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Further Improvement in 3DGRAPE

3DGRAPE/AL:V2 denotes version 2 of the Three-Dimensional Grids About Anything by Poisson's Equation with Upgrades from Ames and Langley computer program. The preceding version, 3DGRAPE/AL, was described in Improved 3DGRAPE (ARC-14069) NASA Tech Briefs, Vol. 21, No. 5 (May 1997), page 66. These programs are so named because they generate volume grids by iteratively solving Poisson's Equation in three dimensions. The grids generated by the various versions of 3DGRAPE have been used in computational fluid dynamics (CFD). The main novel feature of 3DGRAPE/AL:V2 is the incorporation of an optional scheme in which anisotropic Lagrange-based trans-finite interpolation (ALBTFI) is coupled with exponential decay functions to compute and blend interior source terms. In the input to 3DGRAPE/AL:V2 the user can specify whether or not to invoke ALBTFI in combination with exponential-decay controls, angles, and cell size for controlling the character of grid lines. Of the known programs that solve elliptic partial differential equations for generating grids, 3DGRAPE/AL:V2 is the only code that offers a combination of speed and versatility with most options for controlling the densities and other characteristics of grids for CFD.

Alter, Stephen↗

Massively Parallel Algorithms for Real-Time Wavefront Control of a Dense Adaptive Optics System

In this paper massively parallel algorithms and architectures for real-time wavefront control of a dense adaptive optic system (SELENE) are presented. We have already shown that the computation of a near optimal control algorithm for SELENE can be reduced to the solution of a discrete Poisson equation on a regular domain. Although this represents an optimal computation, due the large size of the system and the high sampling rate requirement, the implementation of this control algorithm poses a computationally challenging problem since it demands a sustained computational throughput of the order of 10 GFlops. We develop a novel algorithm, designated as Fast Invariant Imbedding algorithm, which offers a massive degree of parallelism with simple communication and synchronization requirements. Due to these features, our algorithm is significantly more efficient than other Fast Poisson Solvers for implementation on massively parallel architectures.

massively↗

Mount Protects Thin-Walled Glass or Ceramic Tubes from Large Thermal and Vibration Loads

The design allows for the low-stress mounting of fragile objects, like thin walled glass, by using particular ways of compensating, isolating, or releasing the coefficient of thermal expansion (CTE) differences between the mounted object and the mount itself. This mount profile is lower than true full kinematic mounting. Also, this approach enables accurate positioning of the component for electrical and optical interfaces. It avoids the higher and unpredictable stress issues that often result from potting the object. The mount has been built and tested to space-flight specifications, and has been used for fiber-optic, optical, and electrical interfaces for a spaceflight mission. This mount design is often metal and is slightly larger than the object to be mounted. The objects are optical or optical/electrical, and optical and/or electrical interfaces are required from the top and bottom. This requires the mount to be open at both ends, and for the object s position to be controlled. Thin inside inserts at the top and bottom contact the housing at defined lips, or edges, and hold the fragile object in the mount. The inserts can be customized to mimic the outer surface of the object, which further reduces stress. The inserts have the opposite CTE of the housing material, partially compensating for the CTE difference that causes thermal stress. A spring washer is inserted at one end to compensate for more CTE difference and to hold the object against the location edge of the mount for any optical position requirements. The spring also ensures that any fiber-optic or optic interface, which often requires some pressure to ensure a good interface, does not overstress the fragile object. The insert thickness, material, and spring washer size can be traded against each other to optimize the mount and stresses for various thermal and vibration load ranges and other mounting requirements. The alternate design uses two separate, unique features to reduce stress and hold the object. A release agent is applied to the inside surface of the mount just before the binding potting material is injected in the mount. This prevents the potting material from bonding to the mount, and thus prevents stress from being applied, at very low temperatures, to the fragile object being mounted. The potting material mixing and curing is temperature- and humidity-controlled. The mount has radial grooves cut in it that the potting material fills, thus controlling the vertical position of the mounted object. The design can easily be used for long and thin objects, short and wide objects, and any shape in between. The design s advantages are amplified for long and thin fragile objects. The general testing range was 45 to +45 C, but multiple mounts were successfully tested down to 60 and up to 50 C and the design can be adjusted for larger ranges.

Amato, Michael↗

Optimal Dynamic Sub-Threshold Technique for Extreme Low Power Consumption for VLSI

For miniaturization of electronics systems, power consumption plays a key role in the realm of constraints. Considering the very large scale integration (VLSI) design aspect, as transistor feature size is decreased to 50 nm and below, there is sizable increase in the number of transistors as more functional building blocks are embedded in the same chip. However, the consequent increase in power consumption (dynamic and leakage) will serve as a key constraint to inhibit the advantages of transistor feature size reduction. Power consumption can be reduced by minimizing the voltage supply (for dynamic power consumption) and/or increasing threshold voltage (V(sub th), for reducing leakage power). When the feature size of the transistor is reduced, supply voltage (V(sub dd)) and threshold voltage (V(sub th)) are also reduced accordingly; then, the leakage current becomes a bigger factor of the total power consumption. To maintain low power consumption, operation of electronics at sub-threshold levels can be a potentially strong contender; however, there are two obstacles to be faced: more leakage current per transistor will cause more leakage power consumption, and slow response time when the transistor is operated in weak inversion region. To enable low power consumption and yet obtain high performance, the CMOS (complementary metal oxide semiconductor) transistor as a basic element is viewed and controlled as a four-terminal device: source, drain, gate, and body, as differentiated from the traditional approach with three terminals: i.e., source and body, drain, and gate. This technique features multiple voltage sources to supply the dynamic control, and uses dynamic control to enable low-threshold voltage when the channel (N or P) is active, for speed response enhancement and high threshold voltage, and when the transistor channel (N or P) is inactive, to reduce the leakage current for low-leakage power consumption.

Duong, Tuan A.↗

In-Situ Nondestructive Evaluation of Kevlar(Registered Trademark)and Carbon Fiber Reinforced Composite Micromechanics for Improved Composite Overwrapped Pressure Vessel Health Monitoring

NASA has been faced with recertification and life extension issues for epoxy-impregnated Kevlar 49 (K/Ep) and carbon (C/Ep) composite overwrapped pressure vessels (COPVs) used in various systems on the Space Shuttle and International Space Station, respectively. Each COPV has varying criticality, damage and repair histories, time at pressure, and pressure cycles. COPVs are of particular concern due to the insidious and catastrophic burst-before-leak failure mode caused by stress rupture (SR) of the composite overwrap. SR life has been defined [1] as the minimum time during which the composite maintains structural integrity considering the combined effects of stress level(s), time at stress level(s), and associated environment. SR has none of the features of predictability associated with metal pressure vessels, such as crack geometry, growth rate and size, or other features that lend themselves to nondestructive evaluation (NDE). In essence, the variability or surprise factor associated with SR cannot be eliminated. C/Ep COPVs are also susceptible to impact damage that can lead to reduced burst pressure even when the amount of damage to the COPV is below the visual detection threshold [2], thus necessitating implementation of a mechanical damage control plan [1]. Last, COPVs can also fail prematurely due to material or design noncompliance. In each case (SR, impact or noncompliance), out-of-family behavior is expected leading to a higher probability of failure at a given stress, hence, greater uncertainty in performance. For these reasons, NASA has been actively engaged in research to develop NDE methods that can be used during post-manufacture qualification, in-service inspection, and in-situ structural health monitoring. Acoustic emission (AE) is one of the more promising NDE techniques for detecting and monitoring, in real-time, the strain energy release and corresponding stress-wave propagation produced by actively growing flaws and defects in composite materials [3,4,5,6,7,8]. To gain further insight into the mechanisms responsible for composite rupture, broadband modal acoustic emission analysis was used. Also, since AE data reduction proved to be very time consuming, specialized data reduction software was written to automate the process.

Waller, Jess↗

Scaling Climbing Collaborative Mobile Manipulators (C2M2) for Outfitting a Tall Lunar Tower (TLT) and Truss Structures

In-space and planetary truss structures like the Tall Lunar Tower (TLT) can greatly benefit from truss climbing collaborative mobile manipulators (C-CMMs) for outfitting and other servicing tasks. Mobile robotic systems traversing these structures will allow for improved access to the structure for placing equipment and routing cables after the structure has been assembled. The robotic system described in the proposed paper is designed to provide access to the structure through collaborative mobile robotics. The paper will provide a method to constrain the design of such a robot via the geometry of the truss structure and the controlling joint torques across various gaits. The focus of the design is on a six-degree of freedom (DOF) robot arranged with two-DOF at each end and at the center. The variable features of this system are the actuators and the length of the links connecting the two-DOF modules. The result of the analysis is a link sizing range which the robot can be designed within to ensure functionality on the truss structure. A C-CMM will be designed using the scaling utility and several constructed to demonstrate operating both independently and collaboratively.

in-space assembly↗

Use of Design of Experiments and Rule-Based Inference in Determining Neural Network Architectures for Loss of Control Detection

In this work, we describe methods for selecting the neural network architectures and input spaces to implement belief state inference on generic commercial transport aircraft. First, we highlight a case study on the planning, execution, and analysis of a set of experiments to determine the configurations of a conditional variational autoencoder (CVAE). We present a structured method that can be used in a number of aerospace applications, to optimize the structure and training parameters of the CVAE for belief state inference, using Design of Experiments (DOE) statistical methodologies. The motivation for this specific DOE was to identify the appropriate hyperparameters for measuring the CVAE reconstruction probability and latent space, such that the measurements can be used to infer qualitative state changes for the aircraft. We demonstrate that this process yields information about a trained neural network’s utility for this specific application, along with a quantifiable range of certainty. We execute 84 experiments using loss-of-control flight maneuver data from a NASA T-2 aircraft, demonstrating that this empirical process allows us to construct cheap and simple models with specific attributes amenable to belief state inference in aerospace applications. While theoretically, we could create a single CVAE with an input space the size of all measurable flight variables and environmental dynamics, it becomes intractable to use such a neural network in an in-situ intelligent multi-agent system. Using the recommendations from our case study, we introduce a technical approach for feasibly describing the belief space by (1) identifying significant statistical relationships among flight variables using rule induction, (2) using a set of rules that cover all features to define the input space of multiple CVAEs, and (3) forming a belief space based on the joint probability density of their collective latent spaces. This results in a series of relatively small matrix multiplications that can be performed in real time, as opposed to large matrix computations in a single CVAE. We demonstrate the application of this approach on the T-2 flight loss-of control experiments, using the architecture and hyperparameter recommendations from the case study. We compare the utilities of an individual CVAE trained on all flight variables and multiple CVAEs defined on subsets of flight variables for detecting qualitative changes in flight. We demonstrate that the use of multiple CVAEs with smaller input spaces permits the CVAE to capture more granular relationships in the latent space, permitting better state space characterization and loss-of-control detection.

Design of experiments↗

Two-stage, low noise advanced technology fan. 5: Acoustic final report

The NASA Q2S(quiet two-stage) fan is a 0.836m (32.9 in.) diameter model of the STF 433 engine fan, selected in a 1972 study for an Advanced Technology Transport (ATT) airplane. Noise-control features include: low tip speed, moderate stage pressure rise, large blade-vane spacings, no inlet guide vanes, and optimum blade and vane numbers. Tests were run on the baseline Q2S fan with standard inlet and discharge ducts. Further tests were made of a translating centerbody sonic inlet device and treated discharge ducts. Results were scaled to JT8D and JT3D engine fan size for comparison with current two-stage fans, and were also scaled to STF 433 fan size to compare calculated ATT flyover noise with FAR 36 limits. Baseline Q2S results scaled to JT8D and JT3D engine fan sizes showed substantial noise reductions. Calculated unsuppressed baseline ATT flyovers averaged about 2.5 EPNdB below FAR 36 limits. Using measured sonic inlet results, scaled baseline Q2S fan results, and calculated attenuations for a 1975 technology duct liner, projected flyover noise calculations for the ATT averaged about FAR 36 limits minus 10 EPNdB. Advances in suppression technology required to meet the 1985 goal of FAR 36 limits minus 20 EPNdB are discussed.

Sofrin, T. G.↗

Improved Cloud Condensation Nucleus Spectrometer

An improved thermal-gradient cloud condensation nucleus spectrometer (CCNS) has been designed to provide several enhancements over prior thermal- gradient counters, including fast response and high-sensitivity detection covering a wide range of supersaturations. CCNSs are used in laboratory research on the relationships among aerosols, supersaturation of air, and the formation of clouds. The operational characteristics of prior counters are such that it takes long times to determine aerosol critical supersaturations. Hence, there is a need for a CCNS capable of rapid scanning through a wide range of supersaturations. The present improved CCNS satisfies this need. The improved thermal-gradient CCNS (see Figure 1) incorporates the following notable features: a) The main chamber is bounded on the top and bottom by parallel thick copper plates, which are joined by a thermally conductive vertical wall on one side and a thermally nonconductive wall on the opposite side. b) To establish a temperature gradient needed to establish a supersaturation gradient, water at two different regulated temperatures is pumped through tubes along the edges of the copper plates at the thermally-nonconductive-wall side. Figure 2 presents an example of temperature and supersaturation gradients for one combination of regulated temperatures at the thermally-nonconductive-wall edges of the copper plates. c) To enable measurement of the temperature gradient, ten thermocouples are cemented to the external surfaces of the copper plates (five on the top plate and five on the bottom plate), spaced at equal intervals along the width axis of the main chamber near the outlet end. d) Pieces of filter paper or cotton felt are cemented onto the interior surfaces of the copper plates and, prior to each experimental run, are saturated with water to establish a supersaturation field inside the main chamber. e) A flow of monodisperse aerosol and a dilution flow of humid air are introduced into the main chamber at the inlet end. The inlet assembly is designed to offer improved (relative to prior such assemblies) laminar-flow performance within the main chamber. Dry aerosols are subjected to activation and growth in the supersaturation field. f) After aerosol activation, at the outlet end of the main chamber, a polished stainless-steel probe is used to sample droplets into a laser particle counter. The probe features an improved design for efficient sampling. The counter has six channels with size bins in the range of 0.5- to 5.0-micron diameter. g) To enable efficient sampling, the probe is scanned along the width axis of the main chamber (thereby effecting scanning along the temperature gradient and thereby, further, effecting scanning along the supersaturation gradient) by means of a computer-controlled translation stage.

Leu, Ming-Taun↗

Mesoporous optically clear heat insulators for sustainable building envelopes

Mesoporous materials exhibit highly controlled nanoscale structures, often templated by liquid crystalline assemblies of surfactants, with emergent and often designable physical properties. However, scaling their fabrication to be suitable for uses like envelopes of buildings is challenging. Here we describe fabrication of flexible square-meter-sized films and multi-centimeter-thick slabs made of three-dimensional spatial graphs of mesopore tubes having all structural features under 50 nanometers. Solution-based kinetic fabrication process templates growing networks of cylindrical surfactant micelles with thin tubes of polysiloxane forming gel networks and, upon replacing surfactants and solvents with air, yields lightweight materials with >99% visible-range optical transparency and ~10 mW K-1m-1 thermal conductivity. Such predesigned metamaterials enable transparent thermal barriers for wall-grade insulated glass units, square-meter window retrofits and unconcentrated solar thermal energy harnessing.

14 SOLAR ENERGY↗

Permeability-Engineered Compartmentalization Enables In Vitro Reconstitution of Sustained Synthetic Biology Systems

In nature, biological compartments such as cells rely on dynamically controlled permeability for matter exchange and complex cellular activities. Likewise, the ability to engineer compartment permeability is crucial for in vitro systems to gain sustainability, robustness, and complexity. However, rendering in vitro compartments such a capability is challenging. Here, a facile strategy is presented to build permeability-configurable compartments, and marked advantages of such compartmentalization are shown in reconstituting sustained synthetic biology systems in vitro. Through microfluidics, the strategy produces micrometer-sized layered microgels whose shell layer serves as a sieving structure for biomolecules and particles. In this configuration, the transport of DNAs, proteins, and bacteriophages across the compartments can be controlled an guided by a physical model. Through permeability engineering, a compartmentalized cell-free protein synthesis system sustains multicycle protein production; ≈100 000 compartments are repeatedly used in a five-cycle synthesis, featuring a yield of 2.2 mg mL -1 . Further, the engineered bacteria-enclosing compartments possess near-perfect phage resistance and enhanced environmental fitness. In a complex river silt environment, compartmentalized whole-cell biosensors show maintained activity throughout the 32 h pollutant monitoring. It is anticipated that permeability-engineered compartmentalization should pave the way for practical synthetic biology applications such as green bioproduction, environmental sensing, and bacteria-based therapeutics.

59 BASIC BIOLOGICAL SCIENCES↗

Watch what you say, your computer might be listening: A review of automated speech recognition

Spoken language is the most convenient and natural means by which people interact with each other and is, therefore, a promising candidate for human-machine interactions. Speech also offers an additional channel for hands-busy applications, complementing the use of motor output channels for control. Current speech recognition systems vary considerably across a number of important characteristics, including vocabulary size, speaking mode, training requirements for new speakers, robustness to acoustic environments, and accuracy. Algorithmically, these systems range from rule-based techniques through more probabilistic or self-learning approaches such as hidden Markov modeling and neural networks. This tutorial begins with a brief summary of the relevant features of current speech recognition systems and the strengths and weaknesses of the various algorithmic approaches.

Degennaro, Stephen V.↗

Bouguer Images of the North American Craton

Processing of existing gravity and aeromagnetic data with modern methods is providing new insights into crustal and mantle structures for large parts of the United States and Canada. More than three-quarters of a million ground station readings of gravity are now available for this region. These data offer a wealth of information on crustal and mantle structures when reduced and displayed as Bouguer anomalies, where lateral variations are controlled by the size, shape and densities of underlying materials. Digital image processing techniques were used to generate Bouguer images that display more of the granularity inherent in the data as compared with existing contour maps. A dominant NW-SE linear trend of highs and lows can be seen extending from South Dakota, through Nebaska, and into Missouri. This trend is probably related to features created during an early and perhaps initial episode of crustal assembly by collisional processes. The younger granitic materials are probably a thin cover over an older crust.

Arvidson, R. E.↗

Experiments and analysis concerning the use of external burning to reduce aerospace vehicle transonic drag

The external combustion of hydrogen to reduce transonic drag was investigated. A control volume analysis is developed and indicates that the specific impulse performance of external burning is competitive with other forms of airbreathing propulsion and depends on the fuel-air ratio, freestream Mach number, and the severity of the base drag. A method is presented for sizing fuel injectors for a desired fuel-air ratio in the unconfined stream. A two-dimensional Euler analysis is also presented which indicates that the total axial force generated by external burning depends on the total amount of energy input and is independent of the transverse and streamwise distribution of heat addition. Good agreement between the Euler and control volume analysis is demonstrated. Features of the inviscid external burning flowfield are discussed. Most notably, a strong compression forms at the sonic line within the burning stream which may induce separation of the plume and prevent realization of the full performance potential. An experimental program was conducted in a Mach 1.26 free-jet to demonstrate drag reduction on a simple expansion ramp geometry, and verify hydrogen-air stability limits at external burning conditions. Stable combustion appears feasible to Mach number of between 1.4 and 2 depending on the vehicle flight trajectory. Drag reduction is demonstrated on the expansion ramp at Mach 1.26; however, force levels showed little dependence on fuel pressure or altitude in contrast to control volume analysis predictions. Various facility interference mechanisms and scaling issues were studied and are discussed.

Trefny, Charles J.↗

Neural Net Safety Monitor Design

The National Aeronautics and Space Administration (NASA) at the Dryden Flight Research Center (DFRC) has been conducting flight-test research using an F-15 aircraft (figure 1). This aircraft has been specially modified to interface a neural net (NN) controller as part of a single-string Airborne Research Test System (ARTS) computer with the existing quad-redundant flight control system (FCC) shown in figure 2. The NN commands are passed to FCC channels 2 and 4 and are cross channel data linked (CCDL) to the other computers as shown. Numerous types of fault-detection monitors exist in the FCC when the NN mode is engaged; these monitors would cause an automatic disengagement of the NN in the event of a triggering fault. Unfortunately, these monitors still may not prevent a possible NN hard-over command from coming through to the control laws. Therefore, an additional and unique safety monitor was designed for a single-string source that allows authority at maximum actuator rates but protects the pilot and structural loads against excessive g-limits in the case of a NN hard-over command input. This additional monitor resides in the FCCs and is executed before the control laws are computed. This presentation describes a floating limiter (FL) concept1 that was developed and successfully test-flown for this program (figure 3). The FL computes the rate of change of the NN commands that are input to the FCC from the ARTS. A window is created with upper and lower boundaries, which is constantly floating and trying to stay centered as the NN command rates are changing. The limiter works by only allowing the window to move at a much slower rate than those of the NN commands. Anywhere within the window, however, full rates are allowed. If a rate persists in one direction, it will eventually hit the boundary and be rate-limited to the floating limiter rate. When this happens, a persistent counter begins and after a limit is reached, a NN disengage command is generated. The tunable metrics for the FL are (1) window size, (2) drift rate, and (3) persistence counter. Ultimate range limits are also included in case the NN command should drift slowly to a limit value that would cause the FL to be defeated. The FL has proven to work as intended. Both high-g transients and excessive structural loads are controlled with NN hard-over commands. This presentation discusses the FL design features and presents test cases. Simulation runs are included to illustrate the dramatic improvement made to the control of NN hard-over effects. A mission control room display from a flight playback is presented to illustrate the neural net fault display representation. The FL is very adaptable to various requirements and is independent of flight condition. It should be considered as a cost-effective safety monitor to control single-string inputs in general.

Larson, Richard R.↗

Implementation of an Adaptive Controller System from Concept to Flight Test

The National Aeronautics and Space Administration (NASA) at the Dryden Flight Research Center (DFRC) has been conducting flight-test research using an F-15 aircraft (figure 1). This aircraft has been specially modified to interface a neural net (NN) controller as part of a single-string Airborne Research Test System (ARTS) computer with the existing quad-redundant flight control system (FCC) shown in figure 2. The NN commands are passed to FCC channels 2 and 4 and are cross channel data linked (CCDL) to the other computers as shown. Numerous types of fault-detection monitors exist in the FCC when the NN mode is engaged; these monitors would cause an automatic disengagement of the NN in the event of a triggering fault. Unfortunately, these monitors still may not prevent a possible NN hard-over command from coming through to the control laws. Therefore, an additional and unique safety monitor was designed for a single-string source that allows authority at maximum actuator rates but protects the pilot and structural loads against excessive g-limits in the case of a NN hard-over command input. This additional monitor resides in the FCCs and is executed before the control laws are computed. This presentation describes a "floating limiter" (FL) concept that was developed and successfully test-flown for this program (figure 3). The FL computes the rate of change of the NN commands that are input to the FCC from the ARTS. A window is created with upper and lower boundaries, which is constantly "floating" and trying to stay centered as the NN command rates are changing. The limiter works by only allowing the window to move at a much slower rate than those of the NN commands. Anywhere within the window, however, full rates are allowed. If a rate persists in one direction, it will eventually "hit" the boundary and be rate-limited to the floating limiter rate. When this happens, a persistent counter begins and after a limit is reached, a NN disengage command is generated. The tunable metrics for the FL are (1) window size, (2) drift rate, and (3) persistence counter. Ultimate range limits are also included in case the NN command should drift slowly to a limit value that would cause the FL to be defeated. The FL has proven to work as intended. Both high-g transients and excessive structural loads are controlled with NN hard-over commands. This presentation discusses the FL design features and presents test cases. Simulation runs are included to illustrate the dramatic improvement made to the control of NN hard-over effects. A mission control room display from a flight playback is presented to illustrate the neural net fault display representation. The FL is very adaptable to various requirements and is independent of flight condition. It should be considered as a cost-effective safety monitor to control single-string inputs in general.

Larson, Richard R.↗

A New View of the Lunar South Pole from the Lunar Orbiter Laser Altimeter (LOLA)

Upcoming missions to the lunar south pole require detailed maps over large areas to fully characterize landing sites locally and regionally and to place their data into proper geologic context. To that end, we enhanced the Lunar Orbiter Laser Altimeter (LOLA) altimetry dataset for the south polar region, from which we produced new maps of topography, topographic roughness, and permanently shadowed regions (PSRs). The roughness maps reveal a diversity of terrains characterized by hectometer-scale roughness which is controlled in this region primarily by cratering and downslope mass transport. The south polar region is littered with linear roughness features of order ~1 – 10 km wide and ~10s – 100s of km long hypothesized to be secondary impacts within extended ejecta rays. Non uniformities in these features could reflect variations in secondary impactor properties and/or target terrain properties. Poleward of 80° S, the PSR cumulative size-frequency distribution (CSFD) shows an approximately power-law behavior whose exponent has a spatial variation of ~10%. PSRs with areas < 1 km2 contain 15 ± 5% of the total PSR area. Finally, we studied the effect of false positives and false negatives on the accuracy of the measured PSR cumulative size-frequency distribution (CSFD) and on the area for any individual PSR. The new maps presented here have many applications in the science and exploration of the lunar south polar region, such as geologic mapping and traverse planning.

Michael K. Barker↗