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At least 667 records · Page 37

Static Performance of a Wing-Mounted Thrust Reverser Concept

An experimental investigation was conducted in the Jet-Exit Test Facility at NASA Langley Research Center to study the static aerodynamic performance of a wing-mounted thrust reverser concept applicable to subsonic transport aircraft. This innovative engine powered thrust reverser system is designed to utilize wing-mounted flow deflectors to produce aircraft deceleration forces. Testing was conducted using a 7.9%-scale exhaust system model with a fan-to-core bypass ratio of approximately 9.0, a supercritical left-hand wing section attached via a pylon, and wing-mounted flow deflectors attached to the wing section. Geometric variations of key design parameters investigated for the wing-mounted thrust reverser concept included flow deflector angle and chord length, deflector edge fences, and the yaw mount angle of the deflector system (normal to the engine centerline or parallel to the wing trailing edge). All tests were conducted with no external flow and high pressure air was used to simulate core and fan engine exhaust flows. Test results indicate that the wing-mounted thrust reverser concept can achieve overall thrust reverser effectiveness levels competitive with (parallel mount), or better than (normal mount) a conventional cascade thrust reverser system. By removing the thrust reverser system from the nacelle, the wing-mounted concept offers the nacelle designer more options for improving nacelle aero dynamics and propulsion-airframe integration, simplifying nacelle structural designs, reducing nacelle weight, and improving engine maintenance access.

Asbury, Scott C.↗

Magnetoresistive Flux Focusing Eddy Current Flaw Detection

A giant magnetoresistive flux focusing eddy current device effectively detects deep flaws in thick multilayer conductive materials. The probe uses an excitation coil to induce eddy currents in conducting material perpendicularly oriented to the coil s longitudinal axis. A giant magnetoresistive (GMR) sensor, surrounded by the excitation coil, is used to detect generated fields. Between the excitation coil and GMR sensor is a highly permeable flux focusing lens which magnetically separates the GMR sensor and excitation coil and produces high flux density at the outer edge of the GMR sensor. The use of feedback inside the flux focusing lens enables complete cancellation of the leakage fields at the GMR sensor location and biasing of the GMR sensor to a location of high magnetic field sensitivity. In an alternate embodiment, a permanent magnet is positioned adjacent to the GMR sensor to accomplish the biasing. Experimental results have demonstrated identification of flaws up to 1 cm deep in aluminum alloy structures. To detect deep flaws about circular fasteners or inhomogeneities in thick multi-layer conductive materials, the device is mounted in a hand-held rotating probe assembly that is connected to a computer for system control, data acquisition, processing and storage.

Russell A Wincheski↗

Graphite Composite Panel Polishing Fixture

The use of high-strength, lightweight composites for the fixture is the novel feature of this innovation. The main advantage is the light weight and high stiffness-to-mass ratio relative to aluminum. Meter-class optics require support during the grinding/polishing process with large tools. The use of aluminum as a polishing fixture is standard, with pitch providing a compliant layer to allow support without deformation. Unfortunately, with meter-scale optics, a meter-scale fixture weighs over 120 lb (.55 kg) and may distort the optics being fabricated by loading the mirror and/or tool used in fabrication. The use of composite structures that are lightweight yet stiff allows standard techniques to be used while providing for a decrease in fixture weight by almost 70 percent. Mounts classically used to support large mirrors during fabrication are especially heavy and difficult to handle. The mount must be especially stiff to avoid deformation during the optical fabrication process, where a very large and heavy lap often can distort the mount and optic being fabricated. If the optic is placed on top of the lapping tool, the weight of the optic and the fixture can distort the lap. Fixtures to support the mirror during fabrication are often very large plates of aluminum, often 2 in. (.5 cm) or more in thickness and weight upwards of 150 lb (68 kg). With the addition of a backing material such as pitch and the mirror itself, the assembly can often weigh over 250 lb (.113 kg) for a meter-class optic. This innovation is the use of a lightweight graphite panel with an aluminum honeycomb core for use as the polishing fixture. These materials have been used in the aerospace industry as structural members due to their light weight and high stiffness. The grinding polishing fixture consists of the graphite composite panel, fittings, and fixtures to allow interface to the polishing machine, and introduction of pitch buttons to support the optic under fabrication. In its operation, the grinding polishing fixture acts as a reaction structure to the polishing tool. It must be stiff enough to avoid imparting a distorted shape to the optic under fabrication and light enough to avoid self-deflection. The fixture must also withstand significant tangential loads from the polishing machine during operations.

Hagopian, John↗

Space Launch System Vibration Analysis Support

The ultimate goal for my efforts during this internship was to help prepare for the Space Launch System (SLS) integrated modal test (IMT) with Rodney Rocha. In 2018, the Structural Engineering Loads and Dynamics Team will have 10 days to perform the IMT on the SLS Integrated Launch Vehicle. After that 10 day period, we will have about two months to analyze the test data and determine whether the integrated vehicle modes/frequencies are adequate for launching the vehicle. Because of the time constraints, NASA must have newly developed post-test analysis methods proven well and with technical confidence before testing. NASA civil servants along with help from rotational interns are working with novel techniques developed and applied external to Johnson Space Center (JSC) to uncover issues in applying this technique to much larger scales than ever before. We intend to use modal decoupling methods to separate the entangled vibrations coming from the SLS and its support structure during the IMT. This new approach is still under development. The primary goal of my internship was to learn the basics of structural dynamics and physical vibrations. I was able to accomplish this by working on two experimental test set ups, the Simple Beam and TAURUS-T, and by doing some light analytical and post-processing work. Within the Simple Beam project, my role involves changing the data acquisition system, reconfiguration of the test set up, transducer calibration, data collection, data file recovery, and post-processing analysis. Within the TAURUS-T project, my duties included cataloging and removing the 30+ triaxial accelerometers, coordinating the removal of the structure from the current rolling cart to a sturdy billet for further testing, preparing the accelerometers for remounting, accurately calibrating, mounting, and mapping of all accelerometer channels, and some testing. Hammer and shaker tests will be performed to easily visualize mode shapes at low frequencies. Short analytical projects using MATLAB were also assigned to aid in research efforts. These included integration of acceleration data for comparison to measured displacement data. Laplace and Fourier transforms were also investigated to determine viability as a method of modal decoupling. In addition to these projects, I was also able contribute work that would benefit future interns and the division as a whole. I gave a short presentation and answered questions to aid in the recruitment of subsequent interns and co-ops for the division. I also assisted in revisions and additions to Intern/Co-Op Handbook to provide incoming employees with background information on the organization they are about to work for. I further developed tutorial on Pulse software, which was used for data acquisition for both experiments and will be helpful to interns and engineers that may be unfamiliar to the software. I gained a diverse range of experience throughout my internship. I was introduced to advanced dynamics and analytical techniques. This was through new experience with both hands on experimentation and analytical post processing methods. I was exposed to the benefits of interdepartmental collaboration and developed stronger skills in time management by coordinating two different tests at once. This internship provided an excellent opportunity to see how engineering theories applied to real life scenarios, and an introduction to how NASA/JSC solves technical problems.

Johnson, Katie↗

Whirl Flutter Stability and Its Influence on the Design of the Distributed Electric Propeller Aircraft X- 57

This paper studies the whirl flutter stability of the NASA experimental electric propulsion aircraft designated the X-57 Maxwell. whirl flutter stability is studied at two flight conditions: sea level at 2700 RPM to represent take-off and landing and 8000 feet at 2250 RPM to represent cruise. Two multibody dynamics analyses are used: CAMRAD II and Dymore. The CAMRAD II model is a semi-span X-57 model with a modal representation for the wing/pylon system. The Dymore model is a semi-span wing with a propeller composed of beam elements for the wing/pylon system that airloads can be applied to. The two multibody dynamics analyses were verified by comparing structural properties between each other and the NASTRAN analysis. For whirl flutter, three design revisions of the wing and pylon mount system are studied. The predicted frequencies and damping ratio of the wing modes show good agreements between the two analyses. Dymore tended to predict a slightly lower damping ratio as velocity increased for all three dynamic modes presented. Whirl flutter for the semi-span model was not present up to 500 knots for the latest design, well above the operating range of the X-57.

Hoover, Christian B.↗

Characterization of Freestream Disturbances in Conventional Hypersonic Wind Tunnels

While low disturbance ("quiet") hypersonic wind tunnels are believed to provide more reliable extrapolation of boundary layer transition behavior from ground to flight, the presently available quiet facilities are limited to Mach 6, moderate Reynolds numbers, low freestream enthalpy, and subscale models. As a result, only conventional ("noisy") wind tunnels can reproduce both Reynolds numbers and enthalpies of hypersonic flight configurations, and must therefore be used for flight vehicle test and evaluation involving high Mach number, high enthalpy, and larger models. This article outlines the recent progress and achievements in the characterization of tunnel noise that have resulted from the coordinated effort within the AVT-240 specialists group on hypersonic boundary layer transition prediction. New Direct Numerical Simulation (DNS) datasets elucidate the physics of noise generation inside the turbulent nozzle wall boundary layer, characterize the spatiotemporal structure of the freestream noise, and account for the propagation and transfer of the freestream disturbances to a pitot-mounted sensor. The new experimental measurements cover a range of conventional wind tunnels with different sizes and Mach numbers from 6 to 14 and extend the database of freestream fluctuations within the spectral range of boundary layer instability waves over commonly tested models. Prospects for applying the computational and measurement datasets for developing mechanism-based transition prediction models are discussed.

Duan, Lian↗

Mineralogy and Spectroscopy of Mount Etna Lava Flows as an Analogue to Venus

Reports of geologically recent volcanism at Venus [1–3] raise the question of whether Venus is actively resurfacing. Observing the venusian surface is difficult due to the planet’s thick, relatively opaque atmosphere, but emission from the surface is detectable via a few atmospheric windows in the near-infrared (NIR) around 1 μm [4]. Spectroscopy of rocks at these wavelengths varies due to its primary composition and the presence of secondary weathering products [2, 5, 6]. If degree of alteration can be tied to the spectroscopic response, then the weathering of the venusian surface can reveal its age and extent of recent volcanism [2, 7]. Mount Etna on Earth is a potential analogue to Venus that can aid our understanding. The composite volcano is currently active and exhibits a progression of dated lava flows with a range of textures (‘a‘¯a versus p¯ahoehoe flows) and degrees of alteration [8]. While not a perfect analogue due to differing weathering environments, Mount Etna represents a natural age progression of altered basaltic rock [8] that can provide a useful comparison to volcanic structures on Venus. Here we will determine if spectroscopy can determine the alteration state of these flows as a proxy for their age. Future missions to Venus such as VERITAS, En- Vision, and DAVINCI will observe the surface in NIR emissivity. Kirchhoff’s Law holds that e = 1−r, where e is the emissivity and r is the reflectance. NIR emissivity can be reliably calculated from reflectance measurements of rocks [9], so laboratory reflectance spectroscopy is useful to rapidly test potential Venus analogue materials.

Gabriel L. Eggers↗

Two-Dimensional Planetary Surface Landers

We proposed to develop a new landing approach that significantly reduces development time and obviates the most complicated, most expensive, and highest-risk phase of a landing mission. The concept is a blanket- or carpet-like two-dimensional (2D) lander (~1-m × 1-m surface area and <1-cm thick) with a low mass/drag ratio, which allows the lander to efficiently shed its approach velocity and provide a more robust structure for landing integrity. The form factor of these landers allows dozens to be stacked on a single spacecraft for transport and distributed en masse to the surface. Lander surfaces will be populated on both sides by surface-mount, low-profile sensors and instruments, surface-mount telecom, solar cells, batteries, processors, and memory. Landers will also incorporate thin flexible electronics, made possible in part by printable electronics technology. The mass and size of these highly capable technologies further reduces the required stiffness and mass of the lander structures to the point that compliant, lightweight, robust landers capable of passive landings are possible. This capability avoids the costly, complex use of rockets, radar, and associated structure and control systems. This approach is expected to provide an unprecedented science payload mass to spacecraft mass ratio of approximately 80% (estimated based on current knowledge). This compared to ~1% for Pathfinder, ~17% for MER, and 22% for MSL rovers. Clearly, one difference is rovers vs. a lower capability lander. An outcome of the Phase I study is a clear roadmap for near-term demonstration and long-term technology development.

Landers↗

User's guide to computer programs JET 5A and CIVM-JET 5B to calculate the large elastic-plastic dynamically-induced deformations of multilayer partial and/or complete structural rings

These structural ring deflections lie essentially in one plane and, hence, are called two-dimensional (2-d). The structural rings may be complete or partial; the former may be regarded as representing a fragment containment ring while the latter may be viewed as a 2-d fragment-deflector structure. These two types of rings may be either free or supported in various ways (pinned-fixed, locally clamped, elastic-foundation supported, mounting-bracket supported, etc.). The initial geometry of each ring may be circular or arbitrarily curved; uniform-thickness or variable-thickness rings may be analyzed. Strain-hardening and strain-rate effects of initially-isotropic material are taken into account. An approximate analysis utilizing kinetic energy and momentum conservation relations is used to predict the after-impact velocities of each fragment and of the impact-affected region of the ring; this procedure is termed the collision-imparted velocity method (CIVM) and is used in the CIVM-JET 5 B program. This imparted-velocity information is used in conjunction with a finite-element structural response computation code to predict the transient, large-deflection, elastic-plastic responses of the ring. Similarly, the equations of motion of each fragment are solved in small steps in time. Provisions are made in the CIVM-JET 5B code to analyze structural ring response to impact attack by from 1 to 3 fragments, each with its own size, mass, translational velocity components, and rotational velocity. The effects of friction between each fragment and the impacted ring are included.

Wu, R. W. H.↗

Meeting the Grand Challenge of Protecting Astronauts Health: Electrostatic Active Space Radiation Shielding for Deep Space Missions

This report describes the research completed during 2011 for the NASA Innovative Advanced Concepts (NIAC) project. The research is motivated by the desire to safely send humans in deep space missions and to keep radiation exposures within permitted limits. To this end current material shielding, developed for low earth orbit missions, is not a viable option due to payload and cost penalties. The active radiation shielding is the path forward for such missions. To achieve active space radiation shielding innovative large lightweight gossamer space structures are used. The goal is to deflect enough positive ions without attracting negatively charged plasma and to investigate if a charged Gossamer structure can perform charge deflections without significant structural instabilities occurring. In this study different innovative configurations are explored to design an optimum active shielding. In addition, to establish technological feasibility experiments are performed with up to 10kV of membrane charging, and an electron flux source with up to 5keV of energy and 5mA of current. While these charge flux energy levels are much less than those encountered in space, the fundamental coupled interaction of charged Gossamer structures with the ambient charge flux can be experimentally investigated. Of interest are, will the EIMS remain inflated during the charge deflections, and are there visible charge flux interactions. Aluminum coated Mylar membrane prototype structures are created to test their inflation capability using electrostatic charging. To simulate the charge flux, a 5keV electron emitter is utilized. The remaining charge flux at the end of the test chamber is measured with a Faraday cup mounted on a movable boom. A range of experiments with this electron emitter and detector were performed within a 30x60cm vacuum chamber with vacuum environment capability of 10-7 Torr. Experiments are performed with the charge flux aimed at the electrostatically inflated membrane structure (EIMS) in both charged and uncharged configurations. The amount of charge shielding behind and around the EIMS was studied for different combinations of membrane structure voltages and electron energies. Both passive and active shielding were observed, with active shielding capable of deflecting nearly all incoming electrons. The pattern of charge distribution around the structure was studied as well as the stability of the structures in the charge flow. The charge deflection experiments illustrate that the EIMS remain inflated during charge deflection, but will experience small amplitude oscillations. Investigations were performed to determine a potential cause of the vibrations. It is postulated these vibrations are due to the charge flux causing local membrane charge distribution changes. As the membrane structure inflation pressure is changed, the shape responds, and causes the observed sustained vibration. Having identified this phenomenon is important when considering electrostatically inflated membrane structures (EIMS) in a space environment. Additionally, this project included a study of membrane material impacts, specifically the impact of membrane thickness. Extremely thin materials presented new challenges with vacuum preparation techniques and rapid charging. The thinner and lighter membrane materials were successfully inflated using electrostatic forces in a vacuum chamber. However, care must be taken when varying the potentials of such lighter structures as the currents can cause local heating and melting of the very thin membranes. Lastly, a preliminary analysis is performed to study rough order of magnitude power requirements for using EIMS for radiation shielding. The EIMS power requirement becomes increasingly more challenging as the spacecraft voltage is increased. As a result, the emphasis is on the deflection of charges away from the spacecraft rather than totally stopping them. This significantly alleviates the initial power requirements. With modest technological development(s) active shielding is emerging to be a viable option.

Radiation↗

Space exposure of composite materials for large space structures (A0134)

The objective of this experiment is to evaluate the effects of the near-Earth orbital environment on the physical and chemical properties of laminated continuous-filament composites and composites resin films for use in large space structures and advanced spacecraft. The experiment is passive and occupies about one-half of a 6-in.-deep peripheral tray. Specimens of composite materials and polymeric and resin films are arranged above and below the experiment mounting plate to enable both exposure and nonexposure to sunlight. This provides a comparison of the effects of ultraviolet plus vacuum plus thermal cycling and those of vacuum plus thermal cycling on these materials. The experiment tray is thermally isolated from the Long Duration Exposure Facility structure to allow the material specimens to experience a wide range of thermal cycles. Tensile and compression specimens will be used to evaluate the laminated composite materials. A number of the specimens are precut and ready for testing after space exposure, whereas other specimens will be prepared from larger samples.

Wayne S Slemp↗

Vibration Response Predictions for Heavy Panel Mounted Components from Panel Acreage Environment Specifications

The development of new launch vehicles in the Aerospace industry often relies on response measurements taken from previously developed vehicles during various stages of liftoff and ascent, and from wind tunnel models. These measurements include sound pressure levels, dynamic pressures in turbulent boundary layers and accelerations. Rigorous statistical scaling methods are applied to the data to derive new environments and estimate the performance of new skin panel structures. Scaling methods have proven to be reliable, particularly for designs similar to the vehicles used as the basis for scaling, and especially in regions of smooth acreage without exterior protuberances or heavy components mounted to the panel. To account for response attenuation of a panel-mounted component due to its apparent mass at higher frequencies, the vibroacoustics engineer often reduces the acreage vibration according to a weight ratio first suggested by Barrett. The accuracy of the reduction is reduced with increased weight of the panel-mounted component, and does not account for low-frequency amplification of the component/panel response as a system. A method is proposed that combines acreage vibration from scaling methods with finite element analysis to account for the frequency-dependent dynamics of heavy panel-mounted components. Since the acreage and mass-loaded skins respond to the same dynamic input pressure, such pressure may be eliminated in favor of a frequency-dependent scaling function applied to the acreage vibration to predict the mass-loaded panel response. The scaling function replaces the Barrett weight ratio, and contains all of the dynamic character of the loaded and unloaded skin panels. The solution simplifies for spatially uncorrelated and fully correlated input pressures. Since the prediction uses finite element models of the loaded and unloaded skins, a rich suite of response data are available to the design engineer, including interface forces, stress and strain, as well as acceleration and displacement. An extension of the method is also developed to incorporate the effect of a local protuberance near a heavy component. Acreage environments from traditional scaling methods with and without protuberance effects serve as the basis for the extension. Authors:

Harrison, Phillip↗

Complete Tem-Tomography: 3D Structure of Gems Cluster

GEMS (glass with embedded metal and sulfide) grains in interplanetary dust particles (IDPs) are considered to be one of the ubiquitous and fundamental building blocks of solids in the Solar System. They have been considered to be interstellar silicate dust that survived various metamorphism or alteration processes in the protoplanetary disk but the elemental and isotopic composition measurements suggest that most of them have been formed in the protoplanetary disk as condensates from high temperature gas. This formation model is also supported by the formation of GEMS-like grains with respect to the size, mineral assemblage, texture and infrared spectrum by condensation experiments from mean GEMS composition materials. Previous GEMS studies were performed only with 2D observation by transmission electron microscopy (TEM) or scanning TEM (STEM). However, the 3D shape and structure of GEMS grains and the spatial distribution of Fe/FeS's has critical information about their formation and origin. Recently, the 3D structure of GEMS grains in ultrathin sections of cluster IDPs was revealed by electron tomography using a TEM/STEM (JEM-2100F, JEOL). However, CT images of thin sections mounted on Cu grids acquired by conventional TEM-tomography are limited to low tilt angles (e. g., less than absolute value of 75 deg. In fact, previous 3D TEM observations of GEMS were affected by some artifacts related to the limited tilt range in the TEM used. Complete tomographic images should be acquired by rotating the sample tilt angle over a range of more than absolute value of 80 deg otherwise the CT images lose their correct structures. In order to constrain the origin and formation process of GEMS grains more clearly, we performed complete electron tomography for GEMS grains. Here we report the sample preparation method we have developed for this study, and the preliminary results.

Matsuno, J.↗

Primary mirror and mount technology for the Stratospheric Observatory for Infrared Astronomy (SOFIA) telescope

Candidate technologies for a lightweight primary mirror for the SOFIA telescope are evaluated for both mirror blank fabrication and polishing. Two leading candidates for the type mirror blank are considered: the frit-bonded, structured form, and the thin meniscus form. The feasible mirror is required to be very lightweight with an areal density of approximately 100 kg/sq m, have an f/ratio near 1.0, and have surface quality that permits imaging in the visible as well as the infrared. Also considered are the results of a study conducted to assess the feasibility of designing a suitable mounting system for the primary mirror. The requirements for the mount design are given both in terms of the environmental conditions and the expected optical performance. PATRAN and NASTRAN programs are used to model mirror and mounting. The sandwich-type mirror made of ultra low expansion silica with square cells in the core, is modeled using equivalent solid elements for the core. The design study produces primary mirror surface deflections in 1g as a function of mirror elevation angles. The surface is analyzed using an optical analysis program, FRINGE, to give a prediction of the mirror optical performance. Results from this analysis are included.

Melugin, Ramsey K.↗

Structural evaluation of deployable aerodynamic spike booms

An extendable boom consisting of a series of telescopic cylindrical tube segments and overlapping lock joints developed for use as an aerodynamic spike mounted atop a missile is described. Two candidate design concepts differing mainly in the particular overlapping lock joint designs are undergoing a combined analytical/experimental evaluation. Some of the results of this evaluation are presented.

Richter, B. J.↗

Analytical and experimental study of a standing torus with normal loads

Finite element analysis is applied to study the large deflection and stress of a thin-walled pressurized torus loaded by normal contact with a plane. Experimentally determined stresses are compared to those resulting from finite element analysis at various meridional and circumferential coordinates of the torus, including the footprint area. Circumferential strains compare favorably while meridional strains are higher in the finite element analysis, probably due to slippage of the boundary at the rim. The STAGS finite element computer program was used. The purpose of the study was to evaluate the various program options for structural loading, for material modeling, for stress analysis, and for grid refinement. The experimental model, a thin-walled rubber tube mounted on a steel cylindrical rim, provided measured results to compare with various analytical trade-offs. It was found that there was almost no difference in predicted deflections or stress distributions between linear and nonlinear material description. However, the difference between linear analysis and that of geometric nonlinearities utilizing incremental loading was marked.

Mack, M. J., Jr.↗

Development and analysis of a STOL supersonic cruise fighter concept

The application of advanced and emerging technologies to a fighter aircraft concept is described. The twin-boom fighter (TBF-1) relies on a two dimensional vectoring/reversing nozzle to provide STOL performance while also achieving efficient long range supersonic cruise. A key feature is that the propulsion package is placed so that the nozzle hinge line is near the aircraft center-of-gravity to allow large vector angles and, thus, provide large values of direct lift while minimizing the moments to be trimmed. The configurations name is derived from the long twin booms extending aft of the engine to the twin vertical tails which have a single horizontal tail mounted atop and between them. Technologies utilized were an advanced engine (1985 state-of-the-art), superplastic formed/diffusion bonded titanium structure, advanced controls/avionics/displays, supersonic wing design, and conformal weapons carriage. The integration of advanced technologies into this concept indicate that large gains in takeoff and landing performance, maneuver, acceleration, supersonic cruise speed, and range can be acieved relative to current fighter concepts.

Dollyhigh, S. M.↗

Cost considerations in database selection - A comparison of DIALOG and ESA/IRS

It is pointed out that there are many factors which affect the decision-making process in determining which databases should be selected for conducting the online search on a given topic. In many cases, however, the major consideration will be related to cost. The present investigation is concerned with a comparison of the costs involved in making use of DIALOG and the European Space Agency's Information Retrieval Service (ESA/IRS). The two services are very comparable in many respects. Attention is given to pricing structure, telecommunications, the number of databases, prints, time requirements, a table listing online costs for DIALOG and ESA/IRS, and differences in mounting databases. It is found that ESA/IRS is competitively priced when compared to DIALOG, and, despite occasionally higher telecommunications costs, may be even more economical to use in some cases.

Jack, R. F.↗