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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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NASA NTRS2019

Ozonesonde Quality Assurance: JOSIE-SHADOZ (2017) and SHALLOTS (2018)

Ozonesonde data constitute a mainstay of satellite calibration and are used for climatologies and analysis of trends, especially in the lower stratosphere where satellites are most uncertain. The electrochemical-concentration cell (ECC) ozonesonde has been deployed at ~100 stations worldwide since the 1960s, with changes over time in manufacture and procedures, including details of the cell chemical solution and data processing. As a consequence, there are biases among different stations and discontinuities in profile timeseries from individual site records. Since 1996 the Jülich [Germany] Ozone Sonde Intercomparison Experiment (JOSIE) has periodically tested ozonesondes in a simulation chamber designated the World Calibration Centre for Ozonesondes by WMO. In October- November 2017 a JOSIE campaign evaluated the sondes and procedures used in SHADOZ (Southern Hemisphere Additional Ozonesondes), a 14-station tropical and subtropical network. A distinctive feature of the 2017 JOSIE was that the tests were conducted by operators from eight SHADOZ stations; Nairobi, Natal, Irene, Costa Rica, Paramaribo, Reunion, Hanoi, Kuala Lumpur. Experimental protocols and preliminary results for the SHADOZ sonde configurations, which represent most of those in use today, are described. SHADOZ stations that follow WMO-recommended protocols record total ozone within 3% of the JOSIE reference instrument. Instrument biases noted in prior JOSIE and field tests like BESOS (2004) were noted in JOSIE-2017, with maximum effect in the stratosphere. In June 2018 we organized a series of dual launches during the OWLETS II campaign in the Maryland and Chesapeake Bay area (SHALLOTS = SHADOZ-OWLETS ParaLLel Ozonesonde Test Study). Instrument and solution types were varied as in JOSIE-2017 and three radiosonde-ozonesonde variants were tested. An example of a parallel sampling in SHALLOTS, from a Greenbelt EnSCI-iMet sonde combination flown with the Wallops SPCLMS package, is illustrated in the Figure. The result was a range of biases but in general the instrument combination (EnSCI-iMet) deployed at 11 SHADOZ stations recorded ~5-10% less ozone in the stratosphere than the SPC ECC sonde flown with a Vaisala or LMS system. These 2017 and 2018 results and prior JOSIEs demonstrate that regular testing is essential to maintain best practices in ozonesonde operations and to ensure high-quality data for the ozone assessment communities.

Quality assurance↗
NASA NTRS1988

A vision system for a Mars rover

A Mars rover must be able to sense its local environment with sufficient resolution and accuracy to avoid local obstacles and hazards while moving a significant distance each day. Power efficiency and reliability are extremely important considerations, making stereo correlation an attractive method of range sensing compared to laser scanning, if the computational load and correspondence errors can be handled. Techniques for treatment of these problems, including the use of more than two cameras to reduce correspondence errors and possibly to limit the computational burden of stereo processing, have been tested at JPL. Once a reliable range map is obtained, it must be transformed to a plan view and compared to a stored terrain database, in order to refine the estimated position of the rover and to improve the database. The slope and roughness of each terrain region are computed, which form the basis for a traversability map allowing local path planning. Ongoing research and field testing of such a system is described.

Wilcox, Brian H.↗
NASA NTRS1994

Linear quadratic Gaussian and feedforward controllers for the DSS-13 antenna

The controller development and the tracking performance evaluation for the DSS-13 antenna are presented. A trajectory preprocessor, linear quadratic Gaussian (LQG) controller, feedforward controller, and their combination were designed, built, analyzed, and tested. The antenna exhibits nonlinear behavior when the input to the antenna and/or the derivative of this input exceeds the imposed limits; for slewing and acquisition commands, these limits are typically violated. A trajectory preprocessor was designed to ensure that the antenna behaves linearly, just to prevent nonlinear limit cycling. The estimator model for the LQG controller was identified from the data obtained from the field test. Based on an LQG balanced representation, a reduced-order LQG controller was obtained. The feedforward controller and the combination of the LQG and feedforward controller were also investigated. The performance of the controllers was evaluated with the tracking errors (due to following a trajectory) and the disturbance errors (due to the disturbances acting on the antenna). The LQG controller has good disturbance rejection properties and satisfactory tracking errors. The feedforward controller has small tracking errors but poor disturbance rejection properties. The combined LQG and feedforward controller exhibits small tracking errors as well as good disturbance rejection properties. However, the cost for this performance is the complexity of the controller.

Gawronski, W. K.↗
NASA NTRS1971

SSA-A spacecraft magnetic tests

In the initial magnetic tests the spacecraft perm moment as received was 43 milliampere-meter squared (pole-cm), which was reduced by deperm treatment to milliampere-meter squared. Facility fluxgate probe bias results indicated Z axis bias at the SSS-A fluxgate magnetometer position to be about one half nanotesla (gamma) after Z axis deperm. The ASCS magnetometers, 01 and 02, were successfully aligned and proper operation of the ASCS system were verified. The spacecraft fluxgate magnetometer was calibrated in both the high and low sensitivity modes after a defective 01 electronics card was replaced. Problems were encountered in the Z axis search coil during calibration and the test was re-scheduled. Final test results indicated that the total perm moment could not be reduced any lower than 35 milliampere-meter squared by deperm treatment. However, the Z axis moment decreased from 22 milliampere-meter squared to 6 milliampere-meter squared after deperm. Correct operation and calibration was verified for all three axes of the spacecraft fluxgate magnetometer and no significant bias was observed during stray field testing. Null and spot calibration of the ASCS magnetometer was completed and the measured spin and attitude coil moments were: 2535 and 9820 milliampere-meter squared respectively.

Roy, T. N.↗
NASA NTRS2018

An Improved UAV-Based Fog Collector for Local-Scale Aerobiological Sampling

The use of unmanned air vehicles (UAVs) to passively collect fog for microbiological analysis is being investigated at NASA Ames, contributing to our understanding of the dynamics and limits of the biosphere. Current improvements to a preliminary payload design include physically modifying the mesh of the passive impactor collection unit (PICU) to increase fog-capture efficiency and a quick- mounting system to improve sample turnaround and contamination control. Increasing the water-capture efficiency of the PICU involved changing the surface roughness of the polypropylene mesh by abrasive sanding. Four scale models of the PICU were created, with three of those models sanded with 80-, 150-, and 240-grit sand paper for a minimum of thirty seconds on each side. Each mesh was individually tested in a fog-simulation chamber to measure collection efficiency. Tests showed that sanding the mesh will increase the water-capture efficiency by at least 3-fold for the 150- and 240-grit. Next steps are to determine the scaling laws and minimum amount of exposure time as a function of the fog density, to acquire enough microorganisms for analysis; a light-weight ground module for the PICU has been developed to allow rapid, easy field testing. Developing a mounting system that will ensure sterile deployment, as well as prompt changes of PICUs, for collection of fog water, utilized computational fluid dynamics (CFD) for the UAV to ensure that the location of the impactors will not be contaminated by particulates in the UAV downwash. The original design allowed the impactors to remain within sterile packaging until mounted on the UAV but did not address the concerns of contamination from aerodynamic ground effects and particulate lofting during takeoff. Design for a raised launch pad would allow for the sterile PICU to be attached to UAV and launched from outside the region of projected particulate lofting. California coastal sites have been scouted for appropriate testing locations. The improvements to the PICU design and operations will allow for multiple sampling points within a single fog event. The returned fog samples will undergo ion chromatography, qPCR, ATP quantification, and other tests to characterize microbial species and relevant biochemistry.

Wong, Amber↗
NASA NTRS2005

Diagnostics Adapted for Heat-Treating Furnace Environment

Diagnostics developed for the in situ monitoring of rocket combustion environments were adapted for use in heat-treating furnaces. Simultaneous, in situ monitoring of the carbon monoxide, carbon dioxide, methane, water, and hydrogen concentrations in the endothermic gas of a heat-treating furnace were demonstrated under a Space Act Agreement between the NASA Lewis Research Center, the Heat Treating Network, and Akron Steel Treating Company. This endothermic gas, or "endogas," is produced in a catalytic process, where natural gas is "cracked" in the presence of air. Variations in the composition of the natural gas supplied lead to variations in the composition of the endothermic gas. These variations could lead to an unacceptable quality of steel products that are hardened through the carborization process that uses this gas. Conventional methods of monitoring the endogas include measuring the dew point of the gas and the oxygen concentration. From these data, the carbon monoxide content of the gas can be calculated. This carbon monoxide concentration creates the carbon potential needed for carburization. Several weak links are present in this approach. The oxygen monitor deteriorates over time, and the measurement might be inaccurate by 50 percent. Also, the chemistry equations, which are based on several assumptions, such as secondary species concentrations, provide only an approximate estimate of the carbon monoxide concentration. To address these weaknesses, we investigated a new method based on ordinary Raman spectroscopy, in which the carbon monoxide concentration is measured directly and in situ. This method measures the laser light scattered from the molecules. Each species interacts with the light and scatters the light at a different frequency. Spectral monitoring of the scattered light intensity at each molecular frequency of interest provides the species concentrations. One advantage over the conventional method is that several species can be monitored simultaneously. A second advantage is that the measurement is direct; there is no need to make assumptions, to filter the gas, or to calibrate the instrument. An instrument was designed consisting of a laser and a detection system within an enclosure, connected to an optical probe by fibers. For determining carbon monoxide concentration, the probe is mounted on the endothermic gas line, close to the generator. Optical fibers with a length of 150 ft have been used to transmit laser light from the instrument to the probe. There, the light is focused into the gas, and the scattered light is collected and transmitted back to the instrument where it is analyzed with a photomultiplier and lock-in amplifier. Laboratory tests have shown that with the current system the concentration of carbon monoxide, water, nitrogen, oxygen, and hydrogen in the air can be monitored with an accuracy of 1 percent. The concentration of carbon dioxide in the air can be monitored with an accuracy of 0.5 percent, and the concentration of methane with an accuracy of 0.2 percent. This instrument was taken to the Akron Steel Treating Plant, where field tests are in progress to verify the system capabilities. Planned developments are improving the accuracy, monitoring multiple locations, and reducing instrument size and cost.

Source record↗
NASA NTRS2015

Integrated Ultra-Wideband Tracking and Carbon Dioxide Sensing System Design for International Space Station Applications

A three-dimensional (3D) Ultra-Wideband (UWB) Time-of-Arrival (TOA) tracking system has been studied at NASA Johnson Space Center (JSC) to provide the tracking capability inside the International Space Station (ISS) modules for various applications. One of applications is to locate and report the location where crew experienced possible high level of carbon-dioxide (CO2) and felt upset. Recent findings indicate that frequent, short-term crew exposure to elevated CO2 levels combined with other physiological impacts of microgravity may lead to a number of detrimental effects, including loss of vision. To evaluate the risks associated with transient elevated CO2 levels and design effective countermeasures, doctors must have access to frequent CO2 measurements in the immediate vicinity of individual crew members along with simultaneous measurements of their location in the space environment. To achieve this goal, a small, low-power, wearable system that integrates an accurate CO2 sensor with an ultra-wideband (UWB) radio capable of real-time location estimation and data communication is proposed. This system would be worn by crew members or mounted on a free-flyer and would automatically gather and transmit sampled sensor data tagged with real-time, high-resolution location information. Under the current proposed effort, a breadboard prototype of such a system has been developed. Although the initial effort is targeted to CO2 monitoring, the concept is applicable to other types of sensors. For the initial effort, a micro-controller is leveraged to integrate a low-power CO2 sensor with a commercially available UWB radio system with ranging capability. In order to accurately locate those places in a multipath intensive environment like ISS modules, it requires a robust real-time location system (RTLS) which can provide the required accuracy and update rate. A 3D UWB TOA tracking system with two-way ranging has been proposed and studied. The designed system will be tested in the Wireless Habitat Testbed which simulates the ISS module environment. This report describes the research and development effort for this prototype integrated UWB tracking and CO2 sensing system. The remainder of the report is organized as follows. In Section II, the TOA tracking methodology is introduced and the 3D tracking algorithm is derived. The simulation results are discussed in Section III. In Section VI, prototype system design and field tests are discussed. Some concluding remarks and future works are presented in Section V.

Ni, Jianjun (David)↗
NASA NTRS2012

Progress Made in Lunar In-Situ Resource Utilization Under NASA's Exploration Technology and Development Program

Incorporation of In-Situ Resource Utilization (ISRU) and the production of mission critical consumables for 9 propulsion, power, and life support into mission architectures can greatly reduce the mass, cost, and risk of missions 10 leading to a sustainable and affordable approach to human exploration beyond Earth. ISRU and its products can 11 also greatly affect how other exploration systems are developed, including determining which technologies are 12 important or enabling. While the concept of lunar ISRU has existed for over 40 years, the technologies and systems 13 had not progressed much past simple laboratory proof-of-concept tests. With the release of the Vision for Space 14 Exploration in 2004 with the goal of harnessing the Moon.s resources, NASA initiated the ISRU Project in the 15 Exploration Technology Development Program (ETDP) to develop the technologies and systems needed to meet 16 this goal. In the five years of work in the ISRU Project, significant advancements and accomplishments occurred in 17 several important areas of lunar ISRU. Also, two analog field tests held in Hawaii in 2008 and 2010 demonstrated 18 all the steps in ISRU capabilities required along with the integration of ISRU products and hardware with 19 propulsion, power, and cryogenic storage systems. This paper will review the scope of the ISRU Project in the 20 ETDP, ISRU incorporation and development strategies utilized by the ISRU Project, and ISRU development and 21 test accomplishments over the five years of funded project activity.

Sanders, Gerald B.↗
NASA NTRS1981

A comprehensive analysis of the performance characteristics of the Mount Laguna solar photovoltaic installation

This paper represents the first comprehensive survey of the Mount Laguna Photovoltaic Installation. The novel techniques used for performing the field tests have been effective in locating and characterizing defective modules. A comparative analysis on the two types of modules used in the array indicates that they have significantly different failure rates, different distributions in degradational space and very different failure modes. A life cycle model is presented to explain a multimodal distribution observed for one module type. A statistical model is constructed and it is shown to be in good agreement with the field data.

Shumka, A.↗
NASA NTRS2010

Use of a Microphone Phased Array to Determine Noise Sources in a Rocket Plume

A 70-element microphone phased array was used to identify noise sources in the plume of a solid rocket motor. An environment chamber was built and other precautions were taken to protect the sensitive condenser microphones from rain, thunderstorms and other environmental elements during prolonged stay in the outdoor test stand. A camera mounted at the center of the array was used to photograph the plume. In the first phase of the study the array was placed in an anechoic chamber for calibration, and validation of the indigenous Matlab(R) based beamform software. It was found that the "advanced" beamform methods, such as CLEAN-SC was partially successful in identifying speaker sources placed closer than the Rayleigh criteria. To participate in the field test all equipments were shipped to NASA Marshal Space Flight Center, where the elements of the array hardware were rebuilt around the test stand. The sensitive amplifiers and the data acquisition hardware were placed in a safe basement, and 100m long cables were used to connect the microphones, Kulites and the camera. The array chamber and the microphones were found to withstand the environmental elements as well as the shaking from the rocket plume generated noise. The beamform map was superimposed on a photo of the rocket plume to readily identify the source distribution. It was found that the plume made an exceptionally long, >30 diameter, noise source over a large frequency range. The shock pattern created spatial modulation of the noise source. Interestingly, the concrete pad of the horizontal test stand was found to be a good acoustic reflector: the beamform map showed two distinct source distributions- the plume and its reflection on the pad. The array was found to be most effective in the frequency range of 2kHz to 10kHz. As expected, the classical beamform method excessively smeared the noise sources at lower frequencies and produced excessive side-lobes at higher frequencies. The "advanced" beamform routine CLEAN-SC created a series of lumped sources which may be unphysical. We believe that the present effort is the first-ever attempt to directly measure noise source distribution in a rocket plume.

Panda, J.↗
NASA NTRS1971

Theory of the unmagnetized plasma.

The Vlasov mathematical model of a plasma, which has come to be thought more useful than any other in describing the dynamical behavior of the majority of plasmas of interest, is first examined. Macroscopic variables and moment equations; linear electrostatics solutions; plasma oscillations, ion acoustic waves, and linear instabilities are treated, as well as external fields, 'test' charges, and nonlinear Vlasov phenomena. Plasmas are statistically described, and attention is given to the kinetic theory of the stable, uniform plasma and the Balescu-Lenard equation; two-time ensemble averages and fluctuation spectra in stable plasmas; the kinetic theory of the unstable plasma; and ensembles of Vlasov plasmas. Some illustrative experiments are described. Four appendixes deal with the electrostatic approximation and transverse waves; solution of the linearized Vlasov equation in a magnetic field; estimates of correlation functions from thermal equilibrium; and equivalence of spatially uniform BBGKY and Klimontovich correlations.

Montgomery, D. C.↗
NASA NTRS1981

Photovoltaic systems overview

Selected photovoltaic systems currently under user-environment field test by the U.S. Department of Energy Photovoltaics Program are discussed, and operational results are summarized. There are many systems in the stand-alone sector that are cost effective now. As proven products become available, distributed residential, commercial, institutional and industrial on-site systems should be able to displace significant amounts of centrally-generated electricity throughout most of the United States. Finally, utilities should ultimately be able to augment their generating capacity with larger-scale systems. Field experience and industry interface has led to excellent overall product performance.

Hesse, J. L.↗
NASA NTRS2001

A Low-Noise NbTiN Hot Electron Bolometer Mixer

Hot electron bolometer (HEB) mixer elements, based on niobium titanium nitride (NbTiN) thin film technology, have been fabricated on crystalline quartz substrates over a 20 nm thick AlN buffer layer. The film was patterned by optical lithography, yielding bolometer elements that measure about 1 micrometer long and between 2 and 12 micrometers wide. These mixer chips were mounted in a fixed-tuned waveguide mixer block, and tested in the 600 and 800 GHz frequency range. The 3-dB output bandwidth of these mixers was determined to be about 2.5 GHz and we measured a receiver noise temperature of 270 K at 630 GHz using an intermediate frequency of 1.5 GHz. The receiver has excellent amplitude stability and the noise temperature measurements are highly repeatable. An 800 GHz receiver incorporating one of these mixer chips has recently been installed at the Sub-Millimeter Telescope in Arizona for field test and for astronomical observations.

Tong, C. Edward↗
NASA NTRSDate not supplied

Challenges, Considerations, and Opportunities for Exercise and Medical Accommodation Inside a Small Pressurized Rover

Pressurized Rovers (PR) can enable crew to explore away from a lander or surface habitat at distances not possible on foot or even in unpressurized rovers. Sustaining crew for multiple days, they can rove for weeks, independent of other surface elements. Because these are essentially mobile habitats, it is critical that they provide sufficient volume to accommodate the exercise and medical systems to maintain human health in remote, low gravity environments such as the Moon and Mars. This is an area of extensive unknowns as requirements have not yet been developed for exercise or medical systems in pressurized rovers. Yet they must be considered in vehicle sizing studies as they are significant volume drivers, requiring allocation for stowed and deployed hardware inside the rover cabin. Previously flown spacecraft have allocated varying amounts of volume based on the expected crew mission and the state of the art in these systems. NASA-STD-3001 provides high-level requirements for standards of medical care and exercise capabilities. Crew injuries are possible both inside the cabin and on extravehicular activities (EVA), therefore requiring medical capability. Exercise countermeasures are needed to counteract the debilitating effects of lowered gravity. This may include both reconditioning following a lengthy microgravity transit as well as ongoing countermeasures against the effect of low surface gravity. The NASA reference concept for the PR dates back to the Constellation Program and prototypes have been extensively tested in NASA’s Desert Research and Technology Studies (DRATS) program as well as at the NASA Johnson Space Center. The PR cabin is designed to accommodate two crewmembers and is subdivided into a forward cockpit area and a main body for crew habitation. EVAs are accomplished by transitioning through suit ports in the aft bulkhead into spacesuits. While no exercise devices have been developed for the PR, some have been prototyped and demonstrated in DRATS analog missions. A cycle ergometer performed reasonably well in DRATS testing as an aerobic exercise device and recent analysis work has theorized that a combination aerobic and resistive device could be packaged into a form factor similar to the DRATS ergometer. It is therefore suitable for use as an initial volumetric placeholder. No sensorimotor devices have been considered for the PR to aid in adaptation to surface gravity. However, there are commercially available treadmills that at minimum represent examples of the type of exercise system that could potentially be used for such a purpose. A combination of field test data, analysis, and CAD modeling will be used to perform a first pass assessment of whether these exercise devices can be stowed and deployed within the PR. Medical inventories from the International Space Station will be used as a volume placeholder for the PR medical system. A configuration will be discussed for medical deployment, including positioning of caregiver, patient, and medical equipment / supplies.

Pressurized Rover↗
NASA NTRS1986

Measurement of angular distribution of sound emission from training projectiles in subsonic flight

Training projectiles with nose ring cavities that produce intense whistles in stationary free-jet tests were shot in a relatively straight-line trajectory. A ground based microphone was used to obtain the angular distribution of sound intensity produced from the subsonically flying projectile. Data reduction required calculation of Doppler and attenuation factors which were determined based on a non-linear trajectory. Also, the directional sensitivity of the microphone was measured and used in the data reduction. Significant angular variation of sound intensity produced from the projectile was found which can be used to plot an intensity contour map on the ground. A full-scale field test confirmed the validity of the aeroacoustic concept of producing a relatively intense whistle from the projectile, and the usefulness of a real-time data acquisition system.

Cho, Y. I.↗
NASA NTRS2009

Lunar Water Resource Demonstration (LWRD) Test Results

NASA has undertaken the In-Situ Resource Utilization (lSRU) project called RESOLVE (Regolith and Environment Science & Oxygen and Lunar Volatile Extraction). This project is an Earth-based lunar precursor demonstration of a system that could be sent to explore permanently shadowed polar lunar craters, where it would drill into regolith, quantify the volatiles that are present, and extract oxygen by hydrogen reduction of iron oxides. The RESOLVE chemical processing system was mounted within the CMU rover "Scarab" and successfully demonstrated on Hawaii's Mauna Kea volcano in November 2008. This technology could be used on Mars as well. As described at the 2008 Mars Society Convention, the Lunar Water Resource Demonstration (LWRD) supports the objectives of the RESOLVE project by capturing and quantifying water and hydrogen released by regolith upon heating. Field test results for the quantification of water using LWRD showed that the volcanic ash (tephra) samples contained 0.15-0.41% water, in agreement with GC water measurements. Reduction of the RH in the surge tank to near zero during recirculation show that the water is captured by the water beds as desired. The water can be recovered by heating the Water Beds to 230 C or higher. Test results for the capture and quantification of pure hydrogen have shown that over 90% of the hydrogen can be captured and 98% of the absorbed hydrogen can be recovered upon heating the hydride to 400 C and desorbing the hydrogen several times into the evacuated surge tank. Thus, the essential requirement of capturing hydrogen and recovering it has been demonstrated. ,

Muscatello, Anthony C.↗
NASA NTRS2011

Predicting the Consequences of Workload Management Strategies with Human Performance Modeling

Human performance modelers at the US Army Research Laboratory have developed an approach for establishing Soldier high workload that can be used for analyses of proposed system designs. Their technique includes three key components. To implement the approach in an experiment, the researcher would create two experimental conditions: a baseline and a design alternative. Next they would identify a scenario in which the test participants perform all their representative concurrent interactions with the system. This scenario should include any events that would trigger a different set of goals for the human operators. They would collect workload values during both the control and alternative design condition to see if the alternative increased workload and decreased performance. They have successfully implemented this approach for military vehicle. designs using the human performance modeling tool, IMPRINT. Although ARL researches use IMPRINT to implement their approach, it can be applied to any workload analysis. Researchers using other modeling and simulations tools or conducting experiments or field tests can use the same approach.

Mitchell, Diane Kuhl↗
NASA NTRS2008

A Topographical Lidar System for Terrain-Relative Navigation

An imaging lidar system is being developed for use in navigation, relative to the local terrain. This technology will potentially be used for future spacecraft landing on the Moon. Systems like this one could also be used on Earth for diverse purposes, including mapping terrain, navigating aircraft with respect to terrain and military applications. The system has been field-tested aboard a helicopter in the Mojave Desert. When this system was designed, digitizers with sufficient sampling rate (2 GHz) were only available with very limited memory. Also, it was desirable to limit the amount of data to be transferred between the digitizer and the mass storage between individual frames. One of the novelty design features of this system was to design the system around the limited amount of memory of the digitizer. The system is required to operate over an altitude (distance) range from a few meters to approximately 1 km, but for each scan across the full field of view, the digitizer memory is only able to hold data for an altitude range no more than 100 m. Data acquisition methods in support of the limited 100 m wide altitude range are described.

Liebe, Carl Christian↗