Lugano e-cat test report power in measurement anomaly

I'm going to draw some conclusions from the published data in the Lugano Report. I know that others have done similar calculations, but maybe not laid them out with care and clarity.

The measurements I'm going to look at are those for Joule heating in the wires feeding the reactor, and those for total power delivered to the reactor from the control unit. Both sets of measurements are made by the same instrument - a 3 phase power analyser. The Joule heating is calculated from the feed wire (mostly copper) resistivity and the measured RMS current in the wires. The total input power is derived from the power meter. The report authors do not state exactly how this is done but the instrument is very capable and can internally calculate and display many powers. Of particular relevance here it can calculate the total power, and the phase power, which differ by a factor of 3.

The report contains the following measurements for the three cases of dummy test, 1250C test, and 1400C test.

The point is that these measurements are all made by the same equipment, and although assumptions such as the resistivity of the leads etc may be incorrect, the ratio of these powers will always indicate the ratio in resistance of the leads and the Inconel wire heating element. We know the leads are mostly copper and also don't vary much in temperature, so there would seem to be a change in resistivity of the heating element by a factor of 3.3 between the dummy tests and the two active tests.

Interestingly the hotter active test (an extra 150C) does not change the resistivity, as shown by this ratio, by more than 1%. So we have an anomalous 300% change from 500C to 1250C, and a 1% change from 1250C to 1400C.

That is inconceivable, especially because data on Inconel 625 (a high temperature Inconel alloy such as was presumably used) shows less than 5% change over the range 20C to 1090C. See data here.

So we have a X3.3 anomaly in the two methods of measuring power. Either the dummy is wrong or the active test is wrong. We know the dummy is correct (to within 10%) because it matched measured power out. Therefore the dummy ratio is approximately correct, 75, and the correct input power for the active runs is some 3.3X larger than the report power measurement for these cases.

That would make the correct measured COP around 1

Only the report authors can explain how this anomaly came about, but I have a suggestion. Three phase power meters can display phase power or total power. If the equipment was set to total power for the dummy measurement, and set to phase power for the active measurements, it would make a typically X3 difference in the data which would leave an anomaly of only 10%. This could be a result of a small resistivity change and other errors, such as asymmetry of power between the three phases caused by resistance variations causing phase power for a given phase to be different from the typical 1/3 of total power.

The comments above are based solely on the information contained in the published report. I am making no inferences or assumptions about the likelihood or not of LENR, or any matters relating to the probity of the testers or Rossi.

I hope that those who believe this test adds to the evidence for Rossi's e-cat actually having nuclear-level power production will suggest a hypothesis that explains this data in some way consistent with that. I also hope that the authors of the report will identify the error and rewrite the report with consistent data. I note that they have said they may change the report to reflect comment on questions. Perhaps the change in this case could include a description of why the original measurements were inconsistent by a factor of approximately 3 as well as the corrected measurements.

My question, for the authors of the report, would be to explain the above anomaly. In that context it might help to have more information about how the power measurements were taken from the power meter, and whether any checks were made that the measurements taken were in fact identical in the dummy and active run cases. If stored data from the power meter is available this should help to elucidate the matter. Precise information on measurements (are reported currents RMS or average) would also help.

Best wishes, Tom

The calculations are confusing in the report, and i may have got it wrong, but here is my understanding.
The power flux dissipated overall is measured as:
Q_o = radiation from rods + convection from rods + radiation from reactor + convection from reactor

The measured input power power to in the system is equal to:
Q_i = joule heating from wires (Q_jw) + joule heating in heater (Q_jh)

the authors then take
Q_x = Q_o - Q_i + Q_jw

as the supposed LENR reactor power.

Now, practically the wire joule heating Q_jw is not significant, it is much smaller than the other components. But it provides a cross-check of Qi. That is because they calculate Q_jw independently of anything else from the wire current - measured independently of the input power by clamp ammeters - and an estimate of the wire resistance based on wire composition and dimensions. So whatever is their wire resistance estimate (it need not be correct) the stated Q_jw for each of the three tests, calculated from what they call average current but must be average RMS current, must have a ratio the same as the ratio of Q_i for these same tests. Unfortunately this ratio is 3.3X different from the stated measured ratio using the power analyser:
Qjh(active) / Qjh(dummy) = 5.7
Qi(active) / Qi(dummy) = 1.86

The difference, 3.1X is the anomaly. (I've calculated ratios a different way round from above, averaging the two active test powers - but the result is the same).

Sorry for repeating what is maybe obvious but I need to make sure that you understand my assumptions here.

Then, from the report, the power figure of 6.7W is clearly Joule heating, calculated from the stated measured currents in the dummy run.

I get my Joule heating powers for the active tests from Table 7 p22 which is described as:

Quote

Tables 6 and 7 report all the E-Cat test results relevant to the days of testing, approximately two days for each file.
The first table shows the average temperature of each cap and of the entire body of the E-Cat for each of the 16 files analyzed. It should be mentioned that, as in the case of the dummy reactor, analysis on the E-Cat was again performed by dividing the thermal images into 10 areas along the length of the reactor, and into three areas for each cap. In the table, however, the results relevant to each area are further averaged out, in order to facilitate reading.
In the second table, mean power consumption, watts produced and watts dissipated by Joule heating are shown for each file. Uncertainty associated to the result is on average 5% for power consumption and 3% for watts emitted. The last two columns record COP and net production. COP is the ratio of the sum of the mean power, emitted by radiation and convection by both the E-Cat and the rods, to mean power consumption of the reactor minus watts dissipated by the cables through Joule heating.

Therefore I think the "Joule Heating" column of Table 7 is the resistive heating of the cables and therefore must match (as a near constant ratio between joule heating in cables, and total power in) the power in as calculated by the PCE 3 phase analysers.

I take this column as a proxy for the measured current values used to calculate it. That, at least, is what the authors say they do and it makes sense.

What does not make sense is the stated measured input power which is highly inconsistent between the dummy and active tests. I further think it must be wrong for the active test because the dummy test is validated by the output power measurement which matches.

I realise that I'm not commenting on the thermal aspects of this - because the inconsistency I'm highlighting does not depend on that. It depends only on the stated power measurements. Those are, I believe, the powers calculated from wire currents as the report states.

I agree that the temperature of the wires will be affected also by heat conducted from the reactor, and therefore the total rod dissipated power (given in the Rods column of Table 6) will be much higher than the Joule heating power. It is around 300W in the active tests.

Forgive me but you are using Joule heating in a different way from me. Joule heating is heat generated internally (in the wires) from electrical current. Not heat conducted from elsewhere.

The Joule heating of the heater is indeed significant, and conducts significantly to the rods, but it is not what is measured here. The figures here are only for that portion of rod heat that comes from the rod current. To get the total heat you must add in the conducted heat, I agree.

The point is that the inconsistency here has nothing to do with the measured total heat. It has only to do with the calculated Joule heating from the wires. This, the report says, is derived from clamp ammeter current measurements.

Now, to deal with the section you highlight that appears to indicate wire Joule heating of 0.6W. That is calculated assuming a current of 9.85A. That is smaller than the current stated in the dummy calibration calculations (my figure dummy) and certainly smaller than that stated for thg active runs in Table 7. The paragraph is imprecise under what conditions such current might exist, and states it is an example calculation only, whereas the sections I extract numbers from state exactly what are the conditions that lead to the given power.

Now, to reply to your suggested 0.4W heating for all three rows of the table. That is impossible. It is certain that with a change in input power so the wire Joule heating must change.

So let us have a look at page 14 of the report. Section 4.3 sets out to calculate Joule heating in the wires from the measured current in the wires and their calculated resistivity The calculation is:
P = I²R
R is calculated to be 4.374E-3 for each C₁ wire, 2.811E-3 for each C₂ wire. I has two values, 19.7A for C₁ wires, and 9.85A for C₂ wires. Thus the C₁ cables (3 off) represent the first circuit mentioned in the text, the C₂ cables (6 off) represent the 2nd circuit. The Joule heating powers for the two cases are 5.1W for the C₁ wires, and 1.6W for the C₂ wires, giving a total of 6.7W. Note these two components represent Joule heating of different wires, and must be added together for total Joule heating as is done in the text Equation 11.

From the I²R calculations at the top of p14 (Equations 9 and 10) you can see that both components of this are Joule heating. You can also see from Figure 4 what are C₁ and C₂, why the current in C₁ wires is always double C₂, and why this Joule heating is all wire heating and thus the power directly proportions to the square of the heater current, and not affected by the conducted heat from the heater to the wires.

Quote

The cables supplying power to the reactor are made of copper and are several meters long. In the present run of the E-Cat the current flow may actually be higher than 40 A. For this reason, it is expedient to evaluate what portion of the current, fed to the system by the power mains, is dissipated by the cables as Joule heat. Figure 4 shows the cable layout from mains to load: three copper cables (C₁) exit the power regulator, one for each phase, three meters in length each, with a cross-profile of 12.00 mm 2 . In order to allow the delta configuration connection of the resistors, each of these cables is connected to another two cables (C₂), 2 m in length each, having a cross-section of 12.45 mm 2

I've added C₁,C₂ in brackets to the introductory text for clarity.

Finally, note the 3rd paragraph of section 4.3;

Quote

We may calculate the dissipated heat to the limited extent of the dummy reactor: the results relevant to the E-Cat will be given in Table 7, due to the fact that the average current values changed from day to day.

you can see that the equivalent Joule heating figures for the active runs are given in Table 7 and are indeed what I take and use for comparison.

Quote

Note that the copper cables, 12.45 mm 2 in cross section, run through most of the six alumina rods, inside of
which they are joined by a connecting terminal to the Inconel cables coming from the reactor. The length of
Inconel cable inside the rods is but a few centimeters long. Therefore, if one considers that the copper cables
run through almost the whole length of the rods (50 cm), it is possible to calculate what fraction of the 7 W
given by (11) is emitted within the six rods themselves. For each of the six 50 cm lengths of copper cable, the
relevant resistance is 7.028∙10 –4 Ω. From (10) we see that the heat dissipated inside the rods by the copper
cables is = 6 ∙ (7.028 ∙ 10 –4 ∙ (9.85)²) = 0.4 W, that is to say, about 6% of the heat emitted by all the copper
cables together. It is obvious that the heat emitted by the rods (which shall be calculated in detail in the next
paragraph) is only in the least part generated by the cables running through them: on the contrary, that heat
originates almost exclusively from the reactor, which, by conduction through the short lengths of Inconel
cables coming from the caps, transmits it to the rods.

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The above quote, from the end of section 4.3, shows that the 0.4W figure is the small part of the Joule wire heating inside the alumina rods. This is not relevant when comparing the much larger total wire Joule heating. The p19 paragraph is actually incorrect, it refers back to the previous paragraph, which does not contain the 0.4W value. Further, the active test value for this small part of the Joule heating will actually be larger than 0.4W, but it is also negligible so the error has no significance.

The values of 6.7W and 37W, 42W are measured, The first from the dummy setup clamp current readings, the second from clamp current reading data collected over the test period and combined to give an average power, just as the other powers are so combined, in table 7.

Yes, I think the table 7 figures are correct.

(1) they match exactly (within 1%) the ratio of power dissipated as expected for the two active tests
(2) they say that is what they are, and they are of the right order size

Table 4 is a set of figures for the heat measured emitted by the dummy reactor from radiation and convection - note "rods". This is nothing to do with the wire Joule heating (the wires to go through the rods to make that 0.4W but that is a small (6%) correction to the total Joule heating.

there is a question of whether the figures are including or excluding the rod Joule heating. The 6.7W figure is including it. I'm not sure whether the active reactor figures are including or excluding - but I believe also including. Either way, it makes not much difference (6%) to the X3.3.

To be precise:

The 37W lost from the heater power is a small error compared with 800W heater.

The fact that they measure 37W (5.5X higher than what they measure for the dummy run) matters because the Joule heating in the heater must be proportional to the Joule heating in the wire - they have the same current and both are resistors made of metal - whose resistivity does not vary much with temperature.

so if 6.7 W => 486W heater we should have

37W => 2680W heater power.

That gives a COP of < 1 for this electric heater - a pretty clever feat!

This is a dramatically different value from their measured power in of (for the 1250C test) 800W.

It means the COP is now slightly less than 1 (there are however various errors, like the variation in heater resistance with temperature).

That is an ingenious idea. However the testers measured power both before and after the control box. The tables comparing input and output power are precise, so it would be strange indeed if this significant error were left out.

In the case of the dummy reactor the measured output power was close to input. So this would imply that the dummy reactor had a COP of around 3 - surely not tenable?

In fact they were wrong about C1 C2 currents. For any normal 3 phase RMS waveform the ratio is sqrt(3) between RMS line current (C1) and RMS phase current (C2). I should have spotted this earlier - but I want not paying attention to the load configuration.

For a Triac-switched waveform the same partly applies because the triacs switch the line outputs to the instantaneous value of the 3 phase input waveforms - if on 100% duty cycle it is the same as sqrt(3). But if the duty cycle is short the system approximates one in which C1 RMS is double C2 RMS.

This does not really matter. For the dummy reactor case we know the duty cycle is short so the statement made in the report is good enough though not technically correct.

Tom

I'd like to summarise the power in issue.

Either Rossi has an extraordinary and useless NTC heating element (because it is not NTC at the active temperatures, only at lower than expected power out) or the current and power measurements don't match by a factor of 3.3.

(1) This can be checked by the testers with their stored data from the PCE-830, sampled every 0.5s, because we know the current and power data was extracted for the report. During the heatup phase (which was gradual) we will see clearly how heater resistance changes with temperature. Or not.

(2) If in fact the heaters are Inconel wire then there is an error between the power and current measurements between dummy and active tests. this would have the effect of over-estimating COP by X3.3 and can only be resolved by the testers working out what caused this error.