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DOE OSTI2025

Estimating Soil Thermal Inertia Profiles From the Passive Equilibration of a Temperature Probe

Knowledge of the distribution of soil thermal properties is important for understanding subsurface hydrological and biogeochemical processes. This study describes and evaluates quick thermal profiling (QTP), a new measurement technique aimed at providing rapid, depth-resolved measurements of soil thermal inertia at numerous locations across the landscape. A cylindrical probe with temperature sensors at multiple depths is quickly inserted into the ground, and soil thermal inertia is estimated from how quickly the probe temperature equilibrates with the soil. To this end, a finite volume heat transfer model is used to generate temperature equilibration time series across combinations of controlling factors, and a gridded search inversion approach is applied to infer soil thermal inertia. Field tests in the Arctic indicate that QTP measurements have a minimum uncertainty of 0.14 J m −2 K −1 s −1/2 and covary with dual-probe heat pulse thermal analyzer measurements (concordance correlation coefficient = 0.56) with a root-mean-square error of 0.40 J m −2 K −1 s −1/2 . Besides demonstrating the value of QTP for estimating thermal inertia, this study identifies various sources of measurement uncertainty, particularly probe-soil contact resistance and frictional heating. Further, analysis of soil samples indicates that thermal inertia can be used to estimate thermal conductivity and dry bulk density in the studied area, although such inferences are highly site-specific. Overall, the QTP method holds promise to generate thermal inertia data products and to complement other characterization approaches for advancing understanding of soil properties across far more locations than is currently possible.

Lamb, J. R. [Lawrence Berkeley National Laboratory↗

DOE OSTI2025

Optimizing Grid Regulation With Gravity Storage Systems: A Comparative Analysis With Different Motor Inertias

The integration of renewable energy sources into power grids necessitates solutions for grid support and stability during fluctuations in electricity generation and demand. Gravity energy storage systems (GESS) are emerging as a promising technology for managing the balance between energy supply and demand. However, their capacity to optimize energy flow and offer voltage and frequency regulation amid imbalances in generation and demand is less reported. This paper investigates the control of GESS for optimizing energy flow during voltage and frequency regulation. The study evaluates the regulation capabilities of GESS with different motor inertias during a Texas grid event: one with a high-speed, low-inertia motor and another with a low-speed, high-inertia motor. Results indicate that both GESS scenarios provide fast frequency response by converting potential energy into kinetic energy and vice versa, with a response time of 1.5 s from the frequency variation. This aligns with grid requirements for primary frequency response from traditional synchronous generators and motors with large inertia. Furthermore, a GESS based on a high-inertia motor may be able to operate over a broader range of frequency variations, whereas a low-inertia system may be limited by thermal constraints of the motor.

frequency regulation↗

NASA NTRS1995

Atmospheric effects on the mapping of Martian thermal inertia and thermally derived albedo

We examine the effects of a dusty CO2 atmosphere on the thermal inertia and thermally derived albedo of Mars and we present a new map of thermal inertias. This new map was produced using a coupled surface atmosphere (CSA) model, dust opacities from Viking infrared thermal mapper (IRTM) data, and CO2 columns based on topography. The CSA model thermal inertias are smaller than the 2% model thermal inertias, with the difference largest at large thermal inertia. Although the difference between the thermal inertias obtained with the two models is moderate for much of the region studied, it is largest in regions of either high dust opacity or of topographic lows, including the Viking Lander 1 site and some geologically interesting regions. The CSA model thermally derived albedos do not acurately predict the IRTM measured albedos and are very similar to the thermally derived albedos obtained with models making the 2% assumption.

Hayashi, Joan N.↗

NASA NTRS1995

Atmospheric effects on the mapping of Martian thermal inertia and thermally derived albedo

We examine the effects of a dusty C02 atmosphere on the thermal inertia and thermally derived albedo of Mars and we present a new map of thermal inertias. This new map was produced using a coupled surface atmosphere (CSA) model, dust opacities from Viking infrared thermal mapper (IRTM) data, and C02 columns based on topography. The CSA model thermal inertias are smaller than the 2% model thermal inertias, with the difference largest at large thermal inertia. Although the difference between the thermal inertias obtained with the two models is moderate for much of the region studied, it is largest in regions of either high dust opacity or of topographic lows, including the Viking Lander 1 site and some geologically interesting regions. The CSA model thermally derived albedos do not accurately predict the IRTM measured albedos and are very similar to the thermally derived albedos obtained with models making the 2% assumption.

Hayashi, Joan N.↗

NASA NTRS1999

Time course of sleep inertia dissipation in human performance and alertness

Alertness and performance on a wide variety of tasks are impaired immediately upon waking from sleep due to sleep inertia, which has been found to dissipate in an asymptotic manner following waketime. It has been suggested that behavioural or environmental factors, as well as sleep stage at awakening, may affect the severity of sleep inertia. In order to determine the time course of sleep inertia dissipation under normal entrained conditions, subjective alertness and cognitive throughput were measured during the first 4 h after habitual waketime from a full 8-h sleep episode on 3 consecutive days. We investigated whether this time course was affected by either sleep stage at awakening or behavioural/environmental factors. Sleep inertia dissipated in an asymptotic manner and took 2-4 h to near the asymptote. Saturating exponential functions fitted the sleep inertia data well, with time constants of 0.67 h for subjective alertness and 1.17 h for cognitive performance. Most awakenings occurred out of stage rapid eye movement (REM), 2 or 1 sleep, and no effect of sleep stage at awakening on either the severity of sleep inertia or the time course of its dissipation could be detected. Subjective alertness and cognitive throughput were significantly impaired upon awakening regardless of whether subjects got out of bed, ate breakfast, showered and were exposed to ordinary indoor room light (approximately 150 lux) or whether subjects participated in a constant routine (CR) protocol in which they remained in bed, ate small hourly snacks and were exposed to very dim light (10-15 lux). These findings allow for the refinement of models of alertness and performance, and have important implications for the scheduling of work immediately upon awakening in many occupational settings.

Non-NASA Center↗

DOE OSTI2024

Optimizing Grid Regulation With Gravity Storage Systems: A Comparative Analysis With Different Motor Inertias: Preprint

The integration of renewable energy sources into power grids necessitates solutions for grid support and stability during fluctuations in electricity generation and demand. Gravity energy storage systems (GESS) are emerging as a promising technology for managing the balance between the energy supply and demand. However, their capacity to optimize energy flow and offer voltage and frequency regulation amid generation-demand imbalances is less reported. This paper investigates the control of GESS for optimizing energy flow during voltage and frequency regulation. The study evaluates the regulation capabilities of GESS with different motor inertias during a Texas grid event: one with a high-speed, low-inertia motor and another with a low-speed, high-inertia motor. Results indicate that both GESS systems provide fast frequency response by converting potential energy into kinetic energy and vice versa, with a response time of 1.5 seconds from the frequency variation. This aligns with grid requirements for primary frequency response from traditional synchronous generators and motors with large inertia. Furthermore, a GESS with a high-inertia motor may be able operate over a broader range of frequency variations whereas a low-inertia system may be limited by thermal constraints of the motor.

frequency regulation↗

NASA NTRS2007

Sodium Lidar-observed Strong Inertia-gravity Wave Activities in the Mesopause Region over Fort Collins, Colorado (41 deg N, 105 deg W)

In December 2004, the Colorado State University sodium lidar system at Fort Collins, Colorado (41 deg N, 105 deg W), conducted an approximately 80-hour continuous campaign for the simultaneous observations of mesopause region sodium density, temperature, and zonal and meridional winds. This data set reveals the significant inertia-gravity wave activities with a period of approximately 18 hours, which are strong in both wind components since UT day 338 (second day of the campaign), and weak in temperature and sodium density. The considerable variability of wave activities was observed with both wind amplitudes growing up to approximately 40 m/s at 95-100 km in day 339 and then decreasing dramatically in day 340. We also found that the sodium density wave perturbation is correlated in phase with temperature perturbation below 90 km, and approximately 180 deg out of phase above. Applying the linear wave theory, we estimated the wave horizontal propagation direction, horizontal wavelength, and apparent horizontal phase speed to be approximately 25 deg south of west, approximately 1800 +/- 150 km, and approximately 28 +/- 2 m/s, respectively of wave intrinsic period, intrinsic phase speed, and vertical wavelength were also estimated. While the onset of enhanced inertia-gravity wave amplitude in the night of 338 was observed to be in coincidence with short-period gravity wave breaking via convective instability, the decrease of inertia-gravity wave amplitude after noon of day 339 was also observed to coincide with the development of atmospheric dynamical instability layers with downward phase progression clearly correlated with the 18-hour inertia-gravity wave, suggesting likely breaking of this inertia-gravity wave via dynamical (shear) instability.

mesopause region↗

DOE OSTI2025

Regional Inertia Estimation Using Actual Event Measurements: Florida Case

As inverter-based resources’ integration in power grids increases, their uneven distribution across the electrical network leads to the formation of local regions that are weakly coupled to the larger interconnection. This signifies the necessity of regional frequency dynamics investigation and analyzing various inertia metrics. This paper presents a practical methodology for estimating regional rate-of-change of frequency (RoCoF) using actual event recordings, which is then used to evaluate regional inertia. Florida (FL) is selected as the region of interest due to its distinct regional frequency dynamics and the rising levels of solar generation. We identify and analyze confirmed events from 2017 to 2024 that occurred in FL. The results indicate that FL contributes about 14% to the total inertia of the US Eastern Interconnection, which approximately matches its share of generation capacity. Results also highlight seasonal fluctuations in energy generation, which play a significant role in influencing inertia and thus the RoCoF levels. This emphasizes the importance of estimating regional inertia to enhance grid operations for a future that focuses on distributed generation.

Dulal, Saurav [University of Tennessee, Knoxville ↗

DOE OSTI2025

Distributed Control and Optimization of Virtual Inertia in Power Systems

The integration of renewable energy sources into power grids through inverter-based resources (IBRs) reduces system inertia, leading to faster frequency dynamics and potential grid instability. This paper proposes a distributed, consensus-based approach for the real-time control and optimization of inertia sources during system disturbances, enhancing both system stability and economic performance. Furthermore, we integrate this approach with the traditional inertia placement problem, demonstrating its suitability for existing frameworks. We validate its effectiveness in a 4-bus test system and a two-area 8-bus test system, showcasing its potential for scalable, dynamic inertia management in low-inertia grids.

Yadav, Ajay [ORNL] (ORCID:000000016111881X)↗

NASA NTRS1977

Construction and interpretation of a digital inertia image

An image representing the thermal inertia in the vicinity of Pisgah Crater and Lavic Lake in Southern California has been generated from visible, near IR, and thermal images taken from aircraft. Construction of the thermal inertia image required radiometric calibration and geometric rectification of the acquired images as well as registration to a topographic map. The Kahle thermal model used in the construction of the thermal inertia image requires specification of albedo, topographic slope and slope azimuth, diurnal temperature range and local meteorological conditions. Albedo information was derived from the visible image; digital topographic information was computed from digitized stereo aerial photographs; and thermal ranges were calculated by subtracting the predawn from the afternoon thermal image data. Our computed values of thermal inertia were in close agreement with published values for similar surface materials. Thermal inertia provides complementary information to conventional images of reflected solar radiation for use in lithologic mapping.

Gillespie, A. R.↗

NASA NTRS1981

Thermal inertia mapping of Mars from 60 deg S to 60 deg N

The considered region comprises 81% of the surface of Mars. Thermal inertia I is a composite surface property, which is equal to the square root of the product of three factors, including the thermal conductivity, the density, and the specific heat. I is the sole thermal parameter which governs the temperature variation of a periodically heated homogeneous surface, and, as such, is the prime intermediary between remote temperature observations and their geologic interpretation. The values for the thermal inertia found imply particulate surface materials. The variation in Martian surface thermal conductivity is about two orders of magnitude. Three large regions of low-inertia material are defined. Low-inertia material always possesses high albedo. There is a general tendency for higher-thermal-inertia surfaces to be darker but exceptions occur which may be related to a thin mantling of light dust or bonding of light material.

Palluconi, F. D.↗

NASA NTRS1984

Effects of fluid inertia and turbulence on force coefficients for squeeze film dampers

The effects of fluid inertia and turbulence on the force coefficients of squeeze film dampers are investigated analytically. Both the convective and the temporal terms are included in the analysis of inertia effects. The analysis of turbulence is based on friction coefficients currently found in the literature for Poiseuille flow. The effect of fluid inertia on the magnitude of the radial direct inertia coefficient (i.e., to produce an apparent added mass at small eccentricity ratios, due to the temporal terms) is found to be completely reversed at large eccentricity ratios. The reversal is due entirely to the inclusion of the convective inertia terms in the analysis. Turbulence is found to produce a large effect on the direct damping coefficient at high eccentricity ratios. For the long or sealed squeeze film damper at high eccentricity ratios, the damping prediction with turbulence included is an order of magnitude higher than the laminar solution.

Andres, L. S.↗

NASA NTRS1993

Martian particle size based on thermal inertia corrected for elevation-dependent atmospheric properties

Thermal inertia is commonly used to derive physical properties of the Martian surface. If the surface is composed of loosely consolidated grains, then the thermal conductivity derived from the inertia can theoretically be used to compute the particle size. However, one persistent difficulty associated with the interpretation of thermal inertia and the derivation of particle size from it has been the degree to which atmospheric properties affect both the radiation balance at the surface and the gas conductivity. These factors vary with atmospheric pressure so that derived thermal inertias and particle sizes are a function of elevation. By utilizing currently available thermal models and laboratory information, a fine component thermal inertia map was convolved with digital topography to produce particle size maps of the Martian surface corrected for these elevation-dependent effects. Such an approach is especially applicable for the highest elevations on Mars, where atmospheric back radiation and gas conductivity are low.

Bridges, N. T.↗

NASA NTRS2007

The Effect of Increasing Inertia upon Vertical Ground Reaction Forces during Locomotion

The addition of inertia to exercising astronauts could increase ground reaction forces and potentially provide a greater health benefit. However, conflicting results have been reported regarding the adaptations to additional mass (inertia) without additional net weight (gravitational force) during locomotion. We examined the effect of increasing inertia while maintaining net gravitational force on vertical ground reaction forces and kinematics during walking and running. Vertical ground reaction force was measured for ten healthy adults (5 male/5 female) during walking (1.34 m/s) and running (3.13 m/s) using a force-measuring treadmill. Subjects completed locomotion at normal weight and mass, and at 10, 20, 30, and 40% of added inertial force. The added gravitational force was relieved with overhead suspension, so that the net force between the subject and treadmill at rest remained equal to 100% body weight. Peak vertical impact forces and loading rates increased with increased inertia during walking, and decreased during running. As inertia increased, peak vertical propulsive forces decreased during walking and did not change during running. Stride time increased during walking and running, and contact time increased during running. Vertical ground reaction force production and adaptations in gait kinematics were different between walking and running. The increased inertial forces were utilized independently from gravitational forces by the motor control system when determining coordination strategies.

DeWitt, John K.↗

NASA NTRS2007

Estimating the Inertia Matrix of a Spacecraft

A paper presents a method of utilizing some flight data, aboard a spacecraft that includes reaction wheels for attitude control, to estimate the inertia matrix of the spacecraft. The required data are digitized samples of (1) the spacecraft attitude in an inertial reference frame as measured, for example, by use of a star tracker and (2) speeds of rotation of the reaction wheels, the moments of inertia of which are deemed to be known. Starting from the classical equations for conservation of angular momentum of a rigid body, the inertia-matrix-estimation problem is formulated as a constrained least-squares minimization problem with explicit bounds on the inertia matrix incorporated as linear matrix inequalities. The explicit bounds reflect physical bounds on the inertia matrix and reduce the volume of data that must be processed to obtain a solution. The resulting minimization problem is a semidefinite optimization problem that can be solved efficiently, with guaranteed convergence to the global optimum, by use of readily available algorithms. In a test case involving a model attitude platform rotating on an air bearing, it is shown that, relative to a prior method, the present method produces better estimates from few data.

Acikmese, Behcet↗

NASA NTRS2010

Inertia and Double Bending of Light from Equivalence

Careful examination of light paths in an accelerated reference frame, with use of Special Relativity, can account fully for the observed bending of light in a gravitational field, not just half of it as reported in 1911. This analysis also leads to a Machian formulation of inertia similar to the one proposed by Einstein in 1912 and later derived from gravitational field equations in Minkowsky Space by Sciama in 1953. There is a clear inference from equivalence that there is some type of inertial mass increase in a gravitational field. It is the purpose of the current paper to suggest that equivalence provides a more complete picture of gravitational effects than previously thought, correctly predicting full light bending, and that since the theory of inertia is derivable from equivalence, any theory based on equivalence must take account of it. Einstein himself clearly was not satisfied with the status of inertia in GRT, as our quotes have shown. Many have tried to account for inertia and met with less than success, for example Davidson s integration of Sciama s inertia into GRT but only for a steady state cosmology [10], and the Machian gravity theory of Brans and Dicke [11]. Yet Mach s idea hasn t gone away, and now it seems that it cannot go away without also disposing of equivalence.

Shuler, Robert L., Jr.↗

DOE OSTI2024

Optimizing Grid Regulation with Gravity Energy Storage Systems: A Comparative Analysis with Different Motor Inertias

The integration of renewable energy sources into power grids necessitates solutions for grid support and stability during fluctuations in electricity generation and demand. Gravity energy storage systems (GESS) are emerging as a promising technology for managing the balance between energy supply and demand. However, their capacity to optimize energy flow and offer voltage and frequency regulation amid imbalances in generation and demand is less reported. This paper investigates the control of GESS for optimizing energy flow during voltage and frequency regulation. The study evaluates the regulation capabilities of GESS with different motor inertias during a Texas grid event: one with a high-speed, low-inertia motor and another with a low-speed, high-inertia motor. Results indicate that both GESS scenarios provide fast frequency response by converting potential energy into kinetic energy and vice versa, with a response time of 1.5 s from the frequency variation. This aligns with grid requirements for primary frequency response from traditional synchronous generators and motors with large inertia. Furthermore, a GESS based on a highinertia motor may be able to operate over a broader range of frequency variations, whereas a low-inertia system may be limited by thermal constraints of the motor.

ENERGY STORAGE,POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2025

Consensus-Based Control and Optimization of Power System Inertia

The integration of distributed energy resources (DERs), such as solar, wind, and energy storage systems, into power grids through inverter-based resources reduces power system inertia, leading to faster frequency dynamics and potential grid instability. To address this challenge, this paper proposes a distributed, consensus-based approach for the real-time control and optimization of inertia sources (synchronous generators and/or DERs) during system disturbances, enhancing both system stability and economic performance. The distributed control and optimization approach assumes each inertia source exchanges information solely with its neighbor ones, making it easily scalable to large power grid networks. The impacts of the communication connectivity among the inertia sources as well as their generation capacity limits on the distributed approach are investigated. We also demonstrate the approach’s robustness in scenarios involving communication time delays and packet losses, validating its effectiveness through numerical simulations on a 4-bus test system and a two-area 8-bus test system.

Power system inertia↗