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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 1,531 records · Page 85

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NASA NTRS2017

Lessons Learned from OSIRIS-Rex Autonomous Navigation Using Natural Feature Tracking

The Origins, Spectral Interpretation, Resource Identification, Security-Regolith Explorer (Osiris-REx) spacecraft is scheduled to launch in September, 2016 to embark on an asteroid sample return mission. It is expected to rendezvous with the asteroid, Bennu, navigate to the surface, collect a sample (July 20), and return the sample to Earth (September 23). The original mission design called for using one of two Flash Lidar units to provide autonomous navigation to the surface. Following Preliminary design and initial development of the Lidars, reliability issues with the hardware and test program prompted the project to begin development of an alternative navigation technique to be used as a backup to the Lidar. At the critical design review, Natural Feature Tracking (NFT) was added to the mission. NFT is an onboard optical navigation system that compares observed images to a set of asteroid terrain models which are rendered in real-time from a catalog stored in memory on the flight computer. Onboard knowledge of the spacecraft state is then updated by a Kalman filter using the measured residuals between the rendered reference images and the actual observed images. The asteroid terrain models used by NFT are built from a shape model generated from observations collected during earlier phases of the mission and include both terrain shape and albedo information about the asteroid surface. As a result, the success of NFT is highly dependent on selecting a set of topographic features that can be both identified during descent as well as reliably rendered using the shape model data available. During development, the OSIRIS-REx team faced significant challenges in developing a process conducive to robust operation. This was especially true for terrain models to be used as the spacecraft gets close to the asteroid and higher fidelity models are required for reliable image correlation. This paper will present some of the challenges and lessons learned from the development of the NFT system which includes not just the flight hardware and software but the development of the terrain models used to generate the onboard rendered images.

Navigation↗

DOE OSTI2025

Cooperative On-Ramp Merging with Time-Varying Vehicle-to-Vehicle Communication Delay Compensation via a Model-Free Approach

Cooperative merging strategies enabled by vehicle-to-vehicle (V2V) communication have shown promise in addressing congestion, fuel inefficiency, and collision risks. However, their performance can be severely degraded by time-varying and uncertain communication delays-an issue often overlooked in existing research, which primarily focuses on merging sequence determination and trajectory planning. Furthermore, practical considerations such as heterogeneous vehicle dynamics, varying road conditions, and real-time implementation complexities are frequently neglected. This paper presents a model-free, online planning framework for cooperative on-ramp merging of connected and automated vehicles (CAVs), explicitly accounting for time-varying V2V communication delays. Without relying on detailed vehicle dynamics, the proposed method introduces a data-driven delay compensation scheme. A co-simulation platform integrating high-fidelity vehicle dynamics, traffic simulation (SUMO), and V2V communication within MATLAB/Simulink is developed to evaluate the proposed method. Simulation results demonstrate that unaddressed V2V communication delays significantly impair merging performance. In contrast, the proposed framework enhances intervehicle distance tracking and maintains low CO2 emissions and fuel consumption, under communication delay across different communication frequencies. In conclusion, its lightweight design also facilitates real-time implementation, making it well-suited for deployment in practical CAV systems.

Accounting↗

DOE OSTI2026

Holistic Transportation and Energy Modeling

This project advances the development and application of the TEMPO transportation energy systems model to support DOE analysis of evolving mobility futures. Recent work has focused on improving model transparency, performance, and fidelity through a redesigned software architecture and updated technology adoption scenarios aligned with the latest data and assumptions. Ongoing efforts aim to expand TEMPO's ability to assess transportation affordability and consumer decision-making, including vehicle ownership dynamics and distributional impacts across households. These enhancements position TEMPO to better inform policy and R&D decisions by providing more behaviorally realistic and policy-relevant insights into transportation energy use, technology adoption, and system-level outcomes.

29 ENERGY PLANNING, POLICY, AND ECONOMY↗

DOE OSTI2025

Particle collisionality in scaled kinetic plasma simulations

Kinetic plasma processes, such as magnetic reconnection, collisionless shocks, and turbulence, are fundamental to the dynamics of astrophysical and laboratory plasmas. Simulating these processes often requires particle-in-cell (PIC) methods, but the computational cost of fully kinetic simulations can necessitate the use of artificial parameters, such as a reduced speed of light and ion-to-electron mass ratio, to decrease expense. While these approximations can preserve overall dynamics under specific conditions, they introduce nontrivial impacts on particle collisionality that are not yet well understood. In this work, we develop a method to scale particle collisionality in simulations employing an artificial speed of light and/or an artificial ion-to-electron mass ratio. By introducing species-dependent scaling factors, we independently adjust inter- and intra-species collision rates to better replicate the collisional properties of the physical system. Our approach maintains the fidelity of electron and ion transport properties while preserving critical relaxation rates, such as energy exchange timescales, within the limits of weakly collisional plasma theory. Furthermore, we demonstrate the accuracy of this scaling method through benchmarking tests against theoretical relaxation rates and connecting to fluid theory, highlighting its ability to retain key transport properties. Existing collisional PIC implementations can be easily modified to include this scaling, which will enable deeper insights into the behavior of marginally collisional plasmas across various contexts.

Totorica, S. R. [Princeton Univ., NJ (United State↗

DOE OSTI2026

Development of MOSCATO: A CFD-Level Electrochemistry and Corrosion Simulator for Molten Salt Systems

For both coolant and fueled variants of molten salt reactors (MSRs), the corrosion of structural materials is a significant challenge. The corrosion stems from chemical and electrochemical reactions initiated by fissile material, fission products, and impurities in the salt. Lower-fidelity models rely on empirical correlations for mass transfer, simplified lumped temperature profiles, and similar assumptions. They do not capture detailed spatial variations in complex geometries, creating the need for high-fidelity modeling to bridge this gap.As we approach the demonstration and possible deployment of MSRs in this decade, the development of a high-fidelity, high-performance simulator becomes imperative. To simulate the complex electrochemical environment and corrosion within molten salt systems, we have developed the Molten Salt Chemistry And TranspOrt (MOSCATO) code. This endeavor is comprised of three essential components. First, mass transfer equations are coupled with the Navier-Stokes equations in order to account for the transport of species in the salt. Second, the diffusion of alloy constituents, such as Cr, Fe, Ni, etc. is simulated within the structural metals. Third, the alloy and salt domains are coupled to account for the heterogeneous chemical and electrochemical reactions that occur at the salt-alloy interface.MOSCATO manages all three components within the framework of the highly scalable, open-source spectral element method computational fluid dynamics code Nek5000/NekRS. This integration enables MOSCATO to harness the immense computational power of modern high-performance computing resources, ensuring both high fidelity and computational speed.In addition to code development, we have initiated a comprehensive verification and validation campaign, utilizing data from diverse sources. First, MOSCATO's electrochemical solver was verified with reference numerical data. Then validation occurred against experiments: one of a thermal galvanic cell and the other for corrosion in flowing molten salt of FLiNaK (LiF-NaF-KF). This campaign verified and validated MOSCATO as a reliable tool for simulating electrochemical environments and corrosion in molten salt systems.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2023

A Finite-Time Ensemble Method for Mixed Layer Model Comparison

Here, this work evaluates the fidelity of various upper-ocean turbulence parameterizations subject to realistic monsoon forcing and presents a finite-time ensemble vector (EV) method to better manage the design and numerical principles of these parameterizations. The EV method emphasizes the dynamics of a turbulence closure multimodel ensemble and is applied to evaluate 10 different ocean surface boundary layer (OSBL) parameterizations within a single-column (SC) model against two boundary layer large-eddy simulations (LES). Both LES include realistic surface forcing, but one includes wind-driven shear turbulence only, while the other includes additional Stokes forcing through the wave-average equations that generate Langmuir turbulence. The finite-time EV framework focuses on what constitutes the local behavior of the mixed layer dynamical system and isolates the forcing and ocean state conditions where turbulence parameterizations most disagree. Identifying disagreement provides the potential to evaluate SC models comparatively against the LES. Observations collected during the 2018 monsoon onset in the Bay of Bengal provide a case study to evaluate models under realistic and variable forcing conditions. The case study results highlight two regimes where models disagree 1) during wind-driven deepening of the mixed layer and 2) under strong diurnal forcing.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRSDate not supplied

Model-Based Systems Engineering, Real-Time Operations, and Autonomy

Model-Based Systems Engineering has been enabled by the development of the SysML language and software tools to create systems models. Systems models described in SysML incorporate frames (Diagrams) that represent behaviors (activities, sequences, state machines, use cases), requirements, and structure (definitions, internal structure, parametric formulation, and packaging). The SysML models are, in turn, used by applications to do analysis and studies of the designs and operational capabilities. These uses of the model are based on simulations, and do not include hardware. This paper presents a software environment and processes that enables more comprehensive systems models for MBSE, and use of these rich models for real-time operations. The paper describes a software platform that enables creation of comprehensive models, beyond what is now possible with SysML and related software tools, called the NASA Platform for Autonomous Systems (NPAS). The platform encapsulates a paradigm and infrastructure for creating systems models with complexity levels comparable to the ones handled by SysML software tools, but with additional fidelity that includes detailed design diagrams encompassing sensors, components, and design topologies. Furthermore, NPAS enables incorporation of data, information, and knowledge (DIaK) to implement autonomy and Integrated System Health Management (ISHM) and the inherent integration of content encompassing SysML structure and behavior diagrams throughout the NPAS modelAnd lastly, the NPAS models are used in real-time operations, taking advantage of the fidelity and complexity encompassed in the models in order to implement “thinking” ISHM and/or autonomous operations. . Incorporation of SysML model content into an NPAS model is briefly discussed.

MBSE↗

DOE OSTI2026

Impact of Time-Dependent Reactor and Sensor Physics on Core Power Synthesis (Rev.1)

Online synthesis of power distribution is critical in the operation and control of nuclear power reactors to ensure that the core is operating within safety margins and to provide essential knowledge associated with the burnup of the fuel. In light-water reactors, power synthesis is achieved by using some a priori knowledge of the state of the reactor core and updating based on the signals coming from in-core sensors—namely, self-powered neutron detectors (SPNDs). This report examines the effects of fuel burnup and sensor degradation on the ability to accurately synthesize the power distribution in a pressurized water reactor (PWR), considering the typical low-enriched uranium (LEU, 3%-5% enrichment) fuel cycle as well as the higher enrichment LEU+ (5%-8% enrichment) fuel cycle. Several modeling tools were used to simulate power synthesis based on the responses of SPNDs, with emitters made out of Rh or V. A representative PWR LEU core was modeled using the Polaris/Purdue Advanced Reactor Core Simulator (PARCS) approach. The Monte Carlo N-Particle Transport 6 (MCNP6) code was used as well to calculate response functions between different segments of fuel to individual SPNDs; this is a crucial parameter for power synthesis. The Oak Ridge Isotope GENeration (ORIGEN) package in the Standardized Computer Analyses for Licensing Evaluation (SCALE) code was used to model the time-dependent isotopic transmutation in the SPND emitters. All these data were fed into a custom code that enacted the point-based iterative method to simulate power synthesis. Developmental work was also performed on high-fidelity SPND models in the GEometry ANd Tracking 4 (Geant4) code, which enables higher-accuracy modeling of the current responses from SPNDs. In this work, five sets of time-dependent power synthesis test cases were conducted. In these test cases, systematic changes in the input conditions enabled an analysis of the effect of (1) slightly inaccurate a priori power distribution assumptions with respect to fuel burnup, (2) highly inaccurate a priori power distribution assumptions with respect to fuel burnup (such that burnup is not included in the a priori assumed distribution), and (3) differences between Rh and V SPNDs in terms of downstream consequences of the transmutation in the emitters and the extended nature of the LEU+ fuel cycle in comparison with LEU. The authors discovered that one may permissibly have slightly inaccurate a priori assumptions of the fuel burnup (such that the level of burnup may be slightly underapproximated or overapproximated by the accumulated burnup in approximately 9.3 full power days), but to not account for burnup at all in the a priori assumptions leads to severe levels of error, approaching 25% at maximum (for LEU). The authors also discovered that V SPNDs are extraordinarily robust in both the LEU and LEU+ fuel cycles considered in this modeling work, whereas Rh SPNDs undergo significant transmutation that can result in large errors in the synthesized power distribution.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

60 years of science in ICF: from conception to scientific breakeven on the National Ignition Facility

The recent achievements of a burning plasma, fusion ignition, and scientific energy gain with deuterium-tritium (DT) fuel at Lawrence Livermore National Laboratory’s National Ignition Facility (NIF) represents a major milestone in the development of inertial confinement fusion (ICF) and all of fusion research. In these experiments, fuel pressures well in excess of hundreds of GBars were achieved in the compressed fuel, and robust alpha heating of the fuel, far in excess of the energy provided by the implosion, were demonstrated for the first time. These achievements occurred 60 years after the inception of ICF and the first laser demonstration, and were made possible by more than five decades of research at laser facilities around the world. Advances in laser technology both in wavelength and precision, motivated by improved understanding of laser-plasma interaction physics and the demands of targets; improvements in target fabrication inspired by the need to control and minimize hydrodynamic instabilities in the implosion; and multi-dimensional simulations and diagnostics have been critical to this achievement. This paper will summarize the scientific and technical advances, the surprises, and the challenges that had to be overcome to achieve these goals.

fusion↗

DOE OSTI2020

WRF Modelling of Deep Convection and Hail for Wind Power Applications

Deep convection and the related occurrence of hail, intense precipitation and wind gusts represent a hazard to a range of energy infrastructure including wind turbine blades. Wind turbine blade leading edge erosion (LEE) is caused by the impact of falling hydrometeors onto rotating wind turbine blades. It is a major source of wind turbine maintenance costs and energy losses from wind farms. In the United States Southern Great Plains (SGP), where there is widespread wind energy development, deep convection and hail events are common, increasing the potential for precipitation-driven LEE. A 25-day Weather Research and Forecasting (WRF) model simulation conducted at convection-permitting resolution and using a detailed microphysics scheme is carried out for the SGP to evaluate the effectiveness in modelling the wind and precipitation conditions relevant to LEE potential. WRF output for these properties is evaluated using radar observations of precipitation (including hail) and reflectivity, in situ wind speed measurements and wind power generation. This research demonstrates some skill for the primary drivers of LEE. Wind speeds, rainfall rates and precipitation totals show good agreement with observations. Here, the occurrence of precipitation during power producing wind speeds is also shown to exhibit fidelity. Hail events frequently occur during periods when wind turbines are rotating and are especially important to LEE in the SGP. The presence of hail is modelled with a mean proportion correct of 0.77 and an odds ratio 4.55. Further research is needed to demonstrate sufficient model performance to be actionable for the wind energy industry and there is evidence for positive model bias in cloud reflectivity.

17 WIND ENERGY↗

DOE OSTI2025

3D Printing of Highly Porous Polypropylene Separators for Lithium‐Ion Batteries Using Fused Deposition Modeling and Thermally Induced Phase Separation

Appearing as one of the key-components of lithium-ion batteries (LIBs), this work specifically focuses on the additive manufacturing (AM) of custom-shape separators, facilitated by the filament material extrusion process, also called fused deposition modeling (FDM). The development and optimization of composite thermoplastic filament feedstocks combining polypropylene and paraffin wax, followed by the 3D printing of the separator membranes is shown. A post-processing step, based on thermal induced phase separation (TIPS), is introduced to promote porosity formation through removal of the paraffin wax sacrificial phase within the 3D printed items. Separators with different polypropylene/paraffin wax ratios are developed and the impact on printability, mechanical strength, porosity, and electrochemical performances, is thoroughly discussed. X-ray micro-computed tomography is employed to assess the geometric fidelity and to detect printing defects in a complex 3D lattice structure. The performance of the 3D printed porous separators is also compared to a commercial separator. This pioneering research establishes a foundation for the creation of porous separators that can adapt to and conform into 3D printed battery architectures with novel form factors, and also creates opportunities for the use of FDM and TIPS for a wide range of applications that employ porous structures beyond the energy storage field.

3D printing↗

DOE OSTI2026

Investigating property-porosity relationships for micro-architected lattice structures

Micro-architected structures are increasingly valued for their light weight and tunable mechanical properties; this class of material includes sheet structures like the Schöen gyroid and beam lattices like the octet. For design purposes, it is critical to understand how to tune the relative density (RD) to obtain desired mechanical properties. This study investigates the mechanical response of Ti-6Al-4V gyroid structures, spanning a broad range of RDs (0.03–0.90), unit cell sizes (1–4 cm), and sheet thicknesses (0.2–7.8 mm). Results demonstrate that the classical Gibson-Ashby power law scaling between RD and modulus and yield stress does not adequately capture the response over a wide range of RDs, nor does it extrapolate correctly to the fully dense solid. Analytical models, in concert with experimental results and high-fidelity finite element calculations, show that the deviation from Gibson-Ashby reflects a transition from structure-dominated to material-dominated behavior. Distinctions are drawn between scaling relationships and property-porosity models, and an analytical model is proposed to better capture the evolution of mechanical properties with RD. These observations are mirrored in other architected topologies, like the octet, and highlight the importance of understanding the relationship between mechanical properties and geometry for design purposes.

Materials science↗

DOE OSTI2025

SciDAC ISEP: Integrated Simulation of Energetic Particles in Burning Plasmas

The objective of the SciDAC Center for Integrated Simulation of Energetic Particles in Burning Plasmas (ISEP) is to improve physics understanding of energetic particle (EP) confinement and EP interactions with burning thermal plasmas through large-scale simulations. The ISEP center will develop a multiscale and multiphysics ISEP framework for a predictive capability of EP physics and deliver an EP module incorporating both first-principles simulations and high fidelity reduced transport models to the fusion whole device modeling (WDM) project. The ISEP framework will enable us to perform long time, global kinetic simulations of EP physics in burning plasmas, by utilizing the full power of the next generation supercomputers. Our research and development activities will build on fruitful collaborations with computer scientists and applied mathematicians to offer enabling technologies for performance scalability, portability, solvers, coupling for integration with the fusion WDM project, and long-term preservation of data.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2022

Thermal scattering law for structure-dependent-Doppler broadening in FLASSH

Traditional Doppler broadening methods assume that target nuclei velocities follow a Maxwell-Boltzmann distribution which inherently assumes that the atoms are a free gas or that their velocities are independent of each other. This approximation is reasonable at high target temperatures and high neutron energies. However, nuclei are not independent: the lattice temperature and chemical binding will define the atomic motion. The thermal scattering law (i.e., TSL or S(α,β)) is a material property which describes the chemical binding and temperature response in terms of available momentum and energy states. In the thermal energy range, this TSL will define the thermal scattering cross sections. In the resonance region, the TSL offers a first-principles description of the probability distribution function for the velocity of the target nuclei. Using the TSL in Doppler broadening captures the structure of the material consistently from the thermal range into the resonance cross sections. In this work, both traditional free-gas and precise TSL Doppler broadening methods for resonance cross section evaluation have been implemented within the Full Law Analysis Scattering System Hub (FLASSH). This framework provides a generalized formulation for evaluating low-lying resonance data and streamlines nuclear data processing methods. TSL data generated using ab initio lattice dynamics (AILD) can be used to broaden cross section libraries in ENDF format for high-fidelity input into reactor physics calculations. These capabilities are demonstrated for the lowest absorption resonances of {sup 238}U in UO{sub 2}, UC and UN. (authors)

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2025

Partnership Center for High-Fidelity Boundary Plasma Simulation (Final Report)

Within the Partnership Center for High-Fidelity Boundary Plasma Simulation (HBPS), work at UT-Austin was aimed at improved verification, validation, and uncertainty quantification (VVUQ) for edge plasma simulations and on performing gyrokinetics simulations of pedestal instabilities and turbulence in order to expand foundational understanding of pedestal transport. Regarding VVUQ, the accomplishments can be summarized as follows. First, it was shown that the Moment Preserving Constrained Resampling technique, when applied periodically in particle-in-cell simulations in the XGC code, can dramatically improve the accuracy of the simulation at essentially equivalent computational cost. Second, a technique for estimating model correlations, which are required to solve the model selection and sample allocation problem in multifidelity UQ techniques, without sampling the highest fidelity, most computationally expensive model, was developed and demonstrated. Third, previously developed methods for estimating statistical and discretization errors were applied to numerical methods relevant to edge plasma simulations, namely in particle-in-cell-based approaches, and shown to work. Finally, benchmark studies for comparing gyrokinetic codes were developed and performed, leading to reasonable agreement between four commonly used codes. Regarding physics studies, gyrokinetic simulations to investigate microtearing modes in the DIII-D pedestal were performed using the GENE code.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

DOE OSTI2021

Report on High-Fidelity Dynamic Modeling of a Coal-Fired Steam Power Plant

As a result of the growth of renewables including solar and wind energy with fluctuating production, fossil fuel power plants are being required to cycle between high and low power production. This cycling is both at a greater frequency and over a wider range than in the past. In many cases, power plants are not designed for this type of cycling operation but can nonetheless endure these challenging operation requirements under the right conditions. In this project, optimal solution for enhanced flexible operations are being investigated using model based estimation and control techniques. To support the development of model-based estimator and model-based controls at GE Global Research, GE Steam Power configured a dynamic model using a reference steam plant design including the boiler, turbine, and water/steam conditioning systems as well as the controls needed for plant cycling with stability and reliability. The dynamic model was built using the APROS® software from VTT, and then calibrated to multiple load conditions from full load (100%TMCR) to partial loads (75%TMCR, 50%TMCR and 25%TMCR) based on internally developed steady state heat balance models at the unit level. These internal heat balance models are based on first principles and extensive engineering experiences from GE Steam Power as an OEM and a services provider. This topical report presents the structure of the unit level dynamic model, the tuning process, and representative simulation results from typical load cycling simulations using the dynamic model.

01 COAL, LIGNITE, AND PEAT↗

NASA NTRS1998

Development of a Low Cost Data Acquisition System for the Solid Rocket Booster Program

The Space Transportation System's (STS) Solid Rocket Boosters (SRBs) experience a severe environment during their brief flight. During the last few years several SRB's have sustained noticeable structural damage. The environmental characteristics (vibration, structure, and thermal) encountered by the SRB's during ascent, descent and water impact are in most cases unknown. A developmental flight instrumentation (DFI) system collected data from the SRB's first four flights in the early 1980's, and after the first three flights during the shuttle return-to-flight phase after the Challenger accident. However, the DFI data collected are of low fidelity and do not correlate well with the observed structural damage. The DFI system was evaluated for reuse, but the cost to fly it was prohibitive. The STS is presently scheduled to fly until 2030. To support the STS schedule the avionics on SRB's will be upgraded. The environments on the different sections of the SRB will need to be defined to properly qualify the avionics for multiple flights. The DFI data previously gathered does not provide enough information to properly qualify the avionics. Marshall Space Flight Centers (MSFC) SRB Project Office requested the Science and Engineering Directorate to develop a self contained data acquisition system that could collect data from any area of the booster. This paper summarizes the effort to develop, test, qualify and fly an Enhanced Data Acquisition System (EDAS) using state-of-the-art commercial off the shelf (COTS) equipment. The first flight of this system occurred on shuttle mission STS-91 in June 1998.

Crawford, Kevin↗

NASA NTRSDate not supplied

CFD-Based Frequency Domain Method for Dynamic Stability Derivative Estimation with Application to Transonic Truss-Braced Wing

This paper presents a dynamic stability estimation technique obtained from high-fidelity CFD simulations of the Mach 0.8 Transonic Truss-Braced Wing (TTBW). A series of unsteady RANS CFD simulations in FUN3D is performed on the TTBW in pitch and plunge oscillations at various reduced frequencies. The time-domain data are transformed into the frequency-domain data by Fourier series. Transfer functions of the dynamic stability derivatives are then estimated by a frequency-domain regression. The dynamic stability derivatives with respect to the angle of attack are determined by the regression of the unsteady aerodynamic coefficients for the plunge motion. The dynamic stability derivatives with respect to the pitch rate are deter-mined by the regression of the differential unsteady aerodynamic coefficients for the pitch motion upon the removal of the angle of attack contribution by the plunge motion. The steady-state stability derivatives are then compared to the results obtained from a stability analysis code VSPAERO as well as steady-state FUN3D simulations. The comparison of the steady-state stability derivatives shows excellent agreement.

Dynamic Stability Derivatives↗