A Suite of Tools for Predictive Simulation of Plume Surface Interactions
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The robustness of cosmological hydrodynamic simulation predictions to changes in numerics and cooling physics
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Shuiyao Huang↗
Particle Interaction Physics Model Formulation for Plume-Surface Interaction Erosion and Cratering
As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The Predictive Simulation Capability (PSC) Element is focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the predictive simulation capability, the GCD Program also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper will present the status of implementing and maturing particle-particle interaction constituent physics models essential in simulating the landing surface granular material flow under PSI effects. This gas-particle multi-phase interaction modeling of plume impingement flow on the extra-terrestrial soil material is performed with the Gas-Granular Flow Solver (GGFS) addressed in a companion paper. The response of regolith particle flow induced by lander PSI requires accurate representation of the regolith granular material fluidic behavior and gas-granular interactions. The lunar regolith, as the extreme example, is poorly sorted with broad particle size distributions and large fines content. It has significant cohesion, due to interlocking particle shapes for the very jagged particles. The combination of particle shape and size distribution has been identified as major drivers in the complex particle flow response and resulting crater shape characteristics of extraterrestrial granular material. Constituent models for spherical particles can be formulated directly from particle kinetics theory. Complex particle shapes can be modeled by gluing together elemental spherical shapes into composite particles, requiring a Discrete Element Model (DEM) particle kinetics modeling approach to extract data and formulate constituent models. Mixture constituent models for poly-disperse mixtures (i.e, containing distribution of particle sizes) have recently been developed. The required non-spherical particle mixture granular material response closure models are then obtained through small-scale unit physics DEM simulations for the range of particle shapes, mixtures and packing densities. The granular material response closure models are then implemented in the Eulerian granular flow formulation. This DEM-based constituent model extraction process and formulation of poly-disperse particle mixtures has been successfully developed by small business and academic partners in the development of the Gas-Granular Flow Solver (GGFS) simulation program simulation framework. The currently implemented capabilities have reached the capability level of modeling bi-disperse, non-spherical particle mixtures is being continuously extended towards computational modeling of full range irregular particle mixtures. Under the GCD project, this technology is being further developed, transferred to NASA analysts, and matured towards application readiness. The predictive simulation capability team under the GCD project has acquired the modeling tools and processes of the DEM based constituent model formulation from the GGFS development team and is developing the capability to replicate the existing process. This is the first important step towards the ability of the NASA team to independently perform such model development in a production setting. Further efforts are underway to migrate the DEM based model simulation process performed with the academic based tools to more capable Open Source, highly parallelized simulation tools for efficient operation on NASA HPC assets. Evaluation of the currently implemented (such as mono-disperse and bi-disperse spherical and irregular shape particle constituent model applications) and continuously evolving full-range particle physics models in the GGFS tool is performed by the NASA team to advance application readiness of the simulations. Application testing for complex PSI erosions and cratering scenarios such as the Apollo LM is performed for axi-symmetric and full 3D simulations to aid the tool developers in achieving practical application readiness for NASA projects. Important validation and application testing will further be performed against experimental data generated under the GCD PSI project experimental component.
Peter A Liever↗
Gas-Particle Interaction Model Development in Plume Surface Interaction Erosion and Cratering
As part of the Game Changing Development (GCD) Program, funded by NASA’s Space Technology Mission Directorate (STMD), the development of simulation capability for the prediction of extra-terrestrial Plume Surface Interaction (PSI) environments has been undertaken by the Fluid Dynamics Branch at NASA/MSFC. The GCD PSI Project, planned to be completed over a four year period, contains a Predictive Simulation Capability (PSC) Element focused on creating simulation capability for the reliable and accurate prediction of PSI in Martian (~650 Pa) and Lunar (vacuum) ambient environments. In addition to the PSC Element, the GCD Program also contains a companion Ground Testing Element for development of focused datasets for validation of predictive capability as well as a Flight-focused Instrumentation Element. This paper describes the activities and accomplishments of the past year in the gas-particle interaction modeling portion of the GCD PSI project. The objectives of this task are to investigate and construct models of particle drag and gas-particle cloud interactions leading to what is known as particle turbulent kinetic energy (PTKE). While drag on a lone particle suspended in a flow gas of gas is well-known, the drag and drag-induced dynamics of a cloud of particles in a gas flow are not. The PSC element of the PSI project requires models of gas-particle cloud interactions to implement in the Gas Granular Flow Solver (GGFS) in order to arrive at a predictive simulation capability for PSI-induced soil erosion, cratering and ejecta transport. Experiments of dilute mixtures of soil particles in supersonic gas flow are being conducted at Johns Hopkins University in order to provide a dataset describing gas-particle cloud interactions. Augmented by a separate funding source are efforts to perform small-scale particle-resolved direct numerical simulations (PR-DNS) and larger scale Eulerian-Lagrangian simulations. Together, these experiments and simulations are being used to devise models of particle cloud drag and particle cloud drag-induced dynamics. The final product of these efforts will be particle drag models suitable for implementation into the GGFS application and a PTKE model suitable for the same purpose.
Jeff West↗
Simulation and Prediction of Warm Season Drought in North America
This presentation presents our recent work on model simulation and prediction of warm season drought in North America. The emphasis will be on the contribution from the leading modes of subseasonal atmospheric circulation variability, which are often present in the form of stationary Rossby waves. Here we take advantage of the results from observations, reanalyses, and simulations and reforecasts performed using the NASA Goddard Earth Observing System (GEOS-5) atmospheric and coupled General Circulation Model (GCM). Our results show that stationary Rossby waves play a key role in Northern Hemisphere (NH) atmospheric circulation and surface meteorology variability on subseasonal timescales. In particular, such waves have been crucial to the development of recent short-term warm season heat waves and droughts over North America (e.g. the 1988, 1998, and 2012 summer droughts) and northern Eurasia (e.g., the 2003 summer heat wave over Europe and the 2010 summer drought and heat wave over Russia). Through an investigation of the physical processes by which these waves lead to the development of warm season drought in North America, it is further found that these waves can serve as a potential source of drought predictability. In order to properly represent their effect and exploit this source of predictability, a model needs to correctly simulate the Northern Hemisphere (NH) mean jet streams and be able to predict the sources of these waves. Given the NASA GEOS-5 AGCM deficiency in simulating the NH jet streams and tropical convection during boreal summer, an approach has been developed to artificially remove much of model mean biases, which leads to considerable improvement in model simulation and prediction of stationary Rossby waves and drought development in North America. Our study points to the need to identify key model biases that limit model simulation and prediction of regional climate extremes, and diagnose the origin of these biases so as to inform modeling group for model improvement.
Rossby Waves↗
Comparison of simulator fidelity model predictions with in-simulator evaluation data
A full factorial in simulator experiment of a single axis, multiloop, compensatory pitch tracking task is described. The experiment was conducted to provide data to validate extensions to an analytic, closed loop model of a real time digital simulation facility. The results of the experiment encompassing various simulation fidelity factors, such as visual delay, digital integration algorithms, computer iteration rates, control loading bandwidths and proprioceptive cues, and g-seat kinesthetic cues, are compared with predictions obtained from the analytic model incorporating an optimal control model of the human pilot. The in-simulator results demonstrate more sensitivity to the g-seat and to the control loader conditions than were predicted by the model. However, the model predictions are generally upheld, although the predicted magnitudes of the states and of the error terms are sometimes off considerably. Of particular concern is the large sensitivity difference for one control loader condition, as well as the model/in-simulator mismatch in the magnitude of the plant states when the other states match.
Parrish, R. V.↗
The Integrated Medical Model: A Probabilistic Simulation Model Predicting In-Flight Medical Risks
The Integrated Medical Model (IMM) is a probabilistic model that uses simulation to predict mission medical risk. Given a specific mission and crew scenario, medical events are simulated using Monte Carlo methodology to provide estimates of resource utilization, probability of evacuation, probability of loss of crew, and the amount of mission time lost due to illness. Mission and crew scenarios are defined by mission length, extravehicular activity (EVA) schedule, and crew characteristics including: sex, coronary artery calcium score, contacts, dental crowns, history of abdominal surgery, and EVA eligibility. The Integrated Medical Evidence Database (iMED) houses the model inputs for one hundred medical conditions using in-flight, analog, and terrestrial medical data. Inputs include incidence, event durations, resource utilization, and crew functional impairment. Severity of conditions is addressed by defining statistical distributions on the dichotomized best and worst-case scenarios for each condition. The outcome distributions for conditions are bounded by the treatment extremes of the fully treated scenario in which all required resources are available and the untreated scenario in which no required resources are available. Upon occurrence of a simulated medical event, treatment availability is assessed, and outcomes are generated depending on the status of the affected crewmember at the time of onset, including any pre-existing functional impairments or ongoing treatment of concurrent conditions. The main IMM outcomes, including probability of evacuation and loss of crew life, time lost due to medical events, and resource utilization, are useful in informing mission planning decisions. To date, the IMM has been used to assess mission-specific risks with and without certain crewmember characteristics, to determine the impact of eliminating certain resources from the mission medical kit, and to design medical kits that maximally benefit crew health while meeting mass and volume constraints.
Risk Analysis↗
Multi-Model Monte Carlo Estimators for Trajectory Simulation
Predicting landing radius and other quantities of interest (QoI) for entry, descent, andlanding (EDL) applications requires a viable uncertainty propagation method for quantifying the impact of uncertainties in aerodynamics, atmosphere, mass properties, etc. While standard Monte Carlo (MC) simulation is the de facto standard for producing robust and unbiasedstatistical estimators, it is often infeasible for expensive, high-fidelity models. Low-fidelity models are commonly constructed to replace the high-fidelity model in MC simulation for computational speedup, but at the expense of accuracy and unbiasedness. Emerging multi-model MC methods are bridging this gap by combining predictions from two or more modelsof varying fidelity and computational cost for efficient and unbiased uncertainty propagation.This works establishes a proof of concept for using multi-model MC to increase the speed and precision of trajectory simulation for EDL. It is shown that combining a high-fidelity EDL model with low-fidelity models (e.g., data-driven, reduced physics) in this manner has the potential to yield significant efficiency and accuracy gains for certain EDL QoIs versusa standard MC approach. Moreover, the unbiasedness of multi-model MC predictions ishighlighted by showing increased accuracy versus an approach that leverages a low-fidelity model alone.
James E Warner↗
Simulation for Prediction of Entry Article Demise (SPEAD): an Analysis Tool for Spacecraft Safety Analysis and Ascent/Reentry Risk Assessment
For the purpose of performing safety analysis and risk assessment for a probable offnominal suborbital/orbital atmospheric reentry resulting in vehicle breakup, a synthesis of trajectory propagation coupled with thermal analysis and the evaluation of node failure is required to predict the sequence of events, the timeline, and the progressive demise of spacecraft components. To provide this capability, the Simulation for Prediction of Entry Article Demise (SPEAD) analysis tool was developed. This report discusses the capabilities, modeling, and validation of the SPEAD analysis tool. SPEAD is applicable for Earth or Mars, with the option for 3 or 6 degrees-of-freedom (DOF) trajectory propagation. The atmosphere and aerodynamics data are supplied in tables, for linear interpolation of up to 4 independent variables. The gravitation model can include up to 20 zonal harmonic coefficients. The modeling of a single motor is available and can be adapted to multiple motors. For thermal analysis, the aerodynamic radiative and free-molecular/continuum convective heating, black-body radiative cooling, conductive heat transfer between adjacent nodes, and node ablation are modeled. In a 6- DOF simulation, the local convective heating on a node is a function of Mach, angle-ofattack, and sideslip angle, and is dependent on 1) the location of the node in the spacecraft and its orientation to the flow modeled by an exposure factor, and 2) the geometries of the spacecraft and the node modeled by a heating factor and convective area. Node failure is evaluated using criteria based on melting temperature, reference heat load, g-load, or a combination of the above. The failure of a liquid propellant tank is evaluated based on burnout flux from nucleate boiling or excess internal pressure. Following a component failure, updates are made as needed to the spacecraft mass and aerodynamic properties, nodal exposure and heating factors, and nodal convective and conductive areas. This allows the trajectory to be propagated seamlessly in a single run, inclusive of the trajectories of components that have separated from the spacecraft. The node ablation simulates the decreasing mass and convective/reference areas, and variable heating factor. A built-in database provides the thermo-mechanical properties of For the purpose of performing safety analysis and risk assessment for a probable offnominal suborbital/orbital atmospheric reentry resulting in vehicle breakup, a synthesis of trajectory propagation coupled with thermal analysis and the evaluation of node failure is required to predict the sequence of events, the timeline, and the progressive demise of spacecraft components. To provide this capability, the Simulation for Prediction of Entry Article Demise (SPEAD) analysis tool was developed. This report discusses the capabilities, modeling, and validation of the SPEAD analysis tool. SPEAD is applicable for Earth or Mars, with the option for 3 or 6 degrees-of-freedom (DOF) trajectory propagation. The atmosphere and aerodynamics data are supplied in tables, for linear interpolation of up to 4 independent variables. The gravitation model can include up to 20 zonal harmonic coefficients. The modeling of a single motor is available and can be adapted to multiple motors. For thermal analysis, the aerodynamic radiative and free-molecular/continuum convective heating, black-body radiative cooling, conductive heat transfer between adjacent nodes, and node ablation are modeled. In a 6- DOF simulation, the local convective heating on a node is a function of Mach, angle-ofattack, and sideslip angle, and is dependent on 1) the location of the node in the spacecraft and its orientation to the flow modeled by an exposure factor, and 2) the geometries of the spacecraft and the node modeled by a heating factor and convective area. Node failure is evaluated using criteria based on melting temperature, reference heat load, g-load, or a combination of the above. The failure of a liquid propellant tank is evaluated based on burnout flux from nucleate boiling or excess internal pressure. Following a component failure, updates are made as needed to the spacecraft mass and aerodynamic properties, nodal exposure and heating factors, and nodal convective and conductive areas. This allows the trajectory to be propagated seamlessly in a single run, inclusive of the trajectories of components that have separated from the spacecraft. The node ablation simulates the decreasing mass and convective/reference areas, and variable heating factor. A built-in database provides the thermo-mechanical properties of
Ling, Lisa↗
Environmental Factors Affecting Asthma and Allergies: Predicting and Simulating Downwind Exposure to Airborne Pollen
This slide presentation reviews the environmental factors that affect asthma and allergies and work to predict and simulate the downwind exposure to airborne pollen. Using a modification of Dust REgional Atmosphere Model (DREAM) that incorporates phenology (i.e. PREAM) the aim was to predict concentrations of pollen in time and space. The strategy for using the model to simulate downwind pollen dispersal, and evaluate the results. Using MODerate-resolution Imaging Spectroradiometer (MODIS), to get seasonal sampling of Juniper, the pollen chosen for the study, land cover on a near daily basis. The results of the model are reviewed.
Luvall, Jeffrey↗
High Energy Density Physics of Inertial Confinement Fusion Ablator Materials
The historic December 5, 2022 experiment at Lawrence Livermore National Lab’s (LLNL) National Ignition Facility (NIF) reached fusion energy ignition for the first time. This is the most important scientific breakthrough of the 21st century paves the way to future clean inertial fusion energy (IFE). The diamond (high density carbon (HDC)) ablator material used in this experiment displays detrimental effects due to the development of hydrodynamic instabilities at the diamond/fuel interface under shock compression. New alternatives to diamond ablators are required to step up the energy yield in ICF experiments. The unique combination of mechanical strength (approaching that of diamond), the ability to accommodate high-Z dopants (in contrast to diamond), and the tunability of the properties (through synthesis material with varying sp 3 content) make amorphous carbon (a-C) a promising material for next-generation IFE ablative capsules. However, despite its critical importance to the IFE program, the behavior of a-C carbon at extreme temperatures and pressures remains largely unexplored. The primary goals of this project were to perform groundbreaking dynamic compression experiments and predictive simulations to uncover the fundamental high-energy-density physics of amorphous carbon. Our goals were (1) to uncover the metastability range of amorphous carbon and probe phase transitions to diamond or metastable supercooled liquid carbon; (2) to acquire high-quality equation of state (EOS) data and develop an experimentally validated EOS from machine-learning MD simulations of the complex states of carbon; and (3) to uncover the complex behavior of carbon liquid in both thermodynamically stable and metastable supercooled states by accessing large areas of carbon phase diagram with amorphous samples with variable sp 3 content. Our proposed experimental program included measurements of equation of state and diffraction measurements using the Omega EP laser at the Laboratory of Laser Energetics at the University of Rochester. The theoretical/simulation program involved the development of machine-learning models of the complex response of amorphous carbon under dynamic compression by performing molecular dynamics simulations at experimental time and length scales using leadership class DOE supercomputers. Simulations guided experiments to observe predicted phenomena and acquire critical experimental data in specific pressure-temperature domains to validate theoretical models. This research delivered fundamental properties of novel amorphous carbon IFE ablator material, including phase diagram and EOS. These results will aid in IFE target design and implosion experiments. A unique combination of predictive simulations and dynamic and static experiments provided a highly inspirational intellectual environment for graduate students and postdocs involved in this project.
70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
Chapter 6: Evaluation of Cardiothermal Model Prediction of Simulated Lunar Extravehicular Activity
Fewer than 20 extravehicular activities were completed during the Apollo program. The lunar environment has consistent unknowns to address particularly that of suited performance in partial gravity. The moon has altered gravity that is 1/6th that of Earth’s. This study is focused to investigate validation of the regression techniques identified in subsequent chapters and look to improve predictive outcomes during simulated lunar EVA tasks. Heart rate predictions of metabolic energy expenditure are investigated to predict workload throughout simulated lunar EVA conducted in the active response gravity offload system (ARGOS) with in the NASA Mark III space suit. Heart rate variability metrics are utilized to identify periods of high workload. Continually, the lunar offload capacity is further characterized to aid in improving the cardiothermal prediction models including predictions of core temperature, skin temperature and heat storage using heart rate, metabolic rates and suit thermal data during the simulated EVA. The outcome of this model provides an application for future use in contingency predictions of energy expenditure during Lunar EVAs and provide a suite of instrumentation to predict workload during training scenarios.
Simulated EVA↗
GLAS experiments on the impact of FGGE satellite data on numerical weather prediction
Simulation studies and pre-FGGE data impact studies were briefly reviewed. Impact of Goddard Laboratory for Atmospheric Science temperature soundings and cloud tracked winds was also examined.
Kalnay, E.↗
Simulation for Prediction of Entry Article Demise (SPEAD): An Analysis Tool for Spacecraft Safety Analysis and Ascent/Reentry Risk Assessment
For the purpose of performing safety analysis and risk assessment for a potential off-nominal atmospheric reentry resulting in vehicle breakup, a synthesis of trajectory propagation coupled with thermal analysis and the evaluation of node failure is required to predict the sequence of events, the timeline, and the progressive demise of spacecraft components. To provide this capability, the Simulation for Prediction of Entry Article Demise (SPEAD) analysis tool was developed. The software and methodology have been validated against actual flights, telemetry data, and validated software, and safety/risk analyses were performed for various programs using SPEAD. This report discusses the capabilities, modeling, validation, and application of the SPEAD analysis tool.
Ling, Lisa↗
In-Flight Guidance, Navigation, and Control Performance Results for the GOES-16 Spacecraft
The Geostationary Operational Environmental Satellite-R Series (GOES-R), which launched in November 2016, is the first of the next generation geostationary weather satellites. GOES-R provides 4 times the resolution, 5 times the observation rate, and 3 times the number of spectral bands for Earth observations compared with its predecessor spacecraft. Additionally, Earth relative and Sun-relative pointing and pointing stability requirements are maintained throughout reaction wheel desaturation events and station keeping activities, allowing GOES-R to provide continuous Earth and sun observations. This paper reviews the pointing control, pointing stability, attitude knowledge, and orbit knowledge requirements necessary to realize the ambitious Image Navigation and Registration (INR) objectives of GOES-R. This paper presents a comparison between low-frequency on-orbit pointing results and simulation predictions for both the Earth Pointed Platform (EPP) and Sun Pointed Platform (SPP). Results indicate excellent agreement between simulation predictions and observed on-orbit performance, and compliance with pointing performance requirements. The EPP instrument suite includes 6 seismic accelerometers sampled at 2 KHz, allowing in-flight verification of jitter responses and comparison back to simulation predictions. This paper presents flight results of acceleration, shock response spectrum (SRS), and instrument line of sight responses for various operational scenarios and instrument observation modes. The results demonstrate the effectiveness of the dual-isolation approach employed on GOES-R. The spacecraft provides attitude and rate data to the primary Earth-observing instrument at 100 Hz, which are used to adjust instrument scanning. The data must meet accuracy and latency numbers defined by the Integrated Rate Error (IRE) requirements. This paper discusses the on-orbit IRE results, showing compliance to these requirements with margin. During the spacecraft checkout period, IRE disturbances were observed and subsequently attributed to thermal control of the Inertial Measurement Unit (IMU) mounting interface. Adjustments of IMU thermal control and the resulting improvements in IRE are presented. Orbit knowledge represents the final element of INR performance. Extremely accurate orbital position is achieved by GPS navigation at Geosynchronous Earth Orbit (GEO). On-orbit performance results are shown demonstrating compliance with the stringent orbit position accuracy requirements of GOES-R, including during station keeping activities and momentum desaturation events. As we show in this paper, the on-orbit performance of the GNC design provides the necessary capabilities to achieve GOES-R mission objectives.
Chapel, Jim↗
A Cellular Automaton Simulation for Predicting Phase Evolution in Solid-State Reactions
New computational tools for solid-state synthesis recipe design are needed in order to accelerate the experimental realization of novel functional materials proposed by high-throughput materials discovery workflows. This work contributes a cellular automaton simulation framework for predicting the time-dependent evolution of intermediate and product phases during solid-state reactions as a function of precursor choice and amount, reaction atmosphere, and heating profile. The simulation captures the effects of reactant particle spatial distribution, particle melting, and reaction atmosphere. Reaction rates based on rudimentary kinetics are estimated using density functional theory data from the Materials Project and machine learning estimators for the melting point and the vibrational entropy component of the Gibbs free energy. The resulting simulation framework allows for the prediction of the likely outcome of a reaction recipe before any experiments are performed. We analyze five experimental solid-state recipes for BaTiO 3 , CaZrN 2 , and YMnO 3 found in the literature to illustrate the performance of the model in capturing reaction selectivity and reaction pathways as a function of temperature and precursor choice. This simulation framework offers an easier way to optimize existing recipes, aid in the identification of intermediates, and design effective recipes for yet unrealized inorganic solids in silico .
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
Trajectory optimization for an asymmetric launch vehicle
A numerical optimization technique is used to fully automate the trajectory design process for an symmetric configuration of the proposed Advanced Launch System (ALS). The objective of the ALS trajectory design process is the maximization of the vehicle mass when it reaches the desired orbit. The trajectories used were based on a simple shape that could be described by a small set of parameters. The use of a simple trajectory model can significantly reduce the computation time required for trajectory optimization. A predictive simulation was developed to determine the on-orbit mass given an initial vehicle state, wind information, and a set of trajectory parameters. This simulation utilizes an idealized control system to speed computation by increasing the integration time step. The conjugate gradient method is used for the numerical optimization of on-orbit mass. The method requires only the evaluation of the on-orbit mass function using the predictive simulation, and the gradient of the on-orbit mass function with respect to the trajectory parameters. The gradient is approximated with finite differencing. Prelaunch trajectory designs were carried out using the optimization procedure. The predictive simulation is used in flight to redesign the trajectory to account for trajectory deviations produced by off-nominal conditions, e.g., stronger than expected head winds.
Sullivan, Jeanne Marie↗
TASKILLAN - A simulation to predict the validity of multiple resource models of aviation workload
The extent to which flight simulation models of increasing complexity are successful in predicting pilot performance was investigated using four models of increasing sophistication addressed by the TASKILLAN (for task skill analysis) computer-generated helicopter simulation. At the simplest level of complexity was the total task model (Model T), followed by the demand model (Model D), the undifferentiated capacity model (Model U), and, ultimately, by the multiple resources model (Model M), which is at the highest level of sophistication addressed by the TASKILLAN project. It was found that the correlations between variables were higher with the two more sophisticated models (U and M), which impose a penalty for increased difficulty in time-sharing. The performance prediction was best with the Model U, while the best predictors of subjective measures were models D and M.
Larish, Inge A.↗