PDS_VERSION_ID = PDS3 RECORD_TYPE = STREAM OBJECT = TEXT INTERCHANGE_FORMAT = ASCII PUBLICATION_DATE = 1999-07-25 NOTE = "ASCII description of ASI calibration" END_OBJECT = TEXT END CALIBRATION OF THE GALILEO PROBE ATMOSPHERE STRUCTURE INSTRUMENT Tony C.D. Knight and Alvin Seiff 1.0 Instrument Overview ========================== The Galileo Probe Atmosphere Structure Instrument was designed to make in-situ measurements of the thermal structure of the Jovian atmosphere, i.e., the variation of temperature, pressure and density with altitude. The end objective was to improve our understanding of the local dynamics and thermodynamics of the atmosphere at the probe entry site. The specific scientific objectives were summarized at the time of the experiment proposal as: 1. To accurately define the state properties as a function of altitude below the 100 mb level to an atmospheric pressure of about 20 bars. 2. To define the state properties of the upper atmosphere. 3. To measure the stability of the atmosphere, and identify convective layers and stable layers, where they exist. 4. To detect cloud levels from changes in lapse rate at their boundaries. 5. To define state properties within the clouds, and thus provide supplementary information on cloud composition. 6. To search for and characterize wave structures in the atmosphere. 7. To search for and measure intensity and scale of turbulence in the atmosphere. 8. To measure vertical flow velocities above a threshold of about 0.3 m/s. 9. To establish an altitude scale for use in correlating all probe experiment data. 10. To define the probe vertical velocity, necessary to the analysis of the Doppler wind experiment. These objectives can be responded to by analysis of a sufficiently accurate set of data from sensors directly sampling the atmospheric temperature and pressure, and by accelerometers measuring orthogonal accelerations of the probe center of gravity. The Galileo experiment operated in two measurement modes, one to accommodate conditions of high speed entry at low ambient density (entry mode); the other, the very different conditions of parachute descent (descent mode). There was also a calibration mode which provided instrument calibration data whilst still in free-fall prior to entry into the Jovian atmosphere. The entry mode started at a nominal ambient density threshold of about 10^(-11) kg/m^3 where the probe deceleration was about 15 micro g. From measurements of probe deceleration under the action of atmospheric drag, atmospheric densities were derived. The density profile was integrated above a given altitude to define the pressure at that level, and the temperature profile was then obtained through the equation of state, by use of the variation of atmospheric mean molecular weight with altitude we generated by modeling the upper atmosphere consistent with the experiment data. At initial entry the Probe velocity was about 48 km/sec. At high velocities, it was enveloped by a bow shock wave and a thin shock layer of ionized, luminescent gases at extreme temperatures (~15,000K at peak). Under these conditions, measurements of the ambient atmosphere by means of conventional low-density sensors are not possible. Measurements of atmospheric density by way of probe decelerations, however, provides a direct means of sensing the atmosphere ([Seiff et al, 1973], [Seiff and Kirk, 1977], [Seiff et al, 1980]). This mode of operation continued until the parachute was deployed. During the subsequent parachute descent of the probe to the 'end-of-mission', the thermal structure of the atmosphere was defined by direct measurements of temperature, pressure, and acceleration. After the parachute was deployed, the heat shield was jettisoned and temperature and pressure sensors were exposed to the ambient atmosphere. Acceleration measurements were continued at much less frequent intervals. In the absence of large vertical winds the accelerometers continued to define atmospheric density; but since other probe instruments defined atmospheric composition and hence molecular weight, density was defined by the pressure and temperature measurements. This made it possible to use the accelerometer data to define the magnitude of vertical winds above a threshold of a few tenths of a meter/sec. Altitudes relative to the 1 bar level were defined by the temperature and pressure data integrated in the equation of hydrostatic equilibrium. These data were used to establish the altitudes of measurement for all probe experiments. They also defined the rate of descent, necessary to the determination of zonal winds in the analysis of Doppler wind experiment. In addition, atmospheric turbulence and Probe angle of attack were sensed or derived. The measurements were implemented by : a) Four accelerometers located as close to the center of gravity of the probe as was practical. Two accelerometers (z1 and z2) measured the axial accelerations (for redundancy in the critical axial direction) and one sensor measured in each of the lateral directions (x and y). Each of the axial sensors operated in four measurement ranges: 1) 0 to 0.123 m/s/s with a resolution of approximately 3.0x10^(-5) m/s/s per count, 2) 0 to 3.92 m/s/s with a resolution of approximately 0.00096 m/s/s per count, 3) -62.7 to +62.7 m/s/s with a resolution of approximately 0.0306 m/s/s per count, 4) 0 to 4016 m/s/s with a resolution of approximately 0.98 m/s/s per count, The lateral accelerometers operated in three ranges. The magnitude of the resultant of the lateral accelerations was computed for each measurement. The three nominal measurement ranges for the resultant were: 1) -0.17 to +0.17 m/s/s with a resolution of approximately 0.00068 m/s/s per count, 2) -11.0 to +11.0 m/s/s with a resolution of approximately 0.0435 m/s/s per count, 3) -177 g to +177 m/s/s with a resolution of approximately 0.696 m/s/s per count. Range changes were controlled by the central electronics b) Two temperature sensors for direct sampling of the atmospheric temperature were exposed to the ambient atmosphere when the aeroshell was jettisoned. Both were platinum resistance thermometers. One (T1) was designed to have a very rapid response. This resulted in a relatively delicate sensor. The second sensor (T2) was more rugged and provided redundancy, but had a slower response. The measurement ranges were: T1: 0 to 520 K with a resolution of approximately 0.12 K per count, T2: 0 to 560 K with a resolution of approximately 0.13 K per count, c) Three pressure sensors had a common inlet and manifold. The inlet faced into the wind to measure free stream total pressure after it was exposed to the ambient atmosphere by jettisoning of the aeroshell. The pressure sensors ranges were: p1, 0 to 0.5 bars with a resolution of approximately 0.0005 bar per count, p2, 0 to 4 bars with a resolution of approximately 0.004 bar per count, p3, 0 to 28 bars with a resolution of approximately 0.028 bar per count, A summary of all the measurements taken during the operational portion of the mission is shown in Table 1. Table 1 Measurements Summary ================================= Axial Accelerometer Range 1: Nominal Measurement Range: 0 to 0.12255 m/s/s Word Length (bits): 12 Nominal LSB Resolution: 0.000030 m/s/s Axial Accelerometer Range 2: Nominal Measurement Range: 0 to 3.92155 m/s/s Word Length (bits): 12 Nominal LSB Resolution: 0.000958 m/s/s Axial Accelerometer Range 3: Nominal Measurement Range: - 62.745 m/s/s to 62.745 m/s/s Word Length (bits): 12 Nominal LSB Resolution: 0.030652 m/s/s Axial Accelerometer Range 4: Nominal Measurement Range: 0 to 4015.67 m/s/s Word Length (bits): 12 Nominal LSB Resolution: 0.98063 m/s/s Axial Accelerometer Temperatures: Nominal Measurement Range: -75 C to 75 C (also accurate above 75 C) Word Length (bits): 8 Nominal LSB Resolution: 0.6 C Lateral Accelerometer Range 1: Nominal Measurement Range: - 0.17331 m/s/s to 0.17331 m/s/s Word Length (bits): 8 Nominal LSB Resolution: 0.000680 m/s/s Lateral Accelerometer Range 2: Nominal Measurement Range: - 11.0918 m/s/s to 11.0918 m/s/s Word Length (bits): 8 Nominal LSB Resolution: 0.043497 m/s/s Lateral Accelerometer Range 3: Nominal Measurement Range: - 177.469 m/s/s to 177.469 m/s/s Word Length (bits): 8 Nominal LSB Resolution: 0.69596 m/s/s Lateral Accelerometer Temperatures: Nominal Measurement Range: -75 C to 75 C (also accurate above 75 C) Word Length (bits): 8 Nominal LSB Resolution: 0.6 C Science Temperature Sensor 1: Nominal Measurement Range: 0 to 520 K Word Length (bits): 12 Nominal LSB Resolution: 0.12 K In-Flight Calibration: Recorded Measurement Word Length (bits): 12 Nominal LSB Resolution: 0.00122 V Science Temperature Sensor 2: Nominal Measurement Range: 0 to 560 K Word Length (bits): 12 Nominal LSB Resolution: 0.13 K In-Flight Calibration: Recorded Measurement Word Length (bits): 12 Nominal LSB Resolution: 0.00122 V Science Temperature Offset: Recorded Measurement Word Length (bits): 12 Nominal LSB Resolution: 0.00122 V Pressure Sensor 1: Nominal Measurement Range: 0 to 0.5 bars Word Length (bits): 10 Nominal LSB Resolution: 0.000489 bars Sensor Temperature: Nominal Measurement Range: -75 C to 75 C (also accurate above 75 C) Word Length (bits): 8 Nominal LSB Resolution: 0.6 C Pressure Sensor 2: Nominal Measurement Range: 0 to 4 bars Word Length (bits): 10 Nominal LSB Resolution: 0.00391 bars Sensor Temperature: Nominal Measurement Range: -75 C to 75 C (also accurate above 75 C) Word Length (bits): 8 Nominal LSB Resolution: 0.6 C Pressure Sensor 3: Nominal Measurement Range: 0 to 28 bars Word Length (bits): 10 Nominal LSB Resolution: 0.02737 bars Sensor Temperature: Nominal Measurement Range: -75 C to 75 C (also accurate above 75 C) Word Length (bits): 8 Nominal LSB Resolution: 0.6 C Pressure Sensor In-Flight Calibration: 1.25 Volt Stimulus: Recorded Measurement Word Length (bits): 10 Nominal LSB Resolution: 0.00488 V 3.75 Volt Stimulus: Recorded Measurement Word Length (bits): 10 Nominal LSB Resolution: 0.00488 V Central Electronics Temperature: Nominal Measurement Range: -95 C to 110 C (also accurate above 110 C) Word Length (bits): 8 Nominal LSB Resolution: 0.8 C A/D Converter 1: Offset: Recorded Measurement Word Length (bits): 12 Nominal LSB Resolution: 0.00122 V 2.5 Volt Stimulus: Recorded Measurement Word Length (bits): 12 Nominal LSB Resolution: 0.00122 V A/D Converter 2: Offset: Recorded Measurement Word Length (bits): 12 Nominal LSB Resolution: 0.00122 V 2.5 Volt Stimulus: Recorded Measurement Word Length (bits): 12 Nominal LSB Resolution: 0.00122 V ******************** End of Table 1 ******************** The instrument electronics received and executed commands from the Probe systems and thereby set the experiment mode to Calibrate, Entry, or Descent. They controlled the measurement sequences, selected sensor ranges, collected data from the three sensor sets, amplified signals, performed A/D conversions, did some on-board data processing, and conditioned instrument power. There were two A/D converters in the electronics. The assignment of the various sensors to the A/D converters are shown in Table 2. Table 2 A/D converter channel measurement allocations ====================================================== A/D Converter #1 z1 Accelerometer x Accelerometer T1 (Free Wire Sensor) Temperature T1 Reference T2 Reference (during calibration) p1 (0-500mb) pressure Sensor A/D Converter #2 z2 Accelerometer y Accelerometer T2 (Bonded Sensor) Temperature T2 Reference (except during calibration) T Offset p2 (0-4b) pressure Sensor p3 (0-28b) pressure Sensor Engineering Temperatures ******************** End of Table 2 ******************** 2.0 Calibration ================== 2.1 Mission Environmental Considerations =========================================== At the time of instrument design, the thermal environment within the probe during the mission at Jupiter, as specified by the Probe Project Office and implemented by the probe contractor, was to fall between -20 C and +50 C. The pressure sensors were qualified for -30 C to +60 C, and together with the accelerometers, were calibrated for -20 to +50 C. Since it was recognized that the pressure sensors were sensitive to high rates of change of temperature, a science requirement on maximum temperature rate (1 C/min) was written, and the effects on offset of rates of change of temperature were measured for the p2 and p3 sensors at rates between -1 and +3.5 C/min. For the accelerometers, limited measurements of effects of temperature rate were obtained during transition between static calibration temperatures at rates of about 1 C/min. During descent on Jupiter, temperatures within the probe greatly exceeded the predictions. Temperatures within the various ASI sensors ranged from a low of about -50 C to a high of over 117 C, with rates of change of temperature as high as -7.3 C/min. As a consequence, for a considerable part of the mission the sensors were outside the temperature range of calibration and were operated at high rates of temperature change as well, so that they were not at thermal equilibrium. Flight spare and engineering unit sensors were tested after encounter at temperature conditions experienced in Jupiter descent, but the response of all sensors to these extreme conditions is not identical. Procedures used to apply the test and calibration data to flight data were described in Seiff et al, 1998, Appendix B. 2.1.1 Analog to Digital converters. ===================================== The A/D converters were calibrated by applying precise test voltages at 0.02 v intervals to their input terminals and recording output in counts. Internal housekeeping/calibration data shows that the converters remained within calibration temperatures throughout the mission. No corrections are required. 2.1.2 Temperature Sensors ============================ When the temperature of the sensor amplifier became relatively high towards the end of the mission, the offsets of the amplifiers appeared to show some temperature sensitivity. The internal calibrations associated with the temperature sensor measurements allowed appropriate corrections to be made. 2.1.3 Pressure Sensors. ========================= For reasons explained above, it was necessary to extrapolate the calibration data for offset and scale factor for sensor temperatures >50 C and <-20 C. Several methods were explored and compared. Use was made of the Acceptance Test calibrations at temperatures from -30 C to +60 C, as well as data taken from -50 C to +70 C on the Flight Spare and Engineering sensors, to characterize generic behavior. In addition, the sensor manufacturer was consulted. He was able to combine the predicted variation of the temperature compensation network with the empirical observation of the effect of temperature on the sensing head to obtain a partly analytical prediction of the extended calibration. The first and most obvious method of extrapolation was to assume that the calibration equations which fit the calibration data at 5 temperatures within the expected range apply outside this range as well. Since the equations for offset are cubics in temperature, they tend to significant variation outside the calibration temperature range (see Figs. A2 and A3 by Seiff et al., 1998. A second, more conservative approach was to use linear extension of the calibrations at the terminal slopes at high and low ends of the calibration range. The equations finally used reflect engineering judgment to choose among these alternatives. Uncertainty in offset extrapolation is the dominant uncertainty in the pressure data (Table 4, Seiff et al., 1998). The uncertainties quoted by Seiff et al. (1998) are based on the differences among the extrapolation options. The sensor temperature rate corrections on offsets of the p2 and p3 sensors were based on pre-launch data taken with the flight sensors. These data were shown in Fig. A4 of Seiff et al., 1998. They were extremely valuable although limited in range compared to that experienced in flight. It was assumed that the correction was linear with temperature rate beyond the range of the tests. Corrections for hysteresis in the temperature rate effect were based on tests of the Engineering Unit and Flight Spare sensors which extended to the full range of dT/dt experienced in flight. The spare sensor data also confirmed the assumption of linearity in the effect with temperature rate. Sensor temperatures were measured only for the most sensitive sensor on-scale, with the assumption that the other sensor active at the same time would be at the same temperature. In the environment encountered this assumption was seen to be not accurate--there is clear discontinuity in sensor temperature rate at the transition from p2 prime to p3 prime. The estimated temperature of the p3 sensor while p2 was prime has been included in this document. Toward the end of the mission, every 64 seconds, the p3 sensor data jump high for 4 samples, and then return back to the generally increasing curve. These jumps are small at the beginning and grow in size with rising instrument temperature. They occur at the sampling time of one of the engineering temperature sensors, during which a current is passed through a platinum sensor. It is thought that the reading offsets result from leakage within a multiplexer chip caused by the elevated temperatures, allowing a voltage to appear on the p3 calibration line. These high data spikes should be ignored in analyzing data. The calibration data for the pressure sensors in this document include both the equations derived from the calibration data and also the equations used for final decommutation of the data as our best estimates. If you go back to use these data make sure you know which set you are using! 2.1.4 Accelerometer sensors. ============================== The rates of change of temperature were sufficiently high to show some effect on the accelerometers. Without a correction, it can be clearly seen that the differences between the readings of the two z-axis sensors (although small) correlate with the rate of change of temperature. Fortunately, some data were recorded during temperature transients between calibration temperature levels, but only at rates of change of temperature of the order of 1 C/min. These limited data have been used to estimate small corrections. During calibration testing, the x sensor was found not to work reliably at temperatures lower than about -14 C. At the time it was thought that the sensor would not reach this temperature during the mission (or if so, for only a very short time), and since there was no alternate sensor available, this performance was accepted. The actual mission environment put the sensor below this temperature for an extended period of time during which the lateral acceleration output from the instrument is unreliable. There is no evidence that any of the other sensors experienced a similar problem, with onset at minimum temperatures lower than -30 C, during the mission. The calibration equations were used to extrapolate sensor scale factor and offset outside the -20 to +50 C range. The temperature sensitivity of the sensors was such that this was judged to be reasonably accurate. 2.2 Analog to digital converters ================================ 2.2.1 Configuration. =================== Calibrations were performed on the flight instrument analog-to-digital (A/D) converters in 1982 prior to delivery of the instrument. The instrument was installed in a temperature controlled oven in a laboratory environment, and calibrations were performed at three oven temperatures: nominally -20 C, at +24 C, and at +50 C. Decommutation of the internal electronics temperature sensor showed stabilized internal temperatures to be approximately -21 C, +25.5 C, and +51 C. Calibration voltage inputs to the electronics were made through the accelerometer connector and the calibration voltage was applied in parallel to all of the accelerometer inputs (i.e. to the z1, z2, x, and y inputs). The applied voltage was conditioned within the instrument electronics prior to application to the converters. The z1 and z2 sensors signals in ranges 1,2, and 4 pass through a nominal times 2 amplifier. The z1 and z2 sensors in range 3 and all x and y sensor inputs are passed through a nominal 2.5V offset stage with unity gain. This input scheme requires some interpretation of the results, as discussed later. A stable high precision calibration voltage source (with precision voltmeter) was used and the input voltage was stepped to provide calibration data through the nominal range and up to a 28% over-range condition (for conservatism, since it was possible that some outputs could go over-range towards the end of descent). The response to the stimulus was measured by operating the instrument in the calibration mode and consequently at each voltage setting twelve output measurements were made. During calibration each sensor signal is sampled 16 times over a one-half second period and the 16 sample sum is truncated to a 12-bit output. The appropriate A/D converter offset, measured at the start of the calibration cycle, is subtracted from the sensor measurements within the ASI electronics prior to placement of the sensor outputs in the data stream. 2.2.2 Results. ============= The calibrations performed allow several possible analysis paths. The following sections investigate and compare different approaches for the analysis. Recommendations are made in section 2.2.3. The overall result is that the A/D converters were accurate and linear to within about 1 count, but were corrected for these small deviations from linearity and scale factor. 2.2.2.1 A/D converter internal calibration voltage. ================================================== Each A/D converter provides an internal calibration measurement derived from a precision 2.5 volt source. This source is derived from the A/D converter reference voltage (as were all calibration stimuli within the ASI) and consequently should track any changes in the reference voltage. Using this internal calibration data alone the following calibration constants are indicated: A/D converter #1: 1.2201 mV/bit A/D converter #2: 1.2207 mV/bit Nominal performance = 5000 mV/4096 bits = 1.2207 mV/bit The small difference in sensitivity between the two converters is supported by other measurements and appears to be real even though it falls within worst case measurement errors for the data. For example the T2 reference measurement made using A/D #1 during Calibration was a count of 3671 and a count of 3669 when using A/D converter #2 during Descent. 2.2.2.2 A/D converter applied voltage calibration. ================================================= The A/D converter calibrations as measured are potentially impacted by instrument electronics which lie between the applied voltage and the A/D converters. Four items are of interest: 1) The value of the nominal 2.5 V offset associated with the gain of x 1 amplifier 2) The gain of the nominal x 1 amplifier 3) The gain of the nominal x 2 amplifier 4) Amplifier offsets. Any offset of the gain of x 2 amplifier will contribute to the A/D converter offset error and any offset of the gain of x 1 amplifier will contribute to the 2.5 V offset error. Gain errors will result in A/D converter slope errors. In the hardware, as configured, there were two independent accelerometer signal processing channels. The z1 and x accelerometers have their own amplification chain and are converted to digital in A/D #1. The z2 and y accelerometers have their chain and are converted to digital in A/D #2. The accelerometer signal voltage comes into the instrument central electronics through a multiplexer into a high input impedance amplifier with unity gain and then into internal conditioning electronics described above. The gains are controlled by appropriate resistor networks. All resistors for a channel are high stability Vishay resistors contained within a single package and so should provide reasonable gain stability. The 2.5 Volt offset is derived from the A/D converter reference voltage and so should also be very stable in it's tracking of the reference voltage. It would appear that the major potential source of error is a temperature sensitivity in the operational amplifier offset voltages in all stages including the offset voltage. Analyses have been run in which the above parameters have been held constant at the nominal values and also allowed to float while obtaining the best least squares fit to the data. These computations were performed for voltage inputs to the A/D converters in the range 0 to 4.8 Volts. The analysis technique for each of the cases was as follows: Case 1: All parameters were held at the nominal values; Case 2: The gains were held at the nominal values and the 2.5 V offset allowed to float; Case 3: The x 2 gain was held at the nominal value and the other parameters allowed to float; Case 4: The x 1 gain was held at the nominal value and the other parameters allowed to float; Case 5: All parameters were allowed to float Examination of the various fit results shows an obvious temperature sensitivity associated with the 2.5 V offset. Improvements in fit are obtained when all parameters are allowed to float. Although the improvement is not fundamentally significant when the potential data measurement errors are considered it does indicate that we should consider tailoring calibration constants for each measurement type. To be specific, the accelerometer measurements may need a slightly different calibration constants set from all the other measurements. The difference between the input data and the best fits show that the A/D converter linearity begins to roll-off at about the 4.6 Volt input level (about 3750 DN). It must be pointed out however that we can not differentiate between an amplifier characteristic and an A/D converter characteristic as being the cause for this roll-off. The results of these fits, which used data in the 0 to 4.8 V range, can be used with reasonable accuracy to at least the nominal A/D converter full scale. Beyond full scale (a measurement condition not encountered in the mission) additional correction would be advisable. (Note: The p3 data did exceed the 4.8V level when the 1.25V calibration input voltage was applied late in the descent.) The Case 5 data provides the following values for the A/D converter slopes: A/D converter #1: 1.2200 mV/bit A/D converter #2: 1.2205 mV/bit The data also indicate a slight temperature sensitivity with the slope increasing by a total of 0.4 microV/bit over the full 70 C temperature range. This is about +0.0057 microV/bit/degree C. The fits generated by the Case 2 analyses are appropriate for the accelerometer measurements. Temperature sensitivities of the gains are relatively small when compared with the offset variation and very little additional error is generated by rolling all of the temperature effects into the offset variation (it results in an increase in the fit standard deviation of only 6 microV which is insignificant when compared with other error sources, and the assumption certainly simplifies data processing). Case 2 data provides the following values for the A/D converter slopes: A/D converter #1: 1.2198 mV/bit A/D converter #2: 1.2204 mV/bit The linear fit equations for the variation in offset with temperature are: Channel 1: Offset = 2.4988 + Temp x 1.0699 x 10^(-5) Channel 2: Offset = 2.4978 + Temp x 3.5787 x 10^(-5) where the offset is in volts and the temperature in degrees C. The variation with temperature is consistent with case 5. It is important to note that the actual value for the Offset is not really important unless there are significant temperature changes during the mission after the calibration sequence. Actual values, as measured during calibration, were used for internal processing by the instrument. 2.2.3 Discussion and Recommendations. ==================================== The applied voltage calibrations show agreement with the internal calibrations and lie well within the bit error spread. In fact it could be argued that there is little difference of significance between any of the results. The following values for the various calibration constants appear to represent the best data available from the A/D converter calibrations and should be used. 2.2.3.1 Accelerometer Data Measurements. ======================================= Use the following (zero degree C data): A/D converter #1: 1.2198 mV/bit A/D converter #2: 1.2204 mV/bit Slope sensitivity to temperature = +0.0057 microV/bit/degree C. Channel 1: Offset = 2.4988 + Temperature(C) x 1.0699 x.10^(-5) Channel 2: Offset = 2.4978 + Temperature(C) x 3.5787 x.10^(-5) 2.2.3.2 All other Data Measurements. =================================== Use the following (zero degree C data): A/D converter #1: 1.2200 mV/bit A/D converter #2: 1.2205 mV/bit Slope sensitivity to temperature = +0.0057 microV/bit/degree C. 2.3 Temperature Sensors ========================== The flight temperature sensor, SN 153, was the first flight unit manufactured. Its first and probably most accurate calibration was performed on Nov. 25, 1981 at Rosemount, prior to shipment. It was enclosed in a plastic bag, totally immersed in a sequence of 5 baths of known temperature, and, at temperature equilibrium, element resistances were recorded to the nearest tenth milliohm (the last figure and possibly the preceding one are of doubtful repeatability and significance). The baths were ice-water, boiling water, liquid nitrogen, liquid oxygen, and an undescribed bath at a temperature of 477.6 K. Subsequently, the sensor was calibrated at Ames: at the ice point 5 times over the period from Jan., 1983 to Jan., 1988; in liquid nitrogen 6 times from Jan., 83 to May, 85; in a dry-ice/acetone bath in May, 85; and at the boiling point of water 3 times from Jan., 83 to May, 84. The Ames calibration technique evolved over time, but had one essential difference from that at Rosemount: The sensor mounting pad was not immersed in the baths. Thus, there was some conduction of heat down the stem, as there was on the probe at Jupiter. In 1995, an Ames test dedicated to evaluating the effect of temperature difference between the mounting pad and sensor head or stem conduction on measured temperature under conditions simulating those expected in flight indicated that, at the test conditions, the effect was about 0.001 C/degree of temperature difference from mounting pad to atmosphere. Extrapolated to the heat transfer conditions of flight, it was even smaller by orders of magnitude. The associated calibration error in a stirred bath at 0 C was evaluated to be about 10^(-2) C. A second difference between Ames and Rosemount calibrations was that, in early Ames calibrations, the sensor was directly immersed in liquid nitrogen, in an ice bath, and in boiling water without bag enclosure. This practice was later abandoned, being found to degrade the insulation resistance as a result of moisture seeping into the insulation inside the sensor frame through pin hole leaks in the brazed joints of the tubing. Insulation resistance returned to normal values when the sensor was kept at vacuum overnight in an oven at 90 C or higher. To avoid moisture in the insulation, Ames calibrations after 1983 were typically performed with the sensor immersed in intermediate baths of methyl or ethyl alcohol, which do not lower the insulation resistance and which evaporate quickly. To somewhat simulate the flight situation, the sensor was immersed in calibration baths only to the rings on the sensor stem, where the flexible closure to the probe aerofairing was made. Values of Ro, the ice point resistance of T1 and T2, for SN 153 were constant to within 0.01 ohm (0.2 K) over periods of 4 to 5 years. In 1983, repair of an insulation resistance short at the lead-to-sensor junction of T2 caused an increase in (R2)o of 0.11 ohm. In June and July, 1992, from a critical evaluation of the collected data, selected values of the sensor resistances at 0 C, Ro, were 14.007 ohms (T1) and 10.486 ohms (T2). Final values, derived just prior to encounter, and used for mission analyses were 14.017 ohms for T1 and 10.504 ohms for T2. The original Rosemount Ro for T1 was 13.9994 ohms. The difference, 0.0176 ohms, corresponds to 0.32 K. In November, 1983, the sensor was coated with parylene to prevent shorting of the sensor by conductive cloud droplets. This coating was overlaid with 1000 Angstroms of gold to maintain the sensor exterior surface at the electric potential of the probe. Calibrations made before and after this date on SN 153 and other sensors indicated that the calibration was not significantly affected by these thin coatings. Liquid nitrogen calibrations using the above Ro's showed very small uncertainty and excellent repeatability. The T1, T2 differences were extremely small, of order of 0.03 K. To test the sensors over the higher temperature range to 500K, a closed circuit flow channel was built, in which gas (air or helium) was circulated at atmospheric pressure at a velocity of 4.2 m/sec. Electrical heaters warmed the gas to match the rate expected in descent on Jupiter. T1 and T2 readings were compared with one another, and with readings from calibrated thermocouples. There were temporal and spatial variations in temperature of the order of +0.4 K in the flow through this channel. When the environment was cooling from 500K back to room temperature, flow temperatures were more uniform. Under these conditions, T1 and T2 agreed within about 0.3K from 330 to 420 K. With corrections for non-simultaneous sampling and for the response lag of T2, which was 12 to 50 X larger in the channel than on Jupiter, disagreement of the two elements was about 0.15 K at 420 K. The quantitative accuracy of these results was limited to a few tenths K by the spatial and temporal fluctuations, non-simultaneous sampling and response lag of T2. Tests made at the sensor level and end-to-end with the electronics showed that the end-to-end data were consistent with analog sensor level calibrations within 1 count. Tests with and without the electrostatic discharge shield (Seiff and Knight, 1992) showed that it did not significantly affect the readings. Overall, the data suggest a maximum absolute calibration uncertainty for both T1 and T2 sensors of about 0.3K at 500K, where absolute error should be maximum. The uncertainty at 273 K was about 0.1 K, and at 100 K, about 0.1 K. Relative accuracy over short time spans should be limited only by the resolution, 0.013 K. Expected response times are 16 msec at deployment to 5 msec at 16 bars for the primary sensor, and from 300 msec to 80 msec for the secondary. 2.3.1 Calibration Equations: ============================== 2.3.1.1 T > 273.15 K ======================= From the Callendar-Van Dusen equation and constants defined by resistance measurements at three temperatures at Rosemount, T1 = 3409.37 - [3409.37^(2) - 1.71256 x 10^(6) x (R1/(R1)o - 1)]^(1/2) From the collected ice-point calibrations, (R1)o = 14.017 ohms (element resistance at 0 C). R1 = count x 0.00663456 ohms Similarly, for the secondary sensor, T2 = 3638.575 - [3638.575^(2)- 1.83254 x 10^(6) x (R2/(R2)o - 1)]^(1/2) (R2)o = 10.504 ohms (element resistance at 0 C). R2 = count x 0.00545423 ohms 2.3.1.2 T < 273.15 K ======================= Below the freezing point of water, the International Practical Temperature Scale (IPTS) defined by Table 3 gives the "reference function" w(T) = R/Ro(T) for pure platinum wire, where Ro is the wire resistance at 273.15 K. The table extends from 75 K to 273.15 K, where w = 1.0 by definition, at intervals of 1 K. Accuracy is said to be within 0.001K. Values of temperature at an observed ratio of R/Ro can be interpolated from this table. Table 3 International Practical Temperature Scale (IPTS) ============================================================= Temp(K) w(T) Temp(K) w(T) Temp(K) w(T) Temp(K) w(T) 75 0.1779612 125 0.3933832 175 0.6023647 225 0.8066035 76 0.1822761 126 0.3976259 176 0.6064893 226 0.8106505 77 0.1865963 127 0.4018657 177 0.6106121 227 0.8146963 78 0.1909211 128 0.4061025 178 0.6147331 228 0.8187406 79 0.1952499 129 0.4103363 179 0.6188523 229 0.8227836 80 0.1995821 130 0.4145671 180 0.6229697 230 0.8268253 81 0.2039171 131 0.4187951 181 0.6270854 231 0.8308656 82 0.2082544 132 0.4230201 182 0.6311994 232 0.8349046 83 0.2125935 133 0.4272423 183 0.6353116 233 0.8389422 84 0.2169339 134 0.4314617 184 0.6394221 234 0.8429785 85 0.2212752 135 0.4356783 185 0.6435309 235 0.8470135 86 0.2256171 136 0.4398921 186 0.6476381 236 0.8510472 87 0.2299591 137 0.4441032 187 0.6517435 237 0.8550796 88 0.2343010 138 0.4483116 188 0.6558473 238 0.8591107 89 0.2386425 139 0.4525173 189 0.6599495 239 0.8631405 90 0.2429831 140 0.4567203 190 0.6640500 240 0.8671689 91 0.2473229 141 0.4609207 191 0.6681488 241 0.8711961 92 0.2516613 142 0.4651186 192 0.6722461 242 0.8752220 93 0.2559983 143 0.4693138 193 0.6763417 243 0.8792466 94 0.2603337 144 0.4735066 194 0.6804358 244 0.8832699 95 0.2646672 145 0.4776968 195 0.6845282 245 0.8872920 96 0.2689987 146 0.4818846 196 0.6886191 246 0.8913127 97 0.2733281 147 0.4860699 197 0.6927084 247 0.8953322 98 0.2776552 148 0.4902527 198 0.6967961 248 0.8993504 99 0.2819799 149 0.4944332 199 0.7008823 249 0.9033674 100 0.2863020 150 0.4986114 200 0.7049670 250 0.9073831 101 0.2906216 151 0.5027871 201 0.7090501 251 0.9113976 102 0.2949384 152 0.5069606 202 0.7131317 252 0.9154108 103 0.2992524 153 0.5111318 203 0.7172117 253 0.9194227 104 0.3035636 154 0.5153007 204 0.7212903 254 0.9234334 105 0.3078718 155 0.5194673 205 0.7253673 255 0.9274428 106 0.3121771 156 0.5236318 206 0.7294429 256 0.9314510 107 0.3164793 157 0.5277941 207 0.7335169 257 0.9354580 108 0.3207786 158 0.5319542 208 0.7375895 258 0.9394637 109 0.3250747 159 0.5361121 209 0.7416606 259 0.9434682 110 0.3293677 160 0.5402679 210 0.7457303 260 0.9474715 111 0.3336575 161 0.5444217 211 0.7497984 261 0.9514735 112 0.3379442 162 0.5485733 212 0.7538652 262 0.9554743 113 0.3422277 163 0.5527229 213 0.7579305 263 0.9594739 114 0.3465080 164 0.5568705 214 0.7619943 264 0.9634722 115 0.3507852 165 0.5610160 215 0.7660567 265 0.9674693 116 0.3550592 166 0.5651596 216 0.7701177 266 0.9714652 117 0.3593300 167 0.5693012 217 0.7741773 267 0.9754598 118 0.3635976 168 0.5734408 218 0.7782354 268 0.9794532 119 0.3678620 169 0.5775784 219 0.7822922 269 0.9834454 120 0.3721233 170 0.5817142 220 0.7863475 270 0.9874364 121 0.3763815 171 0.5858430 221 0.7904015 271 0.9914262 122 0.3806366 172 0.5899800 222 0.7944541 272 0.9954147 123 0.3848885 173 0.5941101 223 0.7985052 273 0.9994020 124 0.3891374 174 0.5982383 224 0.8025550 273.15 1.0000000 ******************** End of Table 3 ******************** A small further correction given by the Rosemount calibration compensates for deviations of individual sensor calibrations from the International Practical Temperature Scale, IPTS, of Table 3. These corrections, of order 0.15 K maximum, are defined by the respective equations for T1 and T2, Delta(w1) = -4.560x10^(-4)+0.136883x10^(-4)xT-4.40009x10^(-8)xT^(2) Delta(w2) = 22.448x10^(-4)-0.27888x10^(-4)xT+7.201109x10^(-8)xT^(2) These corrections are to be subtracted from measured values of w before converting to temperature. The corrections are not very well defined for temperatures between 110 and 250 K, since the defining data were located only near the end points. Perhaps the greatest contribution of the dry-ice in acetone bath calibration was to provide a confirming point at 188.7 K, where the agreement of the ASI sensors with the Lab Standard thermometer was, in 4 cases out of 8, within 0.1 K. It was improved by the Delta(w) corrections in one comparison, was essentially the same in another, and was worsened in two comparisons. The T1, T2 agreement was improved by the corrections in both of the two tests analyzed. 2.4 Pressure Sensors ======================= 2.4.1 Decalibration Overview. =============================== The response of the Tavis pressure sensors to applied pressure is nearly linear, but the small departures from linearity should not be neglected. The decalibration procedure first defines the pressure for a linear sensor, then applies a small non-linear correction. The primary calibration constants are sensor scale factors, in mb/mV or b/v; the offsets, or readings at zero pressure, in mV; and the characterization of non-linearity. All are slightly sensitive to sensor internal temperatures, which are measured once per major frame. The initial step in the decalibration is to obtain an equation representing sensor temperatures as functions of time. This variation is used to calculate the calibration constants appropriate to each measurement time. Note: Sensor temperatures derived from the mission data are shown as a function of time in Table 4. Sensor temperatures should be derived from this table by interpolation. Sensor offsets, in mV, do not repeat identically from turn-on to turn-on. Nominal variation is about 10 mV (2 counts). The initial offsets at encounter were taken from pre-entry calibration data (PEC). (The offset has been shown to remain stable through full range pressure cycles after turn-on. In the encounter, the sensors were turned on prior to entry and remained on through end of mission.) Test data have shown that offset varies not only with sensor temperature, but also with temperature rate as a result of temperature nonuniformity within the sensor. The corrections for temperature rate have been derived post mission by a series of tests and analytical considerations and the best estimates are shown in Table 5. Values used should be derived from this table by interpolation. The decalibration can thus be represented by the following equation: plin = [Reading - Offset(T, dT/dt)] . SF(T). p = plin + Delta(pnl), Reading and Offset in mV. The notation "Offset(T,dT/dt)" indicates offset is a function of T and dT/dt, while "SF(T)" indicates SF is a function of only T. Equations describing these variations and the non-linear corrections Delta(pnl) are given below. Note also that a final value for atmospheric pressure to be derived from the sensor pressures is a further correction for the ram effect associated with the probe falling through the atmosphere. This dynamic pressure correction is computed from 0.5 rho V^2. It had a nominal value of -5 mb. When computed point-by-point from velocities derived from dp/dt, the rate of pressure increase, it was found to be somewhat noisy, giving values from -4 to -9 mb. The noise was introduced by the digital resolution of the pressure data, and should not be considered to be real variation in the dynamic pressure. It is recommended that a constant value of - 5 mb be used except possibly in the first few pressure samples before equilibrium descent is achieved. 2.4.2 Scale Factors. ====================== For Readings and offsets in mV, the linear scale factors are defined as a function of temperature by: Range 1: SF = 0.099723 + 7.6456x10^(-6)xT mb/mV, T in degrees C, Range 2: SF = 0.80554 mb/mV, no temp dependence. Range 3: SF = 5.58727 + 3.99134x10^(-4)xT + 1.84459x10^(-5)xT^(2) - 2.76134x10^(-7)xT^(3). The behavior of the p3 sensor outside of the calibration range was not so predictable as within the calibration range. It was found necessary to go to a higher order polynomial to match the behavior over the much wider mission temperature range. The modified (for the mission temperature environment) expression for range 3 that should be used for analyses is: SF=5.5891+3.7684x10^(-4)xT+8.74925x10^(-6)xT^(2)-3.31945x10^(-8)xT^(3)- 1.214898x10^(-9)xT^(4) +7.33478x10^(-12)xT^(5). 2.4.3 Offsets: ================ The offset or bias at turn-on a few minutes before Jupiter entry, was measured in Calibrate Mode at temperature T, from which the value at zero degrees C, B0C, is calculated. B0C = (B- Delta(B)pec) DeltaB(T) is given for each range by equations fitted to the calibration data. The values of B at temperatures experienced in Descent are then calculated from B(T) = B0C + Delta(B(T)) 2.4.3.1 Range 1: =================== Tp = -1.23 C in PEC Delta(B) = 0 plus or minus 5 mV (1 count). There was no offset temperature dependence within the narrow temperature range over which this sensor was on-line. 2.4.3.2 Range 2: =================== Tp = -1.15 C in PEC The equation derived from the data of Feb. and July, 88 is, Delta(B) = 0.98757xT + 0.048228xT^(2) - 0.00124071xT^(3) mV, T in deg C. 2.4.3.3 Range 3: =================== Tp = -1.50 C in PEC. The following equation derives from 4 data sets, taken between April, 84 and July, 88, DeltaB = 1.27221xT - 0.0173129xT^(2) + 5.72365xT^(3) mV. 2.4.4 Nonlinearities: ======================= 2.4.4.1 Range 1: =================== The correction is small, and unsymmetrical, and ranges from +0.5 mb at 100 mb to -0.7 mb at 350 mb. Delta(pnl) = 0.905-0.00184xp-2.635x10^(-5)xp^(2)+5.294x10^(-8)x p^(3). This equation represents data taken at temperatures from -15 degrees C to +50 degrees C within the scatter. The correction equation is not applicable at p < 100 mb. It gives the erroneous result Delta(pnl) = 0.905 mb at p = 0, where Delta(pnl) is zero by definition. Through the series of calibrations, corrections repeat only within a few tenths of a mb. In 1983, a peak deviation from linearity of ~-1.2 mb occurred at 300 mb and 50 degrees C (a condition not expected to occur in flight), and at 100 mb, the +0.5 mb correction of the equation was, instead, -0.2 mb. The change is attributed to sensor aging or diaphragm relaxation, and the small diaphragm deflection force available at these pressures. It implies possible errors of 0.5 mb or 0.1% of full scale. 2.4.4.2 Range 2: =================== The behavior on Range 2 was orderly, and is represented by a parabola with its maximum at mid-range and a temperature dependent amplitude. The correction at pressure p is: Delta(pnl) = A[1 - (1 - p/2)^(2)], where 2 bars is the mid-range pressure. The temperature variation of the amplitude is represented by A = -9 - 0.1776xT-0.003436xT^(2)+0.0001158xT^(3) mb, T in degrees C. Note that A is negative. It peaks at -14.5 mb (3.6 counts) at 35 K. Accuracy is probably no better than 1 mb , or 1/4 count on Range 2. The form of A(T) is similar to that of Delta(B(T)). 2.4.4.3 Range 3: =================== The nonlinear corrections are well defined and were stable over a period of years to within a few mb. They were not symmetrical about mid range, but peaked at around 8.5 to 9 bars. No simple, single equation fits the data well. To permit analytical representation, the data were fitted on each side of the peak independently at two temperatures, 20 degrees C and 50 degrees C. Corrections were derived from the 4 equations which follow with linear temperature interpolation. E.g., at sensor temperature = 35 degrees C, the correction was the mean of those at 20 and 50 C. Within 0 to 9 bars range at 20C: Delta(pnl) = 0.16 + 23.216xp + 1.130xp^(2) - 0.187xp^(3) Within 9 to 28 bars range at 20C: Delta(pnl) = 153.7 + 8.362xp - 0.9569xp^(2) + 0.01656xp^(3) Within 0 to 10 bars range at 50C: Delta(pnl) = 0.78 + 19.36xp + 2.351xp^(2) - 0.2537xp^(3) Within 10 to 28 bars range at 50C: Delta(pnl) = 218.9 + 1.372xp - 0.7060xp^(2) + 0.01354xp^(3) 2.4.5 Pressure sensor temperatures derived from Mission data =============================================================== Table 4 Pressure Sensors Temperatures =============================================== Time p3 Temp Time P3 Temp Time p1 Temp (sec) (C) (sec) (C) (sec) (C) 0 0.0 1648 -4.0 0 0.0 50 -0.8 1712 0.7 48 -0.6 100 -3.7 1776 5.4 150 -8.1 1840 10.0 200 -13.5 1904 15.1 250 -19.0 1968 19.6 300 -24.0 2032 24.1 350 -28.3 2096 29.0 400 -32.0 2160 33.9 450 -35.2 2224 38.2 500 -37.7 2288 42.9 550 -39.7 2352 47.6 Time p2 Temp 600 -41.1 2416 52.2 (sec) (C) 650 -42.0 2480 56.7 700 -42.6 2544 61.2 0 0.0 750 -43.0 2608 65.1 48 -0.6 800 -42.9 2672 69.4 112 -5.3 850 -42.5 2736 73.7 176 -11.9 900 -41.7 2800 77.9 240 -19.8 950 -40.8 2864 82.1 304 -27.2 1008 -39.3 2928 85.7 368 -34.2 1072 -37.3 2992 89.7 432 -39.3 1136 -34.8 3056 93.2 496 -43.8 1200 -31.6 3120 97.1 560 -46.4 1264 -28.5 3184 100.4 624 -48.4 1328 -24.7 3248 104.2 688 -49.0 1392 -21.0 3312 107.5 752 -49.0 1456 -16.7 3376 110.7 816 -47.7 1520 -12.4 3440 114.2 880 -45.7 1584 -8.2 3504 117.6 944 -43.1 ******************** End of Table 4 ******************** 2.4.6 Temperature Rate Correction to P2 and P3 Offsets ========================================================= Corrections for temperature rate were derived from tests of the flight sensors before launch, and from tests of the engineering model and flight spare sensors after encounter. These corrections and their derivation were discussed in Appendix B, Seiff et al., 1998. The corrections are tabulated below at each sample interval, first for range 2, the 0 to 4 bar sensor, and then for range 3, the 0 to 28 bar sensor. The corrections are given to the nearest millibar, which is 1/4 count on range 2 and 1/28 count on range 3, but are uncertain to ~20% of the values given (Seiff et al., 1998). Cubic spline interpolation of the following table is recommended for determining correction values at intermediate times. The corrections are to be added to the values of pressure derived by the procedures outlined above. Table 5a Temperature Rate Corrections for P2 Sensor ====================================================== Time Delta P2 Time Delta P2 Time Delta P2 secs bars secs bars secs bars 2.23 -0.001 356.23 -0.102 708.23 -0.016 36.23 -0.010 388.23 -0.097 740.23 -0.011 68.23 -0.018 420.23 -0.089 772.23 -0.005 100.23 -0.025 452.23 -0.079 804.23 -0.001 132.23 -0.033 484.23 -0.069 836.23 0.003 164.23 -0.042 516.23 -0.060 868.23 0.005 196.23 -0.056 548.23 -0.051 900.23 0.008 228.23 -0.080 580.23 -0.042 932.23 0.011 260.23 -0.099 612.23 -0.035 956.23 0.013 292.23 -0.106 644.23 -0.029 324.23 -0.106 676.23 -0.022 ******************** End of Table 5a ******************** Table 5b Temperature Rate Corrections for P3 Sensor ====================================================== Time P3 Delta Time P3 Delta Time P3 Delta secs bars secs bars secs bars 34.2 -0.003 1214.2 -0.123 2430.2 0.304 62.2 -0.047 1278.2 -0.094 2494.2 0.308 126.2 -0.114 1342.2 -0.072 2558.2 0.302 190.2 -0.168 1406.2 -0.053 2622.2 0.279 254.2 -0.269 1470.2 -0.027 2686.2 0.242 318.2 -0.331 1534.2 0.004 2750.2 0.201 382.2 -0.359 1598.2 0.035 2814.2 0.168 446.2 -0.398 1662.2 0.063 2878.2 0.149 510.2 -0.421 1726.2 0.087 2942.2 0.141 574.2 -0.395 1790.2 0.111 3006.2 0.139 638.2 -0.360 1854.2 0.135 3070.2 0.139 702.2 -0.334 1918.2 0.161 3134.2 0.139 766.2 -0.305 1982.2 0.186 3198.2 0.140 830.2 -0.273 2046.2 0.209 3262.2 0.140 894.2 -0.243 2110.2 0.231 3326.2 0.141 958.2 -0.226 2174.2 0.250 3390.2 0.142 1022.2 -0.207 2238.2 0.267 3454.2 0.145 1086.2 -0.177 2302.2 0.282 3502.2 0.148 1150.2 -0.149 2366.2 0.295 ******************** End of Table 5b ******************** 2.5 Accelerometers ===================== 2.5.1 Decalibration Overview. ================================ The basic accelerometer calibrations were done before and after qualification testing at Bell Aerospace in Dec., 1983 and Feb., 1984, at four temperatures from -20 to +50 degrees C. In 1985, a resistor in the temperature compensation network of the z1 sensor failed and had to be replaced by Bell. After repair, on July 2, 1985, the z1, z2, and y sensors were calibrated a third time. The x-axis sensor was not recalibrated at this time because the x axis was used as the horizontal axis of rotation. It is also important to be aware that the x-axis sensor is limited to temperatures above -14.7 degrees C by the available travel of its internal bellows, the function of which is to allow expansion and contraction of the fill fluid. The x-axis calibration became erratic below ~15 degrees C. The other 3 sensors operate properly down to at least -20 degrees C. Scale factors and offsets were measured by rotating the sensors in the Earth's gravity field, used as a calibration standard. In Bell's calibration lab, 1 g = 9.803880 m/s/s. At bench level in the high bay of Ames building 244, it is 9.799284 m/s/s. The difference is 0.047%. On the higher ranges, the sensors were rotated through 360 degrees. For ranges <1g, rotation was stopped at the full scale reading, and bias and scale factor were determined from accurate leveling and accurate angle measure. The zero level orientation was transferred from a range which permits 360 degree rotation. On Range 4, it was considered undesirable to rely on calibration below 1 g to define the full 410 g range. The above procedure was therefore supplemented by stimulus current calibrations to full scale g levels with the sensor at room temperature, both at Bell and at Ames. The stimulus current calibrations were found to agree with the 0 to 1 g calibrations within 0.18% in z1 and 0.15% in z2, which indicates two things: 1) that Bell had measured the signal at 1g accurate within a few micro volts, and 2) that sensor response to acceleration is highly linear. The variations of scale factor with temperature on Range 4 were thus taken from the 0 to 1 g calibrations, and the absolute levels were corrected by use of the more accurate stimulus currents. At Ames, room temperature calibration checks were performed on all ranges at each complete instrument test from 1984 through 1988 in the Ames 1 g field. An accurate dividing head was used to set sensor rotation angles and the ASI electronics were use to take readings. There was no significant disagreement with the Bell results. The three Bell scale factor calibrations repeated typically to 3 significant figures or better. However, bias shifts from turn-on to turn-on, varied by as much as a few hundred micro-g's. The calibration equations were derived from the Bell data by fitting polynomials to the calibration data points. The calibration of July, 1985, was used as the calibration of record, except for x, for which the final calibration after qualification testing in Feb., 1983 was used. The disagreements among Bell calibrations in both scale factor and bias were small uniform shifts of values at all temperatures, indicating that the shifts were systematic. Temperature dependence was well duplicated among them. The conversion of direct acceleration readings from counts to m/s/s is similar to that of the pressure data. First, offset is subtracted from a reading to obtain the net reading, a, in counts. a = Reading - Offset (counts) Offset or bias, B, is the reading at zero input, and is a function of sensor temperature, Ta , which is monitored by internal resistance thermometers in each sensor. B = Bo + DeltaB(Ta) Bo, the bias at 0 degrees C, is obtained from the sensor output during pre-entry calibration (pec), when acceleration is zero. Bo = Bpec - DeltaB(Tpec) where DeltaB(Ta) is defined by the bias temperature dependence equation, DeltaB(Ta) = a1T + a2T^(2) + a3T^(3). The coefficients a1, a2, and a3 are given in the equation for B(T) for each sensor. Since Bo is not constant over long periods of time, values of Bo given in the figures, obtained during calibration, are discarded in favor of those determined from pre-entry calibration. For the z sensors in range 3 and for the x and y sensors in all ranges an additional offset correction needs to be made for the temperature sensitivity of the 2.5 V offset in the A/D converters, using the temperature of the electronics (Te) as the variable (not the temperatures of the accelerometer sensors). The relevant equation then becomes: B = Bo + DeltaB(Ta) + bias(2.5V) With Bo, B, and bias(2.5V) determined, the net reading, a, in counts is obtained and converted to Earth g's (Bell g's) and to m/s/s by multiplying by the sensor scale factor in g/count and by 9.80388 m/s/s/g. a=a(counts)xSF(Ta)x9.80388 m/s/s. 2.5.2 Lateral (x and y) Outputs. =================================== Measurements from the two lateral accelerometers were output directly as 12-bit words only in the pre-entry calibration sequence. During both entry and descent, because of the Probe memory limitation, the measurements were processed within the instrument to provide the absolute magnitude of the resultant lateral accelerations as 8-bit words. The processing comprises the following steps: 1) The x and y measurements were each converted to absolute magnitude and rounded to 8-bit words 2) The 8-bit words were squared and summed. The sum was multiplied by 2 3) The square root of the resulting 18 bit word was computed. 4) The resulting 9-bit word was rounded to 8-bits. This 8-bit word was written into the data stream. Converting the lateral accelerometer outputs to m/s/s involves an assumption and some uncertainty since the relative contributions of the x and y sensors are not known. The truncation of the measured data to 8-bit resolution (made necessary by the available data rate and the memory allocation), simplifies the data conversion in that temperature variation of the 2.5V offset and the effects of temperature rate can be neglected compared with the resolution. The assumption we have made in our processing is that the x and y sensors contribute equally to the resultant. This approach is equivalent to averaging the calibration characteristics of the x and y sensors and is accurate within the 8-bit resolution. (The two sensor calibrations did not differ significantly.) 2.5.3 Scale Factors and Offsets. =================================== All temperatures, T are in degrees C and the temperatures of the relevant sensor should be used. Bo is calculated from the given equations and the data for Bpec at (Ta)pec. 2.5.3.1.1 z1, Range 1 ======================== SF = 3.031112+0.00102733xT micro g/count B(T) = Bo-6.13502xT+0.110072xT^(2)+0.00038325xT^(3) counts 2.5.3.1.2 z1, Range 2 ======================== SF = 97.78687-0.00122819xT+6.75857x10^(-5)xT^(2)-1.097081x10^(-7)xT^(3) micro g/count B(T) = Bo-0.165609xT+0.00310003xT^(2)+1.54201x10^(-5)xT^(3) counts 2.5.3.1.3 z1, Range 3 ======================== SF = 3.124251-8.48344x10^(-5)xT+2.329472x10^(-6)xT^(2)-1.81481x10^(-10)xT^(3) milli g/count B(T)=Bo+0.0027318xT+1.77116x10^(-5)xT^(2)+9.54626x10^(-7)xT^(3) counts bias(2.5V) = 2.4988+1.0699x10^(-5)xTe counts 2.5.3.1.4 z1, Range 4 ======================== SF =0.09992546 -7.37316x10^(-6)xT+1.310541x10^(-7)xT^(2)- 9.35486x10^(-10)xT^(3), g/count B(T) = Bo+0.017111xT-0.00017812xT^(2)+1.18678x10^(-6)xT^(3) counts 2.5.3.2.1 z2, Range 1 ======================== SF = 3.0245+0.0010298xT micro g/count B(T) = Bo+5.80895xT-0.142623xT^(2)-0.00042957xT^(3) counts 2.5.3.2.2 z2, Range 2 ======================== SF = 97.13908-0.0012158xT+5.910831x10^(-5)xT^(2)-2.586876x10^(-8)xT^(3) micro g/count B(T) = Bo+0.20203xT-0.0045407xT^(2)- 1.33422x10^(-5)xT^(3) counts 2.5.3.2.3 z2, Range 3 ======================== SF = 3.129187-8.60259x10^(-5)xT+2.119753x10^(-6)xT^(2)+ 4.724526x10^(-10)xT^(3) milli g/count B(T)=Bo+0.012702xT-0.00020403xT^(2)- 1.13519x10^(-7)xT^(3) counts bias(2.5V) = 2.4978+3.5787x10^(-5)xTe counts 2.5.3.2.4 z2, Range 4 ======================== SF = 0.099980015-6.991454x10^(-6)xT+6.879173x10^(-8)xT^(2)- 1.417768x10^(-10)xT^(3) g/count B(T)=Bo+0.013802xT-0.00014402xT^(2)+9.7716x10^(-7)xT^(3) counts 2.5.3.3.1 X Range 1 ====================== SF = 6.048933+0.001980201xT micro g/count B(T)=Bo+3.072xT-0.13209xT^(2)+1.20379x10^(-5)xT^(3) counts bias(2.5V) = 2.4988+1.0699x10^(-5)xTe counts 2.5.3.3.2 X Range 2 ====================== SF = 389.82933-0.00497574xT+0.000234946xT^(2)+2.91009x10^(-7)xT^(3) micro g/count B(T)= Bo+0.055236xT-0.0021714xT^(2)+8.6857x10^(-7)xT^(3) counts bias(2.5V) = 2.4988+1.0699x10^(-5)xTe counts 2.5.3.3.3 X Range 3 ====================== SF = 6.2529-1.6809x10^(-4)xT+4.8858x10^(-6)xT^(2)-4.566505x10^(-9)xT^(3) milli g/count B(T) = Bo+0.010707xT-0.00021814xT^(2)+6.5343x10^(-7)xT^(3) counts bias(2.5V) = 2.4988+1.0699x10^(-5)xTe counts 2.5.3.4.1 Y Range 1 ====================== SF = 6.054208+0.00209466xT micro g/count B(T)=Bo+1.2272xT-0.0935953xT^(2)+0.00067191xT^(3) counts bias(2.5V) = 2.4978+3.5787x10^(-5)xTe counts 2.5.3.4.2 Y Range 2 ====================== SF = 391.47085-0.00460025xT+0.000235361xT^(2)-4.37728x10^(-8)xT^(3) micro g/count B(T)=Bo+0.026104xT -0.0015002xT^(2)+1.02217x10^(-5)xT^(3) counts bias(2.5V) = 2.4978+3.5787x10^(-5)xTe counts 2.5.3.4.3 Y Range 3 ====================== SF = 6.249576-0.000156474xT+4.34629x10^(-6)xT^(2)-4.65324x10^(-9)xT^(3) milli g/count B(T)=Bo+0.0076413xT-0.00014503xT^(2)+7.9213x10^(-7)xT^(3) counts bias(2.5V) = 2.4978+3.5787x10^(-5)xTe counts 2.5.4 Temperature Rate Correction to z1 and z2 Offsets ========================================================= The data that forms the basis for temperature rate corrections were gathered during the periods of changing temperature during the sensor calibration tests. Data were gathered in transients from 28 degrees C to -20 degrees C, -20 degrees C to 0 degrees C, 0 degrees C to 28 degrees C, and 28 degrees C to 50 degrees C. In each data set the rate would start at zero, increase to some maximum value (a negative maximum for the first transient) and then reduce again to zero. The rates of change of temperature experienced during these tests were bracketed between about -1.2 C/minute and +0.6 C/minute. These data showed an effect on offset of changing temperatures which was not closed and which resulted in offsets from the true steady state conditions as well as offsets during the temperature transients. The rates of change of temperature during these temperature transients did not approach the rates attained during the mission ( which were bracketed between about -4.9 C/minute and +4.3 C/minute.) and consequently analyses have been kept relatively simple. The approach followed has been to compute offsets as a function of temperature rate and compute the best straight line fit for the initial transient to maximum rate of change for each of the temperature transients and then a second fit from the maximum rate of change back to zero. (For example, for z1 for the 28 degrees C to -20 degrees C transient the slope of the fit to the data while the rate was increasing is -8.1373.10^(-5) V/degrees C/min and the slope while the rate was decreasing is -9.237.10^(-5) V/degrees C/min). These slopes are then used for all rates attained during the mission. Based on the above, corrections have been made for data during descent. Temperature transients were observed for the z1 and z2 sensors during the entry phase. However this transient resulted from self-heating as a result of the high energy dissipation within the sensor during the large g portion of deceleration. It is not clear that the results for self-heating should be the same as for external heating, as occurred during testing and descent. Slopes derived from the test data are: z1 Temperature decreasing, rate of change of temperature going more negative: Slope (m1) =-8.1373x10^(-5) V/degrees C/min z1 Temperature decreasing, rate of change of temperature going less negative: Slope (m2) =-9.237x10^(-5) V/degrees C/min z1 Temperature increasing, rate of change of temperature going more positive: Slope (m3) =-7.7796x10^(-5) V/degrees C/min z1 Temperature increasing, rate of change of temperature going less positive: Slope (m4) =-1.0884x10^(-4) V/degrees C/min z2 Temperature decreasing, rate of change of temperature going more negative: Slope (m1) =+1.3265x10^(-4) V/degrees C/min z2 Temperature decreasing, rate of change of temperature going less negative: Slope (m2) =+8.861x10^(-5) V/degrees C/min z2 Temperature increasing, rate of change of temperature going more positive: Slope (m3) =+5.0779x10^(-4) V/degrees C/min z2 Temperature increasing, rate of change of temperature going less positive: Slope (m4) =-4.0007x10^(-5) V/degrees C/min The computational techniques used separately for the z1 and z2 channels were: 1) For each measurement sample, starting at the beginning of descent, compute the rate of change of sensor temperature. 2) Compute the offset using the slope appropriate for the particular phase of the mission. 3) When the rate reaches a transition between slopes use the last computed offset as the starting point for the application of the new slope. 4) Convert the offset in volts to counts using the appropriate A/D converter sensitivity to yield the value for bias(Trate). The relevant bias equation then becomes: Bo+DeltaB(Ta)+bias(2.5V)-bias(Trate) The magnitude of these corrections ranges between -0.3 and +0.3 counts for z1 and between -1.6 to +0.5 counts for z2. 2.5.5 Sensor Temperature Calibrations ====================================== The equations of sensor temperature as a function of internal sensor resistance are given below. This includes data from all three Bell calibrations. Two different equations must be used to convert readings from counts to ohms for the 12 bit data of the PEC, and the 8 bit data of Entry and Descent. During Pre-entry Calibration, the equation is R (ohms) = 0.4016 (ohms/count)xReading (counts) with resolution of 0.4 ohm or about 0.11 degrees C. During Entry and Descent, the 8 bit resolution was improved by discarding the MSB, giving effectively 9 bit resolution. R (ohms) = [Reading (counts)+256]x3.2124 (ohms/cnt) , with resolution of about 0.9 degrees C. To distinguish the 4 sensor temperatures, the notation Tx, Ty, Tz1, and Tz2 is used. The resistance notation is, e.g., Rz1T is the resistance in ohms of the z1 internal temperature sensor. Tz1 = -275.48+0.2741xRz1T-3.675x10^(-5)xRz1T^(2) Tz2 = -285.67+0.2843xRz2T-3.902x10^(-5)xRz2T^(2) Tx = -276.04+0.27205xRxT-3.609x10^(-5)xRxT^(2) Ty = -279.53+0.2775xRyT-3.8363x10^(-5)xRyT^(2) 3.0 References ================= Seiff, A., Reese, D.E., Sommer, S.C., Kirk, D.B., Whiting, E.E., and Niemann, H.B.: 1973, "PAET, An entry probe experiment in the Earth's atmosphere" Icarus, 18, 525. Seiff, A., and Kirk, D.B.: 1977, "Structure of the atmo-sphere of Mars in summer at mid-latitudes", J.Geophys. Res., 82, 4364. Seiff, A., Kirk, D.B., Young, R.E., Blanchard, R.C., Findlay, J.T., Kelly, G.M., and Sommer, S.C.: 1980, "Measurements of thermal structure and thermal contrasts in the atmosphere of Venus and related dynamical observations: results from the four Pioneer Venus Probes", J. Geophys. Res., 85, 7903. Seiff, A.and Knight, T.C.D.: 1992, "The Galileo probe atmosphere structure instrument", Space Science Reviews, 60, 203. Seiff, A., Kirk, D.B., Knight, T.C.D., Young, R.E.,.Milhalov, J.D., Young, L.A., Milos, F.S., Schubert, G., Blanchard, R.C., and Atkinson, D.: 1998, "Thermal Structure of Jupiter's atmosphere near the edge of a 5 micro-metre hot spot in the north equatorial belt", J. Geophys. Res., 103, 22,857.