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A Roadmap to Interstellar Flight

In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration that have shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with the Voyager 1 spacecraft launched in 1977 finally leaving the solar system after 37 years of flight at a speed of 17 km/s or less than 0.006% the speed of light. As remarkable as this is we will never reach even the nearest stars with our current propulsion technology in even 10 millennium. We have to radically rethink our strategy or give up our dreams of reaching the stars, or wait for technology that does not currently exist. While we all dream of human spaceflight to the stars in a way romanticized in books and movies, it is not within our power to do so, nor it is clear that this is the path we should choose. We posit a technological path forward, that while not simple, it is within our technological reach. We propose a roadmap to a program that will lead to sending relativistic probes to the nearest stars and will open up a vast array of possibilities of flight both within our solar system and far beyond. Spacecraft from gram level complete spacecraft on a wafer ("wafersats") that reach more than _ c and reach the nearest star in 20 years to spacecraft with masses more than 105 kg (100 tons) that can reach speeds of greater than 1000 km/s. These systems can be propelled to speeds currently unimaginable with existing propulsion technologies. To do so requires a fundamental change in our thinking of both propulsion and in many cases what a spacecraft is. In addition to larger spacecraft, some capable of transporting humans, we consider functional spacecraft on a wafer, including integrated optical communications, imaging systems, photon thrusters, power and sensors combined with directed energy propulsion. The costs can be amortized over a very large number of missions beyond relativistic spacecraft as such planetary defense, beamed energy for distant spacecraft, sending power back to Earth, stand-off composition analysis of solar system targets, long range laser communications, SETI searches and even terra forming. The human factor of exploring the nearest stars and exo-planets would be a profound voyage for humanity, one whose non-scientific implications would be enormous. It is time to begin this inevitable journey far beyond our home.

Interstellar Flight↗

A Roadmap to Interstellar Flight

In the nearly 60 years of spaceflight we have accomplished wonderful feats of exploration that have shown the incredible spirit of the human drive to explore and understand our universe. Yet in those 60 years we have barely left our solar system with the Voyager 1 spacecraft launched in 1977 finally leaving the solar system after 37 years of flight at a speed of 17 km/s or less than 0.006% the speed of light. As remarkable as this, to reach even the nearest stars with our current propulsion technology will take 100 millennium. We have to radically rethink our strategy or give up our dreams of reaching the stars, or wait for technology that does not currently exist. While we all dream of human spaceflight to the stars in a way romanticized in books and movies, it is not within our power to do so, nor it is clear that this is the path we should choose. We posit a path forward, that while not simple, it is within our technological reach. We propose a roadmap to a program that will lead to sending relativistic probes to the nearest stars and will open up a vast array of possibilities of flight both within our solar system and far beyond. Spacecraft from gram level complete spacecraft on a wafer (“wafersats”) that reach more than ¼ c and reach the nearest star in 20 years to spacecraft with masses more than 105 kg (100 tons) that can reach speeds of greater than 1000 km/s. These systems can be propelled to speeds currently unimaginable with existing propulsion technologies. To do so requires a fundamental change in our thinking of both propulsion and in many cases what a spacecraft is. In addition to larger spacecraft, some capable of transporting humans, we consider functional spacecraft on a wafer, including integrated optical communications, imaging systems, photon thrusters, power and sensors combined with directed energy propulsion. The costs can be amortized over a very large number of missions beyond relativistic spacecraft as such planetary defense, beamed energy for distant spacecraft, sending power back to Earth, stand-off composition analysis of solar system targets, long range laser communications, SETI searches and even terra forming. The human factor of exploring the nearest stars and exo-planets would be a profound voyage for humanity, one whose non-scientific implications would be enormous. It is time to begin this inevitable journey far beyond our home.

Lubin, Philip↗

Dissemination of Global Flood Severity and Surface Water Mapping using Remote Sensing Data to Global Stakeholders

Flooding is a natural event that occurs frequently with high severity worldwide, responsible for significant societal and economic impacts. Disaster managers face significant challenges managing essential information for preparedness, response, and recovery efforts. The development of an open access, global flood alerting system for effective identification of flood impacted areas, classification of potential impacts, and the formulation of effective emergency response measures requires the incorporation of a wide variety of flood models and remote sensing data sources from multiple platforms. NASA is currently funding projects focused on flood forecasting, post-event flood mapping, flood depth estimation and pre-event flood severity estimation using Earth observation (EO) datasets and derived flood products. A new initiative in the Disasters Program is underway to disseminate flood products from different hydrologic models and sensors to global stakeholders via Pacific Disaster Center’s DisasterAWARE®, NASA’s Disasters Mapping Portal and potentially other mechanisms. This initiative focuses on improving response capacity and use of EO products in near real-time by a broader community for resource planning in case of extreme events. As part of this initiative, we have deployed Model of Models (MoM) – an open-source ensemble approach, that integrates outputs from hydrologic models and EO data from optical imagery to assess flood severity daily at sub-watershed level globally. The MoM output is integrated with the incident event system of DisasterAWARE to generate flood severity risk and flood impact boundaries, which are disseminated via the DisasterAWARE platform to different stakeholders globally for decision-making and response efforts. The next step will focus on using MoM outputs to estimate flood depth and extent mapping using high-resolution Synthetic Aperture Radar imagery, impact assessment using optical imagery and population datasets, and damage estimation using critical infrastructure datasets, which would be disseminated via DisasterAWARE to decision-makers, emergency managers and first responders around the world.

flood↗

Eleven Countries, an Integrated Spacecraft: the Story of International Collaboration that Built the Orion Spacecraft and Powered the Success of the Artemis I Mission

The quest to return humans to the Moon in the next step towards humanity's exploration of space is more alive than ever. After a great deal of achievements, failures, and lessons learned, the Artemis I mission set o to the Moon on November 16, 2022, with the goal of testing a new rocket, the Space Launch System, and a new spacecraft, Orion: designed, assembled, and tested across two continents, and 11 countries. Behind this mission, decades of experience with the International Space Station, Autonomous Transfer Vehicle operations, and many other program collaborations built the know-how on how to succeed together in the toughest environment | deep space. The Artemis I mission proved to be an incredible success, meeting 161 total mission objectives, including 21 developed during the flight based on outperforming spacecraft. It was also a case-study in international collaboration, given that ESA, NASA, and industry partners Airbus and Lockheed Martin for the first time had to design, build, test, and fly a fully integrated human-rated spacecraft, with most critical functions dependent and interconnected across U.S. and European systems. The U.S.-built Orion Crew Module and Crew Module Adapter and European-built European Service Module (ESM) shared critical interfaces and commodities, from propulsion, avionics, active/passive thermal, electrical power generation, storage and distribution to the software that managed it all. In this paper, we will describe relevant aspects of the integrated spacecraft design, providing context for the challenges that the team faced in all phases required to get Orion ready to fly, and provide a direct account of how the joint team formed, trained, and supported the operations of the successful Artemis I mission. We will also explore the evolution of the partnerships, given that these allow a multi-national e ort to sustain the program production, share costs, leverage a broader base of engineering expertise, and build more diverse capabilities over the long haul to support the Artemis goals and objectives. Lastly, we will cover critical lessons learned and how the Orion Program has implemented these in preparation of the next Artemis missions to repeat the success of Artemis I. The purpose of this paper is to document knowledge we gained and lessons we learned through the development of an integrated Orion spacecraft, since it is imperative we build on this now, at the dawn of the Artemis Program, an international endeavor to push human space exploration.

Deep Space Exploration↗

Dynamical Chaos in the Wisdom-Holman Integrator: Origins and Solutions

We examine the nonlinear stability of the Wisdom-Holman (WH) symplectic mapping applied to the integration of perturbed, highly eccentric (e-0.9) two-body orbits. We find that the method is unstable and introduces artificial chaos into the computed trajectories for this class of problems, unless the step size chosen 1s small enough that PeriaPse is always resolved, in which case the method is generically stable. This 'radial orbit instability' persists even for weakly perturbed systems. Using the Stark problem as a fiducial test case, we investigate the dynamical origin of this instability and argue that the numerical chaos results from the overlap of step-size resonances; interestingly, for the Stark-problem many of these resonances appear to be absolutely stable. We similarly examine the robustness of several alternative integration methods: a time-regularized version of the WH mapping suggested by Mikkola; the potential-splitting (PS) method of Duncan, Levison, Lee; and two original methods incorporating approximations based on Stark motion instead of Keplerian motion. The two fixed point problem and a related, more general problem are used to conduct a comparative test of the various methods for several types of motion. Among the algorithms tested, the time-transformed WH mapping is clearly the most efficient and stable method of integrating eccentric, nearly Keplerian orbits in the absence of close encounters. For test particles subject to both high eccentricities and very close encounters, we find an enhanced version of the PS method-incorporating time regularization, force-center switching, and an improved kernel function-to be both economical and highly versatile. We conclude that Stark-based methods are of marginal utility in N-body type integrations. Additional implications for the symplectic integration of N-body systems are discussed.

Rauch, Kevin P.↗

Novel Integrated Radial and Axial Magnetic Bearing

Typically, fully active magnetically suspended systems require one axial and two radial magnetic bearings. Combining radial and axial functions into a single device allows for more compact and elegant packaging. Furthermore, in the case of high-speed devices such as energy storage flywheels, it is beneficial to minimize shaft length to keep rotor mode frequencies as high as possible. Attempts have been made to combine radial and axial functionality, but with certain drawbacks. One approach requires magnetic control flux to flow through a bias magnet reducing control effectiveness, thus resulting in increased resistive losses. This approach also requires axial force producing magnetic flux to flow in a direction into the rotor laminate that is undesirable for minimizing eddy-current losses resulting in rotational losses. Another approach applies a conical rotor shape to what otherwise would be a radial heteropolar magnetic bearing configuration. However, positional non-linear effects are introduced with this scheme and the same windings are used for bias, radial, and axial control adding complexity to the controller and electronics. For this approach, the amount of axial capability must be limited. It would be desirable for an integrated radial and axial magnetic bearing to have the following characteristics, separate inputs for radial and axial control for electronics and control simplicity, all magnetic control fluxes should only flow through their respective air gaps and should not flow through any bias magnets for minimal resistive losses, be of a homopolar design to minimize rotational losses, position related non-linear effects should be minimized, and dependent upon the design parameters, be able to achieve any radial/axial force or power ratio as desired. The integrated radial and axial magnetic bearing described in this paper exhibits all these characteristics. Magnetic circuit design, design equations, and analysis results will be presented.

Blumenstock, Kenneth A.↗

Novel Integration Radial and Axial Magnetic Bearing

Typically, fully active magnetically suspended systems require one axial and two radial magnetic bearings. Combining radial and axial functions into a single device allows for more compact and elegant packaging. Furthermore, in the case of high-speed devices such as energy storage flywheels, it is beneficial to minimize shaft length to keep rotor mode frequencies as high as possible. Attempts have been made to combine radial and axial functionality, but with certain drawbacks. One approach requires magnetic control flux to flow through a bias magnet reducing control effectiveness, thus resulting in increased resistive losses. This approach also requires axial force producing magnetic flux to flow in a direction into the rotor laminate that is undesirable for minimizing eddy-current losses resulting in rotational losses. Another approach applies a conical rotor shape to what otherwise would be a radial heteropolar magnetic bearing configuration. However, positional non-linear effects are introduced with this scheme and the same windings are used for bias, radial, and axial control adding complexity to the controller and electronics. For this approach, the amount of axial capability must be limited. It would be desirable for an integrated radial and axial magnetic bearing to have the following characteristics; separate inputs for radial and axial control for electronics and control simplicity, all magnetic control fluxes should only flow through their respective air gaps and should not flow through any bias magnets for minimal resistive losses, be of a homopolar design to minimize rotational losses, position related non-linear effects should be minimized, and dependent upon the design parameters, be able to achieve any radial/axial force or power ratio as desired. The integrated radial and axial magnetic bearing described in this paper exhibits all these characteristics. Magnetic circuit design, design equations, and magnetic field modeling results will be presented.

Blumenstock, Kenneth↗

Radiation of Sound From a Point Source in a Short Duct

It is the purpose of this paper to provide, in relatively brief form, a summary of a boundary integral approach that has been developed for calculating the sound field radiated from short ducts in uniform axial motion. The method was devised primarily to study sound generated by rotating sources in the duct, as is of current practical interest in connection with ducted-fan aircraft engines. Detailed background on the fan source application of the technique can be found. The author has not previously discussed the simpler monopole source case of interest in these proceedings. However, readers desiring a more detailed treatment than will be included here should have little difficulty in extracting it from those references after making the relatively minor modifications necessary to adapt the analyses to the monopole case. It should be noted that other authors have also considered radiation from short ducts. In particular, readers may find the finite-element approach of Eversman of interest as well as the alternate boundary integral method treatments of Martinez and of Dunn, Tweed, and Farassat.

Myers, M. K.↗

Multi-Scale Hydrometeorological Modeling, Land Data Assimilation and Parameter Estimation with the Land Information System

The Land Information System (LIS; http://lis.gsfc.nasa.gov; Kumar et al., 2006; Peters- Lidard et al.,2007) is a flexible land surface modeling framework that has been developed with the goal of integrating satellite- and ground-based observational data products and advanced land surface modeling techniques to produce optimal fields of land surface states and fluxes. As such, LIS represents a step towards the next generation land component of an integrated Earth system model. In recognition of LIS object-oriented software design, use and impact in the land surface and hydrometeorological modeling community, the LIS software was selected ase co-winner of NASA's 2005 Software of the Year award. LIS facilitates the integration of observations from Earth-observing systems and predictions and forecasts from Earth System and Earth science models into the decision-making processes of partnering agency and national organizations. Due to its flexible software design, LIS can serve both as a Problem Solving Environment (PSE) for hydrologic research to enable accurate global water and energy cycle predictions, and as a Decision Support System (DSS) to generate useful information for application areas including disaster management, water resources management, agricultural management, numerical weather prediction, air quality and military mobility assessment. LIS has evolved from two earlier efforts North American Land Data Assimilation System (NLDAS; Mitchell et al. 2004) and Global Land Data Assimilation System (GLDAS; Rodell al. 2004) that focused primarily on improving numerical weather prediction skills by improving the characterization of the land surface conditions. Both of GLDAS and NLDAS now use specific configurations of the LIS software in their current implementations. In addition, LIS was recently transitioned into operations at the US Air Force Weather Agency (AFWA) to ultimately replace their Agricultural Meteorology (AGRMET) system, and is also used routinely by NOAA's National Centers for Environmental Prediction (NCEP)/Environmental Modeling Center (EMC) for their land data assimilation systems to support weather and climate modeling. LIS not only consolidates the capabilities of these two systems, but also enables a much larger variety of configurations with respect to horizontal spatial resolution, input datasets and choice of land surface model through "plugins,". As described in Kumar et al., 2007, and demonstrated in Case et al., 2008, and Santanello et al., 2009, LIS has been coupled to the Weather Research and Forecasting (WRF) model to support studies of land-atmosphere coupling the enabling ensembles of land surface states to be tested against multiple representations of the atmospheric boundary layer. LIS has also been demonstrated for parameter estimation as described in Peters-Lidard et al. (2008) and Santanello et al. (2007), who showed that the use of sequential remotely sensed soil moisture products can be used to derive soil hydraulic and texture properties given a sufficient dynamic range in the soil moisture retrievals and accurate precipitation inputs. LIS has also recently been demonstrated for multi-model data assimilation (Kumar et al., 2008) using an Ensemble Kalman Filter for sequential assimilation of soil moisture, snow, and temperature. Ongoing work has demonstrated the value of bias correction as part of the filter, and also that of joint calibration and assimilation. Examples and case studies demonstrating the capabilities and impacts of LIS for hydrometeoroogical modeling, assimilation and parameter estimation will be presented as advancements towards the next generation of integrated observation and modeling systems.

Peters-Lidard, Christa D.↗

High-Frequency Excitation of a Plane Wake

In the early 1990's, Glezer and his co-workers at Georgia Tech made a startling discovery. They found that forcing at frequencies too high to directly affect the production scales led to a dramatic alteration in the development of a turbulent shear layer. An experimental study of this phenomenon is presented in Wiltse and Glezer. They used piezoelectric actuators located near the jet exit plane to force the shear layers of a square low-speed jet. The actuators were driven at a high frequency in the Kolmogorov inertial subrange, much higher than the frequencies associated with the large-scale motion (where the turbulent energy is produced and located) but much lower than those associated with the Kolmogorov scale (where the turbulent energy is dissipated). Measurements of the shear-layer turbulence showed that direct excitation of small-scale motion by high-frequency forcing led to an increase in the turbulent dissipation of more than an order of magnitude in the initial region of the shear layer! The turbulent dissipation gradually decreased with downstream distance but remained above the corresponding level for the unforced flow at all locations examined. The high-frequency forcing increased the turbulent kinetic energy in the initial region near the actuators, but the kinetic energy decreased quite rapidly with downstream distance, dropping to levels that were a small fraction of the level for the unforced case. Perhaps most importantly from the present standpoint, the high-frequency forcing significantly decreased the energy in the large-scale motion, increasingly so with downstream distance. Wiltse and Glezer interpreted this behavior as an enhanced transfer of energy from the large scales to the small scales. The initial work by Wiltse and Glezer has expanded into other applications. To explore the potential of high-frequency forcing for active acoustic suppression, in 1998 the first author proposed a set of experiments involving an edge tone shear layer and an open cavity flow. This work was funded by the US Air Force Research Laboratory, and the experiments were developed and executed at Boeing by Raman and Kibens. These experiments involved high-frequency forcing applied to low-speed flows using wedge piezo actuators and powered resonance tubes. The system is simple, open loop, compact, potentially requires little power, and is easily integrated. Dramatic results, such as reductions of 20 dB in spectral peaks and 5-8 dB in overall levels across the entire acoustic spectrum, were obtained in some cases. Sample results are presented. Following this success in low-speed flows, an international cooperative program continuing this work involved transonic experiments in a mid-size facility in the United Kingdom. Similar reductions in noise level were obtained in these transonic experiments. Discussion of this work is given in Raman et at. and Stanek, Raman, Kibens, and Ross. Other experiments at Georgia Tech have shown significant potential of high-frequency forcing in controlling reaction rates in chemically reacting flows.

Cain, Alan B.↗

Environmental Control and Life Support (ECLS) Integrated Roadmap Development

This white paper documents a roadmap for development of Environmental Control and Life Support (ECLS) Systems (ECLSS) capabilities required to enable beyond-Low Earth Orbit (LEO) Exploration missions. In many cases, the execution of this Exploration-based roadmap will directly benefit International Space Station (ISS) operational capability by resolving known issues and/or improving overall system reliability. In addition, many of the resulting products will be applicable across multiple Exploration elements such as Multi-Purpose Crew Vehicle (MPCV), Multi-Mission Space Exploration Vehicle (MMSEV), Deep Space Habitat (DSH), and Landers. Within the ECLS community, this white paper will be a unifying tool that will improve coordination of resources, common hardware, and technologies. It will help to align efforts to focus on the highest priority needs that will produce life support systems for future human exploration missions that will simply run in the background, requiring minimal crew interaction.

Metcalf, Jordan L.↗

Formal Methods in Air Traffic Management: The Case of Unmanned Aircraft Systems

As the technological and operational capabilities of unmanned aircraft systems (UAS) continue to grow, so too does the need to introduce these systems into civil airspace. Unmanned Aircraft Systems Integration in the National Airspace System is a NASA research project that addresses the integration of civil UAS into non-segregated airspace operations. One of the major challenges of this integration is the lack of an onboard pilot to comply with the legal requirement that pilots see and avoid other aircraft. The need to provide an equivalent to this requirement for UAS has motivated the development of a detect and avoid (DAA) capability to provide the appropriate situational awareness and maneuver guidance in avoiding and remaining well clear of traffic aircraft. Formal methods has played a fundamental role in the development of this capability. This talk reports on the formal methods work conducted under NASA's Safe Autonomous System Operations project in support of the development of DAA for UAS. This work includes specification of low-level and high-level functional requirements, formal verification of algorithms, and rigorous validation of software implementations. The talk also discusses technical challenges in formal methods research in the context of the development and safety analysis of advanced air traffic management concepts.

Munoz, Cesar A.↗

The generation of gravitational waves. I - Weak-field sources

This paper derives and summarizes a 'plug-in-and-grind' formalism for calculating the gravitational waves emitted by any system with weak internal gravitational fields. If the internal fields have negligible influence on the system's motions, the formalism reduces to standard 'linearized theory'. Independent of the effects of gravity on the motions, the formalism reduces to the standard 'quadrupole-moment formalism' if the motions are slow and internal stresses are weak. In the general case, the formalism expresses the radiation in terms of a retarded Green's function for slightly curved spacetime and breaks the Green's function integral into five easily understood pieces: direct radiation, produced directly by the motions of the source; whump radiation, produced by the 'gravitational stresses' of the source; transition radiation, produced by a time-changing time delay ('Shapiro effect') in the propagation of the nonradiative 1/r field of the source; focusing radiation, produced when one portion of the source focuses, in a time-dependent way, the nonradiative field of another portion of the source; and tail radiation, produced by 'back-scatter' of the nonradiative field in regions of focusing.

Thorne, K. S.↗

Sound diffraction around screens and wedges for arbitrary point source locations

A development is presented for the Green's function for a point source in the vicinity of a rigid wedge. The diffraction contributions to the Green's function for arbitrary source and listener location is expressed in a form which can be readily evaluated using the Laguerre technique for numerical integration. The present approach offers the advantages of efficient numerical evaluation and of relatively straightforward reduction to well-known analytical approximations in limiting cases. Comparisons with previously obtained experimental and numerical results obtained by Ambaud and Bergassoli (1972) are presented. The comparison with the experimental results is excellent; the advantages of the present numerical technique, vis a vis that of Ambaud and Bergassoli, are pointed out.

Hadden, W. J., Jr.↗

On the theory of self-focusing of powerful wave beams in nonhomogeneous media

The stationary self-focusing of the Gauss wave beam is considered in a nonhomogeneous medium in the case of local nonlinearity. Equations of the aberrationless approximation for the beam width, the field on the beam axis and the refraction factor are integrated on a computer. Self-focusing in dependence of the nonlinearity level and initial divergence, the dissipation, the length of nonhomogeneity of the dielectric permittivity nondisturbed by a beam, and the diffraction parameter are investigated.

Yerokhin, N. S.↗

High-temperature molten salt thermal energy storage systems for solar applications

Experimental results of compatibility screening studies of 100 salt/containment/thermal conductivity enhancement (TCE) combinations for the high temperature solar thermal application range of 704 deg to 871 C (1300 to 1600 F) are presented. Nine candidate containment/HX alloy materials and two TCE materials were tested with six candidate solar thermal alkali and alkaline earth carbonate storage salts (both reagent and technical grade of each). Compatibility tests were conducted with salt encapsulated in approx. 6.0 inch x 1 inch welded containers of test material from 300 to 3000 hours. Compatibility evaluations were end application oriented, considering the potential 30 year lifetime requirement of solar thermal power plant components. Analyses were based on depth and nature of salt side corrosion of materials, containment alloy thermal aging effects, weld integrity in salt environment, air side containment oxidation, and chemical and physical analyses of the salt. A need for more reliable, and in some cases first time determined thermophysical and transport property data was also identified for molten carbonates in the 704 to 871 C temperature range. In particular, accurate melting point (mp) measurements were performed for Li2CO3 and Na2CO3 while melting point, heat of fusion, and specific heat determinations were conducted on 81.3 weight percent Na2CO3-18.7 weight percent K2CO3 and 52.2 weight percent BaCO3-47.8 weight percent Na2CO3 to support future TES system design and ultimate scale up of solar thermal energy storage (TES) subsystems.

Petri, R. J.↗

The cross section for double Compton scattering

Employing elementary methods in nonrelativistic quantum electrodynamics, the cross section for gamma sub 0 + e yields e + gamma + gamma is computed for arbitrary energy in the spectrum of the outgoing photons. The final result is given, differential in the energy of one of these photons, for the case where the incident photon is unpolarized and has energy E sub 0 much less than mc-squared, a polarization sum and angular integration being performed for the final-state photons. The cross section has a simple algebraic form resulting from contributions from the sum of squared direct and exchange amplitudes; interference terms from these amplitudes do not contribute to the angular-integrated cross section.

Gould, R. J.↗

Computational engine structural analysis

A significant research activity at the NASA Lewis Research Center is the computational simulation of complex multidisciplinary engine structural problems. This simulation is performed using computational engine structural analysis (CESA) which consists of integrated multidisciplinary computer codes in conjunction with computer post-processing for problem-specific application. A variety of the computational simulations of specific cases are described in some detail in this paper. These case studies include: (1) aeroelastic behavior of bladed rotors, (2) high velocity impact of fan blades, (3) blade-loss transient response, (4) rotor/stator/squeeze-film/bearing interaction, (5) blade-fragment/rotor-burst containment, and (6) structural behavior of advanced swept turboprops. These representative case studies are selected to demonstrate the breath of the problems analyzed and the role of the computer including post-processing and graphical display of voluminous output data.

Chamis, C. C.↗