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At least 217 records · Page 12

Application of Face-Gear Drives in Helicopter Transmissions

The use of face gears in helicopter transmissions was explored. A light-weight, split torque transmission design utilizing face gears was described. Face-gear design and geometry were investigated. Topics included tooth generation, limiting inner and outer radii, tooth contact analysis, contact ratio, gear eccentricity, and structural stiffness. Design charts were developed to determine minimum and maximum face-gear inner and outer radii. Analytical study of transmission error showed face-gear drives were relatively insensitive to gear misalignment, but tooth contact was affected by misalignment. A method of localizing bearing contact to compensate for misalignment was explored. The proper choice of shaft support stiffness enabled good load sharing in the split torque transmission design. Face-gear experimental studies were also included and the feasibility of face gears in high-speed, high-load applications such as helicopter transmissions was demonstrated.

Litvin, F. L.↗

Effects of various cavity designs on the performance of a CO2 TEA laser with an unstable resonator

Unstable resonator modeling has been carried out for an injection-seeded CO2 transversely excited atmosphere (TEA) laser in the NOAA/ERL/Wave Propagation Laboratory (WPL) Doppler lidar to examine the effects of various cavity designs on the quality of the output beam. The results show the effects of an injection pinhole, electrode spacing, mirror tilt, and radial reflectivity function of the output coupler. The electrode spacing in this laser has negligible effect. The injection pinhole, however, produces complicated structures in the output patterns. If the pinhole is removed, the output pattern is much smoother, and the frequency jitter is smaller. Misalignment sensitivity is very closely related to the radial reflectivity function. The superparabolic function provides the highest coupling efficiency, largest beam size, and good collimation, but produces a slightly higher misalignment sensitivity compared with a parabolic function. The Gaussian function provides the lowest misalignment sensitivity, but it produces the smallest beam size and the largest beam divergence. Also, the coupling coefficient is 50 percent lower than the optimum value. Methods for using a flat diffraction grating in unstable resonators are also investigated. The best way is to use a flat grating/positive lens combination to replace the back concave mirror.

Zhao, Yanzeng↗

Face-gear drives: Design, analysis, and testing for helicopter transmission applications

The use of face-gears in helicopter transmissions was explored. A light-weight, split-torque transmission design utilizing face-gears is described. Face-gear design and geometry were investigated. Topics included tooth generation, limiting inner and outer radii, tooth contact analysis, contact ratio, gear eccentricity, grinding, and structural stiffness. Design charts were developed to determine minimum and maximum face-gear inner and outer radii. An analytical study showed that the face-gear drive is relatively insensitive to gear misalignment with respect to transmission errors, but the tooth contact is affected by misalignment. A method of localizing the bearing contact to permit operation with misalignment was explored. Two new methods for grinding of the face-gear tooth surfaces were also investigated. The proper choice of shaft stiffness enabled good load sharing in the split-torque transmission design. Face-gear experimental studies were also conducted. These tests demonstrated the feasibility of face-gears in high-speed, high-load applications such as helicopter transmissions.

Litvin, F. L.↗

Probabilistic micromechanics and macromechanics of polymer matrix composites

A probabilistic evaluation of an eight ply graphite-epoxy quasi-isotropic laminate was completed using the Integrated Composite Analyzer (ICAN) in conjunction with Monte Carlo simulation and Fast Probability Integration (FPI) techniques. Probabilistic input included fiber and matrix properties, fiber misalignment, fiber volume ratio, void volume ratio, ply thickness and ply layup angle. Cumulative distribution functions (CDFs) for select laminate properties are given. To reduce the number of simulations, a Fast Probability Integration (FPI) technique was used to generate CDFs for the select properties in the absence of fiber misalignment. These CDFs were compared to a second Monte Carlo simulation done without fiber misalignment effects. It was found that FPI requires fewer simulations to obtain the cumulative distribution functions as opposed to Monte Carlo simulation techniques. Furthermore, FPI provides valuable information regarding the sensitivities of composite properties to the constituent properties, fiber volume ratio and void volume ratio.

Mase, G. T.↗

Lidar Analyses

A brief description of enhancements made to the NASA MSFC coherent lidar model is provided. Notable improvements are the addition of routines to automatically determine the 3 dB misalignment loss angle and the backscatter value at which the probability of a good estimate (for a maximum likelihood estimator) falls to 50%. The ability to automatically generate energy/aperture parametrization (EAP) plots which include the effects of angular misalignment has been added. These EAP plots make it very easy to see that for any practical system where there is some degree of misalignment then there is an optimum telescope diameter for which the laser pulse energy required to achieve a particular sensitivity is minimized. Increasing the telescope diameter above this will result in a reduction of sensitivity. These parameterizations also clearly show that the alignment tolerances at shorter wavelengths are much stricter than those at longer wavelengths. A brief outline of the NASA MSFC AEOLUS program is given and a summary of the lidar designs considered during the program is presented. A discussion of some of the design trades is performed both in the text and in a conference publication attached as an appendix.

Spiers, Gary D.↗

Nearly Circular Transfer Trajectories for Descending Satellites

Simplified expressions describing the transfer from a satellite bit to the point of atmospheric entry are derived. The expressions are limited to altitude changes that are small compared with the earth's radius, and velocity changes small compared with satellite velocity. They are further restricted to motion about a spherical, nonrotating earth. The transfer orbit resulting from the application of thrust in any direction at any point in an elliptic orbit is considered. Expressions for the errors in distance (miss distance) and entry angle due to an initial misalignment and magnitude error of the deflecting thrust are presented. The largest potential contributing factor towards a miss distance stems from the misalignment of the retrovelocity increment. If this velocity increment is pointed in direct opposition to the path, a 1 deg misalignment leads to a miss distance of 3.45 miles. However, it is shown that this error can be avoided by applying the velocity increment at an angle between 120 deg and 150 deg below the flight-path, direction. The guidance and accuracy requirements to establish a circular orbit, in addition to the corrections applied to to transform elliptic orbits into circular ones, are also discussed.

Low, George M.↗

On-Orbit Performance of the TRMM Mission Mode

This paper presents an overview of the Tropical Rainfall Measuring Mission (TRMM) Attitude Control System along with detailed in-flight performance results of the TRMM Mission mode. The TRMM spacecraft is an Earth-pointed, zero momentum bias satellite launched on November 27, 1997 from Tanegashima Space Center, Japan. TRMM is a joint mission between NASA and the National Space Development Agency of Japan designed to monitor and study tropical rainfall and the associated release of energy. Prior to calibration, the spacecraft attitude showed larger Sun sensor yaw updates than expected. This was traced to not just sensor misalignment but also to a misalignment between the two heads within each Sun sensor. In order to avoid alteration of the flight software, Sun sensor transfer function coefficients were determined to minimize the error due to head misalignment. This paper describes the design, on-orbit checkout, calibration and performance of the TRMM Mission Mode with respect to the mission level requirements.

Robertson, Brent↗

AXAF Coordinate Transformation at XRCF

Coordinate transformation between focal plane and detector pixel systems must be handled carefully at the X-ray Calibration Facility (XRCF) as it will be during flight. The High Resolution Mirror Assembly (HRMA) X-ray Detection System (HXDS) stage dithers, and the five-axis mount (FAM) attachment points underwent various types of motion during testing. At the XRCF when the FAM moved, the Science Instrument Module (SIM) travel direction was not necessarily aligned with the mirror axis motion, and, in addition, an arbitrary position offset had to be calibrated. Misalignment from the mirror axis was assessed by measuring its displacement from the boresight configuration of the default FAM frame, and the HXDS stage was monitored for motion from the default FAM reference point. Mirror position, prescribed in a mirror modal coordinate system, was measured in HRMA pitch and yaw axes. Prior to corrections for dithering and FAM movement, the coordinate data at XRCF also had to be corrected for possible misalignments of the mirror mount relative to XRCF and the default FAM axes due to the movement of the FAM feet. Those misalignments were processed in terms of yaw-pitch-roll Euler angles in the mirror nodal coordinate, and in the default FAM frame, respectively. An AXAF Science Center (ASC) coordinate library, pixlib, has been built to support these coordinate transformations and was used during x-ray calibration at the George C. Marshall Space Flight Center, Huntsville, AL. The design and implementation of this library will be discussed.

He, Helen↗

Experiments in Aligning Threaded Parts Using a Robot Hand

Techniques for determining and correcting threaded part alignment using force and angular position data are developed to augment currently limited techniques for align- ing threaded parts. These new techniques are based on backspinning a nut with respect to a bolt and measuring the force change that occurs when the bolt "falls" into the nut. Kinematic models that describe the relationship between threaded parts during backspinning are introduced and are used to show how angular alignment may be determined. The models indicate how to distinguish between the aligned and misaligned cases of a bolt and a nut connection by using axial force data only. In addition, by tracking the in-plane relative attitude of the bolt during spinning, data can be obtained on the direction of the angular misalignment which, in turn, is used to correct the misalignment. Results from experiments using a bolt held in a specialized fixture and a three fingers Stanford/JPL hand are presented.

Diftler, M. A.↗

Research Capabilities for Oil-Free Turbomachinery Expanded by New Rotordynamic Simulator Facility

A new test rig has been developed for simulating high-speed turbomachinery shafting using Oil-Free foil air bearing technology. Foil air journal bearings are self-acting hydrodynamic bearings with a flexible inner sleeve surface using air as the lubricant. These bearings have been used in turbomachinery, primarily air cycle machines, for the past four decades to eliminate the need for oil lubrication. More recently, interest has been growing in applying foil bearings to aircraft gas turbine engines. They offer potential improvements in efficiency and power density, decreased maintenance costs, and other secondary benefits. The goal of applying foil air bearings to aircraft gas turbine engines prompted the fabrication of this test rig. The facility enables bearing designers to test potential bearing designs with shafts that simulate the rotating components of a target engine without the high cost of building actual flight hardware. The data collected from this rig can be used to make changes to the shaft and bearings in subsequent design iterations. The rest of this article describes the new test rig and demonstrates some of its capabilities with an initial simulated shaft system. The test rig has two support structures, each housing a foil air journal bearing. The structures are designed to accept any size foil journal bearing smaller than 63 mm (2.5 in.) in diameter. The bearing support structures are mounted to a 91- by 152-cm (3- by 5-ft) table and can be separated by as much as 122 cm (4 ft) and as little as 20 cm (8 in.) to accommodate a wide range of shaft sizes. In the initial configuration, a 9.5-cm (3.75-in.) impulse air turbine drives the test shaft. The impulse turbine, as well as virtually any number of "dummy" compressor and turbine disks, can be mounted on the shaft inboard or outboard of the bearings. This flexibility allows researchers to simulate various engine shaft configurations. The bearing support structures include a unique bearing mounting fixture that rotates to accommodate a laserbased alignment system. This can measure the misalignment of the bearing centers in each of 2 translational degrees of freedom and 2 rotational degrees of freedom. In the initial configuration, with roughly a 30.5-cm- (12-in.-) long shaft, two simulated aerocomponent disks, and two 50.8-cm (2-in.) foil journal bearings, the rig can operate at 65,000 rpm at room temperature. The test facility can measure shaft displacements in both the vertical and horizontal directions at each bearing location. Horizontal and vertical structural vibrations are monitored using accelerometers mounted on the bearing support structures. This information is used to determine system rotordynamic response, including critical speeds, mode shapes, orbit size and shape, and potentially the onset of instabilities. Bearing torque can be monitored as well to predict the power loss in the foil bearings. All of this information is fed back and forth between NASA and the foil bearing designers in an iterative fashion to converge on a final bearing and shaft design for a given engine application. In addition to its application development capabilities, the test rig offers several unique capabilities for basic bearing research. Using the laser alignment system mentioned earlier, the facility will be used to map foil air journal bearing performance. A known misalignment of increasing severity will be induced to determine the sensitivity of foil bearings to misalignment. Other future plans include oil-free integral starter generator testing and development, and dynamic load testing of foil journal bearings.

Howard, Samuel A.↗

Attitude-Independent Magnetometer Calibration for Spin-Stabilized Spacecraft

The paper describes a three-step estimator to calibrate a Three-Axis Magnetometer (TAM) using TAM and slit Sun or star sensor measurements. In the first step, the Calibration Utility forms a loss function from the residuals of the magnitude of the geomagnetic field. This loss function is minimized with respect to biases, scale factors, and nonorthogonality corrections. The second step minimizes residuals of the projection of the geomagnetic field onto the spin axis under the assumption that spacecraft nutation has been suppressed by a nutation damper. Minimization is done with respect to various directions of the body spin axis in the TAM frame. The direction of the spin axis in the inertial coordinate system required for the residual computation is assumed to be unchanged with time. It is either determined independently using other sensors or included in the estimation parameters. In both cases all estimation parameters can be found using simple analytical formulas derived in the paper. The last step is to minimize a third loss function formed by residuals of the dot product between the geomagnetic field and Sun or star vector with respect to the misalignment angle about the body spin axis. The method is illustrated by calibrating TAM for the Fast Auroral Snapshot Explorer (FAST) using in-flight TAM and Sun sensor data. The estimated parameters include magnetic biases, scale factors, and misalignment angles of the spin axis in the TAM frame. Estimation of the misalignment angle about the spin axis was inconclusive since (at least for the selected time interval) the Sun vector was about 15 degrees from the direction of the spin axis; as a result residuals of the dot product between the geomagnetic field and Sun vectors were to a large extent minimized as a by-product of the second step.

Natanson, Gregory↗

Calibration of Gimbaled Platforms: The Solar Dynamics Observatory High Gain Antennas

Simple parameterization of gimbaled platform pointing produces a complete set of 13 calibration parameters-9 misalignment angles, 2 scale factors and 2 biases. By modifying the parameter representation, redundancy can be eliminated and a minimum set of 9 independent parameters defined. These consist of 5 misalignment angles, 2 scale factors, and 2 biases. Of these, only 4 misalignment angles and 2 biases are significant for the Solar Dynamics Observatory (SDO) High Gain Antennas (HGAs). An algorithm to determine these parameters after launch has been developed and tested with simulated SDO data. The algorithm consists of a direct minimization of the root-sum-square of the differences between expected power and measured power. The results show that sufficient parameter accuracy can be attained even when time-dependent thermal distortions are present, if measurements from a pattern of intentional offset pointing positions is included.

Hashmall, Joseph A.↗

Alignment system for encoders

An improved encoder alignment system is disclosed which provides an indication of the extent of misalignment and a measure of the rate at which the misalignment may be changing. The invention is adapted for use with a conventional encoder which provides a digital coarse word having at least significant bit and a digital fine word having a least significant bit and a most significant bit. The invention generates the exclusive or of the least significant bit of the coarse digital signal and the least significant bit of the fine digital signal to provide a first signal. The invention then generates the exclusive or of the first signal and the complement of the most significant bit of the fine digital signal to provide an output signal which represents the misalignment of the encoder.

Villani, Daniel D.↗

Tool for Inspecting Alignment of Twinaxial Connectors

A proposed tool would be used to inspect alignments of mating twinaxial-connector assemblies on interconnecting wiring harnesses. More specifically, the tool would be used to inspect the alignment of each contact pin of each connector on one assembly with the corresponding socket in the corresponding connector on the other assembly. It is necessary to inspect the alignment because if mating of the assemblies is attempted when any pin/socket pair is misaligned beyond tolerance, the connection will not be completed and the dielectric material in the socket will be damaged (see Figure 1). Although the basic principle of the tool is applicable to almost any type of mating connector assemblies, the specific geometry of the tool must match the pin-and-socket geometry of the specific mating assemblies to be inspected. In the original application for which the tool was conceived, each of the mating assemblies contains eight twinaxial connectors; the pin diameter is 0.014 in. (.0.35 mm), and the maximum allowable pin/socket misalignment is 0.007 in. (.0.18 mm). Incomplete connections can result in loss of flight data within the functional path to the space shuttle crew cockpit displays. The tool (see Figure 2) would consist mainly of a transparent disk with alignment clocking tabs that can be fitted onto either connector assembly. Sets of circles or equivalent reference markings are affixed to the face of the tool, located at the desired positions of the mating contact pairs. An inspector would simply fit the tool onto a connector assembly, engaging the clocking tabs until the tool fits tightly. The inspector would then align one set of circles positioning a line of sight perpendicular to one contact within the connector assembly. Mis alignments would be evidenced by the tip of a pin contact straying past the inner edge of the circle. Socket contact misalignments would be evidenced by a crescent-shaped portion of the white dielectric appearing within the circle. The tool could include a variable magnifier plus an illuminator that could be configured so as not to cast shadows.

Smith, Christopher R.↗

From the Blazar Sequence to the Blazar Envelope: Revisiting the Relativistic Jet Dichotomy in Radio-Loud AGN

We revisit the concept of a blazar sequence that relates the synchrotron peak frequency (Vpeak) in blazars with synchrotron peak luminosity (Lpeak, in vLv) using a large sample of radio-loud AGN. We present observational evidence that the blazar sequence is formed from two populations in the synchrotron Vpeak - Lpeak plane, each forming an upper edge to an envelope of progressively misaligned blazars, and connecting to an adjacent group of radio galaxies having jets viewed at much larger angles to the line of sight. When binned by jet kinetic power (Lkin; as measured through a scaling relationship with extended radio power), we find that radio core dominance decreases with decreasing synchrotron Lpeak, revealing that sources in the envelope are generally more misaligned. We find population-based evidence of velocity gradients in jets at low kinetic powers (approximately 10(exp 42) - 10(exp 44.5) erg s(exp -1)), corresponding to FR I radio galaxies and most BL Lacs. These low jet power 'weak jet' sources, thought to exhibit radiatively inefficient accretion, are distinguished from the population of non-decelerating, low synchrotron-peaking (LSP) blazars and FR II radio galaxies ('strong' jets) which are thought to exhibit radiatively efficient accretion. The two-population interpretation explains the apparent contradiction of the existence of highly core-dominated, low-power blazars at both low and high synchrotron peak frequencies, and further implies that most intermediate synchrotron peak (ISP) sources are not intermediate in intrinsic jet power between LSP and high synchrotron-peaking (HSP) sources, but are more misaligned versions of HSP sources with similar jet powers.

Meyer, Eileen T.↗

Understanding Beam Alignment in a Coherent Lidar System

Optical beam alignment in a coherent lidar (or ladar) receiver system plays a critical role in optimizing its performance. Optical alignment in a coherent lidar system dictates the wavefront curvature (phase front) and Poynting vector) matching of the local oscillator beam with the incoming receiver beam on a detector. However, this alignment is often not easy to achieve and is rarely perfect. Furthermore, optical fibers are being increasingly used in coherent lidar system receivers for transporting radiation to achieve architectural elegance. Single mode fibers also require stringent mode matching for efficient light coupling. The detector response characteristics vary with the misalignment of the two pointing vectors. Misalignment can lead to increase in DC current. Also, a lens in front of the detector may exasperate phase front and Poynting vector mismatch. Non-Interaction of Waves, or the NIW property indicates the light beams do not interfere by themselves in the absence of detecting dipoles. In this paper, we will analyze the extent of misalignment on the detector specifications using pointing vectors of mixing beams in light of the NIW property.

Prasad, Narasimha S.↗

Risk of Performance Decrements and Adverse Health Outcomes Resulting from Sleep Loss, Circadian Desynchronization, and Work Overload

Sleep loss, circadian desynchronization, and work overload occur to some extent for ground and flight crews, prior to and during spaceflight missions. Ground evidence indicates that such risk factors may lead to performance decrements and adverse health outcomes, which could potentially compromise mission objectives. Efforts are needed to identify the environmental and mission conditions that interfere with sleep and circadian alignment, as well as individual differences in vulnerability and resiliency to sleep loss and circadian desynchronization. Specifically, this report highlights a collection of new evidence to better characterize the risk and reveals new gaps in this risk as follows: Sleep loss is apparent during spaceflight. Astronauts consistently average less sleep during spaceflight relative to on the ground. The causes of this sleep loss remain unknown, however ground-based evidence suggests that the sleep duration of astronauts is likely to lead to performance impairment and short and long-term health consequences. Further research is needed in this area in order to develop screening tools to assess individual astronaut sleep need in order to quantify the magnitude of sleep loss during spaceflight; current and planned efforts in BHP's research portfolio address this need. In addition, it is still unclear whether the conditions of spaceflight environment lead to sleep loss or whether other factors, such as work overload lead to the reduced sleep duration. Future data mining efforts and continued data collection on the ISS will help to further characterize factors contributing to sleep loss. Sleep inertia has not been evaluated during spaceflight. Ground-based studies confirm that it takes two to four hours to achieve optimal performance after waking from a sleep episode. Sleep inertia has been associated with increased accidents and reduced performance in operational environments. Sleep inertia poses considerable risk during spaceflight when emergency situations necessitate that crewmembers wake from sleep and make quick decisions. A recently completed BHP investigation assesses the effects of sleep inertia upon abrupt awakening, with and without hypnotics currently used in spaceflight; results from this investigation will help to inform strategies relative to sleep inertia effects on performance. Circadian desynchrony has been observed during spaceflight. Circadian desynchrony during spaceflight develops due to schedule constraints requiring non-24 operations or 'slam-shifts' and due to insufficient or mis-timed light exposure. In addition, circadian misalignment has been associated with reduced sleep duration and increased medication use. In ground-based studies, circadian desynchrony has been associated with significant performance impairment and increased risk of accidents when operations coincide with the circadian nadir. There is a great deal of information available on how to manage circadian misalignment, however, there are currently no easily collected biomarkers that can be used during spaceflight to determine circadian phase. Current research efforts are addressing this gap. Work overload has been documented during current spaceflight operations. NASA has established work hour guidelines that limit shift duration, however, schedule creep, where duty requirements necessitate working beyond scheduled work hours, has been reported. This observation warrants the documentation of actual work hours in order to improve planning and in order to ensure that astronauts receive adequate down time. In addition to concerns about work overload, ground based evidence suggests that work underload may be a concern during deep space missions, where torpor may develop and physically demanding workload will be exchanged for monitoring of autonomous systems. Given that increased automation is anticipated for exploration vehicles, fatigue effects in the context of such systems needs to be further understood. Performance metrics are needed to evaluate fitness-for-duty during spaceflight. Although ground-based evidence supports the notion that sleep loss, circadian desynchronization and work overload lead to performance impairment, inconsistency in the measures used to evaluate performance during spaceflight make it difficult to evaluate the magnitude of performance impairment during spaceflight. Work is underway to standardize measures of performance evaluation during spaceflight. Once established, such performance indicators need to be correlated with operational performance. Individual differences in sleep need and circadian preference, phase shifting ability and period have been documented in ground-based studies. Individual differences in response to sleep loss and circadian misalignment have also been documented and are presumed to be associated with genetic polymorphisms. No studies have systematically reported individual differences in sleep or circadian-related outcomes during spaceflight. More work is needed in this area in order to identify genetic or phenotypic biomarkers that predict resilience or vulnerability to sleep loss in order to personalize countermeasure strategies and mitigate performance impairment during spaceflight. Two laboratory and field investigations specific to this topic are currently ongoing; additional efforts, including an effort to mine existing biological data from spaceflight relative to sleep and circadian outcomes, are planned. Sex differences in sleep need and circadian period and phase have been reported in ground-based studies. The impact of these sex differences on performance is unclear. Sex differences in sleep need and circadian rhythms have not been systematically studied during spaceflight, presumably due to the small number of women that have flown in space. More research is needed in this area to evaluate whether any of the observed sex differences in physiology lead to altered performance in spaceflight and on the ground.

Flynn-Evans, Erin↗

Modeling Forest Biomass and Growth: Coupling Long-Term Inventory and Lidar Data

Combining spatially-explicit long-term forest inventory and remotely sensed information from Light Detection and Ranging (LiDAR) datasets through statistical models can be a powerful tool for predicting and mapping above-ground biomass (AGB) at a range of geographic scales. We present and examine a novel modeling approach to improve prediction of AGB and estimate AGB growth using LiDAR data. The proposed model accommodates temporal misalignment between field measurements and remotely sensed data-a problem pervasive in such settings-by including multiple time-indexed measurements at plot locations to estimate AGB growth. We pursue a Bayesian modeling framework that allows for appropriately complex parameter associations and uncertainty propagation through to prediction. Specifically, we identify a space-varying coefficients model to predict and map AGB and its associated growth simultaneously. The proposed model is assessed using LiDAR data acquired from NASA Goddard's LiDAR, Hyper-spectral & Thermal imager and field inventory data from the Penobscot Experimental Forest in Bradley, Maine. The proposed model outperformed the time-invariant counterpart models in predictive performance as indicated by a substantial reduction in root mean squared error. The proposed model adequately accounts for temporal misalignment through the estimation of forest AGB growth and accommodates residual spatial dependence. Results from this analysis suggest that future AGB models informed using remotely sensed data, such as LiDAR, may be improved by adapting traditional modeling frameworks to account for temporal misalignment and spatial dependence using random effects.

Babcock, Chad↗