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NASA NTRS2010

Propellant Readiness Level: A Methodological Approach to Propellant Characterization

A methodological approach to defining propellant characterization is presented. The method is based on the well-established Technology Readiness Level nomenclature. This approach establishes the Propellant Readiness Level as a metric for ascertaining the readiness of a propellant or a propellant combination by evaluating the following set of propellant characteristics: thermodynamic data, toxicity, applications, combustion data, heat transfer data, material compatibility, analytical prediction modeling, injector/chamber geometry, pressurization, ignition, combustion stability, system storability, qualification testing, and flight capability. The methodology is meant to be applicable to all propellants or propellant combinations; liquid, solid, and gaseous propellants as well as monopropellants and propellant combinations are equally served. The functionality of the proposed approach is tested through the evaluation and comparison of an example set of hydrocarbon fuels.

Bossard, John A.↗

NASA NTRS2013

Distilling the Verification Process for Prognostics Algorithms

The goal of prognostics and health management (PHM) systems is to ensure system safety, and reduce downtime and maintenance costs. It is important that a PHM system is verified and validated before it can be successfully deployed. Prognostics algorithms are integral parts of PHM systems. This paper investigates a systematic process of verification of such prognostics algorithms. To this end, first, this paper distinguishes between technology maturation and product development. Then, the paper describes the verification process for a prognostics algorithm as it moves up to higher maturity levels. This process is shown to be an iterative process where verification activities are interleaved with validation activities at each maturation level. In this work, we adopt the concept of technology readiness levels (TRLs) to represent the different maturity levels of a prognostics algorithm. It is shown that at each TRL, the verification of a prognostics algorithm depends on verifying the different components of the algorithm according to the requirements laid out by the PHM system that adopts this prognostics algorithm. Finally, using simplified examples, the systematic process for verifying a prognostics algorithm is demonstrated as the prognostics algorithm moves up TRLs.

verification↗

NASA NTRSDate not supplied

Lessons for Future In-Space Telerobotic Servicing from Robotic Refueling Mission

The Robotic Refueling Mission (RRM) was a multi-phased technology development effort by the National Aeronautics & Space Administration (NASA) and the Canadian Space Agency (CSA). The program leveraged the existing robotic systems and expertise of the International Space Station (ISS) program and the tool design and satellite servicing expertise of NASA’s Exploration & In-space Services (NExIS) Projects Division at Goddard Space Flight Center (GSFC) to evaluate new hardware and techniques for on-orbit telerobotic servicing. Between 2011 and 2021, two external ISS payloads housed over a dozen robotic tools and adapters designed to service a variety of existing and novel satellite interfaces. Robot operators at NASA’s Johnson Space Center (JSC) and CSA used the Special Purpose Dexterous Manipulator (SPDM) to retrieve and operate these tools for tasks such as cutting wires or multi-layer insulation blanketing, removing valve caps, mating electrical connectors, transferring fluids, and performing visual inspections inside a vehicle. Each phase of RRM involved years of preparation. Tool and interface designs were prototyped and evaluated using both NASA and Canadian ground robotic systems. Procedures were developed by GSFC engineers and vetted in partnership with JSC and CSA robot operators. GSFC engineers were trained to provide real-time support during on-orbit operations. These preparatory efforts and the successful on-orbit evaluations yielded an array of lessons for future in-space telerobotic missions. Designing robotic tools for the space environment requires special consideration of materials, indicators, and differences between ground and flight use cases and environments. When there is a limited window for on-orbit operations, devoting time and high-fidelity hardware to ground testing can be critical. Needs during potential troubleshooting are more essential to camera view quality, frame rate, and position requirements more than nominal operations. Detailed hardware manuals, nominal and contingency procedures, along with clearly defined operations team roles and protocols are vital for efficiency. RRM also demonstrated how the ISS can be utilized to increase the technology readiness levels required for future missions and led to additional technology partnerships between NExIS and the ISS program. The lessons from RRM are currently being applied to designs, operations concepts, and ground test methodology for missions such as On-orbit Servicing, Assembly, and Manufacturing1(OSAM-1)and Mars Sample Return.

Zakiya Tomlinson↗

NASA NTRS2015

Comments on the MIT Assessment of the Mars One Plan

The MIT assessment of the Mars One mission plan reveals design assumptions that would cause significant difficulties. Growing crops in the crew chamber produces excessive oxygen levels. The assumed in-situ resource utilization (ISRU) equipment has too low a Technology Readiness Level (TRL). The required spare parts cause a large and increasing launch mass logistics burden. The assumed International Space Station (ISS) Environmental Control and Life Support (ECLS) technologies were developed for microgravity and therefore are not suitable for Mars gravity. Growing food requires more mass than sending food from Earth. The large number of spares is due to the relatively low reliability of ECLS and the low TRL of ISRU. The Mars One habitat design is similar to past concepts but does not incorporate current knowledge. The MIT architecture analysis tool for long-term settlements on the Martian surface includes an ECLS system simulation, an ISRU sizing model, and an analysis of required spares. The MIT tool showed the need for separate crop and crew chambers, the large spare parts logistics, that crops require more mass than Earth food, and that more spares are needed if reliability is lower. That ISRU has low TRL and ISS ECLS was designed for microgravity are well known. Interestingly, the results produced by the architecture analysis tool - separate crop chamber, large spares mass, large crop chamber mass, and low reliability requiring more spares - were also well known. A common approach to ECLS architecture analysis is to build a complex model that is intended to be all-inclusive and is hoped will help solve all design problems. Such models can struggle to replicate obvious and well-known results and are often unable to answer unanticipated new questions. A better approach would be to survey the literature for background knowledge and then directly analyze the important problems.

Mars mission↗

NASA NTRS2017

The Large UV/Optical/Infrared Surveyor (LUVOIR): Decadal Mission Concept Technology Development Overview

The Large Ultraviolet / Optical / Infrared (LUVOIR) Surveyor is one of four large mission concept studies being developed by NASA for consideration in the 2020 Astrophysics Decadal Survey. LUVOIR will support a broad range of science objectives, including the direct imaging and spectral characterization of habitable exoplanets around sun-like stars, the study of galaxy formation and evolution, the epoch of reionization, star and planet formation, and the remote sensing of Solar System bodies. The LUVOIR Science and Technology Definition Team (STDT) has tasked a Technology Working Group (TWG), with more than 60 members from NASA centers, academia, industry, and international partners, with identifying technologies that enable or enhance the LUVOIR science mission. The TWG has identified such technologies in the areas of Coronagraphy, Ultra-Stable Opto-mechanical Systems, Detectors, Coatings, Starshades, and Instrument Components, and has completed a detailed assessment of the state-of-the-art. We present here a summary of this technology assessment effort, as well as the current progress in defining a technology development plan to mature these technologies to the required technology readiness level (TRL).

Decadal Study; Technology; LUVOIR↗

DOE OSTI2025

Technology readiness assessment of magnetohydrodynamic stability control

The technology readiness level scale is revised with clear definitions for magnetohydrodynamic stability control technologies for magnetic confinement fusion. The definitions are in the form of a sentence with three dimensions, which are the system complexity, the test environment, and the cost. A clear and simple definition is sought after to make an assessment based on the evidence which is agreeable to the fusion energy development community. A sample technology readiness assessment (TRA) for the electron cyclotron current drive-based control of neoclassical tearing mode for ST Advanced Reactor, using the proposed scale, reveals that the risk of a TRA being misinterpreted is high, which can only be avoided with an understanding of the procedure described in this paper.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS2016

JPL Technology Readiness Assessment Guideline

New capabilities in spaceflight missions are enabled by new technologies. Transitioning new technology to spaceflight elements is difficult and introduces risk, but finding the right balance between benefit and risk leads to scientific advancements and novel space missions. A clear understanding of the risks of new technology can create an environment where innovation is nurtured rather than avoided. The Technology Readiness Level (TRL) was developed as a metric for the maturity of new technology, but, in the past, assessing the TRL was often done informally and inconsistently. This frequently led to discrepancies between the TRL as perceived by the technologist and that perceived by a project. JPL has developed a guideline for their projects to provide a basis for a consistent Technology Readiness Assessment (TRA). Highlights of this guideline are presented here. It is anticipated that the implementation of this guideline will enable the hand-off from technologists to project engineers leading to greater acceptance of technologies by flight projects. On completion of a satisfactory TRA, an agreement can be made between the parties on the maturation plan required for successful infusion of the technology into a flight mission.

Frerking, Margaret A.↗

NASA NTRS2003

An On-Line Technology Information System (OTIS) for Advanced Life Support

An On-line Technology Information System (OTIS) is currently being developed for the Advanced Life Support (ALS) Program. This paper describes the preliminary development of OTIS, which is a system designed to provide centralized collection and organization of technology information. The lack of thorough, reliable and easily understood technology information is a major obstacle in effective assessment of technology development progress, trade studies, metric calculations, and technology selection for integrated testing. OTIS will provide a formalized, well-organized protocol to communicate thorough, accurate, current and relevant technology information between the hands-on technology developer and the ALS Community. The need for this type of information transfer system within the Solid Waste Management (SWM) element was recently identified and addressed. A SWM Technology Information Form (TIF) was developed specifically for collecting detailed technology information in the area of SWM. In the TIF, information is requested from SWM technology developers, based upon the Technology Readiness Level (TRL). Basic information is requested for low-TRL technologies, and more detailed information is requested as the TRL of the technology increases. A comparable form is also being developed for the wastewater processing element. In the future, similar forms will also be developed for the ALS elements of air revitalization, food processing, biomass production and thermal control. These ALS element-specific forms will be implemented in OTIS via a web-accessible interface,with the data stored in an object-oriented relational database (created in MySQLTM) located on a secure server at NASA Ames Research Center. With OTIS, ALS element leads and managers will be able to carry out informed research and development investment, thereby promoting technology through the TRL scale. OTIS will also allow analysts to make accurate evaluations of technology options. Additionally, the range and specificity of information solicited will help educate technology developers of programmatic needs.

Levri, Julie A.↗

NASA NTRS2014

Air Traffic Management Technology Demonstration 1 (ATD-1) Tech Transfer Document Summary: Version 3.0

This document summarizes transfer of NASA's terminal sequencing and spacing (TSS) and interval management (IM) technologies to the FAA (Federal Aviation Administration), as part of its Air Traffic Management Technology (ATM) Demonstration 1 activity. This activity, referred to as ATD-1, is part of NASA's Airspace Systems Program (ASP) specifically, its System Analysis, Integration, and Evaluation (SAIE) Project. ATD-1 is a multi-year research and development effort aimed at accelerating implementation and deployment of NASA-developed ATM technologies by the FAA. These technologies are designed to improve the utilization of Performance-Based Navigation (PBN) procedures inside congested terminal airspace. In terms of NASA's Technology Readiness Levels (TRLs), ATD-1 is focused on maturing its associated technologies from the Technology Development stage (TRL 4) to the Technology Demonstration stage (TRL 6). In order to ensure that the products of this tech-transfer are relevant and useful, NASA has created strong partnerships with the FAA and key industry stakeholders.

Technology transfer↗

NASA NTRS2019

A Single Stage to Orbit Design for a Hybrid Mars Ascent

A Single Stage to Orbit (SSTO) hybrid propulsion system has been previously studied as an option for a conceptual Mars Ascent Vehicle (MAV). The hybrid motor uses a wax-based fuel developed specifically for this application, so it can take advantage of a single port design. The oxidizer is Mixed Oxides of Nitrogen (MON-25). Higher Nitric Oxide concentrations have been discussed in the past, however, the lower temperature capability is no longer needed. The MAV Payload Assembly (MPA), which would house the Orbiting Sample (OS) has changed substantially from previous iterations and has become more compact. Benefits of the hybrid option include its predicted low temperature behavior, high performance and ability to restart (enabling the SSTO). However, the hybrid technology remained at a relatively low Technology Readiness Level (TRL). In an attempt to increase the TRL, a technology development program has been underway for the past four years. The results of the technology development program are now being incorporated to an updated concept for a hybrid Mars Ascent Vehicle, with the eventual goal of informing a hybrid propulsion design that closes under the guidelines currently envisioned for a potential Mars Sample Return campaign. This paper focuses on the hybrid propulsion system design and the preliminary results from the first part of the FY19 technology development program (October 2018 to July 2019) and includes some results from a Preliminary Architecture Assessment (PAA) study. In the PAA, experts from all relevant subsystems (propulsion, avionics, GN&C, structures, thermal, etc.) are brought together to determine an updated vehicle design. The PAA is being run out of Marshall Space Flight Center (MSFC) in coordination with the Mars Sample Return study lead by the Jet Propulsion Laboratory (JPL). Currently, it is thought that the Mars Ascent Vehicle would be housed in a Sample Retrieval Lander (SRL), along with a fetch rover. The SRL would be responsible for several crucial functions on the MAV including heating, erection and providing the ignition signal. This paper will also outline the future testing and path forward through the rest of the fiscal year. This includes full scale testing at Whittinghill Aerospace, hypergolic additive testing at Purdue, evaluation of adding hypergolic additives to a full-scale grain. A hybrid fuel formulation has been updated with a reduced regression rate, which again was developed by Space Propulsion Group. This design will be used to determine the benefits of a hybrid versus solid propulsion system for a MAV, as they fit into the larger vision for a potential Mars Sample Return campaign.

Story, George↗

NASA NTRS2025

State-of-the-Art Small Spacecraft Technology

The objective of this report is to assess and provide an overview of the state of the art in small spacecraft technologies for use by mission designers, project managers, technologists, and students, connecting current small spacecraft missions to available technologies. This report focuses on the spacecraft system in its entirety, provides current best practices for integration and key considerations for the reader where possible, and presents devices from publicly available sources for each specific spacecraft subsystem. This report is a survey of small spacecraft technologies sourced from open literature; it is not an original source. In addition, this report only considers literature in the public domain. Information presented in this report is limited to SmallSat technology that is publicly available as of September 30, 2024. It does not include information on instrumentation, science payloads, or advances or developments that have not been publicly disclosed. Commonly used sources for data include manufacturer data sheets, press releases, conference papers, journal papers, public filings with government agencies, news articles, presentations, the compendium of databases accessed via NASA’s Small Spacecraft Systems Virtual Institute (S3VI) Information Search, and engagement with companies. Data not appropriate for public dissemination, such as proprietary, export controlled, or otherwise restricted data, are not considered. We encourage the SmallSat community to publish mission outcomes and technology development milestones in publicly available conference papers, press releases, or company websites so they can be reflected in future editions of this report. This report is funded by NASA’s Space Technology Mission Directorate (STMD). It was first commissioned by the Small Spacecraft Technology (SST) program within NASA’s STMD in mid2012 in response to the rapid growth in interest in using small spacecraft for low-Earth orbit, lowcost missions. The report was subsequently updated in 2015, 2018, 2020, 2021, 2022, and 2023 to capture SmallSat technology growth and maturation. In addition to reporting currently available state-of-the-art technologies that have achieved Technology Readiness Level (TRL) 5 or above, a prognosis is provided describing technologies as "on the horizon" if they are being considered for future application.

Sasha V Weston↗

NASA NTRS2026

The Habitable Worlds Observatory Technology Development Plan

The Habitable Worlds Observatory (HWO) is NASA’s next large space telescope, selected by the 2020 Decadal Survey in Astronomy and Astrophysics to search for and characterize habitable exoplanets while enabling a broad range of transformative astrophysics. In August 2024, the HWO Technology Maturation Project Office (TMPO) was formed to begin exploring the HWO science, technology, and mission architectures toward a Mission Concept Review (MCR) at the end of the decade. A primary deliverable of this effort is this technology development plan that identifies critical technologies that enable the mission, defines a process for assessing the readiness of those technologies, and outlines a strategy for developing those technologies to a Technology Readiness Level (TRL) of 5 before the MCR. This document covers technologies organized along three “tracks”: Coronagraph System technologies, Ultra-stable Telescope System technologies, and High-sensitivity Ultraviolet and Visible Instrumentation technologies. Additional emerging and enhancing technologies are also discussed.

technology development↗

DOE OSTI2025

Casing Annulus Monitoring of CO 2 Injection Using Wireless Autonomous Distributed Sensor Networks

Effective and secure carbon subsurface storage, involving the deep underground injection of CO 2 into geological formations where it is permanently trapped, is paramount to mitigating CO 2 emissions (Figure I). Ensuring the integrity of these storage sites and detecting potential leakage through the casing annulus necessitates robust monitoring. This work provides the first integrated demonstration of a wireless casing-annulus monitoring architecture that can operate in highly attenuating cement-brine environments relevant to CO 2 storage. This project focused on developing and validating a novel sensor system for integration with autonomous monitoring near the cement reservoir interface. The goal was a fully integrated Technology Readiness Level (TRL) 4/5 field validation of a distributed wireless intelligent sensor system providing real-time, direct subsurface formation measurements to enhance fluid movement monitoring in the cemented casing annulus. Achieving this objective required the development and integration of 1) wireless autonomous microsensor technology by California Institute of Technology (Caltech); 2) sensor packaging and emplacement technology by Research Triangle Institute (RTI); and 3) smart well completions using wireless active casing collars and NOV pipe by the Sandia National Lab (SNL). The collaboration with the Caltech team in this project aimed to develop millimeter-scale radio frequency identification (RFID) sensors capable of detecting CO 2 , pH, and/or methane levels. These sensors are engineered to be impervious to fluids, allowing them to be mixed with cement and installed within the casing annulus. They operate using RFID protocols at frequencies of 902–928 MHz for both power and communication. A Sandia National Laboratories’ team engaged their expertise in the development of a Smart Collar system designed for the wireless data collection from these RFID sensors embedded in the cement annulus and transmission of this information to the ground surface via IntelliPipe/IntelliServ NOV drill pipe. This is accomplished through inductive coupling at the collar, which facilitates data transfer through each segment of the pipe. Because the system cannot transmit a direct current signal to power the Smart Collar, both power and communication were implemented using alternating current and electromagnetic signals at varying frequencies. Furthermore, the developed microsensor technology had to be demonstrated and validated in comparison with reference transducer measurements in a field test site at The University of Texas at Austin (UT-Austin). Although the full sensor suite did not reach field-deployment readiness, the system-level integration achieved in this project establishes a validated pathway for future incorporation of advanced microsensors.

47 OTHER INSTRUMENTATION↗

NASA NTRS2005

Electric Power System Technology Options for Lunar Surface Missions

In 2004, the President announced a 'Vision for Space Exploration' that is bold and forward-thinking, yet practical and responsible. The vision explores answers to longstanding questions of importance to science and society and will develop revolutionary technologies and capabilities for the future, while maintaining good stewardship of taxpayer dollars. One crucial technology area enabling all space exploration is electric power systems. In this paper, the author evaluates surface power technology options in order to identify leading candidate technologies that will accomplish lunar design reference mission three (LDRM-3). LDRM-3 mission consists of multiple, 90-day missions to the lunar South Pole with 4-person crews starting in the year 2020. Top-level power requirements included a nominal 50 kW continuous habitat power over a 5-year lifetime with back-up or redundant emergency power provisions and a nominal 2-kW, 2-person unpressurized rover. To help direct NASA's technology investment strategy, this lunar surface power technology evaluation assessed many figures of merit including: current technology readiness levels (TRLs), potential to advance to TRL 6 by 2014, effectiveness of the technology to meet the mission requirements in the specified time, mass, stowed volume, deployed area, complexity, required special ground facilities, safety, reliability/redundancy, strength of industrial base, applicability to other LDRM-3 elements, extensibility to Mars missions, costs, and risks. For the 50-kW habitat module, dozens of nuclear, radioisotope and solar power technologies were down-selected to a nuclear fission heat source with Brayton, Stirling or thermoelectric power conversion options. Preferred energy storage technologies included lithium-ion battery and Proton Exchange Membrane (PEM) Regenerative Fuel Cells (RFC). Several AC and DC power management and distribution architectures and component technologies were defined consistent with the preferred habitat power generation technology option and the overall lunar surface mission. For rover power, more than 20 technology options were down-selected to radioisotope Stirling, liquid lithium-ion battery, PEM RFC, or primary fuel cell options. The author discusses various conclusions that can be drawn from the findings of this surface power technologies evaluation.

Kerslake, Thomas W.↗

NASA NTRS2007

Technology Maturation and Flight Validation Experience for NASA's ST8 Mission

Background: a) Introduction to ST8 Project; b) ST8 Project timeline; c) ST8 technology payloads. Technology Readiness Levels (TRLs) as interpreted by NASA's New Millennium Program (NMP). Role of Technology Review Boards (TRBs) in the evaluation of technology maturity for the NMP ST8 Project. Lessons learned from the ST8 TRB experience.

New Millennium Program (NMP)↗

NASA NTRS2003

An Overview Of NASA's Solar Sail Propulsion Project

Research conducted by the In-Space Propulsion (ISP) Technologies Projects is at the forefront of NASA's efforts to mature propulsion technologies that will enable or enhance a variety of space science missions. The ISP Program is developing technologies from a Technology Readiness Level (TRL) of 3 through TRL 6. Activities under the different technology areas are selected through the NASA Research Announcement (NRA) process. The ISP Program goal is to mature a suite of reliable advanced propulsion technologies that will promote more cost efficient missions through the reduction of interplanetary mission trip time, increased scientific payload mass fraction, and allowing for longer on-station operations. These propulsion technologies will also enable missions with previously inaccessible orbits (e.g., non-Keplerian, high solar latitudes). The ISP Program technology suite has been prioritized by an agency wide study. Solar Sail propulsion is one of ISP's three high-priority technology areas. Solar sail propulsion systems will be required to meet the challenge of monitoring and predicting space weather by the Office of Space Science s (OSS) Living with a Star (LWS) program. Near-to-mid-term mission needs include monitoring of solar activity and observations at high solar latitudes. Near-term work funded by the ISP solar sail propulsion project is centered around the quantitative demonstration of scalability of present solar sail subsystem designs and concepts to future mission requirements through ground testing, computer modeling and analytical simulations. This talk will review the solar sail technology roadmap, current funded technology development work, future funding opportunities, and mission applications.

Garbe, Gregory↗

NASA NTRS2007

Cooling Technology for Large Space Telescopes

NASA's New Millennium Program funded an effort to develop a system cooling technology, which is applicable to all future infrared, sub-millimeter and millimeter cryogenic space telescopes. In particular, this technology is necessary for the proposed large space telescope Single Aperture Far-Infrared Telescope (SAFIR) mission. This technology will also enhance the performance and lower the risk and cost for other cryogenic missions. The new paradigm for cooling to low temperatures will involve passive cooling using lightweight deployable membranes that serve both as sunshields and V-groove radiators, in combination with active cooling using mechanical coolers operating down to 4 K. The Cooling Technology for Large Space Telescopes (LST) mission planned to develop and demonstrate a multi-layered sunshield, which is actively cooled by a multi-stage mechanical cryocooler, and further the models and analyses critical to scaling to future missions. The outer four layers of the sunshield cool passively by radiation, while the innermost layer is actively cooled to enable the sunshield to decrease the incident solar irradiance by a factor of more than one million. The cryocooler cools the inner layer of the sunshield to 20 K, and provides cooling to 6 K at a telescope mounting plate. The technology readiness level (TRL) of 7 will be achieved by the active cooling technology following the technology validation flight in Low Earth Orbit. In accordance with the New Millennium charter, tests and modeling are tightly integrated to advance the technology and the flight design for "ST-class" missions. Commercial off-the-shelf engineering analysis products are used to develop validated modeling capabilities to allow the techniques and results from LST to apply to a wide variety of future missions. The LST mission plans to "rewrite the book" on cryo-thermal testing and modeling techniques, and validate modeling techniques to scale to future space telescopes such as SAFIR.

DiPirro, Michael↗

NASA NTRS2015

Propulsion Technology Assessment: Science and Enabling Technologies to Explore the Interstellar Medium

The Advanced Concepts Office at NASA’s George C. Marshall Space Flight Center conducted a study to assess what low-thrust advanced propulsion system candidates, existing and near term, could deliver a small, Voyager-like satellite to our solar system’s heliopause, approximately 100 AU from the sun, within 10 years. The advanced propulsion system trade study consisted of three candidates, including a Magnetically Shielded Miniature Hall thruster, a solar sail and an electric sail. A second analysis was conducted to determine which solid rocket motor kick stage(s) would be required to provide additional thrust at various points in the trajectory, assuming a characteristic energy capability provided by a Space Launch System Block 1B vehicle architecture carrying an 8.4 meter payload fairing. Two trajectory profiles were considered, including an escape trajectory using a Jupiter gravity assist and an escape trajectory first performing a Jupiter gravity assist followed by an Oberth maneuver around the sun and an optional Saturn gravity assist. Results indicated that if the Technology Readiness Level of an electric sail could be increased in time, this technology could not only enable a satellite to reach 100 AU in 10 years but it could potentially do so in even less time.

Hopkins, Randall C.↗