Saturday, December 5, 2009

Planning the Steps Involved in Machining A Job

A CNC program is a series of operations performed for specific selections of the tool, for a specific orientation/fixation of the job and at a selected combination of settings of the machine.

The series of operations is decided by the design of the job. So lets start with a simple part such as that shown in the picture below.




Here is a picture of the stock available to you.



Based on the stock and the final object desired, we determine that we need to machine both sides of the stock. We also determine the specific procedures and tools needed for each side and make a list pertinent to each side. 

Based on the two lists, we can already know some of the tools we need to load into the machine. In addition, we also need to determine if some of the steps need to be repeated with a finer tool for better finish. This is usually determined by the machinist after test running a piece to see the quality of the output and checking that against the requirements of the customer. 

For the first side, we need the following procedures performed. Let us assume that we do not need to machine the two off center holes on the job drawing:

a) The top of the cylinder has to be faced in order to me make sure that the the surface is truly perpendicular to the height of the cylinder and to give it a smooth finish.
b) The central hole has to be drilled.
c) The chamfer on the outside rim has to be machined
d) The champfer on the inside rim has to be machined

This is what the job looked like after the first side was done.





For the second side, we determine that the following procedures need to be done.
a) The bottom of the cylinder has to be faced in order to me make sure that the the surface is truly perpendicular to the height of the cylinder and to give it a smooth finish.
b) The outer rim of the cylinder has to be machined for a smooth finish.
c) A large partial hole concentric with the central hole has to be machined.

This is what the job looked like after the second side was done.




Bob and I ran (alright, I admit I didn't write the program or pick the tools) the test run and determined that for the first side, step (c) needed a finishing step after the main step and the same repetition for step (d) for the first side and step (c) for the second side. Thus all in all, we actually ended up with 5 steps on the first side and 4 steps for the second side.

I find that CNC machines are very fascinating! Here is a shot of the machine in action.




Some useful tips to remember:
1. When you start a CNC machine at the beginning of the day, for the first job, you need to back off about a thousandth on your cutting tool calculations because everything is cold. This manifests as the cutting tool cutting a little less. 

2. Conversely, I also observed the opposite - after several runs (this was a 200 piece order), the tool bits do expand from heating and you might have to move in another half-a-thou. Otherwise the holes you drill may be the slightest bit loose.

3. Unloading and Loading tools into a CNC:  In order to change tools on a CNC, you can generally (although this is specific for Mazak) find a TOOL menu item which can be expanded to show several options. Choose the MDI (Manual Data Input) option. Then you will be prompted to enter the tool number you want to change (typically up to 10 tools) and hit INPUT. The machine will then move the tool block so as to present the request tool head to the user. Twist and pull out the tool. 

Putting in the tool must always be done in the same way, with a large dot on the tool always positioned either to the front or the back (depending on the machine involved), so be aware that there is danger for misalignment if this is not observed.



Above you can see some of the finished pieces stacked together.

Tuesday, December 1, 2009

The Kidd Effect and Faraday's Law of Induction










Consider the flywheels of the RelMachine. They are mounted in frames, on ball bearings to facilitate their smooth rotation. The frames themselves are affixed to the (rotatable) central machine axis. When we rotate the flywheel assembly about the central axis of the machine, what are the conditions that obtain? The flywheels have mass. They are being spun about the central machine axis. Under such conditions, the flywheels are being acted upon by the machine axis - the machine axis is exerting a centripetal force.

Wikipedia
http://en.wikipedia.org/wiki/Centrifugal_force

A mass undergoing curved motion, such as circular motion, constantly accelerates toward the axis of rotation. This centripetal acceleration is provided by a centripetal force, which is exerted on the mass by some other object. In accordance with Newton's Third Law of Motion, the mass exerts an equal and opposite force on the object. This is the "real" or "reactive" centrifugal force: it is directed away from the center of rotation, and is exerted by the rotating mass on the object that originates the centripetal acceleration.[5][6][7]
The concept of the reactive centrifugal force is used often in mechanical engineering sources that deal with internal stresses in rotating solid bodies.[8] Newton's reactive centrifugal force still appears in some sources, and often is referred to as the centrifugal force rather than as the reactive centrifugal force.

Now, so far the flywheels haven't themselves been spun up. Therefore, in accordance with Newton's laws, the flywheel then exerts an equal and opposite centrifugal force upon the central machine axis.

What happens if we first set the flywheels spinning to a large, fixed rotational speed ω z rpm and only then started spinning the entire flywheel assembly about the central machine axis? The answer to that question depends on whether or not there is a significant rate of change of angular acceleration in the motion of the flywheel assembly about the main machine axis.

CASE A

If there IS a significant rate of change of angular acceleration, the answer proceeds as follows:

In order to extrapolate the expected behavior of the flywheel in this case, we reason that since the flywheel is inductively suspended, we must look to the behavior of an inductor. An inductor RESISTS a rate of change of current through it.

Thus when an inductor begins to feel the surge of rate of change of current, it will correspondingly generate enough potential difference to overcome and cancel that current so as to maintain its previous state. However, if there is even so much as a tiny bit of capacitance coupled to the inductor, them the together form an LC circuit and will therefore have a unique threshold frequency peculiar to them. - This is an element of a low pass circuit, which means that any and all frequencies below the threshold frequency will receive a 'pass' from this circuit.

The exerted surge can have a periodic character or can be more of a simple speeding up character. Lets analyze the two.

If the surge is cyclical for example like this, the analysis is perfectly analogous to the LC low pass filter circuit. Thus all such inputs will meet the 'pass' condition of the low pass filter circuit.




Under such conditions, the circuit will resonate with the energy and some of it will leak into the ambient surroundings. The equivalent of this in the mechanical case would be the SHEDDING OF CENTRIFUGAL FORCE.

If the surge is more just a transient thing on the way to acheiving a steady torque used to accelerate the assembly to a large angular velocity about the central axis, this is what the time vs angular velocity, acceleration and rate of change of acceleration will look like.




We can see that the inductive phenomenon will only be effective for the following time periods: the beginning when the wheels starts speeding up about the central machine axis, and at the end, when the flywheels were brought to a stop. Thus the effect would be transient and barely noticed excepted at the beginning and the end of the operation.

CASE B

If there isn't a significant rate of change of angular acceleration: This is similar to situations where the flywheel is spinning and the assembly itself is
i) being moved in approximately straight lines,
ii) or being moved at constant accelerations
iii) or being moved at constant velocities.

Under such circumstances, relativistic effects are hidden from our view. The phenomenon proceeds as a Newtonian interaction.


ANALYZING THE KIDD EFFECT VIDEO

We can see from the graph at the very beginning of the Kidd Effect video, that there is large rate of change of acceleration being deliberately induced by vertical motor at the top of the Relmachine, in a cyclical fashion. Thus the flywheels respond as in CASE A.

Now, some energy from this capacitance-inductance circuit will 'leak' into the surroundings i.e. the flywheels will shed centrifugal force. It means the flywheels will lose part or all of their ability to produce a centrifugal force in response to the exerted centripetal force. This shedding of centrifugal force has consequences. The most direct consequence is that if there is a way the flywheels can move, either inwards or upwards they will move. The conditions governing the movement are as follows:

1. The flywheels are spinning fast enough (condition 1) and the applied rate of change of torque is large enough (condition 2) to over the gravitational force acting downwards, and the force rquired to forcibly move the flwheel vertically is less than the force required to move the flywheel horizontally (condition 3): Flight will result.

2. If condition 3 is not met, then if the conditions 1 and 2 are met, then we see what happens in the end of the video, when the flywheels forced themselves inwards.

3. If condition 3 is met but 1 or 2 are not met, then the RelMachine will show no net movement, but will show a net leakage of energy because the energy channel is open. Just not full. As conditions 1 and 2 are fulflled, the channel will fill up and the relMachine will fly. Until then, the leakage of energy to the gravitational field will steadily increase as we increase our ability to meet conditions 1 and 2 (ie we increase the flywheel speed or the rate of change of acceleration).


ANALYZING SANDY'S FIRST MACHINE

In Sandy's patent, he exerted forces on the flywheels in a slightly different, but nonetheless very creative manner.

"means for periodically forcing said masses towards one another from a predetermined position and allowing said masses to return to said predetermined position so as to generate a pulsatile force in said mounting means."

US Patent # 5,024,112

Thus the wheels were physically pushed towards the central machine axis. This is equivalent to the RelMachine's operation. In the RelMachine, that 'pushing' force is being exerted by the centripetal force, which in Sandy's machine, it was being done by a cam, in a very physical way.

Thus, in the case of his machine too, a cyclical consistent amount of lift will be delivered. Depending on the match between the resonance frequency of his machine and the applied cyclical torque, the output could have been suboptimal.

NEXT STEPS

I have determined that at this point, I must amplify the output. I will endeavor to do so in the coming weeks. I expect to run new, amplified experiments within the next 3 weeks.


Saturday, November 28, 2009

Working On A 3-Axis CNC Turning Center

Operating lathes requires exceptional skills. Years of hands-on work hones the superior machinist. I am myself a neophyte - although I admit I did use sturdy old hand-operated lathes in Mechanical Engineering lab back in my  University days to cut, trim, polish, drill and tap various prepared pieces of metal. So I'm not trying to give advice on CNC Machining here. I'm posting this so as to document what I'm picking up before I  forget it all.

A 3-Axis CNC turning center is a combination lathe and computer that gives the user freedom of working in 3-Dimensions, X, Y and Z.  The diagram below illustrates the coordinates system as related to the bed of the lathe. Being a lathe, it has a headstock with a spindle and a tailstock so that the job can be clamped securely and held that way and then spun at selected speeds to enable cutting operations. For small jobs, you can simply clamp the job to the headstock spindle. You can see a small AL 6061 job clamped to the headstock spindle below. You can also see the toolhead with multiple tools  that the machine can switch on the fly for continuous operation.




CNC (Numerical Control) allows us to control the lathe using programming statements and commands. Take a look at the picture below to see the typical interface of one such 3-Axis Turning Center. The machine is operated by a combination of entering commands into the screen and by operating the knobs and levers.




Don't let the formidable looking interface fool you. Learning it is the easy part. By far, the harder part of machining is the set up. With the aim of minimizing the number of cuts you have to make, you have to figure out the exact series of operations you need to make. Simultaneously you have figure out the set up involved in each of those operations. If you want to minimize the time you spend on it (and trust me, it always takes longer that it should, its in the nature of the beast), then you getting the set ups figured out is the most important factor that counts. A major mistake such as overestimating the clearances of the job and the reach of the tool bit can cause a huge headache. You might have to drill with a drill bit thats too long and that will cause vibration issues. Planning the order of the operations is also fairly important, especially if they build on each other and remove material that is critical for certain other operations.

Many thanks to Bob, the Master Machinist!

Wednesday, November 11, 2009

WHAT ARE WE GOING TO MAKE?

Relativistic Flyers, which are of use in the safe transportation of people and material. The Flyer is a Relativistic Machine (RelMachine) involving gyroscopic effects and the motion is achieved by a process which is the Mechanical equivalent of the generation of Electro-Magnetic Waves. In order to understand the basic operating principles of the Flyer, we need to understand the process of generation of Electro-Magnetic waves. The basic components of all circuits that generate Electro-Magnetic waves are capacitors and inductors.

Discovered first by Tesla, capacitor-inductor circuits possessed a property whereby at a unique frequency that is particular to the combination of capacitance and inductance involved, the circuit was susceptible to excitation into states involving the emission of Electro-Magnetic waves, provided this emission was supported by a source of energy that pumped AC current of that specific frequency through the circuit. The differential mathematics underlying the analysis of LC circuits is identical to that of the Relativistic Machines.

The phenomena manifests as kinetic energy flowing to the Frame of Generation (the coordinate frame in which the resonance occurs) causing its movement. In a very real sense, the Frame of Generation rides the resulting resonance wave. The wave is measurable by the physical acceleration pattern experienced by the vehicle.

When a Flyer is operated, the vehicle acquires momentum in a specific (controlled) direction – a result of the resonance that occurs when a gyroscope spinning at a specific speed is then oscillated about another axis that is at 90 degrees (to the axis denoting the gyroscope’s spin velocity vector), at a specific frequency relative to the angular velocity of the spin of the gyroscope.

What are the characteristics of the Engine producing the Flyer motion ?

Calculating from the baseline power requirements of the working prototype, the expected power consumption is in the range of 1500 Watts for an 800 kg payload. The engine will be approximately 1.5m X 1.5m X 1.8m and weigh around 35-40 kg. It will run on solar/battery energy. Current commercial battery technology leads to fair expectations of the battery life to have a range of 12-15 hours of flying.

Further efficiencies will be realized since it moves from a given point in 3-D space to another point by an optimal path without the influence of the gravitation upon the travel path.

How do you operate a Flyer?

This vehicle has 3 degrees of freedom of movement in space. The steering of the vehicle will happen primarily by adjustment of the vertical movement in conjuction with an adjustment of the direction of the horizontal movement and its magnitude. Foot pedals (integrated with cruise control) help set speed of horizontal and vertical movement. The wheel sets the direction of the horizontal movement. A joystick sets the direction of the vertical movement.

Well designed and modularized mass production could ultimately bring costs of a Flyer to less than $5000 per unit. That expected sale price makes this not only a safer, lower power-consuming and a more optimal 3-D P2P (Point-to-Point) transportation engine but also makes the Flyer cheap enough to sell it in very large quantities in the emerging markets of India as well as the mature markets of the West. Therefore those are the logical first targets of the product.

Sunday, October 25, 2009

The Story So Far

I would like to address myself to those fellow enthusiasts who are willing to take at face value, my statment that the Kidd Effect is real and that the experiment showing the Kidd Effect is proof of it. In scientfic research, as in many other facets of life there comes a moment where the curious entertain possibilities even as others blindly turn away from an idea and its powerful potential.

At such moments, our curious eyes must always remain fixed upon the horizon and seek a perspective upon the larger problem if we wish to steer accurately. At present that means that the alarming situation in physics must be called out loud and clear. To extend the sailing analogy, physics today is a current which is being blocked by a large rock dead ahead and that rock is gravity.

This much I know- the inability of quantitatively verified (i.e. experimentally tested) physics to properly integrate gravity with the rest of the forces signifies that something is very wrong with the (standard) model that we are toying with today . This is not a scratch upon an otherwise excellent tea-cup but rather as Auden would say "the crack in the tea-cup opens -A lane to the land of the dead".

For, any theory that cannot integrate gravity with the rest of the forces is essentially D.O.A. -Dead on Arrival. No question about it! And none of the critics of my approach to the problem have any theory that can integrate gravity with the rest of the forces. Nor does any professor in any university in the world at the moment have a theory that is being tested right now that integrates gravity with the other forces. We DEFINITELY don't have an experimentally verified theory that integrates gravity into the rest of the framework as things stand at the moment (October 2009). My theory is offering a way to accomplish exactly that. By folding ElectroMagnetic laws and Mechanical laws into a single framework, I'm providing a credible path to the integration of gravity into the nomological network of the Standard Model.

Therefore, my theory is superior to the Newtonians [Here, Newtonians are those who insist that in explaining a gyroscope's behavior, Newtonian (or Eulerian) analysis is necessary and sufficient.] in the sense that it cannot be refuted by any amount of argumentation from Newtonians who  -by virtue of their failure to provide any credible path towards the integration of gravity with the remaining forces- cannot overcome that fatal flaw first, even before they could debate me about my theory. As long as my critics are unable to present their own nomological network of experiments that can integrate gravity with other forces with in the current paradigm of physics, any and all of their criticism of my theory which limits the discussion to the gyroscopic problem alone will be rendered null and void by the larger problem, the elephant in the room so to speak, that they do not, indeed cannot address. Please refer to my page on the importance of gyroscopic behavior in the analysis of the bigger problem of gravity and its place in the scheme of things.
Not only can the Newtonian fail to explain how gravity fits with the other forces, but also, the Newtonian cannot explain certain features of Gyroscopic behavior - features that my theory can account for logically.
This page dealing with the laws governing gyroscopic behavior, the page dealing with the problem of Effect preceding Cause in gyroscopic behavior and also this page highlight the problems that Newtonians have in explaining Gyroscopic behavior. The links in the previous sentences lead to pages that not only state the problems but also show how they are not an issue in my theory.

I hold that rotation is the fundamental phenomena at work in both Electro Magnetic and Mechanical situations. This is my very own unique hypothesis. From the perspective provided by this unique hypothesis, all the effects are mapped from mechanical to Electro-Magnetic situations via the quanttative laws of mechanics and Electro-Magnetism. That is, every mechanical situation has an Electro-Magnetic couterpart and vice versa.

Verification of the similarity of corresponding quantitative laws in Mechanics and Electro-Magnetism are being provided by

A. Outlining the theory via explicit analogy between the two fields and also the similarity of the calculus underlying the laws and

B. also by the experiments I am performing.

One half of this verification - i.e., the theory, I have already presented in detail. See my pages on capacitors, inductors and spinning wheels, the paradoxical nature of the laws governing gyroscopic behavior.

The other half -the experiment- is in progress.

As I mentioned here, one important consequence of my theory's perspective of rotation as being a fundamental phenomena in both Electro-Magnetic and Mechanical situations is that there is a mechanical equivalent to Inductance in Elecro-Magnetism.

This then led me to the idea of a harmonically oscillating resonant Inductance-Capacitance circuit. And that is what the Relativistic Machine is - A machine which functions upon the relativistic curvature of spacetime to create a feedback loop that enables a build up in amplitude of the circuit's energy output.

Looking at the bigger picture, I'm arguing for the introduction of the new paradigm of capacitor-inductor arrangements as measures of local-to-global space-time interactions (its really just the newest incarnation of the harmonic oscillator) that will model both mechanical and Electro-Magnetic situations (as also counter parts in weak and strong interactions as future research will hopefully prove).

Under such a paradigm, we can explain both electronic LC circuits and the Relativistic Machine in terms of the backreaction of a field upon the source. Time Symmetry is shown to be the source of the unique energy pumping mechanism that is possible with Capacitor-Inductor arrangements.

In conclusion, I'd like to remind everyone that my work is in line with work done by engineers and scientists of a different era when Electro-Magnetism was first being modeled and explored.

Monday, October 12, 2009

Thank You, Damu!

And welcome to the hunt.
From that first time we met for our first Engineering class, you have always shown a youthful spirit and a free way of being and seeing the world.

 దాము,
మరి నువ్వు నిష్కామ కర్మ చేసావు కదా, అయితీ మరి అది భాగ్యం తో నీకు తిరిగిరావాలని నేను భగవంతుని తలుస్తున్నాను.

నీ మిత్రుడు
రవి


Thursday, October 1, 2009

Kidd Effect or Not?

I am forced to conclude that the damage to my machine was caused not by a mechanical malfunction but a true manifestation of the Kidd Effect.  There are two reasons for my conclusion:

1. The picture below is a close up of the damage wrought by the Kidd Effect.






You can see the metal of the wheel was extruded on the outer side of the wheel and the wheel was pulled against the friction of the pin holding it firmly in place. It would take a very large inward force to do this.

There is a slight (~3 degree) inclination of the main axles but the component of the weight of the wheel along the horizontal would be hardly enough to force the wheel and shear the metal.

Centrifugal forces generated due to the application of torque on the wheel assemblies are also only likely cancel out any inward weight component about the horizontal.


Reason # 2:  hmm... suffice it to say it is a very good one. A subject for a new post.

Saturday, September 26, 2009

The Kidd Effect

Sandy Kidd discovered through his experiments with spinning wheels that under certain conditions, the spinning wheels will move inwards. This video is the first visual proof of the effect.


Friday, September 18, 2009

Experiment # 2.2



This experiment doubles the max torque from the previous experiment, which is still only around 10% of the power this machine can generate. Its obvious from the video though that the tipping point has been reached.

Both experiment 2.1 and 2.2 were performed at the same (relatively low) angular velocity of the flywheels. Lets designate this velocity of the flywheel as N0. The max torque for experiment 2.1 is designated T0.

For any pair of values (N, T) there exists one unique resonance frequency for any given relativistic machine we assemble. The experiments will build the angular velocity in order to amplify the relativistic energy transfer.

Thursday, September 17, 2009

Experiment # 2.1



This experiment serves to set the baseline speed/torque requirements to produce a minmal amount of effect. The two wheels are operating within 10 RPM of each other. Having gradually increased the output power of the prototype of the Relativistic Machine to this level, we can now calibrate the device using this information.

As it is, the device outputs ~5% of its power. Even at such a low level of output, the wheels -which account for less than a quarter of the weight- already have a strong destabilizing effect on the Y-axis of the prototype.

Subsequent experiments will ratchet up the power to record any change in the behavior of the prototype.

Friday, September 11, 2009

Derivation of Resonance Frequency

Consider the figure below of a machine made up of an assembly with an outerframe supporting a spinning wheel in a carriage, with the entire carriage being made suitable to spin about the main Y axis of the machine. The spinning motion of the wheel provides the coupling force (inductive) and the non-spinning part of the carriage and the outerframe provide the inertial force (capacitive).



This is identical to the electrical situation below.



By analogy with electrical circuits, the resonance frequency would equal
ωR = 1/sqrt(LC) ~ ωR = 1/sqrt(Inductance of wheel * Capacitance of carriage and frame)

Recall that since by analogy with Faraday’s Law,

ωXprecess (t) = (Inductance of Spinning Wheel)*dαY/dt

=> Inductance of Spinning Wheel = ωXprecess (t)/dαY/dt

Capacitance of carriage and frame is a function of the design and the moments of inertia and is taken to be

IFX* IFY

where the subscript F indicates that its the frame (and w indicates that its the wheel) we are referring to.

Then, ωR = 1/sqrt(ωXprecess (t)* IFX* IFY/ (dαY/dt) )

Also for a spinning wheel, ωXprecess (t) = Torque/AngularMomentum = τwy/(Iwz*ωz)

where ωz is the angular velocity of the spinning wheel.

Substituting this, we get:

ωR = 1/sqrt(τy * IFX* IFY/( (Iwz*ωz)*(dαY/dt) ))

or

ωR = sqrt( ( Iwz*ωz*dαY/dt)/(τwy*IFX* IFY))


Now,

Iwz*dαY/dt = dτFY/dt (since torque to the wheel about the m/c Y axis can only be given by pushing against the frame)

So substituting that into the above equation, we get

ωR = sqrt( ωz*(dτFY/dt)/(τwy * IFX* IFY))

Note that since the frame and the wheels are reacting against each other,

(dτFY/dt)/τwy = (Iz/ sqrt(IFx*IFy))* ωv, i.e. a fixed frequency signifying how many times the torque produced by the vertical motor must change per second.

Substituting that further simplifies the above equation to:

ωR = sqrt( ωz*ωv*Iwz/sqrt(IFx*IFy)*sqrt (IFX* IFY))
Now, suppose we set ωv equal to the resonance frequency, ωR

ωR = sqrt( ωs*ωR*Iwzsquare/(IFx* IFy)

ωR = ωz*Iwz/sqrt(IFx* IFy)

The above formula represents the frequency at which the vertical motor must vary the carriage’s torque in order to emulate resonance conditions for the mechanical LC circuit. At resonance, the torque, angular momentum and angular displacement of the wheel’s center of mass are related as shown in the graph below (only one full cycle of a wave of variable torque is shown).



At resonance, there would be a conversion of internal energy into external energy, resulting in motion of the entire frame under certain conditions. When resonance occurs under such conditions the entire carriage assembly will acquire kinetic energy(’fly’) equal to an amount calculable from the rotational velocity of the flywheel and the moments of inertia of the component parts per every cycle of the variable torque.

Thursday, August 6, 2009

Back-reaction and Time Symmetry

Although the observable universe does not suggest Time Symmetry as an inevitable, inescapable law, the physical laws themselves exibhit an indifference to the direction of flow of time.

Time symmetry itelf is a highly important condition for physical laws.
Source: http://en.wikipedia.org/wiki/T-symmetry
quote
Indeed, there is no apparent reason for which such symmetry should be broken, and therefore one time direction has no privilege to be more important than the other. Thus, a theory that respects this symmetry appears, at least, more elegant than theories with which one has to arbitrarily choose one time direction over the other as the preferred one.
end quote

General Relativity is a time-reversible Lagrangian theory. The Wheeler-Feynman absorber theory assumes that it is happening. Maxwell's equations also exhibit time symmetry i.e. symmetry of results whether we assume time to flow forward or backward. A mathematically rigorous solution of Maxwell's wave equation for EM waves would produce two possible solutions commonly labeled retarded and advanced solutions.

source:http://en.wikipedia.org/wiki/Wheeler%E2%80%93Feynman_absorber_theory
The Maxwell equations and the wave equation for electromagnetic waves (and the accel-gravitic waves we are deducing via the analogy between electricity and mechanics - Ravi) have, in general, two possible solutions: a retarded solution and an advanced one.
end quote

This means that if we have an electromagnetic emitter which generates a wave at time t0 = 0 and point x0 = 0, then the wave of the first solution will arrive at point x1 at the instant t1 = x1 / c after the emission (where c is the speed of light) while the second one will arrive at the same place at the instant t2 = x1 / c before the emission.

I propose that the advanced wave is physically significant for only those situations involving time scales and length scales comparable to that of the resonance frequency of the caacitor-inductor arrangement involved.

Under such circumstances, the wave travels into the past and brings energy with it. In the case of the gyro, the no-nutation condition shows that just the slightest nudge right as we start the inductive suspension is all thats necessary. (i.e the effect isn't travelling into the 'distant' past, for example, I dont need to already give the gyro that nudge several seconds before I release it in inductive suspension).

Besides, this only seems proportional and fair to the way the effect behaves in positive time - Suppose you were to release the gyro at rest, (rather than in the nonutation condition), beyond a few wave lengths of the inductive-capacitive circuit, there would be no noticeable nutation - ie. the tight damping of the nutation is also a measure of the tight damping of the energy travelling backward in time.

Its only that if we appropriately design a RelMachine, we can harness this backward flowing energy to amplify the thrusting torque to significant levels. In the case of non-inductive suspension, it would be capacitance that would be dominant (and capacitive interactions can be analyzed using Newton's Laws) and this would reduce to Newton's Third Law.

source: http://www.mathpages.com/home/kmath528/kmath528.htm
quote
The Wheeler-Feynman absorber theory explains the resistance of a charged particle to changes in its state of motion as being due to advanced waves emanating backwards in time from an all-encompassing array of absorbers in the future, whose waves are excited by the retarded waves emanating forwards in time from the particle.

end quote

Therefore, similarly, we may postulate that inertia of any object is due to the advanced waves emanating backwards in time from an all-encompassing array o absorbers in the future, whose waves are excited by the retarded accel-gravitic waves emanating forwards in time from the particle. Further we may also postulate that in the case o the Relativistic Machine (as also in the case of the LC circuit), in operation at its resonant mode, this backward travelling feature of energy is being built up to create a large response.

Thus we see that the Wheeler-Feynman absorber theory helps explain the self-interactive nature of an inductor (and now, we extend it to an inductively suspended spinning wheel) and the backreaction generated by inductive-capacitive arrangements as arising due to the time-symmetry of natural laws.

Wednesday, July 29, 2009

The Good Professor Vs The Jabberwock

That last paragraph in the previous post bears repetition and reexamination: The back reaction of a particle's own field on itself is necessary to explain the friction on charged particles when they emit radiation.

Now, in order to understand the gyro's behavior in purely electromagnetic terms, it is necessary to see understand how this back reaction works when a gyro is inductively suspended.

Refer to "Roll Isaac Roll" (Laithwaite, 1979): In Professor Eric Laithwaite's paper, "back reaction" are the very words used by him to describe the behavior of a gyroscope.

Quote:
So if the spin momentum remains constant (-for a spinning gyro-and why shouldn't it, if we postulate a wheel in perfect bearings ), then a torque T is seen to give rise to an angular velocity omega** (and for an electrical engineer it can easily be seen as the reverse way around, for a current can be seen as the cause of a voltage in a series circuit). Since when has an angular velocity been capable of producing a back reaction? I thought only an angular acceleration could do that...
End quote

What the good professor is asking is this: Since the gravitational torque produced the angular velocity, any back reaction that the initiating gravitational torque suffers (in this case, it was gravity that initiated the torque and the back reaction cancelled the gravitational torque and kept the gyro horizontal) can only have been initiated by the product of the torque. Since the product of the torque was simply a precession, it means it was the back reaction of the precession that canceled out the torque – ie. A velocity produced an acceleration. That back reaction is identical to the back reaction of a particle's field on itself. That is, inductance is a field element. This is complementary to the fact that capacitances behave as point particles – both in Brillouin's development of electrical/mechanical filters and in Newtonian/Laplacian analysis of lattices. The two together form a harmonic circuit or arrangement – one which we can harness.

We can still continue to follow the analogy- this time with Quantum Electro Dynamics (QED). I propose that what we are seeing here is more commonly called the ‘jangle fallacy’ (Thorndike, 1904) -it refers to cases where two different terms are used for the same entity. That is, self-induction (in EM)/ back-reaction (of gyros) are analogous words describing one and the same phenomenon. ("the jangle") (As opposed to the “jingle” fallacy where we give two different phenomena the same name – thereby introducing another of confusion.)
There are already tantalizing hints that this is correct, from previous attempts to bring Gravity into the framework of the Unified Field Theory. For example, for one such alternate theory to work, it would need a decidedly non-Newtonian head-start:
quote:
The Abraham-Lorentz theory had a non-causal "pre-acceleration". Sometimes an electron would start moving before the force is applied. This is a sign that the point limit is inconsistent. An extended body will start moving when a force is applied within one radius of the center of mass.
end quote

This is strikingly similar to the fact that pure Newtonian predictions would be unable to account for the 'lead' of the precession resulting from a torque over the torque itself. Newtonian predictions will likewise be unable to explain how a Relativistic Machine can function, as in pure Newtonian terms, such a machine would appear as in the Abraham-Lorentz theory, to be “moving when a force is applied within one radius of the center of mass”.

This it would seem that Abraham-Lorentz theory is lacking exactly the same thing that Newtonian Physics is lacking (when it attempts to explain how precession could lead the torque that produces it), when it comes to explaining how gravity fits with the strong and electroweak forces. Solve one and you just might solve the other.

It would also seem that the Abraham-Lorentz theory is implying that in order for a framework to be possible that integrates gravity successfully with the other three forces, it would also have to be possible to have “non-causal preacceleration” i.e. Precession leading torque as well as “an extended body to start moving under certain circumstances when a force is applied within one radius of the center of mass” i.e for a Rel Machine to be able to fly.
What is also being proposed in this discussion is that a gyro ( or a spin angular momentum which has been suspended inductively)'s behavioral response is the ultimate measure of "extension" or space. Therefore it dominates any discussion of field related formulations of gravity in ways that are analogous to inductive elements in Electro-Magnetism. In addition, all non-gyroscopic objects/arrangements can be dealt with as pure point masses without spatial extent.

Now, just how did QED solve the renormalization infinities problem when it first appeared?

The main idea that QED brought to renormalization is to correct the original Lagrangian of a quantum field theory by an infinite series of counterterms, each one of which is labelled by the Feynman Graphs that encode the perturbative expansion.

Quote
In this methodology, the divergences appear in calculations involving Feynman diagrams as closed loops of virtual particles in them.

A Feynman graph consist of loops and edges and satisfies certain conditions. Each loop or edge represents a segment of the worldline of a particle.
End quote

Vacuum bubbles for instances are represented by a simple loop. Since in graph theory, a loop is an edge that connects a vertex to itself. Note that Feynman graphs consist of edges representing segments of the worldline of the particles involved.

Now, the spinning wheel going a-b-c- and-so-on-and-on and then forms vertices like at b over and over.
Thus spinning (a loop) is represented by a vertex with cyclical sets of two edges. (Figure 1) But in the case of a spinning wheel, we know that if a RelMachine is possible then it means that with respect to a stationary inertial frame (whose worldline is represented by a-c), the zig-zagging wheel and its support arrangement will move in space away from the inertial observer, ie there will be a divergence between them(Figure 2). Thus over time, the two sets of lines appear to diverge. Now, suppose both objects have spin – one simply has more spin than the other. Then, in such a case, we can modify the relativistic diagram further to Figure 3.

This is a cumbersome way of representing whats going on in the situation. A simple way would be as in Figure 4, where a single cycle of the spin is shown to both give the frequency and to represent that there is an inductive process at work. Then, we would connect the middle points d and b to indicate that there is an energy exchange going on. We could further encode information into the diagram by using color to indicate whether there is a large amount of energy interchange, color of the edge represents the type of energy of the particle, etc etc. This is infact what a feynman diagram does. (Figure 5)

Thus, the divergences that appear in calculations are implied to be inductive energy exhanges and are symbolically represented by loops. There are further useful deductions to be drawn from the analogy of spin/rotation with the Feynman Rules for loops in QED

Feynman Rule: Incoming and outgoing lines carry an energy, momentum, and spin.
Interpretation: The are inductive + capacitive arrangements (and therefore determined by their harmonic behavior.

Feynman Rule: each vertex where lines meet gives a factor derived from an interaction term in the Lagrangian
Interpretation: Each inductive interaction has its own entry in the Lagrangian.

Feynman Rule: A point where lines connect to other lines is an interaction vertex, and this is where the particles meet and interact--- by emitting or absorbing new particles, deflecting one another, or changing type

Interpretation: The vertexes are situations where an event is occuring with a decay and a collision (analogues of emission and absorption) involved.

It is proposed here that these closed loops that Feynman Diagrams refer to are nothing but representatives of the energy involved in harmonic arrangements involving inductively suspended spinning objects coupled to the capactive elements (point objects), in calculations.

Thus, in a Feynman diagram, the capacitive objects are being shown are particle (localizable) inputs and outputs, while the inductive objects/arrangements are shown only abstractly as a loop similar to a spinning wheel's spacetime trajectory. This would mean that the Feynman diagrams/graphs would be the best choice of schema to sketch the behavior of both inertio-gravitational oscillators and electro-magetic oscillators. Having a single schema to analyze both behaviors, in a way harmonizes the analysis of both phenomena.

A (inductively suspended object) gyro's behavioral response is the ultimate measure of "extension" or space. All non-gyroscopic objects can be dealt with as pure point masses without spatial extent.

The inductive property is disruptive to theories which are based on capacitive rules of interaction. Instead of the object going this way like a billiard ball would, it might go some other way, photons create virtual particles, etc etc. That is why they appear as "violations" of interaction rules which have been capactively founded. Much of this distortion has to do with the fact that most of our 'intuitive' interactions in daily life proceed capacitively (and all purely capacitive interactions can be analyzed using Newton's Laws).

We would expect that accordingly, the need for these 'loops' would coincide with situations where a large amount of inductive capability is trapped inside the particles/arrangments involved in the interactions. Indeed this is the case. Those situations for which the interactions are divergent are significant, which have large momentum/energy values.

Quote:
While virtual particles obey conservation of energy and momentum, they can have any energy and momentum, even one that is not allowed by the relativistic energy-momentum relation for the observed mass of that particle. (That is, E2 - p2 is not necessarily the mass of the particle in that process (e.g. for a photon it could be nonzero).) Such a particle is called off-shell. When there is a loop, the momentum of the particles involved in the loop is not uniquely determined by the energies and momenta of incoming and outgoing particles.
End quote

Interpretation:
i.e., the inductance of the arrangement and the backreaction of that inductance's field upon itself, in response to local forces can play a large enough role in moulding the results of the interaction, even though they are largely invisible to the capacitively oriented Newtonian (Euclidean) laws.

Quote
A variation in the energy of one particle in the loop can be balanced by an equal and opposite variation in the energy of another particle in the loop. So to find the amplitude for the loop process one must integrate over all possible combinations of energy and momentum that could travel around the loop.
These integrals are often divergent, that is, they give infinite answers. The divergences which are significant are the "ultraviolet" (UV) ones. An ultraviolet divergence can be described as one which comes from- the region in the integral where all particles in the loop have large energies and momenta.
End quote

Interpretation:
(i.e. only those inductive processes are significant which have significant/large rotation energy and momentum) For such large energy processes (dubbed Ultraviolet divergences), the net result is calculated by adjusting the capactive laws to include an inductance (and the resulting harmonic oscillations term and its consequences) and its effects. The Feynman diagram is serving to document that adjusted calculation.

Quote
- very short wavelengths and high frequencies fluctuations of the fields, in the path integral for the field.
- Very short proper-time between particle emission and absorption, if the loop is thought of as a sum over particle paths
end quote

Interpretation: Thats exactly what we showed for the rotating wheel- cyclical emission and absorption.
The faster the rotation, the shorter the proper-time between particle emission and absorption, if the loop is thought of as a sum over particle parths.

That is, the loop implies rotational motion of the object or constituents of the object. Infinite answers imply that for large inductances, the resulting precessive output will be large and is going to cause divergences. The formulas are merely reflecting the unsuitability of capactive techniques to analyze inductive phenomena.

Some Final Remarks
Quote
The Higgs field has a non-trivial self-interaction, like the Mexican hat potential, which leads to spontaneous symmetry breaking:
End quote

That is, the Higgs field involved self-induction, which appears in the case of inductively suspended objects harnessed by a local variable torque.
So expect that in analogy, the weak gravitational force, inertia (capacitance) and induction arise through a Unified Field Theory with spin/rotation as a major driver.

Now,
Quote
In particle language, the constant Higgs field is a superfluid of charged particles, and a charged superfluid is a superconductor. Inside a superconductor, the gauge electric and magnetic fields both become short-ranged, or massive.
End quote

Thus, this formulation of the Higgs field as the resonant excitation of inductively suspended spinning objects can form explanations of SuperConductivity as well.

Please note that n this and the previous post, I have quoted from http://en.wikipedia.org/wiki/Feynman_graphs

Monday, July 27, 2009

The Problem With Gravitons

Although Albert Einstein spent the last two decades of his life seeking to unify Gravity with Electro-Magnetism, he did not succeed in building a Unified Field Theory. Even now, the current state of unified field theories is that there is as yet, no accepted unified field theory. Gravity has yet to be successfully included into the framework of such theories.

One of the best weapons in science is analogy. We apply the template of existing known processes in discovering/understanding new processes. Nature seems to somehow agree with us. Wave motion is one example of such a concept. In mathematics and physics, the Laplace operator is a differential operator used in modeling of many different kinds of wave propagation. It is used in formulating equations for acoustics, fluid dynamics heat flow, forming the Helmholtz equation, all the major equations in electrostatics, Electro-Magnetism, and in representing the kinetic energy term of the Schrödinger equation in Quantum Theory.

Harmonic motion is one other such concept - it has been applied successfully, over and over again in various (intially, to an untrained eye atleast) unrelated fields like mass-spring arrangements, a molecule inside a solid, an electron stuck in an atom, a car stuck in a ditch being rocked out, a pendulum and the earth in its orbit. (source: http://www.slideshare.net/makadelhi/applications-of-shm)

Capacitors and Inductors are also such a concept. While capacitors alone interact as point objects, inductive objects (consisting of a spinning object in suspension about an orthogonal axis) behave as objects with a finite extension. Thus, viewing all interactions as being either capacitive or inductive can become a generalized technique that sorts the spatially extended objects (ie field elements) from point objects in both Electro-Magnetism (EM) and Iner-Gravitation (lets say, IG). This analogy raises spin/rotation to a unique postion of being the progenitor of both effects via capacitive and inductive suspension. By giving us the ability to distinguish between capacitive and inductive interactions, this analogy can also help harmonize IG with EM by solving the problem of renormalization when combining gravitons with strong and electroweak interactions. The following section explores one way to resolve this current problem in Physics.

All this means we can guarantee a unified structure to natural laws that would still look very familiar, but with a twist (almost literally) of the third derivative. In merging Mechanics and Gravitation with EM, we open the door to the Unified Field Theory. Lets not forget that Gravitation has long been the wedge that kept the whole structure from beautifully fitting together. In addition, it will give us the key to building ships that can cross space and make green transportation a reality.

In order to incorporate gravity into the Unified Field Theory framework, we have to work to replace curved spacetime as in general relativity with a situation where the gravitational interaction is mediated by gravitons. However, attempts to replace general relativity (GR) with gravitons have run into serious theoretical difficulties at high energies (processes with energies close to or above the Planck scale) because of infinities arising due to quantum effects (in technical terms, gravitation is nonrenormalizable).

Even just trying to combine the graviton with the strong and electroweak interactions runs into fundamental difficulties which boil down to the non-renormalizability of the results. The incompatibility of GR and quantum mechanics (QM) is another current problem in physics. Both these problems involve mechanics/gravitation's relationship with the remaining three forces.

In physics, although in principle we can predict the behavior of matter by keeping track of each atom, it is often more practical to treat matter as a continuum and then taking the continuum limit. Newton for example considered that air could be modeled as a lattice of mass points. He assumed the simplest possible lattice – equal masses spaced equally along the direction of propagation.


Laplace used this conception of air to successfully calculate the speed of sound. In fact, the entire set of Newton's Laws of Motion as well as wave theory itself can be deduced by taking the continuum limit of this simple lattice. If you wish to see the derivation, it is available here:
[http://en.wikibooks.org/wiki/General_Mechanics/The_Continuum_Limit]

In Quantum Field Theory (QED), renormalization refers to a collection of techniques used to take a continuum limit of space and time.

(source: http://en.wikipedia.org/wiki/Renormalization)

When describing space and time as a continuum, certain statistical and quantum mechanical constructions are ill defined. In order to define them, the continuum limit has to be taken carefully.

Renormalization determines the relationship between parameters in the theory, when the parameters describing large distance scales differ from the parameters describing small distances.
end quote

However renormalization when gravitons and strong or electroweak interactions are combined is hindered by the problem of infinities. The problem of infinities is an old one dating back to the 19th and early 20th century. Back then, it arose in the application of classical electrodynamics to point particles. This first version of the problem was solved by QED (as will be discussed immediately below) and the second version of this problem that has arisen with respect to Gravitons is currently unsolved and is an open problem.

To put it simply,
(source: http://en.wikipedia.org/wiki/Renormalization)
quote
the mass of a charged particle should include the mass-energy involved in its electrostatic field. Assume that the particle is a charged spherical shell of radius re. The energy in the field is
end quote

mem = q2/8*P*re

where

mem = electron mass

Now normally, this classical electrodynamics formula performs well for all electromagnetic interactions for which quantum mechanics is not relevant. However, notice what happens when the radius falls to zero. The energy becomes infinite when re is zero. This directly implies that the point particle would be infinitely massive and could never be moved - an absurd conclusion.

Max Born, Werner Heisenberg, Pascual Jordan, and Paul Dirac discovered that in perturbative calculations many integrals were divergent.

Further,(source:http://en.wikipedia.org/wiki/Renormalization) when calculating the electromagnetic interactions of charged particles, it is tempting to ignore the back-reaction of a particle's own field on itself. But this back reaction is necessary to explain the friction on charged particles when they emit radiation. If the electron is assumed to be a point, the value of the back-reaction diverges, for the same reason that the mass diverges, because the field is inverse-square.
end quote

Sunday, July 19, 2009

Estimating Power Supply Required For The Flywheel Motor

Selecting a motor with the right amount of torque to spin up your flywheel to the desired speed is a good first step. However, you still need to figure out how much power (voltage and current values) you will need to get up to the desired operating speed.  There are several factors to consider in such a situation. The motor's speed/torque characteristics and its nominal values of voltage and speed play an important role in all this. Note that we are assuming it is a DC motor that we are using. The required voltage can be estimated as follows:

ML = Operating Torque [mN-m]
NL = Operating Speed [rpm]
V0 = Nominal Voltage of the Motor Selected [V]
N0 = No Load Speed of Motor @ Nominal Voltage [rpm]
Dn/DM = Speed/torque gradient of the Motor [rpm/mN-m]
VL = Operating Voltage [V]


VL = (V0/N0)*(NL + (DN/DM)*ML) [V]

For instance: For the example flywheel we used in sizing the motor,

ML = 2400 mN-m
NL = 16000 rpm

Suppose a motor we are considering has the following additional characteristics

V0 = 24 V
N0 = 8000 rpm
Dn/DM = 8.69 rpm/mN-m

Then we can calculate

VL = 110.6 V

You will need to make sure that your motor is designed to accept this much voltage. If not, you will likely damage it and/or injuring yourself if you feed excessive voltage into it.

If you are going to be using a brushed DC motor along with a controller, it is highly likely it will use PWM technique to do so. In such a case, you will need a somewhat modified formula . Additionally, we also need the following extra data

PC = Pulse Width Modulation Cycle [in %]
VD = Max Voltage Drop Across Controller

VL = (V0/N0)*(NL + (DN/DM)*ML/PC) + VD [V]

So if I had a controller with say an 85% PWM cycle and a 3 V voltage drop across the controller,

VL = 124.6 V

You will need to make sure that your controller is designed to accept this much voltage. If not, you will likely damage it if you feed this voltage into it.

This calculated voltage and the nominal value of current of a given motor together will better guide your motor search/selection.

[Important: The calculations are meant for approximate 'ball parking' of the required power supply only. If you want the exact values, you will need to consult your motor's manufacturer's specs or technical support. Please also note that the actual numerical values used here are for illustration purposes only and do not represent the prototype.]

Sunday, July 12, 2009

On Assigning Cause and Effect in Inductively Suspended Objects

First it might be useful to take a quick refresher of forced oscillations in harmonic systems. Here's a good one I found after a quick search. Although written for a spring pendulum, this applies also to spinning wheels in inductive suspension.

Forced oscillations. (@http://www.walter-fendt.de/ph14e/resonance.htm)
Begin Quote
On the whole you can see three different types of behaviour for forced oscillations:

case A: If the exciter's frequency is very small (this means that the top of the spring pendulum is moved very slowly), the pendulum will oscillate nearly synchronously with the
exciter and nearly with the same amplitude.

case B: If the exciter's frequency agrees with the characteristic frequency of the spring pendulum, the oscillations of the pendulum will build up more and more (resonance); in
this case the oscillations are delayed about one fourth of the oscillation period compared with the exciter.

case C: If the exciter's frequency is very high, the resonator will oscillate only with a very small amplitude and nearly the opposite phase.
End Quote

The gyro and the Rel(ativistic)Machine (that I contend will be able to fly) contain spinning objects. Any spinning object that is inductively suspended can be harmonically excited. Now, case B is the case of such a harmonic system at resonance. i.e. a Rel(ativistic)Machine.

Case C is the gyro in precession under the influence of gravity. The precession exists only as long as a rate of change of angular acceleration exists and cannot exist in the absence of it. Gravity is a high frequency exciter when compared to the characteristic resonance frequency of a spinning gyroscope suspended in inductive conditions. Thus, the gyro responds with a small steady precession & in the opposite phase (i.e. cancelling out gravity).

How do we assign cause and effect in analyzing interactions? Lets analyze the situation. Under routine Euclidean conditions, in analyzing cause and effect, if Y changed when I meddled with X, it can perhaps follow that X is the cause of Y. You would be correct in the sense of action - reaction (i.e. for a gyro on the ‘Eiffel Tower’, even if the physics says precession came first – that’s what the cross-product formula is saying- we 'know' that we initiated the torque first).

Now normally that would work just fine. But in looking at the Gyrscopic interaction that way, one will have missed the temporal aspect. What really matters in interaction analysis in this situation is that we label what comes first as the cause and what comes second as the effect.(And NOT to assign what you 'know' yourself to be doing as the cause and what happens then as the effect.) Otherwise one is liable to become deceived.

Lets look at how, if it were up to a Newtonian, s/he would label the energy flowing into the gyro (in the form of the torque) - S/He would call the torque the cause (lets label it event 1) and the precession as the effect (lets label it event 2). S/He would insist that event 1 came first and event came next.

But according to relativistic analysis, the energy contained in the wheel has a shorter spacetime distance between events. Therefore the energy of the wheel in the present is not in the same phase as the energy of the frame. (Recall this diagram below from this post.



That phase difference bestows upon it (the spinning wheel) a variable ability to oppose or reinforce the arriving energy that can be harnessed most efficiently, if we make the appropriate arrangements (i.e. it’s normally a limited ability but can be harnessed best when we induce resonance), in analogy with a properly tuned LC circuit. For a rate gyro its case C, the lower limit that is applicable.

For spinning wheels (for instance, for the prototype), under inductive resonant conditions, we activate case B, the ability of the momentum in the wheel to push more and more strongly (like a rider on a swing kicking the ground at exactly the right intervals over and over to acheive high amplitude.) against the frame, even as the frame's momentum attempts to act upon the wheel and drag it around, under the influence of that vertically mounted motor.

That means that under resonance conditions of reinforcement, momentum is delivered cyclically from the 'future' of the spinning wheel to the 'present' of the frame. (alternatively we can say energy from the 'present' of the spinning wheel is adding momentum to the 'past' of the frame. - the naming is irrelevant - also note that this doesn't imply time travel of any extended degree, in practical terms its merely saying the phase can be adjusted to be positive). If the cause is in the future and the effect is in the present, then it means the effect will be recorded first and only later the cause, when viewed from an inertial frame.

Since there is a process in play in which energy from the 'future' is influencing energy in the 'present', the actual temporal order of occurrence would be 2-1. That is the energy transfer would temporally execute in the order 2-1, but action-reaction accounting of the entire interaction would run 1-2. THAT mismatch in the ordering (between the temporal perspective and the interactive perspective) of events leads conventional Newtonian analysis of Gyroscopic action into a dilemma.

An analysis that conforms to Newtonian Laws can be achieved only by hewing to the temporal order of manifestation (so as to record the forces, play by play as and when they are manifest). However, in such an analysis, since we label what comes first as the cause and what comes second as the effect, that would also mean accepting cause as effect and vice versa in the situation of the gyroscope. (et voila,.. there you have the formula t = w X L - you gave up what should be the logical choice of what is cause and what is effect in order to preserve Newton's Laws)

Alternatively, we can break the temporal order i.e. we adopt the method of assigning the torque as the cause and precession as the effect. We say torque is the cause and precession is the effect - in which case, we would be forced to write w = t X L which does not conform to actual behaviour, thereby bringing all Newtonian analysis to a halt.

One cannot keep both logical and Newtonian order.
The formula t = w X L allows us to keep the Newtonian mathematics by reversing the logical order i.e. the order that we 'know' we are initiating and replacing it with the opposite situation i.e. the formula assigns cause and effect by temporal order - but at least in return for it, a simple Newtonian analysis of the motion is possible. (But only a limited one any how, because while Newtonian analysis has allowed the exploitation of the gyroscopic principle in constructing useful rate gyros etc, it has also deceived us into thinking we understand everything about the phenomenon. In fact, much more can be done if we harness the effect in a resonant mode.)

Crosscheck:
Suppose we assigned the torque as event 1 and the precession is then event 2 AND we also incorporated the insight (provided by relativistic analogy between Electro-Magnetism and Accelero-Gravitation) that the effect is in the present and the cause in the future, then we can do a modified Newtonian analysis as follows:

We introduce a fourth force (temporarily) right at the beginning of the interaction, equal in magnitude and direction to the effect, to hold the place of the effect until it actually kicks in. This force would account for the fact that the effect will itself be recorded (and will itself be the cause of activity) BEFORE the cause is manifest. In such a situation, we could preserve Newtonian analysis. Such a situation has striking similarity to the No-Nutation condition:

Lets say you have a spinning toy gyro. You've just spun it up. You are positioning one end of the axis on top of the 'Eiffel Tower'. How do you set off the gyroscope without causing nutation? The way to set a gyro precessing without causing any nutation is to give it a gentle nudge even as we let it go and the nudge but be equal in magnitude and direction to the precessive velocity that will be introduced. Then there will be no nutation.

That is we are compelled to introduce that exact 4th force we discussed in the above paragraph. i.e that fourth force is not a mathematical artifice but an actual, real necessity if you want behavior that strictly and smoothly adheres to Newtonian prediction. If not you MUST deal with perturbation (nutation) - perturbations open the door to Quantum Mechanical analysis of energy exchange.

By giving the gyro a velocity in the exact direction and magnitude as the precession would, we are ensuring that temporally, there is in existence exactly as much momentum and angular velocity -both amplitude and direction - identical to what would exist if there was precession - i.e. precession already exists before there is torque effect - or at least a
simultaneous start)

Finally let us analyze the situation where we don’t give it that fourth force. What happens if you don’t give it that extra push? Then you get nutation i.e. precession + torque.

In the best case (we give the push), the precession is already in existence before the torque came into existence. And in the worst case scenario, they are simultaneous. What we deduce is that the physical situations all work smoothly in accordance with Newtonian predictions only when built in the following fashion:

The precessional velocity comes FIRST and THEN the torque appears OR they are simultaneous. Its also how the precession formula works too - with the counterintuitive cross product.

Thus the real test that helps assign cause and effect in a way that conforms to Newton’s Laws is what comes first and what comes second. And in this we find that the precession comes first and then the torque OR they come together. But never torque first and precession second.

Tuesday, July 7, 2009

The Paradox In Gyroscopic Behavior

The vector cross product is an operation on two vectors which yields a third vector in a direction which is perpendicular to the plane containing the two input vectors.

Strictly mathematically speaking, the cross product is a binary operation there by involving two operands, an operation and a single output.
The cross product, A x B, gives a third vector, say C in a direction perpendicular to the plane containing the two input vectors. A famous example of such a vector cross product is the Biot-Savart Law.


The Biot-Savart Law relates the strength of a magnetic field, dB produced due to the current flowing in a length of wire dl, at any distance r from the wire.
                            ®  ®
dB = [μ0/(4*p*r3)]*(I X r)

So, there are two inputs: a current vector and a distance vector that have to be specified. Then, the cross product operation will produce the output, i.e. a magnetic vector that results from that combination.

Note that since the magnetic force is the product of the two inputs (namely current and displacement unit vector) it will figure on
the left side of the equation and the inputs on the right side of the Biot-Savart equation.
Fine!!
Now let us look at the basic operation of a gyroscope. Take a look at the diagram below showing the two inputs (the black arrowheads) and the output (the blue arrow head).




Given that we need two simultaneous inputs - a spinning wheel and a torque upon its axis- to produce the output i.e. precession AND given that a cross product is involved, we might be forgiven for guessing that analogous to Biot-Savart's Law above the formula would read

w = t X L

However we would be wrong. As the correct formula reads:

t = w X L

hhmmm..
well, I thought we APPLIED the torque to RECEIVE the precessive velocity?

The actual formula however seems to be implying that the precessive velocity is an input just as much as the spinning wheel's angular momentum is. The two act upon each other, producing torque.
This is a reversal of cause and efect.

How to understand this? There is no conventional explanation for this reversal. It is merely illustrated without explanation in books. Some attempt vectorial gymnastics in an attempt to show that all is in aacordance with "physics", but none have acknowledged this weirdness and offered an explanation. The simple explanation for this reversal lies in the underlying relativistic analogy between electricity and spinning wheels.

The most useful mnemonic in ElectroMagnetism is probably 'ELI the ICE man'. (The following is excerpted from Resnick & Halliday, Fundamentals of Physics)
ELI contains the letter L (for inductor), and in it the letter I (for current) comes after the letter E (for emf or voltage). Thus, for an inductor, the current lags the voltage. Similarly ICE (which contains a C for capacitor) means that the current leads the voltage. You might also use the modified mnemonic "ELI positively is the ICE man" to remember that the phase constant f is positive for an inductor. End Excerpt

The way to translate "leads" in electricity to the mechanical version is to substitute "appears to be the cause of" in its place.

Note that according to the mnemonic, we can see that Current Leads Voltage in capacitive conditions - that is in our mechanical analogue, we would say Force Leads Angular Velocity or Force appears to be the cause of Angular velocity (via acceleration) and since almost all interactions we see in daily life are capacitive, we have viscerally absorbed the idea that force causes a change in velocity.

Voltage Leads Current in an inductor - so in the Mechanical analogy for a spinning wheel, Precessive Velocity Leads the Applied Torque i.e. Precessive Velocity appears to be the cause of the Applied Torque. Thus inductive behavior is characterized by this kind of a reversal of cause and effect.

While in electricity (due to the wonderful conformation of Maxwell's Laws with the Lorentz Transformations and therefore Relativity), this behavior results in another area of study (ElectroMagnetic oscillations and RLC circuits) and another mnemonic for the student to remember, in mechanics it has been ignored up until now. We are discovering here that in the inductive condition, the precessive velocity appears to be the cause of the force i.e. a gyroscope is an inductive element, unlike non-spinning objects, which are capacitive elements.

Our daily experience with the physical world involves only capactive encounters. There for we have a very hard time 'instinctively' grasping the differences in the behavior. They can appear are riddles at time. Gyroscopic behavior is a perfect example. The analogies between ElectroMagnetism and mechanics & gravitation are deep and the path lies through Kron's Generalized Machine Theory.

The gyroscopic formula is merely reflecting that fact.

Sunday, July 5, 2009

Sizing A Motor For A Gyroscopic Wheel And Other Objects

OK, so you have the gyroscopic wheels and you want to know how powerful your motor has to be in order to power them up to a certain speed. Or perhaps you have some motors and you want to know which one best suits your situation. I hope you have the specs sheets for the motors you are using. If so, the specific formula to calculate the operating torque demanded of a motor spinning a rotating disk is:

T = (1/2)*M*r2*(n/60)*2*p/t [Nm]

Where
n = speed (rpm)
T = Torque (Nm)
I = moment of inertia
a = angular acceleration (rad/s2)
M = Mass
r = disk radius (m)
t = time to top speed (s)

For instance: If your wheel had an MI of 0.2875kg-m2 and you wanted to spin it up to 16000 rpm in 20 seconds, you would need a motor capable of delivering approximately 24N-m of torque.

Note that although the formula implies that you can use a really small motor if you’re willing to wait a long time to get up to maximum speed, this is not necessarily the case if you the mismatch between the motor and load is too large. That’s because motors will stall if hooked up to a load too heavy to start –static friction in the bearing is one contributor to such a stalling torque which prevents the motor from being able to start up the rotation.

You can also use the above formula to calculate the amount of time it will take for your motor to spin up a load of a specific inertia to a specific speed.

The formula above is derived from the simple equation

T = I*a

We substitute
a = w/ t
I = (1/2)*M*r2 for a cylindrical disk
w = (n/60)*2p

Please be careful to substitute the right formula for the moment of inertia to match the object being spun up, for instance if you were spinning up a sphere, the moment of inertia would have to be changed to (2/5)* M*r2. For a ring, with most of the mass on the outer edge, the moment of inertia would be M*r2.

Friday, June 19, 2009

Generalizing Capacitors And Inductors To Include Spinning Wheels

Let us now consider a wheel spinning in its carriage and a capacitor; their workings and similarities.

CapacitorFlywheel
A capacitor is a temporary storage device for electrical energyA flyweel is a temporary storage device for mechanical energy
A given capacitor has a maximum operating voltage beyond which the capacitor will discharge spontaneouslyA given flywheel has a maximum operating angular velocity beyond which it will break apart due to stresses with in the material
A discharging capacitor shows a continuous drop in its potential differenceA discharging flywheel shows a continuous drop in its angular velocity
The capacitance is determined by the surface area of plates and the permeability of the medium between the platesThe moment of inertia is determined by the mass distribution of the flywheel
Charge Q = C*VAngular Momentum L = I*ω
The energy stored in a capacitor is given by E = (1/2)*C*V2The energy stored in a flywheel is given by E = (1/2)*I*ω2
Charge plays the same roleas Angular Momentum
Capacitance plays the same roleas Moment of Inertia
Potential Difference plays thesame role as angular velocity


Accelerated Spinning Wheels and Inductors


Flywheels can also act in more unusual ways reminiscent of inductors under slightly different conditions. Such an arrangement is shown in the figure above.

When the flywheel is suspended in a carriage and the carriage is offset about a Y-axis as shown in the figure, the inductive condition is invoked as follows: The spinning wheel spins at a fixed angular velocity. The carriage is moved about the Y-axis with a torque that changes in time.

The existence of a significant rate of change of torque is a necessary condition to harness a spinning wheel to transfer energy via the inductive process.

Consider the behavior of an induction coil with a steady current through it. It resists the change of an existing current in the coil. Given that charge is analogous to angular momentum (from our discussion above),

Q(charge) ~ Lm (angular momentum)

We diferentiate this once wrt time to get

dQ/dt (current) ~ dLm/dt

Now, dQ/dt is nothing but current ( rate of change of charge with time).
And since dLm/dt is nothing but rate of change of angular momentum, we can write it as I*dω/dt=> I*α (ang acceleration).

That is, we get a NEW analogy
i ~ α
This adds to the previous three analogies regarding charge, capacitance and potential difference we made just now, i.e.

Current plays the same role as Force (= Moment of Inertia * Acceleration)

The characteristic formula for an inductor is its voltage to current relationship in time. An inductor undergoes self-inductance only in the presence of a varying current, i.e. a second derivative of charge over time i.e., di/dt.

now if i ~ α, in order to find ANOTHER NEW analogy, we differentiate it one more time to get

di/dt ~ dα/dt

The analogy above suggests therefore that the mechanical phenomena equivalent to inductance is given by the second derivative of angular momentum over time.

(Now, the first derivative of angular velocity is angular acceleration. The second derivative is therefore the derivative of angular acceleration).

Thus the amount of counter-angular-velocity and counter-angular-acceleration (since the development of the angular velocity will happen at a rate of acceleration that can be measured by measuring the rate of change of angular acceleration of the applied force) developed by a flywheel depends on the imposed rate of change of angular acceleration.

Just as the characteristic formula for an inductor is its voltage to rate-of-change-of-current relationship in time, the characteristic formula for such a spinning wheel would be its precessive angular velocity to its rate of change of angular acceleration relationship in time (taking into account the Moments of Inertia of the structures involved).

An inductor undergoes self-inductance only in the presence of a varying current, i.e. a second derivative of charge over time i.e., di/dt.

Thus, in analogy with the equation Vcounter(t)= L*di/dt for inductor coils, the equation

ωprecess (t) = (Inductance of Spinning Wheel)*dα/dt

represents the characteristic formula for a spinning wheel freely rotatable about a perpendicular, offset axis. Thus, just as voltage leads current in inductors, the precessive velocity leads the angular force (acceleration) in an inductively suspended spinning wheel.

Further, just as the counter e.m.f causes a counter current to flow through the inductor, so also in the flywheel the counter-precessive-angular-velocity would produce a counter-angular-force (acceleration). Understanding this analogy is the foundation for an alternative explaination of gyroscopic action of flywheels.

In a circuit including an inductor, we apply current and receive voltage.
In a gyro too, we apply torque (gravity pulling down on the wheel) and receive angular velocity (precessive motion), instead of receiving angular acceleration as we should, if we were to apply Newton's Second Law.

All this also implies that as a toy gyro spins and whirls, energy is being given away to the gravitational well at a measured rate as the gyro winds down. (unlike conventional explanations which insist that the energy is simply dissipated via bearing friction - now this transfer rate is very small, which is why it would appear that something minor like bearing friction is involved. However that is simply the easy explanation that got us into all this trouble in the first place.)

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