Regression Analysis of Experimental Results

The equations that best predict the # of revolutions travelled by the carriage for a given Tmax ( maximum value of the imposed harmonic torque) were generated by Regression Analysis of the experimental data (Thanks to my statistically significant other, otherwise known as the stats expert K.H.! Thank You!).

Based on this, the best fit lines were generated for each Tmax (1 A, 2 A, 4 A, 5A). The above graph was generated by plotting the best fit lines together and moving their Y intercept to Zero, in order to make the measurement of the relative angles between them easy to measure.

As you can see from the graphs, as the Tmax increased, the slope steadily went from positive to negative. This clearly highlights the fact that as the maximum torque increased, the number of revolutions came down.

Thus, it has been experimentally demonstrated with a very high degree of correlation that increasing the T_max of the imposed harmonic torque decreases the number of actual revolutions of the carriage holding the spinning wheels.

The detailed results of the regression analysis are given below.

What is a Schumann Resonance?

(The following material is taken from a really great little book I have titled "The Astronomy Cafe" 365 Questions and Answers From "Ask the Astronomer" by author Sten Odenwald. Thanks are given to the author for the information reproduced here.)


Believe it or not, Earth behaves like an enormous electric circuit. The atmosphere is actually a weak conductor, and if there were no sources of charge, its existing electric charge would diffuse away in about 10 minutes. There is a cavity defined by the surface of Earth and the inner edge of the ionosphere, 55 km up. At any moment, the total charge residing in this cavity is 500,000 coulombs. There is a vertical current flow between the ground and the ionosphere between 1 to 3 X 10 ^-12 amperes per square meter. The resistance of the atmosphere is 200 ohms. The voltage potential is 20,000 volts. There are about 1000 lightning storms at any given moment worldwide. Each produces 0.5 to 1 ampere, and these collectively account for the measured current flow in Earth's electromagnetic cavity.

The Schumann resonances were predicted to exist in 1952 and were first detected in 1954. They are resonant electromagnetic waves that exist in this cavity. Like waves on a spring, they are not present all the time but have to be excited to be observed. They are not caused by anything internal to Earth, its crust, or its core. They seem to be related to electrical activity in the atmosphere, particularly during times of intense lightning activity. They occur at several frequencies between 6 and 50 cycles per second, specifically, 7.8, 14, 20, 26, 33, and 45 hertz, with a daily variation of about +/- 0.5 hertz. As long as the properties of Earth's electromagnetic cavity remain about the same, these frequencies remain the same. Presumably there is some change due to the solar sunspot cycle as Earth's ionosphere changes in response to the 11-year cycle of solar activity. Schumann resonances are most easily seen between 20:00 and 22:00 universal time (UT).

Given that Earth's atmosphere carries a charge, a current, and a voltage, it is not surprising to find such electromagnetic waves. Much of the research in the past 20 years has been conducted by the Department of the Navy, which investigates extremely low frequency (ELF) communication with submarines. For more information, see Hans Volland, ed., Handbook of Atmospheric Electrodynamics (CRC Press, 1995). Chapter 11 is on Schumann resonances and was written by Davis Campbell of the Geophysical Institute, University of Alaska. There is also a history of this research and an extensive bibliography.

Latest Experimental Results

The latest results are added to the previous results to generate this graph. New information includes the following:

a) Results for harmonic torques of time periods 30 seconds - 38 seconds have been added for 1 Amp, 2 Amp and 4 Amp amplitude. These results continue the trend we've seen earlier, namely, a falling rate of revolutions (i.e. a falling average speed) with an increase in both the time period of the applied rate of change of torque and the maximum amplitude of the torque.

b) Results for harmonic torques for time periods 9 seconds - 16 seconds at a maximum torque amplitude of 5 Amp have been added. These results continue the same trend as mentioned above. Being of higher amplitude, these harmonic torques  result in the lowest number of revolutions yet  (for example, 3 revolutions in 8 seconds which translates to roughly 3.8 revolutions in 10 seconds - compare that to the case of a constant 1 Amp torque which nets us 8 revolutions in 10 seconds)!

New Information: Rate of Change of Torque is an important determinant of the behavior of the Angular Momentum of the Rel.Machine

A note regarding units: I've determined that the dynamic friction coefficient for the entire unit is less than 0.1 A. So you have to take that into account in translating the Amperes into a direct measure of the torque. Here's how it would work. If I applied 1 A, that really means I applied 0.9 units of torque.If I applied 4 A that really means I applied 3.9 units of torque. The ratio of the two torques would there be: 3.9/0.9 = 4.333.

Had you not adjusted the units, the ratio would have come out to be 4/1 = 4.

Thus we see that the torque generated by the 4 Amps is in fact 4.33 times larger than that generated by the 1 Amp, making the effect that much more stunning. Think about it! You applied 4.33 times more torque and you actually got an angular velocity that is LOWER than what you got for 1 unit of torque!

And anyone who thinks that its all well and fine and in agreement with current understanding, must explain the key find of my experiments. Namely, what is the reason in your view for the difference in the response of the flywheels' angular momentum to two situations that involved an identical amount of torque - one a constant torque and another a variable torque, and for one (the constant) we get 7.5-8 revolutions in 10 seconds and for the variable torque, we are getting somewhere around 5?

Not only that you can further see how in the case of the constant torque the whole rel.machine stayed relatively inert and didn't move about while for the variable torque case, the rel.machine executed a much more complex pattern of behavior - one that I emphasize includes lifting force. (Try this: Sit on the floor and try to execute the same motion that the rel.machine is executing without an upward lifting force sustaining your posture.) What is the reason for this difference in your view for this complexity of behavior?

Now the fact that the behavior of the rel.machine shows any difference at all between the two otherwise identical scenarios means that by the rules of logical argumentation, by virtue of experimental proof, the difference is assignable to the parameter that was varied: Namely, the Rate of Change of Torque.

The fact that rate of change of torque has an impact on the response of the angular momentum vector is actually a new find. If you disagree, please find me a detailed reference to it.

Now if you saw the video, you already know my theory. These findings are all confirming my theory that the inductively suspended flywheels show a variable reactance, much as a charged coil of wire would.The reactance is a variable quantity, being higher for higher rates of changes of current. This is strikingly similar to the behavior of the rel.machine - at 4.33 units of torque, the response in the applied plane was lower than the response at 1 unit of torque.

Expts 2.10: Response of The Angular Momentum of The Flywheels to Harmonic Torques of Time Periods up to 30 secs

Keep On Truckin'!

Response of The Rel.Machine to Harmonic Torque

The above graph represents the response of the rel.machine to harmonic torques of 1 Amp, 2 Amp and 4 Amp maxima (i.e. sinusoidal waves of torque whose highest value reached said amplitude) for a range of time periods of the harmonic torque. 

The graph indicates that the carriages actually spun around at the lowest velocity for the 4 Amp maxima i.e. by increasing the rate of change of torque (by increasing the numerator, the torque represented directly by the current level here), we have channeled away increasing amounts of energy from the plane of application.

Also, note how each of the three Tmax torque lines droop as they move to the right, thereby indicating that increasing the time period has increased the energy conversion (thereby leaving less energy in the carriage and therefore fewer rotations and thus a lower slope for the line). This indicates that further testing must continue to increase the time period beyond current levels.

Experiment 2.8: The Inductive Effect

Incontrovertible experimental proof is offered here that Faraday's Law of Induction is applicable to inductively suspended flywheels.