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At least 163 records · Page 9
All sourcesNASA NTRSDOE OSTI
NASA NTRS2004

Performance of Thermal Mass Flow Meters in a Variable Gravitational Environment

The performance of five thermal mass flow meters, MKS Instruments 179A and 258C, Unit Instruments UFM-8100, Sierra Instruments 830L, and Hastings Instruments HFM-200, were tested on the KC-135 Reduced Gravity Aircraft in orthogonal, coparallel, and counterparallel orientations relative to gravity. Data was taken throughout the parabolic trajectory where the g-level varied from 0.01 to 1.8 times normal gravity. Each meter was calibrated in normal gravity in the orthogonal position prior to flight followed by ground testing at seven different flow conditions to establish a baseline operation. During the tests, the actual flow rate was measured independently using choked-flow orifices. Gravitational acceleration and attitude had a unique effect on the performance of each meter. All meters operated within acceptable limits at all gravity levels in the calibrated orthogonal position. However, when operated in other orientations, the deviations from the reference flow became substantial for several of the flow meters. Data analysis indicated that the greatest source of error was the effect of orientation, followed by the gravity level. This work emphasized that when operating thermal flow meters in a variable gravity environment, it is critical to orient the meter in the same direction relative to gravity in which it was calibrated. Unfortunately, there was no test in normal gravity that could predict the performance of a meter in reduced gravity. When operating in reduced gravity, all meters indicated within 5 percent of the full scale reading at all flow conditions and orientations.

Brooker, John E.↗
NASA NTRS2013

Optical Alignment of the Global Precipitation Measurement (GPM) Star Trackers

The optical alignment of the star trackers on the Global Precipitation Measurement (GPM) core spacecraft at NASA Goddard Space Flight Center (GSFC) was challenging due to the layout and structural design of the GPM Lower Bus Structure (LBS) in which the star trackers are mounted as well as the presence of the star tracker shades that blocked line-of-sight to the primary star tracker optical references. The initial solution was to negotiate minor changes in the original LBS design to allow for the installation of a removable item of ground support equipment (GSE) that could be installed whenever measurements of the star tracker optical references were needed. However, this GSE could only be used to measure secondary optical reference cube faces not used by the star tracker vendor to obtain the relationship information and matrix transformations necessary to determine star tracker alignment. Unfortunately, due to unexpectedly large orthogonality errors between the measured secondary adjacent cube faces and the lack of cube calibration data, we required a method that could be used to measure the same reference cube faces as originally measured by the vendor. We describe an alternative technique to theodolite auto-collimation for measurement of an optical reference mirror pointing direction when normal incidence measurements are not possible. This technique was used to successfully align the GPM star trackers and has been used on a number of other NASA flight projects. We also discuss alignment theory as well as a GSFC-developed theodolite data analysis package used to analyze angular metrology data.

Hetherington, Samuel↗
NASA NTRS1992

Age and isotopic relationships among the angrites Lewis Cliff 86010 and Angra dos Reis

The paper presents results of a wide-ranging isotopic investigation of the the Antarctic angrite LEW-86010 (LEW), and reassesses the type angrite Angra dos Reis (ADOR) in order to obtain precise radiometric ages and initial Sr isotopic compositions, and to search for the erstwhile presence of the short-lived nuclei Sm-146 and Al-26 via their daughter products. The isotopic compositions of Sm, U, Ca, and Ti were measured to allow a detailed appraisal to be made of the relations between, and the geneology of, these two angrites. LEW proves to be severely contaminated with modern terrestrial Pb, which is shown to result from terrestrial weathering. Concordant Pb-Pb model ages of pyroxene separates are obtained; uranium isotopic compositions are normal within error. Overall, striking age and isotopic similarities between LEW and ADOR were found, suggesting almost simultaneous production on the same asteroid, even though recent experimental studies imply that the two are not comagmatic.

Lugmair, G. W.↗
NASA NTRS1988

The design of trellis coded MPSK for fading channels: Performance criteria

It has been well established that the appropriate criterion for optimum trellis-coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. It is shown that when the trellis-coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code of optimum performance is guided by other factors, in particular, the length of the shortest error-event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along the path. Athough maximum free distance (dfree) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure of optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing dfree.

Divsalar, Dariush↗
NASA NTRS1992

Turbulent heat flux measurements in a transitional boundary layer

During an experimental investigation of the transitional boundary layer over a heated flat plate, an unexpected result was encountered for the turbulent heat flux (bar-v't'). This quantity, representing the correlation between the fluctuating normal velocity and the temperature, was measured to be negative near the wall under certain conditions. The result was unexpected as it implied a counter-gradient heat transfer by the turbulent fluctuations. Possible reasons for this anomalous result were further investigated. The possible causes considered for this negative bar-v't' were: (1) plausible measurement error and peculiarity of the flow facility, (2) large probe size effect, (3) 'streaky structure' in the near wall boundary layer, and (4) contributions from other terms usually assumed negligible in the energy equation including the Reynolds heat flux in the streamwise direction (bar-u't'). Even though the energy balance has remained inconclusive, none of the items (1) to (3) appear to be contributing directly to the anomaly.

Sohn, K. H.↗
NASA NTRS1999

Spatial Orientation and Balance Control Changes Induced by Altered Gravito-Inertial Force Vectors

Seventeen healthy and eight vestibular deficient subjects were exposed to an interaural centripetal acceleration of 1 G (resultant 45 deg roll tilt of 1.4 G) on a 0.8 meter radius centrifuge for a period of 90 minutes in the dark. The subjects sat with head fixed upright, except every 4 of 10 minutes when instructed to rotate their head so that their nose and eyes pointed towards a visual point switched on every 3 to 5 seconds at random places (within +/- 30 deg) in the Earth horizontal plane. Motion sickness caused some subjects to limit their head movements during significant portions of the 90 minute period, and led three normal subjects to stop the test earlier. Eye movements, including directed saccades for subjective Earth- and head-referenced planes, were recorded before, during, and immediately after centrifugation using electro-oculography. Postural stability measurements were made before and within ten minutes after centrifugation. In normal subjects, postural sway and multisegment body kinematics were gathered during an eyes-closed head movement cadence (sway-referenced support platform), and in response to translational/rotational platform perturbations. A significant increase in postural sway, segmental motion amplitude and hip frequency was observed after centrifugation. This effect was short-lived, with a recovery time of several postural test trials. There were also asymmetries in the direction of post-centrifugation center of sway and head tilt which depended on the subject's orientation during the centrifugation adaptation period (left ear or right ear out). To delineate the effect of the magnitude of the gravito-inertial vector versus its direction during the adaptive centrifugation period, we tilted eight normal subjects in the roll axis at a 45 deg angle in the dark for 90 minutes without rotational motion. Their postural responses did not change following the period of tilt. Based on verbal reports, normal subjects overestimated roll-tilt during 90 minutes of both tilt and centrifugation stimuli. Subjective estimates of head-horizontal, provided by directed saccades, revealed significant errors after approximately 30 minutes that tended to increase only in the group who underwent centrifugation. Immediately after centrifugation, subjects reported feeling tilted on average 10 degrees in the opposite direction, which was in agreement with the direction of their earth-directed saccades. In vestibular deficient (VD) subjects, postural sway was measured using a sway-referenced or earth-fixed support surface, and with or without a head movement sequence. 'Me protocol was selected for each patient during baseline testing, and corresponded to the most challenging condition in which the patient was able to maintain balance with eyes closed. Bilaterally VD subjects showed no postural decrement after centrifugation, while unilateral VD subjects had varying degrees of decrement. Unilateral VD subjects were tested twice; they underwent centrifugation both with right ear out and left ear out. Their post-centrifuation center of sway shifted at right angles depending on the centrifuge GIF orientation. Bilateral VD subjects bad shifts as well, but no consistent directional trend. VD subjects underestimated roll-tilt during centrifugation, These results suggest that orientation of the gravito-inertial vector and its magnitude arc both used by the central nervous system for calibration of multiple orientation systems. A change in the background gravito-inertial force (otolith input) can rapidly initiate postural and perceptual adaptation in several sensorimotor systems, independent of a structured visual surround.

Kaufman, Galen D.↗
NASA NTRS1989

Raman intensity as a probe of concentration near a crystal growing in solution

The feasibility of using Raman spectral scattering signals for measurements of concentration profiles near a crystal interface during growth or dissolution is discussed. With KH2PO4 (KDP) as a test material, optical multichannel analyzer (OMA) detection of a solute Raman vibrational band provided direct quantification of solute concentration with band intensity. The intersection of incident laser and Raman collection optics provided 3-D selective point measurements of the solution concentration field. Unlike many other techniques, the Raman band intensity is not sensitive to the typical temperature variations. Precision calibration of Raman intensity versus KDP concentration with less than 1 pct standard deviation error levels was demonstrated. A fiber optic, which sampled incident laser intensity and coupled it to the OMA, provided a fully synchronized monitor of fluctuations in laser power to correlate with observed Raman signals. With 1 W of laser power at the sample, good data statistics required eight repeated data collections at approximately 2.5 min collection. The accumulated time represents the concentration measurement time at one spatial location. Photomicroscopy documented a 30 micrometer diameter by 200 micrometer of laser Raman scattering region in the solution near the crystal surface. The laser beam was able to approach up to 25 micrometer from the crystal surface. However, a crystal surface reflected intensity contribution was weakly detectable. Nucleated microcrystals were seen in the crystal-growing solution. These microcrystals convect right up to the crystal surface and indicate no quiet diffusion region under normal gravity conditions. Translation of the solution cell with respect to the optics caused systematic intensity errors.

Wilkinson, R. Allen↗
NASA NTRS1987

The design of trellis codes for fading channels

The appropriate criterion for optimum trellis coded modulation design on the additive white Gaussian noise channel is maximization of the free Euclidean distance. When trellis coded modulation is used on a Rician fading channel with interleaving/deinterleaving, the design of the code for optimum performance is guided by other factors, in particular the length of the shortest error event path, and the product of branch distances (possibly normalized by the Euclidean distance of the path) along that path. Although maximum free distance (d sub free) is still an important consideration, it plays a less significant role the more severe the fading is on the channel. These considerations lead to the definition of a new distance measure for optimization of trellis codes transmitted over Rician fading channels. If no interleaving/deinterleaving is used, then once again the design of the trellis code is guided by maximizing d sub free. It is also shown that allowing for multiple symbols per trellis branch, i.e., multiple trellis coded modulation (MTCM), provides an additional degree of freedom for designing a code to meet the above optimization criteria on the fading channel. It is here where the MTCM technique exploits its full potential.

Divsalar, Dariush↗
NASA NTRS2020

Assessment of Ku- and Ka-band Dual-Frequency Radar for Snow Retrieval

Dual-frequency Ku/Ka-band radar retrievals of snow parameters such as liquid-equivalent snowfall rate (R) and mass-weighted diameter (Dm) have two principal errors, namely, the differences between the assumed particle size distribution (PSD) model from the actual PSD and inadequacies in characterizing the single-scattering properties of snowflakes. Regarding the first issue, this study, based on radar simulations from a large amount of observed PSD data, shows that there exist relatively high correlations between the estimated snow parameters and their true values derived directly from the measured PSD. For PSD data with R greater than 0.1 mm h−1, a gamma PSD model with a fixed shape factor (μ) equal to 0 (or exponential distribution) provides the best estimates of R and Dm. This is despite negative biases of up to −15 % in R and underestimates and overestimates in Dm for small and large Dm, respectively. The μ = 0 assumption, however, produces relatively poor estimates of normalized intercepts of a gamma PSD (Nw), whereas the best estimates are obtained when μ is considered either 3 or 6. However, the use of an inappropriate scattering table increases the errors in snow retrieval. Simple evaluations are made for cases where the scattering databases used for the algorithm input differ from that used for retrieval. The mismatched scattering databases alone could cause at least 30 %-50 % changes in the estimates of snow water content (SWC) and R and could affect the retrievals of Dm and Nw and their dependence on μ.

Liang Liao↗
NASA NTRS1978

On the estimation of the vertical ozone distribution from satellite measurements

A simple relationship has been established between the vertical ozone profile above the ozone maximum and satellite measured radiances for wavelengths shorter than 3000 A. The method is based on the computation of the penetration depths for solar radiation entering the atmosphere at wavelengths employed by the BUV satellite. Suitably defined penetration depths are shown to be linear functions of the normalized intensities for typical conditions, eliminating the requirement for iterative solutions and considerably simplifying the error analysis for the system. For ozone distributions which depart significantly from the exponential form, a noniterative extension of the analysis procedure has been developed and tested through application to simulated intensities.

Thomas, R. W. L.↗
NASA NTRS1995

Prototype development and test results of a continuous ambient air monitoring system for hydrazine at the 10 ppb level

A Hydrazine Vapor Area Monitor (HVAM) system is currently being field tested as a detector for the presence of hydrazine in ambient air. The MDA/Polymetron Hydrazine Analyzer has been incorporated within the HVAM system as the core detector. This analyzer is a three-electrode liquid analyzer typically used in boiler feed water applications. The HVAM system incorporates a dual-phase sample collection/transport method which simultaneously pulls ambient air samples containing hydrazine and a very dilute sulfuric acid solution (0.0001 M) down a length of 1/4 inch outside diameter (OD) tubing from a remote site to the analyzer. The hydrazine-laden dilute acid stream is separated from the air and the pH is adjusted by addition of a dilute caustic solution to a pH greater than 10.2 prior to analysis. Both the dilute acid and caustic used by the HVAM are continuously generated during system operation on an "as needed" basis by mixing a metered amount of concentrated acid/base with dilution water. All of the waste water generated by the analyzer is purified for reuse by Barnstead ion-exchange cartridges so that the entire system minimizes the generation of waste materials. The pumping of all liquid streams and mixing of the caustic solution and dilution water with the incoming sample are done by a single pump motor fitted with the appropriate mix of peristaltic pump heads. The signal to noise (S/N) ratio of the analyzer has been enhanced by adding a stirrer in the MDA liquid cell to provide mixing normally generated by the high liquid flow rate designed by the manufacturer. An onboard microprocessor continuously monitors liquid levels, sample vacuum, and liquid leak sensors, as well as handles communications and other system functions (such as shut down should system malfunctions or errors occur). The overall system response of the HVAM can be automatically checked at regular intervals by measuring the analyzer response to a metered amount of calibration standard injected into the dilute acid stream. The HVAM system provides two measurement ranges (threshold limit value (TLV): 10 to 1000 parts per billion (ppb)/LEAK: 100 ppb to 10 parts per million (ppm)). The LEAK range is created by dilution of the sulfuric acid/hydrazine liquid sample with pure water. This dual range capability permits the analyzer to quantify ambient air samples whose hydrazine concentrations range from 10 ppb to as high as 10 ppm. The laboratory and field prototypes have demonstrated total system response times on the order of 10 to 12 minutes for samples ranging from 10 to 900 ppb in the lLV mode and is greater than 2 minutes for samples ranging from 100 to 1300 ppb in the LEAK mode. Service intervals of over 3 months have been demonstrated for continuous 24 hour/day, 7 day/week usage. The HVAM is made up of a purged cabinet that contains power supplies, RS422 signal transmission capabilities, a UPS, an on-site warning system, and a Line Replaceable Unit (LRU). The LRU includes all of the liquid flow system, the analyzer, the control/data system microprocessor and assorted flow and liquid-level sensors. The LRU is mounted on a track slide system so it can be serviced inplace or totally removed and quickly exchanged with another calibrated unit, thus minimizing analyzer downtime. Once an LRU is removed from an analyzer enclosure, it can be brought to a laboratory facility for complete calibration and periodic maintenance.

Meneghelli, Barry↗
NASA NTRS2001

A semi-automatic method for left ventricle volume estimate: an in vivo validation study

This study aims to the validation of the left ventricular (LV) volume estimates obtained by processing volumetric data utilizing a segmentation model based on level set technique. The validation has been performed by comparing real-time volumetric echo data (RT3DE) and magnetic resonance (MRI) data. A validation protocol has been defined. The validation protocol was applied to twenty-four estimates (range 61-467 ml) obtained from normal and pathologic subjects, which underwent both RT3DE and MRI. A statistical analysis was performed on each estimate and on clinical parameters as stroke volume (SV) and ejection fraction (EF). Assuming MRI estimates (x) as a reference, an excellent correlation was found with volume measured by utilizing the segmentation procedure (y) (y=0.89x + 13.78, r=0.98). The mean error on SV was 8 ml and the mean error on EF was 2%. This study demonstrated that the segmentation technique is reliably applicable on human hearts in clinical practice.

NASA Discipline Cardiopulmonary↗
NASA NTRS2012

A First Order Wavefront Estimation Algorithm for P1640 Calibrator

P1640 calibrator is a wavefront sensor working with the P1640 coronagraph and the Palomar 3000 actuator adaptive optics system (P3K) at the Palomar 200 inch Hale telescope. It measures the wavefront by interfering post-coronagraph light with a reference beam formed by low-pass filtering the blocked light from the coronagraph focal plane mask. The P1640 instrument has a similar architecture to the Gemini Planet Imager (GPI) and its performance is currently limited by the quasi-static speckles due to non-common path wavefront errors, which comes from the non-common path for the light to arrive at the AO wavefront sensor and the coronagraph mask. By measuring the wavefront after the coronagraph mask, the non-common path wavefront error can be estimated and corrected by feeding back the error signal to the deformable mirror (DM) of the P3K AO system. Here, we present a first order wavefront estimation algorithm and an instrument calibration scheme used in experiments done recently at Palomar observatory. We calibrate the P1640 calibrator by measuring its responses to poking DM actuators with a sparse checkerboard pattern at different amplitudes. The calibration yields a complex normalization factor for wavefront estimation and establishes the registration of the DM actuators at the pupil camera of the P1640 calibrator, necessary for wavefront correction. Improvement of imaging quality after feeding back the wavefront correction to the AO system demonstrated the efficacy of the algorithm.

Wavefront sensing↗
NASA NTRS2015

Techniques for Estimating Emissions Factors from Forest Burning: ARCTAS and SEAC4RS Airborne Measurements Indicate Which Fires Produce Ozone

Previous studies of emission factors from biomass burning are prone to large errors since they ignore the interplay of mixing and varying pre-fire background CO2 levels. Such complications severely affected our studies of 446 forest fire plume samples measured in the Western US by the science teams of NASA's SEAC4RS and ARCTAS airborne missions. Consequently we propose a Mixed Effects Regression Emission Technique (MERET) to check techniques like the Normalized Emission Ratio Method (NERM), where use of sequential observations cannot disentangle emissions and mixing. We also evaluate a simpler "consensus" technique. All techniques relate emissions to fuel burned using C(sub burn) = delta C(sub tot) added to the fire plume, where C(sub tot) approximately equals (CO2 + CO). Mixed-effects regression can estimate pre-fire background values of Ctot (indexed by observation j) simultaneously with emissions factors indexed by individual species i, delta epsilon lambda tau alpha−x(sub i)/(C(sub burn))i,j., MERET and "consensus" require more than two emissions indicators. Our studies excluded samples where exogenous CO or CH4 might have been fed into a fire plume, mimicking emission. We sought to let the data on 13 gases and particulate properties suggest clusters of variables and plume types, using non-negative matrix factorization (NMF). While samples were mixtures, the NMF unmixing suggested purer burn types. Particulate properties (bscat, babs, SSA, AAE) and gas-phase emissions were interrelated. Finally, we sought a simple categorization useful for modeling ozone production in plumes. Two kinds of fires produced high ozone: those with large fuel nitrogen as evidenced by remnant CH3CN in the plumes, and also those from very intense large burns. Fire types with optimal ratios of delta-NOy/delta- HCHO associate with the highest additional ozone per unit Cburn, Perhaps these plumes exhibit limited NOx binding to reactive organics. Perhaps these plumes exhibit limited NOx binding to reactive organics.

fires↗
NASA NTRS2016

Techniques for Estimating Emissions Factors from Forest Burning: ARCTAS and SEAC4RS Airborne Measurements Indicate which Fires Produce Ozone

Previous studies of emission factors from biomass burning are prone to large errors since they ignore the interplay of mixing and varying pre-fire background CO2 levels. Such complications severely affected our studies of 446 forest fire plume samples measured in the Western US by the science teams of NASA's SEAC4RS and ARCTAS airborne missions. Consequently we propose a Mixed Effects Regression Emission Technique (MERET) to check techniques like the Normalized Emission Ratio Method (NERM), where use of sequential observations cannot disentangle emissions and mixing. We also evaluate a simpler "consensus" technique. All techniques relate emissions to fuel burned using C(burn) = delta C(tot) added to the fire plume, where C(tot) approximately equals (CO2 = CO). Mixed-effects regression can estimate pre-fire background values of C(tot) (indexed by observation j) simultaneously with emissions factors indexed by individual species i, delta, epsilon lambda tau alpha-x(sub I)/C(sub burn))I,j. MERET and "consensus" require more than emissions indicators. Our studies excluded samples where exogenous CO or CH4 might have been fed into a fire plume, mimicking emission. We sought to let the data on 13 gases and particulate properties suggest clusters of variables and plume types, using non-negative matrix factorization (NMF). While samples were mixtures, the NMF unmixing suggested purer burn types. Particulate properties (b scant, b abs, SSA, AAE) and gas-phase emissions were interrelated. Finally, we sought a simple categorization useful for modeling ozone production in plumes. Two kinds of fires produced high ozone: those with large fuel nitrogen as evidenced by remnant CH3CN in the plumes, and also those from very intense large burns. Fire types with optimal ratios of delta-NOy/delta- HCHO associate with the highest additional ozone per unit Cburn, Perhaps these plumes exhibit limited NOx binding to reactive organics. Perhaps these plumes exhibit limited NOx binding to reactive organics

ozone↗
NASA NTRS2017

CEDAR-GEM Challenge for Systematic Assessment of Ionosphere/Thermosphere Models in Predicting TEC During the 2006 December Storm Event

In order to assess current modeling capability of reproducing storm impacts on total electron content (TEC), we considered quantities such as TEC, TEC changes compared to quiet time values, and the maximum value of the TEC and TEC changes during a storm. We compared the quantities obtained from ionospheric models against ground-based GPS TEC measurements during the 2006 AGU storm event (14-15 December 2006) in the selected eight longitude sectors. We used 15 simulations obtained from eight ionospheric models, including empirical, physics-based, coupled ionosphere-thermosphere, and data assimilation models. To quantitatively evaluate performance of the models in TEC prediction during the storm, we calculated skill scores such as RMS error, Normalized RMS error (NRMSE), ratio of the modeled to observed maximum increase (Yield), and the difference between the modeled peak time and observed peak time. Furthermore, to investigate latitudinal dependence of the performance of the models, the skill scores were calculated for five latitude regions. Our study shows that RMSE of TEC and TEC changes of the model simulations range from about 3 TECU (total electron content unit, 1 TECU = 1016 el m2) (in high latitudes) to about 13 TECU (in low latitudes), which is larger than latitudinal average GPS TEC error of about 2 TECU. Most model simulations predict TEC better than TEC changes in terms of NRMSE and the difference in peak time, while the opposite holds true in terms of Yield. Model performance strongly depends on the quantities considered, the type of metrics used, and the latitude considered.

Shim, J. S.↗
NASA NTRS1983

Deformable subreflector computed by geometric optics

Using a Cassegrainian geometry, the 64-meter antenna with its distorted paraboloidal reflecting surface is forced to produce a uniform phase wavefront by a pathlength-compensating subreflector. First, the computed distortion vectors at the joints or nodes of the main reflector structure supporting the surface panels are best fitted to a paraboloid. Second, the resulting residual distortion errors are used to determine a compensating subreflector surface by ray tracing using geometric optics principles. Third, the totally corrected subreflector surface is defined by the normal directions and distances to the surface of the original symmetric hyperboloid for the purpose of evaluation. Finally, contour maps of distortions of the paraboloid reflector and the compensating subreflector are presented. A field-measured check of the subreflector in focused position as computed by the described methodology is also presented for the antenna position at horizon look with the geometry at 45 degrees elevation.

Katow, M. S.↗
NASA NTRS1977

Experimental study of error sources in skin-friction balance measurements

An experimental study has been performed to determine potential error sources in skin-friction balance measurements. A floating-element balance, large enough to contain the instrumentation needed to systematically investigate these error sources has been constructed and tested in the thick turbulent boundary layer on the sidewall of a large supersonic wind tunnel. Test variables include element-to-case misalignment, gap size, and Reynolds number. The effects of these variables on the friction, lip, and normal forces have been analyzed. It was found that larger gap sizes were preferable to smaller ones; that small element recession below the surrounding test surface produced errors comparable to the same amount of protrusion above the test surface; and that normal forces on the element were, in some cases, large compared to the friction force.

Allen, J. M.↗