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27 November 2024 04:14
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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: |
Glenn Hawkins |
| Subject: |
Special mechanics of the gyroscope |
| Question: |
Special mechanics of the gyroscope
By Glenn Marion Hawkins
This is a complete description of the mechanical aspects of precession, of how and why gyroscopes function including that which had remained a mystery.
Inertia is a constant quality of mass that resists acceleration. Gyroscopic deflections occur because inertia resistance to force is greatly increased. During fast curving motion along with other factors, the power of sideway inertia resistance is tremendously increased.
Consider inertia in linear travel. A mass travels through space in a straight line for one mile at 100 miles per hour. A rocket of relatively very weak power is attached sideways to the forward moving mass. After one mile the mass is pushed off course by the right angle rocket force until its path has curved 180 degrees.
Using the same example, except that the mass is traveling at 100 MPH, the mass is forced to curve only 1.8 degrees off course. This is because at greater forward speed the same right angle rocket had only 1/100 as much time to apply its sideways force at the end of the one mile.
Linear traveling and tilting rotation act the same way for the same reasons relating to side-ways inertia resistance. When a wheel is rotating in a plane, though the motion is circular, it is nevertheless rotating within the confines of a straight plane. The faster the rotation of a wheel that is tilting wheel, the less time there is for gravity to exert its force— per each rotation.
As the gyroscope falls in a vertical curve around the pedestal, its top portion is always tilting outward away from the pedestal. At the same time, the bottom potion of the wheel tilts inward toward the pedestal.
Imagine a wheel made of a very thin steel that can be bent. The thin wheel must tilt toward gravity in order to create the deflections and gyroscopic functions. As it does, the increased power of inertia resistance seeks to hold the outer rim in its rotation plane. Therefore the thin wheel bends in resistance. The top portion of the wheel bends curving toward the pedestal, while the bottom bends outward away from the pedestal.
The condition can be likened to a bent spring. The spring so compressed holds ready to spring back with momentum. The compressed upper and lower springs are rotated to an area where no vertical resistance exist. That area is the horizontal diameter of the wheel which acts as a swivel between top and bottom. Here the spring uncoils and the spring-back releasing its stored torque as momentum forward and rearward of the wheel, which twists the wheel into precession. If the wheel is thick and does not bend, think in terms of molecules and atoms being squeezed toward the increased inertial resistance and then released to carry momentum as in spring-back.
At horizontal, the momentum collides into a new and different inertial resistance because the horizontal tilting around the pedestal acts exactly like the vertical tilting. The wheel would seek to bend toward the colliding momentum. The force of gravity is then deflected by the collisions and the deflections are further rotated toward the vertical upper and lower positions of the wheel. In this way, the wheel is held aloft by the vertical and opposite torque of the wheel.
The speed of precision and the speed of gravity is a veritable ratio. When angular momentum is great, the collisions are stronger, and more of the strength of deflections are rotated toward the vertical. At the same time, less strength and speed remain in the horizontal position of the wheel. So little strength is left to precession that a paper napkin can stop a toy gyroscope from precession. When that happens, the wheel is no longer moving, tilting around the pedestal, and there is no horizontal inertial resistance, and collisions and deflections are not possible. The gyroscope collapses into gravity.
PROFESSOR ERIC LAITHWAITE’S FAMOUS 40-POUND WHEEL DEMONSTRATION
There are demonstrations of a man forcing a gyroscope into faster precession. He holds up a three-foot shaft connected at a levered distance to a forty pound wheel. https://www.youtube.com/watch?v=GeyDf4ooPdo
The two questions that arise has baffled everyone: how is he able to grip, hold and lift so much weight at such a levered distance?. Additionally, why does the wheel appears to poses no weight at all as he lifts it without effort?
1 By holding the torqued weight close into his body, as the man does, most of the weight is supported by the skeletal frame of his body and so he exerts less energy in holding it. The simplest example is an African woman caring a heavy burden on her head while exerting little energy.
2 A gyroscope torques the force of gravity to the pivot where it becomes a downward force. Therefore the man’s hands act as a pivot and he does not need to grip and twist his wrist against torque as it is converted into vertical force downward. His hands are free to act as a pivot rotating in the open cup of his hand.
3 In lifting weight we are prone to assume that extra force downward is created. But the energy the lifter exerts is necessary only because of the leverage disadvantage he creates in his limbs and joints as he bends his elbows. Gravity is the same at one foot off the floor as seven feet off the floor. The true resistance is so little that when a man standing on scales lifts a barbell, the scales hardly measure a difference during lifting. That difference is only the inertial resistance from accelerating a mass. A baby anchored to a ship in space could nudge so large a mass forward with ease. That is the only amount of resistance the upward tilting of the wheel creates.
The lifting torque created by the wheel has already been paid by the energy necessary to suspend it in space, and so little extra torque is necessary to lift it further--inertia resistance only.
4 The rising arc of the wheel is caused by strengthening deflections from the man’s right angle push. The rising arc can be vectored in two directions, inward and upward. When the man’s hands lift, his levering force counters the inward force direction of the wheel toward the pivot. Therefore the wheel cannot move inward, only upward. Two torques are created, that of the wheel, countered by that of the man. The wheel continues to rise in one a dimensional direction, 180 degrees, and in veritable amounts and distance equal to the man’s lift. The energy required is divided. The wheel furnishes half the energy and the man furnishes half. Moreover, the man applied torque not at behind the wheel, but to the rear of the shaft at a leverage disadvantage. He had to push harder. The man experiences only light inertial resistance in slowly accelerating a mass upward, and only half of that as the wheel furnishes the other half. He actually lifts no weight at all.
Gyroscopes contain no magic. Every condition is explainable by the laws of motion, particularly that of ignored leverage. There are no additional laws concerning motion or gyroscopes- no mysterious forces at work. From these mechanics, it may become evident to you that gyroscopic inertial propulsion is impossible. Sorry.
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| Date: |
18 November 2018
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Answers (Ordered by Date)
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| Answer: |
Harry K. - 30/12/2018 12:48:50
| | | Hi Glenn,
wrote:
„Consider inertia in linear travel. A mass travels through space in a straight line for one mile at 100 miles per hour. A rocket of relatively very weak power is attached sideways to the forward moving mass. After one mile the mass is pushed off course by the right angle rocket force until its path has curved 180 degrees.“
Your assumption is not correct. The sidewards atached rocket (90 deg. to the straight path) causes the mass to move again in the formerly straight path as well as moves or better accelerates sidewards ar the same time. That means the mass moves in curved path but it will not moving around itself to align the rocket 180 deg. to its formerly straight path. To do this, a toque would be necessary which has to act around the center of mass.
Best regards and for all guys herr all the best for 2018!
Harald
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| Answer: |
Harry K. - 30/12/2018 12:52:33
| | | Sorry, I meant all the best for 2019! :-)
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| Answer: |
Glenn Hawkins - 31/12/2018 01:31:34
| | | Thank you, Harry,
I am not an engineer and I made two mistakes not because of the thinking involved, (it is correct) but because of how I explained the thinking. I see the problem you point out—very good of you.
Are you viewing from the angle of the plane of rotation, while I am viewing from the face-on (sideways angle of both the mass and the same view of the gyroscope? But maybe this is not the issue.
To avoid confusion let me say the mass’ curve would be 45 o. Now, if you speed up the forward moving mass from 100 miles per hour to 1,000 miles an hour for one mile each, the sideways rocket would only have time to curve the path of the mass 4.5 o. This in effect increases the power of inertia in this thought experiment and postulation. The idea conveyed is that speed per distance is what increases sideways inertia force, not that velocity increases mass as is taught. I have reason not to believe it—still, that is not the point of contention here. The overhung gyro is not given time PER EACH ROTATION to allow for hardly even a modest fall into gravity per each rotation—just gradually little.
If this cleared up, what did you think of my mechanics?
Cheers & Happy New Years,
Glenn
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Glenn Hawkins - 20/10/2019 16:32:21
| | | Correction to Harry
Actually, Harry you are wrong.
I wrote, “A rocket of relatively very weak power is attached sideways to the forward moving mass.”
As long as the rocket remains ATTACHED to the mass, the mass’ path would continually curve at 360 degrees until the rocket exhausted its fuel.
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Harry K. - 20/11/2019 07:49:51
| | | You are wrong Glenn. ;-)
I already gave the explanation in my first answer. You need a(n) (initial) torque to force a mass ( assuming the absence of any other forces in the surrounding) to move in an orbit.
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Glenn Hawkins - 24/11/2019 07:31:03
| | | Harry, you are wrong again. I think you do not understand. Anyone who wants to know need only insert, “centripetal force definition” into a search engine.
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Harry K. - 24/11/2019 13:32:39
| | | Glenn, I recommend you to search in Google for „Dunning-Kruger-Effect“. I‘m away now. Bye bye.
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Glenn Hawkins - 24/11/2019 17:40:16
| | | What a hatful, bad-mattered --- and ill-bread thing to relate to me.
If you cannot comment on my findings because you cannot study them, cannot understand them or your jealous -- you should be quiet. You are not very smart and never were.
You try using math to understand what you don’t even know you don’t understand, while mechanics is the only way gyroscopic functions can be understood.
Now you are reduced to using slanderous quotations of other men’s general and unrelated condemnations of me that you search for on the computer. Your further unoriginality, using someone else’s borrowed mathematical methods (as far as they can go) is all you were ever capable of.
I am disgusted with your hatefulness even more than your incompetence.
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Miklos Somos - 25/11/2019 20:57:51
| | | Dear All,
I hate to see, when two people get mad at each other, because of some bloody physics question.
The first problem I see, that it is very hard to argue about a question without any drawing. This is a hindrance of this forum.
Without further informations I could imagine the following two possible configurations:
- first let's suppose that the mass is a sphere with a radius R
- configuration 1: the rocket is attached so, that the line of action of the force of the rocket goes through the center of mass of the sphere
- configuration 2: the line of action does not go through the center of mass of the sphere
Configuration 1:
The mass moves forward at a speed of Vforward.
After the ignition of the rocket, the mass starts to accelerate in the perpendicular direction relative to the original direction.
This acceleration starts to curve the path of the mass. The perpendicular velocity starts to get greater and greater.
If the rocket would go forever, then the perpendicular velocity would be much greater than Vforward.
The trajectory would look like a rounded corner of a rectangle.
Let's say, we would see a vertical line, which would be the original straight path.
The point of the ignition of the rocket is where the rounding starts, not a circle like rounding, but something like a parabola.
After some time, depending on the magnitude of the force, the rounding goes into a horizontal line.
The horizontal will never be totally horizontal, because the original Vforward does not disappear.
But if we would wait long enough, or the rocket would be enormously strong, then we would see the mass moving mainly sideways.
The forward movement would be almost unrecognizable.
So this version agrees with Harry's argument.
Configuration 2:
As Harry said, a force alone is not always enough to generate a continuous "curvig" or rotation.
The main characteristic of a centripetal force, that it always points to the instantaneous center of the curved path.
Therefore the centripetal force needs to change it's direction in every moment.
In configuration 1 it does not happen, because the line of force of the rocket goes through the center of mass, therefore it has no torque,
the mass will not rotate, and the force of line of the rocket will always point in the same direction.
The force won't have the conditions needed to be centripetal.
In configuration 2, the rocket not only pushes the mass sideways as in configuration 1,
but exerts a moment on the mass too, therefore it rotates the mass. If the mass is rotated, then the attached rocket turns with it.
Now it is possible to reach a circling motion. The path will depend on the mass, on the angle of the rocket relative to the mass,
on the force of the rocket, and on the original forward velocity of the mass.
The form of the resulting path could be almost anything from some cycloid to a circle.
I hope this will help to solve the confrontation.
Regards,
Miklos
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Glenn Hawkins - 25/11/2019 23:02:15
| | | Hello Miklos,
My studied friend, this is turning into a marathon of words and complications but I like it simple. That is the purpose always of all my explanations. The greatest accomplishment of man – that is of course mathematics, tells us how much and allows us to relate one thing to another in order to understand what we did not know, distant stars for instance. What number cannot do is explain why something happens or even how it happens. Think of the combustion engine that you know so well that you can see the schematics in your mind’s eye: Intake, Compression, Explosion and Exhaust. That my learned friend is mechanics and mechanics is the only way to learn and understand why and how the gyro functions – not our beautiful, ingenious system of numbers. For lack of everyone always accepting that simple idea, I am the first, so far as I know to give an explanation of why a gyroscope elects to precess in one direction over another-- or precess at all. If you can direct me to another explanation of why and how I would like to know, please. As I have explained so many times and been opposed an equal number of times-- math does not explain. My work is mechanical.
“ . . . AFTER ONE MILE… a mass traveling at one-hundred mph is pushed off course by the right angle rocket force until its path has curved 180 degrees.” This was changed to 45 degrees.”
Using the same example, except that the mass speed is increased to 1,000 MPH, the mass is forced to curve only 4.5 degrees off course. This is because at greater forward speed the same right angle rocket had only 1/10 as much time to apply its sideways force at the end of the one mile.
Linear traveling and tilting rotation act the same way for the same reasons relating to side-ways inertia resistance. When a wheel is rotating in a plane, though the motion is circular, it is nevertheless rotating within the confines of a straight plane. The faster the rotation of a wheel that is tilting, the less time there is for gravity to exert its force- per each rotation. Therefor the wheel’s resistance to tilting can be increased by increasing its RPMs until it hovers above the table.
That is all there is to it. The mass rotation was not mentioned nor was ovals and spirals and exacting physics. All the physics input does not matter one iota to the point I make. In fact, it belabors and hinders my simple and easy understanding that I fraught so hard and long to understand and relay to you if you wished. Simple does not come easy. The explanation is correct to the point and should not be distorted with exactitudes and subject matter unrelated to ---THE EXACT POINT AND EXACT PURPOSE OF MY POSTULATIONS.
Thank you for being nice,
Glenn
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Glenn Hawkins - 26/11/2019 05:34:44
| | | ‘ Woke up in the night as we sometimes do. I will make it simpler for you. Forget the sideways rocket.
Two parallel comets enter and exit the gravitational field of a star. One is traveling faster and so its path is bent less because gravity has less time to apply force to it.
Linear travel and rotation act the same way to time, speed and distance. The faster the linear travel, the faster the rotation, the less time gravity has to act—i.e. per rotation. The results is increased inertia resistance to tilting and that is the only point of my explanation.
If you get caught up in calculating that the comets would not follow a perfectly circular orbit but an elliptical orbit very elongated then you end up with a cigar box of numbers which would be a completely different exercise and you’d lose the point of the stated explanation.
As too the rockets, of course the continuing sideways force would increase the sideways velocity and the shape of the path would be somewhat ‘J’ like but then you lose the whole God-dammed simple-assed point.
I am not angry. I am smiling. I wish you well all. I'll redo this post.
Glenn,
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Harry K. - 26/11/2019 08:42:34
| | | Dear Miklos,
Thank you for your clarifications. I certainly assumed that all involved forces are acting at the center of mass.
One comment to what you have stated in configuration 2:
„Now it is possible to reach a circling motion. The path will depend on the mass, on the angle of the rocket relative to the mass,
on the force of the rocket, and on the original forward velocity of the mass. „
I agree but without the dependence of the original forward velocity. The change into a rotation path will only occur as long as the backward rocket accelerates the rocket. If the backward rocket stops the acceleration, the vehicle would follow the last path in a straight line AND would in addition rotate around its center of mass.
I think you meant that. However, the shape of the path depends on the relative observation point. Only in this respect the original velocity has an effect.
Best regards,
Harald
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Glenn Hawkins - 26/11/2019 15:28:48
| | | Hello boys,
Forget the damn rocket. Ha, ha, ha. Forget the exactitudes of extended motion, for that thinking destroys the simple idea conveyed that speed increases inertial resistance. What you guys are talking about deserves a new posting perhaps not even about gyroscopes.
Clarifications relating to the purpose of this post:
Two parallel comets enter and exit the gravitational field of a star. One is traveling faster and so its path is bent less because gravity has less time to apply force. This concludes how sideways force, gravity, increases the power of inertial resistance as it relates to a tilting gyroscope.
Good will to you and have a great Christmas,
Glenn,
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Miklos Somos - 26/11/2019 21:17:49
| | | Dear colleagues,
@Harry:
I agree about everything You have written. Although I still think, that in certain circumstances, the effect of the initial velocity could be significant.
But it is only a minor detail.
@Glenn:
I think Your further examples have shed some light on the motivation of Your thoughts. The example with the comets are lot better, than the one with the rocket. At least there will be a real centripetal force acting on the comets. ;)
These questions and phenomena grab the very foundations of mechanics. These concepts have been developped for many centuries, and are still under development. The first thoughts about motions are dated back to the greeks.
Maybe it would be useful to take a short look at these ideas, in their present form. Sorry, but I will define them only very vaguely, to save characters...
Inertia
Inertia is the resistance of a body to any change in its velocity. It depends only on the mass of the body (the linear inertia). A body has rotational inertia or moment of inertia too, it depends on the mass and it’s spatial distribution.
Momentum
Simply a mass in motion, or the quantity of motion. It is a vector quantity, it equals with mass times velocity.
I think this is what You have deducted from Your own thought experiments.
Here You can find a good summary:
https://physics.info/momentum/summary.shtml
I agree with You that it can be used to explain the motion of a gyro. There are many levels of explanation, and by level I do not mean, that one is superior to the other. I mean the level of abstraction.
The basic level is, when You consider the gyro as a collection of connected particles, and You analize their velocities, accelerations and the acting forces. My favorite short videos to this topic are these:
https://m.youtube.com/watch?v=33amqcZXeus
https://m.youtube.com/watch?v=BfqTvRi0YvA
The next level of abstraction are the non-inertial reference frames. The well known Newton-equations hold only in inertial reference frames. In non-inertial ones, one should consider forces like centripetal and Coriolis-force. This my favorite method for thinking about gyros.
The final level of abstraction is the conservation laws: the conservation of momentum or angular momentum, and the conservation of energy. They have the advantage, that they are relatively simple to use, at least compared to the other ones. The disadvantage is, that they are using highly abstract ideas, which are hard to grasp. And they hide the actions on the level of particles before our eyes.
Interestingly in the mechanics books You find almost only the latter explanation. Because I’m a gyro freak, I have found some books that at least mention the other means of explanations too.
But at the end, every method will supply the same result. If You do not like abstraction, then You can track each particle burning Your brain down, because there a lot of them... :)
If You like wrapping Your head around suspicious ideas, then conservation laws are Your best friends.
Personally I like both of them.
Regards,
Miklos
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Glenn Hawkins - 27/11/2019 03:04:42
| | | Forgive me Miklos but those things are known. I sat out to explain why and how a gyro does what it does, including how inertia resistance to tilting is increased with increased rotation speed and how that relates exactly to straight-line travel. I was open to varying challenges. I have not received any, only a distraction relating to the behavior and path of a mass under dual, opposing forces. The distraction no matter how true and convoluted, has nothing to do with the simple postulation concerning the nature of a gyroscope to increased inertial resistance to tilting.
I am vacating this post to build post it again when I have time -- but more ironclad against unrelated ideas, correct or not.
Harry you were wrong to relay that to me. I forgive you easily without ever a grudge. It’s my simple nature. I apologize for biting your head off in retaliation. Yes of course, you are a very intelligent man.
Miklos, did you know that Humpty Dumpty said, “When I use a word. . . it means just what I choose it to mean—neither more nor less." Miklos, how would you describe your great love for Harry and me? Make up a word. I hope it will be flattering, because my word for you is excellstanding.
Until we meet again,
Glenn,
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Harry K. - 27/11/2019 07:39:57
| | | Hi Miklos,
I like your way of thinking which is very similar to may way. I think we both try to explain and understand gyro related issues with the classical proved methods in physics instead of inventing a „new“ physic. That is in my opinion the best way in understand of many not trivial mechanical reactions of gyro related issues.
Maybe one day the scientist have to agree to enhance or adapt some physical laws or better axioms (an important difference to laws!), but this can only be done by a prove explained by classical physics.
@Glenn
All is good. After around 15 years staying in this forum I‘m aware if your temperament. ;-)
One hint, try to understand such things in a more logical manner. Simple mathematics helps
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Glenn Hawkins - 27/11/2019 14:27:13
| | | I explained logically.
Do you want to know what ultimately happens to the rocket scenario? Then for all, except our friend Harry who has difficulty in understanding written explanations.
‘If the rocket continually forces in on the traveling mass, the mass will rotate elliptically around an imaginary center point as the point, rocket and mass oscillate back and forth while ultimately moving forward. The rocket will force the mass to move inward toward the imaginary center point, and as it does the motion becomes spherical. Then the closer the mass moves toward the imaginary center point the faster it rotates in order to maintain angular momentum. The faster the rotation, the greater the centrifuge’s outward push against the rocket/mass. After some time the inward force will be balanced by the outward centrifugal force. The rocket force will have been converted to energy used to resist the rocket, hence again we see the evidence of equal and opposite.’
Whether this quickly jotted down scenario is exactly right, as all my other work here has been, I do not know or care because it is a meaningless work in futility just as was the interruptions brought here against the purpose of my writings.
You all can have in now. I am not coming back here. The paper is ruined.
I love you all anyway,
Glenn
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Harry K. - 27/11/2019 22:38:23
| | | Glenn, this is my last reply to this issue.
I assume that the rocket will travel without any influences of other forces like gravitational forces caused by other stars, planets, friction, etc.
Fact 1: The rocket will only move in a curved path if the smaller sidewards rectangular acting rocket engine induce a force which is not aligned to the center of mass of the complete vehicle AND the backward acting rocket engine produce thrust at the same time!
Fact 2: A mass which rotates AT CONSTANT CIRCUMFERENTIAL SPEED around an imaginary center point increases its angular velocity if the radius becomes smaller, caused by the law of conservation of angular momentum.
That means that your assumption is totally wrong. The circumferential speed of the vehicle would be increased caused by the thrust of the backward acting rocket engine which in return would increase its centrifugal force and thus the radius to the system rotation point would be increased as well.
If the backward rocket would not work, the vehicle would move in a straight path and would in addition rotate around its center of mass if the sideward acting rocket engine would induce its thrust not directly aligned to center of mass.
Glenn, that is what I meant in my previous post. You make wrong assumptions at the first steps, caused by ignorance of simple physical facts and thus all following steps are void.
I can not understand your reluctance to learn these relative simple physical facts before posting such nonsense.
Regards
Harald
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Glenn Hawkins - 27/11/2019 23:40:36
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YOU ARE CRAZY, JUST CRAZY. GIBBERISH AND MORE GIBBERISH.
’ SUCH UNINTELLIGIBLE WRITING I HAVE TO GUESS AT WHAT YOU MIGHT HAVE MEAN. IT LOOKS LIKE YOU ARE TRYING TO REPEAT EXACTLY WHAT I ALREADY TOLD YOU. WHO KNOWS WHAT YOU MEAN?
ONE THING HAS BECOME CLEAR FOR THE FIRST TIME -- YOU CAN NOT WRITE -- THEREFORE YOU CAN NOT READ TO UNDERSTAND. YOU SHOULD NEVER ATTEMPT TO COMMIT TO ANYONE’S EXPLANATIONS EVER AGAIN.
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Harry K. - 28/11/2019 09:23:14
| | | I did not expect any serious reply from you. Thank you for your confirmation. :-)
I will not reply to any of your „clever“ wish-wash in the future. That is wasted lifetime for me. Bye bye.
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Miklos Somos - 28/11/2019 18:20:57
| | | Dear All,
@Glenn
I’m sorry that I could not bring any brand new ideas into our discussion.
Yes, what I have written is known for centuries. Mechanics is one of the oldest sciences. The fundamental ideas are known for some hundred years now. Therefore it is very hard to say anything totally new.
In my effort to try to understand Your concept, I have searched for some identical idea in mechanics. I have found that momentum is somewhat similar to Your concept. As far as I can see, I have understood the connection You have described between the resistance of a single linearly moving mass and the resistance of a gyro to tilting. I agree with You, that the same principle works in both cases.
@Harry:
I’m not a very creative person, therefore my idea is, that I try to learn and understand, what our great scientific ancestors have find out. But I try to stay opened for new ideas too. If I’m able, then I investigate these new ideas with the methods, that are currently scientifically accepted. And I hope, that I will find some discrepances, that will lead to a new discovery.
I have learned a lot during that process about mechanics.
I’m glad, that there are other people around, who follow a similar way. There are theories already, that extend newtonian mechanics for example relativity theory. And there could be still some, that are waiting for discovery. I share Your dream, that we will reach a moment in time, where the current axioms have to be reviewed. I agree with Your distinction between axioms and laws.
Regards,
Miklos
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Glenn Hawkins - 28/11/2019 21:10:09
| | | Miklos,
You are the sweetest guy and if my opinion of you and your reasoning and search is of any use to you, then I find you to be most excellent. I was angry at Harry for his unwarranted insults, and I let that spill over to you. I am very sorry for my careless and nonchalant suggestion that your excellent knowledge and useful input were not acknowledged as they deserved to be. I will eventually repost my finding, though you no doubt accentually have much of it, I will try to make it better and hope that you will have something to add.
Take care and I am glad to have met you,
Glenn
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Dave - 12/06/2020 20:25:34
| | | my, my harold?
The gyrotic witch has struck again.
"" Harry K. - 28/11/2019 09:23:14
I did not expect any serious reply from you. Thank you for your confirmation. :-)
I will not reply to any of your „clever“ wish-wash in the future. That is wasted lifetime for me. Bye bye.""
Quickly, complain to Turner!
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