visa versa) may be explored using the intuitive knowledge that rigid substances can telegraph dynamics of motion over distance, and sometimes in unexpected ways.
Thank you, Luis
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Luis AE Gonzalez - 31/12/2006 04:08:59
| | | Why should we seek to understand the “inner” perspective, from the point of view of the spinning gyro disk?
The spinning gyro-disk is where conversion from torque into precession takes place (without spinning disk precession does not occur)! For that reason, to fully understand precession’s attributes and behaviors, we should delve into the “inner” perspective.
We have been exploring how mechanical couple (which is a very close relative of precession) causes spin to respond symmetrically to torque, while torque is not itself applied symmetrically.
Some of us have a good insight about the events that transform torque into an “inner” 90 degree reorientation of the spinning disk. However we need to explain how / why this “inner” change in orientation (of a gyro-flywheel) affects the overall gyro-system becoming full-fledged motion of precession, as we see it in toy gyros. In other words, how changes in orientation of a disk also produce displacement motion in 3-D space.
The following simple experiments establish basic foundations for how simple orientation-precession can extend into compound displacement-precession whose motion extends to the system as a whole.
Distribute several round water containers on the surface of a light turntable.
Float something light on the water of each round container to serve as an indicator of motion (a toothpick or such should work).
Rotate the turntable slowly and note that the floating indicator in the liquid tends to maintain its directional orientation in relationship to the external world.
From a different perspective, of the turn table itself (as if standing on a merry-go-round), the floating indicator appears to be turning within each round container (this is basic but significant).
(Friction of sorts can have effects undesirable to the experiment. The Centripetal-Centrifugal (C-C) forces closer to the turntable edge will cause greater lopsided friction, while the center will be less affected by lopsided friction.)
Next, replace each water filled glass with a hefty metal disk, center mounted via ball bearings upon the vertical axle of a light pedestal. Get the picture? The bearing mounted metal disks replace the water filled glasses.
Spin the turntable again and note that all the metal wheels respond in a similar manner despite whether they are near the center or near the edge of the turntable, except for friction variations (this experiment is also basic but of significance).
In the next experiment we will NOT spin the turntable. This time put only one of the hefty metal disk contraptions on the center of the turntable. Next, turn the hefty metal disk on its bearing without disturbing the turntable, which should be still at this point. (You may need to mount a small motor or a spring-loaded drive etc, on the hefty metal disk).
The turning of the hefty metal disk will cause the light turntable to rotate in response to the motion of the metal disk. (Does anyone disagree?)
If we are all on the same page, we are ready for the next crucial stage of the experiment:
Again place only one of the hefty (motorized) metal disks on the turntable, but this time place it close to the edge.
Turn on the small motor or spring to start the hefty metal disk rotating upon its bearing pedestal (without disturbing the turntable, which should be still at this point).
What do you suppose will happen????
We find that no matter where the hefty metal disk is placed and spun on top of the turntable, it will create an angular action that sets the light turntable in motion.
Is this surprising? (It shouldn’t be!) If you are surprised ask yourself why?!
On the other hand, if you understand the dynamics of the experiments, then you can see that a localized (inner) angular motion can generate larger arcs of motion at the higher level of the system as a whole! (This is very significant!!).
This basic experiment illustrates and proves that localized (inner) angular activity can induce system-wide motion. In a similar manner inner precession (at the disk level) telegraphs its motion into the wider angles of the system as a whole.
The resulting induced motion generally occurs in wider arcs which provide longer segments that are better for conversion into linear motion. However, by definition, precession is highly sensitive to any type of force, responding to obstacles in a nearly fluid manner (Nitro’s law).
The motion of precession does not have equal and opposite reaction; the system simply allows the gyro to revolve around the system in order to reorient itself. Without a leap of imagination we can extrapolate the actions of our experiments to more complex actions that take place in compound precession. In other words, it explains how the symmetrical, localized, inner precession (explained previously) extends to displace the gyro across the space of the system.
This Model explains how the phenomenon of precession occurs on the average toy-gyro (as the layman perceives it). It connects many of the dots in a way that provides answers to most outstanding questions; question such as “Where does the force that drives precession come from?” Of course the answer is that the force that drives precession comes from the applied torque; the model presents a mechanism that converts precession by 90 degrees into a motion without equal and opposite reaction, and is open for scrutiny!
To complete the story one should segregate the angular and linear elements of torque to understand how each of these elements contribute to pure precession so that it yields motion that has no equal and opposite reaction. Consider the following questions:
Why should the “inner” spin perspective ignore linear components in the arcs of the applied torque?
How can deeper analysis regarding independence of angular and linear motion provide the key to reconcile interactions between these two types of motion?
Thank you, Luis
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Luis Gonzalez - 01/01/2007 21:49:56
| | | Correction to my previous posting; the last sentence of the third from last paragraph should state:
“Therefore the DiBella machine would “NOT” make net gains in any particular direction when operating in space.”
Thank you, Luis
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Luis Gonzalez - 01/01/2007 21:52:45
| | | Please disregard my last posting I put it in the wrong thread.
Thank you Luis
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sandy Kidd - 05/01/2007 06:48:27
| | | Luis.
You said:-
In short, the disk itself is a symmetric environment. Can anyone disagree with this? (I refer to it as the inner environment).
I have no disagreement with that statement
You said:
The explanation about “couple” follows naturally from this (inner) perspective;
Why does the explanation about “couple” follow naturally? This is assumption.
You said:
From the symmetric perspective of the gyro-flywheel (inner environment) there is no way to differentiate between changes in orientation which are caused by torque, as opposed to changes in orientation which are caused by a mechanical couple (please compare the 2 definitions).
If you are aware of the meaning of torque and mechanical couple why invoke a couple?
You said:
The highly symmetric spin of the gyro-flywheel environment interacts with the Force of the torque symmetrically, and the Force is perceived as a mechanical couple!!
So it is not a couple, it is only perceived as a couple?
Thank you, That will do me for now.
Sandy Kidd
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Luis Gonzalez - 13/01/2007 17:34:03
| | | Sandy,
Thank you for your nice response. I am also glad that there are things we can agree about.
The symmetric properties (both static and dynamic) of the gyro disk’s environment are a simple fact (not an assumption).
It fallows naturally that in an environment where all the interactions are symmetric, internal causes & effects are symmetric, and the forces involved are symmetric. (Symmetry ergo Couple. Torque is not symmetric.)
It is NOT a matter of invoking, as in one of two options (Torque Vs Couple), it is a matter of using the correct semantics from the disk perspective based on whether all forces involved are symmetric or not (from the perspective of a subsystem).
Think of it from a relative standpoint or perspective; e.g. when two objects are in relative motion to each other, the perspective from each object is that the other object is the one in motion. (Observers see themselves as motionless while seeing the other object as being in motion (derived from the laws of motion). This example is only intended to gain perspective.)
Regarding your fourth quote, I said “…the Force is perceived as a mechanical couple!!” I used the word “perceived” (for lack of better words) NOT to indicate personal interpretations, but rater to indicate how the spinning disk responds to the forces involved, from its subsystem perspective (i.e. how the disk (and its spin) responds symmetrically).
We are trying to think from the perspective of the disk’s subsystem environment.
The disk (not I) receives the force symmetrically; most important, NONE of the non-symmetric qualities of the external torque have meaning or effect within the disk or its dynamics. The disk perspective is completely void of asymmetric dynamics!
Therefore it’s more accurate to see, from inside the subsystem, that the force is a couple.
Though it looks like “splitting hairs,” the difference between symmetric force and one that isn’t, provides added accuracy that permits us to conduct analysis (of the subsystem) without interference from non-symmetric factors that have no effect in causing precession within the subsystem of the disk.
Having said this, it’s time to revisit my silly experiment where we simply dropped a spinning gyro knowing full well that the effects of velocity (induced by falling) can never cause precession! Why, because the REORIENTATION of the gyro disk is the only factor that can produce precession. Reorientation alone and nothing else comes into play as a motive cause for precession (reorientation is necessary and sufficient to produce precession when applied to a spinning disk).
The silly experiment shows that any amount of “differential” between upward-spin-velocity, and downward-spin-velocity, has no effect on precession; this differential is neither sufficient nor necessary for precession. The silly experiment is intended to prove this point through “reduction ad absurdum,” nothing more and nothing less.
Objectors may state that all subsystem perspectives of torque are always symmetric; that whether it is a gyro or not, the subject of the torque does not differentiate from which direction the force is applied; that an external torque has always been a couple when observed from the perspective of the object receiving the torque. Such objections in effect are saying that mechanics has never found it necessary to state that a torque converts into a couple. My response is that most objects subjected to torque do not encounter a subsystem with internal dynamic interactions; up to now only precession requires this rigorous analysis (other exceptions include quantum mechanics and, up to a point, relativity).
Why should we bother “splitting hairs” regarding these 2 types of force? Because the added bit of accuracy makes it clear that non-symmetric factors serve only to skew the premises upon which to base our logical analysis.
I discussed this posting with colleagues and found that they are able to explain it back to me and to each other. It’s nice to know that I am not going off the deep-end (at least not alone). It’s also reassuring to know that others may gain from the material I am writing (even if not everyone does).
Thank you, Luis
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Nitro MacMad - 13/01/2007 19:33:39
| | | Dear Luis,
You are not going off the deep end. However I wish you and Sandy would stop discussing how many angels can alight on the head of a pin and discuss if there is a religion.
Kind regards
NM
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Luis Gonzalez - 15/01/2007 00:21:40
| | | Dear Nitro,
Thank you for the vote of confidence.
Discussing religion at a high level has never produced conclusive results.
We are not discussing how many, but whether there is one or two angels and what to call the name of the dance.
Most important, the choreography may contains the key to enable mere mortals to decipher the spin code (which produces enigmatic phenomena).
Being a foolish human, I am hopeful that if we have the same music sheet and agree on the right key, we may all find some degree of harmony.
Regards,
Luis
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