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291 records · Page 12

Modular Assembled Radiators for Nuclear Electric Propulsion (NEP) VehicLes (MARVL) Project Thermal Technology Development

Nuclear Electric Propulsion (NEP) has been considered for crew and cargo class missions to Mars for more than six decades. The Primary Heat Rejection Subsystem (PHRS) of an NEP vehicle expels the megawatts of waste heat generated by the Power Conversion Subsystem (PCS). In previous studies, integrating the majority of the NEP vehicle within a single launch fairing required the use of complex deployable elements and resulted in reduced PCS efficiency. To achieve the necessary radiating area, past design studies have utilized massive multi-wing folding radiators resulting in conceptual PHRS designs that have been widely acknowledged as non-optimal. The Modular Assembled Radiators for NEP VehicLes (MARVL) project is incorporating in-Space Assembly (iSA) into the design process to realize lightweight, modular, and more capable PHRS radiators. Since the project’s Authority to Proceed (ATP) date of October 2024, the project team has been developing a modular design for the PHRS radiators that will be suitable for both the Mars mission environments and iSA commissioning operations. This document captures the current progress of the incremental technology development for the thermal components of the MARVL System of Interest (SOI).

Modular Radiator

Polymer Composite Material Screening for a Cryotank Application

Composite cryotanks will play a key role in enabling the next generation of efficient aircraft. Carbon fiber reinforced polymer (CFRP) composites have the benefits of reduced weight and potentially higher structural strength compared to traditional metallic fuel tanks. A material screening study was conducted to inform material selection for liquid hydrogen (LH2) fuel storage. Three composite materials were considered because of their aerospace grade toughness, strength, and existing data to compare against. These materials were a thermoplastic low-melt polyaryletherketone (LM-PAEK)/carbon fiber (CF), thermoset/CF, and hybrid thermoset/thermoplastic polyurethane (TPU) veil/CF composite. Mechanical screening tests included tension, compression, in-plane shear (IPS), and tensile-tensile fatigue (TTF). Each material was tested at both a baseline (no liquid nitrogen/LN2 cycling) and 100 LN2-cycled conditions to determine the knockdown factor, if any, of each material when exposed to environmental loading effects in a cryotank. Results show minimal effects of the LN2-cycling compared against baseline values. The three materials behaved similarly in tension; however, the thermoplastic/CF had the highest IPS toughness. The hybrid thermoset/TPU/CF composite had the lowest IPS strength, compressive strength, and toughness. LN2-cycling had minimal effects on tensile-tensile fatigue performance of the thermoplastic/CF material. Mechanical data was captured to guide material down selection for future commercially viable hydrogen aircraft design.

Composites

The HEROIX Broadband X-Ray Space Telescope Mission Concept

The High EneRgy Observatory for Imaging X-rays (HEROIX) Medium-Class Mission concept envisions a next-generation broadband X-ray observatory designed to meet the astrophysics community’s need for high-angular-resolution studies of the Cosmic X-ray Background. Building on the science legacy of NASA’s NuSTAR mission and more than 30 years of advances in replicated NiCo shell technology at NASA Marshall, HEROIX proposes a space observatory comprising four co-aligned telescopes achieving 5 arcsecond half-power diameter (HPD) angular resolution. This capability, approached by the resolution demonstrated in the FOXSI-4 sounding rocket mission and under development through the SuperHERO balloon mission, will be extended to energies up to 80 keV through multilayer coatings. Marshall’s inhouse precision optics manufacturing enables an integrated effective area of 380 cm² at 30 keV, which, combined with high-resolution optics, opens new windows into extreme astrophysical non-thermal processes.

Nick Thomas

A Laboratory Breadboard System for Dual-Arm Teleoperation

The computing architecture of a novel dual-arm teleoperation system is described. The novelty of this system is that: (1) the master arm is not a replica of the slave arm; it is unspecific to any manipulator and can be used for the control of various robot arms with software modifications; and (2) the force feedback to the general purpose master arm is derived from force-torque sensor data originating from the slave hand. The computing architecture of this breadboard system is a fully synchronized pipeline with unique methods for data handling, communication and mathematical transformations. The computing system is modular, thus inherently extendable. The local control loops at both sites operate at 100 Hz rate, and the end-to-end bilateral (force-reflecting) control loop operates at 200 Hz rate, each loop without interpolation. This provides high-fidelity control. This end-to-end system elevates teleoperation to a new level of capabilities via the use of sensors, microprocessors, novel electronics, and real-time graphics displays. A description is given of a graphic simulation system connected to the dual-arm teleoperation breadboard system. High-fidelity graphic simulation of a telerobot (called Phantom Robot) is used for preview and predictive displays for planning and for real-time control under several seconds communication time delay conditions. High fidelity graphic simulation is obtained by using appropriate calibration techniques.

A K Bejczy

Reliability Analysis of Single Crystal NiAl Turbine Blades

As part of a co-operative agreement with General Electric Aircraft Engines (GEAE), NASA LeRC is modifying and validating the Ceramic Analysis and Reliability Evaluation of Structures algorithm for use in design of components made of high strength NiAl based intermetallic materials. NiAl single crystal alloys are being actively investigated by GEAE as a replacement for Ni-based single crystal superalloys for use in high pressure turbine blades and vanes. The driving force for this research lies in the numerous property advantages offered by NiAl alloys over their superalloy counterparts. These include a reduction of density by as much as a third without significantly sacrificing strength, higher melting point, greater thermal conductivity, better oxidation resistance, and a better response to thermal barrier coatings. The current drawback to high strength NiAl single crystals is their limited ductility. Consequently, significant efforts including the work agreement with GEAE are underway to develop testing and design methodologies for these materials. The approach to validation and component analysis involves the following steps: determination of the statistical nature and source of fracture in a high strength, NiAl single crystal turbine blade material; measurement of the failure strength envelope of the material; coding of statistically based reliability models; verification of the code and model; and modeling of turbine blades and vanes for rig testing.

Joseph Palko

Chapter 19A – Radar Cross Section

The material in this Section will provide the novice Flight Test Engineer (FTE) with a brief overview of the radar cross section (RCS) concept. Brief details of radar range descriptions, operations, target calibrations, and data reduction are included. It is noted that these range operations concentrate on the "static" test range rather than the much more sophisticated "dynamic" test range. The dynamic test range is what the FTE will probably work with. Radar reflectivity measurement has developed over the last two decades from a relatively simple endeavor involving the measurement of target RCS amplitude statistics to involving wide band, coherent systems that can measure high resolution images of targets as well as, in many cases, the polarization and phasing properties. This rapid growth in RCS technology has occurred because of the increased use of radar in today's commercial and military systems. In general, the goal for commercial systems is to enhance radar reflectivity, whereas the military goal is to reduce radar reflectivity. Also, classification and identification are important for military purposes because in adverse weather radar may be the only system that may be capable of separating enemy targets from friendly ones. This Section will discuss the fundamentals of RCS. Since the flight test techniques associated with RCS measurements are very similar to those of antenna pattern measurements, both will be presented at the same time in Section 19B Antenna Radiation Pattern Measurements.

Robert W Borek

Spacecraft Conceptual Design for Returning Entire Near-Earth Asteroids

In situ resource utilization (ISRU) in general, and asteroid mining in particular are ideas that have been around for a long time, and for good reason. It is clear that ultimately human exploration beyond low-Earth orbit will have to utilize the material resources available in space. Historically, the lack of sufficiently capable in-space transportation has been one of the key impediments to the harvesting of near-Earth asteroid resources. With the advent of high-power (or order 40 kW) solar electric propulsion systems, that impediment is being removed. High-power solar electric propulsion (SEP) would be enabling for the exploitation of asteroid resources. The design of a 40-kW end-of-life SEP system is presented that could rendezvous with, capture, and subsequently transport a 1,000-metric-ton near-Earth asteroid back to cislunar space. The conceptual spacecraft design was developed by the Collaborative Modeling for Parametric Assessment of Space Systems (COMPASS) team at the Glenn Research Center in collaboration with the Keck Institute for Space Studies (KISS) team assembled to investigate the feasibility of an asteroid retrieval mission. Returning such an object to cislunar space would enable astronaut crews to inspect, sample, dissect, and ultimately determine how to extract the desired materials from the asteroid. This process could jump-start the entire ISRU industry.

solar electric propulsion

Numerical Modeling of the Transient Chilldown Process of a Cryogenic Propellant Transfer Line

Before cryogenic fuel depots can be fully realized, efficient methods with which to chill down the spacecraft transfer line and receiver tank are required. This paper presents numerical modeling of the chilldown of a liquid hydrogen tank-to-tank propellant transfer line using the Generalized Fluid System Simulation Program (GFSSP). To compare with data from recently concluded turbulent LH2 chill down experiments, seven different cases were run across a range of inlet liquid temperatures and mass flow rates. Both trickle and pulse chill down methods were simulated. The GFSSP model qualitatively matches external skin mounted temperature readings, but large differences are shown between measured and predicted internal stream temperatures. Discrepancies are attributed to the simplified model correlation used to compute two-phase flow boiling heat transfer. Flow visualization from testing shows that the initial bottoming out of skin mounted sensors corresponds to annular flow, but that considerable time is required for the stream sensor to achieve steady state as the system moves through annular, churn, and bubbly flow. The GFSSP model does adequately well in tracking trends in the data but further work is needed to refine the two-phase flow modeling to better match observed test data.

Temperature Sensors

AstroDOME: Standardized, Mass-Produceable, Small NASA Astrophysics Observatories for Big Missions

NASA’s Goddard Space Flight Center is investigating the use of small, commercial off the shelf (COTS) spacecraft to enable breakthrough astrophysics research at radically reduced cost over previous generations of missions. This paper will focus on the Mission Systems perspective of this investigation. It will cover the spacecraft to instrument interface, and lessons learned in early concept payload development. Low-cost COTS spacecraft have proliferated in the last ~5 years. They represent an order of magnitude reduction in the cost of spacecraft bus development and acquisition. They are enabled by the advent of low-cost smallsat launch options in the immediately preceding years, and are seeded by recent distributed and disaggregated missions in other sectors such as telecommunications megaconstellations (e.g. Starlink, OneWeb, Project Kuiper) and ongoing Space Development Agency (SDA) developments. Our study was tasked with developing a standardized, mass-produceable, astrophysics payload which is reconfigurable to different wavelength bands while maintaining a single optics bench design, and a standardized mechanical, electrical, data, and thermal interface to the spacecraft bus, and which may be reconfigured to multiple COTS spacecraft offerings. In this paper we will discuss lessons learned from our case study. We will also present identified keys to mission success for performing cutting edge astrophysics observations while taking advantage of economies of scale with a disaggregated, standardized architecture.

Matthew Marcus

Nitrile/Buna N Material Failure Assessment for an O-Ring used on the Gaseous Hydrogen Flow Control Valve (FCV) of the Space Shuttle Main Engine

After the rollout of Space Shuttle Discovery in April 2005 in preparation for return-to-flight, there was a failure of the Orbiter (OV-103) helium signature leak test in the gaseous hydrogen (GH2) system. Leakage was attributed to the Flow Control Valve (FCV) in Main Engine 3. The FCV determined to be the source of the leak for OV-103 is designated as LV-58. The nitrile/Buna N rubber O-ring seal was removed from LV-58, and failure analysis indicated radial cracks providing leak paths in one quadrant. Cracks were eventually found in 6 of 9 FCV O-rings among the three Shuttle Orbiters, though none were as severe as those for LV-58, OV-103. Testing by EM10 at MSFC on all 9 FCV O- rings included: laser dimensional, Shore A hardness and properties from a dynamic mechanical analyzer (DMA) and an Instron tensile machine. The following test data was obtained on the cracked quadrant of the LV-58, OV-103 O-ring: (1) the estimated compression set was only 9.5%, compared to none for the rest of the O-ring; (2) Shore A hardness for the O.D. was higher by almost 4 durometer points than for the rest of the O-ring; and (3) DMA data showed that the storage/elastic modulus E was almost 25% lower than for the rest of the O-ring. Of the 8 FCV O-rings tested on an Instron, 4 yielded tensile strengths that were below the MIL spec requirement of 1350 psi-a likely influence of rubber cracking. Comparisons were made between values of modulus determined by DNA (elastic) and Instron (Young s). Each nitrile/Buna N O-ring used in the FCV conforms to the MIL-P-25732C specification. A number of such O-rings taken from shelf storage at MSFC and Kennedy Space Center (KSC) were used to generate a reference curve of DMA glass transition temperature (Tg) vs. shelf storage time ranging from 8 to 26 years. A similar reference curve of TGA onset temperature (of rubber weight loss) vs. shelf storage time was also generated. The DMA and TGA data for the used FCV O-rings were compared to the reference curves. Correlations were also made between the DMA modulus (at 22 C) and Shore A hardness for all 9 of the FCV O-rings used among the three Shuttle Orbiters. The radial cracking in the FCV O-rings was determined to be due to ozone attack, as nitrile/Buna N rubber is susceptible to such attack. Nitrile/Buna N material under MIL-P25732C should be used in a hydraulic fluid environment to help protect it from cracking. However, the FCV O-rings were used in an air only environment. The FCV design has as much as a 9-mil gap that allows the O.D. of the O-ring to be directly exposed to ozone, pressurized air and some elevated temperatures, accelerating the weathering process that leads to O-ring cracking. Space Shuttle flights will likely not continue past 2010. Therefore, Shuttle management decided to continue using the nitrile/Buna N material for the FCVs, but have each O-ring replaced after 3 years to minimize any chances for crack initiation.

Doug Wingard

Polarized Resonant Soft X-ray Scattering (P-RSoXS) as a New Technique for Characterizing Amorphous Astromaterials

In the coming years, samples will be returned from several asteroids, the lunar surface, and the first material returned directly from the Martian surface. Previous in-situ and remote studies indicate these samples will contain abundant amorphous or weakly crystalline materials. However, detailed characterization and quantification of these amorphous materials remains challenging. Conventional techniques, including electron microscopy and X-ray diffraction, provide important information on material structure, but are generally limited to crystalline materials. Polarized resonant soft X-ray scattering (P-RSoXS) is a synchrotron-based X-ray scattering technique that has been used to characterize and quantify weakly crystalline systems, including soft materials. This research aims to translate this technique to geologic and extraterrestrial materials, building off the knowledge of using P-RSoXS to interrogate soft materials. P-RSoXS is well-suited to interrogate geologic materials, which are often multiphase, heterogeneous systems with crystalline and amorphous components, and domain sizes on the order of tens of nanometers. It is anticipated that future work will help reveal new chemical and structural information in geologic materials. Maturation of this preliminary work to develop P-RSoXS to characterize astromaterial-relevant samples will provide new understanding of the secondary processes responsible for the development of amorphous astromaterials and further elucidate our knowledge of the geologic history and past alteration processes.

Joshua H Litofsky

NASA Space Launch System Artemis I & II Post Flight Ascent Aerothermal Environments Overview

Since 2011 the Aerosciences Branch/EV33 at NASA Marshall Space Flight Center has been involved with the development of ascent external aerothermal environments for the NASA Space Launch System (SLS) Block 1 launch vehicle for the purposes of supporting thermal analysis and the design of thermal protection systems. The SLS Block 1 Artemis I and II launch vehicles successfully launched from Pad39B at NASA Kennedy Space Center on November 16th, 2022 and April 1st, 2026, respectively. Over 70 aerothermal islands, consisting of over 265 operational instruments captured aerodynamic heating and plume induced environments throughout the launch vehicles. Gauges consisted of calorimeters, radiometers, gas temperature probes, pressure transducers, bi-directional pressure probes and thermocouples. Prior to launch, aerothermal design environment models were generated to predict ascent aerodynamic heating and plume induced environments over a design space that covered a range of vehicle trajectories that varied atmospheric, vehicle performance, and off-nominal, engine-out conditions. Post flight reconstruction models were developed for each flight island using the Day-of-Launch (DOL) Best Equivalent Trajectory (BET) that provided freestream conditions and propulsion system boundary conditions. This paper discusses a summary of the ascent aerothermal environments observed during the flights and the respective modelling approaches and the performance of them through comparisons of flight data and predictions.

aerothermodynamics

Hypervelocity Impact Testing of Nickel Hydrogen Battery Cells

Nickel-Hydrogen (Ni/H2) battery cells have been used on several satellites and are planned for use on the International Space Station. In January 1992, the NASA Lewis Research Center (LeRC) conducted hypervelocity impact testing on Ni/H2 cells to characterize their failure modes. The cell's outer construction was a 24 mil-thick Inconel 718 pressure vessel. A sheet of 1.27 cm thick honeycomb was placed in front of the battery cells during testing to simulate the on-orbit box enclosure. Testing was conducted at the NASA White Sands Test Facility (WSTF). The hypervelocity gun used was a 7.6 mm (0.30 caliber) two-stage light gas gun. Test were performed at speeds of 3, 6, and 7 km/sec using aluminum 2017 spherical particles of either 4.8 or 6.4 mm diameter as the projectile. The battery cells were electrically charged to about 75 percent of capacity, then back-filled with hydrogen gas to 900 psi simulating the full charge condition. High speed film at 10,000 frames/sec was taken of the impacts. Impacts in the dome area (top) and the electrode area (middle) of the battery cells were investigated. Five tests on battery cells were performed. The results revealed that in all of the test conditions investigated, the battery cells simply vented their hydrogen gas and some electrolyte, but did not burst or generate any large debris fragments.

Frate, David T.

Development of global/chemistry model for jet-fuel thermal stability based on observations from static and flowing experiments

Two global-chemistry models for oxidative deposition of jet fuels are evaluated by integrating them into a Computational Fluid Dynamics with Chemistry (CFDC) code. A previously developed two-step global-chemistry model was found to be insufficient to describe the thermal-oxidation and -deposition rates associated with a Jet-A fuel. A new global-chemistry model has been developed systematically based on observations from flowing and static experiments. The global-autoxidation reaction is modified such that the reaction rate becomes zeroth-order with respect to the dissolved oxygen concentration. The generation of deposit-forming precursor is coupled with the autoxidation reaction by introducing a radical species ROO. A formulation for the sticking probability has also been developed. Deposition profiles are well represented by this new model under a variety of temperature and flow conditions. The model correctly predicts the changes in magnitude and spatial location of the deposition peak due to changes in flow. The CFDC model, which is designed for flowing systems, has been extended to static experiments. The model incorporates a non-depleting species F(sub s) representing all non-oxygen compounds responsible for deposition. Static experiments were found to provide a useful and inexpensive method for estimating the concentration of F(sub s) in the fuel.

V. R. Katta

Accelerating SNP Development with Radiation Source Approximations for Far-Field Environment Modeling

The successful development and deployment of space nuclear power and propulsion technology requires a high-fidelity, efficient means of modeling ex-core radiation fields. Monte Carlo particle transport codes provide enable the highest level of fidelity in radiation field modeling but are inefficient for modeling ex-core radiation without modification. This paper details the development of an approach to ex-core radiation field modeling that maintains the fidelity of a Monte Carlo transport approach without sacrificing computational efficiency. This approach is based on recent improvements to an existing Monte Carlo transport acceleration technique known as surface source banking. As the transport of many particles is required to ensure adequate uncertainty in far field transport, analytical reconstruction techniques are employed to represent surface source banks as sampleable series of distributions in particle phase from which an arbitrarily large number of particles can be generated and simulated. All steps of this approach are incorporated into an AMA model to test both the underlying mathematics of the analytical source reconstruction process, as well as the relevance of the technique as a whole towards SNP applications. These tests demonstrated that this approach is capable of accelerating far-field radiation modeling in SNP-relevant scenarios by factors of at least nine over purely eigenvalue-based scenarios without significantly sacrificing simulation accuracy.

Surface Source Banking

Assessing the Adhesion of Nanofibrous PVDF-HFP as Passive Thermal Control Coatings for the Extraterrestrial Storage of Cryogenic Propellants

Cryogenic propellant passive thermal management techniques in space are essential complements to active thermal management methods, helping reduce absolute dependence on the latter. Particularly, materials with superior optical properties (high solar reflectance and infrared emittance) would be beneficial for passive thermal control to reject most of the incident solar radiation and enhance thermal emission from the storage tank, leading to self-cooling. We developed a nanofibrous, porous passive thermal control material by electrospinning polyvinylidene fluoride-co-hexafluoropropylene (PVDF-HFP) co-polymer onto an aluminum foil substrate. The material exhibits a very high solar reflectance (>99%) and infrared emittance (~86%) when characterized in the ultraviolet-visible-near infrared and mid-infrared wavelengths. This study focuses on the adhesion of the nanofibrous PVDF-HFP to the substrate. We incorporated in-lab fabricated and commercial adhesives, under normal room conditions, between the nanofibers and the aluminum foil substrate to improve their adhesion. Some samples were also exposed to space-like conditions – vacuum and thermal cycling, to investigate their effects on the strengths of adhesives. Subsequently, adhesion peel tests were conducted on all the samples to assess the peel strengths of the bonds. Peel test strengths after space environment conditioning of the adhesives were generally higher than those observed in the pristine, unaged samples. The results are discussed in this study.

Chieloka Ibekwe

Machine Learning for Predicting Team Functioning in HERA Missions

Team functioning is integral to success in future long term space exploration missions. Proactively detecting declines in team functioning can mitigate conflict and ensure mission success. This project developed a speech-based artificial intelligence (AI) system that unobtrusively predicts degradation in team functioning, including performance and cohesion, in the Human Exploration Research Analog (HERA) Campaigns 4 and 5. The AI system conducted automated analysis of the prosodic (tone of voice) and linguistic (language content) components of speech, modeling interpersonal dynamics at both the turn-taking and day-wide levels. We investigated team functioning via observing structured interactions (i.e., multi-mission space exploration vehicle-extra vehicular activity [MMSEV-EVA], team interaction battery [TIB]) and unstructured interactions before the MMSEV-EVA task. We developed machine learning models to predict team functioning (objective task accuracy, self reported team efficacy and self reported team cohesion) by analyzing OpenSmile acoustic features, linguistic descriptors extracted via the linguistic inquiry and word count (LIWC) dictionary, and semantic embeddings. In the TIB, static models using logistic regression and random forests were not able to predict task accuracy, but predicted team efficacy and cohesion during both the decision making and relational tasks to a moderate level (60-70%). Majority voting on the individual turns to predict day long team efficacy further increased accuracies (70-80%). Finally, long short-term memory (LSTM) models showed the best performance across all variables (80-91%), including task performance. In the MMSEV-EVA, static models achieved an accuracy of 60% with majority voting, which increased to 80% through the incorporation of mission day as a variable, accounting for the learning effect. A key finding across both tasks was the "team-dependent" nature of these interactions; models achieved much higher accuracy when trained on prior days of the same team's data rather than attempting to generalize across entirely different teams, with even 1-2 days of prior data per team achieving 5-15% improvement over team-independent models. In addition, the incorporation of pre-task data from the same team also improves model performance, e.g., incorporating data from the decision-making task of the TIB, which preceded the relational task, improved the prediction of team efficacy and cohesion during the latter. We compared model performance when trained on machine-generated data compared to data that had been further corrected by human annotators. Overall, models trained on human-corrected data exhibited a modest improvement in performance, particularly when acoustic features were used. We found no significant correlation between word error rate (WER) and model accuracy (r(55) = -0.08, p = 0.51), but model’s accuracy was significantly higher for medium/high quality transcription (0.74 (SD = 0.48)) compared to the low-quality group (0.64 (SD = 0.36)) (t(63)=2.82, p = 0.006). Based on these, several design recommendation emerge, that could inform Standards at NASA. Models predicting team functioning should incorporate at least one to two days of historical interaction data, include brief pre-task discussions, and explicitly model temporal learning effects, especially for longer operational tasks. Minimum quality standards for automated speech-processing pipelines are needed, given the performance gains observed with manually corrected acoustic data. Finally, systems should leverage both acoustic features and language embeddings in complementary ways, with modality choices and fusion strategies tailored to mission context, task demands, and data quality requirements.

Shrivatsa Mishra

Battery Charge Equalizer with Transformer Array

High-power batteries generally consist of a series connection of many cells or cell banks. In order to maintain high performance over battery life, it is desirable to keep the state of charge of all the cell banks equal. A method provides individual charging for battery cells in a large, high-voltage battery array with a minimum number of transformers while maintaining reasonable efficiency. This is designed to augment a simple highcurrent charger that supplies the main charge energy. The innovation will form part of a larger battery charge system. It consists of a transformer array connected to the battery array through rectification and filtering circuits. The transformer array is connected to a drive circuit and a timing and control circuit that allow individual battery cells or cell banks to be charged. The timing circuit and control circuit connect to a charge controller that uses battery instrumentation to determine which battery bank to charge. It is important to note that the innovation can charge an individual cell bank at the same time that the main battery charger is charging the high-voltage battery. The fact that the battery cell banks are at a non-zero voltage, and that they are all at similar voltages, can be used to allow charging of individual cell banks. A set of transformers can be connected with secondary windings in series to make weighted sums of the voltages on the primaries.

Davies, Francis