The fact that a few have actually demonstrated a "free energy" operational power gain is important to point out in this turbulent time, when a definitive breakthrough in over-unity electrical power generation is needed so imperatively and so few people are having any real success at achieving one that is practical. Therefore, we are pleased to offer this webpage as a concise but detailed engineering analysis of these fascinating machines, one that appears to be much-needed, in order to foster a proper understanding of them and to assist students and alternative energy enthusiasts in their researches. 

    A Faraday dynamo or unipolar generator doesn't lend itself well to practical commercial development because of the nature of its output, since it produces very low (even fractional) DC voltage at extremely high current. When Nikola Tesla invented polyphase alternating current near the end of the 19th century, the concentrated development of DC power systems based on Faraday's original work virtually ceased. However, Faraday dynamos and generators are well-suited to easy and precise mathematical modeling, both mechanically and electrically. If we clearly show that formal* over-unity operation can be achieved with this technology, it could be that due cause is indicated for its renewed development – given recent advances in solid-state DC-DC current conversion and regulation. And while Michael Faraday's simple "new electrical machine" may not really be suitable for commercial-scale power generation, as we will see, it's quite possible that a stand-alone residential power plant could be developed from it! 

 * For present purposes, we shall define a "formal" or self-sustaining over-unity device as "an electrical machine or self-contained system that, once started, will operate entirely on its own output and supply excess power to a load with no external input energy being provided thereafter by the operator." Thus, an electrical device that operates over-unity is one wherein the dynamic ambient-energy environment contributes sufficient input energy that the true ratio of net power output to gross operator input power [the device's "net output coefficient of performance", or COP(NO)] is greater than one (1). In the case of a typical Faraday dynamo, of course, operator input is made in the form of applied torque. 

   To put AESI's own work and that of every other over-unity systems R&D team in the right perspective, and as a reference resource that OU enthusiasts may not ever have seen elsewhere, it will be helpful to define the following four (4) fundamental interpretations of COP, with a relevant example. The four COP figures (wattage ratios) below show the radical effect that one's choice of interpretation or definition has on the apparent performance of any given over-unity system, and represent a hypothetical 18"-diameter Faraday disk dynamo driven by a standard 1-Hp electric motor. Each of these simple definitions may be useful in certain cases but only one of them is always "correct":

(i) "peak design COP" = ratio of gross output to net input (e.g., 1,248 W / 746 W = 1.673)

(ii) "peak output COP" = ratio of gross output to gross input (e.g., 1,248 W / 900 W = 1.386)

(iii) "net input COP" = ratio of net output to net input (e.g., 882 W / 746 W = 1.182)

(iv) "net output COP" = ratio of net output to gross input (e.g., 882 W / 900 W = 0.980)

    It can be seen here that the "inherent" COP of this particular disk dynamo would be properly OU by the net input definition, but that the disk-dynamo & motor system is not over-unity by the fourth and most stringent measure of I/O efficiency – the net output COP! The typical drive motor is 746 / 900 or ~83% efficient and, curiously enough, while this hypothetical Faraday dynamo would indeed be OU in nature, its intrinsic generator efficiency (or ratio of net power output to gross power generated) is still only 882 / 1,248 = 70.7% due to its substantial internal resistive losses! And, while the peak "design" COP of this system is very impressive indeed, it obviously cannot operate in a self-sustaining mode.

Introduction:  Before we make any detailed analyses of the Faraday disk machines, it will be useful to briefly summarize their essential mechanical and magnetic characteristics. The disk induction dynamo shown below exemplifies the following form of Faraday's Law of Induction: an electromotive force [emf, or voltage] will be induced in any conductor that is moving across or "cutting" magnetic flux lines, and the emf is proportional to the rate at which the flux lines are being cut. Thus, the rotating disk cuts the flux produced by the stationary magnet field pieces, and a voltage appears between the inner and outer edges of the disk in such a machine – also commonly known as a homopolar generator. 

    Of course, we now know with a certainty that the rotor of such a generator is subject to a magnetic back-torque that is proportional to the output current drawn, due to the operation of Lenz's Law, which states that: a current set up by an emf induced due to the motion of a closed-circuit conductor will be in such a direction that its magnetic field will oppose the motion causing the emf. But, as it turns out, it is this same 'limiting' principle which allows this device – and nearly all common rotating power generation equipment – to also function as an electric motor: if the appropriate voltage and current are supplied, in this case between the center and edge of the conductive rotor, the disk will rotate with about the same motor torque as it requires for a corresponding level of generator action. 

    Curiously enough, shortly after Faraday's initial experiments with a primitive version of the induction dynamo he discovered that the same voltage could be induced if the magnetic field pieces were affixed directly to the rotor, but that no voltage at all would be induced if the field pieces were rotated while the conductive disk was held stationary! He logically inferred that even if the field pieces were rotating, their magnetic fields must be stationary, and that the type of uniform magnetic field produced by a cylindrical magnet must therefore be a property of space itself (or perhaps more accurately, space-time) and was independent of the magnetic material which serves to create the field. [This quality or effect is an oddity which to this day has no truly satisfactory explanation, though a very good paper from the University of Maryland (Dept. of Physics; Berg & Alley, 2005) strongly suggests the real explanation may lie within the purview of Special Relativity: see www.physics.umd.edu/ . . . q218unipolar.pdf.]

    Direct experimentation seems to show that a statorless "unipolar" generator (like that shown above) can no longer also serve as a motor, though the reason(s) why this should be so are still hotly debated by theorists.* Presumably, it's because the magnetic field produced by an applied rotor current cannot 'properly' oppose that produced by field magnets which are rotor-mounted, in "normal" accordance with Lenz's Law. A seemingly logical inference then drawn by certain researchers, perhaps most notably the late Bruce DePalma (a physics professor at MIT) and electrical engineer Paramahamsa Tewari in India, was that a statorless generator therefore would not exhibit the expected Lenz losses [as back-torque] provided that the magnets used are nonconductive – and thus it should most assuredly be capable of operating at over-unity output levels!  *[for 1 analysis, see: www.madsci.org/posts/archives/sep99/937493491.Ph.r.html]
    DePalma's explanation for this peculiarity was simply that the interaction of the primary magnetic field with that produced by the radial output current results in a shear torque between the conductive disk and the field pieces which is resisted by mechanical attachment, and so is wholly constrained within the rotor assembly and not reflected back to the mechanical drive! The experimental evidence seems to indicate that the aforesaid purely theoretical assumption is not true, however, as we'll see.
    DePalma's 'discovery' [circa 1977] that a unipolar generator's field pieces should be nonconductive to avoid the production of magnetic back-torque is illustrated by the "N-effect" diagram at left below – and could in fact be arrived at through simple deductive reasoning. If a rotating cylindrical magnet produces a stationary field, and the magnet itself is conductive (e.g., Alnico), then a voltage should appear between the center and outside surface by Faraday's Law of Induction! The trouble is that the act of drawing any load current from such a set-up will once again produce a classical level of back-torque, by Lenz's Law.

    Why DePalma called the device of his design shown on the right above an "N-machine" is something of a mystery, since it is in essence merely a typical unipolar generator. It is also interesting to note that although he has properly indicated the polarity of the induced voltage in the N-effect drawing on the left – according to the traditional left-hand rule** for generator action – the polarity shown in the drawing on the right is incorrect! And, as we've indicated in our preceding drawings, the preferred and logical polarity for any DC disk generator device is that whereby the negative terminal is located at the circumference – so that any "Hooper-effect" electromechanical centrifuging of mobile conduction electrons is series-aiding with respect to the induced load current flow. [In this case, it's important to realize that pure DC current has actual mechanical momentum, whereas AC current does not!]   top of this section     top of page
 
[ **The left-hand rule for generator action is as follows:  Extend the thumb, index finger, and center finger of the left hand at right angles to one another, so that the index finger points in the direction of the flux (north to south) and the thumb points in the direction of the motion; the center finger will then point in the direction of the induced electron flow (negative to positive).]

Review of Prior Art: In an ongoing effort to develop a self-sustaining unipolar generator system that just might be able to serve as a stand-alone residential power plant, Bruce DePalma and his principal correspondent-collaborator Paramahamsa Tewari built and tested very large, unwieldy, and expensive apparatus in reliance on the inherent design scalability of the Faraday machine. A number of perceived "improvements" over the basic technology were also implemented, but the underlying logic with which these changes were selected and made was perhaps inherently flawed – with negative consequences for both the cost-effectiveness and the coefficient of performance (COP) of the equipment [examples of which may be seen at the DePalma website (depalma.pair.com/index.html) and at www.tewari.org.
    The famous Kincheloe Report (1986) on the testing of one of DePalma's larger N-machines may be reviewed at www.totse.com/en/fringe/free_energy/dpalma5.html. Despite the fact that DePalma made a number of questionable design choices in the "Sunburst" device tested by Robert Kincheloe (Professor Emeritus, Electrical Engineering, Stanford Univ.), the data suggests that the back-torque losses were only about 20% of generated power – instead of the classical >100%. Prof. Kincheloe also states that: "while DePalma's [output] numbers were high, his basic [free energy] premise has not been disproved"; and "there is indeed a situation here whereby energy is being obtained from a previously unknown and unexplained source."   top of Introduction     top of page 

    These two pioneering experimenters and many others seem to have made a primary assumption for which we have so far found little supporting evidence: that a disk dynamo-motor could be shaft-coupled to a unipolar generator, which in turn powered it, to great advantage. It might then seem that even if the dynamo-motor itself was not over-unity in nature, the external input electrical power required could be substantially reduced since the two devices have very similar [but difficult to match] voltage and current characteristics. But an under-unity machine of the original stator-and-rotor disk dynamo design would only be as efficient if used as an electric motor as it was as a generator: its motor efficiency would not significantly exceed that of today's best electric drive equipment, and the increased rolling load would tend to offset any "power gain factor" by requiring proportionally greater operator input power and cost.
    The question arises whether such a combination could become input self-sustaining if an over-unity disk induction dynamo was somehow designed and incorporated. And in fact, mathematical modeling suggests that this might be possible, in that the dynamo's power output goes up by the 4th power of increases in the rotor radius while its input power requirement goes up by the square thereof. However, in accordance with the earlier-stated relative equivalence of motor/generator action in almost all rotating electrical equipment, there is every empirical reason for believing that such a Faraday "dynamoelectric" motor could only produce as much torque as it requires as a generator under full load. Therefore, even if a given disk dynamo was able to exhibit a full-load COP of 2 (for example) when used as a generator to convert input torque to output current, it would exhibit a COP of only 1/2 or 0.5 when used as a motor to convert full-load input current into output torque!! Thus, piggybacking the two Faraday machine variants on a common shaft, in hopes of "bootstrapping" the dual device to a state of self-sustaining operation, would actually tend to be self-defeating from a practical standpoint.
    Finally, both DePalma and Tewari elected at some point to try replacing the permanent magnet fields with externally-powered electromagnetic coils, but then a special "test cabinet" source was necessary to supply proper power to these field coils – in addition to the grid power always required by the primary drive motor! This had the minor advantage of making the unipolar generator's DC output fully variable and reversible. However, a flat coil or solenoid produces a nonuniform magnetic field whose flux density falls off with increasing distance from its radial centerline, unlike the uniform field established between facing permanent magnets. With the addition of ferromagnetic cores, the relatively weaker fields of the facing electromagnets could then be greatly augmented and homogenized – and AC power output could even be obtained – but only at the expense of proportionally-increased inductive coupling losses [that could only be minimized by using cores made of a very nonretentive field grade (~3% Si or other low-carbon) steel alloy, such as C1010.]
    Although the N-machine and Tewari's "Space Power Generator" have been claimed to exhibit COPs approaching 3.0 (or more), these devices were never made capable of self-sustaining operation nor were they (of course) ever cost-effectively mass-produced and marketed. And while Tewari maintains that the technology "is indeed commercially viable and should be brought to the attention of the general public", he notes that prospective manufacturers "do not see a market for a low-voltage, high-current machine."

    We feel that successfully bringing an over-unity induction dynamo system to market may actually be achievable, and that the secret to doing so is quite simple: use a back-to-basics "systems approach" to develop a very straightforward yet sophisticated design which avoids all of the unnecessary pitfalls just cited, one which is self-sustaining once started with standard 12vdc car batteries and whose DC output is made inverter-ready using advanced solid-state current converters for output voltage pre-amplification. In keeping with this strategy, we will investigate a feasible design for a product that would hopefully be home-owner affordable (using off-the-shelf or non-exotic materials and components whenever possible) and compact (where the unit's bulk size has been minimized while its output-to-weight ratio has been optimized accordingly). The design theory which we will examine and develop below clearly suggests that this is possible; nevertheless, the system overall might not yet be cost-effective under "normal" circumstances . . . 

Tesla and Back-Torque Theory: There is ample evidence to support both the view that back-torque will be produced in any Faraday disk machine and the claim that 'drag' may be artfully reduced to much less than a classically-figured level. Oddly enough, the notion that rotor back-torque might not be produced in one type of Faraday machine or another can probably be traced back to Nikola Tesla – and an obscure 1891 paper entitled "Notes on a Unipolar Dynamo". If taken out of context, Tesla's blunt statement that "such a machine differs from ordinary dynamos in that there is no reaction between armature and field" was perhaps misconstrued as an absolute in the case of the statorless variant: little was known about it, since no one could otherwise see any good reason to rotate the extra mass of the field pieces, and everyone knew that back-torque was normally produced in a typical fixed-stator dynamo. 

    [Significantly, perhaps, Tesla makes no mention whatever of the statorless Faraday generator variant in this paper. It should also be clarified that while some people may refer to such a statorless homopolar machine as a "unipolar" generator, it's more correct to let the latter term signify – as it did for Tesla – that such an acyclic-voltage device produces pure DC current having only one constant polarity (as in a battery), whether or not the field pieces are stationary.]

    However, careful review of the paper reveals that Tesla was referring specifically to the case where we "assume the current [is] to be taken off . . . by contacts uniformly from all points of the periphery of the disc." His analysis suggests that when a load current is drawn, eddy currents will be confined to those radial sectors of the disk which do not lie directly between the shaft and an outer pickup brush. In other words: regardless of whether we rotate the field pieces or not, or whether they're conductive or not, if we collected the load current from a continuous peripheral brush which enclosed the entire edge of the disk, no rotor eddy currents could be generated and the 'normal' level of counter-torque would not be present. [Its heavy eddy currents are of course a well-known major component of a typical disk dynamo's total magnetic losses. In the analytical model being developed here, radial brush-sector current is seen as strictly laminar in nature, while eddy current flow in intermediary sectors is turbulent.]
    What Tesla is really saying, then, is that the more uniformly a disk dynamo's output current is drawn through the periphery of the disk, the less "armature reaction" can be supported by eddy currents within the disk – which are induced by the stator magnets and therefore attracted to them. [This could also be seen to validate the earlier contention that a disk machine whose output had been sufficiently optimized to allow it to function as an over-unity generator would constitute a proportionally under-unity motor!]

[Note: We can further show that no significant reduction of the Lenz losses expressed in a disk dynamo can be made, even with ideal stator shielding, until the angular width of the primary (radial conduction) "brush sectors" – which is equal to the width of each pickup brush – exceeds that of the adjacent 'neutral' (transverse deflection) "eddy current sectors". Of course, the potential value of a practical liquid metal brush system which provided 100% rotor disk edge 'coverage' is also apparent – in that such a dynamo's Lenz losses could theoretically then be entirely eliminated when ideal stator shielding is also employed – and is no doubt the reason why the U.S. Navy imposed secrecy and gag orders on inventor Adam Trombly.

   It is very important to realize at this point that Lenz losses in a fixed-stator disk dynamo may take two (2) forms: eddy current coupling, and stator inductive coupling. In the first case, a full classical level of rotor counter-torque will tend to be produced due to the attractive magnetic drag or "friction" caused by direct polar coupling between the applied stator field and induced microcirculatory rotor eddy currents.
    As it turns out, though, a full classical measure of similar Lenz losses may also be produced by the stator, as a result of simple attractive polar coupling between the net rotor magnetic field [as expressed by "uncompensated" or asymmetrically-balanced primary load current distribution] and any (i) exposed (unshielded) outer stator magnet poles or (ii) incompletely field-piece-saturated stator shielding. 

[Note: An "ideal stator shielding design" is one wherein the field piece assemblies exhibit no external magnetic field outside of the flux gap (as in the "closed-path" configuration developed by Adam Trombly.]

    Thus, to the extent that stator coupling occurs, it will act to produce additional magnetic drag upon the rotor which is linearly proportional to the load current drawn – and thereby to satisfy "Lenz's Law". We may further infer that, even with perfect (ideal) stator shielding to prevent any load current inductive coupling, a fully-proportional Lenz-loss eddy current counter-torque load will still seek to develop, to the extent possible (or allowed) unless the rotor disk is highly sectored with pickup brushes.

   [The percentage of "normal" eddy current losses that any particular disk dynamo will exhibit is a very complex function of its geometry and that of its collector brush system. However, we have developed a viable proper method for actually calculating the reduced eddy current back-torque ratio that any given design should exhibit. Interested persons may obtain a copy of our definitive Eddy Current & Stator Loss Analysis white paper upon request, with prior submission of a simple 1-pg. NDA.]

   We can arrive at a new and much clearer picture of the nature of reactive stator losses in this device, by means of the following unbroken chain of logic:
 
  – (i) The magnetic field produced by any disk rotor current(s) must rotate with the motion of the disk, being in opposition to the stationary field(s) applied by permanent magnets, or no motor action would result with an applied input current (instead of applying torque); and
  – (ii) this rotor current field must fully enclose the disk without intersecting it, or it would act either to generate a "free" voltage or to influence the disk's own inertia (neither of which can occur, classically).
  – (iii) Ordinarily, in the absence of an applied axial field, the rotor current field would then take up a simple symmetrical dual toroidal configuration (above and below the rotor plane) because of the disk's radial geometry. But in this case, it must establish the attenuated field configuration that's shown in the diagram on the right below, because flux lines never cross – and those of the rotating current field can't intersect those comprising the stationary axial applied field (in which nearly all of the disk is immersed).
 
  
 
  – (iv) Moreover, it can be seen that the rotor current field completely encloses not only the disk but the applied stationary fields as well. Therefore, the disk's rotating current field may inductively couple to any ferromagnetic material on or near the field pieces, which can thereby cause the stationary applied field to impart additional armature reaction (or back-torque) to the rotor, unless that material is magnetically saturated due solely to induction by the field pieces.
  – (v) Toroidal fields exhibit an inherently unfixed "radial polar tendency", and will polarize attractively to any applied axial polar field when radial torque is applied to them. Thus, any extant net rotor field due to self-generated current(s) will experience 'drag' against the stationary applied field, regardless of its own polarity (and disk current flow direction), as classically it must. In practice, end-pole keeper plates can be used to nearly eliminate any magnetic interaction between induced rotor current and the field pieces themselves – even if they're metallic and rotating.
  – (vi) Most importantly, however, it can be shown by integral calculus that the primary rotor current's net magnetic field around the disk is inversely proportional to the extent to which that current is drawn in opposite radial directions (i.e., by pairs of 180°-spaced brushes), because the net load current enclosed [by the path of integration] is then zero – due to equal currents flowing in opposite directions – thereby mathematically confirming the fundamental validity of Tesla's guiding design principle!
 
    Recalling now that a conductor must move relative to a stationary field for voltage to be induced, we may also deduce the following design first-principles: (1) to wit, the primary rotor current field will not act to induce eddy currents in metallic stator magnets, which in turn impose no corresponding additional back-torque (as Lenz losses); but (2) however, when metallic magnets are used for the applied field in a 'unipolar generator', there is relative motion between a rotating conductor and a stationary field, so field piece eddy currents will be induced which may couple to the rotor field and contribute to back-torque!
    Taken together, the preceding material clearly shows that – with ideal stator shielding – back-torque will only be expressed in an induction dynamo (with a fixed stator) to the extent that eddy currents are allowed to circulate in "unused" radial sectors of the disk*, and this principle can now be used to figure what percentage of the classical eddy current back-torque will be produced: it is simply (but not strictly) proportional to the ratio of that portion of the disk's circumference which is not "covered" by its collector brushes to its entire circumference! 
*[Note that this presumes of course the load current is shared equally by uniformly-spaced pairs of oppositely-vectored brushes! Many different brush system configurations are possible for any given size dynamo; e.g., we will employ a total of 64 brushes in the preferred embodiment 18"-dia. prototype we are currently building.]

    This same reduced back-torque ratio also applies, of course, to a 'unipolar' generator. Unfortunately, it can also be seen why only the much-less-powerful nonconductive (ceramic) magnets have generally been used in the statorless variant, since induced field piece eddy currents can transfer magnetic load to the rotor field in a statorless generator if the magnets used are metallic – because the load current's rotating magnetic field encloses the combined stationary fields of the permanent magnets and tends to polarize attractively to them. [The rotor magnetic field that is produced by an applied disk current would (of course) polarize repulsively, resulting in motor action in the absence of an applied radial torque – but only in the fixed-stator variant, it would seem . . .]
    Finally, in this regard, it could be said that in a Faraday disk generator the motor field encloses the stator field, and not the reverse – as almost universally is done in common electromechanical practice. Perhaps the possibilities inherent in this unusual arrangement are part of the mystery and fascination these machines have always held for the engineering-inclined. And the greatest "secret" of both these disk machines (as we see it) is that it's possible in effect to trade the classical Lenz loss back-torque for a much-smaller collector brush torque load requirement [in the generator variants]. 

    In any event, in the linked Analysis sections, we will calculate the input torque, output power, and efficiency (or coefficient of performance ) of both an induction dynamo and a unipolar generator of the same physical size, for both the classical case and the adjusted theoretical model developed from the refined design principles just discussed. It is then up to the reader to empirically decide which results are the more accurate!
    Before proceeding to the Analysis sections, however, a review of the Getting Back to Basics section is highly recommended. In this section, we will show the derivation of some essential formulae which properly govern and define the basic operating characteristics of both the Faraday disk dynamo and its unipolar generator variant (i.e., voltage, power, torque, etc.) . . .
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