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HOTCFGM-2D: A Coupled Higher-Order Theory for Cylindrical Structural Components with Bi-Directionally Components with Bi-Directionally Graded Microstructures

The objective of this two-year project was to develop and deliver to the NASA-Glenn Research Center a two-dimensional higher-order theory, and related computer codes, for the analysis and design of cylindrical functionally graded materials/structural components for use in advanced aircraft engines (e.g., combustor linings, rotor disks, heat shields, brisk blades). To satisfy this objective, two-dimensional version of the higher-order theory, HOTCFGM-2D, and four computer codes based on this theory, for the analysis and design of structural components functionally graded in the radial and circumferential directions were developed in the cylindrical coordinate system r-Theta-z. This version of the higher-order theory is a significant generalization of the one-dimensional theory, HOTCFGM-1D, developed during the FY97 for the analysis and design of cylindrical structural components with radially graded microstructures. The generalized theory is applicable to thin multi-phased composite shells/cylinders subjected to steady-state thermomechanical, transient thermal and inertial loading applied uniformly along the axial direction such that the overall deformation is characterized by a constant average axial strain. The reinforcement phases are uniformly distributed in the axial direction, and arbitrarily distributed in the radial and circumferential direction, thereby allowing functional grading of the internal reinforcement in the r-Theta plane. The four computer codes fgmc3dq.cylindrical.f, fgmp3dq.cylindrical.f, fgmgvips3dq.cylindrical.f, and fgmc3dq.cylindrical.transient.f are research-oriented codes for investigating the effect of functionally graded architectures, as well as the properties of the multi-phase reinforcement, in thin shells subjected to thermomechanical and inertial loading, on the internal temperature, stress and (inelastic) strain fields. The reinforcement distribution in the radial and circumferential directions is specified by the user. The thermal and inelastic properties of the individual phases can vary with temperature. The inelastic phases are presently modeled by the power-law creep model generalized to multi-directional loading (within fgmc3dq.cylindrical.f and fgmc3dq.cylindrical.transient.f for steady-state and transient thermal loading, respectively), and incremental plasticity and GVIPS unified viscoplasticity theories (within the steady-state loading versions fgmp3dq.cylindrical.f and fgmgvips3dq.cylindrical.f).

Pindera, Marek-Jerzy↗

In-Flight Characterization of the Electromagnetic Environment Inside an Airliner

In 1995, the NASA Langley Research Center conducted a series of experimental measurements that characterized the electromagnetic environment (EME) inside a Boeing 757 airliner while in flight, Measurements were made of the electromagnetic energy coupled into a commercially configured aircraft as it was flown in close proximity to ground-based radio frequency (RF) transmitters operating at approximately 26, 173. and 430 MHz. The goal of this experiment was to collect data for the verification of analytical predictions of the internal aircraft response to an external stimulus. This paper describes the experiment, presents the data collected by it, and discusses techniques used to compute both the magnitude of the electric field illuminating the aircraft and its direction of propagation relative to a coordinate system fixed to the aircraft. The latter is determined from Global Positioning System (GPS) and aircraft Inertial Reference Unit (IRU) data. The paper concludes with an examination of the shielding effectiveness of the test aircraft. as determined by comparison of' the measured internal EME and computed external EME.

Moeller, Karl J.↗

Modelling the Centers of Galaxies

The key to studying central regions by means of nobody numerical experiments is to concentrate on the central few parsecs of a galaxy, replacing the remainder of the galaxy by a suitable boundary condition, rather after the manner in which stellar interiors can be studied without a detailed stellar atmosphere by replacing the atmosphere with a boundary condition. Replacements must be carefully designed because the long range gravitational force means that the core region is sensitive to mass outside that region and because particles can exchange between the outer galaxy and the core region. We use periodic boundary conditions, coupled with an iterative procedure to generate initial particle loads in isothermal equilibrium. Angular momentum conservation is ensured for problems including systematic rotation by a circular reflecting boundary and by integrating in a frame that rotates with the mean flow. Mass beyond the boundary contributes to the gravitational potential, but does not participate in the dynamics. A symplectic integration scheme has been developed for rotating coordinate systems. This combination works well, leading to robust configurations. Some preliminary results with this combination show that: (1) Rotating systems are extremely sensitive to non-axisymmetric external potentials, and (2) that a second core, orbiting near the main core (like the M31 second core system), shows extremely rapid orbital decay. The experimental setups will be discussed, along with preliminary results.

Smith, B. F.↗

Extending the ICRF to Higher Radio Frequencies

The ICRF forms the basis for all astrometry including use as the inertial coordinate system for navigating deep space missions. This frame was defined using S/X-band observations over the past 20+ years. In January 2002, the VLBA approved our proposal for observing time to extend the ICRF to K-band (24 GHz) and Q-band (43 GHz). The first step will be observations at K- and Q-bands on a subset of ICRF sources. Eventually, K- and Q-band multi-epoch observations will be used to estimate positions, flux density and source structure for a large fraction of the current S/X-band ICRF source list. This work will benefit the radio astronomy community by extending the VLBA calibrator list at these bands. In the longer term, we would also like to extend the ICRF to Ka-band (32 GHz). A celestial reference frame will be needed at this frequency to support deep space navigation. A navigation demonstration is being considered for NASA's Mars 2005 mission. The initial K- and Q-band work will serve to identify candidate sources at Ka-band for use with that mission.

Jacobs, C. S.↗

A Reference Model for Middle Atmosphere Ozone in 1992-1993

An ozone climatology for the period April 1992 to March 1993 and covering pressures from 0.1 to 100 hPa and from 80 deg N to 80 deg S is derived from satellite-based measurements by the Stratospheric Aerosol and Gas Experiment (SAGE), the Halogen Occultation Experiment (HALOE), and the Microwave Limb Sounder (MLS). At pressures less than 1 hPa, separate distributions are given for daytime and nighttime conditions. From 0.46 to 32 hPa the accuracy of the distribution is estimated to be 5%, and the precision is also approx. 5%. Estimates of atmospheric variability are provided on the basis of standard deviations of the measurements within months. Distributions of ozone monthly means and standard deviations are also given in a potential temperature, equivalent latitude coordinate system. This data set is included in the UARS reference atmosphere, and it is accessible through that web site.

Wang, H. J.↗

Geolocation Assessment Algorithm for CALIPSO Using Coastline Detection

Cloud-Aerosol Lidar Infrared Pathfinder Satellite Observations (CALIPSO) is a joint satellite mission between NASA and the French space agency CNES. The investigation will gather long-term, global cloud and aerosol optical and physical properties to improve climate models. The CALIPSO spacecraft is scheduled to launch in 2004 into a 98.2 inclination, 705 km circular orbit approximately 3 minutes behind the Aqua spacecraft. The payload consists of a two-wavelength polarization-sensitive lidar, and two passive imagers operating in the visible (0.645 mm) and infrared (8.7 - 12.0 mm) spectral regions. The imagers are nadir viewing and co-aligned with the lidar. Earth viewing measurements are geolocated to the Earth fixed coordinate system using satellite ephemeris, Earth rotation and geoid, and instrument pointing data. The coastline detection algorithm will assess the accuracy of the CALIPSO geolocation process by analyzing Wide Field Camera (WFC) visible ocean land boundaries. Processing space-time coincident MODIS and WFC scenes with the coastline algorithm will help verify the co-registration requirement with Moderate Resolution Imaging Spectrometer (MODIS) data. This paper quantifies the accuracy of the coastline geolocation assessment algorithm.

Currey, J. Chris↗

HEASARC Software Archive

(1) Chandra Archive: SAO has maintained the interfaces through which HEASARC gains access to the Chandra Data Archive. At HEASARC's request, we have implemented an anonymous ftp copy of a major part of the public archive and we keep that archive up-to- date. SAO has participated in the ADEC interoperability working group, establishing guidelines or interoperability standards and prototyping such interfaces. We have provided an NVO-based prototype interface, intending to serve the HEASARC-led NVO demo project. HEASARC's Astrobrowse interface was maintained and updated. In addition, we have participated in design discussions surrounding HEASARC's Caldb project. We have attended the HEASARC Users Group meeting and presented CDA status and developments. (2) Chandra CALDB: SA0 has maintained and expanded the Chandra CALDB by including four new data file types, defining the corresponding CALDB keyword/identification structures. We have provided CALDB upgrades for the public (CIAO) and for Standard Data Processing. Approximately 40 new files have been added to the CALDB in these version releases. There have been in the past year ten of these CALDB upgrades, each with unique index configurations. In addition, with the inputs from software, archive, and calibration scientists, as well as CIAO/SDP software developers, we have defined a generalized expansion of the existing CALDB interface and indexing structure. The purpose of this is to make the CALDB more generally applicable and useful in new and future missions that will be supported archivally by HEASARC. The generalized interface will identify additional configurational keywords and permit more extensive calibration parameter and boundary condition specifications for unique file selection. HEASARC scientists and developers from SAO and GSFC have become involved in this work, which is expected to produce a new interface for general use within the current year. (3) DS9: One of the decisions that came from last year's HEADCC meeting was to make the ds9 image display program the primary vehicle for displaying line graphics (as well as images). The first step required to make this possible was to enhance the line graphics capabilities of ds9. SAO therefore spent considerable effort upgrading ds9 to use Tcl 8.4 so that the BLT line graphics package could be built and imported into ds9 from source code, rather than from a pre-built (and generally outdated) shared library. This task, which is nearly complete, allows us to extend BLT as needed for the HEAD community. Following HEADCC discussion concerning archiving and the display of archived data, we extended ds9 to support full access to many astronomical Web-based archives sites, including HEASARC, MAST, CHANDRA, SKYVIEW, ADS, NED, SIMBAD, IRAS, NVRO, SAO TDC, and FIRST. Using ds9's new internal Web access capabilities, these archives can be accessed via their Web page. FITS images, plots, spectra, and journal abstracts can be referenced, down-loaded, and displayed directly and easily in ds9. For more information, see: http://hea-www.harvard.edu/saord/ds9. Also after the HEADCC discussion concerning region filtering, we extended the Funtools sample implementation of region filtering as described in: http://hea-www.harvard.edu/saord/funtools/regions.html. In particular, we added several new composite regions for event and image filtering, including elliptical and box annuli. We also extended the panda (Pie AND Annulus) region support to include box pandas and elliptical pandas. These new composite regions are especially useful in programs that need to count photons in each separate region using only a single pass through the data. Support for these new regions was added to ds9. In the same vein, we developed new region support for filtering images using simple FITS image masks, i.e. 8-bit or 16-bit FITS images where the value of a pixel is the region id number for that pixel. Other important enhancements to DS9 this year, include supporor multiple world coordinate systems, three dimensional event file binning, image smoothing, region groups and tags, the ability to save images in a number of image formats (such as JPEG, TIFF, PNG, FITS), improvements in support for integrating external analysis tools, and support for the virtual observatory. In particular, a full-featured web browser has been implemented within D S 9 . This provides support for full access to HEASARC archive sites such as SKYVIEW and W3BROWSE, in addition to other astronomical archives sites such as MAST, CHANDRA, ADS, NED, SIMBAD, IRAS, NVRO, SA0 TDC, and FIRST. From within DS9, the archives can be searched, and FITS images, plots, spectra, and journal abstracts can be referenced, downloaded and displayed The web browser provides the basis for the built-in help facility. All DS9 documentation, including the reference manual, FAQ, Know Features, and contact information is now available to the user without the need for external display applications. New versions of DS9 maybe downloaded and installed using this facility. Two important features used in the analysis of high energy astronomical data have been implemented in the past year. The first is support for binning photon event data in three dimensions. By binning the third dimension in time or energy, users are easily able to detect variable x-ray sources and identify other physical properties of their data. Second, a number of fast smoothing algorithms have been implemented in DS9, which allow users to smooth their data in real time. Algorithms for boxcar, tophat, and gaussian smoothing are supported.

White, Nicholas↗

On Possible Similarity Solutions for Three-Dimensional Incompressible Laminar Boundary-Layer Flows Over Developable Surfaces and with Proportional Mainstream Velocity Components

Analysis is presented on the possible similarity solutions of the three-dimensional, laminar, incompressible, boundary-layer equations referred to orthogonal, curvilinear coordinate systems. Requirements of the existence of similarity solutions are obtained for the following: flow over developable surface and flow over non-developable surfaces with proportional mainstream velocity components.

Hansen, Arthur G.↗

Alignment of the Grating Wheel Mechanism for a Ground-Based, Cryogenic, Near-Infrared Astronomy Instrument

We describe the population, optomechanical alignment, and alignment verification of near-infrared gratings on the grating wheel mechanism (GWM) for the Infrared Multi-Object Spectrometer (IRMOS). IRMOS is a cryogenic (80 K), principle investigator-class instrument for the 2.1 m and Mayall 3.8 m telescopes at Kitt Peak National Observatory, and a MEMS spectrometer concept demonstrator for the James Webb Space Telescope. The GWM consists of 13 planar diffraction gratings and one flat imaging mirror (58 x 57 mm), each mounted at a unique compound angle on a 32 cm diameter gear. The mechanism is predominantly made of Al 6061. The grating substrates are stress relieved for enhanced cryogenic performance. The optical surfaces are replicated from off-the-shelf masters. The imaging mirror is diamond turned. The GWM spans a projected diameter of approx. 48 cm when fully assembled, utilizes several flexure designs to accommodate potential thermal gradients, and is controlled using custom software with an off-the-shelf controller. Under ambient conditions, each grating is aligned in six degrees of freedom relative to a coordinate system that is referenced to an optical alignment cube mounted at the center of the gear. The local tip/tilt (Rx/Ry) orientation of a given grating is measured using the zero-order return from an autocollimating theodolite. The other degrees of freedom are measured using a two-axis cathetometer and rotary table. Each grating's mount includes a one-piece shim located between the optic and the gear. The shim is machined to fine align each grating. We verify ambient alignment by comparing grating difractive properties to model predictions.

Gutkowski, Sharon M.↗

Is the spatial distribution of brain lesions associated with closed-head injury in children predictive of subsequent development of posttraumatic stress disorder?

PURPOSE: To determine whether there is an association between the spatial distributions of lesions detected at magnetic resonance (MR) imaging of the brain in children, adolescents, and young adults after closed-head injury (CHI) and development of the reexperiencing symptoms of posttraumatic stress disorder (PTSD). MATERIALS AND METHODS: Data obtained in 94 subjects without a history of PTSD as determined by parental interview were analyzed. MR images were obtained 3 months after CHI. Lesions were manually delineated and registered to the Talairach coordinate system. Mann-Whitney analysis of lesion distribution and PTSD status at 1 year (again, as determined by parental interview) was performed, consisting of an analysis of lesion distribution versus the major symptoms of PTSD: reexperiencing, hyperarousal, and avoidance. RESULTS: Of the 94 subjects, 41 met the PTSD reexperiencing criterion and nine met all three PTSD criteria. Subjects who met the reexperiencing criterion had fewer lesions in limbic system structures (eg, the cingulum) on the right than did subjects who did not meet this criterion (Mann-Whitney, P =.003). CONCLUSION: Lesions induced by CHI in the limbic system on the right may inhibit subsequent manifestation of PTSD reexperiencing symptoms in children, adolescents, and young adults. Copyright RSNA, 2002.

Non-NASA Center↗

Testing the PV-Theta Mapping Technique in a 3-D CTM Model Simulation

Mapping lower stratospheric ozone into potential vorticity (PV)- potential temperature (Theta) coordinates is a common technique employed to analyze sparse data sets. Ozone transformed into a flow-following dynamical coordinate system is insensitive to meteorological variations. Therefore data from a wide range of times/locations can be compared, so long as the measurements were made in the same airmass (as defined by PV). Moreover, once a relationship between ozone and PV/Theta is established, a full 3D ozone field can be estimated from this relationship and the 3D analyzed PV field. However, ozone data mapped in this fashion can be hampered by noisy PV fields, or "mis-matches" in the resolution and/or exact location of the ozone and PV measurements. In this study, we investigate the PV-ozone relationship using output from a recent 50-year run of the Goddard 3D chemical transport model (CTM). Model constituents are transported using off-line dynamics from the finite volume general circulation model (FVGCM). By using the internally consistent model PV and ozone fields, we minimize noise due to mis-matching and resolution issues. We calculate correlations between model ozone and PV throughout the stratosphere, and test the sensitivity of the technique to initial data resolution. To do this we degrade the model data to that of various satellite instruments, then compare the mapped fields derived from the sub-sampled data to the full resolution model data. With these studies we can determine appropriate limits for the PV-theta mapping technique in latitude, altitude, and as a function of original data resolution.

Frith, Stacey M.↗

Role of Turbulent Prandtl Number on Heat Flux at Hypersonic Mach Number

Present simulation of turbulent flows involving shock wave/boundary layer interaction invariably overestimates heat flux by almost a factor of two. One possible reason for such a performance is a result of the fact that the turbulence models employed make use of Morkovin's hypothesis. This hypothesis is valid for non-hypersonic Mach numbers and moderate rates of heat transfer. At hypersonic Mach numbers, high rates of heat transfer exist in regions where shock wave/boundary layer interactions are important. As a result, one should not expect traditional turbulence models to yield accurate results. The goal of this investigation is to explore the role of a variable Prandtl number formulation in predicting heat flux in flows dominated by strong shock wave/boundary layer interactions. The intended applications involve external flows in the absence of combustion such as those encountered in supersonic inlets. This can be achieved by adding equations for the temperature variance and its dissipation rate. Such equations can be derived from the exact Navier-Stokes equations. Traditionally, modeled equations are based on the low speed energy equation where the pressure gradient term and the term responsible for energy dissipation are ignored. It is clear that such assumptions are not valid for hypersonic flows. The approach used here is based on the procedure used in deriving the k-zeta model, in which the exact equations that governed k, the variance of velocity, and zeta, the variance of vorticity, were derived and modeled. For the variable turbulent Prandtl number, the exact equations that govern the temperature variance and its dissipation rate are derived and modeled term by term. The resulting set of equations are free of damping and wall functions and are coordinate-system independent. Moreover, modeled correlations are tensorially consistent and invariant under Galilean transformation. The final set of equations will be given in the paper.

Xiao, X.↗

Is the spatial distribution of brain lesions associated with closed-head injury predictive of subsequent development of attention-deficit/hyperactivity disorder? Analysis with brain-image database

PURPOSE: To determine whether there is an association between the spatial distribution of lesions detected at magnetic resonance (MR) imaging of the brain in children after closed-head injury and the development of secondary attention-deficit/hyperactivity disorder (ADHD). MATERIALS AND METHODS: Data obtained from 76 children without prior history of ADHD were analyzed. MR images were obtained 3 months after closed-head injury. After manual delineation of lesions, images were registered to the Talairach coordinate system. For each subject, registered images and secondary ADHD status were integrated into a brain-image database, which contains depiction (visualization) and statistical analysis software. Using this database, we assessed visually the spatial distributions of lesions and performed statistical analysis of image and clinical variables. RESULTS: Of the 76 children, 15 developed secondary ADHD. Depiction of the data suggested that children who developed secondary ADHD had more lesions in the right putamen than children who did not develop secondary ADHD; this impression was confirmed statistically. After Bonferroni correction, we could not demonstrate significant differences between secondary ADHD status and lesion burdens for the right caudate nucleus or the right globus pallidus. CONCLUSION: Closed-head injury-induced lesions in the right putamen in children are associated with subsequent development of secondary ADHD. Depiction software is useful in guiding statistical analysis of image data.

NASA Discipline Neuroscience↗

Lunar Navigation with Libration Point Orbiters and GPS

NASA is currently studying a Vision for Space Exploration based on spiral development of robotic and piloted missions to the moon and Mars, but research into how to perform such missions has continued ever since the first era of lunar exploration. One area of study that a number of researchers have pursued is libration point navigation and communication relay concepts. These concepts would appear to support many of NASA's current requirements for navigation and communications coverage for human and robotic spacecraft operating in lunar space and beyond. In trading libration point concepts against other options, designers must consider issues such as the number of spacecraft, required to provide coverage, insertion and stationkeeping costs, power and data rate requirements, frequency allocations, and many others. The libration points, along with a typical cis-lunar trajectory, are equilibrium locations for an infinitesimal mass in the rotating coordinate system that follows the motion of two massive bodies in circular orbits with respect to their common barycenter. There are three co-linear points along the line connecting the massive bodies: between the bodies, beyond the secondary body, and beyond the primary body. The relative distances of these points along the line connecting the bodies depend on the mass ratios. There are also two points that form equilateral triangles with the massive bodies. Ideally, motion in the neighborhood of the co-linear points is unstable, while motion near the equilibrium points is stable. However, in the real world, the motions are highly perturbed so that a satellite will require stationkeeping maneuvers.

Carpenter, J. Russell↗

Kinematic principles of primate rotational vestibulo-ocular reflex. II. Gravity-dependent modulation of primary eye position

The kinematic constraints of three-dimensional eye positions were investigated in rhesus monkeys during passive head and body rotations relative to gravity. We studied fast and slow phase components of the vestibulo-ocular reflex (VOR) elicited by constant-velocity yaw rotations and sinusoidal oscillations about an earth-horizontal axis. We found that the spatial orientation of both fast and slow phase eye positions could be described locally by a planar surface with torsional variation of <2.0 +/- 0.4 degrees (displacement planes) that systematically rotated and/or shifted relative to Listing's plane. In supine/prone positions, displacement planes pitched forward/backward; in left/right ear-down positions, displacement planes were parallel shifted along the positive/negative torsional axis. Dynamically changing primary eye positions were computed from displacement planes. Torsional and vertical components of primary eye position modulated as a sinusoidal function of head orientation in space. The torsional component was maximal in ear-down positions and approximately zero in supine/prone orientations. The opposite was observed for the vertical component. Modulation of the horizontal component of primary eye position exhibited a more complex dependence. In contrast to the torsional component, which was relatively independent of rotational speed, modulation of the vertical and horizontal components of primary position depended strongly on the speed of head rotation (i.e., on the frequency of oscillation of the gravity vector component): the faster the head rotated relative to gravity, the larger was the modulation. Corresponding results were obtained when a model based on a sinusoidal dependence of instantaneous displacement planes (and primary eye position) on head orientation relative to gravity was fitted to VOR fast phase positions. When VOR fast phase positions were expressed relative to primary eye position estimated from the model fits, they were confined approximately to a single plane with a small torsional standard deviation ( approximately 1.4-2.6 degrees). This reduced torsional variation was in contrast to the large torsional spread (well >10-15 degrees ) of fast phase positions when expressed relative to Listing's plane. We conclude that primary eye position depends dynamically on head orientation relative to space rather than being fixed to the head. It defines a gravity-dependent coordinate system relative to which the torsional variability of eye positions is minimized even when the head is moved passively and vestibulo-ocular reflexes are evoked. In this general sense, Listing's law is preserved with respect to an otolith-controlled reference system that is defined dynamically by gravity.

NASA Discipline Neuroscience↗

What Information Theory Says About Best Response and About Binding Contracts

Product Distribution (PD) theory is the information-theoretic extension of conventional full- rationality game theory to bounded rational games. Here PD theory is used to investigate games in which the players use bounded rational best-response strategies. This investigation illuminates how to determine the optimal organization chart for a corporation, or more generally how to order the sequence of moves of the players / employees so as to optimize an overall objective function. It is then shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. This variant is then investigated for team games, in which the players share the same utility function, by showing that such continuum- limit bounded rational best response is identical to Newton-Raphson iterative optimization of the shared utility function. Next PD theory is used to investigate changing the coordinate system of the game, i.e., changing the mapping from the joint move of the players to the arguments in the utility functions. Such a change couples those arguments, essentially by making each players move be an offered binding contract.

Wolpert, David H.↗

Analysis For Monitoring the Earth Science Afternoon Constellation

The Earth Science Afternoon Constellation consists of Aqua, Aura, PARASOL, CALIPSO, Cloudsat, and the Orbiting Carbon Observatory (OCO). The coordination of flight dynamics activities between these missions is critical to the safety and success of the Afternoon Constellation. This coordination is based on two main concepts, the control box and the zone-of-exclusion. This paper describes how these two concepts are implemented in the Constellation Coordination System (CCS). The CCS is a collection of tools that enables the collection and distribution of flight dynamics products among the missions, allows cross-mission analyses to be performed through a web-based interface, performs automated analyses to monitor the overall constellation, and notifies the missions of changes in the status of the other missions.

Demarest, Peter↗

Rack Distribution Effects on MPLM Center of Mass

This research was in support of exploring the need for more flexible "center of gravity (CG) specifications than those currently established by NASA for the Multi-Purpose Logistics Module (MPLM). The MPLM is the cargo carrier for International Space Station (ISS) missions. The MPLM provides locations for 16 standard racks, as shown in Figure 1; not all positions need to be filled in any given flight. The MPLM coordinate system (X(sub M), Y(sub M), Z(sub M)) is illustrated as well. For this project, the primary missions of interest were those which supply the ISS and remove excess materials on the return flights. These flights use a predominate number of "Resupply Stowage Racks" (RSR) and "Resupply Stowage Platforms" (RSP). In these two types of racks, various smaller items are stowed. Hence, these racks will exhibit a considerable range of mass values as well as a range as to where their individual CG are located.

Tester, John T.↗