SEARCH · Engineering Papers

Results for “model order reduction”

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.

SourceResearch connectionFrom yearThrough year

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

At least 433 records · Page 24

All sources NASA NTRS DOE OSTI

DOE OSTI2023

Interactive Power to Frequency Dynamics Between Grid-Forming Inverters and Synchronous Generators in Power Electronics-Dominated Power Systems

With increased attention on grid-forming inverters as a power system stabilizing device during high shares of inverter-based resource operations, there is a present need for a transparent and methodical investigation of the inverted and direct power to frequency control capabilities and impacts of these devices on emerging power systems. Here, analysis of the frequency dynamics of the droop-controlled grid-forming inverter and the synchronous generator illuminates the inverted active power-frequency relationship and the frequency response order reduction, forming the basis for novel, nonlinear frequency control approaches. Device-level electromagnetic transient domain simulations corroborate the order-reduction findings, establish that a properly designed dc-side system has a negligible impact on power transfer and will not impede frequency regulation, and confirm the primary frequency response improvement with nonlinear control. Simulations of the 9- and 39-bus test systems validate the order reduction and associated decoupling of the nadir and rate of change of frequency in larger networks. Oscillatory mode analysis confirms the grid-forming benefit of increased damping; decreased damping is observed at shares above 80%, but not at 100%. Finally, simulations on a validated Maui power system model with a 96% of inverter-based resources model yield a trend toward a first-order response.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Temporally-consistent koopman autoencoders for forecasting dynamical systems

Absence of sufficiently high-quality data often poses a key challenge in data-driven modeling of high-dimensional spatio-temporal dynamical systems. Koopman Autoencoders (KAEs) harness the expressivity of deep neural networks (DNNs), the dimension reduction capabilities of autoencoders, and the spectral properties of the Koopman operator to learn a reduced-order feature space with simpler, linear dynamics. However, the effectiveness of KAEs is hindered by limited and noisy training datasets, leading to poor generalizability. To address this, we introduce the Temporally-Consistent Koopman Autoencoder (tcKAE), designed to generate accurate long-term predictions even with limited and noisy training data. This is achieved through a consistency regularization term that enforces prediction coherence across different time steps, thus enhancing the robustness and generalizability of tcKAE over existing models. We provide analytical justification for this approach based on Koopman spectral theory and empirically demonstrate tcKAE’s superior performance over state-of-the-art KAE models across a variety of test cases, including simple pendulum oscillations, kinetic plasma, and fluid flow data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2020

Sulfurized Polyacrylonitrile for High-Performance Lithium–Sulfur Batteries: In-Depth Computational Approach Revealing Multiple Sulfur’s Reduction Pathways and Hidden Li + Storage Mechanisms for Extra Discharge Capacity

Like no other sulfur host material, polyacrylonitrile-derived sulfurized carbon (SPAN) promises improved electrochemical performance for lithium–sulfur batteries, based on its compatibility with carbonate solvents and ability to prevent self-discharge and shuttle effect. However, a complete understanding of the SPAN’s lithiation mechanism is still missing because its structural features vary widely with synthesis conditions, and its electrochemical performance deviates from elemental sulfur. This study continues our research on the elucidation of the SPAN’s structural characteristics and lithiation mechanisms via computational approaches. Here, our models reproduce most experimental data regarding carbon’s graphitization level and conjugated ordering, sulfur–carbon covalent bonding, sulfur loading, and elemental composition. Our simulations emulate the discharge voltage observed in experiments for the first discharge, which reveals that sulfur follows multiple reduction pathways based on its interaction with the carbon backbone. Sulfur reduction takes place above 1.0 V vs Li/Li + mostly in the SPAN-like material, with no long-chain lithium polysulfide formation. Below 1.0 V vs Li/Li + , the backbone’s electrochemical activity occurs via multiple C–Li and N–Li interactions, mostly with edge carbon atoms and pyridinic nitrogen. Moreover, we identify Li + binding sites throughout the graphitized backbone that might lead to prohibited energy costs for Li + deintercalation, which may explain the irreversible capacity loss between the first and second discharges. This work improves understanding of lithiation mechanisms in sulfurized carbon, which is useful for rationally designing SPAN synthesis pathways tailored to increase sulfur loading and enhanced electrochemical performance.

25 ENERGY STORAGE↗

NASA NTRS2008

Assessments of Hollow Cathode Wear in the Xenon Ion Propulsion System (XIPs(c)) by Numerical Analyses and Wear Tests

The standard approach presently followed by NASA to qualify electric propulsion for the required mission throughput has been based largely on life tests, which can be costly and time consuming. Revised electric propulsion lifequalification approaches are being formulated that combine analytical and/or computational methods with (shorter-duration) wear tests. As a model case, a wear test is being performed at JPL to assess the lifetime of the discharge hollow cathode in the Xenon Ion Propulsion System (XIPS(c)), a 25-cm ion engine developed by L-3 Communications Electron Technologies, Inc. for commercial applications. Wear and plasma data accumulated throughout this life-assessment program are being used to validate the existing 2-D hollow cathode code OrCa2D. We find that the OrCa2D steady-state solution predicts very well the time-averaged plasma data and the keeper voltage after 5500 hrs of operation in high-power mode. When the wave motion that occurs naturally in these devices is accounted for, based on an estimate of the maximum wave amplitude, the molybdenum-keeper erosion profile observed in the XIPS(c) discharge cathode is also reproduced within a factor of two of the observation. When the same model is applied to predict the erosion of a tantalum keeper we find that erosion is reduced by more than two orders of magnitude compared to the molybdenum keeper due the significantly lower sputtering yield of tantalum. A tantalum keeper would therefore allow keeper lifetimes that greatly exceed the present requirements for deep-space robotic missions considered by NASA. Moreover, such large reduction of the erosion renders the largest uncertainties in the models, which are associated with the wave amplitude estimates and the electron transport model, negligible.

plasma simulations↗

DOE OSTI2022

Multiple magnetic orders in LaFeAs 1-x P x O uncover universality of iron-pnictide superconductors

The iron-pnictide superconductors have generated tremendous excitement as the competition between magnetism and superconductivity has allowed unique in-roads towards elucidating a microscopic theory of unconventional high-temperature superconductivity. In addition to the stripe spin density wave ($C^a_{2M}$) phase observed in the parent compounds of all iron-pnictide superconductors, two novel magnetic orders have recently been discovered in different parent structures: an out-of-plane collinear double-Q ($C^c_{4M}$) structure in the hole-doped (Ca, Sr, Ba) 1-x (Na) x Fe 2 As 2 and Ba 1-x K x Fe 2 As 2 families, and a spin vortex crystal “hedgehog” ($C^{ab}_{4M}$) structure in the CaKFe 4 As 4 family. Using neutron diffraction, we demonstrate that LaFeAs 1-x P x O contains all three magnetic orders within a single-phase diagram as a function of substitution, all of which compete strongly with superconductivity. Our experimental observations combined with theoretical modeling demonstrate how the reduction in electronic correlations by chemical substitution results in larger Fermi surfaces and the sequential stabilization of multiple magnetic anisotropies. Our work presents a unified narrative for the competing magnetic and superconducting phases observed in various iron-pnictide systems with different crystal structures and chemistry.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗

DOE OSTI2026

Variations in lithium vapor cave performance predictions due to radial transport and recycling assumptions

The lithium vapor cave is a detached divertor design that uses a single private flux region baffle to contain a dense cloud of lithium vapor to dissipate heat flux. Plasma flows are created via fuel gas puffing in order to minimize lithium contamination of the main plasma. Significant modeling using the 2D edge code SOLPS-ITER has already been performed, predicting that sufficient target heat flux reductions (q$^{max}_{Target}$ MW m −2 ) with ( $n$ Li /$n$ e ) LCFS < 0.05 is possible in a case with 90 MW m −2 unmitigated heat flux in NSTX-U. Low heat flux and low upstream concentration was found with a variety of combinations of divertor geometries, target recycling coefficients, upstream plasma parameters, lithium evaporation locations and deuterium fueling locations, with variations in performance found for each design choice. However, the most universal uncertainty of SOLPS-ITER simulations has until now remained unaddressed systematically, namely the cross-field anomalous particle and heat diffusivities. This article aims to bound the uncertainty in lithium concentration prediction as a result of the assumed deuterium cross-field transport and recycling. For the simulations presented here, a factor of 2.1 increase in the upstream lithium density prediction across a factor of four decrease to the assumed deuterium radial particle diffusivity is found. This result is compared across different assumed deuterium recycling coefficients, known to reduce with lithium injection. Upstream lithium density is found to vary by a factor of 2.4 across a feasible range of recycling coefficients at similar $n$$^{OMP,sep}_{e}$.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

NASA NTRS1985

An eigensystem realization algorithm for modal parameter identification and model reduction

A method called the eigensystem realization algorithm is developed for modal parameter identification and model reduction of dynamic systems from test data. A new approach is introduced in conjunction with the singular-value decomposition technique to derive the basic formulation of minimum order realization which is an extended version of the Ho-Kalman algorithm. The basic formulation is then transformed into modal space for modal parameter identification. Two accuracy indicators are developed to quantitatively identify the system and noise modes. For illustration of the algorithm, an example is shown using experimental data from the Galileo spacecraft.

Juang, J.-N.↗

NASA NTRS1992

Application of piezoelectric devices to vibration suppression - From modeling and controller designs to implementation

Embedded piezoelectric devices may be ideally suited for vibration control of space structures, which lack an inertial ground. When subjected to an input voltage, an embedded piezoelectric actuator changes its dimensions, which in turn generates a pair of forces exerted on adjacent structural members. From the direct piezoelectric effect, an embedded piezoelectric transducer generates an electric charge proportional to the structural dynamic response. In this paper, the implementation, testing and modeling of an active truss structure consisting of piezoelectric sensors and actuators are described. Linear quadratic Gaussian (LQG), second-order, and direct rate feedback control schemes are designed to suppress the vibrations of the active structure. Simulation and test results are presented. It is shown that special model reduction considerations are required to achieve good correlation between test and analysis.

Won, Chin C.↗

NASA NTRS1992

Control and stabilization of nonholonomic dynamic systems

The paper establishes a theoretical framework for the control of nonholonomic dynamic systems, i.e., dynamic systems with nonintegrable constraints, with emphasis on control properties for nonholonomic systems that have no counterpart in holonomic systems. A model for nonholonomic dynamic systems is presented in terms of differential-algebraic equations defined on a phase space. A reduction procedure is carried out to obtain reduced-order state equations. Conditions for smooth asymptotic stabilization to an m-dimensional equilibrium manifold are presented. It is also demonstrated that a single equilibrium solution cannot be asymptotically stabilized using continuous state feedback. An approach using geometric phases is developed as a basis for the control of Caplygin systems.

Bloch, Anthony M.↗

DOE OSTI2020

Magnetism and its coexistence with superconductivity in CaK(Fe 0.949 Ni 0.051 ) 4 As 4 : Muon spin rotation/relaxation studies

Here, the magnetic response of Ca K ( Fe 0.949 Ni 0.051 ) 4 As 4 was investigated by means of the muon spin rotation/relaxation. The long-range commensurate magnetic order sets in below the Néel temperature T N = 50.0 ( 5 ) K. The density-functional theory calculations have identified three possible muon stopping sites. The experimental data were found to be consistent with only one type of magnetic structure, namely, the long-range magnetic spin-vortex-crystal order with the hedgehog motif within the a b plane and the antiferromagnetic stacking along the c direction. The value of the ordered magnetic moment at T ≈ 3 K was estimated to be m Fe = 0.38 ( 11 ) μ B ( μ B is the Bohr magneton). A microscopic coexistence of magnetic and superconducting phases accompanied by a reduction of the magnetic order parameter below the superconducting transition temperature T c ≃ 9 K is observed. Comparison with 11, 122, and 1144 families of Fe-based pnictides points to existence of correlation between the reduction of the magnetic order parameter at T → 0 and the ratio of the transition temperatures T c / T N . Such correlations were found to be described by Machida's model for coexistence of itinerant spin-density-wave magnetism and superconductivity [K. Machida, J. Phys. Soc. Jpn. 50 , 2195 (1981) ; S. L. Bud'ko et al. , Phys. Rev. B 98 , 144520 (2018) ].

36 MATERIALS SCIENCE↗

NASA NTRS1988

Control of the induced microgravity environment of the Man Tended Free Flyer (MTFF)

Induced disturbance sources have been identified on board the Man Tended Free Flyer (MTFF). Vibration responses at sensitive payload/spacecraft interfaces have been predicted by the application of an empirically found spacecraft dynamic transfer function. Vibrations from fluid loops (Freon, water) and of reaction wheels are assessed to be the main contributors to the induced microgravity environment. The expected payload acceleration response amplitudes presented here are more than one hundred times higher than the admissible values given by the MTFF system requirement, not considering the structural striction-friction effects which could be avoided by appropriate design. Real responses will be significantly lower because the derivation of excitation and transmission functions are based on worst case assumptions. The results indicate that future activities must be concentrated on equipment design improvement and the implementation of vibration reduction along the disturbance transmission path. The activities must be accompanied by early equipment and assembly development tests and transmissibility measurements with the integrated spacecraft engineering and structural models in order to improve the accuracy of payload response predictions.

Schlund, Juergen↗

NASA NTRS2010

A GPS-Based Pitot-Static Calibration Method Using Global Output-Error Optimization

Pressure-based airspeed and altitude measurements for aircraft typically require calibration of the installed system to account for pressure sensing errors such as those due to local flow field effects. In some cases, calibration is used to meet requirements such as those specified in Federal Aviation Regulation Part 25. Several methods are used for in-flight pitot-static calibration including tower fly-by, pacer aircraft, and trailing cone methods. In the 1990 s, the introduction of satellite-based positioning systems to the civilian market enabled new inflight calibration methods based on accurate ground speed measurements provided by Global Positioning Systems (GPS). Use of GPS for airspeed calibration has many advantages such as accuracy, ease of portability (e.g. hand-held) and the flexibility of operating in airspace without the limitations of test range boundaries or ground telemetry support. The current research was motivated by the need for a rapid and statistically accurate method for in-flight calibration of pitot-static systems for remotely piloted, dynamically-scaled research aircraft. Current calibration methods were deemed not practical for this application because of confined test range size and limited flight time available for each sortie. A method was developed that uses high data rate measurements of static and total pressure, and GPSbased ground speed measurements to compute the pressure errors over a range of airspeed. The novel application of this approach is the use of system identification methods that rapidly compute optimal pressure error models with defined confidence intervals in nearreal time. This method has been demonstrated in flight tests and has shown 2- bounds of approximately 0.2 kts with an order of magnitude reduction in test time over other methods. As part of this experiment, a unique database of wind measurements was acquired concurrently with the flight experiments, for the purpose of experimental validation of the optimization method. This paper describes the GPS-based pitot-static calibration method developed for the AirSTAR research test-bed operated as part of the Integrated Resilient Aircraft Controls (IRAC) project in the NASA Aviation Safety Program (AvSP). A description of the method will be provided and results from recent flight tests will be shown to illustrate the performance and advantages of this approach. Discussion of maneuver requirements and data reduction will be included as well as potential applications.

Foster, John V.↗

NASA NTRS2017

Models of Sector Flows Under Local, Regional and Airport Weather Constraints

Recently, the ATM community has made important progress in collaborative trajectory management through the introduction of a new FAA traffic management initiative called a Collaborative Trajectory Options Program (CTOP). FAA can use CTOPs to manage air traffic under multiple constraints (manifested as flow constrained areas or FCAs) in the system, and it allows flight operators to indicate their preferences for routing and delay options. CTOPs also permits better management of the overall trajectory of flights by considering both routing and departure delay options simultaneously. However, adoption of CTOPs in airspace has been hampered by many factors that include challenges in how to identify constrained areas and how to set rates for the FCAs. Decision support tools providing assistance would be particularly helpful in effective use of CTOPs. Such DSTs tools would need models of demand and capacity in the presence of multiple constraints. This study examines different approaches to using historical data to create and validate models of maximum flows in sectors and other airspace regions in the presence of multiple constraints. A challenge in creating an empirical model of flows under multiple constraints is a lack of sufficient historical data that captures diverse situations involving combinations of multiple constraints especially those with severe weather. The approach taken here to deal with this is two-fold. First, we create a generalized sector model encompassing multiple sectors rather than individual sectors in order to increase the amount of data used for creating the model by an order of magnitude. Secondly, we decompose the problem so that the amount of data needed is reduced. This involves creating a baseline demand model plus a separate weather constrained flow reduction model and then composing these into a single integrated model. A nominal demand model is a flow model (gdem) in the presence of clear local weather. This defines the flow as a function of weather constraints in neighboring regions, airport constraints and weather in locations that can cause re-routes to the location of interest. A weather constrained flow reduction model (fwx-red) is a model of reduction in baseline counts as a function of local weather. Because the number of independent variables associated with each of the two decomposed models is smaller than that with a single model, need for amount of data is reduced. Finally, a composite model that combines these two can be represented as fwx-red (gdem(e), l) where e represents non-local constraints and l represents local weather. The approaches studied to developing these models are divided into three categories: (1) Point estimation models (2) Empirical models (3) Theoretical models. Errors in predictions of these different types of models have been estimated. In situations when there is abundant data, point estimation models tend to be very accurate. In contrast, empirical models do better than theoretical models when there is some data available. The biggest benefit of theoretical models is their general applicability in wider range situations once the degree of accuracy of these has been established.

Kulkarni, Deepak↗

NASA NTRS2017

Models of Sector Aircraft Counts in the Presence of Local, Regional and Airport Constraints

Kulkarni, Deepak↗

NASA NTRS1992

Model reduction for Space Station Freedom

Model reduction is an important practical problem in the control of flexible spacecraft, and a considerable amount of work has been carried out on this topic. Two of the best known methods developed are modal truncation and internal balancing. Modal truncation is simple to implement but can give poor results when the structure possesses clustered natural frequencies, as often occurs in practice. Balancing avoids this problem but has the disadvantages of high computational cost, possible numerical sensitivity problems, and no physical interpretation for the resulting balanced 'modes'. The purpose of this work is to examine the performance of the subsystem balancing technique developed by the investigator when tested on a realistic flexible space structure, in this case a model of the Permanently Manned Configuration (PMC) of Space Station Freedom. This method retains the desirable properties of standard balancing while overcoming the three difficulties listed above. It achieves this by first decomposing the structural model into subsystems of highly correlated modes. Each subsystem is approximately uncorrelated from all others, so balancing them separately and then combining yields comparable results to balancing the entire structure directly. The operation count reduction obtained by the new technique is considerable: a factor of roughly r(exp 2) if the system decomposes into r equal subsystems. Numerical accuracy is also improved significantly, as the matrices being operated on are of reduced dimension, and the modes of the reduced-order model now have a clear physical interpretation; they are, to first order, linear combinations of repeated-frequency modes.

Williams, Trevor↗

NASA NTRS2001

Aerodynamic Performance of Scale-Model Turbofan Outlet Guide Vanes Designed for Low Noise

The design of effective new technologies to reduce aircraft propulsion noise is dependent on an understanding of the noise sources and noise generation mechanisms in the modern turbofan engine. In order to more fully understand the physics of noise in a turbofan engine, a comprehensive aeroacoustic wind tunnel test programs was conducted called the 'Source Diagnostic Test.' The text was cooperative effort between NASA and General Electric Aircraft Engines, as part of the NASA Advanced Subsonic Technology Noise Reduction Program. A 1/5-scale model simulator representing the bypass stage of a current technology high bypass ratio turbofan engine was used in the test. The test article consisted of the bypass fan and outlet guide vanes in a flight-type nacelle. The fan used was a medium pressure ratio design with 22 individual, wide chord blades. Three outlet guide vane design configurations were investigated, representing a 54-vane radial Baseline configuration, a 26-vane radial, wide chord Low Count configuration and a 26-vane, wide chord Low Noise configuration with 30 deg of aft sweep. The test was conducted in the NASA Glenn Research Center 9 by 15-Foot Low Speed Wind Tunnel at velocities simulating the takeoff and approach phases of the aircraft flight envelope. The Source Diagnostic Test had several acoustic and aerodynamic technical objectives: (1) establish the performance of a scale model fan selected to represent the current technology turbofan product; (2) assess the performance of the fan stage with each of the three distinct outlet guide vane designs; (3) determine the effect of the outlet guide vane configuration on the fan baseline performance; and (4) conduct detailed flowfield diagnostic surveys, both acoustic and aerodynamic, to characterize and understand the noise generation mechanisms in a turbofan engine. This paper addresses the fan and stage aerodynamic performance results from the Source Diagnostic Test.

Hughes, Christopher E.↗

DOE OSTI2023

A reduced-order modeling of a tubular solar reactor for long duration thermochemical energy storage

The storage of solar energy in a solid form, referred to as a “solar fuel”, can be achieved through a process known as endothermic solar thermochemistry. This process transforms the absorbed solar energy into a stable and retrievable form that can be stored for extended periods of time. This paper presents a low–order heat transfer model of a counter–current tubular falling bed reactor designed to produce thermally reduced magnesium manganese oxide pellets for long duration thermochemical energy storage. The energy required for the endothermic reduction was supplied by concentrated solar energy or renewable electricity via indirect heating of the gas and solid reactants flowing in a ceramic tube. The counter-current gas flow enhances the mixing of the solid particles with the heat recuperation zone, allowing the gas and particles to enter and exit the tubular reactor close to room temperature. Further, the reactor was vertically oriented and was heated circumferentially by an adjustable level heat flux along a finite segment of its length. The temperature distribution of the reactor in response to transient changes along the tube was modeled by considering conduction, convection, and radiation heat transfer. Governing equations for the heat transfer model were solved by discretizing the reactor tube into a finite number of control volumes and using an energy balance for the heat exchange between the reactor wall, gas, and particles within the control volume. The energy absorbed during this endothermic reaction was modeled numerically by fitting the data of the chemical conversion rate with the corresponding temperature of particles in the heating zone. The numerical model has been experimentally validated using a reactor prototype made of a 121.92 cm alumina tube heated by a 7kW electric tube–furnace. The alumina tube receives magnesium manganese oxide pellets of 3.66±0.516 mm in diameter from the top, and a counter–current gas flow from the bottom. The reactor wall temperature was monitored by six thermocouples installed along the reactor tube length. The experimental procedure was numerically simulated, and the temperature variation along the reactor tube was compared with a matrix of experimental runs for a range of particles mass flowrates (0.75–1.25g/s) and corresponding gas flowrates (36–65 SLPM). The reactor system was heated gradually from room temperature to a steady state temperature of 1673K, and then cooled down to room temperature. The heating and cooling processes were simulated, and the numerical and experimental results were compared throughout processes. The numerical model showed similar trends to the experimental results, with an error of 0.69 to 7.9% for the particle inlet and 0.7 to 7.9% for the gas inlet during steady-state operation. The proposed numerical model can be implemented as a simplified physical model to design a feedback control system to regulate reactor temperature.

14 SOLAR ENERGY↗

NASA NTRS2016

Rotary Balance Wind Tunnel Testing for the FASER Flight Research Aircraft

Flight dynamics research was conducted to collect and analyze rotary balance wind tunnel test data in order to improve the aerodynamic simulation and modeling of a low-cost small unmanned aircraft called FASER (Free-flying Aircraft for Sub-scale Experimental Research). The impetus for using FASER was to provide risk and cost reduction for flight testing of more expensive aircraft and assist in the improvement of wind tunnel and flight test techniques, and control laws. The FASER research aircraft has the benefit of allowing wind tunnel and flight tests to be conducted on the same model, improving correlation between wind tunnel, flight, and simulation data. Prior wind tunnel tests include a static force and moment test, including power effects, and a roll and yaw damping forced oscillation test. Rotary balance testing allows for the calculation of aircraft rotary derivatives and the prediction of steady-state spins. The rotary balance wind tunnel test was conducted in the NASA Langley Research Center (LaRC) 20-Foot Vertical Spin Tunnel (VST). Rotary balance testing includes runs for a set of given angular rotation rates at a range of angles of attack and sideslip angles in order to fully characterize the aircraft rotary dynamics. Tests were performed at angles of attack from 0 to 50 degrees, sideslip angles of -5 to 10 degrees, and non-dimensional spin rates from -0.5 to 0.5. The effects of pro-spin elevator and rudder deflection and pro- and anti-spin elevator, rudder, and aileron deflection were examined. The data are presented to illustrate the functional dependence of the forces and moments on angle of attack, sideslip angle, and angular rate for the rotary contributions to the forces and moments. Further investigation is necessary to fully characterize the control effectors. The data were also used with a steady state spin prediction tool that did not predict an equilibrium spin mode.

Denham, Casey↗