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All sources NASA NTRS DOE OSTI

NASA NTRS2008

Static and Dynamic Structural Response of an Aircraft Wing with Damage Using Equivalent Plate Analysis

A process to generate an equivalent plate based on an optimization approach to predict the static and dynamic response of flight vehicle wing structures is proposed. Geometric-scale and frequency-scale factors are defined to construct an equivalent plate with any desired scale to use in simulation and wind tunnel experiments. It is shown that the stiffness and the displacements are scaled linearly with the geometric-scale factor, whereas the load is scaled as the square of the geometric-scale factor. The scaled stiffness of the reference flight vehicle is matched first to construct the equivalent plate. Then the frequency-scale factor is defined to scale the flight vehicle frequencies. The scaled flight vehicle frequencies are matched by placing arbitrary point masses along the equivalent plate geometry. Two simple stiffened-plate examples, one with damage and another without damage, were used to demonstrate the accuracy of the optimization procedure proposed. Geometric-scale factors ranging from 0.2 to 1.0 were used in the analyses. In both examples, the static and dynamic response of the reference stiffened-panel solution is matched accurately. The scaled equivalent plate predicted the first five frequencies of the stiffened panel very accurately. Finally, the proposed equivalent plate procedure was demonstrated in a more realistic typical aircraft wing structure. Two scale equivalent plate models were generated using the geometric-scale factors 1.0 and 0.2. Both equivalent plate models predicted the static response of the wing structure accurately. The equivalent plate models reproduced the first five frequencies of the wing structure accurately.

Krishnamurthy, T.↗

NASA NTRS2009

Validity of the Aluminum Equivalent Approximation in Space Radiation Shielding

The origin of the aluminum equivalent shield approximation in space radiation analysis can be traced back to its roots in the early years of the NASA space programs (Mercury, Gemini and Apollo) wherein the primary radiobiological concern was the intense sources of ionizing radiation causing short term effects which was thought to jeopardize the safety of the crew and hence the mission. Herein, it is shown that the aluminum equivalent shield approximation, although reasonably well suited for that time period and to the application for which it was developed, is of questionable usefulness to the radiobiological concerns of routine space operations of the 21 st century which will include long stays onboard the International Space Station (ISS) and perhaps the moon. This is especially true for a risk based protection system, as appears imminent for deep space exploration where the long-term effects of Galactic Cosmic Ray (GCR) exposure is of primary concern. The present analysis demonstrates that sufficiently large errors in the interior particle environment of a spacecraft result from the use of the aluminum equivalent approximation, and such approximations should be avoided in future astronaut risk estimates. In this study, the aluminum equivalent approximation is evaluated as a means for estimating the particle environment within a spacecraft structure induced by the GCR radiation field. For comparison, the two extremes of the GCR environment, the 1977 solar minimum and the 2001 solar maximum, are considered. These environments are coupled to the Langley Research Center (LaRC) deterministic ionized particle transport code High charge (Z) and Energy TRaNsport (HZETRN), which propagates the GCR spectra for elements with charges (Z) in the range I <= Z <= 28 (H -- Ni) and secondary neutrons through selected target materials. The coupling of the GCR extremes to HZETRN allows for the examination of the induced environment within the interior' of an idealized spacecraft as approximated by a spherical shell shield, and the effects of the aluminum equivalent approximation for a good polymeric shield material such as genetic polyethylene (PE). The shield thickness is represented by a 25 g/cm spherical shell. Although one could imagine the progression to greater thickness, the current range will be sufficient to evaluate the qualitative usefulness of the aluminum equivalent approximation. Upon establishing the inaccuracies of the aluminum equivalent approximation through numerical simulations of the GCR radiation field attenuation for PE and aluminum equivalent PE spherical shells, we Anther present results for a limited set of commercially available, hydrogen rich, multifunctional polymeric constituents to assess the effect of the aluminum equivalent approximation on their radiation attenuation response as compared to the generic PE.

Badavi, Francis F.↗

NASA NTRS2023

A Theoretical and Computational Revisit of Conversions Between Whitham’s F-Function and Equivalent Area

This paper proves mathematically that the integral transforms between Whitham’s F-function and equivalent area are the inverse transforms of each other if and only if the slope of the equivalent area at the origin is zero. This mathematical fact contradicts the accepted unconditional inverse relation between Whitham’s F-function and equivalent area in the sonic boom research literature. Piecewise linear approximations of an F-function and of the second derivative of an equivalent area are used to derive numerical formulas for conversions between Whitham’s F-function and equivalent area. Numerical results are included to show convergence of the numerical conversions as the maximum length of the segments for piecewise linear approximations goes to zero. These numerical conversions are approximately the inverse transforms of each other when the second derivative of an equivalent area is continuous and the slope of the equivalent area at the origin is zero.

Whitham's F-function↗

NASA NTRS1954

Summary of Free-Flight Zero-Lift Drag Results from Tests of 1/5-Scale Models of the Convair YF-102 and F-102A Airplanes and Several Related Small Equivalent Bodies at Mach Numbers from 0.70 to 1.46

One-fifth-scale rocket-propelled models of the Convair YF-102 and F-102A airplanes were tested to determine free-flight zero-lift drag coefficients through the transonic speed range at Reynolds numbers near those to be encountered by the full-scale airplane. Trim and duct characteristics were obtained along with measurements of total-, internal-, and base-drag coefficients. Additional zero-lift drag tests involved a series of small equivalent-body-of-revolution models which were launched to low supersonic speeds by means of a helium gun. The several small models tested corresponded to the following full-scale airplanes: basic, YF-102, 2-foot (full-scale) fuselage extension, F-102A, F-102A (relocated inlets), F-102A (faired nose), and F-102A (parabolic nose) . Equivalent-body models corresponding to the normal area distribution (derived for Mach number 1.0) of each of these airplane shapes were flown and, in addition, equivalent-body models designed to represent the YF-102 and F-102A airplanes at Mach number 1.2 were tested. External-drag coefficients obtained from the 115-scale tests ranged from 0.0094 to 0.0273 for the YF-102 model and from 0.0100 to 0.0255 for the F-102A model. Forebody external-pressure-drag coefficients (drag rise) at Mach number 1.05 of 0.0183 and 0.0134 were obtained from the 115-scale models of the YF-102 and F-102A, respectively, a 16-percent reduction for the F-102A model. Values of drag rise at Mach number 1.05 from the small equivalent-body tests were nearly the same for the basic, YF-102, and 2-foot-fuselage-extension airplane shapes. Equivalent-body tests of the YF-102 and F-102A shapes showed the latter to have about 25 percent less drag rise as compared with a 16-percent reduction illustrated by the 1/5-scale tests. Additional equivalent-body tests illustrating effects of modifications to the F-102A airplane shape shared that relocating the inlets on the fuselage or altering the nose shape to provide a smoother cross-sectional area progression reduced the drag rise by approximately 16 percent. Replacing a major portion of the nose of the F-102A equivalent-body model with one of parabolic shape resulted in about a 21-percent reduction in drag rise. The drag-rise data from the equivalent-body tests include base drag.

Wallskog, Harvey A.↗

NASA NTRS1995

An equivalent body surface charge model representing three-dimensional bioelectrical activity

A new surface-source model has been developed to account for the bioelectrical potential on the body surface. A single-layer surface-charge model on the body surface has been developed to equivalently represent bioelectrical sources inside the body. The boundary conditions on the body surface are discussed in relation to the surface-charge in a half-space conductive medium. The equivalent body surface-charge is shown to be proportional to the normal component of the electric field on the body surface just outside the body. The spatial resolution of the equivalent surface-charge distribution appears intermediate between those of the body surface potential distribution and the body surface Laplacian distribution. An analytic relationship between the equivalent surface-charge and the surface Laplacian of the potential was found for a half-space conductive medium. The effects of finite spatial sampling and noise on the reconstruction of the equivalent surface-charge were evaluated by computer simulations. It was found through computer simulations that the reconstruction of the equivalent body surface-charge from the body surface Laplacian distribution is very stable against noise and finite spatial sampling. The present results suggest that the equivalent body surface-charge model may provide an additional insight to our understanding of bioelectric phenomena.

NASA Discipline Regulatory Physiology↗

NASA NTRS2007

Can the Equivalent Sphere Model Approximate Organ Doses in Space Radiation Environments?

In space radiation calculations it is often useful to calculate the dose or dose equivalent in blood-forming organs (BFO). the skin or the eye. It has been customary to use a 5cm equivalent sphere to approximate the BFO dose. However previous studies have shown that a 5cm sphere gives conservative dose values for BFO. In this study we use a deterministic radiation transport with the Computerized Anatomical Man model to investigate whether the equivalent sphere model can approximate organ doses in space radiation environments. We find that for galactic cosmic rays environments the equivalent sphere model with an organ-specific constant radius parameter works well for the BFO dose equivalent and marginally well for the BFO dose and the dose equivalent of the eye or the skin. For solar particle events the radius parameters for the organ dose equivalent increase with the shielding thickness, and the model works marginally for BFO but is unacceptable for the eye or the skin The ranges of the radius parameters are also shown and the BFO radius parameters are found to be significantly larger than 5 cm in all eases.

Zi-Wei, Lin↗

DOE OSTI2021

Equivalence of a harmonic oscillator to a free particle and Eisenhart lift

Highlights: • Equivalence of a harmonic oscillator to a free particle is considered. • The Eisenhart lift is applied to most general harmonic and linear potentials. • In geometric language, equivalence is the result of the conformal flatness of the Eisenhart metric. It is widely known in quantum mechanics that solutions of the Schrödinger equation (SE) for a linear potential are in one-to-one correspondence with the solutions of the free SE. The physical reason for this correspondence is Einstein’s principle of equivalence. What is usually not so widely known is that solutions of the Schrödinger equation with harmonic potential can also be mapped to the solutions of the free Schrödinger equation. The physical understanding of this equivalence is not known as precisely as in the case of the equivalence principle. We present a geometric picture that will link both of the above equivalences with one constraint on the Eisenhart metric.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2024

Evaluation of the Simplified Assessment Peak Equivalent Stress Design Limit Probability of Failure

The ASME Boiler and Pressure Vessel Code Section III Division 5 Subsection HH Subpart A (HHA) outlines requirements and qualification methods for graphite core components in high temperature reactor environments. One such structural qualification method is the Simplified Assessment outlined in HHA-3220, which represents a comparison of service level specific equivalent stresses to allowable stress values derived from target probability of failures (POFs). The target POF is based on the structural reliability class (SRC) for the components and service condition of interest, and is used to establish design limits for combined membrane and peak equivalent stresses. Combined membrane stress limits are derived from two parameter Weibull distribution fits of the graphite grade specific tensile strength data and the target POF. The combined membrane stress limits are then scaled based on the ratio of flexural strength to tensile strength (referred hereinafter as Rtf) to establish the corresponding peak equivalent stress limits. It is desired that the target POF is at least maintained for both combined membrane and peak equivalent design limits, especially with the use of Rtf. The assessment presented herein examines tensile and flexural data for medium and fine grade graphites relative to the calculated combined membrane and peak equivalent stress limits per HHA-3220 and illustrates the simplified assessment method results in anticipated, or at least conservative, peak equivalent design stress limits.

36 - MATERIALS SCIENCE↗

DOE OSTI2024

Relating flow resistance to equivalent roughness

Describing flow resistance using the physical properties of an underlying surface is a recalcitrant problem in overland flow models. If discharge measurements are available, an equivalent roughness (e.g., Manning’s n) can be calibrated to represent the effects of surface properties within the domain with a single numerical value. Alternatively, the flow resistance can be estimated from discharge and velocity measured at a point, typically a runoff plot outlet. However, such experimental estimates are often inconsistent with the equivalent roughness determined from calibration to discharge, even if both derive from the same dataset. For example, if Manning’s equation is used to parameterize flow resistance, the Manning’s n obtained by calibrating a model to discharge differs from the value of n calculated from measured flow and velocity at the hillslope outlet. Here, this discrepancy is resolved by deriving a correction factor relating experimentally-determined flow resistance to the equivalent roughness. The derived correction factor is tested for four commonly-used resistance formulations using 129 rainfall simulator experiments. The correction factor is necessary to reproduce measured velocities, and yields minor improvements in discharge prediction. Plain Language Summary: Accurate runoff prediction is needed for land and water management in dryland regions, where sporadic and limited rainfall necessitate efficient water use and drought mitigation strategies. The skill of runoff models is known to be hindered by out ability to estimate flow resistance, which is the quantity that describes how energy is lost from flowing water to the underlying surface. Typically, models represent flow resistance with an equivalent roughness, e.g., Manning’s n, that is adjusted until the model can reproduce available discharge observations at watershed scale. However, the flow resistance measured in plot-scale experiments (1–10 m) often exceeds equivalent roughness coefficients by a factor of 10. This means that the direct use of plot-scale experimental data to parameterize runoff models could cause errors in discharge and runoff velocity predictions. Here, we resolve these differences by deriving an analytic correction factor that relates flow resistance to the equivalent roughness required for models to reproduce experimental velocity and discharge data. This correction factor is tested using rainfall simulator data from 129 experiments performed in the US Southwest covering a wide range of precipitation intensities, soil textures and vegetation types. Use of the correction factor substantially improves model prediction of flow velocity, which is needed for reproducing the timing of flood events and the estimation of erosion.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

The emergence of valency in colloidal crystals through electron equivalents

Colloidal crystal engineering of complex, low-symmetry architectures is challenging when isotropic building blocks are assembled. In this study we describe an approach to generating such structures based upon programmable atom equivalents (nanoparticles functionalized with many DNA strands) and mobile electron equivalents (small particles functionalized with a low number of DNA strands complementary to the programmable atom equivalents). Under appropriate conditions, the spatial distribution of the electron equivalents breaks the symmetry of isotropic programmable atom equivalents, akin to the anisotropic distribution of valence electrons or coordination sites around a metal atom, leading to a set of well-defined coordination geometries and access to three new low-symmetry crystalline phases. All three phases represent the first examples of colloidal crystals, with two of them having elemental analogues (body-centred tetragonal and high-pressure gallium), while the third (triple double-gyroid structure) has no known natural equivalent. This approach enables the creation of complex, low-symmetry colloidal crystals that might find use in various technologies.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Lift Equivalence and Cancellation for Airfoil Surge–Pitch–Plunge Oscillations

A NACA 0018 airfoil in freestream velocity is oscillated in longitudinal, transverse, and angle-of-attack directions with respect to the freestream velocity, known as surge, plunge, and pitch. The lift-based equivalence method introduces phase shifts between these three motions to construct in-phase sinusoidal components for maximum lift, waveform construction. Lift cancellation is also determined with the exact negative pitch and plunge motion amplitudes found from the equivalence method to achieve out-of-phase wave destruction. Lift cancellation occurs when a combination of these motions is sought to obtain a constant lift magnitude throughout the oscillation cycle. To achieve both equivalence and cancellation of lift, a prescribed pure pitch amplitude through the Theodorsen theory equates the corresponding equivalent plunge amplitude and pitch–plunge phase shift. These Theodorsen, linear superposition findings of pitch–plunge are leveraged toward the Greenberg theory to determine a closed-form, surge–pitch–plunge solution through the addition of a surge–plunge phase shift and optimal surge amplitude for lift cancellation. The lift cancellation surge–pitch–plunge amplitudes define the equivalence amplitude investigated here and theoretically limit the experiment to combinations of the first lift harmonic of the Greenberg theory. The analytical results are then compared with experimental lift force measurements and dye visualization. Finally, the normalized lift differences due to unsteady wake and boundary-layer behavior are examined to explore the extents of the Greenberg theory for these cases of lift-based equivalence and cancellation.

42 ENGINEERING↗

NASA NTRS1995

Emergence of Relations and the Essence of Learning: A Review of Sidman's Equivalence Relations and Behavior: A Research Story

Sidman addresses two very important questions in Equivalence Relations and Behavior: A Research Story: What are the bases of behavioral competence? And how do units of learning become related? The book recounts the story of how an understanding of emergent relations and competencies was achieved through studies in his teaching-research program with mentally retarded subjects. Although children normally accrue vast networks of relations between stimuli and events, those with mental retardation typically do not. Consequently, by learning how to establish those networks, Sidman and his students contribute richly both to the cultivation of competencies by their subjects and, more generally, to an understanding of real-world human behavior. The basic equivalence paradigm affords the subject feedback and reinforcement for very specific choices during training, but the test is not for those choices! Rather, tests for equivalence look for new choices, ones seemingly quite foreign to the training regimen. The tests for equivalence relations entail presentations of stimuli that were the options for conditional choice during reinforced training. In tests of equivalence, correct choices are novel; hence, they have never been reinforced during training. The study of equivalence relations can encourage the emergence of new perspectives that are more symbiotic than competitive. In full acknowledgment of the important role and contributions made by those who identify themselves as experimental analysts of behavior, it is timely that rapprochements be worked toward, as indeed they are, to meld that perspective with others of our time. Both our research methods and our expectations about the nature of the learning process and the abilities of our subjects can delimit what they might learn and what we, in turn, learn about their learning. The text will be of great value for instruction at the upper-division and graduate levels. Its impact will be substantial, for it defines an important advance in our efforts to understand the richness of behavior in both humans and nonhuman animals. Although not presented to that end, the book might also serve to bridge communications with other groups of animal researchers whose interests lie more in a comparative or ethological framework.

Rumbaugh, Duane M.↗

NASA NTRS2002

Response of a tissue equivalent proportional counter to neutrons

The absorbed dose as a function of lineal energy was measured at the CERN-EC Reference-field Facility (CERF) using a 512-channel tissue equivalent proportional counter (TEPC), and neutron dose equivalent response evaluated. Although there are some differences, the measured dose equivalent is in agreement with that measured by the 16-channel HANDI tissue equivalent counter. Comparison of TEPC measurements with those made by a silicon solid-state detector for low linear energy transfer particles produced by the same beam, is presented. The measurements show that about 4% of dose equivalent is delivered by particles heavier than protons generated in the conducting tissue equivalent plastic. c2002 Elsevier Science Ltd. All rights reserved.

NASA Center JSC↗

NASA NTRS2013

Application of Adjoint Methodology to Supersonic Aircraft Design Using Reversed Equivalent Areas

This paper presents an approach to shape an aircraft to equivalent area based objectives using the discrete adjoint approach. Equivalent areas can be obtained either using reversed augmented Burgers equation or direct conversion of off-body pressures into equivalent area. Formal coupling with CFD allows computation of sensitivities of equivalent area objectives with respect to aircraft shape parameters. The exactness of the adjoint sensitivities is verified against derivatives obtained using the complex step approach. This methodology has the benefit of using designer-friendly equivalent areas in the shape design of low-boom aircraft. Shape optimization results with equivalent area cost functionals are discussed and further refined using ground loudness based objectives.

Rallabhandi, Sriram K.↗

DOE OSTI2024

Equivalence Ratio Scans in a Rotating Detonation Engine

Published data for run times exceeding a few seconds in rotating detonation engines (RDEs) is rare, but long duration tests are necessary to understand both transient and persistent phenomena in RDE operation. Previous work has noted different detonation wave modes at different equivalence ratios. In the current study, multiple long-duration runs with constant air flow rate and variable equivalence ratio are conducted in a hydrogen-fueled, water-cooled RDE. Analysis of the capillary tube averaged pressure (CTAP) data reveals a strong correlation with equivalence ratio as well as a small time dependency due to transient thermal processes. Ion probe measurements are used to analyze detonation wave frequencies and modes, both of which are strongly dependent on the equivalence ratio. Mode transitions are observed to occur consistently as the equivalence ratio is traversed between 0.55 and 0.60. These transitions are also found to be a function of the direction of changing equivalence ratio (ascending or descending) and time.

Boyette, Wesley R.↗

DOE OSTI2024

Equivalence Ratio Scans in a Rotating Detonation Engine

Boyette, Wesley R.↗

DOE OSTI2024

QED: A Powerful Query Equivalence Decider for SQL

Checking query equivalence is of great significance in database systems. Prior work in automated query equivalence checking sets the first steps in formally modeling and reasoning about query optimization rules, but only supports a limited number of query features. In this paper, we present Qed, a new framework for query equivalence checking based on bag semantics. Qed uses a new formalism called Q-expressions that models queries using different normal forms for efficient equivalence checking, and models features such as integrity constraints and NULLs in a principled way unlike prior work. Our formalism also allows us to define a new query fragment that encompasses many real-world queries with a complete equivalence checking algorithm, assuming a complete first-order theory solver. Empirically, Qed can verify 299 out of 444 query pairs extracted from the Calcite framework and 979 out of 1287 query pairs extracted from CockroachDB, which is more than 2× the number of cases proven by prior state-of-the-art solver.

Computer Science↗

NASA NTRS1980

The equivalent depth of burst for impact cratering

The concept of modeling an impact cratering event with an explosive event with the explosive buried at some equivalent depth of burst (d.o.b.) is discussed. Various and different ways to define this equivalent d.o.b. are identified. Recent experimental results for a dense quartz sand are used to determine the equivalent d.o.b. for various conditions of charge type, event size, and impact conditions. The results show a decrease in equivalent d.o.b. with increasing energy for fixed impact velocity and a decrease in equivalent d.o.b. with increasing velocity for fixed energy. The values for an iron projectile are on the order of 2-3 projectile radii for energy equal to one ton of TNT, decreasing to about 1.5 radii at a megaton of TNT. The dependence on projectile and target mass density matches that included in common jet-penetration formulas for projectile densities greater than target densities and for the higher energies.

Holsapple, K. A.↗