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Turbulence Model Validation Through Joint Experimental /Computational Studies of Separated Flow Over A Three-Dimensional Tapered Bump: Part I - Experimental Investigation

The results of a three-year experimental campaign aimed at comprehensively documenting the separated flow over a three-dimensional bump are presented with the purpose of generating a benchmark experimental database useful in validating computational fluid dynamics (CFD) flow simulations. The bump model geometry was designed to provide well-defined and repeatable smooth-body flow separation conditions that were suitable for both experiments and simulations. The bump had a Gaussian streamwise profile with a constant height equal to 8.5% of its width over the central 60% of the test section width. The remaining 40% were outboard spanwise portions that gradually taper to zero using an error function profile to minimize side-wall boundary layer effects. The model was immersed in a turbulent boundary layer that was developed on a suspended flat plate in the Notre Dame Mach 0.6 Wind Tunnel. In order to document the effect of the incoming boundary layer thickness on the flow separation, the bump model could be located at two streamwise positions. The mean velocity and turbulence intensity of the wind tunnel freestream flow field and approaching turbulent boundary layer were fully documented. The measurements of the flow separation region included surface visualization, wall shear stress using oil-film interferometry, mean and dynamic surface pressure, and planar and stereoscopic particle image velocimetry. The experiments were conducted over a range of Mach numbers from 0.05 to 0.2 corresponding to a range of Reynolds numbers based on the test section spanwise dimension (0.914m) of 1.0 × 10 6 ≤ Re L = U ∞ L/ν ≤ 4.0 × 10 6 . The bulk of the results are presented for the higher Mach number conditions of 0.1 and 0.2 with Re L = 2.0 × 10 6 and 4.0 × 10 6 , respectively. Extensive uncertainty analysis of the data was performed. The data is archived in the NASA Langley Turbulence Modeling Resource website at https://turbmodels.larc.nasa.gov/Other_exp_Data/speedbump_sep_exp.html. In addition to the experiments, a computational effort was made in parallel by the CFD group at Boeing Research & Technology highlighting the usefulness of the data set, which is outlined in the accompanying CFD report.

Flow separation↗

NASA Tech Briefs, June 2009

Topics covered include: Device for Measuring Low Flow Speed in a Duct, Measuring Thermal Conductivity of a Small Insulation Sample, Alignment Jig for the Precise Measurement of THz Radiation, Autoignition Chamber for Remote Testing of Pyrotechnic Devices, Microwave Power Combiners for Signals of Arbitrary Amplitude, Synthetic Foveal Imaging Technology, Airborne Antenna System for Minimum-Cycle-Slip GPS Reception, Improved Starting Materials for Back-Illuminated Imagers, Multi-Modulator for Bandwidth-Efficient Communication, Some Improvements in Utilization of Flash Memory Devices, GPS/MEMS IMU/Microprocessor Board for Navigation, T/R Multi-Chip MMIC Modules for 150 GHz, Pneumatic Haptic Interfaces, Device Acquires and Retains Rock or Ice Samples, Cryogenic Feedthrough Test Rig, Improved Assembly for Gas Shielding During Welding or Brazing, Two-Step Plasma Process for Cleaning Indium Bonding Bumps, Tool for Crimping Flexible Circuit Leads, Yb14MnSb11 as a High-Efficiency Thermoelectric Material, Polyimide-Foam/Aerogel Composites for Thermal Insulation, Converting CSV Files to RKSML Files, Service Management Database for DSN Equipment, Chemochromic Hydrogen Leak Detectors, Compatibility of Segments of Thermoelectric Generators, Complementary Barrier Infrared Detector, JPL Greenland Moulin Exploration Probe, Ultra-Lightweight Self-Deployable Nanocomposite Structure for Habitat Applications, and Room-Temperature Ionic Liquids for Electrochemical Capacitors.

Source record↗

Fast Imaging Detector Readout Circuits with In-Pixel ADCs for Fourier Transform Imaging Spectrometers

Focal plane arrays (FPAs) with high frame rates and many pixels benefit several upcoming Earth science missions including GEO-CAPE, GACM, and ACE by enabling broader spatial coverage and higher spectral resolution. FPAs for the PanFTS, a high spatial resolution Fourier transform spectrometer and a candidate instrument for the GEO-CAPE mission are the focus of the developments reported here, but this FPA technology has the potential to enable a variety of future measurements and instruments. The ESTO ACT Program funded the developed of a fast readout integrated circuit (ROIC) based on an innovative in-pixel analog-to-digital converter (ADC). The 128 X 128 pixel ROIC features 60 ?m pixels, a 14-bit ADC in each pixel and operates at a continuous frame rate of 14 kHz consuming only 1.1 W of power. The ROIC outputs digitized data completely eliminating the bulky, power consuming signal chains needed by conventional FPAs. The 128 X 128 pixel ROIC has been fabricated in CMOS and tested at the Jet Propulsion Laboratory. The current version is designed to be hybridized with PIN photodiode arrays via indium bump bonding for light detection in the visible and ultraviolet spectral regions. However, the ROIC design incorporates a small photodiode in each cell to permit detailed characterization of the ROICperformance without the need for hybridization. We will describe the essential features of the ROIC design and present results of ROIC performance measurements.

focal plane arrays (FPAs)↗

Revised Reynolds Stress and Triple Product Models

Revised versions of Lag methodology Reynolds-stress and triple product models are applied to accepted test cases to assess the improvement, or lack thereof, in the prediction capability of the models. The Bachalo-Johnson bump flow is shown as an example for this abstract submission.

fluid dynamics↗

The experimental verification of wall movement influence coefficients for an adaptive walled test section

Flexible walled wind tunnels have for some time been used to reduce wall interference effects at the model. A necessary part of the 3-D wall adjustment strategy being developed for the Transonic Self-Streamlining Wind Tunnel (TSWT) of Southampton University is the use of influence coefficients. The influence of a wall bump on the centerline flow in TSWT has been calculated theoretically using a streamline curvature program. This report details the experimental verification of these influence coefficients and concludes that it is valid to use the theoretically determined values in 3-D model testing.

Neal, G.↗

Phase-Shifting Liquid Crystal Point-Diffraction Interferometry

Microgravity fluid physics experiments frequently measure concentration and temperature. Interferometers such as the Twyman Green illustrated have performed full-field measurement of these quantities. As with most such devices, this interferometer uses a reference path that is not common with the path through the test section. Recombination of the test and reference wavefronts produces interference fringes. Unfortunately, in order to obtain stable fringes, the alignment of both the test and reference paths must be maintained to within a fraction of the wavelength of the light being used for the measurement. Otherwise, the fringes will shift and may disappear. Because these interferometers are extremely sensitive to bumping, jarring and transmitted vibration, they are typically mounted on optical isolation tables. Schlieren deflectometers or the more recent Shack-Hartmann wavefront sensors also measure concentration and temperature in laboratory fluid flows. Ray optics describe the operation of both devices. In a schlieren system, an expanded, collimated beam passes through a test section where refractive index gradients deflect rays. A lens focuses the beam to a filter placed in the rear focal plane of the decollimating lens. In a quantitative color schlieren system, gradients in the index of refraction appear as colors in the field of view due to the action of the color filter. Since sensitivity is a function of the focal length of the decollimating lens, these systems are rather long and filter fabrication and calibration is rather difficult. A Shack-Hartmann wavefront sensor is an array of small lenslets. Typical diameters are on the order of a few hundred microns. Since these lenslets divide the test section into resolution elements, the spatial resolution can be no smaller than an individual lenslet. Such a device was recently used to perform high-speed tomography of heated air exiting a 1.27 cm diameter nozzle. While these wavefront sensors are very compact, the limited spatial resolution and the methods required for data reduction suggest that a more useful instrument needs to be developed. The category of interferometers known as common path interferometers can eliminate much of the vibration sensitivity associated with traditional interferometry as described above. In these devices, division of the amplitude of the wavefront following the test section produces the reference beam. Examples of these instruments include shearing and point diffraction interferometers. In the latter case, shown schematically, a lens focuses light passing through the test section onto a small diffracting object. Such objects are typically either a circle of material on a high quality glass plate or a small sphere in a glass cell. The size of the focused spot is several times larger than the object so that the light not intercepted by the diffracting object forms the test beam while the diffracted light generates a spherical reference beam. While this configuration is mechanically stable, phase shifting one beam with respect to the other is difficult due to the common path. Phase shifting enables extremely accurate measurements of the phase of the interferogram using only gray scale intensity measurements and is the de facto standard of industry. Mercer and Creath 2 demonstrated phase shifting in a point diffraction interferometer using a spherical spacer in a liquid crystal cell as the diffracting object. By changing the voltage across the cell, they were able to shift the phase of the undiffracted beam relative to the reference beam generated by diffraction from the sphere. While they applied this technology to fluid measurements, the device shifted phase so slowly that it was not useful for studying transient phenomena. We have identified several technical problems that precluded operation of the device at video frame rates and intend to solve them to produce a phase-shifting liquid crystal point-diffraction interferometer operating at video frame rates. The first task is to produce high contrast fringes. Since the diffracted beam is much weaker than the transmitted beam, interferograms have poor contrast unless a dye is added to the liquid crystal to reduce the intensity of the undiffracted light. Dyes previously used were not rigorously characterized and suffered from hysteresis in both the initial alignment state of the device and the electro-optic switching characteristics. Hence, our initial effort will identify and characterize dyes that do not suffer from these difficulties and are readily soluble in the liquid crystal host. Since the ultimate goal of this research is to produce interferometers capable of phase shifting at video frame rates, we will quantify the difference in switching times between ferroelectric and nematic liquid crystals. While we have more experience with nematic crystals, they typically switch more slowly than ferroelectric cells. As part of that effort, we will investigate the difference in the modulation of the interferograms as a function of the type of liquid crystal in the cell. Because the temporal switching response of a liquid crystal cell is directly related its thickness, we intend to explore techniques required to produce cells that are as thin as possible. However, the cells must still produce a total phase shift of two pi radians.

Griffin, DeVon W.↗

On the use of wall functions as boundary conditions for two-dimensional separated compressible flows

A new and improved wall function method for compressible turbulent flows has been developed and tested. This method is applicable to attached and separated flows, to both high- and low-Reynolds number flows, and to flows with adiabatic and nonadiabatic surfaces. This wall function method has been applied to the Launder-Spalding k-epsilon two-equation model of turbulence. The tests consist of comparisons of calculated and experimental results for: (1) an axisymmetrical transonic shock-wave/boundary-wave interaction flow at low Reynolds number in an adiabatic tube, (2) an axisymmetrical high-Reynolds number transonic flow over a nonadiabatic bump, and (3) a two-dimensional supersonic high-Reynolds number flow on a nonadiabatic deflected flap. Each of these experiments had significant regions of flow separation. The calculations are performed with an implicit algorithm that solves the Reynolds-averaged Navier-Stokes equations. It is shown that the results obtained agree very well with the data for the complex compressible flows tested.

Viegas, J. R.↗

The case for antiparticles in the extragalactic cosmic radiation

The presence of an excess of low energy antiprotons in the primary cosmic radiation has given rise to a number of possible explanations. The possibility that these are extragalactic in origin is considered and it is shown that there are interesting implications for the bulk of the cosmic radiation at higher energies. In particular, it may be possible to account for a previously puzzling feature, a bump in the cosmic ray energy spectrum in the energy range 10(14) to 10(15) eV, with this primary extragalactic origin hypothesis. A method for testing this hypothesis experimentally is also described.

Stecker, F. W.↗

Corrugated Quantum Well Infrared Photodetector Focal Plane Array Test Results

The corrugated quantum-well infrared photodetector (C-QWIP) uses total internal reflection to couple normal incident light into the optically active quantum wells. The coupling efficiency has been shown to be relatively independent of the pixel size and wavelength thus making the C-QWIP a candidate for detectors over the entire infrared spectrum. The broadband coupling efficiency of the C-QWIP makes it an ideal candidate for multiwavelength detectors. We fabricated and tested C-QWIP focal plane arrays (FPAs) with cutoff wavelengths of 11.2 and 16.2 micrometers. Each FPA has 256 x 256 pixels that are bump-bonded to a direct injection readout circuit. Both FPAs provided infrared imagery with good aesthetic attributes. For the 11.2-micrometers FPA, background-limited performance (BLIP) was observed at 60 K with f/3 optics. For the 16.2-micrometers FPA, BLIP was observed at 38 K. Besides the reduction of dark current in C-QWIP structures, the measured internal quantum efficiency (eta) remains to be high. The values for responsivity and quantum efficiency obtained from the FPA results agree well with those measured for single devices.

Goldberg, A.↗

Spatial Convergence of Three Dimensional Turbulent Flows

Finite-volume and finite-element schemes, both implemented within the FUN3D flow solver, are evaluated for several test cases described on the Turbulence-Modeling Resource (TMR) web site. The cases include subsonic flow over a hemisphere cylinder, subsonic flow over a swept bump configuration, and supersonic flow in a square duct. The finite- volume and finite-element schemes are both used to obtain solutions for the first two cases, whereas only the finite-volume scheme is used for the supersonic duct. For the hemisphere cylinder, finite-element solutions obtained on tetrahedral meshes are compared with finite- volume solutions on mixed-element meshes. For the swept bump, finite-volume solutions have been obtained for both hexahedral and tetrahedral meshes and are compared with finite-element solutions obtained on tetrahedral meshes. For the hemisphere cylinder and the swept bump, solutions are obtained on a series of meshes with varying grid density and comparisons are made between drag coefficients, pressure distributions, velocity profiles, and profiles of the turbulence working variable. The square duct shows small variation due to element type or the spatial accuracy of turbulence model convection. It is demonstrated that the finite-element scheme on tetrahedral meshes yields similar accuracy as the finite- volume scheme on mixed-element and hexahedral grids, and demonstrates less sensitivity to the mesh topology (biased tetrahedral grids) than the finite-volume scheme.

Park, Michael A.↗

The Lyman edge test of the quasar emission mechanism

The Lyman edge region in the spectra of 11 high-redshift quasars is studied using data designed to detect broadened Lyman edge absorption predicted by thermal models of the 'big blue bump' continuum component, especially thin accretion disks. Three objects have broadened, partial edges near the systemic redshifts, as expected for thermal models. In two cases, however, narrow Lyamn lines with the edge absorption, ruling out the disk interpretation. Thus, the data are negative for thermal models, at least for opaque thin accretion disks.

Antonucci, R. R. J.↗

MEMS Microshutter Array System for James Webb Space Telescope

A complex MEMS microshutter array system has been developed at NASA Goddard Space Flight Center (GSFC) for use as a multi-object aperture array for a Near-Infrared Spectrometer (NIRSpec). The NIRSpec is one of the four major instruments carried by the James Webb Space Telescope (JWST), the next generation of space telescope after the Hubble Space Telescope retires. The microshutter arrays (MSAs) are designed for the selective transmission of light with high efficiency and high contrast. It is demonstrated in Figure 1 how a MSA is used as a multiple object selector in deep space. The MSAs empower the NIRSpec instrument simultaneously collect spectra from more than 100 targets therefore increases the instrument efficiency 100 times or more. The MSA assembly is one of three major innovations on JWST and the first major MEMS devices serving observation missions in space. The MSA system developed at NASA GSFC is assembled with four quadrant fully addressable 365x171 shutter arrays that are actuated magnetically, latched and addressed electrostatically. As shown in Figure 2, each MSA is fabricated out of a 4' silicon-on-insulator (SOI) wafer using MEMS bulk-micromachining technology. Individual shutters are close-packed silicon nitride membranes with a pixel size close to 100x200 pm (Figure 3). Shutters are patterned with a torsion flexure permitting shutters to open 90 degrees with a minimized mechanical stress concentration. In order to prevent light leak, light shields are made on to the surrounding frame of each shutter to cover the gaps between the shutters and the Game (Figure 4). Micro-ribs and sub-micron bumps are tailored on hack walls and light shields, respectively, to prevent sticktion, shown in Figures 4 and 5. JWST instruments are required to operate at cryogenic temperatures as low as 35K, though they are to be subjected to various levels of ground tests at room temperature. The shutters should therefore maintain nearly flat in the entire temperature range between 35K and 300K. Through intensive numerical simulations and experimental studies, an optically opaque and electrically conductive metal-nitride thin film was selected as a coating material deposited on the shutters with the best thermal-expansion match to silicon nitride - the shutter blade thin film material. A shutter image shown in Figure 6 was taken at room temperature, presenting shutters slightly bowing down as expected. Shutters become flat when the temperature decreases to 35K. The MSAs are then bonded to silicon substrates that are fabricated out of 6" single-silicon wafers in the thickness of 2mm. The bonding is conducted using a novel single-sided indium flip-chip bonding technology. Indium bumps fabricated on a substrate are shown in Figure 7. There are 180,000 indium bumps for bonding a flight format MSA array to its substrate. Besides a MSA, each substrate houses five customer-designed ASIC (Application Specific Integrated Circuit) multiplexer/address chips for 2-dimensional addressing, twenty capacitors, two temperature sensors, numbers of resistors and all necessary interconnects, as shown in Figure 8. Complete MSA quadrant assemblies have been successfully manufactured and fully functionally tested. The assemblies have passed a series of critical reviews required by JWST in satisfying all the design specifications. The qualification tests cover programmable 2-D addressing, life tests, optical contrast tests, and environmental tests including radiation, vibration, and acoustic tests. A 2-D addressing pattern with 'ESA' letters programmed in a MSA is shown in Figure 9. The MSAs passed 1 million cycle life tests and achieved high optical contrast over 10,000. MSA teams are now making progress in final fabrication, testing and assembly (Figure 10). The delivery of flight-format MSA system is scheduled at the end of 2008 for being integrated to the focal plane of the NIRSpec detectors.

Li, Mary J.↗

The SKY SHARK: an RPV Designed to Investigate the Pressure Distribution on a Lifting Surface

The objective was to design a remotely piloted vehicle which is capable of gathering in-flight pressure distribution data on a lifting test specimen, and then test the design by constructing a subscale demonstrator, to prove the flight worthiness of the concept. The technology demonstrator was scheduled for takeoff at approximately, 7:20 AM on Thursday April 27th. There was a light wind from the southeast. The plane was hand-launched and made an initial dip, most likely due to the poor trim conditions at launch. It then began to climb and bank into a left turn. The aircraft climbed to an altitude of approximately 150 ft and circled. The plane flew for several minutes and at times appeared to bump around, which was due to thermal activity disrupting the flight of the aircraft. The aircraft was brought slowly down in a power-off condition and glided in for a belly landing and landed without incident. Results of the flight test proved the general capability of the design to maintain flight stability throughout the take off, cruise, turning, and landing flight regimes. We were not able to demonstrate stability with the test specimen in place as the control surfaces designed to counteract the instabilities induced in the static system, winglets and ailerons, were not included.

Ziemba, Rob↗

Evaluation of advanced microelectronic fluxless solder-bump contacts for hybrid microcircuits

Technology for interconnecting monolithic integrated circuit chips with other components is investigated. The advantages and disadvantages of the current flip-chip approach as compared to other interconnection methods are outlined. A fluxless solder-bump contact technology is evaluated. Multiple solder-bump contacts were formed on silicon integrated circuit chips. The solder-bumps, comprised of a rigid nickel under layer and a compliant solder overlayer, were electroformed onto gold device pads with the aid of thick dry film photomasks. Different solder alloys and the use of conductive epoxy for bonding were explored. Fluxless solder-bump bond quality and reliability were evaluated by measuring the effects of centrifuge, thermal cycling, and high temperature storage on bond visual characteristics, bond electrical continuity, and bond shear tests. The applicability and suitability of this technology for hybrid microelectronic packaging is discussed.

Mandal, R. P.↗

The Primordial Inflation Polarization Explorer (PIPER)

The Primordial Inflation Polarization ExploreR (Piper) is a balloon-borne cosmic microwave background (CMB) polarimeter designed to search for evidence of inflation by measuring the large-angular scale CMB polarization signal. Bicep2 recently reported a detection of B-mode power corresponding to the tensor-to-scalar ratio r = 0.2 on approximately 2 degree scales. If the Bicep2 signal is caused by inflationary gravitational waves (IGWs), then there should be a corresponding increase in B-mode power on angular scales larger than 18 degrees. Piper is currently the only suborbital instrument capable of fully testing and extending the Bicep2 results by measuring the B-mode power spectrum on angular scales theta θ = approximately 0.6 deg to 90 deg, covering both the reionization bump and recombination peak, with sensitivity to measure the tensor-to-scalar ratio down to r = 0.007, and four frequency bands to distinguish foregrounds. Piper will accomplish this by mapping 85% of the sky in four frequency bands (200, 270, 350, 600 GHz) over a series of 8 conventional balloon flights from the northern and southern hemispheres. The instrument has background-limited sensitivity provided by fully cryogenic (1.5 K) optics focusing the sky signal onto four 32×40-pixel arrays of time-domain multiplexed Transition-Edge Sensor (TES) bolometers held at 140 milli-Kelvin. Polarization sensitivity and systematic control are provided by front-end Variabledelay Polarization Modulators (VPMs), which rapidly modulate only the polarized sky signal at 3 Hz and allow Piper to instantaneously measure the full Stokes vector (I,Q,U,0V) for each pointing. We describe the Piper instrument and progress towards its first flight.

polarimeter↗

Radial Clearance Found To Play a Key Role in the Performance of Compliant Foil Air Bearings

Compliant foil air bearings are at the forefront of the Oil-Free turbomachinery revolution, which supports gas turbine engines with hydrodynamic bearings that use air instead of oil as the working fluid. These types of bearings have been around for almost 50 years and have found a home in several commercial applications, such as in air cycle machines, turbocompressors, and microturbines, but are now being aggressively pursued for use in small and midrange aircraft gas turbine engines. Benefits include higher operating speeds and temperatures, lower maintenance costs, and greater reliability. The Oil-Free Turbomachinery team at the NASA Glenn Research Center is working to foster the transition of Oil-Free technology into gas turbine engines by performing in-house experiments on foil air bearings in order to gain a greater insight into their complex operating principles. A research program recently undertaken at Glenn focused on the concept of radial clearance and its influence on bearing performance. The tests were conducted on foil bearings with different radial clearances. As defined for a foil bearing, radial clearance is a measure of the small amount of shaft radial motion that is present from play that exists in the elastic support structure, such as between the top and bump foils and the bump foils and bearing shell (see the drawing). With an insufficient amount of radial clearance, the bearing imparts a high preload on the shaft, which when excessive, can reduce the loadcarrying capability of the bearing. On the other hand, systems using foil bearings with excessive radial clearance may experience rotordynamic instabilities because of low bearing preload. Therefore, without a more thorough understanding of radial clearance, it is difficult to accurately predict the performance of a given bearing design. The test program demonstrated that there is a direct correlation between radial clearance and the performance of foil air bearings. As shown in the graph, an optimum radial clearance exists that will maximize the amount of load that the bearing is capable of supporting. With respect to this optimum, two different performance regimes were observed that are a function of the amount of radial clearance. Tests showed that bearings with radial clearances below the optimum in regime I were susceptible to sudden seizure, a failure mode indicative of thermal runaway caused by high preload. The high preload is in response to an insufficient amount of radial clearance available to accommodate the thermal growth of the bearing and shaft. However, radial clearances greater than the optimum in regime II resulted in low bearing preloads that did not cause any heat-related problems, and the failure mode was due to fluid-film breakdown. In fact, bearings operating with radial clearances twice as much as the optimum suffered a decrease in the maximum load capacity of only about 20 percent. Therefore, special attention has to be given to the range of operating conditions expected in the bearing/shaft system since changes in temperature, centrifugal, and hydrodynamic effects can all affect radial clearance. This enhanced understanding of foil air bearing behavior will greatly aid our efforts to transition Oil-Free technology to future aircraft engines.

Radil, Kevin C.↗

Aerodynamic Characteristics of Various Configurations of a Model of a 45 Degree Swept-wing Airplane at a Mach Number of 2.01

An investigation has been conducted at the Langley 4- by 4-foot supersonic pressure tunnel at a Mach nmber of 2.01 to determine the aerodynamic characteristics of several configurations of a model of a 45 deg swept-wing airplane. The basic configuratin had a wing with 45 deg sweepback at the quarter-chord line, aspect ration 3.2, taper ration 0.468, NACA 65A005.5 sections just outboard of the inlet and NACA 65A003.7 sections at the tip. The wing was mounted slightly above the body center line and an all-movable horizantal tail was located slightly below the extended chord line of the wing. Tre design incorporated twin wing-root supersonic inlets ducted to a single exit at the base of the fuselage. The configurations investigated included an extended nose length, a bumped-fuselage afterbody, an inlet droop, an lncreased wing aspect ratio, and a revised canopy shape. Configurations employing the wing of increased aspect ratio of 3.7, which constituted the bulk of the tests, produced about a 10-percent increase in lift and in longitudinal stability as compared with the basic wing of aspect ratio 3.2. There was a slight but masurable increase in minimum drag and maximum lift-drag ratio.

Spearman, Leroy M↗

The use and misuse of statistical analyses

The statistical techniques most often used in space physics include Fourier analysis, linear correlation, auto- and cross-correlation, power spectral density, and superposed epoch analysis. Tests are presented which can evaluate the significance of the results obtained through each of these. Data presented without some form of error analysis are frequently useless, since they offer no way of assessing whether a bump on a spectrum or on a superposed epoch analysis is real or merely a statistical fluctuation. Among many of the published linear correlations, for instance, the uncertainty in the intercept and slope is not given, so that the significance of the fitted parameters cannot be assessed.

Reiff, P. H.↗