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NASA Technical Memorandum 4777 Design and Laboratory Validation of a Capacitive Sensor for Measuring the Recession of a Thin-Layered Ablator Gregory K. Noffz and Michael P. Bowman November 1996

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NASA Technical Memorandum 4777 Design and Laboratory Validation of a Capacitive Sensor for Measuring the Recession of a Thin-Layered Ablator Gregory K. Noffz and Michael P. Bowman Dryden Flight Research Center Edwards, California National Aeronautics and Space Administration Office of Management Scientific and Technical Information Program 1996

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CONTENTS ABSTRACT .............................................................................. 1 NOMENCLATURE ........................................................................ l Acronyms ............................................................................. 1 Symbols .............................................................................. 1 INTRODUCTION .......................................................................... 1 Background ............................................................................ 2 Thin Film Work ......................................................................... 4 SYSTEM OVERVIEW ...................................................................... 5 CANDIDATE DESIGNS, FABRICATION, AND PACKAGING .................................... 7 THEORY AND MODELING ................................................................ 10 Analytical Models ...................................................................... 10 Finite-Element Models .................................................................. 12 GAGE TESTING ......................................................................... 15 Results of Phase 1 Testing of the Initial 12 Gages ............................................. 19 Results of Phase 2 Testing ............................................................... 22 DISCUSSION ............................................................................ 25 CONCLUSIONS .......................................................................... 26 REFERENCES. .......................................................................... 28 APPENDIX: FINITE-ELEMENT GEOMETRY INPUT .......................................... 29 TABLE I. Gage geometries tested ................................................................ 13 FIGURES 1. Ablation situation ...................................................................... 2. Breakwire ablation gage ....... .......................................................... 3 3. Light pipe gage ........................................................................ 4 4. Brown's thin film probe ................................................................. 5 5. Benn's test probe (from ref. 6) ............................................................ 5 6. System setup .......................................................................... 6 7. Static measurement test setup with oscillator, reflection coefficient bridge, multimeter, and gage .................................................................... 7 iii

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, Brass ring gage ........................................................................ 8 9. Candidate geometries ................................................................... 8 10. First-generation gages ................................................................... 9 11. Second-generation gage before and after final assembly ........................................ 9 12. The 60 ... 10 gage geometry plus gage parts detail ........................................... I0 13. General gage face layout ................................................................ l 1 14. Zahn's method of approximating fringe field lines ............................................ II 15. Typical mesh geometry ................................................................. 12 16. Potential regions for 10/20 geometry; ablator thickness = 0 .................................... 14 17. Closeup of potential regions around 10/20 geometry; ablator thickness = 0 ........................ 14 18. Closeup of potential regions around 10/20 geometry; ablator thickness = 0.050 in. (1.27 mm) ......... 14 19. Electrostatic code results; capacitance as a function of ablator thickness; conductor widths = 0.005 in. (0.127 mm) ........................................................... 15 20. Electrostatic code results; capacitance as a function of ablator thickness; conductor widths = 0.010 in. (0.254 mm) ........................................................... 16 21. Electrostatic code results; capacitance as a function of ablator thickness; conductor widths = 0.020 in. (0.508 mm) ........................................................... 16 22. Electrostatic code results; capacitance as a function of ablator thickness; conductor widths = 0.040 in. (1.016 ram) ........................................................... 17 23. Summary of electrostatic code results ..................................................... 7 24. Closeup of gage test panel for phase 2 testing ............................................... 18 25. Shim test results; RCB output for gage geometries 5/10, 5/15, and 5/20 ........................... 19 26. Shim test results; RCB output for gage geometry 10/10 (sensors 2 and 8) ......................... 20 27. Shim test results; RCB output for gage geometry 10/20 (sensors 3 and 11) ........................ 20 28. Shim test results; RCB output for gage geometries 20/10/5 and 20/10/10 .......................... 21 29. Shim test results; RCB output for gage geometries 20/10 and 20/20 (sensors 1 and 5) ................ 21 30. Shim test results; RCB output for gage geometry 40/40 (sensors 13 and 14) ....................... 22 31. Shim test results; RCB output for gage geometry 40/40 (sensors 15 and 16) ....................... 23 32. Shim test results; RCB output for gage geometries 40/40 (sensor 17) and 30/30 (sensor 18) ..................................................................... 23 33. Shim test results; RCB output for gage geometries 60/20 and 60 ... 10 ........................... 24 34. Ablator test results; RCB output for gage geometry 40/40 (sensors 13, 14, 15, and 16) ............... 24 iv

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ABSTRACT RTV room-temperature vulcanized silicon RV reentry vehicle Flight vehicles are typically instrumented with SCAT shape change ablation transducer subsurface thermocouples to estimate heat transfer at the surface using inverse analysis procedures. If the vehicle has an ablating heat shield, however, temperature time histories from subsurface thermocouples no longer TC thermocouple TPS thermal protection system provide enough information to estimate heat flux at the Symbols surface. In this situation, the geometry changes and thermal energy leaves the surface in the form of ablation products. The ablation rate is required to estimate heat transfer to the surface. A new concept for a capacitive a length dimension, m or cm b length dimension, m or cm sensor has been developed to measure ablator depth us- C capacitance, pF ing the ablator's dielectric effect on a capacitor's fringe region. Relying on the capacitor's fringe region enables the gage to be flush mounted in the vehicle's permanent structure and not intrude into the ablative heat shield ap- % specific heat, J/kg-K E stored electric energy per unit length, J/m or J/cm plied over the gage. This sensor's design allows nonin- fo resonant frequency, MHz trusive measurement of the thickness of dielectric materials, in particular, the recession rates of lowtemperature ablators applied in thin (0.020 to 0.060 in. with qconduction conduction heat flux, W/m 2 (0.05 to 0.15 mm)) layers. Twenty capacitive gages k thermal conductivity, W/m. K L unit length, m or cm, or inductance, H 13 different sensing element geometries were designed, convective heat flux, W/m 2 fabricated, and tested. A two-dimensional finite-element analysis was performed on several candidate geablator- Rm x maximum radius, m ometries. Calibration procedures using qconvection q radiation radiation heat flux, W/m 2 simulating shims are described. A one-to-one corre- V spondence between system output and dielectric material thickness was observed out to a thickness of 0.055 in. (1.4 mm) for a material with a permittivity about three times that of air or vacuum. A novel method of monitoring the change in sensor capacitance was developed. This technical memorandum suggests further improvements in gage design and fabrication techniques. NOMENCLATURE Acronyms BNC bayonet navy connector BRAG backscatter radiation ablation gage PC printed circuit RAT radiation transducer (sensor) RCB reflection coefficient bridge RF radio frequency RLC resistive, inductive, and capacitive termination to a waveguide electric potential, V £t angle between plates, rad E permittivity, (C2/N • m 2) P charge density, C/m 3 Pm mass density, kg/m 3 INTRODUCTION Aerospace vehicles subjected to significant aerodynamic heating often rely on ablating thermal protection systems (TPSs) to keep the internal structure and equipment below critical operating temperatures. An ablating TPS undergoes chemical decomposition or phase change (or both) below the internal structure's critical temperature. Incident thermal energy is then channeled into melting, subliming, or decomposing the ablator. Ablator recession rate is directly proportional to the heat flux at the surface. Unless a char layer forms, the surface remains at ablation temperature as ablation products are blown into the airstream. As long as some virgin ablator remains, the substructure does not exceed ablation temperature. Figure 1 depicts a schematic of an ablating surface.

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Flow / qconvection --_ • • • • Ablator layer J / / Permanent / structure qconduction Subsurface qradiation • • • Ablation products boundary Moving Surface thermocouple thermocouple 96o5o8 Figure 1. Ablation situation. Measuring the heat flux to an ablating vehicle presents a difficult challenge. Several operational problems arise with embedding heat-flux gages or thermocouples in an ablating TPS. First, as the ablator recedes, the gage's sides are exposed to the airstream. The thermal input to the gage's side invalidates calibrations where the temperature gradient is assumed to be normal to the gage's sensing face. Second, any protruding object affects the recession rate of the surrounding ablator. Third, ablation products may contaminate the sensor's face. Finally, after ablation begins, temperatures often attain a steady state where recession rate is proportional to heat flux. A measure of ablator thickness is now required to estimate surface heat flux. The measurement method must not affect the recession rate or severely alter the conduction path through the ablator; to ensure this, the sensor is located in the permanent structure below the ablating layer. The sensor should be insensitive to temperature and, over the expected temperature range, be capable of calibration. Background Past efforts to measure recession of TPSs have concentrated on nosetips of ballistic reentry vehicles (RVs). RVs typically experience very high heating rates and are constructed with relatively thick, high-temperature ablators when compared with vehicles subjected only to ascent heating. Sensors developed for RVs can be grouped into two categories, intrusive and nonintrusive. The intrusive concepts involve installing hardware in the ablator or seeding the ablator with radioactive material. Nonintrusive methods rely on sensors and hardware in the substructure below the ablator. Legendre (ref. 1) surveys instrumentation techniques tested or proposed through 1975. Intrusive recession measurement techniques include the breakwire ablation gage, radiation transducer (RAT) sensor, and light pipe. The breakwire ablation gage consists of several thin wires implanted at various known levels in an ablator. As the material progressively erodes, each successive wire is broken and results in an open circuit. Figure 2 illustrates this concept. In some cases (ref. 2), each breakwire doubles as a thermocouple (TC) and each is situated so that no breakwire TC is directly above another. This arrangement allows an unobstructed conduction path through the ablator to each breakwire TC, including those at lower levels. Although the breakwire method provides temperature time histories until the last TC is exposed and destroyed, this method only provides recession data at a few distinct points. As another intrusive method, the RAT sensor relies on small radioactive sources placed at known depths within the TPS. As the ablator recedes, radiation sources are removed and the reduction in radiation is measured by a Geiger counter (ref. 1). A variation of this method is the shape change ablation transducer (SCAT). Implemented behind a graphite nosetip uniformly seeded with

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Ablating substructure i !i£i_I Breakwires 960509 Figure 2. Breakwire ablation gage. radioactive material, the SCAT detects recession in ar- concept; however, this sensor has radioactive "line" eas away from the nosetip using moving radiation de- sources implanted in the nosetip. A completed graphite tectors. The RAT sensor provides distinct data points nosetip is subjected to high-energy proton beams from a corresponding to the number of implant sources, where- linear accelerator. The portion of graphite that the beam as the SCAT provides continuous data. Only the RAT passes through becomes radioactive, that is, the line sensor has met with operational success. source. The advantage of this sensor is that many line sources can be induced in a single nosecap, thus indicat- The light pipe sensor consists of quartz fibers ing recession away from the stagnation point. implanted in an ablator and terminated at known depths (fig. 3). When the TPS recedes to where a fiber termi- McGunigle and Jennings (ref. 4) described an ultranates, light transmits down to a photodiode. Arrays of sonic nosetip recession sensor. This instrument emits lightpipes have been used in nosetips to ascertain shape sound waves and then measures the time required for change up to three nose radii aft of the tip. This method the echo to return from the ablator surface. This sensor provides recession data at distinct points only and was successfully tested on the ground and in flight. does not provide temperature data, as the breakwire method does. An example of a nonintrusive sensor is the backscatter Ground tests involved placing an instrumented nosetip in an arc-jet tunnel or rocket exhaust facility and comparing sensor output with motion-picture footage of the test. The sensor, essentially a microphone, detected not radiation ablation gage (BRAG). The BRAG consists of only the echo from the ablator surface but also any a gamma ray source and detector unit. The radiation amount that is reflected from the ablator is directly proportional to its thickness. According to Legendre (ref. 1), this sensor provides a useful method of measuring recession on graphite nosetips without disturbing the material. Armini and Bunker (ref. 3) developed a sensor concept with gamma ray detectors, as in the BRAG aerodynamic noise from the rocket exhaust, thus making ground tests more difficult. As the ablator (in this case, graphite, carbon composites, or metals) began to recede, a change in the speed of sound within the ablator due to elevated temperatures distorted the recession measurements. The sensors discussed above share some or all of the following traits that make them unsuitable for

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Ablating material Photo r--n S Quartz fibers 960510 Figure 3. Light pipe gage. measuring recession of the relatively thin thermal protection systems found on booster vehicles: • Resolution is of the order of the ablator thickness (0.015 to 0.060 in. or 0.381 to 1.524 mm). • Hardware tends to be large or have high power requirements (or both). • Signal-to-noise ratios are low. • The handling of radioactive materials is required. Of these sensor concepts, the ultrasonic ablation measurement system comes closest to being usable for thin TPSs: it is nonintrusive and does not involve radioactive materials. Instrumentation concepts better suited for use with thin TPSs, however, were found in connection with work on measuring thin liquid films. Thin Film Work Brown et al. (ref. 5) determined liquid film thickness by measuring the capacitance between two small wire probes protruding into the liquid. The liquid acted as a dielectric between two plates of a capacitor with the plates being two small wire probes (fig. 4). If the liquid has a different dielectric constant than air, a change in liquid level results in a change in the probe's capacitance. Benn (ref. 6) was interested in measuring film thicknesses of electrically conducting liquids. This approach involved installing two metal probes flush with the wall and measuring the electrical resistance between them. As the film got thinner, the resistance increased. This method was nonintrusive to the film layer and was unhindered by surface tension considerations, as the Brown probe was. Eventually, Benn wanted to measure film thicknesses of a nonconducting liquid, Freon 12. The same probe was used, but it measured the capacitance between the two probe elements. This technique was distinctive from other methods of measuring film thickness in that the liquid was not directly between the plates of the capacitive probe. The liquid affected only the capacitor's fringe field lines. This layout lowered the sensitivity but eliminated problems such as the liquid clinging to the probe by surface tension. Gage output was affected by changes in temperature and lead wire position. Figure 5 shows the probe geometry, with one lead being a metal tube and the second lead being a wire suspended within. The entire length of the probe assembly contributed to its total capacitance. The probe capacitance increased, but the percentage change due to changes in film thickness decreased. The capacitance changes were measured by incorporating the probe into a frequency modulation circuit. A fixed frequency was the input to the circuit, and the output frequency depended on probe capacitance. The output frequency was channeled through various filters, rectifiers, and linearizers until the system produced a DC voltage that varied linearly with film thickness. The research described in this memorandum builds on the thin film work of Benn and attempts to adopt this concept to measuring ablator layer thicknesses, in particular, those designed to protect launch vehicles like

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/ / /i iiii!i Capacitance measured between wires 960511 Wire probes / ! Solid structure Figure 4. Brown's thin film probe. S P.E.T. plug Connecting LEMO plug/ socket Wire Calibration support --_ sleeve _ /-- P.T.F.E. / / / / _- Sensor / / face wire j Thermistor--/ //End view Earth V 'f_7 connections J 960512 Figure 5. Benn's test probe (from ref. 6). the Pegasus® from ascent heating (ref. 7). Before this compared based on sensitivity, usable range of dielecsensor concept can be used on flight vehicles, several tric thickness, and ease of fabrication. To determine modifications must be made. • First, the gage sensitivity must be increased to give a high-level output. This increase makes the task signal conditioning and calibration easier. • Second, the probe's total capacitance must be general trends, various gage geometries were modeled and evaluated using a commercially available finiteof element code. Operational issues such as fabrication, system shielding and packaging, and calibration are discussed. contained as much as possible in the sensing part of Use of trade names or names of manufacturers in the probe, reducing the effect of lead-wire position this document does not constitute an official endorseand temperature. • Third, the effect of gage temperature on the measurement must be minimized with proper fabrication techniques. • Fourth, the probe's size itself must be much smaller for flight applications. ment of such products or manufacturers, either expressed or implied, by the National Aeronautics and Space Administration. SYSTEM OVERVIEW As mentioned earlier, Benn used the capacitive probe This memorandum documents the evolution of the as part of a frequency modulation circuit. The present sensor concept. Candidate designs were evaluated and work used a different concept that takes advantage of ® Pegasus is a trademark of Orbital Sciences Corp., Fairfax, Virginia. off-the-shelf hardware used for antenna tuning. The capacitive sensor is placed in series with an inductor and a resistor forming an resistive, inductive, and capacitive

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(RLC)terminationtoawaveguide(i.e.,acoaxialcable). Thearrangementshownin figure6 is verysimilarto a transmitter-antennaconfiguration.The RLC terminationhasaresonantfrequencyapproximatedby 1 fo = 2 _ ,,/L--C (1) When electromagnetic energy at the resonant frequency is sent down the waveguide, all the energy dissipates in the resistor. If, however, the resonant Ablation products • • / / Permanent structure RLC termination Wevegulde l DC out RCB frequency of the termination changes (say, because of a change in capacitance), a fraction of the energy is reflected back toward the source. As the capacitance continues to change, the energy reflected increases. Antennas that work like this are said to be out of tune. In this situation, one could use a commercially available reflection coefficient bridge (RCB) between the radio frequency (RF) source and the waveguide termination. The RCB generates a DC voltage proportional to the energy reflected. Then the antenna can be adjusted until the bridge output voltage is a minimum and the energy transmitted is a maximum. • • Abletor / f0 -- 2rt-,/"£5- ._J VHF oscillator 960513 Figure 6. System setup.

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This concept is the basis for the probe's system cir- them as thin as possible. This design maximizes the cuitry (fig. 6). The probe, along with the inductor and fraction of total gage capacitance that the fringe field resistor that form the RLC termination, is connected via lines account for. coaxial cable to a signal generator. A reflection coefficient bridge is placed between the signal generator and The first candidate design (fig. 8) consists of two the probe, and output to a voltmeter (for static measure- concentric brass rings 0.1 in. (2.54 mm) thick with the ments and calibrations) or data recorder (for transient outer ring 0.5 in. (12.7 mm) in diameter. A Delrin chasmeasurements). Figure 7 is a photograph of the bench sis holds the rings concentric. This design has a roomtest setup. The sensor mounts in the aluminum plate at temperature capacitance of 4.7 pE The design is a direct the front of the table. The signal generator is in the back- descendant of the Benn probe and served as a gage proground, and the small aluminum box next to the multi- totype for setting up the system circuitry. Using this meter is the RCB. The basic procedure involves varying gage proved that small percentage changes in gage the frequency of the signal generator until the bridge capacitance resulting from simply passing one's hand output is a minimum (ideally near zero) while the face over the gage surface could be monitored. Because it of the probe is exposed only to air. Delrin® shims of was quickly realized that a different fabrication method similar dielectric constant to the ablator and known would further increase sensitivity while simultaneously thicknesses are then placed on the probe face. Capaci- providing a convenient method to mount the other tance (and RCB output) increases with shim thickness, required electrical components, no real testing of this and a calibration curve is obtained. CANDIDATE DESIGNS, FABRICATION, AND PACKAGING design was undertaken. To minimize the thickness of the conductors, probes were made from raw circuit board material using standard techniques for printed circuit (PC) board fabrication. Figure 9 shows some candidate geometries. All To increase sensitivity of a flush capacitive sensor to geometries have a surface area of 0.25 in 2 (about changes in dielectric thickness, the volume directly be- 161 ram2). The concentric circle geometries connect tween the conductors must be minimized by making every other circle to a trace on the backside of the 060514 Figure 7. Static measurement test setup with oscillator, reflection coefficient bridge, multimeter, and gage. ® Delrin is a trademark of Dupont, Wilmington, Delaware. 7

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EC9442548-4 Figure8.Brassringgage. Through-holes required for each ring ---_ \ C A B \ Only two throughholes required 960515 Figure 9. Candidate geometries. PC board. This design requires two-sided circuit boards nonconcentric geometries, item C in figure 9, were with many connection holes drilled through the board. pursued fu_her. This presents a tedious fabrication task when the conductors become narrow. The square geometries Some preliminary tests were performed on circuitand the nonconcentric round geometries require board gages with the associated electronic components only two through-holes because the capacitor is com- attached to the board near the gage itself (fig. 10). A posed of only two plates. Consequently, only the round, more desirable arrangement, however, combines the

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Resistor ii face pattern 960516 Figure 10. First-generation gages. RLC portion of the system into a single, shielded unit of the casing opposite the sensing face. The brass casing that can be handled without fear of changing gage out- connects to the shield side of the incoming coaxial put due to changes in lead-wire location or inductor windings. Figure 11 shows such a unit. The prototype cable, thus shielding all components except the sensing element itself. The entire assembly is held together and gages consist of a brass casing (later prototypes used potted with standard room-temperature vulcanized aluminum) surrounding a Delrin chassis that holds the (RTV) silicon. Although this design is robust and easy inductor and resistor. The gage face mounts on the sur- to handle and mount in test fixtures, the use of RTV in face of the Delrin, flush with the end of the casing. A lieu of mechanical fasteners makes it unsuitable for male bayonet navy connector (BNC) installs in the rear elevated temperatures. BNC Resistor, inductor and gage face Figure 11. Second-generation 960517 gage before and after final assembly. 9

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The pattern of the capacitor itself (item C in fig. 9), while circular, does not require the extensive throughhole connections like the concentric circle pattern (item A in fig. 9) previously discussed. Initially, 12 plug-type gages were fabricated using nine of these nonconcentric round geometries with two of the geometries duplicated. After testing, 8 more gages were fabricated, for a total of 20. The last eight gages used faces etched by a company that fabricates circuit boards. Using these allowed the conductors on the gage face to connect to the backside of the board via plated throughholes, eliminating the solder bumps of the first 12 gages. The first 12 sensor casings were fabricated from brass in anticipation of soldering the shield side of the coaxial cable to the casing. During the fabrication process, a method of press-fitting a small terminal post to the inside of the casing (fig. 12) eliminated the need for a solder joint to the brass. All 20 gages use this terminal post arrangement, but the design allowed the last eight casings to be fabricated from aluminum. To further miniaturize the gage, the aluminum casings were initially made 0.1 in. (2.54 mm) shorter for an overall length of 1.13 in. (28.32 mm). THEORY AND MODELING Early in the prototyping process it became apparent that the sensor face configurations would consist of Resistor, inductor and alternating capacitor plates on a fiat substrate, as shown in figure 13. Preliminary tests also showed that several factors, including calibration procedures, slight variations in system setup, and manufacturing tolerances, could affect results. Because one purpose of this study was to determine the optimal sensor geometry (i.e., conductor width and gap configuration), we compared sensor geometries using analytical and computational methods that eliminate experimental errors. In this section, analytical approximations are explored and twodimensional, finite-element analyses of some gage geometries using a commercially available code that calculates electrostatic fields (ref. 8) are described. Analytical Models The literature about calculating parasitic capacitances of integrated circuits is one source for analytical approximations to similar geometries. As these circuits become increasingly compact, parasitic capacitance between neighboring conductors becomes more problematic. Considerable effort has gone into developing numerical and analytical approximations that give reasonable estimates of the capacitance per unit length between nearby conductors (refs. 9, 10, and 11). Zahn (ref. 12) described a method valid for pairs of roughly rectangular conductors in close proximity on the same plane (fig. 14). The fringe field lines are approximated 960518 Figure 12. The 60 ... 10 gage geometry plus gage parts detail. 10

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Substrate 960519 Figure 13. General gage face layout. I I 0 a c_= EIn(a) L I b ( 960520 Figure 14. Zahn's method of approximating fringe field lines. by semicircles and the capacitance per unit length is semicircle radius grows. In this simplistic model, a given by C/L- Eln(b/a) (2) face than a gage geometry with narrow conductors and gage geometry with wide conductors and gaps is sensitive to the presence of a dielectric further from its surgaps. This trend is evident in results from the Equation (2) only estimates the fringing component. As finite-element analysis and lab tests, described in the the conductors or gaps become wider, the maximum following section. 11

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Finite-Element Models The two-dimensional, finite-element model of each configuration consists of the maximum conductors and gaps that can fit into a distance of 0.565 in. (14.35 mm), which is the inside diameter of the casings used in all the sensors tested. In some cases, the total width was _-+0.565 in. (14.35 mm), but never deviated more than 0.010 in. (0.254 mm). Figure 15 shows a closeup of the mesh near some of the conductors for the 10/20 geometry (conductor width of 0.010 in. (0.254 mm) and gap width of 0.020 in. (0.508 mm)). From bottom to top, the model includes: • The entire thickness of the PC-board • The conductors themselves, which are represented by appropriate potential boundary conditions • A filler between and slightly above the conductors • Five successive layers of dielectric elements The first three layers of elements are 0.010 in. (0.254 mm) thick, and the last two are 0.020 in. (0.508 ram) thick. These layers can be assigned either the permittivity of air or a dielectric (i.e., ablator). For Dielectric layer number Jll[lllrllllltllllllllll 5 JlJtl[li[t[l[rllJIIllrll JIIl[lll]lllllll instance, to simulate the presence of a dielectric 0.020 in. (0.508 mm) thick, the dielectric permittivity is assigned to the first two element layers above the probe and air permittivity to the remaining three. Thus dielectric thicknesses of 0, 0.010 in. (0.254 mm), 0.020 in. (0.508 mm), 0.030 in. (0.762 mm), 0.050 in. (1.27 mm), and 0.070 in. (1.778 mm) can be simulated. Because many of the geometries were apparently unsuitable for measuring dielectric thicknesses above 0.050 in. (1.27 mm), results are presented only for the dielectric range of 0 to 0.050 in. (1.27 ram). The following is a note on nomenclature. The gage face geometries are designated by two or three numbers separated by a slash (/) or ellipsis ( ... ). The first number is the conductor width in thousandths of an inch, while the second number is the gap width. For example, 20/10 indicates a conductor width of 0.020 in. (0.508 mm) and a gap width of 0.010 in. (0.254 ram). When three numbers are used, they indicate, in order, widths of the first plate conductor, gap, and second plate conductor. Serial numbers are also used to distinguish duplicate geometries. Table 1 lists the gage geometries and their corresponding serial numbers. The 60 ... 10 geometry is a design whose conductor widths vary from 0.060 to 0.010 in. (1.524 to 0.254 mm). i liiiiiiiiiiiiiiiiirrllltrl lllll lllllllllllrrjllllllf llllll Substrete _ :fiiiitrrrl fiJiiJjii ---1 Filler _ _-- Conductors - [[IJ[rJIIIJ]lfr[lltllllJJIlllllJllllJl[Jllllltrltjiiiillrlll 960_1 Figure 15. Typical mesh geometry. 12

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Table I. Gage geometries tested. freq., gives an example of a geometry input file. Serial Conductor/gap Dry resonant number designation MHz 1 20/20 117 2 10/10 114 3 10/20 122 4 20/10/5" 130 5 20/20 124 6 20/10/10" 122 7 5/15 121 8 10/10 128 9 5/10 148 10 5/20 118 11 10/20" 117 12 20/10 132 13 40/40 93 14 40/40 95 15 40/40 98 16 40/40 97 17 40/40 98 18 30/30* 100 19 60/20 * 113 20 60 ... 10" 120 *Geometries not modeled with finite elements. An effort was made to standardize the finite-element elements along its horizontal dimension. The appendix As discussed above, the probes are fabricated using two-sided PC board. The copper is left intact on most of the probe's back side except the two solder pads surrounding the through-holes. The finite-element model approximates this uncharged conductor as a boundary at zero potential (the lower edge of figure 15). Alternating conductors are assigned potentials of+l V. The remaining three boundaries (right, left, and top) of the mesh are truncated with so-called absorbing boundary conditions (ABCs) (ref. 13) to approximate regions extending to infinity. Open region problems can require many mesh nodes, but ABCs appear to allow efficient, accurate truncation of meshes much nearer the structure of interest. The governing equation for electrostatic analysis in the presence of dielectrics is V.£VV = -p (3) where P is the charge density and V is the potential difference. The code solves for the electric field, displays the potential map, and calculates the stored energy. The capacitance of the geometry (in pF/cm normal to the plane) is found from 2E C/L = _ (4) V 2 where E is the stored electrical energy per unit length. Figures 16 and 17 are two views of the output from the models so that the effects of different conductor/gap ge- 10/20 geometry. Shaded areas represent ranges of poometries are accentuated. The models contain only the tential, with interfaces between different shades repreconductors and gaps of each configuration--not the senting curves of constant potential. Figure 16 depicts widened areas near the edges that incorporate the sol- about half the problem domain, while figure 17 is a dered through-holes on the actual sensors--because closeup. Figures 16 and 17 show elements above the these areas tend to be proportioned differently from gage surface up to a distance of 0.050 in. (1.27 mm) that gage to gage. No effort was made to incorporate the in- are assigned a dielectric constant of 3 (representative of strument casing; instead the PC board, filler, and all five an ablator). Figure 18 depicts the case when no ablator dielectric layers are extended 0.050 in. (1.27 mm) past is present. Note (fig. 18) how the curves of constant pothe end of the last conductor on each side. The computational elements nearest the conductors are a standard size independent of the configuration being modeled tential lie farther above the conductor surfaces when compared with the case for the ablator. (0.0005 in. by 0.0025 in., or 0.0127 mm by 0.0635 mm). Recall the basic parallel plate capacitor. When a This choice of size allows a constant number of ele- material with a higher permittivity than air is placed ments (four) along the vertical dimension of the conductors and some integer number along the horizontal dimension, depending on line width. Even the smallest between the plates, the capacitor can store more energy at a given voltage, that is, its capacitance increases. To see this happening more clearly for the geometries line width (0.005 in. (0.129 mm)) has at least two analyzed here, figures 19 through 22 plot capacitance 13

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Figure 16. Potential regions for 10/20 geometry; ablator thickness = 0. Figure 17. Closeup of potential regions around 10/20 Figure 18. Closeup of potential regions around 10/20 geometry; ablator thickness = 0. geometry; ablator thickness = 0.050 in. (1.27 ram). 14

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(in picofarads per centimeter) as a function of ablator slope and lower level combine for a larger percentage thickness. The slopes between five data points are indi- change in capacitance in this region than the 5/10 geomcated for each gage geometry. As expected, every gage etry. The trends continue for conductor widths of geometry is most sensitive (i.e., steep slope) to changes 0.010in. (0.254 mm), 0.020 in. (0.508 mm), and in ablator thickness between 0 and 0.010 in. (0.254 ram) 0.040 in. (1.016 mm) shown in figures 20, 21, and 22. and least sensitive to changes in ablator thickness be- Figure 23 summarizes gage average sensitivities tween 0.030 and 0.050 in. (0.762 and 1.27 mm). This re- (ApF/cm)/(mm dielectric) for dielectric thicknesses besult indicates how the gage output varies as the tween 0.030 and 0.050 in. (0.762 and 1.27 mm). Over dielectric thickness changes. When comparing different geometries, the percentage change in capacitance is important. For instance, as the this range of dielectric thickness, the 40/40 configuration's sensitivity is almost two orders of magnitude larger than that for the 5/10 geometry. gaps become wider (fig. 19) for a fixed conductor width GAGE TESTING of 0.005 in. (0.127 mm), the capacitance as a function of ablator thickness becomes more linear; that is. there are lower slopes for the thin ablator thicknesses and higher slopes for the thicker ablator thicknesses. Note, however, that the capacitance level per unit length goes down as the gap width increases. Comparing the 5/10 and 5/20 geometries in figure 19, the 5/20 geometry seems to be less sensitive to ablator thicknesses between 0 and Testing was divided into two phases, which were both conducted under room temperature conditions. The first phase involved bench-testing the candidate gages using an ablator substitute. During this phase, the ablator was simulated by Delrin shims machined to various thicknesses. The results of phase 1 testing consist of a single curve of RCB output as a function of shim thickness for 0.010 in. (0.254 mm) because its slope in this region is each probe. less than half of that for the 5/10 geometry. However, the capacitance change over this region is roughly the same percentage for both geometries. For ablator thicknesses between 0.030 to 0.050 in. (0.762 and 1.27 mm), the 5/20 geometry's higher m Slope = 0.141 Slope = 0.008 7.013 5 Capacitance, Slope = 0.255 pFIcm 4 Slope = 0.323 The second phase involved flush-mounting the gages to an aluminum plate and applying an ablator in a layer of suitable thickness. The ablator was sanded off to produce a single curve of RCB output as a function of ablator thickness for each gage. s11o Slope = 0.002 C) _ 5115 -- _" -- 5/20 Slope = 0.003 [] Slope = 0.004 3[ _ _<> __<> Slope = 0.033 / /Slope = 3.390 2 I I 0 .254 .5O8 I I I .762 1.016 1.270 Ablator thickness, mm Figure 19. Electrostatic code results; capacitance 0.005 in. (0.127 mm). 960525 as a function of ablator thickness; conductor widths = 15

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7 -- Slope = 0.406 6 - _ j Slope = 7.008 5 V Capacitance, Slope = 0.512 pFlcm 4 _ I /Slope=4.762 / Slope = 3.439 ,Y l I 0 .254 .508 10/10 Slope = 0.004 _ 10/15 --"- 10/20 Slope = 0.006 3 ........... DD t I I .762 1.016 1.270 Ablator thickness, mm 960526 Figure 20. Electrostatic code results; capacitance as a function of ablator thickness; conductor widths = 0.010 in. (0.254 mm). 7 j 6 I Slope = 0.128 5 - _ Capacitance, pFIcm | 4__ / Slope = 5.533 Ijs, ope=3..2 _ 20/20 20/10 Slope = 0.015 [] 0 .254 .508 .762 1.016 1.270 Ablotor thickness, mm 960527 Figure 21. Electrostatic code results; capacitance as a function of ablator thickness; conductor widths = 0.020 in. (0.508 mm). 16

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6 -- Capacitance, pF/cm 0 .254 Figure 22. Electrostatic code results; capacitance 0.040 in. (1.016 mm). .14 r .12 .10 Average .08 sensitivities, (ApFIcm)/ (mm thickness) .06 .04 .02 0 5110 5/15 5/20 40/40 Slope = 0.325 O Slope = 0.125 I I .508 .762 1.016 1.270 Ablator thickness, mm 960528 as a function of ablator thickness; conductor widths = 10/10 10115 10/20 20/10 20120 40/40 Geometriee 960529 Figure 23. Summary of electrostatic code results. 17

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Thephase1procedurefollows: 1. Setup theoscillator/RCB/gagecircuitasshown in figure7,usinganordinaryvoltmetertomonitor RCBoutput. 2. With nothingon the faceof the gage,varythe frequencyof the signal generatoruntil the minimumRCBoutputis notedonthevoltmeter. 3. ApplyDelrinshimsof differentthicknesseswhile recordingtheoutputof theRCB.Takecarethat eachshimis placedin thesameaxialorientation with respectto the gage.Careful placement ensuresthateachgageismeasuringthesamepart ofa possiblywarpedor unevenshim. 4. Repeatsteps1through3 for all of theremaining gages. Phase2 testinginvolvedplacingfourgagesintoa test fixturewith an ablatorcoveringthem.Thefixturewas built to allowaccuratemeasurementof ablatorthicknessovereachgageusinga dial indicator(fig.24).A two-component,commercially available ablator (ref. 14)wasappliedin liquidform.(ThermalpropertiesincludePm=1440kg/m3,k = 0.138 W/m • K, c_ = 1248 J/kg-K). Aside from the requirements of dealing with an actual ablator, phase 2 procedures were similar to those in phase 1. The phase 2 procedure follows: 1. Mount four gages at a time flush with the surface of the test fixture. 2. Set up the signal generator/RCB/voitmeter system as in phase 1 (fig. 7). Connect the termination side of the RCB to only one gage at a time. 3. For each gage in turn, vary the signal generator frequency to find the minimum RCB output. 4. Zero the dial indicator over each bare fixture. 5. Apply a layer of ablator over the fixture and gages to a depth of about 0.10 in. (2.54 mm). Allow the ablator to cure. . Record the depth of ablator over the face of each gage, using the dial indicator. . Record the RCB output for all gages in turn, while taking care to return the signal generator to the proper frequency for each gage found in step 3. . Remove a layer of ablator. Repeat steps 6 and 7. Figure 24. Closeup of gage test panel for phase 2 testing. 18

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Results of Phase 1 Testing of the Initial 12 Gages Figures 25 through 29 depict RCB output as a function of shim thickness from the initial 12 candidate geometries. Most graphs appear jagged because some shims had uneven thicknesses and some were warped after manufacture. If a shim was warped, part of it rode above the gage surface, lowering output. Compounding the problem was the solder through-holes on the 12 gages. Often, a small bead of solder formed and protruded slightly above the gage surface. If a fiat shim was placed on such a gage, it rode slightly above the gage surface thus lowering gage output. While these defects prevented us from attaining a smooth, one-to-one correspondence between RCB output and dielectric shim thickness, they were repeatedly detected by most gages. Generally, the higher the gage capacitance (narrow lines and gaps), the lower the maximum output and the lower the sensitivity or slope. Based on the finite-element analysis described earlier, we expected a lower maximum output for these gages. Over the entire dielectric range, capacitance increased by about 36 percent for the 5/10 geometry and by about 50 percent for the 20/20 geometry (figs. 19 and 21). Recall that for narrow line or gap geometries, a larger percentage change occurs over the thickness range of 0 to 0.010 in. (0.254 mm) than for wide line or gap geometries. Thus, if a shim rides above the gage surface because of warping or the presence of solder beads, it lowers the output of the gages with narrow line or gaps more severely than the output of gages with wide line or gaps. The shim tests of the initial 12 gages verified the in. ( 1.27 mm) trends evident in the finite-element analysis and predict- For instance, the third-largest shim, 0.050 (the third data point from the right on all the graphs), returned a lower RCB output than either of its neighbors state- layers of dielectric or ablator. With this lesson learned on most gages in figures 25 through 29. The same shim and the fabrication experience of the first 12 gages in ment can be made about the 0.039-in. (0.991-mm) (the fifth data point from the right). ed by Zahn's fringe field approximation; that is, wider line or gap geometries are more sensitive to the thicker mind, we designed and constructed 8 more gages. The new geometries included a 30/30, a 60 ... 10, a 60/20, Maximum RCB output ranged from less than I0 mV and five 40/40s. Figure 12 shows the 60 ... 10 gage (5/10, fig. 25) to more than 200 mV (20/20, fig. 29). before assembly. 250 2OO 150 RCB output, mV 100 50 ,y .5 1.0 511 O, gage 9 5115,gage7 --'_-- 5/20, gage 10 [] I ol 1.5 2.0 2.5 Shim thickness, mm 960531 Figure 25. Shim test results; RCB output for gage geometries 5/10, 5/15, and 5/20. 19

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250 2OO 150 RCB output, mV 100 so 0 .5 1.0 Shlm thlcknesa, mm 10110, gage 2 10110, gage 8 -;_ 1 I 1.5 2.0 2.5 960532 Figure 26. Shim test results; RCB output for gage geometry 10/10 (sensors 2 and 8). 250 200 150 RCB output, mV 100 5O [ ( 0 .5 1.0 Shlm thickness, mm 10120, gage3 10/20, gage 11 [3 I I I 1.5 2.0 2.5 960533 Figure 27. Shim test results; RCB output for gage geometry 10/20 (sensors 3 and 11). 20

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250 200 150 RCB output, mV 100 m so 0 .5 --O'-- 2011015, gage 4 20110/10, gage 6 I 1.0 1.5 2.0 2.5 Shim thickness, mm 960534 Figure 28. Shim test results; RCB output for gage geometries 20/10/5 and 20/10/10. 20110, gage 12 2sor -- ...... 2o0 ,, 150 RCB output, mV 100 50 0 .5 1.0 Shim thickness, mm 20/20, gage 1 --'-- 20120, gage 5 1.5 2.0 2.5 960535 Figure 29. Shim test results; RCB output for gage geometries 20/10 and 20/20 (sensors 1 and 5). 21

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Figures30through33depictresultsof theshimtests for thelasteightgages.Notethechangein scalecomparedwiththeplotsforthefirst12gages.Maximumoutput is morethan400 mV (sensor15and16,fig. 31) comparedwith200mVforthefirst12gagestested.For the40/40and30/30gages(figs.30 through32),RCB outputhasnearlya one-to-onecorrespondencewith shimthicknessthroughthethird-largestshim,in particularfor sensors13and15.The30/30gageoutput(sensor18,fig.32)appearsabit morejaggedthanthatforthe 40/40gagesandhasa lowermaximumofabout360mV. The60/20gage(sensor19,fig. 33)performsverysimilarlytothe30/30onlywitha lowerzeroandamaximum of about350mV. All gagesfrom 13to 19havehighoutputscompared with theinitial 12gages,andall havediscernible,positive slopesout to thethickest(0.092in. or 2.337mm) shim.The60 ... 10geometryfaredmorelikeitspredecessorsbut no worsethanthe 20/20geometries.The 60 ... 10gageresonatedatthetargetfrequencyof 120 MHzandhada verysmallzeroreading. Results of Phase 2 Testing Phase 2 testing was performed on four gages of the 40/40 geometry (sensors 13 through 16). Figure 34 400 350 300 RCB 250 output, mV 200 150 100 50 ___ I I 0 , .5 1.0 Shim thickness, mm shows the results. Note that the zero thickness output for all four gages was virtually the same as their respective zeros for the shim tests of phase 1 (figs. 30 and 31). In the shim tests of phase 1, the gages were held upright by their coaxial cables, not mounted in an aluminum plate as in phase 2. Unchanging zeros between the two tests demonstrate that the gages are properly shielded and are indifferent to the method of mounting. The gages, however, must be electrically isolated from their mounting. Maximum outputs for the phase 2 tests were about 200 mV higher than for the phase 1 shim tests. Delrin (acetal) and the ablator have similar dielectric constants (-- 3), but the rigid shims of phase l rested on top of the conductors while the ablator of phase 2, applied in liquid form, occupied the volume directly between the plates of the capacitors. The presence of ablator material in the most sensitive region of the gage resulted in a large output even when very little material remained above the conductors. This large initial jump tended to wash out the response to thicker layers of material. Nevertheless, one can still see a discernible slope at the thicker layers and similar curves to those generated by the shim tests, particularly for sensors 15 and 16. _ 40/40, gage 14 --O--- 40140, gage 13 I I I 1.5 2.0 2.5 96o536 Figure 30. Shim test results; RCB output for gage geometry 40/40 (sensors 13 and 14). 22

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450 400 350 300 RCB 250 output, mV 200 150 100 50 r l 1 0 .5 15 _ 40140, gage 16 I I I I 1.0 1.5 2.0 2.5 Shim thickness, mm 960537 Figure 31. Shim test results; RCB output for gage geometry 40/40 (sensors 15 and 16). 450 400 350 300 250 RCB output, mV 200 150 100 50 I 0 .5 O -D 40140, gage 17 30130, gage 18 I I I I 1.0 1.5 2.0 2.5 Shim thickness, mm 960538 Figure 32. Shim test results; RCB output for gage geometries 40/40 (sensor 17) and 30/30 (sensor 18). 23

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45O 350 300 25O RCB output, mV 21111 150 5O t I 0 .5 1.0 Shim thickness, mm O O 60/20, gage 19 60110, gage 20 I I I 1.5 2.0 2.5 960539 Figure 33. Shim test results; RCB output for gage geometries 60/20 and 60 ... 10. 6OO 500 400 RCB output, mV 300 200 Ill 100_-- I . _ .': -": -':- -':"" --O-- 40140,gage la _ 40140, gage 14 --'-- 40140, gage 15 ---/--- 40140, gage 16 I I I f I 0 .5 1.0 1.5 2.0 2.5 Shim thickness, mm 960540 Figure 34. Ablator test results; RCB output for gage geometry 40/40 (sensors 13, 14, 15, and 16). 24

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DISCUSSION The primary lesson learned is the effect of gage geometry on sensitivity. Finite-element analyses, analytical approximations, and test results all indicate that wider lines and gaps increase sensitivity to material above the conductors and increase the range of material thicknesses that can be quantified. Wider lines and gaps also lead to lower gage face capacitances, thus increasing the effect of stray capacitance or inductance in the rest of the gage and making it harder to produce a tuned gage using future shown in figure 7, can generate a wide range of frequenthe fabrication method described here. Because designs will incorporate wide lines and gaps, a method of tuning the gage after final assembly is required. Small, tunable capacitors and inductors are commercially available (ref. 15) and could be integrated into the RLC termination. In the present method of fabrication, the gage face, inductor, resistor, and Delrin chassis are placed in the useful. The line or gap geometry of a capacitive gage would be placed on a substrate of sufficient thickness to allow simple thermal modeling and protection for the associated electronic components. The thickness of the traces is significantly thinner (on the order of microns) than traces etched on PC board, further reducing the parallel plate component and eliminating the problem of a large initial jump in output when a material is sprayed or poured on without a coating. Although the signal generator used for this test, and cies, the gages are intended to resonate close to the same frequency (-- 120 MHz) in anticipation of using a much smaller crystal oscillator that is only slightly adjustable. Recall that after a gage's capacitance is fixed, its resonant frequency is primarily controlled by the number of turns on the inductor. From equation (1), for a given frequency, a lower capacitance gage requires a larger inductance (i.e., more turns). For the toroidal cores used the induc- in these gages, the required number of turns is quite front casing. Three lead wires (one each from tor, resistor, and casing) protrude from the casing's back. The inductor and casing leads are soldered to the shield side of the BNC and the resistor lead is soldered of the equation (1) and the core manufacturer's specifications to the other pin. Potting is forced into the back casing and air bubbles are given time to escape. The dou- be adjusted before final assembly. BNC is then simply pressed into the casing's back, bling over the lead wires connected to it. Future designs of Table 1 summarizes the resonant frequency for all the should incorporate a BNC mounted so that the axis cas- gages. While some resonated very close to the desired the BNC is parallel to the gage face. Access to the ing's back should allow soldering of lead wires without This tempted to remedy the situation. These tactics included having to double them over as the BNC is inserted. design would further cut down on stray capacitances and allow access to a tunable capacitor or inductor. All gages described here are compact and mechanically stable, and some accurately measure the thickness of dielectric materials placed above them. All, however, are unsuitable for working in high-temperature the Phase 2 testing solved some problems from the shim (= 120 °C) environments. As mentioned earlier, nonhomogeneous construction of the gage (i.e., printed circuit board, Delrin chassis, and potting with possible diffi- poured in liquid form, continuous contact was ensured air bubbles) make accurate thermal modeling very cult. In addition, the fiberglass circuit board and potting are not intended for use at these temperatures. A homogeneous substructure is needed that has known thermal properties and high-temperature capability. A technique used for depositing metallic traces on high-temperature substrates, such as quartz and Macor_, using "organo-metallic" materials could prove small, varying between about 13 and 23. In practice, all the wires within the gage contribute to the inductance and capacitance so the number of turns derived from is only a rough estimate, and the number of turns must 120 MHz, many did not, and several tactics were atusing thick-walled silicon tubing around some of the internal wires to keep them from coming too close to one another after final assembly and lengthening the sensor case to prevent wires from doubling over. The entire ordeal demonstrated the need for the ability to tune the gage after final assembly. tests but brought up new ones. The question of warped material was eliminated; because the material was with the gage surface. As the material was removed by sanding with a fiat sanding block, however, two problems arose. First, although care was taken to remove an even layer of ablator between data points, measurements indicated that the thickness of material removed ® Macor is a trademark of Coming Glass, Coming, New York. 25

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variedfor differentgagelocations.Thesevariations geometries were fabricated and tested. A twowereminimal,andaconstantmaterialthicknesscanbe assumedovereachgagefacewithouttoo mucherror. Second,smallvoids(< 0.4 mm)becameexposedand tendedtopackwiththesandingresidue.Vacuumingremovedtheresiduefrommostvoidsbutleftthesmallest onespacked.A higheroutputthanexpectedresulted afteralayerof giventhicknesswasremoved. Althougheventuallynecessaryfor everynewdesign, testingwith the actualablativematerialis inherently messy.Fortunately,most problemsassociatedwith phase2 testing(i.e.,ablatormaterialbetweentheconductors,uneventhicknessabovethegages,andthepresenceof voids)seemavoidable.First, if a dielectric material,forinstanceacommoncircuitboardcoatingis placedonthegageface,theablatormaterialcannotget into the interplateregion.Any materialpouredor sprayedoverthegageactsmoreliketherigid shimsof phase1. Recallthat this is how the finite-element modelsweresetup.Careshouldbetakentofindasuitablematerialwith aslowadielectricconstantaspossible.If theorgano-metallictechniquedescribedearlieror a similardepositionmethodis used,thinnerconductor traceswill result and the between-platevolumeis significantlyreducedto beginwith. Second,theproblemof unevenmaterialremovalcan besolvedif theentiretestfixtureis placedin a milling machineandtheablatorsimplymachinedoff. Theablatormaterialusedin this testexhibitedfinemechanical properties(it sandedmuchlikea softwoodfiller).If a differentmaterialis used,thesecharacteristicswould haveto be demonstratedfirst. A thicker test panel (i.e., about 1 to 1.5 cm) would also be required to increase rigidity. Third, if the ablator material is mixed and allowed to settle for about an hour in a sealed container (curing time is about 12 hr after the volatiles are allowed to evaporate) before application, most small bubbles from the mixing of components dissipate. This additional step, along with the use of a milling machine, helps to alleviate the void-packing problem. CONCLUSIONS A capacitive sensor concept that can nonintrusively measure the thickness of dielectric materials was developed for measuring ablator thicknesses on boost vehicles. Twenty capacitive gages with 13 sensing element 26 dimensional finite-element analysis was performed on several geometries. Calibration procedures using an ablator, as well as ablator-simulating shims, are described. 1. Through design and fabrication iterations, a capacitive gage concept that can nonintrusively measure the thickness of an adjacent dielectric shim was demonstrated. A one-to-one correspondence between system output and dielectric thickness was attained to dielectric thicknesses of about 0.055 in. (1.4 mm) for the ablatorsimulating shims. The permittivity of the material was about three times that of air or vacuum. Changes in designs, calibration procedures, and fabrication techniques are suggested to improve this performance. These changes include (a) using organo-metallic or other techniques to deposit conductors on a high-temperature substrate, (b) using a tunable capacitor to force all gages to resonate at a given frequency, and (c) using machine tools to remove ablator material during laboratory tests in lieu of hand sanding. 2. Gages with wide conductors and gaps are sensitive to a dielectric further from their surfaces than gage geometries with narrow conductors and gaps. This finding was verified by a finite-element analysis and laboratory tests, and is consistent with an analytical approximation. 3. Minimizing the parallel plate component of capacitance by decreasing the thickness of the conductors is necessary to increase sensitivity to useful levels. This finding was demonstrated by the success of 20 PC board gages relative to the gage constructed of machined brass rings. Reducing the parallel plate component further over the PC board gages by using the fabrication techniques described in this technical memorandum would improve gage performance when an ablator is applied in liquid form (as in phase 2 testing) and might eliminate the need for a permanent coating. 4. A novel system circuitry was developed that (a) gives a high-level output, (b) is insensitive to cable position and outside noise, and (c) isolates the capacitance being measured to the sensor itself. This circuitry represents a significant improvement over past designs intended for

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thin-film measurement that integrated the gage resonate at an equal frequency, they can be capacitance into a frequency modulation circuit. . The more sensitive, wide conductor or gap gages excited by a fixed-frequency crystal oscillator. . Wiring the gage casing to the shield side of the are more incoming coaxial cable provided adequate have a lower gage face capacitance and the shielding and eliminated the sensitivity of the easily affected by stray capacitances within body of the resistive, inductive, and capacitive termination (i.e., gage casing). This design makes gage to its mounting arrangement. it more difficult to have different gages resonate at Dryden Flight Research Center the same frequency using the present untunable National Aeronautics and Space Administration designs. If different gages can be made to Edwards, California, July 2, 1996 27

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REFERENCES 1. Legendre, Phillip J., "Reentry Vehicle Nosetip Instrumentation," Proceedings of the 22nd International Instrumentation Symposium, San Diego, California, 1975. 2. Hycal Engineering, "In-Depth Ablative Plug Transducers," Series #S-2835, 9650 Telstar Avenue, P. O. Box 5488, El Monte, Califomia, 1992. 3. Armini, A.J. and S.N. Bunker, "A Re-entry Vehicle Nosetip Shape Change Sensor," Proceedings of the 21st International Instrumentation Symposium, Philadelphia, Pennsylvania, 1975. 4. McGunigle, Richard D. and Michael Jennings, "Ultrasonic Ablation Recession Measurement System," Proceedings of the 21st International Instrumentation Symposium, Philadelphia, Pennsylvania, 1975. 5. Brown, Robert C., Paolo Andreussi, and Severino Zanelli, "The Use of Wire Probes for the Measurement of Liquid Film Thickness in Annular Gas- Liquid Flows," The Canadian Journal of Chemical Engineering, vol. 56, Dec. 1978, pp. 754-757. 6. Benn, D.N., "An Experimental Capacitance Liquid Film Thickness Monitor, Operating Instructions and Circuit Details," United Kingdom Atomic Energy Authority Research Group Report, Atomic Energy Research Establishment, Harwell, Berkshire, 1972. 7. Noffz, Gregory K., Robert E. Curry, Edward A. Haering, Jr., and Paul Kolodziej, Aerothermal Test Results From the First Flight of the Pegasus® Air- Launched Space Booster, NASA TM-4330. Oct. 1991. 28 8. Structural Research and Analysis Corp., COS- MOS/M Version 1.71, "Basic FEA System User Guide, Part 1," vol. 3, 2951 28th Street, Suite 1000, Santa Monica, California, May 1994. 9. Ruehli, Albert E. and Pierce A. Brennan, "Capacitance Models for Integrated Circuit Metallization Wires," IEEE Journal of Solid-State Circuits, vol. SC-10, no. 6, Dec. 1975. 10. Ruehli, Albert E., "Survey of Computer-Aided Electrical Analysis of Integrated Circuit Interconnections," IBM Journal of Research and Development, vol. 23, no. 6, Nov. 1979. 11. Shrivastava, Ritu and Kelly Fitzpatrick, "A Simple Model for the Overlap Capacitance of a VLSI MOS Device," IEEE Transactions on Electronic Devices, vol. ED-29, no. 12, Dec. 1982, pp. 1870-1875. 12. Zahn, Marcus, Electromagnetic Field Theory: A Problem Solving Approach, New York, Wiley, 1979, pp. 272-273. 13. Khebir, A., A.B. Kouki, and R. Mittra, "An Absorbing Boundary Condition for Quasi-TEM Analysis of Microwave Transmission Lines via the Finite Element Method," Journal of Electromagnetic Waves and Applications, vol. 4, no. 2, 1990, pp. 145-157. 14. Charwat, A.F., "Exploratory Studies on the Sublimation of Slender Camphor and Naphthalene Models in a Supersonic Wind Tunnel," Memorandum RM-5506-ARPA (AD-673531), July 1968. 15. Johanson Manufacturing Corp., "Thin-Trim® and Seal-Trim® Trimmer Capacitors," Rockaway Valley Road, Boonton, New Jersey, n.d.

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APPENDIX: FINITE-ELEMENT GEOMETRY INPUT C* C* COSMOS/M Geostar VI.70 C* Problem : 2010 Date : 5-SEP-93 C* C* This problem will calculate the total stored energy in the C* 20.10 geometry (from which capacitance can be derived). No C* solder pad effects are included. C* C* ASSIGN THE WORKING PLANE AS X-Y, AND VIEW AS THE X-Y PLANE, C" AND, SCALE THE PICTURE UP ONCE. PLANE,Z,0,1, VIEW, 0,0,1,0, SCALE,0, C _ C* CREATE PARAMETRIC VARIABLES FOR THE MODEL GEOMETRY, AND C" ASSIGN VALUES. C* INCHES TO METERS CONVERSION FACTOR. (FEM MODEL IS 10X) PARASSIGN,CONFAC,REAL,.254, C" C * THICKNESS VARIABLES FOR THE REPEATING LINE AND GAP. PARASSIGN,TLINE,REAL,.020CONFAC, PARASSIGN,TGAP,REAL,.010CONFAC, C* C* THICKNESS VARIABLES FOR CONDUCTORS, PCBOARD, C* FILLER,EDGES AND THE LAYERS OVER THE GAGE. THE LAYERS C* WILL BE ASSIGNED PERMITTIVITIES LATER, THUS DETERMINING C* THE THICKNESS OF THE ABLATOR PARASSIGN,TLI,REAL,.01CONFAC, PARASSIGN,TL2,REAL,.01CONFAC, PARASSIGN,TL3,REAL,.01CONFAC, PARASSIGN,TL4,REAL,.02CONFAC, PARASSIGN,TCOND,REAL,.002CONFAC, PARASSIGN,TPC,REAL,.063"CONFAC, PARASSIGN,TAIR,REAL,.02CONFAC, PARASSIGN,TFIL,REAL,.0025CONFAC, PARASSIGN,TEDG,REAL,.05CONFAC, C _ C* DEFINE MATERIAL PROPERTY SETS MPROP,I,PERMIT,17.7E-12, MPROP, 2,PERMIT, 8.65E-12, MPROP, 3,PERMIT,26.5E-12, MPROP,4,PERMIT, 8.85E-12, C _ C* VARIABLES FOR POSITIVE, AND NEGATIVE POTENTIALS. PARASSIGN, POSP,REAL, I, PARASSIGN,NEGP,REiLL,-I, C* C* SET POINT MERGE TOLERANCE PTTOL,0.000005, C* C* ASSIGN POINTS USING PARAMETRIC VARIABLES TO THE C* LEFT BOUNDARY. TPC IN THE X-DIRECTION IS USED SO C* THAT THE LEFT BOUNDARY IS NOT ON THE COORDINATE C* AXIS (SO THAT THE INFINITE BOUNDARY ELEMENTS WILL C* WORK HERE) PT,I,TPC,0,0, PT,2,TPC,TPC, 0, PT,3,TPC,TPC+TCOND, 0, C" C* FIT DRAWING TO SCREEN SCALE,0, C* C* CREATE A POINT 29

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PT,4,TPC,TPC+TFIL,0, PT,5,TPC,TPC+TFIL+TLI,0, PT,6,TPC,TPC+TFIL+TLI÷TL2,0, PT,7,TPC,TPCTFIL÷TL!÷TL2_TL3,0, PT,8,TPC,TPCTFIL÷TLI÷TL2+TL3+TL4,0, PT,9,TPC,TPC+TFIL÷TLI+TL2+TL3÷TL4,TAIR, 0, C • C* ASSIGN POINTS TO THE RIGHT BOUNDARY PT, I0 TPC+2TEDS+Ig'TLINE+ISTGAP, 0,0, PT, II TPC2TEDS+IgTLINE÷IS"TGAP,TPC,0, PT, 12 TPC+2TEDS÷I9"TLINE+ISTGAP,TPC+TCOND, 0, PT, 13 TPC+2TEDS÷I9TLINE+I8"TGAP,TPC+TFIL,0, PT, 14 TPC+2"TEDS+I9TLINE÷I8tTGAP,TPC+TFIL+TLI,0, PT, 15 TPC÷2"TEDS÷I9TLINEISTGAP,TPC+TFIL÷TLI.TL2,0, PT, 16 TPC+2TEDS÷I9TLINE+ISTGAP,TPC+TFIL+TLI+TL2+TL3,0, PT, 17 TPC+2TEDS÷I9"TLINE÷I8TGAP,TPC+TFIL÷TLI+TL2+TL3+TL4,0, PT, 18 TPC÷2TEDS÷I9TLINE+ISTGAP,TPC÷TFIL÷TLI+TL2+TL3+TL4÷TAIR,0, C C* FIT DRAWING TO SCREEN SCALE,0, C* C* ASSIGN THE MAXIMUM NUMBER OF CONDUCTORS, THE 'EQUAL' FLAG, AND C* THE COUNTER PARASSIGN,MAXLIN,INT, 19, PARASSIGN, IEQL,INT,I, PARASSIGN, ICT, INT,0, C _ #LOOP LI0 MAXLIN #LOOP L20 2 C* C" C" IF WERE AT THE LEFT SIDE OF A CONDUCTOR... C* #IF (IEQL==I) PT,,TPC+TEDG÷ICTTLINE+ICT'TGAP, 0,0, PT,,TPC+TEDG÷ICTTLINE+ICTTGAP,TPC, 0, PT,,TPC+TEDG+ICTTLINE÷ICT'TGAP,TPC+TCOND, 0, PT,,TPC+TEDG+ICTTLINE+ICTTGAP,TPC÷TFIL, 0, PARRASIGN, IEQL, INT, 0, C* C* IF WERE AT THE RIGHT SIDE OF A CONDUCTOR... C* #ELSE C* PT,,TPC+TEDG+(I+ICT)TLINE+ICT'TGAP, 0,0, PT,,TPC+TEDG÷(I+ICT]TLINE+ICTTGAP,TPC, 0, PT,,TPC+TEDG÷(I+ICT)TLINE+ICTTGAP,TPC+TCOND, 0, PT,,TPC+TEDG+(I+ICT)'TLINE+ICTTGAP,TPC+TFIL, 0, PARASSIGN, IEQL,INT, I, C* #ENDIF C" #LABEL L20 PARASSIGN, ICT, INT,ICT÷I, #LABEL LI0 C* C" ACTIVATE THE POINTS,CURVES, AND SURFACES TO PROTECT THEM FROM C* BEING ERASED WHEN YOU ERASE HIGHER PRIMITIVES LIKE THE MESHES C _ YOU CREATE. ACTKEEP,PT, I, ACTKEEP,CR,I, ACTKEEP,SF,I, C* C* VERTICALLY CONNECT THE POINTS ON THE BOUNDARIES #LOOP L28 8 CRLINE,,CRMAX+I,CRMAX+2, 3O

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#LABEL L28 #LOOP L29 8 CRLINE,,CRMAX+2,CRMA_÷3, #LABEL L29 C" C _ VERTICALLY CONNECT THE POINTS AT THE COMMON X LOCATION PARASSIGN,JCNT,INT,2, #LOOP L30 19"2 #LOOP L40 3 CRLINE,,CRMAX÷JCNT÷I,CRMAX+JCNT÷2, #LABEL L40 PARASSIGN,JCNT,INT,JCNT÷I, #LABEL L30 C* C* CREATE SURFACES ABOVE THE FILLER (CANT START A LOOP WITH A C* ZERO LABEL) SF2CR,I,4,12,0, SF2CR,2,5,13,0, SF2CR,3,6,14,0, SF2CR,4,7,15,0, SF2CR,5,8,16,0, C* C* NOW THE LEFT END SF2CR,6,1,17,0, SF2CR,7,2,18,0, SF2CR,8,3,19,0, C* C" NOW THE RIGHT END SF2CR,9,128,9,0, SF2CR,10,129,10,0, SF2CR,II,130,11,0, C* C* CREATE SURFACES FROM TWO LINES C T FIRST THE AREAS ABOVE, BELOW AND INCLUDING THE GAPS PARASSIGN,KCNT, INT,9, #LOOP L50 18 #LOOP L60 3 SF2CR,,SFMAX+KCNT,SFMAX+KCNT+3,0, #LABEL L60 PARASSIGN,KCNT,INT,KCNT+3, #LABEL L50 C* C * CREATE SURFACES IN THE REGIONS ABOVE AND BELOW THE CONDUCTORS PARASSIGN,LCNT, INT,0, #LOOP L70 19 SF2CR,,SFMAX+LCNT-48,SFMAX+LCNT-45,0, SF2CR,,SFMAX÷LCNT-47,SFMAX+LCNT-44,0, PARASSIGN,LCNT,INT,LCNT÷4, #LABEL L70 C* C* ACTIVATE PROPERTIES AND MESH C* C* C* MESH THE PC BOARD UNDER THE LEFT END... ACTSET,MP, I, M_SF,6,6,1,4,16,20,0.08,1, C* C* AND NOW THE RIGHT END M_SF,9,9,1,4,16,20,0.08,1, C t C* MESH THE PC BOARD UNDER THE GAPS M_SF, 12,63,3,4,16,4,0.08, I, C* C* MESH THE PC BOARD UNDER THE CONDUCTORS M_SF,66,102,2,4,16,8,0.08,1, C* 3]

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C" MESH THE FILLER ON THE LEFT END._. ACTSET,MP,2, M_SF,7,7,1,4,4,20,1,!, C" C" AND NOW THE RIGHT END M SF,I0,I0,I,4,4,20,I,I, C* C _ AND NOW THE GAPS M_SF,13,64,3,4,4,4,1,1, C* C* MESH THE FILLER ABOVE THE GAPS... M SF,14,65,3,4,1,4,1,I, C _ C* AND NOW ABOVE THE CONDUCTORS M_SF,67,103,2,4,1,8,1,1, C * C* MESH THE REGION ABOVE THE LEFT END... M_SF,8,8,1,4,1,20,1,1, C" C" AND ABOVE THE RIGHT END M_SF,II,II,I 4,1,20,I,i, C" C* MESH THE FIRST LEVEL ABOVE THE GAGE... ACTSET,MP,4, M_SF,I,I,I,4 12,264,1.38,1, C * C* MESH THE SECOND LEVEL ABOVE THE GAGE... ACTSET,MP,4, M_SF,2,2,1,4 8,264,1.38,1, C* C* MESH THE THIRD LEVEL... ACTSET,MP,4, M_SF,3,3,1,4 6,264,1.38,1, C" C* MESH THE FOURTH LEVEL... ACTSET,MP,4, M_SF,4,4,1,4 6,264,2.76,1, C* C* MESH THE AIR... ACTSET,MP,4, M_SF,5,5,1,4 4,264,4,1, C" C* SET THE ELEMENT GROUP TO BE 2D ELECTROMAGNETIC PLANAR ELEMENTS EGROUP, I,MAG2D,0,0,0,0,0,0,0, C* C * SET INFINITE BOUNDARY CONDITION ELEMENTS AT THE LEFT AND RIGHT C* BOLPNDARIES... BECR i,i,I, BECR 2 2,1, BECR 3 3,1, BECR 4 4,1, BECR 5 5,1, BECR 6 6,1, BECR 7 7,1 BECR 88,1 BECR 99,1 BECR I0, 10 BECR ii, ii BECR 12, 12 BECR 13, 13 BECR 14, 14 BECR 15,15 BECR 16,16 C* C* AND ALONG THE TOP BECR, 136,136, i, 32

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REPORT DOCUMENTATION PAGE FormApproved PuDIIc reporting burOen for this colleclion of lnformat_on is estlmatecl to average 1 hour per response, OMB No. 0704-0188 including the time for reviewing instructions, searchmg existing data sources, gathering and maintaining the Uara needed, and completing and reviewing the collection ot informahon Send comments regarding this burden estimate or any other aspect of this collection of information. including suggestions for reducing this burden, to Washington Hea(._cluarters Services. Directorate for Information Operations and Re _orts. 1215 Jefferson Davis Highway. Suite 1204. Arhngton. VA 22202-4302. and to the Office of Management and Budget. Paperwork Reduct,on Project (0704-0188). Wasr_ington. DC 20503. 1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE November 1996 4.TITLE AND SUBTITLE 3. REPORTTYPE AND DATES COVERED Technical Memorandum 5. FUNDING NUMBERS Design and Laboratory Validation of a Capacitive Sensor for Measuring the Recession of a Thin-Layered Ablator 6. AUTHOR(S) Gregory K. Noffz and Michael E Bowman 7. PERFORMINGORGANIZATIONNAME(S)ANDADDRESS(ES) NASA Dryden Flight Research Center P.O. Box 273 Edwards, California 93523-0273 9. SPONSORING/MONOTORINGAGENCYNAME(S)ANDADDRESS(ES) National Aeronautics and Space Administration Washington, DC 20546-0001 11. SUPPLEMENTARY NOTES 12a. DISTRIBUTION/AVAILABILITY STATEMENT Unclassified--Unlimited Subject Category 34 13. ABSTRACT (Maximum 200 words) WU 505-68-30 8. PERFORMING ORGANIZATION REPORT NUMBER H-2111 10. SPONSORING/MONITORING AGENCY REPORT NUMBER NASA TM-4777 12b, DISTRIBUTION CODE Flight vehicles are typically instrumented with subsurface thermocouples to estimate heat transfer at the surface using inverse analysis procedures. If the vehicle has an ablating heat shield, however, temperature time histories from subsurface thermocouples no longer provide enough information to estimate heat flux at the surface. In this situation, the geometry changes and thermal energy leaves the surface in the form of ablation products. The ablation rate is required to estimate heat transfer to the surface. A new concept for a capacitive sensor has been developed to measure ablator depth using the ablator's dielectric effect on a capacitor's fringe region. Relying on the capacitor's fringe region enables the gage to be flush mounted in the vehicle's permanent structure and not intrude into the ablative heat shield applied over the gage. This sensor's design allows nonintrusive measurement of the thickness of dielectric materials, in particular, the recession rates of low-temperature ablators applied in thin (0.020 to 0.060 in. (0.05 to 0.15 mm)) layers. Twenty capacitive gages with 13 different sensing element geometries were designed, fabricated, and tested. A two-dimensional finite-element analysis was performed on several candidate geometries. Calibration procedures using ablator-simulating shims are described. A one-to-one correspondence between system output and dielectric material thickness was observed out to a thickness of 0.055 in. (1.4 mm) for a material with a permittivity about three times that of air or vacuum. A novel method of monitoring the change in sensor capacitance was developed. This technical memorandum suggests further improvements in gage design and fabrication techniques. 14. SU BJECT TERMS 15. NUMBER OF PAGES 39 Ablation, Ablation measurement, Capacitive sensors, Fringe field, Thin film measurement 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION OF REPORT OFTHIS PAGE Unclassified Unclassified Information, 800 Elkridge Landing Road, Standard Form 298 (Rev. 2-89) NSN 7540-01-280-5500 Available from the NASA Center for AeroSpace Linthicum Heights, MD 21090; (301)621-0390 16. PRICE CODE A03 19. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF ABSTRACT Unclassified Unlimited Prescribed i_y ANSI Stcl Z39-18 298-102

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C* C" SET POTENTIALS AT VERTICAL CONDUCTOR CURVES ON THE MODEL C _ FIRST POSITIVE... PARASSIGN,MCNT,INT,0, #LOOP L85 I0 NPCR,18÷MCNT6,POSP,18+MCNT'6÷3,3, PARASSIGN,MCNT,INT,MCNT2, #LABEL L85 C* C" THEN NEGATIVE PARASSIGN,NCNT,INT,I, #LOOP L90 9 NPCR, 18NCNT'6,NEGP,18÷NCNT'6+3,3, PARASSIGN,NCNT,INT,NCNT+2, #LABEL L90 C C* SET POTENTIALS ALONG THE TOP AND BOTTOM OF CONDUCTORS NPCR,218,POSP,290,8, NPCR,219,POSP, 291,8, NPCR,222,NEGP, 286,8, NPCR,223,NEGP,287,8, C - C* SET THE GROUND PLANE NPCR, 137,0,137,1, NPCR, 141,0,141,1, NPCR,145,0,213,4, NPCR,217,0,289,4, C _ C* MERGE THE NODES AND COMPRESS EXTRANEOUS ONES NMERGE, I,,I,0.000001,0,1,0, NCOMPRESS,I,,I, C _ C* CALCULATE STORED ELECTRICAL ENERGY EM_OUTPUT,I,I,0,1,0,0, C* C" ACTIVATE THE EMAGNETIC ANALYSIS MODE USING THE C" ELECTROSTATIC OPTION AND GAUSSIAN SOLVER A_MAGNETIC,E,MKS,0.0001,15,1,0,0, C*R_CHECK, EMAGNETIC, R_MAGNETIC 33