GP-B Post-Flight Analysis—Final Report - Gravity Probe B - Stanford ...

12.4.4 Update of lifetime estimateAfter the passage of over a year since launch, six HPM measurements (see below) had been made and otherinformation became available that caused a significant change in our lifetime estimate. Our new estimate wasfor depletion to occur on September 1, 2005, for a total lifetime of 499 days or 16.4 months, an increase of 1.7months over the initial estimate. This corresponds to an average boil-off rate of 7.8 mg/s. The reason for thechange was that early in the mission there were insufficient HPM operations to establish a trendline and it wasassumed that the flow meter results were accurate. As more HPM data, which correlated well with ATC flowrate values, became available, it became clear that the flow meter results were too high, and they wereconsequently discounted.12.5 Heat pulse measurement (HPM) operationThis section discusses the heat pulse measurement (HPM) procedure that was used to determine the amount ofliquid helium remaining in the dewar at various points in the mission.12.5.1 Principle of operationThe HPM operation is a calorimetric technique involving the addition of a known amount of thermal energy tothe main tank and measuring the resulting temperature rise to determine the mass of liquid helium. This can bedone to a reasonable degree of accuracy for three reasons: 1) The heat capacity of the main tank is dominated bythat of the liquid helium, 2) the thermodynamic properties of liquid helium are well known, and 3) the fact thatthe measurement involves superfluid helium means that the liquid is highly isothermal and that its thermalrelaxation time is virtually instantaneous. (This is true of even separate pockets of liquid but not true of thevapor phase, as will be discussed below.) In order to make the most accurate measurement, however, it is usefulto defeat the ATC pressure control loop and maintain a constant flow rate throughout the entire heat pulseperiod. The amount of heat added is chosen such that it is expected that the temperature rise will be on the orderof 10 mK. This is a large enough temperature rise to allow a reasonably accurate measurement of thetemperature rise yet not so large as to significantly affect dewar lifetime. Because of the potential to adverselyaffect lifetime, the hardware used to supply power to the heat pulse heaters is designed with redundant shutoffmechanisms. In addition, they are limited in number (four in a year vs. typically four a day for the flow meter)in order to limit impact on lifetime and risk.There is another issue that should be noted. The amount of helium deduced from the HPM for a giventemperature rise is proportional to the amount of thermal energy deposited into the main tank. The intentionwas to infer the energy from the measurement of the voltage across the heater resistance in conjunction with themeasured current or known heater resistance. The measurement was to be made with a standard four-terminaltechnique. This is important because the electrical leads that traverse the thermal gradient of a dewar are madeof a relatively resistive material (manganin) in order to limit thermal conductance. Unfortunately, due to adesign oversight, the input of the op-amp used to measure the voltage was referenced to ground, as was thecurrent source. This meant the measured voltage included the voltage drop across some of the electrical leads,which, in turn, introduces a potential scale factor error. This also meant that the inferred quantity of heliumcould be in error by some factor and the consumption rate could also be off by the same factor. It is essential tonote, however, that since this is a scale factor error, it does not affect the zero intercept, the projected time ofdepletion.The only effect that is likely to cause a bias error, which does affect the projected time of depletion, is a source ofheat capacity in addition to that of the liquid helium. Additional, unaccounted for, heat capacity would lead toover-estimation of the quantity of liquid and the lifetime. There are two candidates in this regard: the main tankassembly and the helium vapor. The former is completely negligible: The main tank, taken as 250 kg ofaluminum, has a heat capacity approximately equal to one part in 10 4 of 100 kg (~1/3 of initial fill) of liquidGravity Probe B — Post Flight Analysis • Final Report March 2007 341