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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.

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At least 1,225 records · Page 68
All sourcesNASA NTRSDOE OSTI
DOE OSTI2020

Longitudinal coherence and short-term wind speed prediction based on a nacelle-mounted Doppler lidar

The spatial structure of turbulence in atmospheric boundary layer flows is highly relevant to wind energy. In particular, wind turbine control strategies based on inflow preview measurements require knowledge of the longitudinal evolution of turbulent flow as it approaches the rotor. These upstream measurements are usually obtained with nacelle-mounted wind lidars. In contrast to traditional in situ anemometry, lidars collect measurements within a probe volume which varies in size depending on the technology of the commercial system being used. Here, we address two issues related to the use of wind lidar to measure the incoming flow to a wind turbine: (i) whether existing longitudinal coherence models can be used to predict flow at the rotor, based on measurements performed at a distance away from the rotor; and (ii) what effect probe-volume averaging has on the inflow predictions. These two questions are critical to the design and implementation of robust wind turbine control strategies. To address these questions, we perform field measurements and large-eddy simulations to determine which incoming flow structures can be readily predicted with existing coherence models, and which require additional corrections to account for lidar volumetric averaging effects. Results reveal that the wind turbine induction zone has a negligible impact on the longitudinal coherence and first-order turbulence quantities, such as the standard deviation of velocity fluctuations. However, the phase of the signal, from which advection time periods of the turbulent structures are derived, is affected by the rotor blockage effect.

17 WIND ENERGY↗
NASA NTRS1989

Predictive Attitude Maintenance For A Space Station

Paper provides mathematical basis for predictive management of angular momenta of control-moment gyroscopes (CMG's) to control attitude of orbiting space station. Numerical results presented for pitch control of proposed power-tower space station. Based on prior orbit history and mathematical model of density of atmosphere, predictions made of requirements on dumping and storage of angular momentum in relation to current loading state of CMG's and to acceptable attitude tolerances.

Hattis, Philip D.↗
DOE OSTI2025

Cryogenic thermal modeling of microwave high density signaling

Superconducting quantum computers require microwave control lines running from room temperature to the mixing chamber of a dilution refrigerator. Adding more lines without preliminary thermal modeling to make predictions risks overwhelming the cooling power at each thermal stage. In this paper, we investigate the thermal load of SC-086/50-SCN-CN semi-rigid coaxial cable, which is commonly used for the control and readout lines of a superconducting quantum computer, as we increase the number of lines to a quantum processor. We investigate the makeup of the coaxial cables, verify the materials and dimensions, and experimentally measure the total thermal conductivity of a single cable as a function of the temperature from cryogenic to room temperature values. We also measure the cryogenic DC electrical resistance of the inner conductor as a function of temperature, allowing for the calculation of active thermal loads due to Ohmic heating. Fitting this data produces a numerical thermal conductivity function used to calculate the static heat loads due to thermal transfer within the wires resulting from a temperature gradient. The resistivity data is used to calculate active heat loads, and we use these fits in a cryogenic model of a superconducting quantum processor in a typical Bluefors XLD1000-SL dilution refrigerator, investigating how the thermal load increases with processor sizes ranging from 100 to 225 qubits. We conclude that the theoretical upper limit of the described architecture is approximately 200 qubits. However, including an engineering margin in the cooling power and the available space for microwave readout circuitry at the mixing chamber, the practical limit is approximately 140 qubits.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2023

Directed Energy Deposition Process Modeling, Validation, and Process-Informed Optimization

The directed energy deposition (DED) process, one of the most popular additive manufacturing techniques in use today, involves various complex physical mechanisms that are not yet well understood. In this regard, computational tools show promise for elucidating the manufacturing process and enabling nondestructive performance evaluations of manufactured parts. To better control and optimize the DED process?thereby improving the manufactured product? the present work develops and demonstrates a novel artificial intelligence (AI)-based process control and optimization technique. Specifically, a geometry-free thermo-mechanical model with adaptive subdomain construction is developed to accurately capture the material?s thermo-mechanical response under cyclical reheating and high cooling rates [1]. The model is demonstrated and validated with experimental measurements, in light of various geometries and processing parameters. Moreover, based on this thermo-mechanical model, a physics-informed reduced-order model is developed to enable quick predictions of the temperature field at every time step. Furthermore, an AI-based controller is developed that can adapt to the ever-changing system states by automatically adjusting the manufacturing process parameters. This entire work is based on the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE) [2] and its recent integration with Libtorch (the C++ frontend of PyTorch [3]). The combined development of the adaptive material deposition scheme, thermo-mechanical model, associated reduced-order model, and AI-based process controller carries great potential for improving advanced manufacturing processes.

36 MATERIALS SCIENCE↗
NASA NTRS1994

The SILEX experiment system operations

The European Space Agency is going to conduct an inter orbit link experiment which will connect a low Earth orbiting satellite and a Geostationary satellite via optical terminals. This experiment has been called SILEX (Semiconductor Inter satellite Link EXperiment). Two payloads will be built. One called PASTEL (PASsager de TELecommunication) will be embarked on the French Earth observation satellite SPOT4. The future European experimental data relay satellite ARTEMIS (Advanced Relay and TEchnology MISsion) will carry the OPALE terminal (Optical PAyload Experiment). The principal characteristic of the mission is a 50 Megabits flow of data transmitted via the optical satellite link. The relay satellite will route the data via its feeder link thus permitting a real time reception in the European region of images taken by the observation satellite. The PASTEL terminal has been designed to cover up to 9 communication sessions per day with an average of 5. The number of daily contact opportunities with the low earth orbiting satellite will be increased and the duration will be much longer than the traditional passes over a ground station. The terminals have an autonomy of 24 hours with respect to ground control. Each terminal will contain its own orbit model and that of its counter terminal for orbit prediction and for precise computation of pointing direction. Due to the very narrow field of view of the communication laser beam, the orbit propagation calculation needs to be done with a very high accuracy. The European Space Agency is responsible for the operation of both terminals. A PASTEL Mission Control System (PMCS) is being developed to control the PASTEL terminal on board SPOT4. The PMCS will interface with the SPOT4 Control Centre for the execution of the PASTEL operations. The PMCS will also interface with the ARTEMIS Mission Control System for the planning and the coordination of the operation. It is the first time that laser technology will be used to support inter-satellite links in Europe. Due to the complexity and experimental character of this new optical technology, the SILEX experiment control facilities will be designed to allow as much operational flexibility as possible.

Demelenne, B.↗
DOE OSTI2020

Dual frequency comb spectroscopy of solid fuel pyrolysis and combustion: Quantifying the influence of moisture content in Douglas fir

As the fire research community develops multi-scale models to predict the spread of wildland fires, there is a need for well-controlled, small-scale experiments which provide benchmark data and fundamental understanding of the effects of key parameters on the combustion of wildland fuels. Here, we implement a unique suite of non-intrusive, quantitative diagnostics that simultaneously measure mass loss, surface temperature, in situ gas temperature and water vapor concentration, including the first implementation of dual frequency comb spectroscopy for the study of solid fuels. As a demonstration, we examine the effect of fuel moisture content on the burning of Douglas fir wood samples that are ignited under constant radiative heat flux from a cone calorimeter to provide benchmark data for multi-scale models. Peak flame temperatures 3 mm above the sample surface measured with the dual frequency comb laser spectrometer are in excess of 1200 K. The flame temperature decreases by over 150 K as fuel moisture content increases from 0.7% to 40%. This work demonstrates a platform for simultaneous, quantitative measurements of well-controlled small-scale experiments which provide benchmark data for the development of advanced modeling and simulations capable of capturing the complex physics present in wildland fire systems.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1979

Initial comparison of single cylinder Stirling engine computer model predictions with test results

A NASA developed digital computer code for a Stirling engine, modelling the performance of a single cylinder rhombic drive ground performance unit (GPU), is presented and its predictions are compared to test results. The GPU engine incorporates eight regenerator/cooler units and the engine working space is modelled by thirteen control volumes. The model calculates indicated power and efficiency for a given engine speed, mean pressure, heater and expansion space metal temperatures and cooler water inlet temperature and flow rate. Comparison of predicted and observed powers implies that the reference pressure drop calculations underestimate actual pressure drop, possibly due to oil contamination in the regenerator/cooler units, methane contamination in the working gas or the underestimation of mechanical loss. For a working gas of hydrogen, the predicted values of brake power are from 0 to 6% higher than experimental values, and brake efficiency is 6 to 16% higher, while for helium the predicted brake power and efficiency are 2 to 15% higher than the experimental.

Tew, R. C., Jr.↗
DOE OSTI2023

Cost-constrained adaptive simulations of transient spray combustion in a gas turbine combustor

Predictive high-fidelity simulations of turbulent spray combustion must capture the combined effects of complex chemistry, multiphase evaporating flow and spray-flame interactions to achieve physical accuracy. Finite-rate chemistry (FRC) combined with a realistic chemical mechanism is a combustion model well-suited for this purpose, but has a high computational cost due to the large number and stiffness of transported chemical species. In contrast, flamelet-based models achieve lower cost by transporting a small number of quantities of reduced stiffness, but assumptions regarding local flame topology, boundary conditions and inter-phase coupling limit their physical accuracy. Recently, the Pareto-efficient combustion (PEC) framework was developed to dynamically assign combustion models based on local cost and accuracy metrics in gas-phase reacting flows. In this work, we extend this PEC framework to spray combustion through the rigorous analysis of the multiphase coupling terms in the governing equations. The derivation shows that spray evaporation causes errors in the prediction of species mass fractions for flamelet-based models due to the sensitivity of the local thermo-chemical state to changes in composition caused by fuel vaporization across combustion regimes present in practical spray combustion devices. Sub-model assignment is formulated as a multiple-choice knapsack problem, where computational cost is directly controlled through the fraction of the domain assigned to the FRC sub-model. The extended PEC formulation is applied to the simulation of a realistic rich-quench-lean gas turbine combustor at steady-state conditions, as well as transient operation resulting in lean blow-out (LBO). Analysis of transient simulations during LBO demonstrates the extended PEC formulation’s capacity to dynamically adapt to changing conditions within the combustor. Transient combustor dynamics are shown to approach convergence with limited increases in computational cost, while retaining substantial computational cost reduction compared to monolithic FRC simulations. Through PEC simulations with increasing fractions of the domain assigned to FRC, monolithic flamelet simulations are shown to over-predict flame stability during LBO. Finally, the extended PEC formulation is thus shown to overcome deficiencies of monolithic models by controlling modeling error for multiphase combustion modeling.

33 ADVANCED PROPULSION SYSTEMS↗
DOE OSTI2020

An a priori evaluation of a principal component and artificial neural network based combustion model in diesel engine conditions

A principal component analysis (PCA) and artificial neural network (ANN) based chemistry tabulation approach is presented. ANNs are used to map the thermochemical state onto a low-dimensional manifold consisting of five control variables that have been identified using PCA. Three canonical configurations are considered to train the PCA-ANN model: a series of homogeneous reactors, a nonpremixed flamelet, and a two-dimensional lifted flame. The performance of the model in predicting the thermochemical manifold of a spatially-developing turbulent jet flame in diesel engine thermochemical conditions is a priori evaluated using direct numerical simulation (DNS) data. The PCA-ANN approach is compared with a conventional tabulation approach (tabulation using ad hoc defined control variables and linear interpolation). The PCA-ANN model provides higher accuracy and requires several orders of magnitude less memory. Here, these observations indicate that the PCA-ANN model is superior for chemistry tabulation, especially for modelling complex chemistries that present multiple combustion modes as observed in diesel combustion. The performance of the PCA-ANN model is then compared to the optimal estimator, i.e. the conditional mean from the DNS. The results indicate that the PCA-ANN model gives high prediction accuracy, comparable to the optimal estimator, especially for major species and the thermophysical properties. Higher errors are observed for the minor species and reaction rate predictions when compared to the optimal estimator. It is shown that the prediction of minor species and reaction rates can be improved by using training data that exhibits a variation of parameters as observed in the turbulent flame. The output of the ANN is analysed to assess mass conservation. It is observed that the ANN incurs a mean absolute error of 0.05% in mass conservation. Furthermore, it is demonstrated that this error can be reduced by modifying the cost function of the ANN to penalise for deviation from mass conservation.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗
DOE OSTI2021

Identifying Entangled Physics Relationships Through Sparse Matrix Decomposition to Inform Plasma Fusion Design

We report a sustainable burn platform through inertial confinement fusion (ICF) has been an ongoing challenge for over 50 years. Mitigating engineering limitations and improving the current design involves an understanding of the complex coupling of physical processes. While sophisticated simulation codes are used to model ICF implosions, these tools contain necessary numerical approximation but miss physical processes that limit predictive capability. Identification of relationships between controllable design inputs to ICF experiments and measurable outcomes (e.g., neutron yield, neutron velocity, areal density) from performed experiments can help guide the future design of experiments and development of simulation codes, to potentially improve the accuracy of the computational models used to simulate ICF experiments. We use sparse matrix decomposition methods to identify clusters of a few related design variables. Sparse principal component analysis (SPCA) identifies groupings that are related to the physical origin of the variables (laser, hohlraum, and capsule). A variable importance analysis finds that in addition to variables highly correlated with neutron yield, such as picket power and laser energy, variables that represent a dramatic change of the ICF design, such as number of pulse steps, are also very important. The obtained sparse components are then used to train a random forest (RF) regression surrogate for predicting total yield. The RF performance on the training and testing data compares with the performance of the RF trained using all the design variables considered. This work is intended to inform design changes in future ICF experiments by augmenting the expert intuition and simulation results.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗
DOE OSTI2022

A Data-Driven Algorithm for Enabling Delay Tolerance in Resilient Microgrid Controls Using Dynamic Mode Decomposition

The increased implementation of smart grid technologies in the power distribution grid presents unique opportunities that enable resiliency, but also brings challenges motivating needs for novel solutions and mitigation techniques. The bi-directional power and data flow allow for the grid to operate with increased resiliency, which is the ability to avoid discontinuity of service to end-use loads during extreme events. However, in applications where control of the distribution grid or microgrid relies on communication networks, the degradation of communication systems in the form of loss or high latency can cause maloperation and result in loss of end-use loads. Here this paper presents a novel framework to enable delay tolerance of centralized microgrid control schemes to mitigate communication system latency impacts and guarantee successful control action. We demonstrate the delay tolerance on a control scheme that operates a battery energy storage system (BESS) to offset the sudden loss of generation and maintain system frequency. During periods of severely degraded communication system performance, the proposed delay-tolerant algorithm compensates for the latency by utilizing a data-driven model generated at the device level using dynamic mode decomposition (DMD) to determine the performance of the communications. The DMD technique predicts the system’s frequency using device-level terminal measurements and provides updated control signals. The HELICS cosimulation platform evaluates the cyber-physical interaction of the power system model in GridLAB-D, the centralized control agent in Python, and the discrete network model in NS-3. The framework is tested and validated on the IEEE-123 node system modified to represent a networked remote microgrid model, and the results show an improvement in the dynamic performance

24 POWER TRANSMISSION AND DISTRIBUTION↗
DOE OSTI2023

Machine learning surrogate of physics-based building-stock simulator for end-use load forecasting

Building energy models are used to simulate heat and mass transfer and estimate end-use load in buildings. With the proliferation of solar photovoltaics on residential and commercial buildings, increasingly, buildings are expected to provide grid services, for which accurate and computationally efficient building energy simulations and end-use load prediction are imperative. Existing building energy simulation tools, however, have significant computational overhead that make them less practical in real-time deployment for optimization, design, uncertainty quantification and control in building energy management systems. Here this article presents a data-driven machine learning model based on light gradient boosting method (LightGBM) as a surrogate for a physics-based simulator for residential buildings to predict end-use load. The machine learning based surrogate model accounts for time-series related variables, seasonality and trend component of end-use load, and history of end-use load. The accuracy of the surrogate model is assessed on the prediction of the load profiles of 100 different houses in Cook County, Illinois, USA. The LightGBM surrogate model is shown to reduce the root-mean-squared error by 53% relative to a reference decision tree (DT) based model reported previously in the literature. Moreover, the model predicts the load spikes and high-ramp rate events throughout the year which are often the Achilles heel of other models in the literature. The machine learning based surrogate model is demonstrated to be computationally efficient, with a ten-fold reduction in the computational time compared to a physics-based building energy simulation, and suitable for uncertainty analysis and real-time control of building characteristics in response to uncertainty.

32 ENERGY CONSERVATION, CONSUMPTION, AND UTILIZATI↗
DOE OSTI2024

Topographical Controls on Hillslope-Scale Hydrology Drive Shrub Distributions on the Seward Peninsula, Alaska: Modeling Archive

The dataset is a model output used in a study that examined the role topography plays in determining shrub expansion by applying a coupled transect version of a mechanistic ecosystem model (ecosys) in a tundra hillslope site in the Seward Peninsula, Alaska. The study highlights the importance of mechanistically representing hillslope-scale coupled surface and sub-surface hydrology to accurately predict current plant distributions and future trajectories in Arctic ecosystems. The dataset contain ecosys model outputs used in a study: Article Title - Topographical Controls on Hillslope-Scale Hydrology Drive Shrub Distributions on the Seward Peninsula, Alaska. It includes the data files (ten *.csv files) used in creating figures in the publication and three *.pdf files (user guide and two Supplementary Information documents).The Next-Generation Ecosystem Experiments: Arctic (NGEE Arctic), was a research effort to reduce uncertainty in Earth System Models by developing a predictive understanding of carbon-rich Arctic ecosystems and feedbacks to climate. NGEE Arctic was supported by the Department of Energy's Office of Biological and Environmental Research.The NGEE Arctic project had two field research sites: 1) located within the Arctic polygonal tundra coastal region on the Barrow Environmental Observatory (BEO) and the North Slope near Utqiagvik (Barrow), Alaska and 2) multiple areas on the discontinuous permafrost region of the Seward Peninsula north of Nome, Alaska.Through observations, experiments, and synthesis with existing datasets, NGEE Arctic provided an enhanced knowledge base for multi-scale modeling and contributed to improved process representation at global pan-Arctic scales within the Department of Energy's Earth system Model (the Energy Exascale Earth System Model, or E3SM), and specifically within the E3SM Land Model component (ELM).

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2014

Using Historical Data to Automatically Identify Air-Traffic Control Behavior

This project seeks to develop statistical-based machine learning models to characterize the types of errors present when using current systems to predict future aircraft states. These models will be data-driven - based on large quantities of historical data. Once these models are developed, they will be used to infer situations in the historical data where an air-traffic controller intervened on an aircraft's route, even when there is no direct recording of this action.

trajectory generation↗
NASA NTRS1994

Measurement of Effective Canopy Temperature: The Missing Link to Modeling Transpiration in Controlled Environments

The objectives were to apply energy balance principles to plant canopies, and to determine which parameters are essential for predicting plant canopy transpiration (E) in controlled environments. Transpiration was accurately measured in a gas-exchange system. Absorbed radiation (R(sub abs)) by the canopy was measured with a net radiometer and calculated from short and long-wave radiation components. Average canopy foliar temperature T(sub L) can be measured with an infrared radiometer, but since T(sub L) is seldom uniform, a weighed average measurement of T(sub L) must be made. The effective canopy temperature T(sub C) is that temperature that balances the energy flux between absorbed radiation and latent heat L(sub E) and sensible heat (H) fluxes. TC should exactly equal air temperature T(sub A) when L(sub E) equals R(sub abs). When unnecessary thermal radiation from the lighting system is removed by a water filter, the magnitude of L(sub E) from transpiration approaches Rabs and T(sub C) is close to T(sub A). Unlike field models, we included the energy used in photosynthesis and found that up to 10% of Rabs was used in photosynthesis. We calculated aerodynamic conductance for H from measurements of wind speed and canopy height using the wind profile equation. Canopy aerodynamic conductance ranged from.03 to.04 m/s for wind speeds from.6 to 1 m/s; thus a 0.1 C canopy to air temperature difference results in a sensible heat flux of about 4 W/sq m, which is only 1% of R(sub abs). We examined the ability of wide angle infrared transducers to accurately integrate T(sub L) from the top to the bottom of the canopy. We measured evaporation from the hydroponic media to be approximately 1 micro mol/sq m s or 10% of R(sub abs). This result indicates that separating evaporation from transpiration is more important than exact measurement of canopy temperature.

Monje, O. A.↗
NASA NTRS2011

Control System Modeling for the Thirty Meter Telescope Primary Mirror

The Thirty Meter Telescope primary mirror is composed of 492 segments that are controlled to high precision in the presence of wind and vibration disturbances, despite the interaction with structural dynamics. The higher bandwidth and larger number of segments compared with the Keck telescopes requires greater attention to modeling to ensure success. We focus here on the development and validation of a suite of quasi-static and dynamic modeling tools required to support the design process, including robustness verification, performance estimation, and requirements flowdown. Models are used to predict the dynamic response due to wind and vibration disturbances, estimate achievable bandwidth in the presence of control-structure-interaction (CSI) and uncertainty in the interaction matrix, and simulate and analyze control algorithms and strategies, e.g. for control of focus-mode, and sensor calibration. Representative results illustrate TMT performance scaling with parameters, but the emphasis is on the modeling framework itself.

uncetainty↗
DOE OSTI2024

Probabilistic projections of the Amery Ice Shelf catchment, Antarctica, under conditions of high ice-shelf basal melt

Abstract. Antarctica's Lambert Glacier drains about one-sixth of the ice from the East Antarctic Ice Sheet and is considered stable due to the strong buttressing provided by the Amery Ice Shelf. While previous projections of the sea-level contribution from this sector of the ice sheet have predicted significant mass loss only with near-complete removal of the ice shelf, the ocean warming necessary for this was deemed unlikely. Recent climate projections through 2300 indicate that sufficient ocean warming is a distinct possibility after 2100. This work explores the impact of parametric uncertainty on projections of the response of the Lambert–Amery system (hereafter “the Amery sector”) to abrupt ocean warming through Bayesian calibration of a perturbed-parameter ice-sheet model ensemble. We address the computational cost of uncertainty quantification for ice-sheet model projections via statistical emulation, which employs surrogate models for fast and inexpensive parameter space exploration while retaining critical features of the high-fidelity simulations. To this end, we build Gaussian process (GP) emulators from simulations of the Amery sector at a medium resolution (4–20 km mesh) using the Model for Prediction Across Scales (MPAS)-Albany Land Ice (MALI) model. We consider six input parameters that control basal friction, ice stiffness, calving, and ice-shelf basal melting. From these, we generate 200 perturbed input parameter initializations using space filling Sobol sampling. For our end-to-end probabilistic modeling workflow, we first train emulators on the simulation ensemble and then calibrate the input parameters using observations of the mass balance, grounding line movement, and calving front movement with priors assigned via expert knowledge. Next, we use MALI to project a subset of simulations to 2300 using ocean and atmosphere forcings from a climate model for both low- and high-greenhouse-gas-emission scenarios. From these simulation outputs, we build multivariate emulators by combining GP regression with principal component dimension reduction to emulate multivariate sea-level contribution time series data from the MALI simulations. We then use these emulators to propagate uncertainty from model input parameters to predictions of glacier mass loss through 2300, demonstrating that the calibrated posterior distributions have both greater mass loss and reduced variance compared to the uncalibrated prior distributions. Parametric uncertainty is large enough through about 2130 that the two projections under different emission scenarios are indistinguishable from one another. However, after rapid ocean warming in the first half of the 22nd century, the projections become statistically distinct within decades. Overall, this study demonstrates an efficient Bayesian calibration and uncertainty propagation workflow for ice-sheet model projections and identifies the potential for large sea-level rise contributions from the Amery sector of the Antarctic Ice Sheet after 2100 under high-greenhouse-gas-emission scenarios.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS1985

Stability and control of VTOL capable airships in hovering flight

The stability and control characteristics of an airship equipped with lifting rotors to provide a modest VTOL capability are discussed. The rotors are used for control and maneuvering in near-hovering flight. Configurations with two, three, and four lifting rotors are examined and compared with respect to control capabilities and dynamic response characteristics. Linearized models of the dynamics are employed for this study. A new approach to the prediction of rotor derivatives for operation near zero thrust in hover is presented. It is found that all three configurations have similar control and response characteristics. The responses are characterized by long time constants and low levels of angular damping.

Curtiss, H. C., Jr.↗