Search NASA⌕ Search

SEARCH · Search NASA

Results for “Profiling optimization”

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.

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

At least 685 records · Page 38

Determining Spacecraft Reaction Wheel Friction Parameters

Software was developed to characterize the drag in each of the Cassini spacecraft's Reaction Wheel Assemblies (RWAs) to determine the RWA friction parameters. This tool measures the drag torque of RWAs for not only the high spin rates (greater than 250 RPM), but also the low spin rates (less than 250 RPM) where there is a lack of an elastohydrodynamic boundary layer in the bearings. RWA rate and drag torque profiles as functions of time are collected via telemetry once every 4 seconds and once every 8 seconds, respectively. Intermediate processing steps single-out the coast-down regions. A nonlinear model for the drag torque as a function of RWA spin rate is incorporated in order to characterize the low spin rate regime. The tool then uses a nonlinear parameter optimization algorithm based on the Nelder-Mead simplex method to determine the viscous coefficient, the Dahl friction, and the two parameters that account for the low spin-rate behavior.

Sarani, Siamak↗

The OMPS Limb Profiler Instrument: Two-Dimensional Retrieval Algorithm

The upcoming Ozone Mapper and Profiler Suite (OMPS), which will be launched on the NPOESS Preparatory Project (NPP) platform in early 2011, will continue monitoring the global distribution of the Earth's middle atmosphere ozone and aerosol. OMPS is composed of three instruments, namely the Total Column Mapper (heritage: TOMS, OMI), the Nadir Profiler (heritage: SBUV) and the Limb Profiler (heritage: SOLSE/LORE, OSIRIS, SCIAMACHY, SAGE III). The ultimate goal of the mission is to better understand and quantify the rate of stratospheric ozone recovery. The focus of the paper will be on the Limb Profiler (LP) instrument. The LP instrument will measure the Earth's limb radiance (which is due to the scattering of solar photons by air molecules, aerosol and Earth surface) in the ultra-violet (UV), visible and near infrared, from 285 to 1000 nm. The LP simultaneously images the whole vertical extent of the Earth's limb through three vertical slits, each covering a vertical tangent height range of 100 km and each horizontally spaced by 250 km in the cross-track direction. Measurements are made every 19 seconds along the orbit track, which corresponds to a distance of about 150km. Several data analysis tools are presently being constructed and tested to retrieve ozone and aerosol vertical distribution from limb radiance measurements. The primary NASA algorithm is based on earlier algorithms developed for the SOLSE/LORE and SAGE III limb scatter missions. All the existing retrieval algorithms rely on a spherical symmetry assumption for the atmosphere structure. While this assumption is reasonable in most of the stratosphere, it is no longer valid in regions of prime scientific interest, such as polar vortex and UTLS regions. The paper will describe a two-dimensional retrieval algorithm whereby the ozone distribution is simultaneously retrieved vertically and horizontally for a whole orbit. The retrieval code relies on (1) a forward 2D Radiative Transfer code (to model limb radiances within a non-uniform atmosphere and evaluate 2D analytical partial derivatives) and (2) an optimal estimator inversion routine. The algorithm uses the typically sparse nature of the kernel matrices as well as fast matrix inversion techniques to allow for fast inversion of limb data with efficient memory management (as was done for MIPAS data processing). While the method has so far only been developed in the context of Single Scatter, the paper will show how the CPU intensive Multiple Scatter modeling can be implemented using parallel CPU processing. Initial results will be presented in terms of retrieved ozone profiles and code performance.

Rault, Didier F.↗

Propagation model for the Land Mobile Satellite channel in urban environments

This paper presents the major characteristics of a simulation package capable of performing a complete narrow and wideband analysis of the mobile satellite communication channel in urban environments for any given orbital configuration. The wavelength-to-average urban geometrical dimension ratio has required the use of the Geometrical Theory of Diffraction (GTD). For the RF frequency range, the model has been designed to be (1 up to 60 GHz) extended to include effects of non-perfect conductivity and surface roughness. Taking advantage of the inherent capabilities of such a high frequency method, we are able to provide a complete description of the electromagnetic field at the mobile terminal. Using the information made available at the ray-tracer and GTD solver outputs, the Land Mobile Satellite (LMS) urban model can also give a detailed description of the communication channel in terms of power delay profiles, Doppler spectra, channel scattering functions, and so forth. Statistical data, e.g. cumulative distribution functions, level crossing rates or distributions of fades are also provided. The user can access the simulation tool through a Design-CAD user-friendly interface by means of which she can effectively design her own urban layout and run consequently all the envisaged routines. The software is optimized in its execution time so that numerous runs can be achieved in a considerably short time.

Sforza, M.↗

The 2004 NASA Aerospace Battery Workshop

Topics covered include: Super NiCd(TradeMark) Energy Storage for Gravity Probe-B Relativity Mission; Hubble Space Telescope 2004 Battery Update; The Development of Hermetically Sealed Aerospace Nickel-Metal Hydride Cell; Serial Charging Test on High Capacity Li-Ion Cells for the Orbiter Advanced Hydraulic Power System; Cell Equalization of Lithium-Ion Cells; The Long-Term Performance of Small-Cell Batteries Without Cell-Balancing Electronics; Identification and Treatment of Lithium Battery Cell Imbalance under Flight Conditions; Battery Control Boards for Li-Ion Batteries on Mars Exploration Rovers; Cell Over Voltage Protection and Balancing Circuit of the Lithium-Ion Battery; Lithium-Ion Battery Electronics for Aerospace Applications; Lithium-Ion Cell Charge Control Unit; Lithium Ion Battery Cell Bypass Circuit Test Results at the U.S. Naval Research Laboratory; High Capacity Battery Cell By-Pass Switches: High Current Pulse Testing of Lithium-Ion; Battery By-Pass Switches to Verify Their Ability to Withstand Short-Circuits; Incorporation of Physics-Based, Spatially-Resolved Battery Models into System Simulations; A Monte Carlo Model for Li-Ion Battery Life Projections; Thermal Behavior of Large Lithium-Ion Cells; Thermal Imaging of Aerospace Battery Cells; High Rate Designed 50 Ah Li-Ion Cell for LEO Applications; Evaluation of Corrosion Behavior in Aerospace Lithium-Ion Cells; Performance of AEA 80 Ah Battery Under GEO Profile; LEO Li-Ion Battery Testing; A Review of the Feasibility Investigation of Commercial Laminated Lithium-Ion Polymer Cells for Space Applications; Lithium-Ion Verification Test Program; Panasonic Small Cell Testing for AHPS; Lithium-Ion Small Cell Battery Shorting Study; Low-Earth-Orbit and Geosynchronous-Earth-Orbit Testing of 80 Ah Batteries under Real-Time Profiles; Update on Development of Lithium-Ion Cells for Space Applications at JAXA; Foreign Comparative Technology: Launch Vehicle Battery Cell Testing; 20V, 40 Ah Lithium Ion Polymer Battery for the Spacesuit; Low Temperature Life-Cycle Testing of a Lithium-Ion Battery for Low-Earth-Orbiting Spacecraft; and Evaluation of the Effects of DoD and Charge Rate on a LEO Optimized 50 Ah Li-Ion Aerospace Cell.

Source record↗

Isolating Curvature Effects in Computing Wall-Bounded Turbulent Flows

The flow over the zero-pressure-gradient So-Mellor convex curved wall is simulated using the Navier-Stokes equations. An inviscid effective outer wall shape, undocumented in the experiment, is obtained by using an adjoint optimization method with the desired pressure distribution on the inner wall as the cost function. Using this wall shape with a Navier-Stokes method, the abilities of various turbulence models to simulate the effects of curvature without the complicating factor of streamwise pressure gradient can be evaluated. The one-equation Spalart-Allmaras turbulence model overpredicts eddy viscosity, and its boundary layer profiles are too full. A curvature-corrected version of this model improves results, which are sensitive to the choice of a particular constant. An explicit algebraic stress model does a reasonable job predicting this flow field. However, results can be slightly improved by modifying the assumption on anisotropy equilibrium in the model's derivation. The resulting curvature-corrected explicit algebraic stress model possesses no heuristic functions or additional constants. It lowers slightly the computed skin friction coefficient and the turbulent stress levels for this case (in better agreement with experiment), but the effect on computed velocity profiles is very small.

Rumsey, Christopher L.↗

Shewanella amazonensis sp. nov., a novel metal-reducing facultative anaerobe from Amazonian shelf muds

A new bacterial species belonging to the genus Shewanella is described on the basis of phenotypic characterization and sequence analysis of its 16S rRNA-encoding and gyrase B (gyrB) genes. This organism, isolated from shallow-water marine sediments derived from the Amazon River delta, is a Gram-negative, motile, polarly flagellated, facultatively anaerobic, rod-shaped eubacterium and has a G&C content of 51.7 mol%. Strain SB2BT is exceptionally active in the anaerobic reduction of iron, manganese and sulfur compounds. SB2BT grows optimally at 35 degrees C, with 1-3% NaCl and over a pH range of 7-8. Analysis of the 16S rDNA sequence revealed a clear affiliation between strain SB2BT and members of the gamma subclass of the class Proteobacteria. High similarity values were found with certain members of the genus Shewanella, especially with Shewanella putrefaciens, and this was supported by cellular fatty acid profiles and phenotypic characterization. DNA-DNA hybridization between strain SB2BT and its phylogenetically closest relatives revealed low similarity values (24.6-42.7%) which indicated species status for strain SB2BT. That SB2BT represents a distinct bacterial species within the genus Shewanella is also supported by gyrB sequence analysis. Considering the source of the isolate, the name Shewanella amazonensis sp. nov. is proposed and strain SB2BT (= ATCC 700329T) is designated as the type strain.

NASA Discipline Exobiology↗

Cure Cycle Design Methodology for Fabricating Reactive Resin Matrix Fiber Reinforced Composites: A Protocol for Producing Void-free Quality Laminates

For the fabrication of resin matrix fiber reinforced composite laminates, a workable cure cycle (i.e., temperature and pressure profiles as a function of processing time) is needed and is critical for achieving void-free laminate consolidation. Design of such a cure cycle is not trivial, especially when dealing with reactive matrix resins. An empirical "trial and error" approach has been used as common practice in the composite industry. Such an approach is not only costly, but also ineffective at establishing the optimal processing conditions for a specific resin/fiber composite system. In this report, a rational "processing science" based approach is established, and a universal cure cycle design protocol is proposed. Following this protocol, a workable and optimal cure cycle can be readily and rationally designed for most reactive resin systems in a cost effective way. This design protocol has been validated through experimental studies of several reactive polyimide composites for a wide spectrum of usage that has been documented in the previous publications.

Hou, Tan-Hung↗

Advanced interactive display formats for terminal area traffic control

The basic design considerations for perspective Air Traffic Control displays are described. A software framework has been developed for manual viewing parameter setting (MVPS) in preparation for continued, ongoing developments on automated viewing parameter setting (AVPS) schemes. The MVPS system is based on indirect manipulation of the viewing parameters. Requests for changes in viewing parameter setting are entered manually by the operator by moving viewing parameter manipulation pointers on the screen. The motion of these pointers, which are an integral part of the 3-D scene, is limited to the boundaries of screen. This arrangement has been chosen, in order to preserve the correspondence between the new and the old viewing parameter setting, a feature which contributes to preventing spatial disorientation of the operator. For all viewing operations, e.g. rotation, translation and ranging, the actual change is executed automatically by the system, through gradual transitions with an exponentially damped, sinusoidal velocity profile, in this work referred to as 'slewing' motions. The slewing functions, which eliminate discontinuities in the viewing parameter changes, are designed primarily for enhancing the operator's impression that he, or she, is dealing with an actually existing physical system, rather than an abstract computer generated scene. Current, ongoing efforts deal with the development of automated viewing parameter setting schemes. These schemes employ an optimization strategy, aimed at identifying the best possible vantage point, from which the Air Traffic Control scene can be viewed, for a given traffic situation.

Grunwald, Arthur J.↗

Microwave Treatment for Cardiac Arrhythmias

NASA seeks to transfer the NASA developed microwave ablation technology, designed for the treatment of ventricular tachycardia (irregular heart beat), to industry. After a heart attack, many cells surrounding the resulting scar continue to live but are abnormal electrically; they may conduct impulses unusually slowly or fire when they would typically be silent. These diseased areas might disturb smooth signaling by forming a reentrant circuit in the muscle. The objective of microwave ablation is to heat and kill these diseased cells to restore appropriate electrical activity in the heart. This technology is a method and apparatus that provides for propagating microwave energy into heart tissues to produce a desired temperature profile therein at tissue depths sufficient for thermally ablating arrhythmogenic cardiac tissue while preventing excessive heating of surrounding tissues, organs, and blood. A wide bandwidth double-disk antenna is effective for this purpose over a bandwidth of about six gigahertz. A computer simulation provides initial screening capabilities for an antenna such as antenna, frequency, power level, and power application duration. The simulation also allows optimization of techniques for specific patients or conditions. In comparison with other methods that involve direct-current pulses or radio frequencies below 1 GHz, this method may prove more effective in treating ventricular tachycardia. This is because the present method provides for greater control of the location, cross-sectional area, and depth of a lesion via selection of the location and design of the antenna and the choice of microwave power and frequency.

Hernandez-Moya, Sonia↗

Sensitivity Analysis for Atmospheric Infrared Sounder (AIRS) CO2 Retrieval

The Atmospheric Infrared Sounder (AIRS) is a thermal infrared sensor able to retrieve the daily atmospheric state globally for clear as well as partially cloudy field-of-views. The AIRS spectrometer has 2378 channels sensing from 15.4 micrometers to 3.7 micrometers, of which a small subset in the 15 micrometers region has been selected, to date, for CO2 retrieval. To improve upon the current retrieval method, we extended the retrieval calculations to include a prior estimate component and developed a channel ranking system to optimize the channels and number of channels used. The channel ranking system uses a mathematical formalism to rapidly process and assess the retrieval potential of large numbers of channels. Implementing this system, we identifed a larger optimized subset of AIRS channels that can decrease retrieval errors and minimize the overall sensitivity to other iridescent contributors, such as water vapor, ozone, and atmospheric temperature. This methodology selects channels globally by accounting for the latitudinal, longitudinal, and seasonal dependencies of the subset. The new methodology increases accuracy in AIRS CO2 as well as other retrievals and enables the extension of retrieved CO2 vertical profiles to altitudes ranging from the lower troposphere to upper stratosphere. The extended retrieval method for CO2 vertical profile estimation using a maximum-likelihood estimation method. We use model data to demonstrate the beneficial impact of the extended retrieval method using the new channel ranking system on CO2 retrieval.

sensitivity analysis↗

Evaluation of a Variable Facesheet Liner Configuration in Grazing Incidence for Broadband Noise Reduction

Abstract Tests were conducted in the NASA Langley Grazing Flow Impedance Tube (GFIT) to determine the broadband noise reduction capability of a variable facesheet liner. Three uniform liners were designed to achieve sound absorption over distinct frequency regimes at Mach 0.0. Each liner was fabricated and tested in the GFIT at sound pressure levels of 120 and 140 dB, and at tangential flow velocities up to Mach 0.5. A variable facesheet liner was fabricated to combine the geometries of these three liners, such that the facesheet geometry (hole diameter and porosity) was varied across the liner surface. The Prony method was used to educe the impedance of each sample, and these impedances were input to the CHE (Convected Helmholtz Equation) propagation code to predict the acoustic pressure profiles in the GFIT. Comparisons of predicted and measured acoustic pressure profiles were used to confirm the uniformity of all four liners, and to demonstrate the suitability of the CHE code in analysis of the variable facesheet concept. Results showed good comparison at no flow and Mach 0.3, and acceptable comparison at Mach 0.5. The variable facesheet liner provides enhanced broadband noise reduction at the no-flow condition for which it was designed, but further optimization is needed to target flow conditions.

acoustic↗

The human role in space: Technology, economics and optimization

Man-machine interactions in space are explored in detail. The role and the degree of direct involvement of humans that will be required in future space missions are investigated. An attempt is made to establish valid criteria for allocating functional activities between humans and machines and to provide insight into the technological requirements, economics, and benefits of the human presence in space. Six basic categories of man-machine interactions are considered: manual, supported, augmented, teleoperated, supervised, and independent. Appendices are included which provide human capability data, project analyses, activity timeline profiles and data sheets for 37 generic activities, support equipment and human capabilities required in these activities, and cumulative costs as a function of activity for seven man-machine modes.

Hall, S. B.↗

A Ground-Based 2-Micron DIAL System to Profile Tropospheric CO2 and Aerosol Distributions for Atmospheric Studies

System will operate at a temperature insensitive CO2 line (2050.967 nm) with side-line tuning and off-set locking. Demonstrated an order of magnitude improvement in laser line locking needed for high precision measurements, side-line operation, and simultaneously double pulsing and line locking. Detector testing of phototransistor has demonstrated sensitivity to aerosol features over long distances in the atmosphere and resolve features approx. 100m. Optical systems that collect light onto small area detectors work well. Receiver optical designs are being optimized and data acquisition systems developed. CO2 line parameter characterization in progress In situ sensor calibration in progress for validation of DIAL CO2 system.

Ismail, Syed↗

Vectorization of a penalty function algorithm for well scheduling

In petroleum engineering, the oil production profiles of a reservoir can be simulated by using a finite gridded model. This profile is affected by the number and choice of wells which in turn is a result of various production limits and constraints including, for example, the economic minimum well spacing, the number of drilling rigs available and the time required to drill and complete a well. After a well is available it may be shut in because of excessive water or gas productions. In order to optimize the field performance a penalty function algorithm was developed for scheduling wells. For an example with some 343 wells and 15 different constraints, the scheduling routine vectorized for the CYBER 205 averaged 560 times faster performance than the scalar version.

Absar, I.↗

Extraction and Separation Modeling of Orion Test Vehicles with ADAMS Simulation

The Capsule Parachute Assembly System (CPAS) project has increased efforts to demonstrate the performance of fully integrated parachute systems at both higher dynamic pressures and in the presence of wake fields using a Parachute Compartment Drop Test Vehicle (PCDTV) and a Parachute Test Vehicle (PTV), respectively. Modeling the extraction and separation events has proven challenging and an understanding of the physics is required to reduce the risk of separation malfunctions. The need for extraction and separation modeling is critical to a successful CPAS test campaign. Current PTV-alone simulations, such as Decelerator System Simulation (DSS), require accurate initial conditions (ICs) drawn from a separation model. Automatic Dynamic Analysis of Mechanical Systems (ADAMS), a Commercial off the Shelf (COTS) tool, was employed to provide insight into the multi-body six degree of freedom (DOF) interaction between parachute test hardware and external and internal forces. Components of the model include a composite extraction parachute, primary vehicle (PTV or PCDTV), platform cradle, a release mechanism, aircraft ramp, and a programmer parachute with attach points. Independent aerodynamic forces were applied to the mated test vehicle/platform cradle and the separated test vehicle and platform cradle. The aero coefficients were determined from real time lookup tables which were functions of both angle of attack ( ) and sideslip ( ). The atmospheric properties were also determined from a real time lookup table characteristic of the Yuma Proving Grounds (YPG) atmosphere relative to the planned test month. Representative geometries were constructed in ADAMS with measured mass properties generated for each independent vehicle. Derived smart separation parameters were included in ADAMS as sensors with defined pitch and pitch rate criteria used to refine inputs to analogous avionics systems for optimal separation conditions. Key design variables were dispersed in a Monte Carlo analysis to provide the maximum expected range of the state variables at programmer deployment to be used as ICs in DSS. Extensive comparisons were made with Decelerator System Simulation Application (DSSA) to validate the mated portion of the ADAMS extraction trajectory. Results of the comparisons improved the fidelity of ADAMS with a ramp pitch profile update from DSSA. Post-test reconstructions resulted in improvements to extraction parachute drag area knock-down factors, extraction line modeling, and the inclusion of ball-to-socket attachments used as a release mechanism on the PTV. Modeling of two Extraction parachutes was based on United States Air Force (USAF) tow test data and integrated into ADAMS for nominal and Monte Carlo trajectory assessments. Video overlay of ADAMS animations and actual C-12 chase plane test videos supported analysis and observation efforts of extraction and separation events. The COTS ADAMS simulation has been integrated with NASA based simulations to provide complete end to end trajectories with a focus on the extraction, separation, and programmer deployment sequence. The flexibility of modifying ADAMS inputs has proven useful for sensitivity studies and extraction/separation modeling efforts. 1

Fraire, Usbaldo, Jr.↗

Materials Combustion Testing and Combustion Product Sensor Evaluations in FY12

NASA Centers continue to collaborate to characterize the chemical species and smoke particles generated by the combustion of current space-rated non-metallic materials including fluoropolymers. This paper describes the results of tests conducted February through September 2012 to identify optimal chemical markers both for augmenting particle-based fire detection methods and for monitoring the post-fire cleanup phase in human spacecraft. These studies follow up on testing conducted in August 2010 and reported at ICES 2011. The tests were conducted at the NASA White Sands Test Facility in a custom glove box designed for burning fractional gram quantities of materials under varying heating profiles. The 623 L chamber was heavily instrumented to quantify organics (gas chromatography/mass spectrometry), inorganics by water extraction followed by ion chromatography, and select species by various individual commercially-available sensors. Evaluating new technologies for measuring carbon monoxide, hydrogen cyanide, hydrogen fluoride, hydrogen chloride and other species of interest was a key objective of the test. Some of these sensors were located inside the glovebox near the fire source to avoid losses through the sampling lines; the rest were located just outside the glovebox. Instruments for smoke particle characterization included a Tapered Element Oscillating Microbalance Personal Dust Monitor (TEOM PDM) and a TSI Dust Trak DRX to measure particle mass concentration, a TSI PTrak for number concentration and a thermal precipitator for collection of particles for microscopic analysis. Materials studied included Nomex®, M22759 wire insulation, granulated circuit board, polyvinyl chloride (PVC), Polytetrafluoroethylene (PTFE), Kapton®, and mixtures of PTFE and Kapton®. Furnace temperatures ranged from 340o to 640o C, focusing on the smoldering regime. Of particular interest in these tests was confirming burn repeatability and production of acid gases with different fuel mixture compositions, as well as the dependence of aerosol concentrations on temperature.

Smoke↗

Materials Combustion Testing and Combustion Product Sensor Evaluations in FY12

NASA Centers continue to collaborate to characterize the chemical species and smoke particles generated by the combustion of current space-rated non-metallic materials including fluoropolymers. This paper describes the results of tests conducted February through September 2012 to identify optimal chemical markers both for augmenting particle-based fire detection methods and for monitoring the post-fire cleanup phase in human spacecraft. These studies follow up on testing conducted in August 2010 and reported at ICES 2011. The tests were conducted at the NASA White Sands Test Facility in a custom glove box designed for burning fractional gram quantities of materials under varying heating profiles. The 623 L chamber was heavily instrumented to quantify organics (gas chromatography/mass spectrometry), inorganics by water extraction followed by ion chromatography, and select species by various individual commercially-available sensors. Evaluating new technologies for measuring carbon monoxide, hydrogen cyanide, hydrogen fluoride, hydrogen chloride and other species of interest was a key objective of the test. Some of these sensors were located inside the glovebox near the fire source to avoid losses through the sampling lines; the rest were located just outside the glovebox. Instruments for smoke particle characterization included a Tapered Element Oscillating Microbalance Personal Dust Monitor (TEOM PDM) and a TSI Dust Trak DRX to measure particle mass concentration, a TSI PTrak for number concentration and a thermal precipitator for collection of particles for microscopic analysis. Materials studied included Nomex(R), M22759 wire insulation, granulated circuit board, polyvinyl chloride (PVC), Polytetrafluoroethylene (PTFE), Kapton(R), and mixtures of PTFE and Kapton(R). Furnace temperatures ranged from 340 to 640 C, focusing on the smoldering regime. Of particular interest in these tests was confirming burn repeatability and production of acid gases with different fuel mixture compositions, as well as the dependence of aerosol concentrations on temperature.

Combustion↗

An investigation of the effects of mass loss, shape change and real gas aerodynamics on a Jovian atmospheric reconstruction experiment

A survey of the effects of mass loss, shape change and real-gas aerodynamics on a Jovian atmospheric reconstruction experiment is carried out. Techniques used to reconstruct atmospheric profiles from entry probe measurements are discussed and some of the parameters which affect their accuracy are identified. Trajectory analyses and real-gas, radiatively-coupled flow field analyses (which include the effects of mass loss and shape change) are carried out for several candidate probe configurations. From these analyses, uncertainties in the atmospheric reconstruction procedure are estimated. Finally, the prospects for reducing these uncertainties by optimizing probe configuration and by instrumentation of the probe heat shield to measure actual shape change are considered.

Walberg, G. D.↗