Eric,
Originally I was expecting to have a forth order relationship due to radiation but it did not happen. I have made numerous curve fits to the data shown on the live site of the MFMP and it always fits to a nearly perfect quadratic. The typical R^2 value is .9998 with the values. I just completed another fit to the latest USA calibration run and then used my solution to the non linear differential equation along with a short time constant adjustment for the leading edge and it is virtually a perfect match to their data. I used the transition of input power from 58.6 watts to 79.9 watts. The temperature began at 127.5 degrees C and ended at 153.3 degrees C. I applied a digital filter with a time constant of 100 seconds to the error data and the end result is quite good. The worst case error is + and - .4 degrees C over the complete time range. The end noise appears random about the zero error line and has the appearance of 1/f or 1/f^2 electronic noise. I do not see any evidence of the transition waveform in the final result so the differential equation solution must be ideal. I wonder if the remaining noise is due to supply output voltage noise? Of course slow changing long term noise of this nature most likely contains effects due to ambient air currents, etc. I think that I will be capable of detecting excess power is it is compared to this same calibration cell. 1 watt stands out quite well. The time domain technique should be more sensitive to changes within the cell than just one average temperature reading. I have no idea of how accurate their power measurements are, but DC can be determined very accurately. The time ahead will be interesting. Dave -----Original Message----- From: Eric Walker <[email protected]> To: vortex-l <[email protected]> Sent: Wed, Dec 26, 2012 9:08 pm Subject: Re: [Vo]:Non Linear Model of Celani Device On Dec 25, 2012, at 11:15, David Roberson <[email protected]> wrote: During the night Santa brought me a gift! A thought occurred to me that there is a very good explanation for the 30 to 40 second time constant exponential waveform that I have been seeking. In order to get the best curve fit to the exact solution of the differential equation I have been forced to modify the constant of integration slightly away from the ideal value as determined by steady state measurements. Interesting discussion concerning the model you've been working on. Concerning the second-order equation, what you're describing sounds quite similar to the equation Ed Storms proposes in his Calorimetry 101 paper. I believe he is consciously ignoring radiative losses. Concerning the calculation of the error, there is the error of the fit of your curve with the MFMP data, and there is the error of the MFMP instrumentation (I assume). The error of the latter is related to the scatter in their calibration runs and is of two kinds -- stochastic and systematic. I believe that the instrumentation error could easily swamp out 1W purported XP. Concerning the 40 second constant you're adding, I wonder if this is related to the time the system requires to reach equilibrium; when you're calibrating the device, I think you need steps that last long enough for the cell to attain a new equilibrium after the change in input power. In a live cell, I suspect this same characteristic of the operation of the cell would manifest itself as a kind of momentum. Forty seconds might be too short to be this, however. Eric
