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NASA NTRS2008

High Vertically Resolved Atmospheric and Surface/Cloud Parameters Retrieved with Infrared Atmospheric Sounding Interferometer (IASI)

The Joint Airborne IASI Validation Experiment (JAIVEx) was conducted during April 2007 mainly for validation of the IASI on the MetOp satellite. IASI possesses an ultra-spectral resolution of 0.25/cm and a spectral coverage from 645 to 2760/cm. Ultra-spectral resolution infrared spectral radiance obtained from near nadir observations provide atmospheric, surface, and cloud property information. An advanced retrieval algorithm with a fast radiative transfer model, including cloud effects, is used for atmospheric profile and cloud parameter retrieval. This physical inversion scheme has been developed, dealing with cloudy as well as cloud-free radiance observed with ultraspectral infrared sounders, to simultaneously retrieve surface, atmospheric thermodynamic, and cloud microphysical parameters. A fast radiative transfer model, which applies to the cloud-free and/or clouded atmosphere, is used for atmospheric profile and cloud parameter retrieval. A one-dimensional (1-d) variational multi-variable inversion solution is used to improve an iterative background state defined by an eigenvector-regression-retrieval. The solution is iterated in order to account for non-linearity in the 1-d variational solution. It is shown that relatively accurate temperature and moisture retrievals are achieved below optically thin clouds. For optically thick clouds, accurate temperature and moisture profiles down to cloud top level are obtained. For both optically thin and thick cloud situations, the cloud top height can be retrieved with relatively high accuracy (i.e., error < 1 km). Preliminary retrievals of atmospheric soundings, surface properties, and cloud optical/microphysical properties with the IASI observations are obtained and presented. These retrievals will be further inter-compared with those obtained from airborne FTS system, such as the NPOESS Airborne Sounder Testbed - Interferometer (NAST-I), dedicated dropsondes, radiosondes, and ground based Raman Lidar. The capabilities of satellite ultra-spectral sounder such as the IASI are investigated indicating a high vertical structure of atmosphere is retrieved.

Zhou, Daniel K.↗
NASA NTRS2007

Atmospheric, Cloud, and Surface Parameters Retrieved from Satellite Ultra-spectral Infrared Sounder Measurements

An advanced retrieval algorithm with a fast radiative transfer model, including cloud effects, is used for atmospheric profile and cloud parameter retrieval. This physical inversion scheme has been developed, dealing with cloudy as well as cloud-free radiance observed with ultraspectral infrared sounders, to simultaneously retrieve surface, atmospheric thermodynamic, and cloud microphysical parameters. A fast radiative transfer model, which applies to the clouded atmosphere, is used for atmospheric profile and cloud parameter retrieval. A one-dimensional (1-d) variational multivariable inversion solution is used to improve an iterative background state defined by an eigenvector-regression-retrieval. The solution is iterated in order to account for non-linearity in the 1-d variational solution. This retrieval algorithm is applied to the MetOp satellite Infrared Atmospheric Sounding Interferometer (IASI) launched on October 19, 2006. IASI possesses an ultra-spectral resolution of 0.25 cm(exp -1) and a spectral coverage from 645 to 2760 cm(exp -1). Preliminary retrievals of atmospheric soundings, surface properties, and cloud optical/microphysical properties with the IASI measurements are obtained and presented.

Zhou, Daniel K.↗
NASA NTRS2008

Current Sounding Capability From Satellite Meteorological Observation With Ultraspectral Infrared Instruments

Ultraspectral resolution infrared spectral radiance obtained from near nadir observations provide atmospheric, surface, and cloud property information. The intent of the measurement of tropospheric thermodynamic state and trace abundances is the initialization of climate models and the monitoring of air quality. The NPOESS Airborne Sounder Testbed-Interferometer (NAST-I), designed to support the development of future satellite temperature and moisture sounders, aboard high altitude aircraft has been collecting data throughout many field campaigns. An advanced retrieval algorithm developed with NAST-I is now applied to satellite data collected with the Atmospheric InfraRed Sounder (AIRS) on the Aqua satellite launched on 4 May 2002 and the Infrared Atmospheric Sounding Interferometer (IASI) on the MetOp satellite launched on October 19, 2006. These instruments possess an ultra-spectral resolution, for example, both IASI and NAST-I have ~0.25 cm-1 and a spectral coverage from 645 to 2760 cm-1. The retrieval algorithm with a fast radiative transfer model, including cloud effects, is used for atmospheric profile and cloud parameter retrieval. The physical inversion scheme has been developed, dealing with cloudy as well as cloud-free radiance observed with ultraspectral infrared sounders, to simultaneously retrieve surface, atmospheric thermodynamic, and cloud microphysical parameters. A fast radiative transfer model, which applies to the clouded atmosphere, is used for atmospheric profile and cloud parameter retrieval. A one-dimensional (1-d) variational multi-variable inversion solution is used to improve an iterative background state defined by an eigenvector-regression-retrieval. The solution is iterated in order to account for non-linearity in the 1-d variational solution. It is shown that relatively accurate temperature and moisture retrievals can be achieved below optically thin clouds. For optically thick clouds, accurate temperature and moisture profiles down to cloud top level are obtained. For both optically thin and thick cloud situations, the cloud top height can be retrieved with relatively high accuracy (i.e., error less than 1 km). Retrievals of atmospheric soundings, surface properties, and cloud microphysical properties with the AIRS and IASI observations are obtained and presented. These retrievals are further inter-compared with those obtained from airborne FTS system, such as the NPOESS Airborne Sounder Testbed? Interferometer (NAST I), dedicated dropsondes, radiosondes, and ground based Raman Lidar. The capabilities of satellite ultra-spectral sounder such as the AIRS and IASI are investigated. These advanced satellite ultraspectral infrared instruments are now playing an important role in satellite meteorological observation for numerical weather prediction.

Zhou, Daniel K.↗
NASA NTRS2009

Subspace Iteration Method for Complex Eigenvalue Problems with Nonsymmetric Matrices in Aeroelastic System

Modern airplane design is a multidisciplinary task which combines several disciplines such as structures, aerodynamics, flight controls, and sometimes heat transfer. Historically, analytical and experimental investigations concerning the interaction of the elastic airframe with aerodynamic and in retia loads have been conducted during the design phase to determine the existence of aeroelastic instabilities, so called flutter .With the advent and increased usage of flight control systems, there is also a likelihood of instabilities caused by the interaction of the flight control system and the aeroelastic response of the airplane, known as aeroservoelastic instabilities. An in -house code MPASES (Ref. 1), modified from PASES (Ref. 2), is a general purpose digital computer program for the analysis of the closed-loop stability problem. This program used subroutines given in the International Mathematical and Statistical Library (IMSL) (Ref. 3) to compute all of the real and/or complex conjugate pairs of eigenvalues of the Hessenberg matrix. For high fidelity configuration, these aeroelastic system matrices are large and compute all eigenvalues will be time consuming. A subspace iteration method (Ref. 4) for complex eigenvalues problems with nonsymmetric matrices has been formulated and incorporated into the modified program for aeroservoelastic stability (MPASES code). Subspace iteration method only solve for the lowest p eigenvalues and corresponding eigenvectors for aeroelastic and aeroservoelastic analysis. In general, the selection of p is ranging from 10 for wing flutter analysis to 50 for an entire aircraft flutter analysis. The application of this newly incorporated code is an experiment known as the Aerostructures Test Wing (ATW) which was designed by the National Aeronautic and Space Administration (NASA) Dryden Flight Research Center, Edwards, California to research aeroelastic instabilities. Specifically, this experiment was used to study an instability known as flutter. ATW was a small-scale airplane wing comprised of an airfoil and wing tip boom. This wing was formulated based on a NACA-65A004 airfoil shape with a 3.28 aspect ratio. The wing had a span of 18 inch with root chord length of 13.2 inch and tip chord length of 8.7 inch. The total area of this wing was 197 square inch. The wing tip boom was a 1 inch diameter hollow tube of length 21.5 inch. The total weight of the wing was 2.66 lbs.

Pak, Chan-gi↗
NASA NTRS2010

A General Algorithm for Reusing Krylov Subspace Information. I. Unsteady Navier-Stokes

A general algorithm is developed that reuses available information to accelerate the iterative convergence of linear systems with multiple right-hand sides A x = b (sup i), which are commonly encountered in steady or unsteady simulations of nonlinear equations. The algorithm is based on the classical GMRES algorithm with eigenvector enrichment but also includes a Galerkin projection preprocessing step and several novel Krylov subspace reuse strategies. The new approach is applied to a set of test problems, including an unsteady turbulent airfoil, and is shown in some cases to provide significant improvement in computational efficiency relative to baseline approaches.

Carpenter, Mark H.↗
NASA NTRS2006

Using Quasiparticle Poisoning To Detect Photons

According to a proposal, a phenomenon associated with excitation of quasiparticles in certain superconducting quantum devices would be exploited as a means of detecting photons with exquisite sensitivity. The phenomenon could also be exploited to perform medium-resolution spectroscopy. The proposal was inspired by the observation that Coulomb blockade devices upon which some quantum logic gates are based are extremely sensitive to quasiparticles excited above the superconducting gaps in their leads. The presence of quasiparticles in the leads can be easily detected via the charge states. If quasiparticles could be generated in the leads by absorption of photons, then the devices could be used as very sensitive detectors of electromagnetic radiation over the spectral range from x-rays to submillimeter waves. The devices in question are single-Cooper-pair boxes (SCBs), which are mesoscopic superconducting devices developed for quantum computing. An SCB consists of a small superconducting island connected to a reservoir via a small tunnel junction and connected to a voltage source through a gate capacitor. An SCB is an artificial two-level quantum system, the Hamiltonian of which can be controlled by the gate voltage. One measures the expected value of the charge of the eigenvectors of this quantum system by use of a radio-frequency single-electron transistor. A plot of this expected value of charge as a function of gate voltage resembles a staircase that, in the ideal case, consists of steps of height 2 e (where e is the charge of one electron). Experiments have shown that depending on the parameters of the device, quasiparticles in the form of "broken" Cooper pairs present in the reservoir can tunnel to the island, giving rise to steps of 1 e. This effect is sometimes called "poisoning." Simulations have shown that an extremely small average number of quasiparticles can generate a 1-e periodic signal. In a device according to the proposal, this poisoning would be turned to advantage. Depending on the wavelength, an antenna or other component would be used to couple radiation into the reservoir, wherein the absorption of photons would break Cooper pairs, thereby creating quasiparticles that, in turn, would tunnel to the island, creating a 1-e signal. On the basis of conservative estimates of device parameters derived from experimental data and computational simulations that fit the data, it has been estimated that the noise equivalent power of a device according to the proposal could be as low as 6 10(exp -22) W/Hz(exp 1/2). It has also been estimated that the spectroscopic resolution (photon energy divided by increment of photon energy) of such a device in visible light would exceed 100.

Echternach, Pierre↗
NASA NTRS2010

A Spectral Lyapunov Function for Exponentially Stable LTV Systems

This paper presents the formulation of a Lyapunov function for an exponentially stable linear timevarying (LTV) system using a well-defined PD-spectrum and the associated PD-eigenvectors. It provides a bridge between the first and second methods of Lyapunov for stability assessment, and will find significant applications in the analysis and control law design for LTV systems and linearizable nonlinear time-varying systems.

Zhu, J. Jim↗
NASA NTRS2011

Canopy Spectral Invariants. Part 1: A New Concept in Remote Sensing of Vegetation

The concept of canopy spectral invariants expresses the observation that simple algebraic combinations of leaf and canopy spectral reflectance become wavelength independent and determine two canopy structure specific variables the recollision and escape probabilities. These variables specify an accurate relationship between the spectral response of a vegetation canopy to incident solar radiation at the leaf and the canopy scale. They are sensitive to important structural features of the canopy such as forest cover, tree density, leaf area index, crown geometry, forest type and stand age. This paper presents the mathematical basis of the concept which is linked to eigenvalues and eigenvectors of the three-dimensional radiative transfer equation.

Knyazikhin, Yuri↗
NASA NTRS2010

Hyperspectrally-Resolved Surface Emissivity Derived Under Optically Thin Clouds

Surface spectral emissivity derived from current and future satellites can and will reveal critical information about the Earth s ecosystem and land surface type properties, which can be utilized as a means of long-term monitoring of global environment and climate change. Hyperspectrally-resolved surface emissivities are derived with an algorithm utilizes a combined fast radiative transfer model (RTM) with a molecular RTM and a cloud RTM accounting for both atmospheric absorption and cloud absorption/scattering. Clouds are automatically detected and cloud microphysical parameters are retrieved; and emissivity is retrieved under clear and optically thin cloud conditions. This technique separates surface emissivity from skin temperature by representing the emissivity spectrum with eigenvectors derived from a laboratory measured emissivity database; in other words, using the constraint as a means for the emissivity to vary smoothly across atmospheric absorption lines. Here we present the emissivity derived under optically thin clouds in comparison with that under clear conditions.

Zhou, Daniel K.↗
NASA NTRS2012

The High-Resolution Wave-Propagation Method Applied to Meso- and Micro-Scale Flows

The high-resolution wave-propagation method for computing the nonhydrostatic atmospheric flows on meso- and micro-scales is described. The design and implementation of the Riemann solver used for computing the Godunov fluxes is discussed in detail. The method uses a flux-based wave decomposition in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The two advantages of the technique are: 1) the need for an explicit definition of the Roe matrix is eliminated and, 2) the inclusion of source term due to gravity does not result in discretization errors. The resulting flow solver is conservative and able to resolve regions of large gradients without introducing dispersion errors. The methodology is validated against exact analytical solutions and benchmark cases for non-hydrostatic atmospheric flows.

Ahmad, Nashat N.↗
NASA NTRS2012

An Algorithm for Detection of Ground and Canopy Cover in Micropulse Photon-Counting Lidar Altimeter Data in Preparation of the ICESat-2 Mission

The Ice, Cloud and Land Elevation Satellite-II (ICESat-2) mission has been selected by NASA as a Decadal Survey mission, to be launched in 2016. Mission objectives are to measure land ice elevation, sea ice freeboard/ thickness and changes in these variables and to collect measurements over vegetation that will facilitate determination of canopy height, with an accuracy that will allow prediction of future environmental changes and estimation of sea-level rise. The importance of the ICESat-2 project in estimation of biomass and carbon levels has increased substantially, following the recent cancellation of all other planned NASA missions with vegetation-surveying lidars. Two innovative components will characterize the ICESat-2 lidar: (1) Collection of elevation data by a multi-beam system and (2) application of micropulse lidar (photon counting) technology. A micropulse photon-counting altimeter yields clouds of discrete points, which result from returns of individual photons, and hence new data analysis techniques are required for elevation determination and association of returned points to reflectors of interest including canopy and ground in forested areas. The objective of this paper is to derive and validate an algorithm that allows detection of ground under dense canopy and identification of ground and canopy levels in simulated ICESat-2-type data. Data are based on airborne observations with a Sigma Space micropulse lidar and vary with respect to signal strength, noise levels, photon sampling options and other properties. A mathematical algorithm is developed, using spatial statistical and discrete mathematical concepts, including radial basis functions, density measures, geometrical anisotropy, eigenvectors and geostatistical classification parameters and hyperparameters. Validation shows that the algorithm works very well and that ground and canopy elevation, and hence canopy height, can be expected to be observable with a high accuracy during the ICESat-2 mission. A result relevant for instrument design is that even the two weaker beam classes considered can be expected to yield useful results for vegetation measurements (93.01-99.57% correctly selected points for a beam with expected return of 0.93 mean signals per shot (msp9) and 72.85% - 98.68% for 0.48 msp (msp4)). Resampling options affect results more than noise levels. The algorithm derived here is generally applicable for analysis of micropulse lidar altimeter data collected over forested areas as well as other surfaces, including land ice, sea ice and land surfaces.

Herzfeld, Ute C.↗
NASA NTRS2013

A Coupled Approach for Structural Damage Detection with Incomplete Measurements

This historical work couples model order reduction, damage detection, dynamic residual/mode shape expansion, and damage extent estimation to overcome the incomplete measurements problem by using an appropriate undamaged structural model. A contribution of this work is the development of a process to estimate the full dynamic residuals using the columns of a spring connectivity matrix obtained by disassembling the structural stiffness matrix. Another contribution is the extension of an eigenvector filtering procedure to produce full-order mode shapes that more closely match the measured active partition of the mode shapes using a set of modified Ritz vectors. The full dynamic residuals and full mode shapes are used as inputs to the minimum rank perturbation theory to provide an estimate of damage location and extent. The issues associated with this process are also discussed as drivers of near-term development activities to understand and improve this approach.

James, George↗
NASA NTRS2013

Quantitative Comparison of the Variability in Observed and Simulated Shortwave Reflectance

The Climate Absolute Radiance and Refractivity Observatory (CLARREO) is a climate observation system that has been designed to monitor the Earth's climate with unprecedented absolute radiometric accuracy and SI traceability. Climate Observation System Simulation Experiments (OSSEs) have been generated to simulate CLARREO hyperspectral shortwave imager measurements to help define the measurement characteristics needed for CLARREO to achieve its objectives. To evaluate how well the OSSE-simulated reflectance spectra reproduce the Earth s climate variability at the beginning of the 21st century, we compared the variability of the OSSE reflectance spectra to that of the reflectance spectra measured by the Scanning Imaging Absorption Spectrometer for Atmospheric Cartography (SCIAMACHY). Principal component analysis (PCA) is a multivariate decomposition technique used to represent and study the variability of hyperspectral radiation measurements. Using PCA, between 99.7%and 99.9%of the total variance the OSSE and SCIAMACHY data sets can be explained by subspaces defined by six principal components (PCs). To quantify how much information is shared between the simulated and observed data sets, we spectrally decomposed the intersection of the two data set subspaces. The results from four cases in 2004 showed that the two data sets share eight (January and October) and seven (April and July) dimensions, which correspond to about 99.9% of the total SCIAMACHY variance for each month. The spectral nature of these shared spaces, understood by examining the transformed eigenvectors calculated from the subspace intersections, exhibit similar physical characteristics to the original PCs calculated from each data set, such as water vapor absorption, vegetation reflectance, and cloud reflectance.

Roberts, Yolanda, L.↗
NASA NTRS2014

In-Flight Aeroelastic Stability of the Thermal Protection System on the NASA HIAD, Part I: Linear Theory

Conical shell theory and piston theory aerodynamics are used to study the aeroelastic stability of the thermal protection system (TPS) on the NASA Hypersonic Inflatable Aerodynamic Decelerator (HIAD). Structural models of the TPS consist of single or multiple orthotropic conical shell systems resting on several circumferential linear elastic supports. The shells in each model may have pinned (simply-supported) or elastically-supported edges. The Lagrangian is formulated in terms of the generalized coordinates for all displacements and the Rayleigh-Ritz method is used to derive the equations of motion. The natural modes of vibration and aeroelastic stability boundaries are found by calculating the eigenvalues and eigenvectors of a large coefficient matrix. When the in-flight configuration of the TPS is approximated as a single shell without elastic supports, asymmetric flutter in many circumferential waves is observed. When the elastic supports are included, the shell flutters symmetrically in zero circumferential waves. Structural damping is found to be important in this case. Aeroelastic models that consider the individual TPS layers as separate shells tend to flutter asymmetrically at high dynamic pressures relative to the single shell models. Several parameter studies also examine the effects of tension, orthotropicity, and elastic support stiffness.

Goldman, Benjamin D.↗
NASA NTRS2014

Algorithm for Detection of Ground and Canopy Cover in Micropulse Photon-Counting Lidar Altimeter Data in Preparation for the ICESat-2 Mission

NASA's Ice, Cloud and Land Elevation Satellite-II (ICESat-2) mission is a decadal survey mission (2016 launch). The mission objectives are to measure land ice elevation, sea ice freeboard, and changes in these variables, as well as to collect measurements over vegetation to facilitate canopy height determination. Two innovative components will characterize the ICESat-2 lidar: 1) collection of elevation data by a multibeam system and 2) application of micropulse lidar (photon-counting) technology. A photon-counting altimeter yields clouds of discrete points, resulting from returns of individual photons, and hence new data analysis techniques are required for elevation determination and association of the returned points to reflectors of interest. The objective of this paper is to derive an algorithm that allows detection of ground under dense canopy and identification of ground and canopy levels in simulated ICESat-2 data, based on airborne observations with a Sigma Space micropulse lidar. The mathematical algorithm uses spatial statistical and discrete mathematical concepts, including radial basis functions, density measures, geometrical anisotropy, eigenvectors, and geostatistical classification parameters and hyperparameters. Validation shows that ground and canopy elevation, and hence canopy height, can be expected to be observable with high accuracy by ICESat-2 for all expected beam energies considered for instrument design (93.01%-99.57% correctly selected points for a beam with expected return of 0.93 mean signals per shot (msp), and 72.85%-98.68% for 0.48 msp). The algorithm derived here is generally applicable for elevation determination from photoncounting lidar altimeter data collected over forested areas, land ice, sea ice, and land surfaces, as well as for cloud detection.

Algorithms↗
NASA NTRS2018

Assessment and Verification of SLS Block 1-B Exploration Upper Stage State and Stage Disposal Performance

One of the SLS Navigation System's key performance requirements is a constraint on the payload system's delta-v allocation to correct for insertion errors due to vehicle state uncertainty at payload separation. The SLS navigation team has developed a Delta-Delta-V analysis approach to assess the effect on trajectory correction maneuver (TCM) design needed to correct for navigation errors. This approach differs from traditional covariance analysis based methods and makes no assumptions with regard to the propagation of the state dynamics. This allows for consideration of non-linearity in the propagation of state uncertainties. The Delta-Delta-V analysis approach re-optimizes perturbed SLS mission trajectories by varying key mission states in accordance with an assumed state error. The state error is developed from detailed vehicle 6-DOF Monte Carlo analysis or generated using covariance analysis. These perturbed trajectories are compared to a nominal trajectory to determine necessary TCM design. To implement this analysis approach, a tool set was developed which combines the functionality of a 3-DOF trajectory optimization tool, Copernicus, and a detailed 6-DOF vehicle simulation tool, Marshall Aerospace Vehicle Representation in C (MAVERIC). In addition to delta-v allocation constraints on SLS navigation performance, SLS mission requirement dictate successful upper stage disposal. Due to engine and propellant constraints, the SLS Exploration Upper Stage (EUS) must dispose into heliocentric space by means of a lunar fly-by maneuver. As with payload delta-v allocation, upper stage disposal maneuvers must place the EUS on a trajectory that maximizes the probability of achieving a heliocentric orbit post Lunar fly-by considering all sources of vehicle state uncertainty prior to the maneuver. To ensure disposal, the SLS navigation team has developed an analysis approach to derive optimal disposal guidance targets. This approach maximizes the state error covariance prior to the maneuver to develop and re-optimize a nominal disposal maneuver (DM) target that, if achieved, would maximize the potential for successful upper stage disposal. For EUS disposal analysis, a set of two tools was developed. The first considers only the nominal pre-disposal maneuver state, vehicle constraints, and an a priori estimate of the state error covariance. In the analysis, the optimal nominal disposal target is determined. This is performed by re-formulating the trajectory optimization to consider constraints on the eigenvectors of the error ellipse applied to the nominal trajectory. A bisection search methodology is implemented in the tool to refine these dispersions resulting in the maximum dispersion feasible for successful disposal via lunar fly-by. Success is defined based on the probability that the vehicle will not impact the lunar surface and will achieve a characteristic energy (C3) relative to the Earth such that it is no longer in the Earth-Moon system. The second tool propagates post-disposal maneuver states to determine the success of disposal for provided trajectory achieved states. This is performed using the optimized nominal target within the 6-DOF vehicle simulation. This paper will discuss the application of the Delta-Delta-V analysis approach for performance evaluation as well as trajectory re-optimization so as to demonstrate the system's capability in meeting performance constraints. Additionally, further discussion of the implementation of assessing disposal analysis will be provided.

Patrick, Sean↗
NASA NTRS2018

High-resolution Wave Propagation Method for Stratified Flows

The implementation of the multidimensional f-waves Riemann solver for the time-dependent, three-dimensional, nonhydrostatic, meso- and microscale atmospheric flows is described in detail. The Riemann solver employs flux-based wave decomposition (f-waves) for the calculation of Godunov fluxes in which the flux differences are written directly as the linear combination of the right eigenvectors of the hyperbolic system. The scheme incorporates the source term due to gravity without introducing discretization errors which is an important property in the context of atmospheric flows. The resulting flow solver is conservative, accurate, stable, and well-balanced. The implementation of the solver is evaluated using benchmark test cases for atmospheric dynamics.

Riemann problem↗
NASA NTRS2019

A Multi-Blade Model for Heliogyro Solar Sail Structural Dynamics Analysis

An analytical model is derived to study the structural dynamic stability behavior for the free-flying heliogyro solar sail consisting of a finite set of symmetric or evenly distributed thin blades on a flat surface. Key properties of the flutter instability are described in terms of the relationship among the eigenvalues and eigenvectors associated with a flutter instability frequency. Various simulation cases for an idealized single blade, fixed rotational speed heliogyro model, and a generalized multi-bladed, freely spinning heliogyro model are presented to show how the flutter instability frequencies change as a function of the solar radiation pressure and the size of the dynamic model. Convergence of the flutter instability frequency versus the system order is demonstrated.

Juang, Jer-Nan↗