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NASA NTRS1995

Sea surface topography fields of the tropical Pacific from data assimilation

Time series of maps of monthly tropical Pacific dynamic topography anomalies from 1979 through 1985 were constructed by means of assimilation of the tide gauge and expendable bathythermograph (XBT) data into a linear model driven by observed winds. Estimates of error statistics were calculated and compared to actual differences between hindcasts and observations. Four experiements were performed as follows: one with no assimilation, one with assimiation of sea level anomaly data from eight selected island tide gauge stations, one with assimilation of dynamic height anomalies derived from XBT data, and one with both XBT and tide gauge data assimilated. Data from seven additional tide gauge stations were withheld from the assimilation process and used for verification in all four experiements. Statistical objective maps based on data alone were also constructed for comparison purposes. The dynamic response of the model without assimilation was, in general, weaker than the observed response. Assimilation resulted in enhanced signal amplitude in all three assimilation experiments. With few exceptions the error estimated generated by the Kalman filter appeared quite reasonable. Since the error processes cannot be assumed to be white or stationary, we could find no straightforward way to test the formal statistical hypothesis that the time series of differences between the filter ouput and the actual observations were drawn from a population with statistics given by the Kalman filter estimaes. We found that the best filter we could devise was still short of the goal of producing a white innovation sequence. Extensive changes in the assumed error statistics make only marginal differences. The same is true for long time and space scale behavior of different models with richer physics and finer resolution. Better data assimilation results will probably require relaxation of the assumptions of stationarity and serial independence of the errors. Formation of such detailed noise models will require longer time series, with the attendant problems of matching very different data sets.

Miller, Robert N.↗

NASA NTRS1995

Acoustic calibration apparatus for calibrating plethysmographic acoustic pressure sensors

An apparatus for calibrating an acoustic sensor is described. The apparatus includes a transmission material having an acoustic impedance approximately matching the acoustic impedance of the actual acoustic medium existing when the acoustic sensor is applied in actual in-service conditions. An elastic container holds the transmission material. A first sensor is coupled to the container at a first location on the container and a second sensor coupled to the container at a second location on the container, the second location being different from the first location. A sound producing device is coupled to the container and transmits acoustic signals inside the container.

Zuckerwar, Allan J.↗

NASA NTRS1995

Fast temporal neural learning using teacher forcing

A neural network is trained to output a time dependent target vector defined over a predetermined time interval in response to a time dependent input vector defined over the same time interval by applying corresponding elements of the error vector, or difference between the target vector and the actual neuron output vector, to the inputs of corresponding output neurons of the network as corrective feedback. This feedback decreases the error and quickens the learning process, so that a much smaller number of training cycles are required to complete the learning process. A conventional gradient descent algorithm is employed to update the neural network parameters at the end of the predetermined time interval. The foregoing process is repeated in repetitive cycles until the actual output vector corresponds to the target vector. In the preferred embodiment, as the overall error of the neural network output decreasing during successive training cycles, the portion of the error fed back to the output neurons is decreased accordingly, allowing the network to learn with greater freedom from teacher forcing as the network parameters converge to their optimum values. The invention may also be used to train a neural network with stationary training and target vectors.

Toomarian, Nikzad↗

NASA NTRS1996

Advanced interactive display formats for terminal area traffic control

This report describes the basic design considerations for perspective air traffic control displays. A software framework has been developed for manual viewing parameter setting (MVPS) in preparation for continued, ongoing developments on automated viewing parameter setting (AVPS) schemes. Two distinct modes of MVPS operations are considered, both of which utilize manipulation pointers imbedded in the three-dimensional scene: (1) direct manipulation of the viewing parameters -- in this mode the manipulation pointers act like the control-input device, through which the viewing parameter changes are made. Part of the parameters are rate controlled, and part of them position controlled. This mode is intended for making fast, iterative small changes in the parameters. (2) Indirect manipulation of the viewing parameters -- this mode is intended primarily for introducing large, predetermined changes in the parameters. Requests for changes in viewing parameter setting are entered manually by the operator by moving viewing parameter manipulation pointers on the screen. The motion of these pointers, which are an integral part of the 3-D scene, is limited to the boundaries of the screen. This arrangement has been chosen in order to preserve the correspondence between the spatial lay-outs of the new and the old viewing parameter setting, a feature which contributes to preventing spatial disorientation of the operator. For all viewing operations, e.g. rotation, translation and ranging, the actual change is executed automatically by the system, through gradual transitions with an exponentially damped, sinusoidal velocity profile, in this work referred to as 'slewing' motions. The slewing functions, which eliminate discontinuities in the viewing parameter changes, are designed primarily for enhancing the operator's impression that he, or she, is dealing with an actually existing physical system, rather than an abstract computer-generated scene. The proposed, continued research efforts will deal with the development of automated viewing parameter setting schemes. These schemes employ an optimization strategy, aimed at identifying the best possible vantage point, from which the air traffic control scene can be viewed for a given traffic situation. They determine whether a change in viewing parameter setting is required and determine the dynamic path along which the change to the new viewing parameter setting should take place.

Grunwald, Arthur J.↗

NASA NTRS1995

The NASA landing gear test airplane

A tire and landing gear test facility has been developed and incorporated into a Convair 990 aircraft. The system can simulate tire vertical load profiles to 250,000 lb, sideslip angles to 15 degrees, and wheel braking on actual runways. Onboard computers control the preprogrammed test profiles through a feedback loop and also record three axis loads, tire slip angle, and tire condition. The aircraft to date has provided tire force and wear data for the Shuttle Orbiter tire on three different runways and at east and west coast landing sites. This report discusses the role of this facility in complementing existing ground tire and landing gear test facilities, and how this facility can simultaneously simulate the vertical load, tire slip, velocity, and surface for an entire aircraft landing. A description is given of the aircraft as well as the test system. An example of a typical test sequence is presented. Data collection and reduction from this facility are discussed, as well as accuracies of calculated parameters. Validation of the facility through ground and flight tests is presented. Tests to date have shown that this facility can operate at remote sites and gather complete data sets of load, slip, and velocity on actual runway surfaces. The ground and flight tests have led to a successful validation of this test facility.

Carter, John F.↗

NASA NTRS1995

Urine Pretreat Injection System

A new method of introducing the OXONE (Registered Trademark) Monopersulfate Compound for urine pretreat into a two-phase urine/air flow stream has been successfully tested and evaluated. The feasibility of this innovative method has been established for purposes of providing a simple, convenient, and safe method of handling a chemical pretreat required for urine processing in a microgravity space environment. Also, the Oxone portion of the urine pretreat has demonstrated the following advantages during real time collection of 750 pounds of urine in a Space Station design two-phase urine Fan/Separator: Eliminated urine precipitate buildup on internal hardware and plumbing; Minimized odor from collected urine; and Virtually eliminated airborne bacteria. The urine pretreat, as presently defined for the Space Station program for proper downstream processing of urine, is a two-part chemical treatment of 5.0 grams of Oxone and 2.3 ml of H2SO4 per liter of urine. This study program and test demonstrated only the addition of the proper ratio of Oxone into the urine collection system upstream of the Fan/Separator. This program was divided into the following three major tasks: (1) A trade study, to define and recommend the type of Oxone injection method to pursue further; (2) The design and fabrication of the selected method; and (3) A test program using high fidelity hardware and fresh urine to demonstrate the method feasibility. The trade study was conducted which included defining several methods for injecting Oxone in different forms into a urine system. Oxone was considered in a liquid, solid, paste and powered form. The trade study and the resulting recommendation were presented at a trade study review held at Hamilton Standard on 24-25 October 94. An agreement was reached at the meeting to continue the solid tablet in a bag concept which included a series of tablets suspended in the urine/air flow stream. These Oxone tablets would slowly dissolve at a controlled rate providing the proper concentration in the collected urine. To implement the solid tablet in a bag approach, a design concept was completed with prototype drawings of the complete urine pretreat prefilter assembly. A successful fabrication technique was developed for retaining the Oxone tablets in a fabric casing attached to the end of the existing Space Station Waste Collection System urine prefilter assembly. The final pretreat prefilter configuration held sufficient Oxone in a tablet form to allow normal scheduled daily (or twice daily) change out of the urine filter depending on the use rate of the Space Station urine collection system. The actual tests to prove the concept were conducted using the Urine Fan/Separator assembly that was originally used in the STS-52 Design Test Objective (DTO) urinal assembly. Other related tests were conducted to demonstrate the actual minimum ratio of Oxone to urine that will control microbial growth.

Source record↗

NASA NTRS1996

High-Speed Civil Transport Forecast: Simulated Airlines Scenarios for Mach 1.6, Mach 2.0, and Mach 2.4 Configurations for Year 2015

The report describes the development of a database of fuel burn and emissions from projected High Speed Civil Transport (HSCT) fleets that reflect actual airlines' networks, operational requirement, and traffic flow as operated by simulated world wide airlines for Mach 1.6, 2.0, and 2.4 HSCT configurations. For the year 2015, McDonnell Douglas Corporation created two supersonic commercial air traffic networks consisting of origin-destination city pair routes and associated traffic levels. The first scenario represented a manufacturing upper limit producible HSCT fleet availability by year 2015. The fleet projection of the Mach 2.4 configuration for this scenario was 1059 units with a traffic capture of 70 percent. The second scenario focused on the number of units that can minimally be produced by the year 2015. Using realistic production rates, the HSCT fleet projection amounts to 565 units. The traffic capture associated with this fleet was estimated at 40 percent. The airlines network was extracted from the actual networks of 21 major world airlines. All the routes were screened for suitability for HSCT operations. The route selection criteria included great circle distance, difference between flight path distance and great circle distance to avoid overland operations, and potential flight frequency.

Metwally, Munir↗

NASA NTRS1996

Analytical Fuselage and Wing Weight Estimation of Transport Aircraft

A method of estimating the load-bearing fuselage weight and wing weight of transport aircraft based on fundamental structural principles has been developed. This method of weight estimation represents a compromise between the rapid assessment of component weight using empirical methods based on actual weights of existing aircraft, and detailed, but time-consuming, analysis using the finite element method. The method was applied to eight existing subsonic transports for validation and correlation. Integration of the resulting computer program, PDCYL, has been made into the weights-calculating module of the AirCraft SYNThesis (ACSYNT) computer program. ACSYNT has traditionally used only empirical weight estimation methods; PDCYL adds to ACSYNT a rapid, accurate means of assessing the fuselage and wing weights of unconventional aircraft. PDCYL also allows flexibility in the choice of structural concept, as well as a direct means of determining the impact of advanced materials on structural weight. Using statistical analysis techniques, relations between the load-bearing fuselage and wing weights calculated by PDCYL and corresponding actual weights were determined.

Chambers, Mark C.↗

NASA NTRS1996

Study of the Radiative Properties of Inhomogeneous Stratocumulus Clouds

Clouds play an important role in the radiation budget of the atmosphere. A good understanding of how clouds interact with solar radiation is necessary when considering their effects in both general circulation models and climate models. This study examined the radiative properties of clouds in both an inhomogeneous cloud system, and a simplified cloud system through the use of a Monte Carlo model. The purpose was to become more familiar with the radiative properties of clouds, especially absorption, and to investigate the excess absorption of solar radiation from observations over that calculated from theory. The first cloud system indicated that the absorptance actually decreased as the cloud's inhomogeneity increased, and that cloud forcing does not indicate any changes. The simplified cloud system looked at two different cases of absorption of solar radiation in the cloud. The absorptances calculated from the Monte Carlo is compared to a correction method for calculating absorptances and found that the method can over or underestimate absorptances at cloud edges. Also the cloud edge effects due to solar radiation points to a possibility of overestimating the retrieved optical depth at the edge, and indicates a possible way to correct for it. The effective cloud fraction (Ne) for a long time has been calculated from a cloud's reflectance. From the reflectance it has been observed that the N, for most cloud geometries is greater than the actual cloud fraction (Nc) making a cloud appear wider than it is optically. Recent studies we have performed used a Monte Carlo model to calculate the N, of a cloud using not only the reflectance but also the absorptance. The derived Ne's from the absorptance in some of the Monte Carlo runs did not give the same results as derived from the reflectance. This study also examined the inhomogeneity of clouds to find a relationship between larger and smaller scales, or wavelengths, of the cloud. Both Fourier transforms and wavelet transforms were used to analyze the liquid water content of marine stratocumulus clouds taken during the ASTEX project. From the analysis it was found that the energy in the cloud is not uniformly distributed but is greater at the larger scales than at the smaller scales. This was determined by examining the slope of the power spectrum, and by comparing the variability at two scales from a wavelet analysis.

Batey, Michael↗

NASA NTRS1996

Artificial Boundary Conditions for Computation of Oscillating External Flows

In this paper, we propose a new technique for the numerical treatment of external flow problems with oscillatory behavior of the solution in time. Specifically, we consider the case of unbounded compressible viscous plane flow past a finite body (airfoil). Oscillations of the flow in time may be caused by the time-periodic injection of fluid into the boundary layer, which in accordance with experimental data, may essentially increase the performance of the airfoil. To conduct the actual computations, we have to somehow restrict the original unbounded domain, that is, to introduce an artificial (external) boundary and to further consider only a finite computational domain. Consequently, we will need to formulate some artificial boundary conditions (ABC's) at the introduced external boundary. The ABC's we are aiming to obtain must meet a fundamental requirement. One should be able to uniquely complement the solution calculated inside the finite computational domain to its infinite exterior so that the original problem is solved within the desired accuracy. Our construction of such ABC's for oscillating flows is based on an essential assumption: the Navier-Stokes equations can be linearized in the far field against the free-stream back- ground. To actually compute the ABC's, we represent the far-field solution as a Fourier series in time and then apply the Difference Potentials Method (DPM) of V. S. Ryaben'kii. This paper contains a general theoretical description of the algorithm for setting the DPM-based ABC's for time-periodic external flows. Based on our experience in implementing analogous ABC's for steady-state problems (a simpler case), we expect that these boundary conditions will become an effective tool for constructing robust numerical methods to calculate oscillatory flows.

Tsynkov, S. V.↗

NASA NTRS1996

Verification of Orthogrid Finite Element Modeling Techniques

The stress analysis of orthogrid structures, specifically with I-beam sections, is regularly performed using finite elements. Various modeling techniques are often used to simplify the modeling process but still adequately capture the actual hardware behavior. The accuracy of such 'Oshort cutso' is sometimes in question. This report compares three modeling techniques to actual test results from a loaded orthogrid panel. The finite element models include a beam, shell, and mixed beam and shell element model. Results show that the shell element model performs the best, but that the simpler beam and beam and shell element models provide reasonable to conservative results for a stress analysis. When deflection and stiffness is critical, it is important to capture the effect of the orthogrid nodes in the model.

Steeve, B. E.↗

NASA NTRS1991

On the Power of Abstract Interpretation

Increasingly sophisticated applications of static analysis place increased burden on the reliability of the analysis techniques. Often, the failure of the analysis technique to detect some information my mean that the time or space complexity of the generated code would be altered. Thus, it is important to precisely characterize the power of static analysis techniques. We follow the approach of Selur et. al. who studied the power of strictness analysis techniques. Their result can be summarized by saying 'strictness analysis is perfect up to variations in constants.' In other words, strictness analysis is as good as it could be, short of actually distinguishing between concrete values. We use this approach to characterize a broad class of analysis techniques based on abstract interpretation including, but not limited to, strictness analysis. For the first-order case, we consider abstract interpretations where the abstract domain for data values is totally ordered. This condition is satisfied by Mycroft's strictness analysis that of Sekar et. al. and Wadler's analysis of list-strictness. For such abstract interpretations, we show that the analysis is complete in the sense that, short of actually distinguishing between concrete values with the same abstraction, it gives the best possible information. We further generalize these results to typed lambda calculus with pairs and higher-order functions. Note that products and function spaces over totally ordered domains are not totally ordered. In fact, the notion of completeness used in the first-order case fails if product domains or function spaces are added. We formulate a weaker notion of completeness based on observability of values. Two values (including pairs and functions) are considered indistinguishable if their observable components are indistinguishable. We show that abstract interpretation of typed lambda calculus programs is complete up to this notion of indistinguishability. We use denotationally-oriented arguments instead of the detailed operational arguments used by Selur et. al.. Hence, our proofs are much simpler. They should be useful for further future improvements.

Reddy, Uday S.↗

NASA NTRS1996

Multi-Dimensional Measurements of Combustion Species in Flame Tube and Sector Gas Turbine Combustors

The higher temperature and pressure cycles of future aviation gas turbine combustors challenge designers to produce combustors that minimize their environmental impact while maintaining high operation efficiency. The development of low emissions combustors includes the reduction of unburned hydrocarbons, smoke, and particulates, as well as the reduction of oxides of nitrogen (NO(x)). In order to better understand and control the mechanisms that produce emissions, tools are needed to aid the development of combustor hardware. Current methods of measuring species within gas turbine combustors use extractive sampling of combustion gases to determine major species concentrations and to infer the bulk flame temperature. These methods cannot be used to measure unstable combustion products and have poor spatial and temporal resolution. The intrusive nature of gas sampling may also disturb the flow structure within a combustor. Planar laser-induced fluorescence (PLIF) is an optical technique for the measurement of combustion species. In addition to its non-intrusive nature, PLIF offers these advantages over gas sampling: high spatial resolution, high temporal resolution, the ability to measure unstable species, and the potential to measure combustion temperature. This thesis considers PLIF for in-situ visualization of combustion species as a tool for the design and evaluation of gas turbine combustor subcomponents. This work constitutes the first application of PLIF to the severe environment found in liquid-fueled, aviation gas turbine combustors. Technical and applied challenges are discussed. PLIF of OH was used to observe the flame structure within the post flame zone of a flame tube combustor, and within the flame zone of a sector combustor, for a variety of fuel injector configurations. OH was selected for measurement because it is a major combustion intermediate, playing a key role in the chemistry of combustion, and because its presence within the flame zone can serve as a qualitative marker of flame temperature. All images were taken in the environment of actual engines during flight, using actual jet fuel. The results of the PLIF study led directly to the modification of a fuel injector.

Hicks, Yolanda Royce↗

NASA NTRS1996

System Guidelines for EMC Safety-Critical Circuits: Design, Selection, and Margin Demonstration

Demonstration of required safety margins on critical electrical/electronic circuits in large complex systems has become an implementation and cost problem. These margins are the difference between the activation level of the circuit and the electrical noise on the circuit in the actual operating environment. This document discusses the origin of the requirement and gives a detailed process flow for the identification of the system electromagnetic compatibility (EMC) critical circuit list. The process flow discusses the roles of engineering disciplines such as systems engineering, safety, and EMC. Design and analysis guidelines are provided to assist the designer in assuring the system design has a high probability of meeting the margin requirements. Examples of approaches used on actual programs (Skylab and Space Shuttle Solid Rocket Booster) are provided to show how variations of the approach can be used successfully.

Lawton, R. M.↗

NASA NTRS1996

Study of Critical Heat Flux and Two-Phase Pressure Drop Under Reduced Gravity

The design of the two-phase flow systems which are anticipated to be utilized in future spacecraft thermal management systems requires a knowledge of two-phase flow and heat transfer phenomena in reduced gravities. This program was funded by NASA headquarters in response to NRA-91-OSSA-17 and was managed by Lewis Research Center. The main objective of this program was to design and construct a two-phase test loop, and perform a series of normal gravity and aircraft trajectory experiments to study the effect of gravity on the Critical Heat Flux (CHF) and onset of instability. The test loop was packaged on two aircraft racks and was also instrumented to generate data for two-phase pressure drop. The normal gravity tests were performed with vertical up and downflow configurations to bound the effect of gravity on the test parameters. One set of aircraft trajectory tests was performed aboard the NASA DC-9 aircraft. These tests were mainly intended to evaluate the test loop and its operational performance under actual reduced gravity conditions, and to produce preliminary data for the test parameters. The test results were used to demonstrate the applicability of the normal gravity models for prediction of the two-phase friction pressure drop. It was shown that the two-phase friction multipliers for vertical upflow and reduced gravity conditions can be successfully predicted by the appropriate normal gravity models. Limited critical heat flux data showed that the measured CHF under reduced gravities are of the same order of magnitude as the test results with vertical upflow configuration. A simplified correlation was only successful in predicting the measured CHF for low flow rates. Instability tests with vertical upflow showed that flow becomes unstable and critical heat flux occurs at smaller powers when a parallel flow path exists. However, downflow tests and a single reduced gravity instability experiment indicated that the system actually became more stable with a parallel single-phase flow path. Several design modifications have been identified which will improve the system performance for generating reduced gravity data. The modified test loop can provide two-phase flow data for a range of operating conditions and can serve as a test bed for component evaluation.

Abdollahian, Davood↗

NASA NTRS1996

Emission Spectral Measurements in the Plenum of an Arc Jet Wind Tunnel

Arc jet wind tunnel facilities are used to evaluate thermal protection system materials for re-entry vehicles. The high speed, high temperature flowfield generated by the arc jet can simulate the extreme aerodynamic heating environment experienced during re-entry so that the survivability of heat shield materials and performance of various designs options can be tested. Although the re-entry heating environment can be approximated in the arc jet facility, the flowfield only partially simulates the actual re-entry flight conditions. Reynolds numbers are not matched so that surface shear stress distributions and mass transfer rates due to ablation or other mechanisms are not modeled correctly. Unlike flight conditions the arc freestream air is in non-equilibrium because of the rapid expansion that occurs in the supersonic nozzle. To properly study the actual re-entry flow environment, computational fluid dynamics, computational chemistry and radiation models must be used. Arc jet tunnel tests serve to validate these models. To perform accurate simulations inlet and boundary-conditions are needed, which come from measurements of the flowfield. The present study is concerned with measurements in the plenum region of an arc heater. In the past, conditions in the arc heater flowfield have been predicted using simulations since conventional measurement techniques could not be used in the harsh extremely high temperature environment. The present study is part of a recent push to utilize optical techniques to help better characterize the arc jet flowfields. Emission measurements have been made in the shock layer and the constrictor section of the arc heater to determine temperatures and species number densities. LIF measurements have been made in the free stream to determine temperature and velocity.

Donohue, Jim↗

NASA NTRS1996

The Effect of Wake Passing on Turbine Blade Film Cooling

The effect of upstream blade row wake passing on the showerhead film cooling performance of a downstream turbine blade has been investigated through a combination of experimental and computational studies. The experiments were performed in a steady-flow annular turbine cascade facility equipped with an upstream rotating row of cylindrical rods to produce a periodic wake field similar to that found in an actual turbine. Spanwise, chordwise, and temporal resolution of the blade surface temperature were achieved through the use of an array of nickel thin-film surface gauges covering one unit cell of showerhead film hole pattern. Film effectiveness and Nusselt number values were determined for a test matrix of various injectants, injectant blowing ratios, and wake Strouhal numbers. Results indicated a demonstratable reduction in film effectiveness with increasing Strouhal number, as well as the expected increase in film effectiveness with blowing ratio. An equation was developed to correlate the span-average film effectiveness data. The primary effect of wake unsteadiness was found to be correlated well by a chordwise-constant decrement of 0.094-St. Measurable spanwise film effectiveness variations were found near the showerhead region, but meaningful unsteady variations and downstream spanwise variations were not found. Nusselt numbers were less sensitive to wake and injection changes. Computations were performed using a three-dimensional turbulent Navier-Stokes code which was modified to model wake passing and film cooling. Unsteady computations were found to agree well with steady computations provided the proper time-average blowing ratio and pressure/suction surface flow split are matched. The remaining differences were isolated to be due to the enhanced mixing in the unsteady solution caused by the wake sweeping normally on the pressure surface. Steady computations were found to be in excellent agreement with experimental Nusselt numbers, but to overpredict experimental film effectiveness values. This is likely due to the inability to match actual hole exit velocity profiles and the absence of a credible turbulence model for film cooling.

Heidmann, James David↗

NASA NTRS1994

X-Ray Emission from a Simulated Cluster of Galaxies

Using the 1993 cluster simulation of Katz & White, we analyze the intracluster medium and investigate the accuracy of the standard hydrostatic method for determining cluster masses. We show that the simulated cluster gas is in hydrostatic equilibrium with a subsonic flow toward the center. Inside a radius of (approx.) 100 kpc, this flow is in a steady state. The cooling time is shorter than a Hubble time within the central 50 kpc. The flow rate is regulated by the gas sink in the middle of the cluster and the PdV work done as the gas flows in, verifying the standard cooling flow scenario. We simulate observations of the cluster using the instrument parameters of the EXOSAT ME detector and the Einstein IPC detector. Even though the intracluster gas is not isothermal, isothermal models of the cluster, excluding regions within 100 kpc of galaxies, fit the EXOSAT X-ray spectra as well as they fit real clusters. The X- ray surface brightness distribution is similar to that of real clusters, again excluding the galaxies. We simulate the procedure used to determine the masses of real clusters. We use the equation of hydrostatic equilibrium together with the temperature derived from an isothermal fit to the simulated EXOSAT spectrum and the density profile derived from a fit to the simulated IPC surface brightness profile to determine the mass. A comparison of the derived mass profile to the actual mass profile shows that errors of a factor of 2 are possible. If the actual temperature profile is used, the cluster mass is found to an accuracy of better than 25% within the virial radius.

Tsai, John C.↗