Results for “Dynamical System Scaling” — Page 12

NASA NTRS2011

The Impact of Microphysical Schemes on Hurricane Intensity and Track

During the past decade, both research and operational numerical weather prediction models [e.g. the Weather Research and Forecasting Model (WRF)] have started using more complex microphysical schemes originally developed for high-resolution cloud resolving models (CRMs) with 1-2 km or less horizontal resolutions. WRF is a next-generation meso-scale forecast model and assimilation system. It incorporates a modern software framework, advanced dynamics, numerics and data assimilation techniques, a multiple moveable nesting capability, and improved physical packages. WRF can be used for a wide range of applications, from idealized research to operational forecasting, with an emphasis on horizontal grid sizes in the range of 1-10 km. The current WRF includes several different microphysics options. At NASA Goddard, four different cloud microphysics options have been implemented into WRF. The performance of these schemes is compared to those of the other microphysics schemes available in WRF for an Atlantic hurricane case (Katrina). In addition, a brief review of previous modeling studies on the impact of microphysics schemes and processes on the intensity and track of hurricanes is presented and compared against the current Katrina study. In general, all of the studies show that microphysics schemes do not have a major impact on track forecasts but do have more of an effect on the simulated intensity. Also, nearly all of the previous studies found that simulated hurricanes had the strongest deepening or intensification when using only warm rain physics. This is because all of the simulated precipitating hydrometeors are large raindrops that quickly fall out near the eye-wall region, which would hydrostatically produce the lowest pressure. In addition, these studies suggested that intensities become unrealistically strong when evaporative cooling from cloud droplets and melting from ice particles are removed as this results in much weaker downdrafts in the simulated storms. However, there are many differences between the different modeling studies, which are identified and discussed.

Tao, Wei-Kuo↗

NASA NTRS2019

A Pulsar-Based Time-Scale from the International Pulsar Timing Array

We have constructed a new time-scale, TT(IPTA16), based on observations of radio pulsars presented in the first data release from the International Pulsar Timing Array (IPTA). We used two analysis techniques with independent estimates of the noise models for the pulsar observations and different algorithms for obtaining the pulsar time-scale. The two analyses agree within the estimated uncertainties and both agree with TT(BIPM17), a post-corrected time-scale produced by the Bureau International des Poids et Mesures (BIPM). We show that both methods could detect significant errors in TT(BIPM17) if they were present. We estimate the stability of the atomic clocks from which TT(BIPM17) is derived using observations of four rubidium fountain clocks at the US Naval Observatory. Comparing the power spectrum of TT(IPTA16) with that of these fountain clocks suggests that pulsar-based time-scales are unlikely to contribute to the stability of the best time-scales over the next decade, but they will remain a valuable independent check on atomic time-scales. We also find that the stability of the pulsar-based time-scale is likely to be limited by our knowledge of solar-system dynamics, and that errors in TT(BIPM17) will not be a limiting factor for the primary goal of the IPTA, which is to search for the signatures of nano-Hertz gravitational waves.

G. Hobbs↗

NASA NTRS2015

Airborne Simulation of Launch Vehicle Dynamics

In this paper we present a technique for approximating the short-period dynamics of an exploration-class launch vehicle during flight test with a high-performance surrogate aircraft in relatively benign endoatmospheric flight conditions. The surrogate vehicle relies upon a nonlinear dynamic inversion scheme with proportional-integral feedback to drive a subset of the aircraft states into coincidence with the states of a time-varying reference model that simulates the unstable rigid body dynamics, servodynamics, and parasitic elastic and sloshing dynamics of the launch vehicle. The surrogate aircraft flies a constant pitch rate trajectory to approximate the boost phase gravity turn ascent, and the aircraft's closed-loop bandwidth is sufficient to simulate the launch vehicle's fundamental lateral bending and sloshing modes by exciting the rigid body dynamics of the aircraft. A novel control allocation scheme is employed to utilize the aircraft's relatively fast control effectors in inducing various failure modes for the purposes of evaluating control system performance. Sufficient dynamic similarity is achieved such that the control system under evaluation is configured for the full-scale vehicle with no changes to its parameters, and pilot-control system interaction studies can be performed to characterize the effects of guidance takeover during boost. High-fidelity simulation and flight-test results are presented that demonstrate the efficacy of the design in simulating the Space Launch System (SLS) launch vehicle dynamics using the National Aeronautics and Space Administration (NASA) Armstrong Flight Research Center Fullscale Advanced Systems Testbed (FAST), a modified F/A-18 airplane (McDonnell Douglas, now The Boeing Company, Chicago, Illinois), over a range of scenarios designed to stress the SLS's Adaptive Augmenting Control (AAC) algorithm.

airborne simulation↗

NASA NTRS1988

Placing dynamic sensors and actuators on flexible space structures

Input/Output Cost Analysis involves decompositions of the quadratic cost function into contributions from each stochastic input and each weighted output. In the past, these suboptimal cost decomposition methods of sensor and actuator selection (SAS) have been used to locate perfect (infinite bandwidth) sensor and actuators on large scale systems. This paper extends these ideas to the more practical case of imperfect actuators and sensors with dynamics of their own. NASA's SCOLE examples demonstrate that sensor and actuator dynamics affect the optimal selection and placement of sensors and actuators.

Norris, Gregory A.↗

NASA NTRSDate not supplied

State of Wildfires

Fire is an essential component of ecosystems and acts as key driver of biogeochemical cycling with impacts on vegetation structure and composition, soil conditions, and climate feedbacks. Fire behavior and effects vary based on the types of fuel, fuel dryness, and frequency of ignition. Due to changing climate and land use patterns, fire danger is increasing in many regions globally, and fires are having increasingly devastating impacts on human health, infrastructure, and ecosystem services. Recurrent fires help to determine the distribution of trees and grasses, and overall fuel load, which inform the behavior of future fires. Process-based models can be used to capture multi-scale impacts at the forest stand-level up to the landscape level, and across minutes to centuries, but must capture variation in fire behavior and intensity as a function of the fuel and climate, from high intensity forest crown fires within boreal regions to low intensity rapid grass fires of the tropics. Fire model development demonstrates our ability to capture large scale fire influenced biogeography and vegetation distribution at the earth system scale through vegetation traits and fire feedbacks. At the individual stand scale the importance of interactions and feedbacks between above and below ground process is essential to capturing the vegetation dynamics across boreal forest systems. Improving the mechanics of including plant physiology and specifically live fuel moisture content is the next step to advancing the capability of process based models to inform fire research. Advances in the testing and creation of a mechanistic live fuel moisture model demonstrate the foundation for future live fuel dynamics research that can be informed by field and remote sensing information. Improved remote sensing, technological and modeling capabilities support a more comprehensive and cohesive fire response that will be better equipped to overcome current barriers and anticipate the new reality of fires in a warming world.

wildfires↗

NASA NTRS2008

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively. The Mach Number distribution shows small yet distinct differences between the two cases such as locations of shocks/shock reflections and a slightly different impingement point on the wall of the diffuser from the expansion at the exit of the nozzle. Similarly the temperature distribution indicates different flow recirculation patterns in the test cell. Both cases capture all the essential flow phenomena such as the shock-boundary layer interaction, plume expansion, expansion of the first stage ejectors, mixing between the engine plume and the first stage ejector flow and pressurization due to the first stage ejectors. The final paper will discuss thermal loads on the walls of the diffuser and cooling mechanisms investigated.

Allgood, Daniel C.↗

NASA NTRS2010

Computational Analyses in Support of Sub-scale Diffuser Testing for the A-3 Facility: Steady Predictions - Part 1

Simulation technology can play an important role in rocket engine test facility design and development by assessing risks, providing analysis of dynamic pressure and thermal loads, identifying failure modes and predicting anomalous behavior of critical systems. Advanced numerical tools assume greater significance in supporting testing and design of high altitude testing facilities and plume induced testing environments of high thrust engines because of the greater inter-dependence and synergy in the functioning of the different sub-systems. This is especially true for facilities such as the proposed A-3 facility at NASA SSC because of a challenging operating envelope linked to variable throttle conditions at relatively low chamber pressures. Facility designs in this case will require a complex network of diffuser ducts, steam ejector trains, fast operating valves, cooling water systems and flow diverters that need to be characterized for steady state performance. In this paper, we will demonstrate with the use of CFD analyses s advanced capability to evaluate supersonic diffuser and steam ejector performance in a sub-scale A-3 facility at NASA Stennis Space Center (SSC) where extensive testing was performed. Furthermore, the focus in this paper relates to modeling of critical sub-systems and components used in facilities such as the A-3 facility. The work here will address deficiencies in empirical models and current CFD analyses that are used for design of supersonic diffusers/turning vanes/ejectors as well as analyses for confined plumes and venting processes. The primary areas that will be addressed are: (1) supersonic diffuser performance including analyses of thermal loads (2) accurate shock capturing in the diffuser duct; (3) effect of turning duct on the performance of the facility (4) prediction of mass flow rates and performance classification for steam ejectors (5) comparisons with test data from sub-scale diffuser testing and assessment of confidence levels in CFD based flowpath modeling of the facility. The analyses tools used here expand on the multi-element unstructured CFD which has been tailored and validated for impingement dynamics of dry plumes, complex valve/feed systems, and high pressure propellant delivery systems used in engine and component test stands at NASA SSC. The analyses performed in the evaluation of the sub-scale diffuser facility explored several important factors that influence modeling and understanding of facility operation such as (a) importance of modeling the facility with Real Gas approximation, (b) approximating the cluster of steam ejector nozzles as a single annular nozzle, (c) existence of mixed subsonic/supersonic flow downstream of the turning duct, and (d) inadequacy of two-equation turbulence models in predicting the correct pressurization in the turning duct and expansion of the second stage steam ejectors. The procedure used for modeling the facility was as follows: (i) The engine, test cell and first stage ejectors were simulated with an axisymmetric approximation (ii) the turning duct, second stage ejectors and the piping downstream of the second stage ejectors were analyzed with a three-dimensional simulation utilizing a half-plane symmetry approximation. The solution i.e. primitive variables such as pressure, velocity components, temperature and turbulence quantities were passed from the first computational domain and specified as a supersonic boundary condition for the second simulation. (iii) The third domain comprised of the exit diffuser and the region in the vicinity of the facility (primary included to get the correct shock structure at the exit of the facility and entrainment characteristics). The first set of simulations comprising the engine, test cell and first stage ejectors was carried out both as a turbulent real gas calculation as well as a turbulent perfect gas calculation. A comparison for the two cases (Real Turbulent and Perfect gas turbulent) of the Ma Number distribution and temperature distributions are shown in Figures 1 and 2 respectively.

Allgood, Daniel C.↗

NASA NTRS2020

Cascading toward a Kilometer‐scale GCM: Impacts of a Scale‐aware Convection Parameterization in the Goddard Earth Observing System GCM.

The NASA Goddard Earth Observing System global model is evaluated through a cascade of simulations with increasing horizontal resolution. This model employs a non-hydrostatic dynamical core and includes a scale-aware, deep convection parameterization (DPCP). 40-daysimulations at six resolutions (100km to 3km) with unvarying model formulation were produced. At the highest resolution, extreme experiments were carried out; one with no DPCP, and one with its scale-awareness eliminated. Simulated precipitation, radiative balance, and atmospheric thermodynamic and dynamical variables are well reproduced with respect to both observational and reanalysis data. As model resolution increases, the convective precipitation smoothly transitions from being mostly produced by the convection parameterization to the cloud microphysics parameterization. However, contrary to current thought, these extreme cases argue for maintaining, to some extent, the scale-aware deep convection parameterization even at 3kmscale, as the run relying solely on explicit grid-scale production of rainfall performs more poorly at this resolution.

Saulo Freitas↗

NASA NTRS1976

Trends in modern system theory

The topics considered are related to linear control system design, adaptive control, failure detection, control under failure, system reliability, and large-scale systems and decentralized control. It is pointed out that the design of a linear feedback control system which regulates a process about a desirable set point or steady-state condition in the presence of disturbances is a very important problem. The linearized dynamics of the process are used for design purposes. The typical linear-quadratic design involving the solution of the optimal control problem of a linear time-invariant system with respect to a quadratic performance criterion is considered along with gain reduction theorems and the multivariable phase margin theorem. The stumbling block in many adaptive design methodologies is associated with the amount of real time computation which is necessary. Attention is also given to the desperate need to develop good theories for large-scale systems, the beginning of a microprocessor revolution, the translation of the Wiener-Hopf theory into the time domain, and advances made in dynamic team theory, dynamic stochastic games, and finite memory stochastic control.

Athans, M.↗

NASA NTRS1992

Non-scalar uncertainty: Uncertainty in dynamic systems

The following point is stated throughout the paper: dynamic systems are usually subject to uncertainty, be it the unavoidable quantic uncertainty when working with sufficiently small scales or when working in large scales uncertainty can be allowed by the researcher in order to simplify the problem, or it can be introduced by nonlinear interactions. Even though non-quantic uncertainty can generally be dealt with by using the ordinary probability formalisms, it can also be studied with the proposed non-scalar formalism. Thus, non-scalar uncertainty is a more general theoretical framework giving insight into the nature of uncertainty and providing a practical tool in those cases in which scalar uncertainty is not enough, such as when studying highly nonlinear dynamic systems. This paper's specific contribution is the general concept of non-scalar uncertainty and a first proposal for a methodology. Applications should be based upon this methodology. The advantage of this approach is to provide simpler mathematical models for prediction of the system states. Present conventional tools for dealing with uncertainty prove insufficient for an effective description of some dynamic systems. The main limitations are overcome abandoning ordinary scalar algebra in the real interval (0, 1) in favor of a tensor field with a much richer structure and generality. This approach gives insight into the interpretation of Quantum Mechanics and will have its most profound consequences in the fields of elementary particle physics and nonlinear dynamic systems. Concepts like 'interfering alternatives' and 'discrete states' have an elegant explanation in this framework in terms of properties of dynamic systems such as strange attractors and chaos. The tensor formalism proves especially useful to describe the mechanics of representing dynamic systems with models that are closer to reality and have relatively much simpler solutions. It was found to be wise to get an approximate solution to an accurate model than to get a precise solution to a model constrained by simplifying assumptions. Precision has a very heavy cost in present physical models, but this formalism allows the trade between uncertainty and simplicity. It was found that modeling reality sometimes requires that state transition probabilities should be manipulated as nonscalar quantities, finding at the end that there is always a transformation to get back to scalar probability.

Martinez, Salvador Gutierrez↗

NASA NTRS1984

Transonic wind-tunnel investigation of the Galileo Probe parachute configuration

Wind-tunnel tests have been made of 1/4-scale and 1/2-scale models of the Galileo Probe conical ribbon-parachute at flight conditions. For the Galileo mission, the parachute is deployed behind a blunt shape at transonic speed. The investigation was initiated to verify the solutions to the delayed main-parachute opening with squidding that was observed in the 1982 Galileo Probe system balloon drop test. In addition to varying model scale, the forebody shape, angle of attack, dynamic pressure, Mach number, and canopy trailing distance behind the forebody were varied to determine their effect on parachute performance. Both steady-state and deployment tests were conducted. Parachute drag was measured and was seen to degrade severely at canopy trailing distances of 5.5 and 7 forebody diameters. Performance was shown to be good at the trailing distances of 9 and 11 diameters. A second balloon drop test demonstrated the desired parachute performance at the system level.

Corridan, R. E.↗

NASA NTRS1990

Stratiform clouds and their interaction with atmospheric motion

During 1989 and 1990, the researchers saw the publication of two papers and the submission of a third for review on work supported primarily by the previous contract, NAS8-36150; the delivery of an invited talk at the SIAM Conference on Dynamical Systems in Orlando, Florida; and the start of two new projects on the radiative effects of stratocumulus on the large-scale flow. The published papers discuss aspects of stratocumulus circulations (Laufersweiler and Shirer, 1989) and the Hadley to Rossby regime transition in rotating spherical systems (Higgins and Shirer, 1990). The submitted paper (Haack and Shirer, 1990) discusses a new nonlinear model of roll circulations that are forced both dynamically and thermally. The invited paper by H. N. Shirer and R. Wells presented an objective means for determining appropriate truncation levels for low-order models of flows involving two incommensurate periods; this work has application to the Hadley to Rossby transition problem in quasi-geostrophic flows (Moroz and Holmes, 1984). The new projects involve the development of a multi-layered quasi-geostrophic channel model for study of the modulation of the large-scale flow by stratocumulus clouds that typically develop off the coasts of continents. In this model the diabatic forcing in the lowest layer will change in response to the (parameterized) development of extensive fields of stratocumulus clouds. To guide creation of this parameterization scheme, researchers are producing climatologies of stratocumulus frequency and the authors correlate these frequencies with the phasing and amplitude of the large-scale flow pattern. Researchers discuss the above topics in greater detail.

Clark, John H. E.↗

NASA NTRS1974

Skylab 2 ground winds data reduction and statistical analysis

A ground winds test was conducted on the Skylab 2 spacecraft in a subsonic wind tunnel and the results were tape recorded for analysis. The data reduction system used to analyze the tapes for full scale, first and second mode bending moments, or acceleration plots versus dynamic pressure or wind velocity is explained. Portions of the Skylab 2 tape data were analyzed statistically in the form of power spectral densities, autocorrelations, and cross correlations to introduce a concept of using system response decay as a measure of linear system damping.

Source record↗

NASA NTRS2011

Integrating Systems Health Management with Adaptive Controls for a Utility-Scale Wind Turbine

Increasing turbine up-time and reducing maintenance costs are key technology drivers for wind turbine operators. Components within wind turbines are subject to considerable stresses due to unpredictable environmental conditions resulting from rapidly changing local dynamics. Systems health management has the aim to assess the state-of-health of components within a wind turbine, to estimate remaining life, and to aid in autonomous decision-making to minimize damage. Advanced adaptive controls can provide the mechanism to enable optimized operations that also provide the enabling technology for Systems Health Management goals. The work reported herein explores the integration of condition monitoring of wind turbine blades with contingency management and adaptive controls. Results are demonstrated using a high fidelity simulator of a utility-scale wind turbine.

Frost, Susan A.↗

NASA NTRS2011

The Solar Dynamics Observatory, Studying the Sun and Its Influence on Other Bodies in the Solar System

The solar photon output, which was once thought to be constant, varies over all time scales from seconds during solar flares to years due to the solar cycle. These solar variations cause significant deviations in the Earth and space environments on similar time scales, such as affecting the atmospheric densities and composition of particular atoms, molecules, and ions in the atmospheres of the Earth and other planets. Presented and discussed will be examples of unprecedented observations from NASA's new solar observatory, the Solar Dynamics Observatory (SDO). Using three specialized instruments, SDO measures the origins of solar activity from inside the Sun, though its atmosphere, then accurately measuring the Sun's radiative output in X-ray and EUV wavelengths (0.1-121 nm). Along with the visually appealing observations will be discussions of what these measurements can tell us about how the plasma motions in all layers of the Sun modifies and strengthens the weak solar dipole magnetic field to drive large energy releases in solar eruptions. Also presented will be examples of how the release of the Sun's energy, in the form of photons and high energy particles, physically influence other bodies in the solar system such as Earth, Mars, and the Moon, and how these changes drive changes in the technology that we are becoming dependent upon. The presentation will continuously emphasize how SDO, the first satellite in NASA's Living with a Star program, improving our understanding of the variable Sun and its Heliospheric influence.

Chamberlin, P. C.↗

NASA NTRS1985

On the accuracy of modelling the dynamics of large space structures

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the space shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modeling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.

Diarra, C. M.↗

NASA NTRS1985

On the accuracy of modelling the dynamics of large space structures

Proposed space missions will require large scale, light weight, space based structural systems. Large space structure technology (LSST) systems will have to accommodate (among others): ocean data systems; electronic mail systems; large multibeam antenna systems; and, space based solar power systems. The structures are to be delivered into orbit by the Space Shuttle. Because of their inherent size, modelling techniques and scaling algorithms must be developed so that system performance can be predicted accurately prior to launch and assembly. When the size and weight-to-area ratio of proposed LSST systems dictate that the entire system be considered flexible, there are two basic modelling methods which can be used. The first is a continuum approach, a mathematical formulation for predicting the motion of a general orbiting flexible body, in which elastic deformations are considered small compared with characteristic body dimensions. This approach is based on an a priori knowledge of the frequencies and shape functions of all modes included within the system model. Alternatively, finite element techniques can be used to model the entire structure as a system of lumped masses connected by a series of (restoring) springs and possibly dampers. In addition, a computational algorithm was developed to evaluate the coefficients of the various coupling terms in the equations of motion as applied to the finite element model of the Hoop/Column.

Diarra, C. M.↗

NASA NTRS1990

Scaling laws for light weight optics, studies of light weight mirrors mounting and dynamic mirror stress, and light weight mirror and mount designs

Scaling laws for light-weight optical systems are examined. A cubic relationship between mirror diameter and weight has been suggested and used by many designers of optical systems as the best description for all light-weight mirrors. A survey of existing light-weight systems in the open literature was made to clarify this issue. Fifty existing optical systems were surveyed with all varieties of light-weight mirrors including glass and beryllium structured mirrors, contoured mirrors, and very thin solid mirrors. These mirrors were then categorized and weight to diameter ratio was plotted to find a best curve for each case. A best fitting curve program tests nineteen different equations and ranks a goodness-to-fit for each of these equations. The resulting relationship found for each light-weight mirror category helps to quantify light-weight optical systems and methods of fabrication and provides comparisons between mirror types.

Vukobratovich, Daniel↗