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.

## Saturday, September 26, 2009

## 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 N

_{0}. The max torque for experiment 2.1 is designated T

_{0}.

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.

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.

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