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At least 253 records · Page 14

Characterization of Ring Wave Spectra for Natural Rain: Measurements and Model for Remote Sensing Applications

Ring waves generated by natural rains from 1 to 100 mm/hr were measured in a small tank located in a field. Time series were obtained: (a) from a wire capacitance probe that measured surface elevation, (b) from an optical gauge that measured rain rates R, (c) from an anemometer that measured wind speeds and (d) from a 13.5 GHz scatterometer (w polarization, and 30 degree incidence angle). Ring wave frequency spectra are computed from the surface elevation data for each minute of rain. All the spectra have a similar shape, with a maximum near 5 Hz, and with a more rapid decay towards higher frequencies than towards lower frequencies. A log-Gaussian spectral model provides a useful representation of these data and analysis of the model coefficients shows that the peak frequency and bandwidth are approximately constant, but the magnitude increases as R increases, Additionally, the normalized radar cross section from the scatterometer varies approximately linearly with the spectral line corresponding to the Bragg-wavelength, so together the log-Gaussian ring wave model and the Bragg scattering theory should be useful for a broad range of applications. These findings can be used to help interpret remote sensing data during rain events and to guide model development for radar scattering from rain roughened seas.

Bliven, L.↗

Inferring Selected Cloud Properties from Satellite Lightning Data

The recent advent of satellite lightning detection programs has introduced a new potential for obtaining global information about other (hard to measure) cloud properties. We have made use of observations together with numerical model studies to show that positive correlations exist between: (1) lightning flashrate (F) and vertical velocity (w); and (2) flashrate (F) and the amount of condensate (water and ice) lofted through the -10 C isotherm (C(sub u)). The lightning flashrate appears to be very sensitive to the magnitude of the updraft velocity, with F increasing rapidly with w above a threshold of w approx. = 5-10 m/s. By contrast, we have found that the flashrate/condensate relationship appears to be approximately linear. We are currently refining the F-updraft and F-condensate relationships with further model studies before applying them to lightning data from the Optical Transient Detector (OTD) and the Lightning Imaging Sensor (LIS). We hope, with this method, to provide estimates of the large scale vertical water transport by continental convective systems over seasonal timescales.

Schroeder, Vicki↗

UV Spectral Variability and the Lyman-Alpha Forest in the Lensed Quasar Q0957+561

Far-ultraviolet spectra of the gravitational lens components Q0957+561 A and B were obtained with the Hubble Space Telescope Faint Object Spectrograph (FOS) at five equally spaced epochs, one every two weeks. We confirm the flux variability of the quasar's Lyman-alpha and O VI lambda 1037 emission lines reported in IUE (International Ultraviolet Explorer) spectra. The fluxes in these lines vary on a time scale of weeks in the local rest frame (LRF), independently of each other and of the surrounding continuum. The individual spectra of each image were co-added to investigate the properties of the Lyman-alpha forest along the two lines of sight to the quasar. Absorption lines having equivalent width W (sub lambda) greater than or equal to 0.3 Angstroms in the LRF not previously identified as interstellar lines, metal lines, or higher order Lyman lines were taken to be LY-alpha forest lines. The existence of each line in this consistently selected set was then verified by its presence in two archival FOS spectra with approx. 1.5 times higher signal to noise than our co-added spectra. Ly-alpha forest lines with W (sub lambda) greater than or equal to 0.3 Angstroms appear at 42 distinct wavelengths in the spectra of the two images. Two absorption lines in the spectrum of image A have no counterpart at that wavelength in the spectrum of image B, and two lines in image B have no counterpart in image A. Based on the separation of the lines of sight at the redshift of the absorption lines appearing in only one spectrum, the density of the absorbing clouds in the direction of Q0957+561 must change significantly over a distance of 79 (+34, -26) h (sub 50) (sup -1) kpc in the simplified model where the absorbers are treated as spherical clouds and the characteristic dimension is the radius. (We adopt H (sub 0)= 50 h (sub 50) km s (sup -1) kpc (sup -1), q (sub 0) = 1/2, and LAMBDA = 0 throughout the paper.) The two limits define the 68% confidence interval on the characteristic dimension, equivalent to the 1 sigma confidence interval for a Gaussian distribution. The 95% confidence interval extends from (32 - 250) h (sub 50) (sup -1) kpc. We show in the Appendix that the fraction of Ly-alpha forest lines that appear in only one spectrum can be expressed as a rapidly converging power series in 1/r, where r the ratio of the radius of the cloud to the separation of the two LOS at the redshift of the cloud. This power series can be rewritten to give r in terms of the fraction of Ly-alpha forest wavelengths that appear in the spectrum of only one image. A simple linear approximation to the solution which everywhere agrees with the power series solution to better than 0.8% for r greater than or equal to 2 is derived in the Appendix.

Dolan, J. F.↗

Far UV Spectroscopy of eta Carinae

We present the first high spectral resolution observations of the Luminous Blue Variable eta Carinae between the Lyman limit and 1180 A. High resolution spectra (R approx. 20,000) were obtained with the Far Ultraviolet Spectroscopic Explorer (FUSE) satellite on Feb. 1 and Mar. 20, 2000. The observations were made with a 30 x 30 arcsec aperture and includes the entire Homunculus region. However, the spatial extent of the far UV flux is consistent with a point source. With the limited spatial resolution of the FUSE instrument, we can only constrain the far UV emission to be within +/- 5 arcsec of the star. The far UV spectrum of eta Car is dominated by strong absorption features of molecular hydrogen. The observed flux level at 1150A is approx. 4 times 10(exp 12) erg /cm(exp -2) /sec(exp -1) / A(exp -1) and decreases approximately linearly to approx. 920 A where converging H1 and H2 features completely blanket the spectrum. These observations were obtained as part of the FUSE Early Release Observation program.

Iping, R. C.↗

Nondestructive Determination of Bond Strength

Although many nondestructive techniques have been applied to detect disbonds in adhesive joints, no absolutely reliable nondestructive method has been developed to detect poor adhesion and evaluate the strength of bonded joints prior to the present work which used nonlinear ultrasonic methods to investigate adhesive bond cure conditions. Previously, a variety of linear and nonlinear ultrasonic methods with water coupling had been used to study aluminum-adhesive-aluminum laminates, prepared under different adhesive curing conditions, for possible bond strength determination. Therefore, in the course of this research effort, a variety of finite-amplitude experimental methods which could possibly differentiate various cure conditions were investigated, including normal and oblique incidence approaches based on nonlinear harmonic generation as well as several non-collinear two-wave interaction approaches. Test samples were mechanically scanned in various ways with respect to the focus of a transmitting transducer operated at several variable excitation frequencies and excitation levels. Even when powerful sample-related resonances were exploited by means of a frequency scanning approach, it was very difficult to isolate the nonlinear characteristics of adhesive bonds. However, a multi-frequency multi-power approach was quite successful and reliable. Ultrasonic tone burst signals at increasing power levels, over a wide frequency range, were transmitted through each bond specimen to determine its excitation dependent nonlinear harmonic resonance behavior. Relative amplitude changes were observed particularly in the higher harmonic spectral data and analyzed using a local displacement and strain analysis in the linear approximation. Two analysis approaches of the excitation-dependent data at specific resonances were found to be quite promising. One of these approaches may represent a very robust algorithm for classifying an adhesive bond as being properly cured or not. Another approach, in addition to differentiation between various cure conditions, may even provide information with respect to the bond strength. Several technical papers were published during the course of this research and a summary is presented in the Ph.D. dissertation of Tobias P. Berndt, a graduate student financially supported by this NASA Grant.

Source record↗

The Lyman-Alpha Forest in the Lensed Quasar Q0957+561 and the Characteristic Dimension of the Absorbing Clouds

Far-ultraviolet spectra of the gravitational lens components Q0957+561 A and 9 were obtained with the Hubble Space Telescope Faint Object Spectrograph (FOS) at five equally spaced epochs, one every two weeks. We confirm the flux variability of the quasar's Lyman-alpha and 0 VI emission lines reported by Dolan et al. (1995) in IUE spectra. The fluxes in these lines vary on a time scale of weeks in the observer's rest frame, independently of each other and of the surrounding continuum. The individual spectra of each image were co-added to investigate the properties of the Lyman-alpha forest along the two lines of sight to the quasar. Absorption lines having equivalent width W > 0.3 A in the observer's frame not previously identified by Michalitsianos et al. (1997) as interstellar lines, metal lines, or higher order Lyman lines were taken to be Ly-alpha forest lines. The existence of each line in this consistently selected set was then verified by its presence in two archival FOS spectra with -1.5 times higher signal to noise than our co-added spectra. Ly-alpha forest lines with W > 0.3 A appear at 41 distinct wavelengths in the spectra of the two images. one absorption line in the spectrum of image A has no counterpart in the spectrum of image B and one line in image B has no counterpart in image A. Based on the separation of the lines of sight over the redshift range searched for Ly-forest lines, the density of the absorbing clouds in the direction of Q0957+561 must change significantly over a distance R = 160 (+120, -70)/ h(sub 50) kpc in the simplified model where the absorbers are treated as spherical clouds and the characteristic dimension, R, is the radius. (We adopt H(sub 0) = 50 h(sub 50) km/s/ kpc, q(sub 0) = 1/2, and lambda = 0 throughout the paper.) The 95% confidence interval on R extends from (50 - 950)/h(sub 50) kpc We show in the Appendix that the fraction of Ly-alpha forest lines that appear in only one spectrum can be expressed as a rapidly converging power series in 1/r, where r the ratio of the radius of the cloud to the separation of the two lines of sight at the redshift of the cloud. This power series can be rewritten to give r in terms of the fraction of Ly-forest wavelengths that appear in the spectrum of only one image. A simple linear approximation to the solution that everywhere agrees with the power series solution to better than 0.8% for r > 2 is derived in the Appendix.

Dolan, Joseph↗

Studies of the Retardation Force Developed on an Aircraft Tire Rolling in Slush or Water

A series of unbraked (freely rolling) taxi tests were conducted at the Langley landing-loads track with a 32 x 8.8, type 7, 22-ply-rating ribbed-tread aircraft tire to obtain data on tire retardation forces developed during rolling in both slush and water. The forward speeds of the tests ranged from 59 to 104 knots. Tire inflation pressures of 350 and 115 pounds per square inch were used. Results indicated a parabolic increase of retardation force with increasing forward velocity for both slush- and water-covered runway surfaces. The retardation force was found to increase approximately linearly with increasing water depth. Drag coefficients appropriate to the equations used are presented. Calculations made to determine the effect of slush on the take-off distance of a jet transport are in agreement with data obtained from an actual take-off in slush for this airplane. This is an interim report which deals with the effect of slush on the acceleration and the ground-run distance of airplanes during take-off.

Horne, Walter B.↗

Crops Models for Varying Environmental Conditions

New variable environment Modified Energy Cascade (MEC) crop models were developed for all the Advanced Life Support (ALS) candidate crops and implemented in SIMULINK. The MEC models are based on the Volk, Bugbee, and Wheeler Energy Cascade (EC) model and are derived from more recent Top-Level Energy Cascade (TLEC) models. The MEC models simulate crop plant responses to day-to-day changes in photosynthetic photon flux, photoperiod, carbon dioxide level, temperature, and relative humidity. The original EC model allows changes in light energy but uses a less accurate linear approximation. The simulation outputs of the new MEC models for constant nominal environmental conditions are very similar to those of earlier EC models that use parameters produced by the TLEC models. There are a few differences. The new MEC models allow setting the time for seed emergence, have realistic exponential canopy growth, and have corrected harvest dates for potato and tomato. The new MEC models indicate that the maximum edible biomass per meter squared per day is produced at the maximum allowed carbon dioxide level, the nominal temperatures, and the maximum light input. Reducing the carbon dioxide level from the maximum to the minimum allowed in the model reduces crop production significantly. Increasing temperature decreases production more than it decreases the time to harvest, so productivity in edible biomass per meter squared per day is greater at nominal than maximum temperatures, The productivity in edible biomass per meter squared per day is greatest at the maximum light energy input allowed in the model, but the edible biomass produced per light energy input unit is lower than at nominal light levels. Reducing light levels increases light and power use efficiency. The MEC models suggest we can adjust the light energy day-to- day to accommodate power shortages or Lise excess power while monitoring and controlling edible biomass production.

Jones, Harry↗

On the Possibility of Ill-Conditioned Covariance Matrices in the First-Order Two-Step Estimator

The first-order two-step nonlinear estimator, when applied to a problem of orbital navigation, is found to occasionally produce first step covariance matrices with very low eigenvalues at certain trajectory points. This anomaly is the result of the linear approximation to the first step covariance propagation. The study of this anomaly begins with expressing the propagation of the first and second step covariance matrices in terms of a single matrix. This matrix is shown to have a rank equal to the difference between the number of first step states and the number of second step states. Furthermore, under some simplifying assumptions, it is found that the basis of the column space of this matrix remains fixed once the filter has removed the large initial state error. A test matrix containing the basis of this column space and the partial derivative matrix relating first and second step states is derived. This square test matrix, which has dimensions equal to the number of first step states, numerically drops rank at the same locations that the first step covariance does. It is formulated in terms of a set of constant vectors (the basis) and a matrix which can be computed from a reference trajectory (the partial derivative matrix). A simple example problem involving dynamics which are described by two states and a range measurement illustrate the cause of this anomaly and the application of the aforementioned numerical test in more detail.

Garrison, James L.↗

Localization and pattern of graviresponse across the pulvinus of barley Hordeum vulgare

Pulvini of excised stem segments from barley (Hordeum vulgare cv Larker') were pretreated with 1 millimolar coumarin before gravistimulation to reduce longitudinal cell expansion and exaggerate radial cell enlargement. The cellular localization and pattern of graviresponse across individual pulvini were then evaluated by cutting the organ in cross-section, photographing the cross-section, and then measuring pulvinus thickness and the radial width of cortical and epidermal cells in enlargements of the photomicrographs. With respect to orientation during gravistimulation, we designated the uppermost point of the cross-section 0 degrees and the lowermost point 180 degrees. A gravity-induced increase in pulvinus thickness was observable within 40 degrees of the vertical in coumarin-treated pulvini. In upper halves of coumarin-treated gravistimulated pulvini, cells in the inner cortex and inner epidermis had increased radial widths, relative to untreated gravistimulated pulvini. In lower halves of coumarin-treated pulvini, cells in the central and outer cortex and in the outer epidermis showed the greatest increase in radial width. Cells comprising the vascular bundles also increased in radial width, with this pattern following that of the central cortex. These results indicate (a) that all cell types are capable of showing a graviresponse, (b) that the graviresponse occurs in both the top and the bottom of the responding organ, and (c) that the magnitude of the response increases approximately linearly from the uppermost point to the lowermost. These results are also consistent with models of gravitropism that link the pattern and magnitude of the graviresponse to graviperception via statolith sedimentation.

Non-NASA Center↗

Permeation of protons, potassium ions, and small polar molecules through phospholipid bilayers as a function of membrane thickness

Two mechanisms have been proposed to account for solute permeation of lipid bilayers. Partitioning into the hydrophobic phase of the bilayer, followed by diffusion, is accepted by many for the permeation of water and other small neutral solutes, but transient pores have also been proposed to account for both water and ionic solute permeation. These two mechanisms make distinctively different predictions about the permeability coefficient as a function of bilayer thickness. Whereas the solubility-diffusion mechanism predicts only a modest variation related to bilayer thickness, the pore model predicts an exponential relationship. To test these models, we measured the permeability of phospholipid bilayers to protons, potassium ions, water, urea, and glycerol. Bilayers were prepared as liposomes, and thickness was varied systematically by using unsaturated lipids with chain lengths ranging from 14 to 24 carbon atoms. The permeability coefficient of water and neutral polar solutes displayed a modest dependence on bilayer thickness, with an approximately linear fivefold decrease as the carbon number varied from 14 to 24 atoms. In contrast, the permeability to protons and potassium ions decreased sharply by two orders of magnitude between 14 and 18 carbon atoms, and leveled off, when the chain length was further extended to 24 carbon atoms. The results for water and the neutral permeating solutes are best explained by the solubility-diffusion mechanism. The results for protons and potassium ions in shorter-chain lipids are consistent with the transient pore model, but better fit the theoretical line predicted by the solubility-diffusion model at longer chain lengths.

NASA Program Exobiology↗

Transonic Stability and Control Investigation of a 1/80-Scale Model of the Consolidated Vultee Skate 9 Seaplane, TED No. NACA DE 345: Transonic-Bump Method

An investigation of the longitudinal stability and of the all-movable horizontal tail and aileron control of a 1/80-scale reflection-plane model of the Consolidated Vultee Skate 9 seaplane has been made through a Mach number range of 0.6 to 1.16 on the transonic bump of the Langley high-speed 7- by 10-foot tunnel. At moderate lift coefficients (0.4 to 0.8) and below a Mach number of 1.0 the model was statically unstable longitudinally. The static longitudinal stability of the model at low lift coefficients increased with Mach number corresponding to a shift in aerodynamic center from 37 percent mean aerodynamic chord at a Mach number of 0.60 to 64 percent at a Mach number of 1.10. Estimates indicate that the tail deflection angle required for steady flight and for accelerated maneuvers of the Skate 9 airplane would probably not vary greatly with Mach number at sea level, but for accelerated maneuvers at altitude the tail deflection angle would probably vary erratically with Mach number. The variation of rolling-moment coefficient with aileron deflection angle was approximately linear, agreed well with theory, and held for the range of aileron deflections tested (-17.1 deg to 16.6 deg). At low lift coefficients the drag rise occurred at Mach numbers of 0.95 and 0.90 for the wing alone and the complete model, respectively. The effects of the canopy on the model were small. For the ranges investigated, angle-of-attack and Mach number changes caused no large pressure drops in the jet-engine duct.

Riebe, John M.↗

HSCT Sector Combustor Hardware Modifications for Improved Combustor Design

An alternative to the stepped-dome design for the lean premixed prevaporized (LPP) combustor has been developed. The new design uses the same premixer types as the stepped-dome design: integrated mixer flameholder (IMFH) tubes and a cyclone swirler pilot. The IMFH fuel system has been taken to a new level of development. Although the IMFH fuel system design developed in this Task is not intended to be engine-like hardware, it does have certain characteristics of engine hardware, including separate fuel circuits for each of the fuel stages. The four main stage fuel circuits are integrated into a single system which can be withdrawn from the combustor as a unit. Additionally, two new types of liner cooling have been designed. The resulting lean blowout data was found to correlate well with the Lefebvre parameter. As expected, CO and unburned hydrocarbons emissions were shown to have an approximately linear relationship, even though some scatter was present in the data, and the CO versus flame temperature data showed the typical cupped shape. Finally, the NOx emissions data was shown to agree well with a previously developed correlation based on emissions data from Configuration 3 tests performed at GEAE. The design variations of the cyclone swirler pilot that were investigated in this study did not significantly change the NOx emissions from the baseline design (GEAE Configuration 3) at supersonic cruise conditions.

Greenfield, Stuart C.↗

Effects of Incident Electron Fluence and Energy on the Election Yield Curves and Emission Spectra of Dielectrics

We present an experimental study of evolution of electron emission yields and spectra as a result of internal charge build up due to electron dose. Reliable total, backscattered and secondary yield curves and electron emission spectra for un-charged insulators using a low fluence, pulsed electron beam (= or < 5 microsec at = or < 3 nA/sq mm or = or < 10(exp 5) e/sq mm per pulse) with low energy electron and UV flooding to neutralize the charging between pulses. Quantifiable changes in yield curves are observed due to < 100 fC/sq mm fluences for several excellent dielectric thin film materials. We find good agreement with a phenomenological argument based on insulator charging predicted by the yield curve; this includes an approximately linear decrease in the magnitude of the yield as incident energies approach the crossover energies and an exponential decrease in yield as accumulated internal charge reduces the landing energy to asymptotically approach a steady state surface charge and unity yield. We also find that the exponential decay of yield curves with fluence exhibit an energy dependent decay constant, alpha(E), over a broad range of incident energies below, between and above the crossover energies. Finally, we present some preliminary physics-based models for this energy dependence and attempt to relate our charging measurements to knowledge of how charge is deposited within the insulator, the mechanisms for charge trapping and transport, and how the profile of trapped charge affects the transport and emission of charges from insulators.

Sim, Alec↗

Semi-Analytic Reconstruction of Flux in Finite Volume Formulations

Semi-analytic reconstruction uses the analytic solution to a second-order, steady, ordinary differential equation (ODE) to simultaneously evaluate the convective and diffusive flux at all interfaces of a finite volume formulation. The second-order ODE is itself a linearized approximation to the governing first- and second- order partial differential equation conservation laws. Thus, semi-analytic reconstruction defines a family of formulations for finite volume interface fluxes using analytic solutions to approximating equations. Limiters are not applied in a conventional sense; rather, diffusivity is adjusted in the vicinity of changes in sign of eigenvalues in order to achieve a sufficiently small cell Reynolds number in the analytic formulation across critical points. Several approaches for application of semi-analytic reconstruction for the solution of one-dimensional scalar equations are introduced. Results are compared with exact analytic solutions to Burger s Equation as well as a conventional, upwind discretization using Roe s method. One approach, the end-point wave speed (EPWS) approximation, is further developed for more complex applications. One-dimensional vector equations are tested on a quasi one-dimensional nozzle application. The EPWS algorithm has a more compact difference stencil than Roe s algorithm but reconstruction time is approximately a factor of four larger than for Roe. Though both are second-order accurate schemes, Roe s method approaches a grid converged solution with fewer grid points. Reconstruction of flux in the context of multi-dimensional, vector conservation laws including effects of thermochemical nonequilibrium in the Navier-Stokes equations is developed.

Gnoffo, Peter A.↗

Status and Plans for the WCRP/GEWEX Global Precipitation Climatology Project (GPCP)

Status and plans for GPCP are presented along with scientific findings from the current data set. Global and large regional rainfall variations and possible long-term changes are examined using the 26-year (1979-2004) monthly dataset from the Global Precipitation Climatology Project (GPCP). One emphasis is to discriminate among the variations due to ENSO, volcanic events and possible long-term changes. Although the global change of precipitation in the data set is near zero, the data set does indicate an upward trend (0.13 mm/day/25yr) and a downward trend (-0.06 mm/day/25yr) over tropical oceans and lands (25S-25N), respectively. This corresponds to a 4% increase (ocean) and 2% decrease (land) during this time period. Simple techniques are derived to attempt to eliminate variations due to ENSO and major volcanic eruptions in the Tropics. Using only annual values two "volcano years" are determined by examining ocean-land coupled variations in precipitation related to ENSO and other phenomena. The outlier years coincide with Pinatubo and El Chicon eruptions. The ENSO signal is reduced by deriving mean ocean and land values for El Nino, La Nina and neutral conditions based on Nino 3.4 SST and normalizing the annual ocean and land precipitation to the neutral set of cases. The impact of the two major volcanic eruptions over the past 25 years is estimated to be about a 5% reduction in tropical rainfall. The modified data set (with ENSO and volcano effect at least partially removed) retains the same approximate linear change slopes over the data set period, but with reduced variance leading to significance tests with results in the 90-95% range. Intercomparisons between the GPCP, SSM/I (1988-2004), and TRMM (1998-2004) satellite rainfall products and alternate gauge analyses over land are made to attempt to increase or decrease confidence in the changes seen in the GPCP analysis.

Adkerm Robert F.↗

Relationships of Upper Tropospheric Water Vapor, Clouds and SST: MLS Observations, ECMWF Analyses and GCM Simulations

The relationships of upper tropospheric water vapor (UTWV), cloud ice and sea surface temperature (SST) are examined in the annual cycles of ECMWF analyses and simulations from 15 atmosphere-ocean coupled models which were contributed to the IPCC AR4. The results are compared with the observed relationships based on UTWV and cloud ice measurements from MLS on Aura. It is shown that the ECMWF analyses produce positive correlations between UTWV, cloud ice and SST, similar to the MLS data. The rate of the increase of cloud ice and UTWV with SST is about 30% larger than that for MLS. For the IPCC simulations, the relationships between UTWV, cloud ice and SST are qualitatively captured. However, the magnitudes of the simulated cloud ice show a considerable disagreement between models, by nearly a factor of 10. The amplitudes of the approximate linear relations between UTWV, cloud ice and SST vary by a factor up to 4.

sea surface temperature (SST)↗

Contact position sensor using constant contact force control system

A force control system (50) and method are provided for controlling a position contact sensor (10) so as to produce a constant controlled contact force therewith. The system (50) includes a contact position sensor (10) which has a contact probe (12) for contacting the surface of a target to be measured and an output signal (V.sub.o) for providing a position indication thereof. An actuator (30) is provided for controllably driving the contact position sensor (10) in response to an actuation control signal (I). A controller (52) receives the position indication signal (V.sub.o) and generates in response thereto the actuation control signal (I) so as to provide a substantially constant selective force (F) exerted by the contact probe (12). The actuation drive signal (I) is generated further in response to substantially linear approximation curves based on predetermined force and position data attained from the sensor (10) and the actuator (30).

Sturdevant, Jay↗