[Note: Any updates made to this page will involve no non-textual changes of any kind, to preserve the integrity of the design models discussed in the Analysis sections as valid reference material. The Tesla & Back-Torque Theory feature section has been revised to include a more accurate and complete discussion of eddy current and stator coupling losses. Our thanks to the huge number of visitors this webpage receives, and to the many students and engineers who have written us about the report.]

 

Synopsis:
    As many students, engineers, and over-unity researchers may already know, it's very hard to find a single good Internet reference resource which soundly assesses the  early Faraday induction dynamo in comparison to a latter-day derivative – the "unipolar generator". Basic engineering design information on either device is often inaccurate or misleading, and sometimes erroneous.

Quite a number of determined inventors and experimenters have attempted to develop a "formal" self-sustaining over-unity variant of the disk dynamo which was 'unipolar' in that it was statorless, but virtually none have ever succeeded.
    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!
 
[ *Note: For our purposes here, we 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 zero-point-energy environment contributes enough input energy that the ratio of output to operator-input ( "coefficient of performance", or COP) is greater than 1.0. Operator input is made, of course, in the form of applied torque.]

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.
 

correct interpretation of disk dynamo action, as shown, whether field pieces are conductive or not.

 
    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 satisfactory explanation.
 

incorrect interpretation of statorless generator action, promulgated by certain researchers.

 
    Some theorists mistakenly assumed that a statorless "unipolar" generator (like that shown above) can no longer also serve as a motor, presumably because the magnetic field produced by an applied rotor current can't 'properly' oppose that produced by field pieces which are rotor-mounted, in "normal" accordance with Lenz's Law. The 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 normal Lenz losses [as back-torque] provided that the magnets used are nonconductive – and so it should most assuredly be capable of functioning at an over-unity level of output!
    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 neither of these two predicate assumptions is 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!]  
 
[ **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."  
 
    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 achieved – but only at the expense of proportionally increased eddy current (Lenz) 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 absolutely optimized). The design theory we will examine and develop below clearly sugggests that, under properly controlled conditions, this is possible; it could turn out, however, that the system as a whole might not yet be cost-effective under 'normal' circumstances . . .
 
Tesla and Back-Torque Theory:  There's 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 Generator". Taken out of context, Tesla's bald 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.]
    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's 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).
 

      Obviously, it is decidedly to our advantage to use the largest practical number of "pickup" brushes, although extensive mathematical modeling suggests that the total outer brush contact width should not be more than 50% of the disk's circumference in a disk induction dynamo intended for use as a motor. Accordingly, the brush current density rating will serve to limit the number of outer brushes used and the maximum possible current. The current density limit of the 93%Ag brushes we've specified is 300 A/in². In practice, total brush ampacity should be strictly matched to the highest I max figure derived that does not exceed the calculated safe ampacity of the rotor disk (as discussed further below) and total pickup brush width should be absolutely maximized,  approaching 100% of the disk's entire circumference,  in all generator (non-motoring) variants.
    All things considered, we will assume that the 4-pole/16-point pickup brush circuit just described will be used in our 'prototype' model and in the calculations to follow.
 
    To get a better figure for our model dynamo's actual total circuit resistance Rt, we will now calculate the resistances of the brushes, rotor shaft, and disk.
    Given the OEM specs for brush current density (300 A/sq.in.) and resistivity (2.0 x 10^–6 ohm-cm), we may simply divide the value for I max by 16 to find the ampacity of each negative (pickup) brush and then divide the result by the current density limit to find the contact area required. Therefore, the area of each outer brush An = (977.39 / 16) / 300 = 0.2036 sq.in. or 1.314 cm². Outer brush thickness should be > ½ and < 2/3 of the disk thickness, as the disk's outer edges should be slightly chamfered. So, the width of each pickup brush will be 0.2036 / 0.125" = 1.63". The rotor's circumference is equal to 2πRo = 56.55", the total pickup brush width is 16 (1.63) = 26.08", and so the edge-width 'coverage' ratio is 26.08 / 56.55 or 46% (which is nearly optimum for a motor variant).
    Using brushholders which are only 5/8" 'tall', a good minimum brush length L is 1.0" or 2.54 cm. So, each pickup brush's resistance will be (2.0 x 10^–6)(2.54) / 1.314 = 3.866 x 10^–6 ohm, or Rn = ~ 4 μohm. Applying the same method to the 4 positive shaft brushes, with an assigned thickness of 0.50" the area Ap = 4An = 0.8144 sq.in. (5.254 cm²) and width again equals 1.63" or 4.14 cm. With length once again of 1.0", each inner brush resistance Rp = ~ 1 μohm. Finally, it will be important in practice to use the heaviest and shortest brush shunts (buss bar leads) feasible.
    The rotor shaft alloy that is greatly to be preferred is CDA17200 1.9% beryllium copper, with volume resistivity of 7.733 x 10^–6 ohm-cm but the highest tensile strength of any copper-base alloy. To figure a liberal resistance for the rotor shaft, we will allocate 5" or 12.7 cm as its "electrical" length by mounting the positive brushes inboard of the bearings and drive coupling. The axial end area of the shaft is equal to π(½")² = 0.7854 sq.in. = 5.067 cm², and the shaft resistance Rs = ~ 19 μohm.
    The rotor disk's greatest electrical resistance is expressed through the edge of the 1"-diameter center shaft hole, the circumference of which is 3.1416". Given a thickness of 0.187", this inner edge area then equals 0.5875 sq.in. or 3.790 cm². The volume resistivity of pure copper is 1.724 x 10^–6 ohm-cm, and the disk's radial conduction length L is equal to Ro – ½" = 8.5" = 0.216 m = 21.6 cm. Accordingly, we find the resulting maximum possible rotor disk resistance Rd = ~ 10 μohm.
 
    Finally, we can now make the best possible projection of the rotor circuit Rt in milli-ohms as follows:
 
 

 
Thus, it's conclusively demonstrated just how little effect the electrical 'hardware' really has on the total rotor circuit resistance of a Faraday disk dynamo (if properly designed), since the figure we just derived with fair effort differs from the quick estimate we made earlier by only 7 micro-ohms! Our revised figure for the "nominal" output current is then equal to 0.9163 / 0.000945 = nom. Io = 969.6 A.
   

Output Power:  The output power of our model dynamo at the given nominal rotation speed of 850 rpm (14.167 rps) is equal to I²R = Po = 888 watts. But, at the 'peak' rotation speed of 1150 rpm (19.167 rps), the output power would be equal to V²/R = (1.24)² / 0.000945 = Ppeak = 1,627 watts. It can therefore be seen that in raising the operating speed by 1150 / 850 or 35.3%, the output current possible would rise to peak Io = 1,312 amps and the available power would nearly double! Of course, every brush's contact area would also have to be increased by 35.3%, and in the case of the outer brushes by increasing the brush width to 2.02". Total pickup brush contact width then increases to 35.29" or a reasonable 62.4% of disk circumference.
    Unfortunately, it can be shown by rather involved numerical anlysis of existing copper wire data that the safe ampacity of the 0.187"-thick rotor disk is 'only' 1,129 amps around its inner circumference. By increasing the shaft size to 1¼" the safe ampacity could be raised to 1,376 amps, thereby enabling the dynamo to be operated at its peak Io. Rather than effect such a substantial device redesign, though, we will continue our analysis on the assumption that the brush size and operating speed shall be adjusted such that max. Io = 1,129 amps.
    Accordingly, the pickup brush width will have to be increased by 1,129 / 969.6 or 16.44% (to 1.90"). The total pickup brush width is 16(1.90) = 30.37", and so the edge-width coverage ratio is 30.37/ 56.55 or 54%. The new value for max. Vo = 1.067 volts, and the corresponding maximum rotor speed is then 990 rpm or f = 16.497 rps. And so, the maximum allowable output power is equal to (1.067)(1,129) or max. Po = 1,205 watts, and the new maximum brush speed is 4,665 fpm.
   

Input Torque & Power:  Although it might seem that we now have good final figures for operating speed and output power, we have yet to determine if the rotation speed we just derived is acceptably close to that of an off-the-shelf electric motor (as a practical source of input torque) which will provide adequate start and run torque at a given available horsepower rating. This will not be nearly as difficult as it might sound, with the aid of a simple yet indispensable electric motor formula that relates speed (rpm), torque (T), and power (Hp):  T = (Hp x 5252) / (rpm) , where the constant 5252 is equal to 33,000 ft.lbs./min./Hp divided by 2π radians/rev., and T is the torque in ft.lbs. [The equivalent metric expression is:  T = P / ω , where ω = 2πf , P is power in watts, and T is torque in N-m.]  
 
For the 'classical' case:
  [i] primary full-load counterforce = Fa = B I Ra = (.43)(1,129)(.180) = 87.39 N
  [ii] primary back-torque = Ta = Fa (r) = (87.39)(.133) = 11.62 N-m = 8.57 ft.lb.
  [iii] neg. brush counterforce (ea.) = Fnb = pkA = (4)(0.2)[.125 x (1.1644 x 1.63)] = 0.190 lb. (run)
  [iv] pos. brush counterforce (ea.) = Fpb = pkA = (4)(0.2)[(1.1644 x .500) x 1.63] = 0.759 lb. (run)
  [v] total brush retarding torque = Tb = 16(Fnb)(Ro) + 4(Fpb)(½") = 28.88 in.lb. = 2.41 ft.lb.
  [vi] total load torque T = Ta + Tb = 8.58 + 2.41 = 10.98 ft.lb. (treating the ~ 0.5% rolling losses as negligible).
 
    Correctly matching a standard electric motor to the mechanical load in this unusual application can be a complex and challenging task. All things considered, there are a number of reasons for selecting a permanent magnet or shunt-wound (wound field) DC motor, since the required AC input converter (as the power source) is usually also an economical variable speed control. This feature is especially desirable in situations like the present case, where our tentative operating speed falls right between the 'standard' 1150 and 850 rpm motor speeds. Also, in certain cases it may be inadvisable (although less expensive) to use an AC capacitor-start motor in this application, since they're designed to start under fully-loaded conditions and can briefly draw over 300% of normal running amps to do so. [In an average-load starting situation like the present case, this will also put a huge and unnecessary strain on the rotor assembly, due to its large moment of inertia.]
    Referring to a motor selection and ordering guide (such as any recent Grainger catalog), we find that a 2 Hp 1150 rpm PM motor (with 180vdc armature; FL amps = 9.8) is available [GE 5CD125TP002B] that develops full-load torque of 9.133 ft.lb. (109.6 in.lb.). Even though this is rather less than the 10.98 ft.lb. that would be needed to operate our model dynamo at its maximum capability, it must be remembered that (according to the torque formula above) this motor's output torque will climb as its speed is reduced – and it may be that just enough torque will be available at or very near the maximum 990 rpm operating speed we desire.
    The most straightforward way of determining that point on the selected motor's output power / torque curve where its operating speed is maximized for this particular application's input torque requirement is by repeated spreadsheet calculations to assemble tabular data, from which the best 'solution' of such a complex covariable problem is obtained when the net motor torque developed (Tm) just exceeds the total load torque (Tn) required at the reduced speed.
    Starting at 985 rpm and figuring output voltages in descending 5-rpm increments at first, the following optimal resolution was found at 970 rpm (f = 16.167 rps):
 
  – net Vo = 1.0457 volts, net Io = 1,106.5 amps, and net Po = 1,157 watts ;
  – net Fa = B I Ra = (.43)(1,106.5)(.180) = 85.643 N ;
  – net Ta = Fa(r) = (85.643)(.133) = 11.39 N-m = 8.40 ft.lb. ; and
  – total load torque = Ta + Tb = 8.40 + 2.41 = Tn = 10.81 ft.lb. [treating the ~ 0.5% rolling losses as negligible].
  – net motor torque developed = Tm = (2 x 5252) / 970 = 10.83 ft.lb. > Tn (@ 10.81 ft.lb.).
 
  – nominal motor efficiency = (Hp x 746) / (V x I) = 1,492 / 1,764 = ~ 84.6%
  – nominal dynamo efficiency = Po / (Hp x 746) = 1,157 / 1,492 = ~ 77.5%
  – combined system efficiency = (0.846)(0.775) = ~ 65.6%
 
  – letting avg. brush k = ½ (0.3 + 0.2) = 0.25,  avg.Tb = (0.25 / 0.2)(2.41) = 3.01 ft.lb.
  – avg. no-load motor torque  Tnl = Tm – avg.Tb = 10.83 – 3.01 = 7.82 ft.lb.
  – no-load motor starting time  min. ts = ωI / Tnl = 2πf (.181) / 7.82 = 2.35 sec.
  – Pr = mπ²R²f ² / ts = (6.965)(9.8696)(0.052)(261.37) / 2.35 = 934.00 / 2.35 = 397.5 watts

  – avg. full-load motor torque  Tf = Tm – (½ Ta + avg.Tb) = 10.83 – (4.20 + 3.01) = 3.62 ft.lb.
  – full-load motor starting time  max. ts = ωI / Tf = 2πf (.181) / 3.62 = 5.08 sec.
  – rotor mechanical power expended = Pr = mπ²R²f ² / ts = 934.00 / 5.08 = 183.9 watts

    The start times just calculated are entirely acceptable for a PM-DC drive motor, providing for 'gentle' starting considering the disk's large moment of inertia. And it may indeed be permissible in cases with extended no-load start times of between about 2.25 and 3 seconds to use an AC capacitor-start motor as a drive if necessary and if it so happens that the factory speed of the motor selected is acceptably close to the preferred operating speed of the dynamo/generator. [Longer start times may overload the additional start windings in a capacitor-start motor, damaging or destroying the coils and/or tripping a circuit breaker, even though the effective start times will be lower by ~300%].
    It's interesting to note that our model dynamo's actual induction efficiency can be found by simply refiguring its torque requirement without considering brush drag. Thus, at 953 rpm, a 1.5 Hp PM-DC motor would be adequate to power the dynamo at a voltage of 1.0273, current of 1,087.1 amps, and output power of 1,116.8 watts. With just the reasonable added proviso that the stator's outside poles must be wholly keepered at saturation, and at less than the full disk diameter, real  induction efficiency   is then 1,116.8 / 1.5 (746) = 99.8%! [The foregoing criteria regarding the essential use of saturated steel end-plates to keeper the outer stator poles are derived from the innovative "closed (flux) path" homopolar generator design of Trombly & Kahn (1982). A saturated material will support no further passage of flux nor any further external magnetic induction – in the form of eddy current losses, in this case.]
    Purists may also notice that the motor's own armature inertia has not been considered above in the interests of clarity and brevity, having been treated as negligible since it corresponds to just 0.3% of its output torque (by OEM specs) in this particular case. The same consideration also applies to the rotor shaft's miniscule inertia in relation to that of the disk.
 
And in the best-case theoretical model: The following computations are based on what we believe is a justifiable application of the 'Tesla' reduced back-torque ratio to our model dynamo in actual operation. As we developed earlier above, in this case that ratio is equal to 1 – 0.56 = 0.46.
 
  [i] primary full-load counterforce = Fa = 46% [B I Ra] = 0.46[(.43)(1,129)(.180)] = 40.20 N
  [ii] primary back-torque = Ta = Fa (r) = (40.20)(.133) = 5.35 N-m = 3.94 ft.lb.
  [iii] total brush retarding torque = Tb = 16(Fnb)(Ro) + 4(Fpb)(½") = 2.41 ft.lb. (same as before)
  [iv] total load torque T = Ta + Tb = 3.94 + 2.41 = 6.35 ft.lb. (treating the ~ 0.5% rolling losses as negligible).
 
    Referring again to the motor selection and ordering guide, we find that a 1.5 Hp 1150 rpm PM motor (with 180vdc armature; FL amps = 7.2) is available [GE 5CD125TP001B] that develops full-load torque of 6.85 ft.lb. (82.2 in.lb.). In this case, the motor will have more than enough torque for the dynamo to be operated at the maximum allowable rotor speed (and disk ampacity limit) of 990 rpm (f = 16.5 rps):
 
  – max. Vo = 1.067 volts, max. Io = 1,129 amps, and max. Po = 1,205 watts (from preceding subsection);
  – net Ta = Fa(r) = 3.94 ft.lb. (from above); and
  – total load torque Tn = 6.35 ft.lb. [treating the ~ 0.5% rolling losses as negligible].
  – net motor torque developed = Tm = (1.5 x 5252) / 990 = 7.96 ft.lb. > Tn (@ 6.35 ft.lb.).
 
  – nominal motor efficiency = (Hp x 746) / (V x I) = 1,119 / 1,296 = ~ 86.3%
  – nominal dynamo efficiency = Po / (Hp x 746) = 1,205 / 1,119 = ~ 107.7% (or COP = 1.077)
  – combined system efficiency = (0.863)(1.077) = ~ 92.9%
 
  – avg. starting brush retarding torque avg.Tb = 3.01 ft.lb. (same as before)
  – avg. no-load motor torque  Tnl = Tm – avg.Tb = 7.96 – 3.01 = 4.95 ft.lb.
  – no-load motor starting time  min. ts = ωI / Tnl = 2πf (.181) / 4.95 = 3.79 sec.
  – Pr = mπ²R²f ² / ts = (6.965)(9.8696)(0.052)(272.25) / 3.79 = 973.18 / 3.79 = 256.8 watts

  – avg. full-load motor torque  Tf = Tm – (½ Ta + avg.Tb) = 7.96 – (1.97 + 3.01) = 2.98 ft.lb.
  – full-load motor starting time  max. ts = ωI / Tf = 2πf (.181) / 2.98 = 6.30 sec.
  – rotor mechanical power expended = Pr = mπ²R²f ² / ts = 973.18 / 6.30 = 154.5 watts

Conclusions:
    We interpret the dynamo efficiency calculated above to be definitive and exciting proof [within the framework of this rigorous treatment] that our 18" Faraday disk dynamo model could in fact be built to exhibit bona fide over-unity operation, if not yet necessarily in a self-sustaining manner. As mentioned early in the course of this study, it would require a separate bank of solid-state DC-DC step-up current converters to pre-amplify the output voltage of such a device before that output can be accepted by the vast majority of available AC inverters. Most inverters today have a reliable nominal efficiency of  93%, and there are now several extant types of suitable pre-amplifying converters having similar efficiency. So, the combined 'in-line' efficiency for our model would at best be only (1.077)(.93)(.93) = ~ 93.15%, and the integrated 'system loop' – including drive motor – would obviously not be self-sustaining.
    [For an excellent and quite readable pdf technical paper (Starzyk et al.; 1999) on just one such DC current converter methodology, entitled "A DC-DC Charge Pump Design Based on Voltage Doublers", just click here.
    However, there are a number of things that can yet be done to significantly enhance the performance of our model 18"-diameter dynamo, not the least of which is to thicken the rotor disk slightly (for added rotor ampacity). We've also designed a more refined dynamo model (using many more brushes) whose inherent COP would approach 1.50, and which will in fact – if reality meets the best theoretical model – be demonstrably self-sustaining, given the typical converter, inverter, and drive motor efficiencies cited.*
    We therefore feel that an imperative course of research and development is plainly indicated.
  * [We've also drawn up an "integrated system loop flow chart for a self-sustaining Faraday generator" having a feasible 20% net back-torque ratio and COP = 1.5, whereby it can be seen that the integrated system's net over-unity COP will be 1.12 – and thus it's more than inverter-self-running – but have been advised against its publication.]
   

Statorless ('Unipolar') Generator Analysis:  In the preceding Induction Dynamo Design Analysis, we discovered undeniable evidence that the traditional stator-and-rotor Faraday disk dynamo has inherent over-unity potential – at least when ultra-high-strength NdFeB field magnets (of over 1.0 Tesla residual induction) are used. However, it could be shown from the preceding Conclusions that any such disk generator designed according to the specific design principles discussed herein would have to exhibit an over-unity COP of at least ~1.20 before it could 'drive' a self-sustaining output system of the type described.  
    And what of the homopolar disk dynamo's 'unipolar' statorless variant(s)? Wherein, so many people have tried to use Ferrite magnets which are attached unnecessarily to the rotor disk – and which have only about 30–35% of the residual induction of the available (albeit expensive) NdFeB magnets! It will obviously be a fair challenge to design such a generator which is in any way competitive with the prior model, but the process involved may serve to further illuminate the engineering methods and principles used so successfully in the preceding case.
    In that first Design Analysis section, we considered a disk induction dynamo with a pure copper rotor 18" in diameter and 0.187" thick, and in the interests of making a true and fair performance comparison we will do so again here. However, in this case the disk will be mounted to a 1½"-dia. dual-bearing drive shaft made of the same Cu/Be alloy, which will raise the rotor ampacity to 1,579 amps at the disk/shaft joint. As before, the disk will be secured to the shaft using press-fit Cu/Cd/Cr-alloy split flanges that are silver-soldered to the disk and then set-screwed both to each other and to the shaft, with the latter once again being 8.5" in length.
    Two field piece arrays, each comprising 173 Ferrite-5 disk magnets that are 1" in diameter and 5/8" thick, will be epoxy-resin-bonded into solid pole-set assemblies and mounted directly on the rotor disk (in this case) with an electrical clearance of 0.0085" on each side (as the thickness of each intervening adhesive layer). [These Ferrite magnets are equal in number and diameter to the NdFeB magnets used in the previous Analysis, although their thickness is 25% greater to enhance the much-lower gap flux density produced.] Silver-graphite brushes (93%Ag) will then be mounted and connected as before (with the negative brushes contacting the disk's outer edge and the positive brushes running directly on the rotor shaft).  
 
    
 
    The primary practical engineering problem inherent in the statorless generator design is, of course, achieving adequate dynamic balancing of each 'composite' pole-set assembly. Not only must the "one-spot" radial symmetry of magnet layout depicted in the diagram on the left above be uniformly broken, so that the magnet mass incorporated within any given-size radial sector of the rotor area is as equal as possible (across the concentric rings of magnets), but a saturated steel band which can be spot-drilled as needed to obtain maximum possible dynamic balance must encircle each pole-set assembly. We'll assume that such is the case here, although this would be difficult to manage in practice.
    Also, the outer brushes in this model will be parallel-connected in double sets of three (3) per inner brush, each set being separated by 60° of rotation, and once again an even multi-pole number of such double brush sets should be uniformly distributed around the rotor by equal sectoring to maximize rotor current and to allow the corresponding inner brushes to be installed uniformly on the shaft. As before, these inner brushes are assumed to be positive [see the 2nd following graphic].

 
Rotor dimensions & flux density:
  [i]  flux gap radial width = Ra = 0.180 m  (from Analysis 1 above)
  [ii]  mean induction radius = r = 0.133 m  (from Analysis 1 above)
  [iii]  net flux gap area = 233.26 sq.in. (from Analysis 1 above)
  [iv]  vol. of each pole-set assy. = (233.26)(0.6335) = 147.77 in³
  [v]  total magnet area = 173 (0.7854) = 135.87 sq.in.
  [vi]  vol. of each pole-set = (135.87)(.625) = 84.92 in³
  [vii]  gap area B-factor = (135.87 / 233.26) = 0.5825 = 58.25%
  [viii]  disk magnet residual induction = Br = 3,800 gauss
  [ix]  computed gap flux density* = 2375 gauss (see graph at right)
  [x]  net flux density = (0.5825)(2375 gauss) = B = 0.1383 T
* flux density graph courtesy of Australian Magnetic Solutions

 
Rotor mass & moment of inertia:
  [i]  disk mass md = 6.965 kg  (from Analysis 1 above)
  [ii]  disk equiv. inertial radius = (A /π)^1/2 = 8.986 in. = 0.228 m
  [iii]  disk moment of inertia = ½(6.965)(0.228)² = 0.181 kg-m²
  [iv]  volume of epoxy = 147.77 – 84.92 = 62.85 in³
  [v]  density of epoxy = 0.0715 lb/in³
  [vi]  wt. = (62.85)(0.0715) = 4.494 lb., and mass me = 2.043 kg
  [vii]  density of Ferrite magnets = 0.177 lb/in³
  [viii]  wt. = (84.92)(0.177) = 15.031 lb., and mass mps = 6.832 kg
  [ix]  pole-set inertial radius = (233.26 /π)^1/2 = 8.617" = 0.219 m
  [x]  moment of inertia (ea.) = ½(8.875)(0.219 m)² = 0.213 kg-m²
 
Shaft mass & moment of inertia:
  [i]  shaft mass ms = 0.917 kg  (from Analysis 1 above)
  [ii]  moment of inertia = ½(0.917)(0.0127 m)² = 7.40 x 10^–5 kg-m²
 
    Now that we have developed the necessary physical data for an 18"-dia. statorless generator model, we need only specify a few more operating parameters before beginning a concise series of definitive performance calculations. The magnets' residual induction (Br) has already been selected, and in this case is 3,800 gauss (0.38T) for standard grade-5 Ferrite disk magnets that are readily available and very reasonably priced. The flux gap distance is readily figured from previous data, and is 0.204" or 5.2 mm. These criteria and the specified magnet dimensions were used to generate the flux density calculator graph provided above, from which the resultant gap flux density (quoted above) was obtained.
    Next, a rotation speed f must be selected which is not only within the brushes' maximum rating but is also hopefully at or very near an industry-standard electric motor speed. Additional data (like brush spring pressure) will be furnished as needed from OEM / vendor recommendations and specifications.
 
Voltage:  For the brush material grade selected, the maximum suggested contact speed is 5,000 fpm. While speeds as high as 6,500 fpm are possible, brush wear may become excessive in a continuous-duty application. Therefore, our tentative design operating speed will be 1150 rpm,  with f = 19.167 rps, again using a permanent magnet (PM) DC drive motor. This yields an acceptably-high brush speed of 5,419 fpm.
    Therefore, at 1150 rpm, Vo = (6.283)(0.133)(0.180)(19.167)(0.1383) = 0.3987 volts.  

Resistance:  Similarly to the procedure used in the preceding Analysis section, we'll ignore the trivial disk, brush, and shaft resistances for now and consider just the interface resistance of two sets of 3 negative brushes, each connected to a single positive brush. The combined parallel resistances of several even-numbered multiples of such brush sets can then be easily figured, to provide a means of increasing the output current. There will then be 1/3rd as many positive brushes as negative brushes, and for convenience we will consider the number of dynamo/generator poles to be equal to the number of positive brushes (same as before).    
    For optimum performance, current must be drawn from the rotor disk in as radially uniform a manner possible. Therefore, a 4-pole (4-set) brush arrangement is much better than the basic 2-pole (double-set) connection shown in the preceding graphic, and an 8-pole connection having 4 separate 2-pole systems in parallel is better yet. Based only on the ~0.003-ohm per-brush interface resistance, these connection options result in the following minimum rotor circuit resistances and corresponding maximum currents:
 
 

      Again, the brush current density rating will serve to limit the number of outer brushes used and the maximum possible current. The current density limit of the 93%Ag brushes we've specified is 300 A/in². In practice, total brush ampacity should be strictly matched to the highest I max figure derived that does not exceed the calculated safe ampacity of the rotor disk (as discussed further below) and total pickup brush width should be absolutely maximized,  approaching 100% of the disk's entire circumference,  in all generator (non-motoring) variants.
    Since the base 16-pole circuit resistance yields a figure for I max that is so close to the above-stated ampacity of the rotor disk, we will assume that the tentative 1150-rpm operating speed selected will be very slightly reduced to match that figure and that a 16-pole/48-point pickup brush circuit can therefore be used in this 'prototype' model and in the calculations to follow.
 
    To get a better figure for our model dynamo's actual total circuit resistance Rt, we will now calculate the resistances of the brushes, rotor shaft, and disk.
    Given the OEM specs for brush current density (300 A/sq.in.) and resistivity (2.0 x 10^–6 ohm-cm), we may simply divide the value for I max by 48 to find the ampacity of each negative (pickup) brush and then divide the result by the current density limit to find the contact area required. Therefore, the area of each outer brush An = (1,579 / 48) / 300 = 0.1097 sq.in. or 0.708 cm². Outer brush thickness should be > ½ and < 2/3 of the disk thickness, as the disk's outer edges should be slightly chamfered. So, the width of each pickup brush will be 0.1097 / 0.125" = 0.88". The rotor's circumference is equal to 2πRo = 56.55", the total pickup brush width is 48 (0.88) = 42.24", and so the edge-width 'coverage' ratio is 42.24 / 56.55 or 74.7%.
    Using brushholders which are only 5/8" 'tall', a good minimum brush length L is 1.0" or 2.54 cm. So, each pickup brush's resistance will be (2.0 x 10^–6)(2.54) / 0.708 = 7.175 x 10^–6 ohm, or Rn = ~ 7 μohm. Applying the same method to the 3 positive shaft brushes, at an assigned thickness of 0.375" the area Ap = 3An = 0.3291 sq.in. (2.123 cm²) and width again equals 0.88" or 2.24 cm. With length once again of 1.0", each inner brush resistance Rp = ~ 2 μohm. [As before, it will be important in practice to use the heaviest and shortest brush shunts (buss bar leads) feasible.]
    The rotor shaft alloy that is greatly to be preferred is CDA17200 1.9% beryllium copper, with volume resistivity of 7.733 x 10^–6 ohm-cm but the highest tensile strength of any copper-base alloy. To figure a liberal resistance for the rotor shaft, we'll once again allocate 5" or 12.7 cm as its "electrical" length by mounting the positive brushes inboard of the bearings and drive coupling. The axial end area of the shaft is equal to π( ¾")² = 1.767 sq.in. = 11.4 cm², and the shaft resistance Rs = ~ 9 μohm.
    The rotor disk's greatest electrical resistance is expressed through the edge of the 1½"-dia. central shaft hole, the circumference of which is 4.7124". Given a thickness of 0.187", this inner edge area then equals 0.8812 sq.in. or 5.685 cm². The volume resistivity of pure copper is 1.724 x 10^–6 ohm-cm, and the disk's radial conduction length L is equal to Ro – ¾" = 8.25" = 0.210 m = 21.0 cm. Accordingly, we find the resulting maximum possible rotor disk resistance Rd = ~ 6 μohm.
 
    Finally, we can now make the best possible projection of the rotor circuit Rt in milli-ohms as follows:
 
 

 
    As we saw before, the electrical 'hardware' really has little impact on the total rotor circuit resistance of a Faraday disk generator – if properly designed – since the figure we just derived with fair effort differs from the quick estimate we made earlier by only 1 micro-ohm! The rotor current developed at a preferred operating voltage of 0.3978 (as derived above) would then be equal to 0.3978 / 0.000251 or 1,588 amps, since I = V/R. Unfortunately, it can be shown using rather involved numerical anlysis of existing copper wire data that the safe ampacity of the 0.187"-thick rotor disk is 'only' 1,579 amps (as mentioned above) around its inner circumference. Our revised figure for the "nominal" output current will then be equal to the calculated safe rotor ampacity = nom. Io = 1,579 A.
   

Output Power:  The new value for max. Vo = 0.3963 volts, and the corresponding maximum rotor speed is then 1143 rpm or f = 19.05 rps (since f = Vo / 2πrRaB). And so, the maximum allowable output power is equal to (0.3963)(1,579) or max. Po = 625.8 watts, and the new maximum brush speed is 5,386 fpm. The pickup brush width will not have to be increased, and so the edge-width coverage ratio is still 74.7%.
   

Input Torque & Power:  Although it might seem that we now have good final figures for operating speed and output power, we have yet to determine if the rotation speed we just derived is acceptably close to that of an off-the-shelf electric motor (as a practical source of input torque) which will provide adequate start and run torque at a given available horsepower rating. This will not be nearly as difficult as it might sound, with the aid of a simple yet indispensable electric motor formula that relates speed (rpm), torque (T), and power (Hp):  T = (Hp x 5252) / (rpm) , where the constant 5252 is equal to 33,000 ft.lbs./min./Hp divided by 2π radians/rev., and T is the torque in ft.lbs. [The equivalent metric expression is:  T = P / ω , where ω = 2πf , P is power in watts, and T is torque in N-m.]  
 
For the 'classical' case:
  [i] primary full-load counterforce = Fa = B I Ra = (.1383)(1,579)(.180) = 39.31 N
  [ii] primary back-torque = Ta = Fa (r) = (39.31)(.133) = 5.23 N-m = 3.86 ft.lb.
  [iii] neg. brush counterforce (ea.) = Fnb = pkA = (4)(0.2)(.125 x .88) = 0.088 lb. (run)
  [iv] pos. brush counterforce (ea.) = Fpb = pkA = (4)(0.2)(.375 x .88) = 0.264 lb. (run)
  [v] total brush retarding torque = Tb = 48(Fnb)(Ro) + 16(Fpb)(¾") = 41.18 in.lb. = 3.43 ft.lb.
  [vi] total load torque T = Ta + Tb = 3.86 + 3.43 = 7.29 ft.lb. (treating the ~ 0.5% rolling losses as negligible).
 
    As stated earlier, there are a number of reasons for selecting a permanent magnet or shunt-wound [wound field] DC drive motor in this application, since they will operate on normal AC line power and an economical variable speed control is usually also available. This feature is especially desirable in cases where the tentative operating speed falls somewhere between standard electric motor speeds. However, in the case of a statorless Faraday generator with a large moment of inertia, it may be permissible (and less expensive) to use an AC capacitor-start motor if it so happens that a standard-speed motor can be used – since they are designed to start under heavily-loaded conditions. Although they may briefly draw over 300% of normal running amps to do so, a capacitor-start motor can be used in certain instances to effect a corresponding reduction in generator starting time.
    Referring again to the motor selection and ordering guide, we find that a 1.5 Hp 1150 rpm PM motor (with 180vdc armature; FL amps = 7.2) is available [GE 5CD125TP001B] that develops full-load torque of 6.85 ft.lb. (82.2 in.lb.). Even though this is somewhat less than the 7.29 ft.lb. that would be needed to operate our model dynamo at its maximum capability, it must be remembered that the motor's output torque will climb as its speed is reduced – and it may be that just enough torque will be available very near the maximum 1143 rpm operating speed we desire.
    The most straightforward way of determining that point on the selected motor's output power / torque curve where its operating speed is maximized for this particular application's input torque requirement is by repeated spreadsheet calculations to assemble tabular data, from which the best 'solution' of such a complex covariable problem is obtained when the net motor torque developed (Tm) just exceeds the total load torque (Tn) required at the reduced speed.
    Starting at 1125 rpm and calculating output voltages in descending 5-rpm increments, the following optimal resolution was found at 1100 rpm (f = 18.333 rps):
 
  – net Vo = 0.3814 volts, net Io = 1,519.5 amps, and net Po = 579.5 watts ;
  – net Fa = B I Ra = (.1383)(1,519.5)(.180) = 37.826 N ;
  – net Ta = Fa(r) = (37.826)(.133) = 5.031 N-m = 3.71 ft.lb. ; and
  – total load torque = Ta + Tb = 3.71 + 3.43 = Tn = 7.14 ft.lb. [treating the ~ 0.5% rolling losses as negligible].
  – net motor torque developed = Tm = (1.5 x 5252) / 1100 = 7.16 ft.lb. > Tn (@ 7.14 ft.lb.).
 
  – nominal motor efficiency = (Hp x 746) / (V x I) = 1,119 / 1,296 = ~ 86.3%
  – nominal dynamo efficiency = Po / (Hp x 746) = 579.5 / 1,119 = ~ 51.8%
  – combined system efficiency = (0.863)(0.518) = ~ 44.2%
 
  – letting avg. brush k = ½ (0.3 + 0.2) = 0.25,  avg.Tb = (0.25 / 0.2)(3.43) = 4.29 ft.lb.
  – avg. no-load motor torque  Tnl = Tm – avg.Tb = 7.16 – 4.29 = 2.87 ft.lb.
  – no-load motor starting time  min. ts = ωI / Tnl = 2πf [.181 + 2(0.213)] / 2.87 = 24.36 sec.
  – Pr = mπ²R²f ² / ts = (24.715)(9.8696)(0.0491)(336.1) / 24.36 = 4,025.4 / 24.36 = 165.2 watts

  – avg. full-load motor torque  Tf = Tm – (½ Ta + avg.Tb) = 7.16 – (1.86 + 4.29) = 1.01 ft.lb.
  – full-load motor starting time  max. ts = ωI / Tf = 2πf (.607) / 1.01 = 69.23 sec.
  – rotor mechanical power expended = Pr = mπ²R²f ² / ts = 4,025.4 / 69.23 = 58.1 watts

    These starting times are of questionable acceptability even for a PM-DC drive motor, and are far too extended for a capacitor-start motor to be used [since no-load start times longer than about 3 seconds may overload the additional start windings in a capacitor-start motor, damaging or destroying the coils and/or tripping a circuit breaker, even though the effective start times will be lower by ~300%]. Also, it can be seen that the much lower gap flux density in the Ferrite-rotor generator has caused an almost 50% reduction in output power and a 33% drop in efficiency, despite the greatly increased rotor current, as compared to the induction dynamo in the previous example. And, the additional brush drag and far-higher rotor mass have served to cause what might be considered an unacceptably long starting time.
    It should be noted that this statorless generator's actual induction efficiency can be found by simply figuring its torque requirement without considering brush drag. Thus, at 1075 rpm, a ¾-Hp PM-DC motor would be adequate to power the generator at rotor voltage of 0.3727, current of 1,485 amps, and output power of 553.5 watts. Provided both field pieces' outside poles will be wholly keepered at saturation, and at less than the disk's full diameter, real induction efficiency would be 553.5 / 0.75 (746) = 98.9%! [These criteria regarding the essential use of saturated steel end-plates to 'keeper' the outer stator poles derive from the innovative prior-art "closed (flux) path" homopolar generator design of Trombly & Kahn (~1982). A saturated material will support no further passage of flux nor any further external magnetic induction – in the form of eddy current losses, in this case.]
    Purists may also notice that the motor's own armature inertia has not been considered above in the interests of clarity and brevity, having been treated as negligible since it corresponds to just 0.4% of its output torque (by OEM specs) in this particular case. The same consideration also applies to the rotor shaft's miniscule inertia in relation to that of the disk. The non-trivial inertia of the steel end-plates has also not been considered, however, which would act to further extend the start times figured.
 
And in the best-case theoretical model: The following computations are based on the application of the 'Tesla' reduced back-torque ratio to the model 'unipolar' generator in question. As we developed earlier above, in this case that ratio is equal to 1 – 0.747 = 0.253.
 
  [i] primary full-load counterforce = Fa = 25.3% [B I Ra] = 0.253[(.1383)(1,519.5)(.180)] = 9.57 N
  [ii] primary back-torque = net Ta = Fa (r) = (9.57)(.133) = 1.273 N-m = 0.94 ft.lb.
  [iii] total brush retarding torque = Tb = 48(Fnb)(Ro) + 16(Fpb)(¾") = 3.43 ft.lb. (same as before)
  [iv] total load torque Tn = Ta + Tb = 0.94 + 3.43 = 4.37 ft.lb. (treating the ~ 0.5% rolling losses as negligible).
 
    Referring again to the motor selection and ordering guide, we find that a 1 Hp 1150 rpm PM motor (with 180vdc armature; FL amps = 5.0) is available [GE 5CD123GP001B] that develops full-load torque of 4.57 ft.lb. (54.8 in.lb.). In this case, the 1-Hp motor seems to have enough torque for the generator to be operated at the same rotor speed as it was with the 1.5-Hp motor in the classical case, at 1100 rpm (with f = 18.333 rps), thereby nicely illustrating the effective proportional reduction in input power:
 
  – net Vo = 0.3814 volts, net Io = 1,519.5 amps, and net Po = 579.5 watts (from classical case above);
  – net Ta = Fa(r) = 0.94 ft.lb. (from above); and
  – total load torque Tn = 4.37 ft.lb. [treating the ~ 0.5% rolling losses as negligible].
  – net motor torque developed = Tm = (1.0 x 5252) / 1100 = 4.77 ft.lb. > Tn (@ 4.37 ft.lb.).
 
  – nominal motor efficiency = (Hp x 746) / (V x I) = 746 / 900 = ~ 82.9%
  – nominal generator efficiency = Po / (Hp x 746) = 579.5 / 746 = ~ 77.7% (or COP = 0.777)
  – combined system efficiency = (0.829)(0.777) = ~ 64.4%
 
  – avg. starting brush retarding torque avg.Tb = 4.29 ft.lb. (same as before)
  – avg. no-load motor torque  Tnl = Tm – avg.Tb = 4.77 – 4.29 = 0.48 ft.lb.
  – no-load motor starting time  min. ts = ωI / Tnl = 2πf [.181 + 2(0.213)] / 0.48 = 145.7 sec.
  – Pr = mπ²R²f ² / ts = (6.965)(9.8696)(0.0491)(336.1) / 145.7 = 4,025.4 / 145.7 = 27.6 watts

  – avg. full-load motor torque  Tf = Tm – (½ Ta + avg.Tb) = 4.77 – (0.47 + 4.29) = 0.01 ft.lb.
  – full-load motor starting time  max. ts = ωI / Tf = 2πf (.607) / 0.01 = 6,992 sec.
  – rotor mechanical power expended = Pr = mπ²R²f ² / ts = 4,025.4 / 6,992 = 0.58 watts.

Conclusions:
    As should perhaps have been apparent from the outset of this example, there would be no reason not to use the far-stronger NdFeB magnets in this statorless generator model, since the generator's output power must be proportionally lower if the Ferrite magnets are used – and by all appearances achieving a COP > 1.0 would simply not be possible, unless perhaps a non-statorless dynamoelectric motor stage was very carefully employed [with far greater system size, complexity, and cost].
    Also, in much the same way, there would be no point in rotating the additional mass of the pole-sets (even if using metallic NdFeB magnets!) when the result must be an undesirable and perhaps untenable increase in the starting time and in the net mechanical torque requirement, which works against a best efficiency in disk generator design. With so much misinformation disseminated about the statorless Faraday dynamo variant, it might be tempting to speculate how much of it is truly inadvertent.  
   

The Time Machine Project © 2005 Cetin BAL - GSM:+90  05366063183 -Turkiye/Denizli 

Ana Sayfa /index /Roket bilimi / E-Mail /CetinBAL/Quantum Teleportation-2   

Time Travel Technology /Ziyaretçi Defteri /UFO Technology/Duyuru

Kuantum Teleportation /Kuantum Fizigi /Uçaklar(Aeroplane)

New World Order(Macro Philosophy)  /Astronomy