Tag Archives: systems

Eric Dollard’s Versor Algebra Part 1 – Now available in paperback on Amazon

Versor Algebra Part 1 by Eric Dollard
Versor Algebra Part 1 by Eric Dollard


It’s taken a lot of work to get this into a paperback template, but Versor Algebra – As Applied to Polyphase Power Systems Part 1 is now on Amazon!!!

Go here: Versor Algebra

Eric Dollard’s description of the book: “Charles Proteus Steinmetz’s original math model is a natural outgrowth of Nikola Tesla’s polyphase power systems. Tesla was the discoverer, but Steinmetz was the builder who first applied Versor Algebra to the analysis of alternating current power systems.

In my presentation and book Four Quadrant Representation of Electricity, my extension of Steinmetz’s work is presented in the most simple way possible using very simple analogies, pictures and diagrams. It was a very difficult task as the goal was to facilitate an understanding for the layman.

That presentation was given at the 2013 Energy Science & Technology Conference and shortly thereafter, the book version was released, which went into more detail that was not covered in the presentation.

Tesla’s polyphase power system was originally four poles or four phases. Steinmetz is the one who adapted it into a three pole or three phase system, which is the prominent system of today. The complication is that three phase systems cannot be explained by conventional mathematics. With three phase systems, there is no plus or minus and that is the reason why the conventional math doesn’t work anymore.That left a big gap in polyphase power systems until Dr. Fortescue came up with the system of Symmetrical Coordinates. This laid the groundwork for polyphase mathematics for any number of phases. And ultimately, it can be extended into the Pythagorean understanding of numbers.The “Fortescue Method” was never fully developed because of its complexity.

The proper name for this is “Sequence Algebra” and the rudiments were presented in my presentation and book Four Quadrant Representation of Electricity.

Even though the system has become adopted for general engineering usage, Versor Algebra as Applied to Polyphase Power Systems and/or Versor Algebra Vol. II, Special Theories of Sequence Operators as Applied to Power Engineering is the first theoretical basis that has ever been presented on the subject.Versor Algebra as Applied to Polyphase Power Systems and/or Versor Algebra Vol. II, Special Theories of Sequence Operators as Applied to Power Engineering is the next logical step after Four Quandrant Representation of Electricity as it takes the reader into the mathematical journey of the mathematical model and theory that is necessary to realize the unique electrical waves that exist in polypahse power systems.

These waves are actually beyond the original understanding of Tesla and Steinmetz with regard to polyphase power systems.It is important to understand that this is all possible with simple 9th grade algebra. I take the reader through a step-by-step process from very basic algebra and log-rhythms into the more complex subject.

The process involves very simple but numerous steps to guide the reader into the understanding of polyphase mathematics.Through my own journey in writing this Versor Algebra book, I have been able to unify the polyphonic music of Bach and his contemporaries as this music follows the logic of sequence algebra perfectly.In fact, the book was written when listening to this music, which aided the process greatly.

Get your copy here: Versor Algebra

Special thanks to Jeff Moe and Simon Davies of http://teslascientific.com for editing and formatting the book.

For Eric Dollard’s other book, which is for any engineer at any level, get Lone Pine Writings.

The Meaning of Unity in Energy Conversion Systems by Jim Murray

The Meaning of Unity in Energy Conversion Systems by Jim Murray
The Meaning of Unity in Energy Conversion Systems by Jim Murray

Initially, it had been assumed that a simple ratio computed by dividing the output power by the input power would provide a reliable yardstick for motor power efficiency. The basic idea, was sound, for the closer the quotient came to unity, the nearer the motor efficiency would be to 100%. Hence began the so-called “Quest for Unity.”

However, early “electric engines” were very inefficient, probably delivering no more than 30% of the electrical input power to the output shaft. Therefore, it quickly became evident that not all of the applied power was being converted to a mechanical output. Clearly, inefficiencies were involved, and they would have to be accounted for. Until this was complete, the simplified approach to establishing a Factor of Unity could not be realized.

What is remarkable, in the history of motor development, is the curious degree of synergy that seems to have accompanied these early pioneering efforts. Between 1839 and 1850 the British Brew Master James Joule conducted an elegant series of experiments, in which he sought to unify electrical, chemical and thermal phenomena by demonstrating their inter-convertibility and their quantitative equivalence. The results of Joule’s work were published in the Philosophical Transactions of the Royal Society, with a very impressive title: “On the Mechanical Equivalence of Heat.”

The contributions of Lord Kelvin must be considered next. His paper, “The Dynamical Equivalent of Heat,” published in 1851, contended that energy could be “lost to man irrecoverably; but not lost to the material world”. Thomson was thus the first person to understand that all energy changes involve energy dissipation, and losses.

During the second half of the nineteenth century Kelvin and other scientists, including Clausius, Rankine, Maxwell and, Boltzmann, continued to develop these ideas. Their combined efforts resulted in the establishment of the Science of Thermodynamics; with Conservation of Energy as its First Law and the Dissipation of Energy as its Second Law.

Accordingly, motor researchers were thus made aware of the extreme importance of classifying all known motor losses, and accounting for them with the same degree of accuracy as would be exhibited in the well established science of corporate book-keeping.

Ultimately, such practices would lead to the development of two principle kinds of Efficiency Measurements, both very valuable in all research pertaining to rotating components, but, particularly valuable for developing an understanding of over-unity as a scientific fact. Both efficiency concepts shall be fully explained in this presentation.

To get your copy now, go here: The Meaning of Unity in Energy Conversion Systems

Use this coupon to receive 25% off for a limited time: UNITY25