Search NASASearch

SEARCH · Search NASA

Results for “optimal control”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

371 records · Page 19

Effects of Multisensory Virtual Reality Nature on Affect, Presence, and Restorativeness

Virtual reality (VR) can provide access to restorative environments and sensory stimulation for individuals in isolated, confined, and extreme environments. We developed a nature-based VR intervention featuring three scenes (Garden, Forest, Beach) and examined the effects of multisensory augmentation with location-based olfactory, wind, and thermal stimuli (VR+OWT). Over a two-week period, fifty-one participants were assigned to a no-intervention control, standard audiovisual VR, or augmented VR (VR+OWT) condition. Data collection included weekly assessments of affect, stress, and cognitive performance; post-VR measures of affect, presence, and perceived restorativeness; and open-ended feedback. Both VR and VR+OWT groups produced immediate and sustained reductions in negative affect with no sustained systematic benefits on cognitive performance. The addition of olfactory, wind, and thermal stimuli enhanced presence for some scenes; however, feedback indicated that sensory mismatches and stimulus intensity occasionally detracted from the experience and may have contributed to lower coherence ratings in the VR+OWT group. In contrast, the perceived restorativeness of the VR environment was driven primarily by scene content (Garden vs Forest vs Beach) rather than the level of sensory stimulation. These findings support the potential of virtual nature to promote well-being and underscore the importance of coherence across sensory modalities for multisensory augmentation.

Virtual Reality Intervention

Preliminary Dynamic Modeling of the Quarter-Scale Distributed Electric Propulsion Aircraft

This paper describes the early-stage modeling of a quarter-scale distributed electric propulsion aircraft, based on the SUbsonic Single Aft eNgine (SUSAN) Electrofan, a transformative concept aircraft for which a model exists. The full-scale 180 passenger SUSAN concept has a single turbofan engine in the tail that both produces thrust and provides electrical power to 16 electric fans distributed across the wings utilizing a series/parallel hybrid architecture. The quarter-scale version would have an internal combustion piston engine to provide power to 17 electric fans–16 on the wings, one in the tail–in a series hybrid configuration, and no vertical or horizontal stabilizers. It would also have a reduced flight envelope in terms of both altitude and speed. The initial modeling approach is to scale down the original airframe model to capture the dynamic behavior of a much smaller aircraft, albeit with an empennage. The original powertrain model is then replaced with one representing the physical components of that of the quarter-scale vehicle. This powertrain model is suitable for control design and analysis, and the fully integrated, although preliminary, aircraft model allows flight simulator testing and evaluation. Results from simulations are presented.

electrified aircraft propulsion

Preliminary Dynamic Modeling of the Quarter-Scale Distributed Electric Propulsion Aircraft

This presentation describes the early-stage modeling of a quarter-scale distributed electric propulsion aircraft, based on the SUbsonic Single Aft eNgine (SUSAN) Electrofan, a transformative concept aircraft for which a model exists. The full-scale 180 passenger SUSAN concept has a single turbofan engine in the tail that both produces thrust and provides electrical power to 16 electric fans distributed across the wings utilizing a series/parallel hybrid architecture. The quarter-scale version would have an internal combustion piston engine to provide power to 17 electric fans–16 on the wings, one in the tail–in a series hybrid configuration, and no vertical or horizontal stabilizers. It would also have a reduced flight envelope in terms of both altitude and speed. The initial modeling approach is to scale down the original airframe model to capture the dynamic behavior of a much smaller aircraft, albeit with an empennage. The original powertrain model is then replaced with one representing the physical components of that of the quarter-scale vehicle. This powertrain model is suitable for control design and analysis, and the fully integrated, although preliminary, aircraft model allows flight simulator testing and evaluation. Results from simulations are presented.

electrified aircraft propulsion

Preliminary Dynamic Modeling of the Quarter-Scale Distributed Electric Propulsion Aircraft

This paper describes the early-stage modeling of a quarter-scale distributed electric propulsion aircraft, based on the SUbsonic Single Aft eNgine (SUSAN) Electrofan, a transformative concept aircraft for which a model exists. The full-scale 180 passenger SUSAN concept has a single turbofan engine in the tail that both produces thrust and provides electrical power to 16 electric fans distributed across the wings utilizing a series/parallel hybrid architecture. The quarter-scale version would have an internal combustion piston engine to provide power to 17 electric fans–16 on the wings, one in the tail–in a series hybrid configuration, and no vertical or horizontal stabilizers. It would also have a reduced flight envelope in terms of both altitude and speed. The initial modeling approach is to scale down the original airframe model to capture the dynamic behavior of a much smaller aircraft, albeit with an empennage. The original powertrain model is then replaced with one representing the physical components of that of the quarter-scale vehicle. This powertrain model is suitable for control design and analysis, and the fully integrated, although preliminary, aircraft model allows flight simulator testing and evaluation. Results from simulations are presented.

Electrified powertrain

Thermal Neutral Format Based on the Step Technology

The exchange of models is one of the most serious problems currently encountered in the practice of spacecraft thermal analysis. Essentially, the problem originates in the diversity of computing environments that are used across different sites, and the consequent proliferation of native tool formats. Furthermore, increasing pressure to reduce the development's life cycle time has originated a growing interest in the so-called spacecraft concurrent engineering. In this context, the realization of the interdependencies between different disciplines and the proper communication between them become critical issues. The use of a neutral format represents a step forward in addressing these problems. Such a means of communication is adopted by consensus. A neutral format is not directly tied to any specific tool and it is kept under stringent change control. Currently, most of the groups promoting exchange formats are contributing with their experience to STEP, the Standard for Exchange of Product Model Data, which is being developed under the auspices of the International Standards Organization (ISO 10303). This paper presents the different efforts made in Europe to provide the spacecraft thermal analysis community with a Thermal Neutral Format (TNF) based on STEP. Following an introduction with some background information, the paper presents the characteristics of the STEP standard. Later, the first efforts to produce a STEP Spacecraft Thermal Application Protocol are described. Finally, the paper presents the currently harmonized European activities that follow up and extend earlier work on the area.

P Planas Almazan

ISS Radiator Face Sheet Anomaly Investigation and Return to Function

Maintaining sufficient heat rejection on the International Space Station (ISS) is critical to the function of the Low-Earth Orbit station. The External Active Thermal Control System (EATCS) rejects the excess heat generated by the US On-Orbit Segment (USOS) modules. The system uses single-phase liquid ammonia to collect the heat and reject it to six radiators (three on the Starboard side, three on the Port side). Each radiator is made up of eight panels. In September 2008, imagery of the Starboard radiators was conducted and showed one of the panels’ face sheets had peeled up from the internal honeycomb core structure. Out of an abundance of caution, the radiator was isolated from the rest of the EATCS and the ammonia was vented to space. Since the radiator was vented, periodic imagery of all radiator panels was taken to monitor any changes in the face sheet and inspect for other radiator anomalies. In January 2025, after years of trending and inspections, the radiator was reintegrated into the system to increase heat rejection capabilities. This paper will document the multi-year investigation that took place to determine root cause and mitigations implemented to reduce risk to the system. A summary of the data since the investigation will show rationale for reintegrating the radiator even with the damaged panel. The goal of the paper is to document the investigation for historical purposes and provide future programs with findings discovered during the investigation.

Aaron Rodriguez

ISS Radiator Face Sheet Anomaly Investigation and Return to Function

Maintaining sufficient heat rejection on the International Space Station (ISS) is critical to the function of the Low-Earth Orbit station. The External Active Thermal Control System (EATCS) rejects the excess heat generated by the US On-Orbit Segment (USOS) modules. The system uses single-phase liquid ammonia to collect the heat and reject it to six radiators (three on the Starboard side, three on the Port side). Each radiator is made up of eight panels. In September 2008, imagery of the Starboard radiators was conducted and showed one of the panels’ face sheets had peeled up from the internal honeycomb core structure. Out of an abundance of caution, the radiator was isolated from the rest of the EATCS and the ammonia was vented to space. Since the radiator was vented, periodic imagery of all radiator panels was taken to monitor any changes in the face sheet and inspect for other radiator anomalies. In January 2025, after years of trending and inspections, the radiator was reintegrated into the system to increase heat rejection capabilities. This paper will document the multi-year investigation that took place to determine root cause and mitigations implemented to reduce risk to the system. A summary of the data since the investigation will show rationale for reintegrating the radiator even with the damaged panel. The goal of the paper is to document the investigation for historical purposes and provide future programs with findings discovered during the investigation.

Aaron Rodriguez

Design, Development, and Test of the Advanced Apollo Orbital Assembly System

As spaceflight moves toward commercial solutions for Crew Vehicles and Space Stations, opportunity exists to lower costs with novel designs. Probe and cone docking systems provide a lightweight, low cost, and high-performance docking solution. This work revisits the Apollo probe and cone design and modifies it for the requirements of today’s computer-controlled spacecraft. This new system is called the Advanced Apollo Orbital Assembly (APOA) system, and is intended to support satellite, cargo, and space station assembly missions. A simulation of the APOA was programmed, components were sized, and a design was created by scaling the probe to the size of an EELV Secondary Payload Adapter (ESPA) tunnel. Prototype test hardware was 3D printed using Fused Deposition Modeling (FDM) methods with Polylactic Acid (PLA) material. Testing of the APOA-ESPA was conducted at Marshall Space Flight Center’s (MSFC) Flat Floor, and a test-correlated simulation is used to evaluate a Monte-Carlo of Initial Contact Conditions (ICC’s) to establish baseline performance. The successful development, test, and correlation of the APOA-ESPA proves the design validity and increases Technology Readiness Level (TRL) from 2 to 4. This work opens the door to construction of an APOA-ESPA from flight like materials, and to develop a larger scale prototype APOA. When the full scale APOA is incorporated with the Common Berthing Mechanism (CBM), becomes the Hybrid Berthing System (HBS), which allows for berthing without a robotic arm.

Berthing

Flammability Test Method for Materials Intended for Use as Fire Barriers in Crewed Habitats

In some crewed-spacecraft applications, onboard materials are intentionally selected to function as hazard control barriers to prevent powered hardware and/or ignited flammable items from igniting nearby flammable materials by acting as non-breaching, non-flammable containment (e.g., cargo transfer bags, zero gravity stowage racks, and jettison stowage bags on the International Space Station). Historically, flammability self-extinguishment testing of broad acreage or outermost layer materials alone was believed to be sufficient to verify overall flammability compliance. Though required, testing on design features such as threaded seams and zippers was not performed due to the incorrect assumption that flammability performance would not be impacted. However, recent coupon level testing of layups and configurations consisting of multiple materials have revealed that these features may be more susceptible to ignition and fire propagation than the bulk material. Additionally, configurational coupon ignition and propagation testing does not explicitly determine a material’s ability to provide protection to vulnerable flammable hardware. The need to evaluate this gap in assessing material or layup effectiveness as fire barriers between ignition sources and flammable materials led to the development of a new configuration-based fire barrier test. Test setup, relevant configurations, and test validation are discussed. The new barrier test method establishes a configuration for the test apparatus, identifies a conservative ignitor configuration, and defines pass/fail criteria. Test setup, relevant configurations, and test validation are discussed.

Susana Harper

Hubble Space Telescope On-orbit NiH2 Battery Performance

This paper summarizes the Hubble Space Telescope (HST) nickel-hydrogen (NiH2) battery performance from launch to the present time. Over the life of HST vehicle configuration, charge system degradation and failures together with thermal design limitations have had a significant effect on the capacity of the HST batteries. Changes made to the charge system configuration in order to protect against power system failures and to maintain battery thermal stability resulted in undercharging of the batteries. This undercharging resulted in decreased usable battery capacity as well as battery cell voltage/capacity divergence. This cell divergence was made evident during on-orbit battery capacity measurements by a relatively shallow slope of the discharge curve following the discharge knee. Early efforts to improve the battery performance have been successful. On-orbit capacity measurement data indicates increases in the usable battery capacity of all six batteries as well as improvements in the battery cell voltage/capacity divergence. Additional measures have been implemented to improve battery performance, however, failures within the HST Power Control Unit (PCU) have prevented verification of battery status. As this PCU fault prevents the execution of on-orbit capacity testing, the HST Project has based the battery capacity on trends, which utilizes previous on-orbit battery capacity test data, for science mission and servicing mission planning. The Servicing Mission 38 (SM-3B) in March 2002 replaced the faulty PCU. Following the servicing mission, on-orbit capacity test resumed. A summary of battery performance is reviewed since launch in this paper.

Rao, Gopalakrishna M.

Artemis Suit Material Optical Property Testing of Dust Exposed Fabrics

This paper highlights one aspect of NASA’s ongoing technology-infusion effort to design, fabricate, and test a next-generation outer shell fabric for a lunar Extravehicular Activity (EVA) space suit, a critical component of sustained lunar exploration. Managing thermal loads on the Moon is essential for astronaut safety and suit performance. The suit’s exterior fabric directly influences heat gain and loss through its optical properties: low solar absorptivity minimizes sunlight absorption, while high infrared emissivity aids radiative cooling. Lunar regolith complicates this balance. Its fine, abrasive particles possess unique optical behavior that can lower reflectivity and raise emissivity when embedded in or adhered to fabric surfaces, degrading thermal control and increasing the risk of overheating or cooling inefficiency. To quantify these effects, the Artemis Suit Materials (ASM) team measured solar absorptance and infrared emissivity of clean and dust-soiled Ortho Fabric, establishing beginning-of-life (BOL) and end-of-life (EOL) benchmarks. EOL conditions were simulated with a rotary tumbler abrasion process using lunar dust simulant and ceramic media to reproduce cumulative wear expected during surface operations. Tests also included unmodified fabrics and a fabric/film laminate system containing titanium dioxide to evaluate potential improvements in dust resistance and optical performance. Results from these evaluations provide critical insight into how lunar dust alters fabric thermal behavior and inform the design of bespoke suit materials that maintain required optical properties throughout mission life, supporting safe and effective long-duration EVA on the lunar surface.

Textile

Artemis Suit Material Optical Property Testing of Dust Exposed Fabrics

This paper highlights one aspect of NASA’s ongoing technology-infusion effort to design, fabricate, and test a next-generation outer shell fabric for a lunar Extravehicular Activity (EVA) space suit, a critical component of sustained lunar exploration. Managing thermal loads on the Moon is essential for astronaut safety and suit performance. The suit’s exterior fabric directly influences heat gain and loss through its optical properties: low solar absorptivity minimizes sunlight absorption, while high infrared emissivity aids radiative cooling. Lunar regolith complicates this balance. Its fine, abrasive particles possess unique optical behavior that can lower reflectivity and raise emissivity when embedded in or adhered to fabric surfaces, degrading thermal control and increasing the risk of overheating or cooling inefficiency. To quantify these effects, the Artemis Suit Materials (ASM) team measured solar absorptance and infrared emissivity of clean and dust-soiled Ortho Fabric, establishing beginning-of-life (BOL) and end-of-life (EOL) benchmarks. EOL conditions were simulated with a rotary tumbler abrasion process using lunar dust simulant and ceramic media to reproduce cumulative wear expected during surface operations. Tests also included unmodified fabrics and a fabric/film laminate system containing titanium dioxide to evaluate potential improvements in dust resistance and optical performance. Results from these evaluations provide critical insight into how lunar dust alters fabric thermal behavior and inform the design of bespoke suit materials that maintain required optical properties throughout mission life, supporting safe and effective long-duration EVA on the lunar surface.

space

On-Orbit Calibration Assessment of NOAA-21 VIIRS Thermal Emissive Bands and Implications for JPSS-4 VIIRS

The Visible Infrared Imaging Radiometer Suite (VIIRS) instrument onboard the NOAA-21 (N21) satellite has been successfully operating for over three years collecting valuable scientific measurements. A large suite of weather forecasting models and scientific research applications are supported with the VIIRS measurements from N21 combined with those acquired from the VIIRS instrument onboard the S-NPP and NOAA-20 spacecraft. Among the 22 VIIRS spectral bands, there are seven thermal emissive bands (TEB) covering the 3.7 to 12.2 µm spectral range at two different spatial resolutions. The VIIRS TEB detectors are calibrated onboard using a blackbody at a controlled temperature and a space view for background signal measurement. In this paper, we discuss the on-orbit performance of the N21 VIIRS TEB using various parameters such as the detector gain, noise, and offset. This on-orbit assessment provides critical insights into instrument behavior and calibration performance that will inform pre-launch testing and post-launch validation strategies for the upcoming JPSS-4 VIIRS mission scheduled for launch in 2027. The methodologies and lessons learned from characterizing the N21 TEB performance will enable more efficient and comprehensive radiometric assessment of the next VIIRS instrument. Specific focus is placed on identifying performance trends and anomaly signatures observed during the N21 commissioning phase that can enhance the JPSS4 instrument checkout procedures and accelerate the transition to routine on-orbit operations. The established performance baselines and uncertainty estimates will serve as an acceptance criterion for the JPSS-4 commissioning activities, ensuring mission readiness and data continuity for operational users.

Amit Angal

Following the αCen Ab Candidate Using the Roman Coronagraph Instrument

The Roman Space Telescope Coronagraph offers a unique opportunity to observe our nearest solar twin, Alpha Centauri A, and characterize the habitable-zone gas giant candidate, Alpha Cen Ab. The candidate uniquely stands out among all imaged exoplanets to date as the one most similar in temperature, age and location to the planets in our own Solar System. Roman CGI offers the tantalizing opportunity to observe the candidate—determining its radius, temperature, and albedo—and to constrain its orbit. Observing Alpha Cen Ab with Roman would make it the first exoplanet to be imaged in both thermal emission and reflected light and would motivate an exciting search for habitable exomoons with the upcoming ELTs and HWO. In addition, this candidate will inform the planet formation history and current dynamics of the Alpha Centauri AB system, including potentially habitable planets around both stars. In this talk, we describe our plan to observe this target using the Roman CGI, including the timing strategy to minimize contrast and avoid background objects. We also describe the key technical insights about coronagraph performance that we aim to gain, such as measuring companion leakage intensity, evaluating the impact of the large stellar diameter, and assessing CGI performance on very bright targets. In subsequent observations, we aim to demonstrate Multi-Star Wavefront Control (MSWC) on-sky, observing Alpha Cen A using the Wide FoV Shaped Pupil MSWC contributed mode in the Roman CGI. The insights from these technology demonstrations are crucial preparation for the planned HWO mission.

Coronagraph

Mass Economy Evaluation for Integrated ECLSS and Propulsion Architecture

As missions in Low Earth Orbit (LEO) lengthen and extend to deep space, minimizing resupply needs becomes vital for sustaining crewed operations. Traditional life support systems depend on consumables resupplied from Earth, a method that is increasingly impractical for missions beyond LEO, such as lunar outposts or Mars transit. Long-duration missions require more efficient, autonomous systems that can recycle essential resources, particularly water and oxygen, to minimize the frequency and mass of resupply missions. The Environmental Control and Life Support System (ECLSS) is essential to such missions, with the International Space Station (ISS) serving as a testbed for advanced water recovery and partial oxygen recycling via physico-chemical methods. Yet, ECLSS and propulsion subsystems generally operate independently, despite overlapping requirements and potential areas for synergy. For instance, ECLSS byproducts, water, CO₂, and hydrogen, could be repurposed for propulsion, potentially reducing dedicated propellant mass and increasing overall system efficiency. One promising approach is to develop shared-resource architectures that integrate ECLSS with propulsion systems. This study examines the potential of such integration through the Sabatier CO₂ reduction process, focusing on water management as a key factor in system mass trade-offs. The Sabatier reaction produces water and methane from metabolic CO₂ and electrolytic hydrogen, partially closing the life support loop and providing methane, which could serve as a propellant. This integration could minimize waste, reduce resupply requirements, and enhance mission mass efficiency. A dynamic modeling framework will be used to simulate resource flows over long missions, capturing interactions between life support and propulsion. By comparing integrated versus separate system configurations, the study aims to quantify mass benefits and penalties, informing future habitat designs and trade studies for missions prioritizing autonomy and mass efficiency.

ECLSS

Mass Economy Evaluation for Integrated ECLSS and Propulsion Architecture

As missions in low Earth orbit (LEO) lengthen and extend to deep space, minimizing resupply needs becomes vital for sustaining crewed operations. Traditional life support systems depend on consumables resupplied from Earth, a method that is increasingly impractical for missions beyond LEO, such as lunar outposts or Mars transit. Long-duration missions require more efficient, autonomous systems that can recycle essential resources, particularly water and oxygen, to minimize the frequency and mass of resupply missions. The Environmental Control and Life Support System (ECLSS) is essential to such missions, with the International Space Station (ISS) serving as a testbed for advanced water recovery and partial oxygen recycling via physico-chemical methods. Yet, ECLSS and propulsion subsystems generally operate independently, despite overlapping requirements and potential areas for synergy. For instance, ECLSS byproducts, water, CO 2 , and hydrogen, could be repurposed for propulsion, potentially reducing dedicated propellant mass and increasing overall system efficiency. One promising approach is to develop shared-resource architectures that integrate ECLSS with propulsion systems. This study examines the potential of such integration through the Sabatier CO₂ reduction process, focusing on water management as a key factor in system mass trade-offs. The Sabatier reaction produces water and methane from metabolic CO 2 and electrolytic hydrogen, partially closing the life support loop and providing methane, which could serve as a propellant. This integration could minimize waste, reduce resupply requirements, and enhance mission mass efficiency. A dynamic modeling framework will be used to simulate resource flows over long missions, capturing interactions between life support and propulsion. By comparing integrated versus separate system configurations, the study aims to quantify mass benefits and penalties, informing future habitat designs and trade studies for missions prioritizing autonomy and mass efficiency.

ECLSS

Improving Adhesive Bondline Time of Flight Predictions During Autoclave Cure Utilizing Machine Learning

Composite materials are increasingly being used in aerospace applications due to their superior strength-to-weight ratio compared to commonly used metals. A current limitation to widespread adoption is the certification of adhesively bonded joints. One approach to improving adhesive bonding in composites is accurately measuring the thickness of adhesive bondlines in composite laminates. Precise bondline thickness control is essential for aerospace applications where adhesive layer thickness directly affects joint fracture properties and structural performance. This study focused on implementing machine learning techniques to determine the ultrasonic time of flight (directly correlated to thickness) in adhesive bondlines throughout autoclave cure cycles. A high-temperature (use up to 180°C) ultrasonic scanning system was deployed in an autoclave to provide time of flight data through composite panels. Three experiments were conducted on the curing of 305 mm × 305 mm unidirectional composite panels. In the first experiment, a piecewise function was fit for the temperature correction factor to account for changing autoclave temperatures. Due to deficiencies in the first calibration experiment, a second experiment was run, and the results were used to train a machine learning model. The revised experiment, in combination with the machine learning model, significantly increased the accuracy of the bondline time of flight predictions (~14% error reduced to <1%). Data was processed using the Regression Learner Application in MATLAB®, with a Support Vector Machine selected for the model. The result was a machine learning algorithm capable of reliably quantifying ultrasonic time of flight through adhesive bondlines. The third experiment provided independent test data for the machine learning model, demonstrating that the model produces accurate predictions from data beyond its training set.

Machine Learning

Ranger Spacecraft

The thermal-control philosophy of the spacecraft currently under development by the Jet Propulsion Laboratory is design by passive means to maintain all components within the tolerances specified by cognizant engineers. Due to the complexity of the configurations, calculations are) of necessity, fairly generalized and final design is based upon tests in an environmental chamber. The Ranger series spacecraft is designed with a basic structure which is common to all models, with additional hardware to suit the individual mission. This basic structure of Rangers A-1 and A-2 is seen as the hexagonal instrument section, the erectable solar panels, the movable antenna, and the omniantenna. The Ranger A-1 and A-2 configuration is for engineering tests and space-exploration, with the scientific instrumentation isolation requirement dictating the spread-out design. The spacecraft stands 12 feet high, weighs 700 to 800 pounds, and has an internal power of 150 watts. Rangers A-3, A-4, and A-5 are designed to rough land a capsule on the moon. For these, a capsule and retrorocket replace the scientific instruments, occupying the space inside the tower structure. The spacecraft must survive many environments. Chronologically they are: 1) Folded configuration inside an aerodynamic shroud on the pad. 2) Thermal flux from shroud aerodynamically heated during boost phase. 3) Coasting up to 30 minutes attached to Agena stage after booster and shroud are separated. 4) Agena stage burning. 5) Coasting and tumbling after separation from Agena until it passes from earth's shadow. 6) Upon reaching sunlight, panels open and begin sun acquisition. 7) Antenna seeks earth after spacecraft locks onto sun. 8) Space phase- "steady state" with vehicle's vertical axis locked on sun, communicating with earth. The philosophy is to design for the sun-acquired mode, making allowances for the transient conditions.

T. O. Thostesen