Question |
| Asked by: |
Harry K. |
| Subject: |
Basic & enhanced maths for the balance theory |
| Question: |
Dear forum,
For those who are interested in this matter, I will present here in this thread the TRUE maths behind my balance theory, which I have stated in this thread:
http://www.gyroscopes.org/forum/questions.asp?id=922
I have also noticed that some of us are missing general physics and maths behind basic gyro behavior and thus I hope to bring some light into the dark...
Fair comment or contributions at all are appreciated and of course you may write or contribute here directly in this thread! ;-)
Regards,
Harry K. |
| Date: |
20 October 2008
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Answers (Ordered by Date)
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| Answer: |
Harry K. - 20/10/2008 20:45:29
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| | Hello forum,
Firstly I want introduce the symbols I may intend to use. Don't be frightened about the number of symbols because I'm sure not to use all of them. ;-)
Please note that I use the metric SI-system for all symbols, units and equations.
I. Symbol [Unit] - Definition
1. Constants
1.1 Pi = 3.1416
2. Masses "m"
2.1 mG [kg] - Spinning mass of gyro
2.2 mD [kg] - Deadweight mass of gyro (not spinning part)
3. Mass Inertia "J"
3.1 JGx [kg*m*m] - mass inertia of spinning gyro in x-axis
3.2 JGy [kg*m*m] - mass inertia of spinning gyro in y-axis
3.3 JGz [kg*m*m] - mass inertia of spinning gyro in z-axis
3.4 JD [kg*m*m] - mass inertia of Deadweight mass of gyro (not spinning part)
4. Radii "r" or "R"
4.1 rG [m] - Radius of spinning gyro mass
4.2 RG [m] - Outside radius of spinning mass (for hallow sphere)
4.3 ri [m] - Radius of acting input force
4.4 rp [m] - Radius of acting precessing force
5. Lever arms "l"
5.1 li [m] - Distance of Fi to pivot
5.2 lp [m] - Distance of Fp to pivot
5.3 lz [m] - Distance of Fz to pivot
5.4 lr [m] - Distance of Fr to pivot
5.5 lf [m] - Disdtance of Ff to pivot
6. Forces "F"
6.1 FG [N] - Tangential force spinnning mass gyro
6.2 Fi [N] - Tangential force of tilting torque
6.3 Fp [N] - Tangential force of precessing gyro
6.4 Fz [N] - Centrifugal force
6.5 Ff [N] - Force acting against precession force Fp
6.5 Fr [N] - Resultant force by Fz and Fp
6.6 Fg [N] - Gravity force
7. Torques "T"
7.1 Ti [Nm] - Necessary torque acting around hub
7.2 Tp [Nm] - Torque caused by precession
7.3 Tz [Nm] - Torque caused by centrifugal force Fz
7.4 Tf [Nm] - Torque caused by constraint against precession
8. Angles "A"
8.1 A [° or DEG] - Balance angle "alpha" between torques Tp and Tz
9. Angular velocities "W"
9.1 WG [1/s] - Angular velocity (Omega) of spinning mass gyro
9.2 Wi [1/s] - Angular velocity (Omega) of rotated hub
9.3 Wp [1/s] - Angular velocity (Omega) of precessing gyro
10. Revolution speeds "n"
10.1 nG [1/s] - Revolution speed of spinning mass gyro
10.2 Wi [1/s] - Revolution speed of rotated hub
10.3 Wp [1/s] - Revolution speed of precessing gyro
11. Circumferential velocities "v"
11.1 vG [m/s] - Circumferential velocity of spinning mass gyro
11.2 vi [m/s] - Circumferential velocity of rotated hub
11.3 vp [m/s] - Circumferential velocity of precessing gyro
12 Angular momenta "L"
12.1 LGx [kg*m*m/s or Nms] - Angular momentum of spinning gyro around x-axis
12.2 LGy [kg*m*m/s or Nms] - Angular momentum of spinning gyro around y-axis
12.3 LGz [kg*m*m/s or Nms] - Angular momentum of spinning gyro around z-axis
12.4 LD [kg*m*m/s or Nms] - Angular momentum of deadweight mass (non-spinning)
12.5 Li [kg*m*m/s or Nms] - Angular momentum of rotated hub
12.6 Lp [kg*m*m/s or Nms] - Angular momentum of precessing gyro
12.7 Lz [kg*m*m/s or Nms] - Angular momentum caused by centrifugal
13 Power "P"
13.1 PG [W] - Mechanical power of spinning gyro
13.2 PG [W] - Mechanical power of rotated hub
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Units:
1kg - 1 kilogram = 1000 gram
1m - 1 meter
1s - 1 second
1N - 1 Newton [kg*m/s*s]
1Nm - 1 Newton meter [kg*m*m/s*s]
1W - 1 Watt; 1kW = 1000W
If I should have forgotten some or more symbols I will introduce them later if necessary.
In my next posting I will introduce some essential gyro equations.
Regards,
Harry K.
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| Answer: |
Harry K. - 20/10/2008 20:53:09
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| | I have found a little mistake in the brackets of unit Nm:
Units:
1Nm - 1 Newton meter [kg*m*m/(s*s)]
Thank you for your attention!
Harry K.
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| Answer: |
patrick - 02/11/2008 02:05:22
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| | try in 360 degrees 359 to367 both prime numbers but in 360 degree circle give a repultion to all opposinng magnetic feilds in prime number ratio
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| Answer: |
PATRICK - 08/11/2008 11:22:51
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| | Not just basic physics and maths. But what of maths itself as in agyro surely it would be easier to work in decimal 8?? but i will leave that with you..Obviously it is not hard for me to write but jus dam awkward so i will jus contribute,
To throw some light into the dark, now theres a thing."Now theres a thing" an obvious ans really as i would suppose that to actualy throw some light into the dark as being a black hole on my assumption would hve been created by imploding but in an outwards direction, simply cos after beta decay of throwing out all of its electrons over billions of years enhasing a mass so possitive and of weight or mass--but yearning 4 electrons so much that its field rises to then strech appart the protons which then trigers an elasticity to rebound an tighten the grouping of protons to cause heat and therefore implode but upon itself then send out its mass.This then leaves behind a centre that is so negative that it will eventually try to draw back and anything near will be drawn in simply to be absorbed for its make up of possitive and negative to be broken up of thier very own structure to build the neccesary high mass pinicle of a new begining centre. .EVENTUALITY ENSURES a new begining and the light that was thrown out by the pulsar will turn to absorb the light thrown into the dark of its very dark centre.
To create is to produce.. Upon a blanc canvas creative ideas and positive actions and thoughts are placed..Where as no creation is ammased from a mind full of negative thoughts as is non productive and understood be be in confusion of trying to amass a conclution to its creative side.Although a creativive method may well be distructive at times only concluding or travelling the path that it wants to go.
But with the atomic and biological make up of life there is and does not hold a choice of decision it has only simplicity to evolve in natures hands.
Now to pont out...A full circle is taken as being 360 degrees,And we know that 359 is a prime number and the next to be 367--if a cicle was then to be an outer circle made up of 359 points or segments and an inner tob made up of 367 points or segments, the gap or air gap between is of measurement X.remember X its important.
Now 359 prime 367 prime so both being primes absolutely ensures that only one point or segment can alighn to a point or segment on the outer circle from the inner.Lets call this point ALFA.On the inner circle 183 points will be before ALFA and 183 will be after ALFA.As the points come neare to ALFA the distance betwen inner and outer oppositional points of alighnment will depreciate until becoming in alighnment, and after alighnment wil increase in distance untill at the oposing side to alighnment at about 183 degrees fro alighnment based upon a 367 degree or segmented circle.
If the inner and outer were obviously shaped as cogs then each face of a cog could then be possitive one side and negative on the other...upon doing this then the inner circle would have 183 faces atracted to the outer one in alighnment then 183 being pushed away...mmm i see the probability of perpatuality.
The outer is conicaly shaped and reduces in diameter upwards--as does the inner.If the inner cone is spinning inside the outer then gyroscopicaly it will hold its horizontal via fluidicity.The whole of the module will still weigh its actual weight on the scales but missed by laithwaite---is that its fluidicity actualy makes it weightless when the speed of each revolution or its precesion in time is equal to BETA.
BETA is the calculation of the cicumferance in distance against the amount of magnetic repultion of the outer body and other factors of which why the **** should i say.
The air gap between the faces i call CAYA and this air is used and compressed to the outside to be released to atmosphere at controlled points in precise aplication for lit and to hold a perfect horizontal axis.
One thing i must state in any magnetic module of repultion or to crate any movement mechanically DO NOT WORK IN DECIMAL 10. Decimal 10 does not arrise in nature!!!
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| Answer: |
Harry K. - 09/11/2008 13:26:20
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| | Hello Patrick,
Thank you for your contribution. Your thoughts sound very interesting but it's difficult for me to follow in some pa´rts of your "special" language, because I'm not an English native. You state the use of the decimal system would be wrong but on the other side you deal with prime numbers based on the decimal system? Please note that the division of 360 parts of a circle is only per an arbitrary definition. If you like you could devide a circle in 359 parts or in any other numbers of parts as well, however, you must adjust you calculations accordingly. Can you provide a sketch or something else for better understanding?
Anyway, I will state here in this thread prevailing basic maths for gyro calculations and thus I think it would be better if you would start your own thread where you can introduce your interesting alternative concepts and thouhgts.
Thanks and best regards,
Harry K.
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| Answer: |
Harry K. - 09/11/2008 14:19:46
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| | Dear forum,
Sorry for the long delay, but I had less time in the last weeks. In the second posting in this thread I had introduced the symbols, which I will use in my calculations. So let's begin with the first chapter:
1. MASS INERTIA
The basic calculation of mass inertia of a single mass is defined by the following equation:
J = m * r * r
The formula of inertia for a rigid body with a certain geometric shape will be more complex. I will present only calculations of mass inertia for 3 different geometric shapes:
- Flat disk
- Massive sphere
- Hallow sphere
You will find a calculation sheet for these 3 geometric shapes under the following link:
http://www.misc.keipert.net/gyro/Mass_Inertia.pdf
1.1 Mass inertia of flat disk
For disk thickness much smaller than disk radius s << rG:
Mass inertia around x-axis:
Jx = mG * rG * rG / 2
Mass inertia around y and z-axis:
Jy = Jz = mG * rG * rG / 4
1.2 Mass inertia of massive sphere
Mass inertia is equal for all 3 axes in space:
Jx = Jy = Jz = mG * rG * rG * 2 / 5
1.3 Mass inertia of hallow sphere
Mass inertia is equal for all 3 axes in space:
For wall thickness much smaller than sphere radius s << rG:
Jx = Jy = Jz = mG * rG * rG * 2 / 3
In the next chapter I will present equations for calculation of revolution speed, angular velocity, circumferential speed and angular momentum.
Please be patient... ;-)
Thanks,
Harry K.
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| Answer: |
PATRICK - 12/11/2008 03:00:23
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| | Harry i cannot appologise enough fof my typing or for that of my own inadequate way that i am trying to relay info, would be much easier to relay via post as the old way of pen to paper would be much easier until i can find someone or a secratary to relay what i think at hand.If you and i do ask of you to send writen word and an adress then this would be far simpler for me. My E mail i cannot enter it simply will not let me, my address is in conversation in the forum,.....ITis very important that many see my drawings of maglev ammased by laithwaites work.Repultion via magntics in a circular module.
I hope you see 359 367,because honestly and please let me show u drawings to prove that i have solved perpetuality.
Just because my typing or language and not using spell check or my punctuation is incorect and that i would rather meet or convey through ink, pls do not evaluate your acceptance upon capability of using the "NET" or correct punctuation to prelude a seclution.
Surely u either c or u dont and on the most what i c is mechanical structures made up of maths.
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| Answer: |
Harry K. - 12/11/2008 14:08:40
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| | Dear Patrick,
Thank you for your reply and there is no need to apologise for anything.
If you write here in my thread, I can see the Email-address which you have entered in the text box "Email". However I have doubts about the correctness of of the email address which you have entered in your last posting.
Please understand that I do not want to publish my private postal address and thus I would prefer to communicate via email. What kind of problems do you have with your email access? Maybe I can help?
Regards,
Harry K.
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| Answer: |
Harry K. - 18/11/2008 10:39:31
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| | Hello forum,
Although some of you might not be interested and bored in all the maths or physics, I will nevertheless continue with basic calculation equations. I think it is a good idea to find gyro related equations on this site for better understanding of some gyro behavior. If some of you don't like this maths stuff there is no need to read this thread. Anyway, I have noticed that a contributor states simply wrong equations here in this forum...
If you have doubts about the correctness of my stated equations here then please post your objections and I will comment on them. Thanks.
And a last thing. I've never claimed to achieve propulsion with the balance point theory but only to achieve a static balance point with useful parameters and boundary conditions. And by the way I'm working currently on a test setup to prove or disprove my claims.
To be continued...
Regards,
Harry K.
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| Answer: |
Harry K. - 18/11/2008 20:31:31
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| | Dear forum,
Unfortunately I have discovered some mistakes in the introduced symbols and units postet on 20/10/2008 20:45:29.
Wrong symbols:
10.2 Wi [1/s] - Revolution speed of rotated hub
10.3 Wp [1/s] - Revolution speed of precessing gyro
Corrected symbols:
10.2 ni [1/s] - Revolution speed of rotated hub
10.3 np [1/s] - Revolution speed of precessing gyro
Please apolgise my mistakes. Please find below the complete corrected symbol list.
Regards,
Harry K.
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SYMBOL LIST
I. Symbol [Unit] - Definition
1. Constants
1.1 Pi = 3.1416
2. Masses "m"
2.1 mG [kg] - Spinning mass of gyro
2.2 mD [kg] - Deadweight mass of gyro (not spinning part)
3. Mass Inertia "J"
3.1 JGx [kg*m*m] - mass inertia of spinning gyro in x-axis
3.2 JGy [kg*m*m] - mass inertia of spinning gyro in y-axis
3.3 JGz [kg*m*m] - mass inertia of spinning gyro in z-axis
3.4 JD [kg*m*m] - mass inertia of Deadweight mass of gyro (not spinning part)
4. Radii "r" or "R"
4.1 rG [m] - Radius of spinning gyro mass
4.2 RG [m] - Outside radius of spinning mass (for hallow sphere)
4.3 ri [m] - Radius of acting input force
4.4 rp [m] - Radius of acting precessing force
5. Lever arms "l"
5.1 li [m] - Distance of Fi to pivot
5.2 lp [m] - Distance of Fp to pivot
5.3 lz [m] - Distance of Fz to pivot
5.4 lr [m] - Distance of Fr to pivot
5.5 lf [m] - Disdtance of Ff to pivot
6. Forces "F"
6.1 FG [N] - Tangential force spinnning mass gyro
6.2 Fi [N] - Tangential force of tilting torque
6.3 Fp [N] - Tangential force of precessing gyro
6.4 Fz [N] - Centrifugal force
6.5 Ff [N] - Force acting against precession force Fp
6.5 Fr [N] - Resultant force by Fz and Fp
6.6 Fg [N] - Gravity force
7. Torques "T"
7.1 Ti [Nm] - Necessary torque acting around hub
7.2 Tp [Nm] - Torque caused by precession
7.3 Tz [Nm] - Torque caused by centrifugal force Fz
7.4 Tf [Nm] - Torque caused by constraint against precession
8. Angles "A"
8.1 A [° or DEG] - Balance angle "alpha" between torques Tp and Tz
9. Angular velocities "W"
9.1 WG [1/s] - Angular velocity (Omega) of spinning mass gyro
9.2 Wi [1/s] - Angular velocity (Omega) of rotated hub
9.3 Wp [1/s] - Angular velocity (Omega) of precessing gyro
10. Revolution speeds "n"
10.1 nG [1/s] - Revolution speed of spinning mass gyro
10.2 ni [1/s] - Revolution speed of rotated hub
10.3 np [1/s] - Revolution speed of precessing gyro
11. Circumferential velocities "v"
11.1 vG [m/s] - Circumferential velocity of spinning mass gyro
11.2 vi [m/s] - Circumferential velocity of rotated hub
11.3 vp [m/s] - Circumferential velocity of precessing gyro
12 Angular momenta "L"
12.1 LGx [kg*m*m/s or Nms] - Angular momentum of spinning gyro around x-axis
12.2 LGy [kg*m*m/s or Nms] - Angular momentum of spinning gyro around y-axis
12.3 LGz [kg*m*m/s or Nms] - Angular momentum of spinning gyro around z-axis
12.4 LD [kg*m*m/s or Nms] - Angular momentum of deadweight mass (non-spinning)
12.5 Li [kg*m*m/s or Nms] - Angular momentum of rotated hub
12.6 Lp [kg*m*m/s or Nms] - Angular momentum of precessing gyro
12.7 Lz [kg*m*m/s or Nms] - Angular momentum caused by centrifugal
13 Power "P"
13.1 PG [W] - Mechanical power of spinning gyro
13.2 PG [W] - Mechanical power of rotated hub
+++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Units:
1kg - 1 kilogram = 1000 gram
1m - 1 meter
1s - 1 second
1N - 1 Newton [kg*m/s*s]
1Nm - 1 Newton meter [kg*m*m/s*s]
1W - 1 Watt; 1kW = 1000W
If I should have forgotten some or more symbols I will introduce them later if necessary.
In my next posting I will introduce some essential gyro equations.
Regards,
Harry K.
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| Answer: |
Harry K. - 18/11/2008 21:21:26
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| | Hello forum,
For those who are interested in this stuff, let's continue with gyro maths.
Btw, the senior should better read a (very very simple) science fiction book, because he isn't able to understand the difference between an overhung gyro which precession is caused by gravity and a forced precessed gyro which is driven by a motor hub! Listen up, the senior demonstrates his knowledges and wisdoms about gyro behavior... :-D :-D :-D (Translation for senior: HA HA HA)
This was really my last comment to the "pieces of wisdom" stated from our "nice" and "polite" senior "contributor".
Let's continue with much more important issues:
1.4 Angular velocity
Angular velocity is defined by the angle distance of a point on a circle after 1 second.
W = 2 * Pi * n
Balance point related equations:
WG = 2 * Pi * nG
Wi = 2 * Pi * ni
Wp = 2 * Pi * np
1.5 Revolution speed
n = W / 2 / Pi
Balance point related equations:
nG = WG / 2 / Pi
ni = Wi / 2 / Pi
np = Wp / 2 / Pi
1.6 Circumferential velocity
Circumferential velocity is the distance of a point on a circuit after a defined time unit.
v = r * W
v = Pi * d * n
Balance point related equations:
vG = rG * WG
vG = Pi * 2 * rG * nG
vi = ri * Wi
vi = Pi * 2 * ri * ni
vp = rp * Wp
vp = Pi * 2 * rp * np
1.7 Angular momentum
Angular momentum vector "L" is defined by the product of mass inertia "J" and angular velocity "W".
L = J * W
Balance point related equations:
LGx = JGx * WG
LGy = JGy * WG
LGz = JGz * WG
LD = JD * Wi (Wp)
Li = Ji * Wi
Lp = Jp * Wp
Lz = Jz * Wi
1.8 Centrifugal / Centripetal force
The centripetal force is acting to the center of rotation and forces a mass to move on a circuit. The centrifugal force ist acting in counter direction to centripetal and has the same size.
Fz = r * m * W * W
Fz = m * v * v / r
Balance point related equations:
Fz = (ri* mG * Wi * Wi) + (rD * mD * Wi * Wi)
Fz = (mG * vi * vi / ri) + (mD * vD * vD /rD)
---------------------------------------------------------------------------------
To be continued.
Regards,
Harry K.
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| Answer: |
Harry K. - 20/11/2008 10:50:32
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| | Dear forum,
BYE
Harry
Not to be continued...
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