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NASA NTRS1940

Pressure and temperature measurement in supercharger investigations

With the further development of the supercharger, requirements with regard to measuring accuracy increase while at the same time the conditions under which the measurements must be carried out become more difficult. The present paper is a contribution toward the improvement and refinement of the measuring methods. For pressure measurements some suggestions are made with regard to design and location of the measuring stations. The question of temperature measurement in rapid air flow is discussed, new instruments for the direct measurement of the temperature in the rapid airstream are described and the results obtained with the various instruments presented.

Franz, A↗
NASA NTRS1993

Ionospheric calibration for single frequency altimeter measurements

This report investigates the potential of using Global Positioning System (GPS) data and a model of the ionosphere to supply a measure of the sub-satellite Total Electron Current (TEC) of the required accuracy (10 TECU rms) for the purpose of calibrating single frequency radar altimeter measurements. Since climatological (monthly mean) models are known to be in error by as much as 50 percent, this work focused on the Parameterized Real-Time Ionospheric Specification Model (PRISM) which has the capability to improve model accuracy by ingesting (adjusting to) in situ ionospheric measurements. A set of globally distributed TEC measurements were generated using GPS data and were used as input to improve the accuracy of the PRISM model. The adjusted PRISM TEC values were compared to TOPEX dual frequency TEC measurements (which are considered truth) for a number of TOPEX sub-satellite tracks. The adjusted PRISM values generally compared to the TOPEX measurements within the 10 TECU accuracy requirements when the sub-satellite track passed within 300 to 400 km of the GPS TEC data or when the track passed through a night time ionosphere. However, when the sub-satellite points were greater than 300 to 400 km away from the GPS TEC data or when a local noon ionosphere was sampled, the adjusted PRISM values generally differed by greater than 10 TECU rms with data excursions from the TOPEX TEC measurements of as much as 40 TECU (an 8 cm path delay error at K band). Therefore, it can be concluded from this analysis that an unrealistically large number of GPS stations would be needed to predict sub-satellite TEC at the 10 TECU level in the day time ionosphere using a model such as PRISM. However, a technique currently being studied at the Jet Propulsion Laboratory (JPL) may provide a means of supplying adequate TEC data to meet the 10 TECU ionospheric correction accuracy when using a realistic number of ionospheric stations. This method involves using global GPS TEC data to estimate a global grid of vertical ionospheric TEC as a function of time (i.e. every one half hour) in a sun-fixed longitude frame. Working in a sun-fixed longitude frame, one is not limited by the spatial decorrelation distance of the ionosphere, but instead is limited more by the temporal correlations of the ionosphere in the sun-fixed frame which are a smaller effect. It is the opinion of the authors that using the global sun-fixed TEC grid data, in particular, ingesting it into PRISM, offers the best possibility of meeting the 10 TECU ionospheric correction accuracy requirement, and should be the subject of further study.

Schreiner, William S.↗
NASA NTRS1993

Investigation of the feasibility of optical diagnostic measurements at the exit of the SSME

Under Contract NAS8-36861 sponsored by NASA Marshall Space Flight Center, the United Technologies Research Center is conducting an investigation of the feasibility of remote optical diagnostics to measure temperature, species concentration and velocity at the exit of the Space Shuttle Main Engine (SSME). This is a two phase study consisting of a conceptual design phase followed by a laboratory experimental investigation. The first task of the conceptual design studies is to screen and evaluate the techniques which can be used for the measurements. The second task is to select the most promising technique or techniques, if as expected, more than one type of measurement must be used to measure all the flow variables of interest. The third task is to examine in detail analytically the capabilities and limitations of the selected technique(s). The results of this study are described in the section of this report entitled Conceptual Design Investigations. The conceptual design studies identified spontaneous Raman scattering and photodissociative flow-tagging for measurements respectively of gas temperature and major species concentration and for velocity. These techniques and others that were considered are described in the section describing the conceptual design. The objective of the second phase of investigations was to investigate experimentally the techniques identified in the first phase. The first task of the experimental feasibility study is to design and assemble laboratory scale experimental apparatus to evaluate the best approaches for SSME exit optical diagnostics for temperature, species concentrations and velocity, as selected in the Phase I conceptual design study. The second task is to evaluate performance, investigate limitations, and establish actual diagnostic capabilities, accuracies and precision for the selected optical systems. The third task is to evaluate design requirements and system trade-offs of conceptual instruments. Spontaneous Raman scattering excited by a KrF excimer laser pulse was investigated for SSME exit plane temperature and major species concentration measurements. The relative concentrations of molecular hydrogen and water vapor would be determined by measuring the integrated Q-branch scattering signals through narrow bandpass filters in front of photomultipliers. The temperature would be determined by comparing the signal from a single hydrogen rotational Raman line to the total hydrogen Q-branch signal. The rotational Raman line would be isolated by a monochromator and detected with a PMT.

Shirley, John A.↗
NASA NTRS1993

Dynamic measurements of thermophysical properties of metals and alloys at high temperatures by subsecond pulse heating techniques

Rapid (subsecond) heating techniques developed at the National Institute of Standards and Technology for the measurements of selected thermophysical and related properties of metals and alloys at high temperatures (above 1000 C) are described. The techniques are based on rapid resistive self-heating of the specimen from room temperature to the desired high temperature in short times and measuring the relevant experimental quantities, such as electrical current through the specimen, voltage across the specimen, specimen temperature, length, etc., with appropriate time resolution. The first technique, referred to as the millisecond-resolution technique, is for measurements on solid metals and alloys in the temperature range 1000 C to the melting temperature of the specimen. It utilizes a heavy battery bank for the energy source, and the total heating time of the specimen is typically in the range of 100-1000 ms. Data are recorded digitally every 0.5 ms with a full-scale resolution of about one part in 8000. The properties that can be measured with this system are as follows: specific heat, enthalpy, thermal expansion, electrical resistivity, normal spectral emissivity, hemispherical total emissivity, temperature and energy of solid-solid phase transformations, and melting temperature (solidus). The second technique, referred to as the microsecond-resolution technique, is for measurements on liquid metals and alloys in the temperature range 1200 to 6000 C. It utilizes a capacitor bank for the energy source, and the total heating time of the specimen is typically in the range 50-500 micro-s. Data are recorded digitally every 0.5 micro-s with a full-scale resolution of about one part in 4000. The properties that can be measured with this system are: melting temperature (solidus and liquidus), heat of fusion, specific heat, enthalpy, and electrical resistivity. The third technique is for measurements of the surface tension of liquid metals and alloys at their melting temperature. It utilizes a modified millisecond-resolution heating system designed for use in a microgravity environment.

Cezairliyan, Ared↗
NASA NTRS1994

The active titration method for measuring local hydroxyl radical concentration

We are developing a method for measuring ambient OH by monitoring its rate of reaction with a chemical species. Our technique involves the local, instantaneous release of a mixture of saturated cyclic hydrocarbons (titrants) and perfluorocarbons (dispersants). These species must not normally be present in ambient air above the part per trillion concentration. We then track the mixture downwind using a real-time portable ECD tracer instrument. We collect air samples in canisters every few minutes for roughly one hour. We then return to the laboratory and analyze our air samples to determine the ratios of the titrant to dispersant concentrations. The trends in these ratios give us the ambient OH concentration from the relation: dlnR/dt = -k(OH). A successful measurement of OH requires that the trends in these ratios be measureable. We must not perturb ambient OH concentrations. The titrant to dispersant ratio must be spatially invariant. Finally, heterogeneous reactions of our titrant and dispersant species must be negligible relative to the titrant reaction with OH. We have conducted laboratory studies of our ability to measure the titrant to dispersant ratios as a function of concentration down to the few part per trillion concentration. We have subsequently used these results in a gaussian puff model to estimate our expected uncertainty in a field measurement of OH. Our results indicate that under a range of atmospheric conditions we expect to be able to measure OH with a sensitivity of 3x10(exp 5) cm(exp -3). In our most optimistic scenarios, we obtain a sensitivity of 1x10(exp 5) cm(exp -3). These sensitivity values reflect our anticipated ability to measure the ratio trends. However, because we are also using a rate constant to obtain our (OH) from this ratio trend, our accuracy cannot be better than that of the rate constant, which we expect to be about 20 percent.

Sprengnether, Michele↗
NASA NTRS1994

Measuring track densities in lunar grains using image analysis

We have used digitized scanning electron micrographs and computer image analysis programs to measure track densities in lunar soil grains. Tracks were formed by highly ionizing solar energetic particles and cosmic rays. Back-scattered electron images produced suitable high contrast images for analysis. We used computer counting and measurement of area to obtain track densities. We found an excellent correlation with manual measurements for track densities below 1x10(exp 8) cm(exp -2). For track densities between 1x10(exp 8) to 1x10(exp 9) cm(exp -2) we found that a regression formula using the percentage area covered by tracks gave good agreement with manual measurements. Measurement of tract densities in lunar samples has been a very rewarding technique for measuring exposure ages and soil maturation processes. We have shown that we can reliably measure track densities in lunar grains using image analysis techniques. Automating track counting may allow application of this technique to important problems in regolith dynamics including the ratio of radiation exposure to reworking in various surface and core samples and in regolith breccias.

Blanford, G. E.↗
NASA NTRS1994

Measurement of a surface heat flux and temperature

The Heat Flux Microsensor is a new sensor which was recently patented by Virginia Tech and is just starting to be marketed by Vatell Corp. The sensor is made using the thin-film microfabrication techniques directly on the material that is to be measured. It consists of several thin-film layers forming a differential thermopile across a thermal resistance layer. The measured heat flux q is proportional to the temperature difference across the resistance layer q= k(sub g)/delta(sub g) x (t(sub 1) - T(sub 2)), where k(sub g) is the thermal conductivity and delta (sub g) is the thickness of the thermal resistance layer. Because the gages are sputter coated directly onto the surface, their total thickness is less than 2 micrometers, which is two orders of magnitude thinner than previous gages. The resulting temperature difference across the thermal resistance layer (delta is less than 1 micrometer) is very small even at high heat fluxes. To generate a measurable signal many thermocouple pairs are put in series to form a differential thermopile. The combination of series thermocouple junctions and thin-film design creates a gage with very attractive characteristics. It is not only physically non-intrusive to the flow, but also causes minimal disruption of the surface temperature. Because it is so thin, the response time is less than 20 microsec. Consequently, the frequency response is flat from 0 to over 50 kHz. Moreover, the signal of the Heat Flux Microsensor is directly proportional to the heat flux. Therefore, it can easily be used in both steady and transient flows, and it measures both the steady and unsteady components of the surface heat flux. A version of the Heat Flux Microsensor has been developed to meet the harsh demands of combustion environments. These gages use platinum and platinum-10 percent rhodium as the thermoelectric materials. The thermal resistance layer is silicon monoxide and a protective coating of Al2O3 is deposited on top of the sensor. The superimposed thin-film pattern of all six layers is presented. The large pads are for connection with pins used to bring the signal out the back of the ceramic. In addition to the heat flux measurement, the surface temperature is measured with a platinum resistance layer (RTS). The resistance of this layer increases with increasing temperature. Therefore, these gages simultaneously measure the surface temperature and heat flux. The demonstrated applications include rocket nozzles, SCRAM jet engines, gas turbine engines, boiling heat transfer, flame experiments, basic fluid heat transfer, hypersonic flight, and shock tube testing. The laboratory involves using one of these sensors in a small combustion flame. The sensor is made on a 2.5 cm diameter piece of aluminum nitride ceramic.

Davis, R. M.↗
NASA NTRS1995

The effect of sensor spacing on wind measurements at the Shuttle Landing Facility

This document presents results of a field study of the effect of sensor spacing on the validity of wind measurements at the Space Shuttle landing Facility (SLF). Standard measurements are made at one second intervals from 30 foot (9.1m) towers located 500 feet (152m) from the SLF centerline. The centerline winds are not exactly the same as those measured by the towers. This study quantifies the differences as a function of statistics of the observed winds and distance between the measurements and points of interest. The field program used logarithmically spaced portable wind towers to measure wind speed and direction over a range of conditions. Correlations, spectra, moments, and structure functions were computed. A universal normalization for structure functions was devised. The normalized structure functions increase as the 2/3 power of separation distance until an asymptotic value is approached. This occurs at spacings of several hundred feet (about 100m). At larger spacings, the structure functions are bounded by the asymptote. This enables quantitative estimates of the expected differences between the winds at the measurement point and the points of interest to be made from the measured wind statistics. A procedure is provided for making these estimates.

Merceret, Francis J.↗
NASA NTRS1995

Absorbed dose and LET spectra measurements on LDEF

Total absorbed doses measured with TLD's, linear energy transfer (LET) spectra measured with plastic track detectors, and low energy neutrons measured on LDEF have been compared with model calculations. The total absorbed doses measured in TLD's were higher than predicted in the calculations of Armstrong et al. and differ from the calculations of Atwell et al. LDEF LET spectra are dependent on detector orientation, shielding and experiment location. These factors need to be taken into account when modeling the LDEF LET spectra. LET spectra measured with plastic nuclear track detectors (PNTD's) also deviate significantly from calculations especially for high LET particles (LET(sub infinity) H2O greater than 100keV/micron). Modeling efforts to date do not include the contribution of proton induced secondaries. Analysis of polycarbonate PNTD's from the West-side of LDEF has revealed a very high fluence of tracks (greater than 1 x 10(exp 7) tracks/cm(exp 2) under 2 gm/cm(exp 2) shielding). Fluence drops off rapidly as shielding depth increases. Tracks only form in the region of the detector closest to the surface, not in the bulk of the detector. To date no adequate explanation for this observation has been found. We plan to measure range distribution of very high LET (LET (sub infinity) H2O greater than 500 keV/micron) secondary particles produced in silicon wafer by high energy primary cosmic ray particles. Refinements of experimental techniques and model calculations are being carried out in order to understand existing discrepancies between experimental measurements and calculations.

Benton, E. V.↗
NASA NTRS1994

Latitudinal variation of speed and mass flux in the acceleration region of the solar wind inferred from spectral broadening measurements

Spectral broadening measurements conducted at S-band (13-cm wavelength) during solar minimum conditions in the heliocentric distance range of 3-8 R(sub O) by Mariner 4, Pioneer 10, Mariner 10, Helios 1, Helios 2, and Viking have been combined to reveal a factor of 2.6 reduction in bandwidth from equator to pole. Since spectral broadening bandwidth depends on electron density fluctuation and solar wind speed, and latitudinal variation of the former is available from coherence bandwidth measurements, the remote sensing spectral broadening measurements provide the first determination of the latitudinal variation of solar wind speed in the acceleration region. When combined with electron density measurements deduced from white-light coronagraphs, this result also leads to the first determination of the latitudinal variation of mass flux in the acceleration region. From equator to pole, solar wind speed increases by a factor of 2.2, while mass flux decreases by a factor of 2.3. These results are consistent with measurements of solar wind speed by multi-station intensity scintillation measurements, as well as measurements of mass flux inferred from Lyman alpha observations, both of which pertain to the solar wind beyond 0.5 AU. The spectral broadening observations, therefore, strengthen earlier conclusions about the latitudinal variation of solar wind speed and mass flux, and reinforce current solar coronal models and their implications for solar wind acceleration and solar wind modeling.

Woo, Richard↗
NASA NTRS1994

Validation of stratospheric aerosol and gas experiments 1 and 2 satellite aerosol optical depth measurements using surface radiometer data

The stratospheric aerosol measurement 2, stratospheric aerosol and gas experiment (SAGE) 1, and SAGE 2 series of solar occultation satellite instruments were designed for the study of stratospheric aerosols and gases and have been extensively validated in the stratosphere. They are also capable, under cloud-free conditions, of measuring the extinction due to aerosols in the troposphere. Such tropospheric extinction measurements have yet to be validated by appropriate lidar and in situ techniques. In this paper published atmospheric aerosol optical depth measurements, made from high-altitude observatories during volcanically quiet periods, have been compared with optical depths calculated from local SAGE 1 and SAGE 2 extinction profiles. Surface measurements from three such observatories have been used, one located in Hawaii and two within the continental United States. Data have been intercompared on a seasonal basis at wave-lenths between 0.5 and 1.0 micron and found to agree within the range of measurement errors and expected atmospheric variation. The mean rms difference between the optical depths for corresponding satellite and surface measured data sets is 29%, and the mean ratio of the optical depths is 1.09.

Kent, G. S.↗
NASA NTRS1993

Pinatubo and pre-Pinatubo optical-depth spectra: Mauna Loa measurements, comparisons, inferred particle size distributions, radiative effects, and relationship to lidar data

The Ames airborne tracking sunphotometer was operated at the National Oceanic and Atmospheric Administration (NOAA) Mauna Loa Observatory (MLO) in 1991 and 1992 along with the NOAA Climate Monitoring and Diagnostics Laboratory (CMDL) automated tracking sunphotometer and lidar. June 1991 measurements provided calibrations, optical-depth spectra, and intercomparisons under relatively clean conditions; later measurements provided spectra and comparisons for the Pinatubo cloud plus calibration checks. June 1991 results are similar to previous MLO springtime measurements, with midvisible particle optical depth at the near-background level of 0.012 +/- 0.006 and no significant wavelength dependence in the measured range (lambda = 0.38 to 1.06 micrometers). The arrival of the Pinatubo cloud in July 1991 increased midvisible particle optical depth by more than an order of magnitude and changed the spectral shape of to an approximate power law with an exponent of about -1.4. By clearly September 1991, the spectrum was broadly peaked near 0.5 micrometers, and by July 1992, it was peaked near 0.8 micrometers. Our optical-depth spectra include corrections for diffuse light. NOAA- and Ames Research Center (ARC)-measured spectra are in good agreement. Columnar size distributions inverted from the spectra show that the initial (July 1991) post-Pinatubo cloud was relatively rich in small particles (r less than 0.25 micrometers), which were progressively depleted in the August-September 1991 and July 1992 periods. Conversely, both of the later periods had more of the optically efficient medium-sized particles (0.25 less than r less than 1 micrometers) than did the fresh July 1991 cloud. These changes are consistent with particle growth by condensation and coagulation. Photometer-inferred column backscatter values agree with those measured by the CMDL lidar on nearby nights. Combining lidar-measured backscatter profiles with photometer-derived backscatter-to-area ratios gives peak particle areas that could cause rapid heterogeneous loss of ozone, given sufficiently low particle acidity and suitable solar zenith angles (achieved at mid- to high latitudes). Top-of-troposphere radiative forcings for the September 1991 and July 1992 optical depths and size distributions over MLO are about -5 and -3 W/sq m, respectively (hence comparable in magnitude but opposite in sign to the radiative forcing caused by the increase in manmade greenhouse gases since the industrial revolution). Heating rates in the Pinatubo layer over MLO are 0.55 +/- 0.13 and 0.41 +/- 0.14 K/d for September 1991 and July 1992, respectively.

Russell, P. B.↗
NASA NTRS1993

An intercomparison of aircraft instrumentation for tropospheric measurements of carbonyl sulfide, hydrogen sulfide, and carbon disulfide

This paper reports results of NASA's Chemical Instrumentation and Test Evaluation (CITE 3) during which airborne measurements for carbonyl sulfide (COS), hydrogen sulfide (H2S), and carbon disulfide (CS2) were intercompared. Instrumentation included a gas chromatograph using flame photometric detection (COS, H2S, and CS2), a gas chromatograph using mass spectrometric detection (COS) and CS2), a gas chromatograph using fluorination and subsequent SF6 detection via electron capture (COS and CS2), and the Natusch technique (H2S). The measurements were made over the Atlantic Ocean east of North and South America during flights from NASA's Wallops Flight Center, Virginia, and Natal, Brazil, in August/September 1989. Most of the intercomparisons for H2S and CS2 were at mixing ratios less than 25 pptv and less than 10 pptv, respectively, with a maximum mixing ratio of about 100 pptv and 50 pptv, respectively. Carbonyl sulfide intercomparisons were at mixing ratios between 400 and 600 pptv. Measurements were intercompared from data bases constructed from time periods of simultaneous or overlapping measurements. Agreement among the COS techniques averaged about 5%, and individual measurements were generally within 10%. For H2S and at mixing ratio greater than 25 pptv, the instruments agreed on average to about 15%. At mixing ratios less than 25 pptv the agreement was about 5 pptv. For CS2 (mixing ratios less than 50 pptv), two techniques agreed on average to about 4 pptv, and the third exhibited a bias (relative to the other two) that varied in the range of 3-7 pptv. CS2 mixing ratios over the ocean east of Natal as measured by the gas chromatograph-mass spectrometer technique were only a few pptv and were below the detection limits of the other two techniques. The CITE 3 data are used to estimate the current uncertainty associated with aircraft measurements of COS, H2S, and CS2 in the remote troposphere.

Gregory, Gerald L.↗
NASA NTRS1995

Robust Quantitative Measurement of Flows and Transparent or Highly Reflective Objects

The liquid crystal point diffraction interferometer (LCPDI) is a new instrument that has been developed for the measurement of phase objects. The LCPDI uses the compact, robust design of Linnik's point diffraction interferometer and adds to it phase stepping capability for quantitative interferogram analysis. The result is a compact, simple to align, environmentally insensitive interferometer capable of accurately measuring optical wave-fronts. A solid state camera provides very high data density and automated data reduction. The instrument can measure either transparent objects like fluids and lenses, or highly reflective opaque objects like mirrors. In the former case, the refractive index distribution is measured and then related to various properties like temperature, density, chemical composition, or thickness. In the latter case, the measured phase distribution is related to the object shape. The objects measured must be stationary or quasisteady state because the measurement requires the acquisition of several frames of image data during which time the object's properties must not have changed. The data acquisition time depends on the speed of the frame grabber and the required number of data frames. Typically, three to five frames taking 1 to 2 seconds are required. The potential for faster data acquisition exists.

Mercer, Carolyn R.↗
NASA NTRS1995

PULSAUR 2: Rocket and groundbased measurements in a pulsating aurora

The second pulsating aurora rocket (PULSAUR 2) rocket was launched into a pulsating aurora on 9 February 1994 and carried a broad range of instruments in order to perform a study of this type of aurora. The rocket measurements were complemented with a set of ground-based measurements. The particle measurements performed in the rocket are related to the ground-based optical measurements performed along the rocket trajectory. It is found that the high energy electrons are largely in phase with the measured luminosity. The EISCAT measurements carried out during the flight are reviewed. The PULSAUR 2 campaign is described. Results concerning the auroral conditions and the particle measurements are presented.

Soeraas, Finn↗
NASA NTRS1996

Apparatus Measures Thicknesses Of Ice On Bars

Semiautomated apparatus measures diameters, at selected lengthwise positions, of nine vertical ice-coated bars in icing-research wind tunnel. Includes measuring head that travels on rails parallel to bar, driven by ball screw actuated by stepping motor. Position of measuring head along bar measured by string potentiometer, providing position feedback for closed-loop control circuit. Circuit provides for smooth motion of measuring head, and used to select various programmed sequences of motions and measurements. Measurements needed to determine degree of uniformity of icing conditions for experiments on aircraft models.

Gibson, Theresa L.↗
NASA NTRS1995

Morphology of solar wind fluctuations and structure in the vicinity of the Sun from radio propagation measurements

Radio propagation measurements represent a powerful means for remote probing of electron density and solar wind speed in the acceleration region of the solar wind not yet explored by in situ measurements. Recent investigations based on radio propagation measurements have led to considerable progress in our knowledge of the general morphology of solar wind fluctuations and structure, especially in terms of their relationship to solar wind properties that have been observed directly by fields and particles measurements, and to coronal features observed in white-light measurements. The purpose of this paper is to present an overview of the latest results on quasi-stationary structure covering the large scale variation of solar wind speed over the streamer belt and coronal hole regions, coronal streamers (source of slow solar wind) and their associated small-scale electron density structure, plumes, density and fractional or relative density fluctuations, and the spectral characteristics of the electron density fluctuations. The radio propagation measurements not only reveal new information on the structure near the Sun, but also show that the structure appears to undergo substantial evolution on its way to 0.3 AU, the closest radial distance for which direct in situ spacecraft measurements are available.

Woo, R.↗
NASA NTRS1995

Modal Correction Method For Dynamically Induced Errors In Wind-Tunnel Model Attitude Measurements

This paper describes a method for correcting the dynamically induced bias errors in wind tunnel model attitude measurements using measured modal properties of the model system. At NASA Langley Research Center, the predominant instrumentation used to measure model attitude is a servo-accelerometer device that senses the model attitude with respect to the local vertical. Under smooth wind tunnel operating conditions, this inertial device can measure the model attitude with an accuracy of 0.01 degree. During wind tunnel tests when the model is responding at high dynamic amplitudes, the inertial device also senses the centrifugal acceleration associated with model vibration. This centrifugal acceleration results in a bias error in the model attitude measurement. A study of the response of a cantilevered model system to a simulated dynamic environment shows significant bias error in the model attitude measurement can occur and is vibration mode and amplitude dependent. For each vibration mode contributing to the bias error, the error is estimated from the measured modal properties and tangential accelerations at the model attitude device. Linear superposition is used to combine the bias estimates for individual modes to determine the overall bias error as a function of time. The modal correction model predicts the bias error to a high degree of accuracy for the vibration modes characterized in the simulated dynamic environment.

Buehrle, R. D.↗