Well, I'm fast approaching the half-way mark of the self-imposed 60 day deadline to come up with a good prototype.

I'm pleased to say it seems miraculously I'm still on target. The flywheel is now fully ready. The housing is now fully designed and dimensioned. I've been back and forth from the machine shop a LOT. But I'm now confident my machinist and I see eye to eye on the details.

Also, the ball bearing were a big time-killer. Please make sure to check or speed ratings for ball bearings carefully as also the availability of the sizes you are planning on using, first.

## Sunday, May 24, 2009

## Saturday, May 16, 2009

### Interesting Facts About Rate Gyros

Momentum can be the cause of a force under certain circumstances.

One such circumstance involves the imposition of rotation of an angular momentum vector (i.e. the angular momentum vector is rotated at a certain angular velocity)- The force produced in this manner is called Coriolis Force.

When a rotation occurs, the angular momentum vector (representing the stored kinetic energy of the rotating element) causes an out-of-plane bending force (called Coriolis force) that can be successfully used to accurately measure and represent the rotation rate i.e., measuring the coriolis force, is equivalent to measuring the rotation rate.

Because rate gyros depend on angular momentum as their workhorse, they are constrained to measuring ABOUT an axis i.e., they serve to measure rotation correctly only if the rotation axis is perfectly perpendicular to the angular momentum vector doing the work in the rate gyro. If the rotation happens about an axis that has an angle different from 90degrees to the angular momentum vector, then a second rate gyro is required to acquire additional information in order to give an accurate reading of the rotation being imposed.

Thus, for 3-D motion, one pair of gyroscopes is sufficient to deduce full orientation-change information. (However, commercial technology incorporates redundancies. The Hubble telescope for instance has 3 pairs of rate gyros.)

In solid state rate gyros, the electron serves as a spinning object and the rotation is measured by measuring the magnetic force created by the electron's perturbation.

One such circumstance involves the imposition of rotation of an angular momentum vector (i.e. the angular momentum vector is rotated at a certain angular velocity)- The force produced in this manner is called Coriolis Force.

When a rotation occurs, the angular momentum vector (representing the stored kinetic energy of the rotating element) causes an out-of-plane bending force (called Coriolis force) that can be successfully used to accurately measure and represent the rotation rate i.e., measuring the coriolis force, is equivalent to measuring the rotation rate.

Because rate gyros depend on angular momentum as their workhorse, they are constrained to measuring ABOUT an axis i.e., they serve to measure rotation correctly only if the rotation axis is perfectly perpendicular to the angular momentum vector doing the work in the rate gyro. If the rotation happens about an axis that has an angle different from 90degrees to the angular momentum vector, then a second rate gyro is required to acquire additional information in order to give an accurate reading of the rotation being imposed.

Thus, for 3-D motion, one pair of gyroscopes is sufficient to deduce full orientation-change information. (However, commercial technology incorporates redundancies. The Hubble telescope for instance has 3 pairs of rate gyros.)

In solid state rate gyros, the electron serves as a spinning object and the rotation is measured by measuring the magnetic force created by the electron's perturbation.

## Wednesday, May 13, 2009

### Flywheel Design Basics

Designing a flywheel is serious business because a flywheel operating beyond its design stress can explode, sending shards of sharp metal debris flying in unpredictable directions. Safety is the key guide to flywheel sizing.

As a measure of reference, only atomic (i.e. nuclear chain reactions) and chemical sources (ie exploding C4, TNT etc) have higher energy release potential than flywheels.

Safety is number 1 with flywheels because of their potential for damage. If you cannot explicitly overcome a safety issue, you just can't go further with the design - the design is flawed and potentially dangerous. Before you can design a flywheel, you have to already pass the following safety audit:

a) How sure can you be about the absence of air bubbles or other structural problems within the material ? There are ways to look inside using powerful electromagnetic rays. If you don't or can't do that, what can you do to take into account a bubble that is located within the thinnest parts of the central area of the wheel? Such a bubble could fatally undermine the correctness of your calculations. Therefore, you have to explicitly include a large safety factor. For the novice, I recommend a minimum safety factor of 4.4 - which means you design your wheel such that it's experiences no more stress than 1/20 of Yield Strength of the material.

b) What is the maximum velocity at which the wheel will be spinning? Suppose you want to operate your wheels at 5000 rpm. The maximum is not 5000 rpm – rather there is a working range around it, say 46,00-5400 where your motor is likely to jog, depending on the relative size and type of electronics of your motor. Also, make sure you check your electrical supply for the motor has a max. cut off current or voltage that is variable. This way you can set it deliberately to trip in case of an electrical surge. If that is not something you want to do, then you have to answer the problem of how you intend to personally monitor the velocity of the flywheel while it is spinning. How you intend to prevent others, for example children from being able to power up the flywheel inadvertently in a way that makes it keep speeding up.

c) What is the material you are going to use to make the flywheel? A closely related question is: What is the radius of your flywheel? Answering these questions is impossible without knowing what kind of lift your vehicle will produce (or at least guesstimating it, using sound calculations) and how much motion you want to produce. At this point, only you can answer these questions, but you have some tools to do the job right.

I am listing one of the two formulae that I have found to be good.

I recommend using both of them to calculate the stress on the flywheel and compare the two. So if you want to seriously do this, contact me and I will look the other one up too. The two dont agree with each other exactly, but they are close to each other and serve as a cross check for the designer.

Any good mechanics book will tell you that a flywheel undergoes two kinds of stress:

i) Tensile Stress

ii) Bending Stress

The following are both formula and a composite formula for combining the two, to help determine the total stress on the flywheel.

Source: Machine Design Handbook, Lingaiah, Bangalore University, Call Number TJ 230.L65

Tensile Stress

σ

where

ρ is in N/m

g is 9.8 m/s

r is the mean radius in m (in)

n = mean speed (rpm)

Bending Stress

σ

h = depth of rim in m (in)

i = number of arms

Total Rim Stress (Tensile) = 0.75*σ

This total rim stress MUST be less than the Yield Strength by 20 times, in order to account safely for common flaws probably present in your wheel (it its made to the good standards - if its inferior material, it might have to be 30 or 40 times or more). 20 times would give you a safety factor of roughly 4.4.

d) What about balancing the flywheel? Dynamic balancing of flywheels is another important safety feature we just cannot skip if there is even a suspicion of imbalance in the mass distribution of the flywheel. It will also save you a lot of grief later on, if you have the wheel balanced BEFORE you install it because otherwise you will be disassembling a lot of parts to correct this mistake.

Click here to see one of the flywheels machined from these calculations.

Click here to read how flywheels maybe the key to a new kind of flying machine.

Click here to read the latest on my research and see videos of the experiments I am currently conducting to make such a flying machine.

Thanks

Ravi

As a measure of reference, only atomic (i.e. nuclear chain reactions) and chemical sources (ie exploding C4, TNT etc) have higher energy release potential than flywheels.

Safety is number 1 with flywheels because of their potential for damage. If you cannot explicitly overcome a safety issue, you just can't go further with the design - the design is flawed and potentially dangerous. Before you can design a flywheel, you have to already pass the following safety audit:

a) How sure can you be about the absence of air bubbles or other structural problems within the material ? There are ways to look inside using powerful electromagnetic rays. If you don't or can't do that, what can you do to take into account a bubble that is located within the thinnest parts of the central area of the wheel? Such a bubble could fatally undermine the correctness of your calculations. Therefore, you have to explicitly include a large safety factor. For the novice, I recommend a minimum safety factor of 4.4 - which means you design your wheel such that it's experiences no more stress than 1/20 of Yield Strength of the material.

b) What is the maximum velocity at which the wheel will be spinning? Suppose you want to operate your wheels at 5000 rpm. The maximum is not 5000 rpm – rather there is a working range around it, say 46,00-5400 where your motor is likely to jog, depending on the relative size and type of electronics of your motor. Also, make sure you check your electrical supply for the motor has a max. cut off current or voltage that is variable. This way you can set it deliberately to trip in case of an electrical surge. If that is not something you want to do, then you have to answer the problem of how you intend to personally monitor the velocity of the flywheel while it is spinning. How you intend to prevent others, for example children from being able to power up the flywheel inadvertently in a way that makes it keep speeding up.

c) What is the material you are going to use to make the flywheel? A closely related question is: What is the radius of your flywheel? Answering these questions is impossible without knowing what kind of lift your vehicle will produce (or at least guesstimating it, using sound calculations) and how much motion you want to produce. At this point, only you can answer these questions, but you have some tools to do the job right.

I am listing one of the two formulae that I have found to be good.

I recommend using both of them to calculate the stress on the flywheel and compare the two. So if you want to seriously do this, contact me and I will look the other one up too. The two dont agree with each other exactly, but they are close to each other and serve as a cross check for the designer.

Any good mechanics book will tell you that a flywheel undergoes two kinds of stress:

i) Tensile Stress

ii) Bending Stress

The following are both formula and a composite formula for combining the two, to help determine the total stress on the flywheel.

Source: Machine Design Handbook, Lingaiah, Bangalore University, Call Number TJ 230.L65

Tensile Stress

σ

_{t}= 0.01095*ρ*r^{2}*n^{2}/g MPa (psi)where

ρ is in N/m

^{3}(lbf/in^{3})g is 9.8 m/s

^{2}r is the mean radius in m (in)

n = mean speed (rpm)

Bending Stress

σ

_{b}= 0.2146*ρ*r^{3}*n^{2}/(g*h*i^{2}) MPa (psi)h = depth of rim in m (in)

i = number of arms

Total Rim Stress (Tensile) = 0.75*σ

_{t}+ 0.25*σ_{b}This total rim stress MUST be less than the Yield Strength by 20 times, in order to account safely for common flaws probably present in your wheel (it its made to the good standards - if its inferior material, it might have to be 30 or 40 times or more). 20 times would give you a safety factor of roughly 4.4.

d) What about balancing the flywheel? Dynamic balancing of flywheels is another important safety feature we just cannot skip if there is even a suspicion of imbalance in the mass distribution of the flywheel. It will also save you a lot of grief later on, if you have the wheel balanced BEFORE you install it because otherwise you will be disassembling a lot of parts to correct this mistake.

Click here to see one of the flywheels machined from these calculations.

Click here to read how flywheels maybe the key to a new kind of flying machine.

Click here to read the latest on my research and see videos of the experiments I am currently conducting to make such a flying machine.

Thanks

Ravi

## Sunday, May 10, 2009

### On The Importance Of The Gyro - Inductor Analogy

To understand why gyroscopic action especially under certain specific conditions described later cannot be analyzed in a Newtonian manner but can be analyzed in an ElectroMagnetic way, let us argue as follows: If it were true that there exists a machine that can convert internal (Potential) energy into external (Kinetic) energy, then we want to observe the operation of such a machine from an inertial frame in which the entire machine is initially at rest.

(When the machine is operated, energy of a minimum amount of N joules = m*g*h (where h is height to which the machine rises in time T given by h = (1/2)*g*Tsquare) is 'converted' or 'pumped' from the spinning wheels to the machine frame to the gravitational field. )

Now, how do we explain this 'conversion' ?

Although a more fundamental explanation that involves Special Relativity with CT-X graphs etc has been cited earlier, there is another, bird's eye view explanataion - one that relies on analogy. Lets start by saying, the potential energy in this machine is converted to KE in the same way that an LC Circuit converts the internal (Potential) energy of an AC wave flowing through the LC circuit into an externally realized (Kinetic) energy of Electro-Magnetic waves.

Hypothesis: Resonance in electronics and mechanics is really only a manifestation caused by the invocation of the same fundamental interaction of matter with space-time (a la Relativity) involving spin (i.e. angular momentum) - in one field, its the electron, in another, its the spinning flywheel that supply the spin component.

What the device accomplishes is the conversion of internal energy (i.e. a potential energy) into external energy (kinetic energy). The potential energy is the stored energy within the rotating wheels, the rotating carriage. The machine is a way to convert it into KE of the moving assembly so that the framework transports through space.

Now, that is a direct violation of Newton's first and third laws, and indirectly even the second. [- Since an observer who is located in an inertial frame in which the machine initially rested would record the acquisition of velocity by the machine, in defiance of the local gravitational field, but would be unable to assign the action that caused the reactive movement to any external object. Under further experimentation, it becomes clear that the energy gained by the frame came from the internal interactions of on the spinning wheels.]

In LC circuits too, the internal (& therefore a potential tank of ) energy of the AC current is converted into a radiative KE in the form of the leakage of ElectroMagnetic waves from such an assembly at resonance.

Yet it is not the case for LC circuits that when radiation is given out by a resonant circuit that it is seen as being a violation of any EM laws. The only reason that the operation of an LC circuit doesn't seem to be a violation of some basic EM law or another is because Maxwell's laws which govern EM are also already consistent with Special Relativity.

However, since Newton's Laws are not 'relativised', the contention here is that this machine might APPEAR to violate them, but only because it is Newton's laws that are in violation of SR/General Relativity (as we know, Newton's laws are approximations that are infact inadequate to analyze relativistic phenomena. Newton's Laws are inadequate to deal with what we might even think of as Accelo-Gravitic radiation). Thus in the analysis of 'compound objects' containing more than one worldline, Newton's Laws will yield the wrong results, even if the energy conservation laws can be satisfied. Unlike EM waves which themselves travel and emanate from the generating circuit, AG waves are literally 'ridden' or 'sailedon' by the generating machineframe.

[Here we might wonder why if this is the case, an LC circuit doesn't up and fly. An argument can be made that it is figuratively what's happenning. In the case of the LC circuit, the energy entering the circuit is being molded to a specific frequency. The overflow of this energy from the circuit in geometrically determined directions results in the flow of energy to remote areas. Yet, for the actual circuit to move, it is protons that must be moved. Yet, since its the electrons that are responsible for EM effects and they have a much, much smaller mass, they cannot reach the threshold levels of energy required to move the LC circuit. - Now, the electric motor which used (electron) current does accomplish motion. But it cannot change the frame associated with the energy, i.e. convert internal energy into external energy - all conversions acheived by an electric motor are locally tied to the reference frame to which the motor is attached.]

Essentially it is being claimed that this is a relativistic machine which is why Newtonian laws will appear to be violated. In analyzing this experimental set up as a relativistic machine, we may utilize a shortcut in the form of Electro-Magnetism. Since EM is already consistent with SR/GR, if we form the proper analogies from mechanics to EM, we can analyze Mechanical problems as if they are electromagnetic problems, in a way that is consistent with SR/GR.

Now take a look at this post which shows how well-fitting the analogy between EM and Mechanics is. This is the reason why the LC circuit analogy to the gyroscope is critical to understanding how this machine can be operated successfully.

Evidence uncovered here implies that gravitational force specifically and gravitation generally is related to inertial force and acceleration generally much as Magnetism and Electricity are related each other. The two sets of fields should be unified through the consideration of the complimentary nature of the two sets of forces.

(When the machine is operated, energy of a minimum amount of N joules = m*g*h (where h is height to which the machine rises in time T given by h = (1/2)*g*Tsquare) is 'converted' or 'pumped' from the spinning wheels to the machine frame to the gravitational field. )

Now, how do we explain this 'conversion' ?

Although a more fundamental explanation that involves Special Relativity with CT-X graphs etc has been cited earlier, there is another, bird's eye view explanataion - one that relies on analogy. Lets start by saying, the potential energy in this machine is converted to KE in the same way that an LC Circuit converts the internal (Potential) energy of an AC wave flowing through the LC circuit into an externally realized (Kinetic) energy of Electro-Magnetic waves.

Hypothesis: Resonance in electronics and mechanics is really only a manifestation caused by the invocation of the same fundamental interaction of matter with space-time (a la Relativity) involving spin (i.e. angular momentum) - in one field, its the electron, in another, its the spinning flywheel that supply the spin component.

What the device accomplishes is the conversion of internal energy (i.e. a potential energy) into external energy (kinetic energy). The potential energy is the stored energy within the rotating wheels, the rotating carriage. The machine is a way to convert it into KE of the moving assembly so that the framework transports through space.

Now, that is a direct violation of Newton's first and third laws, and indirectly even the second. [- Since an observer who is located in an inertial frame in which the machine initially rested would record the acquisition of velocity by the machine, in defiance of the local gravitational field, but would be unable to assign the action that caused the reactive movement to any external object. Under further experimentation, it becomes clear that the energy gained by the frame came from the internal interactions of on the spinning wheels.]

In LC circuits too, the internal (& therefore a potential tank of ) energy of the AC current is converted into a radiative KE in the form of the leakage of ElectroMagnetic waves from such an assembly at resonance.

Yet it is not the case for LC circuits that when radiation is given out by a resonant circuit that it is seen as being a violation of any EM laws. The only reason that the operation of an LC circuit doesn't seem to be a violation of some basic EM law or another is because Maxwell's laws which govern EM are also already consistent with Special Relativity.

However, since Newton's Laws are not 'relativised', the contention here is that this machine might APPEAR to violate them, but only because it is Newton's laws that are in violation of SR/General Relativity (as we know, Newton's laws are approximations that are infact inadequate to analyze relativistic phenomena. Newton's Laws are inadequate to deal with what we might even think of as Accelo-Gravitic radiation). Thus in the analysis of 'compound objects' containing more than one worldline, Newton's Laws will yield the wrong results, even if the energy conservation laws can be satisfied. Unlike EM waves which themselves travel and emanate from the generating circuit, AG waves are literally 'ridden' or 'sailedon' by the generating machineframe.

[Here we might wonder why if this is the case, an LC circuit doesn't up and fly. An argument can be made that it is figuratively what's happenning. In the case of the LC circuit, the energy entering the circuit is being molded to a specific frequency. The overflow of this energy from the circuit in geometrically determined directions results in the flow of energy to remote areas. Yet, for the actual circuit to move, it is protons that must be moved. Yet, since its the electrons that are responsible for EM effects and they have a much, much smaller mass, they cannot reach the threshold levels of energy required to move the LC circuit. - Now, the electric motor which used (electron) current does accomplish motion. But it cannot change the frame associated with the energy, i.e. convert internal energy into external energy - all conversions acheived by an electric motor are locally tied to the reference frame to which the motor is attached.]

Essentially it is being claimed that this is a relativistic machine which is why Newtonian laws will appear to be violated. In analyzing this experimental set up as a relativistic machine, we may utilize a shortcut in the form of Electro-Magnetism. Since EM is already consistent with SR/GR, if we form the proper analogies from mechanics to EM, we can analyze Mechanical problems as if they are electromagnetic problems, in a way that is consistent with SR/GR.

Now take a look at this post which shows how well-fitting the analogy between EM and Mechanics is. This is the reason why the LC circuit analogy to the gyroscope is critical to understanding how this machine can be operated successfully.

Evidence uncovered here implies that gravitational force specifically and gravitation generally is related to inertial force and acceleration generally much as Magnetism and Electricity are related each other. The two sets of fields should be unified through the consideration of the complimentary nature of the two sets of forces.

## Friday, May 8, 2009

### 50

Well, we're down to 50 days. The flywheel is finally designed.

I cannot count on fingers and toes, the number of times I had to revisit the design to dig deeper and deeper into the calculations. Here are a few words of advice from me if you're attempting to design something for the first time(or first few).

First, breakdown the assembly into elementary parts.

Then, make a list of parts that have to be custom designed/assembled and parts (or sub-assemblies) that are commercially available.

Survey the commercial products first before you begin the design of the custom parts.

Pay particular attention to the dimensions. You must make sure that you know not only the dimensions and strength/desired properties of the parts you need, but also if those dimensions are supported by the commercial off the shelf manufacturers.

For example I was going to choose a X cm diameter shaft but found that while bearing were available for such a dimension, if you wanted mounted bearings (with the housing, making it easy to install), you were out of luck - and for cost reasons, it became apparant to me that I had to redesign the shaft and with it, the method to fasten the flywheel to the shaft as well as the couplings, which then cascaded into further designs. Since couplings with certain combinations of dimensions can be hard to find and expensive, further changes had to be made.

And it goes on and on and on.

Choosing your working range speed is also important because especially for rolling stock, you're going to find your options getting steadily smaller as you look for higher speeds. Misalignments become major issues and machining becomes the determining factor in the quality of the coupling junction. Skimp in a hurry there now and you will be able to regret it at leisure later.

If your speeds call for 30,000 rpm say, you're talking a whole another ball game with magnetic bearings and heavy steel casings to contain flywheel blow outs.

Keep safety factors in mind AT ALL TIMES. Know when your design is most likely to fail, know what safety measures you took to mitigate that eventuality - install safety kill switches.

Test as you go. Dont move past a subassembly unless its tested OK.

One simple, inexpensive but useful trick you can use is as follows, however be warned that you must not be pulling more juice for the entire set up than could be handled safely in a single power strip - because in the end, thats where its all going into and coming from. If the power load you will consume can all be handled safely by a single power strip, you could choose to cascade several power strips (a master power strip controlling the overal power and a power strip per subassembly/important part that you want to power up or down at some specific point/situation) to give the researcher the ability to start up/cut off power to selective subassemblies safely or start up/cut off the power to the entire set up at once. I use that one when I see a minor problem - a loose screw for instance. I shut down the relevant subassembly without closing down the computer interface I regularly use to control the subassembly - it allows me to work safely while at the same time allowing me to power back up and resume without going through laborious countdown checklists.

Once you have a prototype you want to run, you should prepare a countdown checklist - things you have to do in the order in which you have to do them to safely powerup the machine and power down the machine on a regular run.

Make observations diligently and sign and date them.

Things are looking good. Its fun regardless of the end results I obtain from the device regarding the theories I am testing.

Its expensive but it can be fairly affordable IF (and its a pretty big if) this is you make this your main vocation. Because then it becomes a game of installments - of work and pay, work and pay. If time is on your side, no problem.

I cannot count on fingers and toes, the number of times I had to revisit the design to dig deeper and deeper into the calculations. Here are a few words of advice from me if you're attempting to design something for the first time(or first few).

First, breakdown the assembly into elementary parts.

Then, make a list of parts that have to be custom designed/assembled and parts (or sub-assemblies) that are commercially available.

Survey the commercial products first before you begin the design of the custom parts.

Pay particular attention to the dimensions. You must make sure that you know not only the dimensions and strength/desired properties of the parts you need, but also if those dimensions are supported by the commercial off the shelf manufacturers.

For example I was going to choose a X cm diameter shaft but found that while bearing were available for such a dimension, if you wanted mounted bearings (with the housing, making it easy to install), you were out of luck - and for cost reasons, it became apparant to me that I had to redesign the shaft and with it, the method to fasten the flywheel to the shaft as well as the couplings, which then cascaded into further designs. Since couplings with certain combinations of dimensions can be hard to find and expensive, further changes had to be made.

And it goes on and on and on.

Choosing your working range speed is also important because especially for rolling stock, you're going to find your options getting steadily smaller as you look for higher speeds. Misalignments become major issues and machining becomes the determining factor in the quality of the coupling junction. Skimp in a hurry there now and you will be able to regret it at leisure later.

If your speeds call for 30,000 rpm say, you're talking a whole another ball game with magnetic bearings and heavy steel casings to contain flywheel blow outs.

Keep safety factors in mind AT ALL TIMES. Know when your design is most likely to fail, know what safety measures you took to mitigate that eventuality - install safety kill switches.

Test as you go. Dont move past a subassembly unless its tested OK.

One simple, inexpensive but useful trick you can use is as follows, however be warned that you must not be pulling more juice for the entire set up than could be handled safely in a single power strip - because in the end, thats where its all going into and coming from. If the power load you will consume can all be handled safely by a single power strip, you could choose to cascade several power strips (a master power strip controlling the overal power and a power strip per subassembly/important part that you want to power up or down at some specific point/situation) to give the researcher the ability to start up/cut off power to selective subassemblies safely or start up/cut off the power to the entire set up at once. I use that one when I see a minor problem - a loose screw for instance. I shut down the relevant subassembly without closing down the computer interface I regularly use to control the subassembly - it allows me to work safely while at the same time allowing me to power back up and resume without going through laborious countdown checklists.

Once you have a prototype you want to run, you should prepare a countdown checklist - things you have to do in the order in which you have to do them to safely powerup the machine and power down the machine on a regular run.

Make observations diligently and sign and date them.

Things are looking good. Its fun regardless of the end results I obtain from the device regarding the theories I am testing.

Its expensive but it can be fairly affordable IF (and its a pretty big if) this is you make this your main vocation. Because then it becomes a game of installments - of work and pay, work and pay. If time is on your side, no problem.

## Monday, May 4, 2009

**Spin, Angular Momentum And Worldlines**

Spin -conceptualized as a ring of mass spinning about its center of mass-has basis in Relativistic descriptions as being the phenomena governing all physical motion. It appears that spin/rotation's relativistic effects are at the origin of force itself. We may visualize spin as simply an angular momentum vector in space-time. The angular momentum of spin of an electron can be visualized as analogous to the angular momentum of a spinning wheel.

A common framework could be expressed something like this: Consider a set up shown in the figure below.

On a ct-x plane, we plot the rotational motion of a point P on the rim of the spinning wheel as approximately the path a-b-c below.

The point's angular position shifts uniformly (since the wheel has a constant angular velocity), starting at time 0 at point 'a', moving about the rim, getting farther and farther away from its original position until its diametrically on the other side of the wheel (point 'b'), before moving back towards its original position at the end of the rotation period (point 'c'). Plotted on a ct-x plane, with the t on the vertical (y)axis and the position i.e., x on the horizontal axis, it would mean a straight line of a fixed slope specifically tied to the velocity of the point would start at 'a', reaching a mid-interval maximum before returning to the original position.

(The following derivation is performed by James Hartle in his book Gravity: An Introduction although he might disagree my representation of the trajectory abc as the spin of the wheel.)

We know that the distance element on the ct-x plane will be

dS

^{2}=-(ct)

^{2}+dx

^{2}

If the angles are conveniently angle(a) = 45 degrees, angle(c) = 45 degrees, and sides ab=bc=L, we can evaluate the distance element, ds.

Since dS

^{2}=-(ct)

^{2}+dx

^{2}=>ab=bc=-(L)

^{2}+L

^{2}=0 On the other hand, ac = 2L

It is important to realize that ac is always the longest side while a path running ab+bc will always have a shorter length than ac, tending towards zero (if the angles a and c are greater than zero but less than 45degrees) or have zero length (if angles a and c are 45degrees i.e. at the speed of light) compared to ac.

dS

_{a-b-c}£ dS

_{a-c}

This geometric result obtained due to the nature of the distance element of spacetime has an important consequence for spin/rotation. Path ac represents the worldline of a non-rotating wheel. Path ab+bc represents the worldline of a point on the rim of a rotating wheel. Using the preceding result, we see that the rotating wheel always has a shorter path from a to c than a non-rotating wheel. In fact, what is actually guaranteed (by the construction of the spacetime distance element) is that ac will be the longer path under any circumstance ie. a nonrotating wheel has a longer spacetime distance between two events than a rotating one.

Energy absorbed by the wheel will take the shorter path (ab+bc) and arrive at event c on the ct-x plane out of phase with the energy absorbed by the supporting frame. Energy contained in the wheel (including its mass energy, ewheel = mwheel*c2) always arrives at point c with a phase difference w.r.t. the energy contained in the supporting frame (including its mass energy, eframe = mframe*c2).

This phase difference is the key process that is harnessed by the relativistic machine- it is exploited both for the angular momentum vector of the electrons that are spinning round the inductor coil's loops as well as for the angular momentum vector of the spinning wheels in the relativistic flying machine being discussed here in analogous ways to create resonance.

But before we talk about the machine, lets just ask the seemingly simple question:

**What is an object?**

At the risk of seeming to digress, we investigate what we mean when we refer to something as an ‘object’.

An Object is that aggregation, (the sequence of spacetime events corresponding to) whose history can be described in terms of a worldline running through its center of mass.

We may recall that in Einstein’s SR, if we picture two world lines starting at the same event in spacetime, but each following its own path for subsequent events, such a diagram may represent the decay of a particle into two others or the emission of one particle by another.

Now, consider the diagram below which represents the first half of the rotation of the wheel - that part of the rotation where the point on the rim of the wheel leaves its original location and traverses space, thereby increasing its distance from its original position, reaching a maximum when the point reaches a location that is diametrically opposite to its starting location. (Thereafter, the point only moves closer to its original location, with the cycle being completed when the particle completes one full rotation.) - Such a process maybe described as a decay into two objects.

Now we recall that in Einstein’s SR, two world lines that start out separately and then intersect will represent a collision/encounter. The diagram below represents the second half of the rotation of the wheel which represents exactly such a collision. During the collision process, force is exerted by one object on another.

The path abc represents the worldline of the spinning wheel. On the other hand, the diagram below represents the world line of the carriage that holds the spinning wheel. The spinning wheel is mounted on ballbearings which are embedded in the carriage.

Thus, for a carriage holding a spinning wheel, we would need TWO worldlines to describe its history accurately. Incidentally this is why Newton’s Laws cannot analyze this situation correctly. Newton’s Laws contain an implicit assumption that every object has exactly ONE worldline.

Thus we may assert that a carriage with a spinning wheel is in actuality 2 separate objects. We deduce that when we start spinning up the wheels, we trigger an energy trapping process which consists of repeated cycles of first a decay of one object into two objects and then a collision. Thus energy is transferred during the collision process from a formerly internal object to its formerly complimentary part. Energy can be pumped into the tank circuit during the decay process. Energy can be pumped from the tank, via an antenna, into the environment during the collision process.

During the Decay stage, the worldline of the entire set up splits into 2 wordlines

During the collision stage, the 2 worldlines of the set up merge into 1 line. In ElectroMagnetic resonance, this can be exploited to pump EM radiation by the tuned LC circuit or in the case of the Relativistic Machine presented in this paper, this results in the pumping of directed Kinetic Energy to the frame holding the machine.

This is the commonality between Electro Magnetism And Accelo Gravitic phenomena

and indicates rotation and its manipulation to be the fundamental process at work in both.

It is posited here that resonance is actually the harnessing of the decay-collision process to transfer energy from an internal frame (or potential energy contained within a tank) to the external frame (or into kinetic energy flowing to the inertial frame that contains such a ‘live’ energy transference process).

This implies that the arrangement of spinning wheels presented later on, can be used to constitute a mechanical (Gravitronic?) Capacitor-Inductor circuit.

## Friday, May 1, 2009

### 58

So today was spent in the design of the flywheel - and redesign and redesign and redesign..

Note for Monday: The ballbearing blocks have to be spec'd out, sized, priced and surveyed.

Note for Monday: The ballbearing blocks have to be spec'd out, sized, priced and surveyed.

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