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**HP-41C RECURSION SOLVES IT**

*Posted by designnut on 25 Feb 2008, 3:54 p.m.*

THE SEALED VOLUME Cubic supplied a telemetry transmitter to be injected into orbit that had to operate on the ascent as well as in orbit. The high power section only was to be enclosed in a pressurized sealed chamber to prevent arc-over due to the RF power level. The lower power stages were not pressurized. A hermetic coaxial connector seal and mating surface was ordered to an 80-microinch finish. Inspection checked the surface for roughness, and then scribed crossed lines to check the centering. That did wonders for the finish. It was flushed with a mixture of helium and nitrogen, in a glove box, and then sealed. After sealing with an O ring, it was necessary to check the leak rate as it was to hold pressure for 24 months. The initial leak rate seemed much higher than the published seal leak rate. Leakage from the whole package was read. Data was available every 5 minutes for 4 hours, where the leakage seemed to stabilize at the rate the seal manufacturer predicted. The customer thought the low leak rate might mean the gas had all leaked out, and needed proof. Cubic and Lockheed had been faced with this problem for 2 years. CURVE PLOTTING Everyone had the same data. My boss, Blair plotted data on linear graphs 25 feet long, in an attempt to explain the behavior. I bought a new HP 41C pocket calculator with curve fitting capability. I keyed in the data, assuming an exponential leak rate, the correlation was 0.384, definitely not exponential. I retried it using a power law curve, and got a 0.996 correlation, it was a power law curve. The leakage rate was in very small numbers, like 10^-8 to 10^-11 cc/second. People had used time scales in minutes, hours, days and months to graph the data. I chose seconds to plot the time scale as the leakage rate was in cc/sec. I used a log-log plot to cover data from 5 minutes to 2 years, and the long leakage scale. Data fell on a straight line and after 4 hours became asymptotic to a constant leak rate predicted by the seal manufacturer. I knew a power law curve plotted as a straight line on log-log paper. I have always been expert at graphing. THE VOLUME LINE Since I had a rate in cc/seconds and a seconds time scale I realized the product was the volume of the enclosed space. I got an estimate of 50cc for that volume and plotted a sloping volume line at 50cc. There was a surprising piece of data that had been run on the equipment with the unit processed but no seal installed; none was available. I plotted the measured leakage rate after two months, it was almost off the graph, but when the initial line was extended it ran right through this point. Now I knew what was happening, it was all the parts that had adsorbed helium, and were outgassing. The customer was able to supply some long term data at 18 and 24 months. When plotted, it was on a transitional curve from the predicted seal leak rate, to the volume line. When back tracked, you could see a slight fall in the leakage rate as it neared the volume line. An exponential curve on a log-log plot would show a slight drop before the time constant point. It dropped 10% at 0.1 of the time constant. The data all fit. The leak history was nowhere near the volume line, until the long term data points, the gas could not have leaked out. RESULTS! I showed Blair and the customer the results, nobody cared. When asked, Blair thought someone else had made the plot. Nothing succeeds like success. Their nose was bent out of shape as I solved a 2 year old problem that neither company had solved. It took me a few hours to solve this knotty problem.