Lateral Cutoff Research Articles

Split-step simulations of sonic boom propagation beyond the lateral cutoff in a turbulent atmosphere

Recent flight tests during the Quiet Supersonic Flights 2018 (QSF18) study reported sonic booms heard outside of the primary carpet region. In the absence of turbulence, the lateral cutoff region separates the primary sonic boom carpet from the shadow zone, where the sonic boom signal experiences significant attenuation. However, when turbulence is present in the atmospheric boundary layer (ABL), additional scattering of the sonic boom to the shadow zone region occurs. A method is presented for simulating sonic boom propagation in a turbulent atmospheric boundary layer beyond the lateral cutoff region into the shadow zone. A split-step method is used to integrate a partially one-way equation for the acoustic pressure. Inhomogeneous turbulence, representative of the ABL, is generated in the computational domain with a Fourier synthesis approach. Distributions of several loudness metrics in the shadow zone region for a sonic boom N-wave and a shaped boom are examined. Increasing both turbulence root-mean-square velocity and integral length scale are found to increase the average loudness of booms in the shadow zone. (This research is supported by the Commercial Supersonic Technology Project of the National Aeronautics and Space Administration under Grant No. 80NSSC19K1685.)

Implementation of a sonic boom propagation algorithm with the augmented Burgers equation

For the purpose of sonic boom carpet determination for an optimized routing of supersonic aircraft around landmasses, a sonic boom propagation code was implemented at the Institute of Air Transportation Systems. The implementation is based on the well-known augmented Burgers equation for stratified atmospheres and extends the sole geometric ray tracing that has been used at the institute to determine the lateral cutoff distance of sonic booms so far. For the quantification of sonic boom signatures on ground, algorithms for the computation of noise metrices, namely, the perceived level of noise Stevens Mk VII (PL) and the sound exposure level (SEL) with several frequency weightings are also implemented. This work describes the implementation of the sonic boom propagation algorithm and the methods used for loudness calculation briefly. For the evaluation of the implemented code, pre-defined cases from the Third Sonic Boom Prediction Workshop are simulated, and the computed results are compared to the published results of that workshop. The similarities and differences are discussed in detail, such that the general implementation of the propagation code can be verified, whereas potential inaccuracies, especially for the off-track determination, can be detected and quantified.

A mixed Fourier transform for impedance boundary conditions of acoustic waves at grazing incidence

Acoustic propagation in the atmosphere near the Earth’s surface at grazing incidence is influenced by ground impedance. Consequently, numerical simulations must use an impedance ground boundary condition in order to accurately predict ground effects associated with grazing incidence. A mixed Fourier transform method for impedance boundary conditions has been developed for parabolic approaches by the electromagnetics community. Here, the mixed Fourier transform method is adapted and validated for acoustic wave propagation. The one-way solution of the Helmholtz equation is computed with a modified angular spectrum approach to account for a locally reacting surface using a mixed Fourier transform in the vertical direction. Numerical simulations are presented that focus on sonic boom propagation near the ground in the shadow zone. The simulations demonstrate the utility of the mixed Fourier transform method to account for ground impedance effects that are ignored by ray theory-based propagation codes. Consequently, the method extends sonic boom prediction to the lateral cutoff and shadow zone regions. [This research is supported by the Commercial Supersonic Technology Project of the National Aeronautics and Space Administration under Grant No. 80NSSC19K1685.]

Summary of Propagation Cases of the Third AIAA Sonic Boom Prediction Workshop

A summary is provided for the propagation portion of the Third AIAA Sonic Boom Prediction Workshop held on January 4–5, 2020, in conjunction with the AIAA SciTech 2020 conference. Near-field pressure waveforms for two cases were supplied at multiple azimuthal angles. Ground signatures across the breadth of the sonic boom primary carpet and their corresponding loudness metrics were requested. Each case had some required, as well as some optional, runs. The required cases included atmospheric profiles with measured data including winds. Optional cases included a level-acceleration sonic boom focusing case and prediction under standard atmospheric conditions. Participants provided ground signatures along with several loudness metrics using their best sonic boom prediction practices. All the participants’ submissions are compared and discussed for each case. Noise or loudness measures are calculated, and detailed comparisons and statistical analyses are performed and presented. Compared with previous workshops, the selected cases in the current workshop have much lower boom loudness levels. As was observed in the past workshops, the variation in the loudness measures and spread between participants’ submissions increased as the computation proceeded from undertrack locations toward the lateral cutoff. Lessons learned during this workshop are discussed, and recommendations are made for potential improvements and possible subsequent workshops as we collectively attempt to refine our analysis methods.

PCBoom Propagation Modeling for the Third AIAA Sonic Boom Prediction Workshop

The PCBoom suite of tools was used to model atmospheric propagation cases and the optional focus case as part of the Third AIAA Sonic Boom Prediction Workshop. The Focused Boom module FOBoom version 7.1.0 was used to complete ray tracing calculations using computational fluid dynamics pressure data as the source. Lossy propagation was modeled using PCBoom’s interactive Burgers equation solver, PCBurg, and final results were obtained with the batch analysis tool HeadlessBurgers. The effects of sampling rate, time-step factor, and other factors on model results were investigated. Lateral cutoff angles were refined by finely incrementing azimuth angles and examining propagation paths and ground metrics. The optional focus case, in which the vehicle trajectory included acceleration, was also modeled using PCBoom. An interactive program (RayCau) was used to generate ray diagrams showing the caustic and the delta-tangent ray to confirm the focus condition and to facilitate identification of the ray and signature for input to the lossy nonlinear Tricomi equation (LNTE) solver. PCBurg was used to obtain the lossy signature at the delta tangent position. Finally, the LNTE module was used to compute signatures in the vicinity of the focal zone.

Sonic boom simulation for boom carpet determination

The Institute of Air Transportation Systems in Hamburg, Germany, researches methodologies for optimized supersonic flight routing that prevents the (primary) sonic boom from reaching the ground. The sonic boom shall either be cut off vertically or laterally. In initial trials, lateral cutoff positions of the sonic boom carpet were searched geometrically by ray tracing. Thereby, it was found that smooth interpolation of atmospheric data is necessary for geometrical convergence of different ray tracing methods, and that determining the marginal ray was oftentimes virtually impossible leeward. (These findings will be elaborated in more detail.) For those reasons, acoustic propagation has been introduced based on the Augmented Burgers equation, and implementing the Tricomi equation for covering flight maneuvers is planned in the short term. Our main research goal is finding numerical methods for determining the acoustic sonic boom cutoff that are first and foremost practical, i.e., fast, accurate, and robust. In this respect, we will discuss different termination conditions in signature propagation for the purpose of sonic boom carpet computation.

Lateral cutoff analysis of sonic boom using full-field simulation

This paper describes the world's first successful simulation for lateral cutoff phenomena of sonic boom far from the flight path due to variation in atmospheric temperature with altitude. A flow field around an axi-symmetric paraboloid has been analyzed by the full-field simulation method that solves the three-dimensional Euler equations with a gravity term to create a horizontally stratified atmosphere. A solution-adapted structured grid is constructed to align the grid lines with the front and rear shock-wave surfaces in the entire domain, including the near field around a supersonic body and far field reaching the ground beyond lateral cutoff. The flight is assumed to have a speed of Mach 1.2 at an altitude of 10 km, and the computational domain ranges over a distance of 30 km from the axis of symmetry. The computational results show that the evanescent wave in the shadow zone beyond lateral cutoff decays exponentially and changes into a progressive rounding waveform. The characteristics of the waveform transition are in good agreement with those observed in the flight tests. Therefore, the full-field simulation is recognized as a promising approach for investigating sonic boom strength in the full extent of sonic boom noise, including lateral cutoff and evanescent waves. Moreover, the computational results clarify that sonic boom focusing occurs above the ground, except for the vicinity of the ground, and the focusing strength along the lateral cutoff curve detected from the three-dimensional shock-wave surface increases with altitude. The results of ray tracing analysis collaborate the reasonability of the simulation results, and the caustic of downward convex agrees well with the lateral cutoff curve. In the shadow zone, the magnitude of exponential decay increases with altitude, and the lateral distance where the pressure rise decreases rapidly shortens with altitude.

Summary of Propagation Cases of the Second AIAA Sonic Boom Prediction Workshop

A summary is provided for the propagation portion of the second AIAA Sonic Boom Prediction Workshop, held 8 January 2017 in conjunction with the AIAA SciTech 2017 Conference. Near-field pressure waveforms for two cases were supplied, and ground signatures at multiple azimuthal angles as well as their corresponding loudness metrics were requested from 10 participants, representing three countries. Each case had some required as well as some optional runs. The required cases included atmospheric profiles with measured data including winds, using radiosonde balloon data at multiple geographically spread locations. The humidity profiles provided for the optional cases were taken from American National Standards Institute guidance. Participants provided ground signatures along with the requested data, including some loudness metrics using their best practices, which included lossy as well as lossless atmospheric propagation schemes. All the participants’ submissions, for each case, are compared and discussed. Noise or loudness measures are calculated, and detailed comparisons and statistical analyses are performed and presented. It has been observed that the variation in the loudness measures and spread between participants’ submissions increased as the computation proceeded from undertrack locations toward the lateral cutoff. Lessons learned during this workshop are discussed, and recommendations are made for potential improvements and possible subsequent workshops.

Probing the surface microstructure of layer-by-layer self-assembly chitosan/poly(l-glutamic acid) multilayers: A grazing-incidence small-angle X-ray scattering study.

This study characterized the surface structure of layer-by-layer self-assembly chitosan/poly(L-glutamic acid) multilayers through grazing-incidence small-angle X-ray scattering (GISAXS), X-ray reflectivity (XRR), and atomic force microscopy (AFM). A weakly long-period ordered structure along the in-plane direction was firstly observed in the polyelectrolyte multilayer by the GISAXS technique. This structure can be attributed to the specific domains on the film surface. In the domain, nanodroplets that were formed by polyelectrolyte molecules were orderly arranged along the free surface of the films. This ordered structure gradually disappeared with the increasing bilayer number because of the complex merging behavior of nanodroplets into large islands. Furthermore, resonant diffuse scattering became evident in the GISAXS patterns as the number of bilayers in the polyelectrolyte multilayer was increased. Notably, the lateral cutoff length of resonant diffuse scattering for these polyelectrolyte films was comparable with the long-period value of the ordered nanodroplets in the polyelectrolyte multilayer. Therefore, the nanodroplets could be considered as a basic transmission unit for structure propagation from the inner interface to the film surface. It suggests that the surface structure with length scale larger than the size of nanodroplets was partially complicated from the interface structure near the substrate, but surface structure smaller than the cutoff length was mainly depended on the conformation of nanodroplets.

Radiographic evaluation of complete and incomplete discoid lateral meniscus

ObjectivesThe aim of this retrospective study was (1) to evaluate the radiographic features to differentiate arthroscopically confirmed complete and incomplete discoid lateral meniscus (DLM) (2) to determine the cutoff values for any parameter that was found to differentiate complete from incomplete DLM. Materials and MethodsWe retrospectively analyzed plain knee radiographs of 130 arthroscopically proven DLM. Seventy-nine patients had complete DLM and 51 patients incomplete DLM. Knee radiographs from 52 patients with arthroscopically proven normal lateral meniscus acted as control group. Radiographic parameters measured included fibular height, lateral joint space, condylar cutoff sign, height of lateral tibial spine, obliquity of lateral tibial spine, squaring of the lateral femoral condyle, and cupping of the lateral tibial plateau. ResultsAmong radiographic parameters, high fibular head, widening of the lateral joint space and femoral condylar cutoff sign showed statistically significant (p<0.0001) differences between complete and incomplete DLM. At specific threshold points of fibular height<11mm, lateral joint space>6mm and condylar cutoff sign<0.80, the diagnosis of complete DLM revealed 87.3% sensitivity, 81.6% specificity and 78.4% positive predictive value (PPV) for the fibular height, 81.0% sensitivity, 86.6% specificity and 83.1% PPV for the lateral joint space, and 86.1% sensitivity, 83.5% specificity and 80% PPV for the condylar cutoff sign. ConclusionsRadiographic features of fibular height, lateral joint space and condylar cut off sign can be used for screening of a complete type of DLM. However, radiographs are not a reliable screening tool for an incomplete DLM. Level of evidenceIV, Case Series

Admittance of diffusion limited adsorption coupled to reversible charge transfer on rough and finite fractal electrodes

A theoretical model is developed to quantify the effect of diffusion controlled adsorption of electroactive species on (reversible) charge transfer admittance at a rough electrode. Results are obtained for the linearized isotherm and applied on various electrode roughness models, viz. (i) deterministic surface profile, (ii) roughness as random surface profile with known statistical properties, viz. the power spectrum of roughness and (iii) random profile function with finite self-affine fractal properties. The general expressions for admittance density and total admittance have a systematic operator structure in Fourier transformed surface profile function. Realistic model of roughness requires inclusion of randomness in surface morphology, hence the quantity of interest, the mean admittance is obtained (by taking ensemble average over all possible random configurations). Mathematical expression for the mean admittance of random morphology is the functional of the power spectrum of roughness. A special case of finite fractal roughness is characterized as self-affine scaling property over limited length scales and hence possess two lateral cutoff lengths along with the fractal dimension and a topothesy length (ℓτ). Our analysis explicitly relates the problem of rough electrode admittance with diffusion length (D/ω), isotherm (length) parameter (K) and fractal morphological characteristics. The three characteristic frequencies in this theory are: (a) lower adsorption crossover frequency –ωad≈D/K2, (b) adsorption–roughness topothesy dependent weak pseudo-quasireversibility characteristic frequency –ωq≈D/(ℓτK) and (c) high frequency small cutoff length (ℓ) dependent Warburg – anomalous Warburg crossover frequency –ωw≈D/ℓ2. Finally, theory shows emergence of pseudo-quasireversibility in intermediate frequency region due to electrode roughness in adsorption–diffusion system and curtailment of high frequency anomalous diffusion regime.

Theory of quasi-reversible charge transfer admittance on finite self-affine fractal electrode

Response of an electrode under finite charge transfer rate is strongly influenced by morphological and electrochemical heterogeneity of the surface. Here, we developed a theoretical model for quasi-reversible charge transfer admittance of a random finite fractal electrode. These random heterogeneities are characterized by their roughness power spectrum. The power spectrum of the finite fractal roughness is approximated in terms of a power-law function for the intermediate wave numbers (spatial frequency components in roughness). The mathematical expression for the admittance response of a finite fractal electrode depends on diffusion length ( D / ω ) , charge transfer resistance ( R CT ) and its fractal morphological characteristics. Fractals are characterized by the fractal dimension ( D H ) and the surface roughness amplitude ( μ), but finite fractals includes two lateral cutoff lengths. These lengths are the smallest length of roughness ( ℓ ) and the lateral correlation length ( L). The impedance of the electrode shows three frequency regimes, viz., (i) low frequency region, which has a classical Warburg impedance, (ii) anomalous Warburg behavior for intermediate frequency and their phase angle, ϕ( ω) > 45°, and (iii) high frequency impedance is controlled by charge transfer kinetics, and its phase angle follows the constraint: 0 ≤ ϕ( ω) < 45°. Finally, we can say that finite fractal model accounts for fractal as well as nonfractal roughnesses of the electrode, and it strongly influences the admittance response.

Anomalous Warburg Impedance: Influence of Uncompensated Solution Resistance

We present the theoretical results elucidating the influence of uncompensated solution resistance on anomalous Warburg’s impedance. Here, we obtain the mathematical expression which incorporates the diffusion at the rough electrode/electrolyte interface and bulk solution resistance via phenomenological length scales—diffusion length ((D/ω)1/2) and pseudoreaction penetration length (LΩ). The roughness at the interface is contained in the expression through the surface structure factor, which can be used to describe statistically any random surface morphology. Detailed analysis for realistic fractal electrodes, characterized as a finite self-affine scaling property with two lateral cutoff lengths, is presented. Limiting behavior in higher frequency is attributed to resistive effects of the electrolyte, and surface roughness is seen through the roughness factor. In the intermediate frequency regime, the anomalous power law behavior is attributed to the diffusion length weighted spatial frequency features of roughness (marking impedance loss) along with the interplay of LΩ and at lower frequencies the response crossover to classical Warburg’s behavior. This crossover frequency is dependent on the smallest of root-mean-square width (h) or lateral correlation length (L), while high-frequency crossover is dependent largely on LΩ. Phase response also shows the maximum phase gain for intermediate frequencies owing to the roughness features and is a signature to the fractal or nonfractal roughness at the interface. Our results show that owing to solution resistance the impedance response can mimic pseudo-quasireversibilty inducing a delay in the onset of diffusion-controlled regime and can hack the anomalous response due to roughness partially or completely.

Nanoscale surface roughening in ultrathin aluminum films

We report studies of the formation of aluminum structures, with nanometer length scales, in ultrathin layers deposited on glass and analyzed using atomic force microscopy. Surface roughness, lateral cutoff length, and surface scaling exponent are all found to vary systematically with Al thickness. The initial nanocrystal formation is described by stress-energy minimization. We interpret the observed scaling behavior based on the kinetic theory of roughening. For very thin layers (&amp;lt;50nm) the roughness is consistent with a ∇4h growth factor, where h is surface height. For thick layers (&amp;gt;50nm) the ∇2(∇h)2 conserved mechanism is dominant. Substrate stress is not found to influence the scaling exponent through the kinetic theory.

X-ray scattering from freestanding polymer films with geometrically curved surfaces.

We show that the x-ray surface scattering from a freestanding polymer film exhibits features that cannot be explained by the usual stochastic formalism for surfaces with random height fluctuations. Instead, a geometric description of the film morphology assuming two curved surfaces characterized by a radius of curvature and a lateral cutoff length successfully accounts for the phase difference between the Kiessig fringes of the nominal "specular" and "off-specular" components of the scattering. The formalism allows one to distinguish unambiguously between conformal and anticonformal curvature morphologies at long length scales.

Comparison of measured and predicted lateral distribution of sonic boom overpressures from the United States Air Force sonic boom database

In 1987 the United States Air Force (USAF) collected the lateral distribution of sonic booms produced by 43 supersonic flights of military aircraft near Edwards Air Force Base (EAFB). These flights were accomplished using eight different aircraft at several Mach number and altitude combinations. The flights were planned for steady and level operation, but unsteadiness and maneuvering in some of the flight profiles caused variability and focusing of the propagated booms along the lateral measurement array. The full sonic boom waveforms collected during this study are included in a digital database, BoomFile, which is accessible to researchers. The database also includes the aircraft tracking and local weather profiles. A comparison of the measured to predicted peak overpressures along the lateral spread of the boom carpet demonstrates the results from this study agree as expected with previous sonic boom studies. The measurements are compared with predictions calculated by Carlson’s simplified sonic boom model and a sonic boom ray tracing model. The analysis demonstrates that, in general, the predictions are in good agreement with the measured data, but the models overestimate the overpressures as the lateral cutoff is approached. Moreover, the comparison reveals that Carlson’s method is a robust tool for predicting sonic booms produced by nonmaneuvering flights.

Evolution of Interfacial Roughness Correlations of Fe Au Films Grown on Mgo(001) Substrates

AbstractThe growth by sputtering of a series of thin films of Fe/Au on MgO(001) substrates was analyzed using Bragg and diffuse X-ray scattering. The Fe (bcc) layer grows rotated by 45° with respect to the MgO – Au(fcc) (001) epitaxial orientation, resulting in an almost perfect match between the two metallic structures. By collecting the X-ray diffuse scattering under grazing incidence using a 2-dimensional image plate detector, we mapped the reciprocal space of these films. We characterized the correlated interface roughness starting with a buffer of Fe in which only three interfaces are present. The propagation of the roughness was subsequently characterized for Fe/Au multilayers with 40 and 100 bilayers. We observe an enlargement of the surface features as a function of time, evidenced by the longer lateral cutoff length measured for thicker films.

Prediction of sonic boom overpressures near lateral cutoff

Two methods of sonic boom predictions are used to compare predicted overpressures to measured sonic booms to quantify the effects of weather and flight variability on the lateral propagation of the booms. The sonic boom measurements were collected by the US Air Force at Edwards AFB, CA using a variety of supersonic aircraft. The testing included 43 flights from eight different aircraft at several Mach number and altitude combinations. The flights were planned for steady and level operation but some maneuvering of the aircraft caused focusing of the propagated booms at several measurement locations. The comparison of measured to predicted peak overpressures uses both Carlson and Full ray-tracing algorithms. The comparison examines the lateral spread of the boom and the effects on local weather profiles and variability of the flight profile on the propagated boom. This analysis demonstrates that, in general, predictions are in good agreement with the measured values but tend to overestimate the peak overpressures near the lateral cutoff.

Analysis of Sonic Boom Flight Test Measurements Near the Shock Wave Extremity

A NASA flight test program conducted by Langley Research Center personnel during the summer and fall of 1970 was devoted to investigating the sonic boom phenomena near caustics formed by steady flight near the threshold Mach number, during accelerations, and at the lateral extremes of the ground carpet. The vertical extent of the shock waves attached to near sonic (M < 1.0) airplanes was also investigated. The flights were conducted over the 1500 ft instrumented BREN tower so that vertical surveys through the shock waves were measured. These data on caustic phenomena near the shock wave extremity were analyzed in detail and compared with linear theory. Amplifications of shock wave strength varied from 2 to 5 during longitudinal accelerations, from 1 to 1.8 during steady threshold Mach number flight, and up to 3 for small inadvertent accelerations during flight near the threshold Mach number. Caustic-like pressure signatures were also measured near lateral cutoff. However, these were of very low intensity, less than one-half the intensity beneath the flight path. The analysis has indicated the range of validity of linear theory.

Arch Dams: Rio Freddo Dam with Gravity Abutments and Cut-offs

Italian double curvature dam with gravity abutments and lateral cutoff wings; theoretical stress analysis, structural model testing and construction plant; instrumentation for determining actual behavior of dam.