--- Robin van Spaandonk <[EMAIL PROTECTED]> wrote: > In reply to Paul's message of Sun, 21 Jan 2007 > 09:05:43 -0800 (PST): > Hi Paul, > [snip] > >If you place a load on > >the both air coils you can collect > >such energy. That's why pure inductors dissipate > zero > >energy; i.e., energy goes in the > >inductor in the form of a magnetic field, but > during > >the other half of the cycle such > >energy goes back to the source. There is more here then meets the eye. A reactance such as an inductance or capacity indeed does return energy to the source on an alternating current input upon collapse of the fields. Here are some former somewhat lengthy speculations: Transcending Reactive vs Real Power Concepts. Sun May 29, 2005 As most of us know the REASON that we cannot simply multiply the voltage times the amperage, (VI); to obtain the power expressed in an inductor placed across AC, is that there is a time lag between the cause and effect; where voltage being the cause, and its amperage being the effect. For the AC inductor, because of this time lag, that for the external AC source we can speculate that if the current were truly 90 degrees out of phase with the voltage, (this often stated premise is not completely true, it depends whether the inductor has a large enough inductive reactance X(L)= 2pi*F*L to form a phase angle near 90 degrees); but if the amperage were near 90 degrees out of phase with the voltage, by the time the AC voltage input has made a complete pulse in one polarity, and thus gone back to its zero crossing point; at that moment in time the amperage in the coil will have reached its maximum, again using the 90 degree phase angle example. Up until this starting point 180 degrees into the AC cycle, a magnetic field from the inductor is established that agrees with its polarity input. But in the third quadrant of the AC cycle, the voltage input reverses polarity, but the current has not yet followed its example, because of the time lag the current is going in the opposite direction then what its voltage source would cause it to act. In the third quadrant then the magnetic field of that inductor is then causing a self induction by virtue of its magnetic field collapse that establishes a polarity OPPOSITE to the polarity of the source. This is why back emf, or a backwards working voltage source established by mistimed magnetic fields exists. The net result of this backward working voltage during portions of the AC cycle is that the forward working voltage does not conduct it's OHM's law amount of amperage, because of this extra effect of AC resistance. We call this AC resistance inductive reactance. The effects of both the actual resistance and its inductive reactance is reffered to as impedance, noted as Z where the effects of both principles are obtained by summing the squares of both quantities, and taking the square root of this result shown as the impedance equation Z= sq rt[R^2+ X(L)^2].
Now some commentators note that because the coils magnetic field establishes its own self induction, we are actually dealing with the summation of two power sources. They explain that because of the storage of energy manifested as a magnetic field, in certain portions of the AC cycle the coils collapsing magnetic field is establishing a polarity opposite to its source, and in terms of the AC source being a generator, that generator as its VI apparent power input also experiences borrowed and returned energy. When the coils magnetic field collapses a portion of the power input is returned to the generator. Now the real amount of energy expeneded on the coil is just its conversion to heat by I^2R heat losses, and the rest is just borrowed and returned energy. The essential question then becomes does this source also act like a banker and charge interest on its borrowed and returned assets? This would seem the sensible thing to do, but perhaps nature doesnt always model mans actions. So we have two aspects, and this is where the third aspect comes into being, where the concept of phase angles comes into play. We have the apparent power input which is just the voltage times the amperage across the load,or (VI) of the generator as the apparent power input. Then we have the real power input which is undeniable because we can measure the heat release as the I^2R quantity. Because we have a load containing reactance, or a reactive load, the difference between the real and apparent power inputs is merely the % of borrowed and returned energies vs real energy output. But we also have a method to compute what this heat release should be by methods of trigonometry. We can draw out the AC voltage and amperage AC cycles, and find out the % portions where they are in agreement, where this portion will be expressed as a cosine angle. The real power input therefore becomes VI* cos( acting phase angle of the inductor), and we conclude that this also equals I^2R as the heat loss. Recall that in trigonometry we have a y coordinant, [expressed as X(L)in phase angles]: where y/radius is the sine quantity of the angle, and conversely x/radius is the cosine. (In trigonmetry we allow the radius of the circle to be the unit 1 to simplify these calculations.) To find the phase angle of an inductor we let the inductive reactance to be the positive y quantity, and the actual resistance R to be the x quantity. But a little more trig is need to find the actual phase angle which can be calculated with any calculator having trig functions. The tangent of the angle is expressed as y/x. So if we have a coil where X(L) and R is both known, the tangent is easily known; it is just X(L)/R, which is also the theoretical Q factor of the coil. But what we NEED to find out is the inverse of this, which will tell us the radians, which can further be reduced to an angle by multiplying by 360 degrees/ 2pi radians, which is the conversion factor to degrees. Suppose I have an inductive reactance 5 times the resistance; what is the phase angle? We know the tangent is merely 5, but this tells us nothing. Instead what we NEED to find out is the answer to the question; the tangent of what amount of radians will give an answer of 5. Thus we use the inverse function, called the co-tangent, or tan^-1 to determine the answer. And tan^-1 (5) = an answer in radians that can be converted to degrees, and this is the method for finding the phase angle. Now if X(L)is very large vs the R quantity of resistance, X((L) forms the y axis, R forms the x axis, and the hypotenus, (ordinarily the radius quantity in trig functions) becomes the impedance Z. We already know by the Pythagorean theorem that the sum of the squares of the right angle triangle sides is equal to the square of the hypotenus, and by then taking the square root of both sides of the equation we reach the same equation for the impedance Z. And if X(L)>> R then X(L)~= Z. The length of the radius and its y reflection are almost equal, but the x reflection as the additive vector is very small compared to the other two quatites by definition since we have initially made the condition X(L) is far greater then R. The x reflection is also the cosine of the phase angle, and it is this no. as a percentage that is used for the real power calculations. Thus with this condition the apparent power will be far greater then the real power. These things are all rudimentary for the electrical engineer. Now we come to electrical resonance, where X(C) forms the negative Y axis, the opposite reactances in series can cancel, leaving R as the predominant factor for conduction, and in this condition then we suspect that now the apparent power will be the same thing as the real power, and the amperage has now come closely in phase with the impressed voltage. However because of a factor known as "internal capacity" we may not always arrive at a conduction that equals ohms law requirements. The depends on the construction of the inductor we are resonating. However a VERY misunderstood thing can happen here. We might assume that since now the apparent power equals the real power, which also occurs in DC circuits after the magnetic field is established, that % wise the generator is no longer having a significant portion of "borrowed and returned" energy allocations. We have cancelled the reactive state of the circuit, so have we not also cancelled the "borrowed and returned" field energies? The generator would seem to indicate so, because the apparent power equals the real power, and we are not seeing differences between those definitions. However in actuality the opposite thing has occured, the borrowed and returned field energies will have gone up q times, even though the generator does not seem to indicate this % wise in its allocations. A simple proof of this is the definition of stored energy for the L and C components. The energy stored in C is defined as [CV^2]/2, and for L it is [LI^2]/2. In series resonance each L and C component developes an internal voltage rise against each other, in opposite directions with respect to each other, so that on the outside of the circuit, the generator only sees this net cancellation. For the C case, since the V term is squared, and we are obtaining series resonant internal voltage rise, the stored energy has gone up Q times, where the acting Q factor is the ratio of the inside voltage rise to the outside voltage source. We then have increased the borrowed and returned energies, but now a different relationship exists. Formerly the energy was borrowed and returned to the generator, but now the borrowed and returned energies only exist between the L and C values... It is literally as if the expanded electric and magnetic field energies were being obtained in resonance for free... But can we use this fact to power another load? That isnt so easy a proposition. If we divert the expanded voltages to another circuit, this in turn destroys the properties of the resonance itself, so that the actual resonant rise of voltage is wiped out. A little over a year ago I set up some circuits where the resonances were obtained from a 3 phase alternator functioning @ 480 hz. These resonances were special in that they were designed to be maximum energy transfer circuits, generally defined as a circuit that drops the open circuit voltage of the source in half, but on the only side of the coin, the maximum amount of power to load is obtained from that generator. Between these 3 AC phases, set up as Delta Series Resonances, (DSR's), the voltage rise q factor of 5 was noted. What this means is that 5 times more amperage is procurred then what exists in the reactive state, and also the internal rise of voltage was 5 times that of the source. Now between these three 120 degrees of voltage rises, the AC was turned into DC by means of full wave rectifications, which because of the poly phased inputs, thus fills up the DC ripple without use of a filter capacity. The load for these DC currents was a 3/8ths inch width of a ferrite block, normally considered an insulator. Now ferrite is actually considered a class of semiconductor, in that it looses resistance with heat. The ferrite in this case gradually grew hot, its resistance decreased phenomenally going from 30,000 ohms to around 7 ohms, until it began to glow on a corner, the temp around 900 degree fahrenheit. Meanwhile the outside coils, where this internal current was obtained from on the rectifications also experienced a drop of current from what existed in its resonant state. The addition of this low ohmic load between the resonances had caused its amperage input to drop, in fact it drops low enough so that only half of the current that the coils would consume in its reactive state was noted. We might say that X(L) of the coils appeared to double. What this also means is that once again we should be dealing with apparent vs real power input ratios. Now the inside load, being DC has no power factor arguments associated with it, but the outside coils do, because they are AC reactances, placed into resonance, and then reduced from resonance by addition of the interphasal load. This load has become a 2nd generation maximum power transfer principle, where the internal impedance or reactance of the outside coil systems have been matched by an equal resistive load. In terms of this Z(int) of the source has been given an equal R(load) in ohmic values, the requirement for maximum energy transfer. The outside spiral coils themselves, constructed as maxium energy tranfer resonances, (METR components), use the same principle in the R(int) of the alternator stator coils equals R(load) of the coils resistance R value. Now in the cited circumstance, the stator lines each serving two phases contains ~ 2.0 -2.4 Amps, and the division into phase currents should reduce this by about 1.7 times the stator line currents. The outer phase currents derived from these stator line currents are somewhat inbalanced, and the pic I took of the power input shows 1.4, .85 and 1 amp currents on this outer triangle, a sum of 3.25 Amps. On the DC current procurred from the outside misphased AC currents I arrive at a sum of 3 DC amps, obtained from this outside AC current oscillation. Both the alternator input voltage and the ferrite DC voltage are about equalized at 17 volts. As such no resonant rise of voltage is taking place, the voltage input is about the same as the voltage output to the load. Now if we average the phases currents to ~ 1.1 amps, with 17 volts across them, the apparent power input is 17* 1.1 = 18.7 watts per phase, or the generator is inputing an apparent power of 56.1 watts. But the REAL power of the inside triangle load being shown by the 900 degree heat of the ferrite is also 17VDC*3A = 51 watts. The coils themselves that lay on the delivery lines to the ferrite have a combined 3 watts heat loss, close to what the apparent power shows itself as, where the combined loads of 51 + 3 watts almost equals the apparent power input of 56 watts. Here is where the kicker comes in; the apparent power in is yeilding almost the same amount as real power out!. We surmise that since no resonant rise of voltage is occuring on the outer triangle coils, that we should treat this as a apparent power input, and not a real one. Now we have about a 84 degree phase angle, made as tan^-!(10), from a situation that started out with a phase angle dictated by the tan^-1(5), from the coil systems having a q of 5. After the load was added the coils appeared to have about double the impedance on their conductions, which is where the 10 figure in tan^-1 estimations comes in. If this were true, the mechanical energy required to turn the alternator should only reflect a real power load of only 10 watts, by the conventional phase angle analysis, but yet we have a bonafide real power load of 5 times this amount! Have we indeed turned an apparent power input into a real one? Perhaps the apparent vs real power arguments do not apply for this special case. What I would like to be able to do is power the alternator with a geared up bicycle gearing rig, and drive the alternator by bicycled leg power. For only a 10 watt power requirement to make 900 degrees, this seems possible with a human energy input. Then I could stick in real resistive power loads, and compare the respective drags for both situations. In any case the above arguments either show that the current electrical phase angle theory is inadequate to explain the above situation, or conversely we have used the "free" field oscillations inherent in resonance to create a situation of overunity. The calculations also show that ~ 6 times the energy transfer occurs in the LC field energy transfers then do the actual real power being inputed as I^2R heat losses on the DSR's themselves, which are just under 1 ohms resistance. Sincerely Harvey D Norris 2006 Postnote; In the ferrite heating phenomenon, we see an example of impedance matching of source with load. The reactance of the coils as delivery lines are balanced by an opposite capacitive reactance equal in ohmic value to the frequency input. At any point in the three phase circuit application to the load, in this case being the ferrite heating effect, we can interpret this load as a resistance rather then a reactance in ohmic values. Now INITIALLY the comparison between the reactance and the resistance of the delivery coils is fairly high at ~ 7/1 ratio. Now essentially we have added a resistance load to a resonant circuit, extracted BETWEEN phasings, and if the resistance of the delivery coils are then neglected as minimal compared to the actual load resistance; what we have essentially done is to add a resistance to a resonant circuit, and in terms of ohms then the load being equal to the reactance on the delivery lines; What the phase angle laws tell us is that when the reactance X(L) and R are equal, this is a functioning 45 degree phase angle. Now the mistake I made above was to assume that the matched impedance as a 7 ohm load; since this cause the reactive current to drop in half, I then made the phase angle calculations as if X(L) were doubled resting in a calculation of the above tan^-1(10)= 84 degree phase angle. However instead of twice the reactance being added to the circuit a resistance equal to the reactance was instead added to the circuit in series which would mean the true phase angle should be closer to a 45 degree angle. So for the above example we should reanalyze things as a 45 degreee phase angle "Now if we average the phases currents to ~ 1.1 amps, with 17 volts across them, the apparent power input is 17* 1.1= 18.7 watts per phase, or the generator is inputing an apparent power of 56.1 watts. But the REAL power of the inside triangle load being shown by the 900 degree heat of the ferrite is also 17VDC*3A = 51 watts. In the above example then we have procurred an extraction of 3.25 Amps from the 17 volt 3 phase alternator, but this 3.25 amps should be measured as a true power output obtained as a 45 degree phase angle. Since the amperage is lagging the voltage I would assume that since cos 45 degrees equal .707, that only .707(56.1 watts) = 39.6 watts were expended as true power input. If this were truly the case for these somewhat sloppy calculations then about 27% more energy is being released in the resonant circuit then is being inputed by phase angle laws. HDN Tesla Research Group; Pioneering the Applications of Interphasal Resonances http://groups.yahoo.com/group/teslafy/
