Search NASA⌕ Search

SEARCH · Search NASA

Results for “shock simulation test”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 109 records · Page 6

DSMC Simulations of Hypersonic Flows and Comparison With Experiments

This paper presents computational results obtained with the direct simulation Monte Carlo (DSMC) method for several biconic test cases in which shock interactions and flow separation-reattachment are key features of the flow. Recent ground-based experiments have been performed for several biconic configurations, and surface heating rate and pressure measurements have been proposed for code validation studies. The present focus is to expand on the current validating activities for a relatively new DSMC code called DS2V that Bird (second author) has developed. Comparisons with experiments and other computations help clarify the agreement currently being achieved between computations and experiments and to identify the range of measurement variability of the proposed validation data when benchmarked with respect to the current computations. For the test cases with significant vibrational nonequilibrium, the effect of the vibrational energy surface accommodation on heating and other quantities is demonstrated.

Moss, James N.↗

AI-Enhanced Computational Tools for Entry Systems Modeling

To advance the understanding of complex atmospheric entry phenomena, NASA’s Entry Systems Modeling (ESM) team [1] has developed high-fidelity computational tools addressing multiscale challenges, from material microstructures to full-scale heatshield response. This abstract highlights a subset of ESM tools, focusing on AI integration to enhance workflows and predictive modeling. - PuMA [2] computes effective material properties from high-resolution micro-CT scans, supporting TPS analysis for NASA missions. - TomoSAM [3] automates 3D tomography dataset segmentation for PuMA using the Segment Anything Model, reducing manual effort and improving accuracy. - PATO [4] models porous reactive materials under extreme conditions, with advancements such as unified solvers, mechanical erosion, and TPS coatings for NASA missions. - arcjetCV [5] employs deep learning to analyze arc jet test footage, measuring recession rates, shape changes, and shock standoff distances, bridging simulations, and experiments to reveal TPS ablation behavior. - ARCHeS [6] simulates arc heater plasma flows, modeling turbulence, radiation, and electromagnetic interactions to optimize arc heater performance, validate TPS under extreme conditions, and serve as a foundation for developing digital twins of arc heater facilities. - SPARTA [7] simulates rarefied hypersonic flows and gas-surface interactions for planetary entry missions, leveraging GPU architectures for scalable and efficient aerothermal and ablation analyses. AI-driven solutions, such as deep learning segmentation, have streamlined workflows in ESM tools and still hold significant potential to further accelerate processes and enhance automation in entry systems modeling. [1] Haskins, J.B. (2023), [2] Ferguson, J.C. (2018), [3] Meurisse, J.B.E. (2018), [4] Semeraro, F. (2023), [5] Quintart, A. (2024) [6] Meurisse, J.B.E. (2022), [7] Plimpton, S.J. (2019)

Predictive Modeling↗

Laser High-Cycle Thermal Fatigue of Pulse Detonation Engine Combustor Materials Tested

Pulse detonation engines (PDE's) have received increasing attention for future aerospace propulsion applications. Because the PDE is designed for a high-frequency, intermittent detonation combustion process, extremely high gas temperatures and pressures can be realized under the nearly constant-volume combustion environment. The PDE's can potentially achieve higher thermodynamic cycle efficiency and thrust density in comparison to traditional constant-pressure combustion gas turbine engines (ref. 1). However, the development of these engines requires robust design of the engine components that must endure harsh detonation environments. In particular, the detonation combustor chamber, which is designed to sustain and confine the detonation combustion process, will experience high pressure and temperature pulses with very short durations (refs. 2 and 3). Therefore, it is of great importance to evaluate PDE combustor materials and components under simulated engine temperatures and stress conditions in the laboratory. In this study, a high-cycle thermal fatigue test rig was established at the NASA Glenn Research Center using a 1.5-kW CO2 laser. The high-power laser, operating in the pulsed mode, can be controlled at various pulse energy levels and waveform distributions. The enhanced laser pulses can be used to mimic the time-dependent temperature and pressure waves encountered in a pulsed detonation engine. Under the enhanced laser pulse condition, a maximum 7.5-kW peak power with a duration of approximately 0.1 to 0.2 msec (a spike) can be achieved, followed by a plateau region that has about one-fifth of the maximum power level with several milliseconds duration. The laser thermal fatigue rig has also been developed to adopt flat and rotating tubular specimen configurations for the simulated engine tests. More sophisticated laser optic systems can be used to simulate the spatial distributions of the temperature and shock waves in the engine. Pulse laser high-cycle thermal fatigue behavior has been investigated on a flat Haynes 188 alloy specimen, under the test condition of 30-Hz cycle frequency (33-msec pulse period and 10-msec pulse width including a 0.2-msec pulse spike; ref. 4). Temperature distributions were calculated with one-dimensional finite difference models. The calculations show that that the 0.2-msec pulse spike can cause an additional 40 C temperature fluctuation with an interaction depth of 0.08 mm near the specimen surface region. This temperature swing will be superimposed onto the temperature swing of 80 C that is induced by the 10-msec laser pulse near the 0.53-mm-deep surface interaction region.

Zhu, Dong-Ming↗

Demonstration of a Pyrotechnic Bolt-Retractor System

A paper describes a demonstration of the X-38 bolt-retractor system (BRS) on a spacecraft-simulating apparatus, called the Large Mobility Base, in NASA's Flight Robotics Laboratory (FRL). The BRS design was proven safe by testing in NASA's Pyrotechnic Shock Facility (PSF) before being demonstrated in the FRL. The paper describes the BRS, FRL, PSF, and interface hardware. Information on the bolt-retraction time and spacecraft-simulator acceleration, and an analysis of forces, are presented. The purpose of the demonstration was to show the capability of the FRL for testing of the use of pyrotechnics to separate stages of a spacecraft. Although a formal test was not performed because of schedule and budget constraints, the data in the report show that the BRS is a successful design concept and the FRL is suitable for future separation tests.

Johnston, Nick↗

Statistical Treatment of Earth Observing System Pyroshock Separation Test Data

The Earth Observing System (EOS) AM-1 spacecraft for NASA's Mission to Planet Earth is scheduled to be launched on an Atlas IIAS vehicle in June of 1998. One concern is that the instruments on the EOS spacecraft are sensitive to the shock-induced vibration produced when the spacecraft separates from the launch vehicle. By employing unique statistical analysis to the available ground test shock data, the NASA Lewis Research Center found that shock-induced vibrations would not be as great as the previously specified levels of Lockheed Martin. The EOS pyroshock separation testing, which was completed in 1997, produced a large quantity of accelerometer data to characterize the shock response levels at the launch vehicle/spacecraft interface. Thirteen pyroshock separation firings of the EOS and payload adapter configuration yielded 78 total measurements at the interface. The multiple firings were necessary to qualify the newly developed Lockheed Martin six-hardpoint separation system. Because of the unusually large amount of data acquired, Lewis developed a statistical methodology to predict the maximum expected shock levels at the interface between the EOS spacecraft and the launch vehicle. Then, this methodology, which is based on six shear plate accelerometer measurements per test firing at the spacecraft/launch vehicle interface, was used to determine the shock endurance specification for EOS. Each pyroshock separation test of the EOS spacecraft simulator produced its own set of interface accelerometer data. Probability distributions, histograms, the median, and higher order moments (skew and kurtosis) were analyzed. The data were found to be lognormally distributed, which is consistent with NASA pyroshock standards. Each set of lognormally transformed test data produced was analyzed to determine if the data should be combined statistically. Statistical testing of the data's standard deviations and means (F and t testing, respectively) determined if data sets were significantly different at a 95-percent confidence level. If two data sets were found to be significantly different, these families of data were not combined for statistical purposes. This methodology produced three separate statistical data families of shear plate data. For each population, a P99.1/50 (probability/confidence) per-separation-nut firing level was calculated. By using the binomial distribution, Lewis researchers determined that this pernut firing level was equivalent to a P95/50 per-flight confidence level. The overall envelope of the per-flight P95/50 levels led to Lewis' recommended EOS interface shock endurance specification. A similar methodology was used to develop Lewis' recommended EOS mission assurance levels. The available test data for the EOS mission are significantly larger than for a normal mission, thus increasing the confidence level in the calculated expected shock environment. Lewis significantly affected the EOS mission by properly employing statistical analysis to the data. This analysis prevented a costly requalification of the spacecraft's instruments, which otherwise would have been exposed to significantly higher test levels.

McNelis, Anne M.↗

Design and Development of a Laboratory-Scale Ice Adhesion Testing Device

When an aircraft traverses through clouds containing supercooled water droplets, in-flight icing can occur that negatively affects vehicle performance by increasing weight and drag leading to loss of lift. Super-cooled water droplets present in clouds that impact vehicle surfaces can lead to inflight icing any time during the year.1 Most events occur at temperatures ranging from 0 to -20degC. Ice generated on the aircraft can vary between clear/glaze, rime, and mixed (Fig. 1) depending on air temperature (-5 to -20degC), liquid water content (0.3-0.6 g/m3), and droplet size (median volumetric diameter of 15-40 μm). Current strategies to remove ice are based on active technologies such as pneumatic boots, heated surfaces, and deicing agents (i.e., ethylene- and propylene-based glycols). The latter have potential environmental concerns. A passive approach to mitigate accreting ice that is actively being investigated are protective coatings. An ice mitigating coating could potentially be used as a stand-alone material, but more likely in combination with an active approach. In the latter scenario, potential reduction in power consumption by the active approach may be realized. To determine the ice adhesion strength of impact ice that is representative of the aircraft environment is not a trivial matter. Test methods utilizing slowly formed ice (i.e., freezer ice) do not accurately simulate this environment. Likewise, some testing methodologies involve sample relocation from the icing environment to the test chamber that can result in thermal shock to the sample, thus affecting the results. The Adverse Environment Rotor Test Stand (AERTS) located at Pennsylvania State University (PSU) has been demonstrated to simulate impact icing conditions within the icing envelope for the determination of ice adhesion shear strength (IASS) without removal/relocation of the sample.2 Due to the confidence in results obtained from AERTS, this instrument is in high demand and requires a significant amount of lead time and capital investment to obtain IASS results. As a solution for quickly and economically screening coatings in a controlled manner under impact icing conditions, a laboratory-scale ice adhesion test and dead blades were then removed from the rotor/blade assembly to obtain the final mass. The IASS of the live blade was determined from the difference in mass (before and after testing) of the live and dead blades, the ice shed area, and the rpm of the shed event. The same live blade sample was tested in triplicate at all three test temperatures. Surface roughness was determined using a Bruker Dektak XT Stylus Profilometer. Measurements were conducted using a 12.5 μm tip at a vertical range of 65.5 μm with an applied force of 3 mg. Data were collected over a 1.0 mm length at a resolution of 0.056 μm/point. Five single line scans at different locations were collected and processed using a two-point leveling subtraction. The resultant Ra (arithmetic roughness) and Rq (root mean square roughness) average values were calculated.

Smith, Joseph G., Jr.↗

Wind Tunnel Model Design for Sonic Boom Studies of Nozzle Jet Flows with Shock Interactions

NASA and the U.S. aerospace industry are performing studies of supersonic aircraft concepts with low sonic boom pressure signatures. The computational analyses of modern aircraft designs have matured to the point where there is confidence in the prediction of the pressure signature from the front of the vehicle, but uncertainty remains in the aft signatures due to boundary layer and nozzle exhaust jet effects. Wind tunnel testing without inlet and nozzle exhaust jet effects at lower Reynolds numbers than in-flight make it difficult to accurately assess the computational solutions of flight vehicles. A wind tunnel test in the NASA Ames 9- by 7-Foot Supersonic Wind Tunnel is planned for February 2016 to address the nozzle jet effects on sonic boom. The experiment will provide pressure signatures of test articles that replicate waveforms from aircraft wings, tails, and aft fuselage (deck) components after passing through cold nozzle jet plumes. The data will provide a variety of nozzle plume and shock interactions for comparison with computational results. A large number of high-fidelity numerical simulations of a variety of shock generators were evaluated to define a reduced collection of suitable test models. The computational results of the candidate wind tunnel test models as they evolved are summarized, and pre-test computations of the final designs are provided.

Wind Tunnel↗

USM3D Simulations for Third Sonic Boom Workshop

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases include a nearfield biconvex shock-plume interaction wind tunnel model, and the C608 Low Boom Flight Demonstrator. Numerical simulations were conducted on the mixed-element and tetrahedral grids provided by the workshop committee, as well as a family of grids generated by an in-house approach for sonic boom analyses known as BoomGrid. The near-field pressure signatures were extracted, propagated to the ground and the perceived loudness levels on the ground were computed. The USM3D near-field pressure signatures, corresponding ground signatures, and loudness levels on the ground are compared with that of mean values from other workshop participants. The effect of three flux-limiters on the accuracy of near-field pressure signatures prediction was investigated and results are compared with that of mean values from other workshop participants. The effect of using wall function grids in accurately predicting near-field pressure signatures was also evaluated.

Supersonics↗

System level mechanical testing of the Clementine spacecraft

This paper discusses the system level structural testing that was performed to qualify the Clementine Spacecraft for flight. These tests included spin balance, combined acoustic and axial random vibration, lateral random vibration, quasi-static loads, pyrotechnic shock, modal survey and on-orbit jitter simulation. Some innovative aspects of this effort were: the simultaneously combined acoustic and random vibration test; the mass loaded interface modal survey test; and the techniques used to assess how operating on board mechanisms and thrusters affect sensor vision.

Haughton, James↗

USM3D Simulations for the Third AIAA Sonic Boom Prediction Workshop

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases included a nearfield biconvex shock-plume interaction wind tunnel model and the C608 Low Boom Flight Demonstrator. Numerical simulations were conducted on the mixed-element and tetrahedral grids provided by the workshop committee, as well as a family of grids generated by an in-house approach known as BoomGrid. The nearfield pressure signatures were extracted and propagated to the ground, and the perceived loudness levels on the ground were computed. The USM3D nearfield pressure signatures, corresponding ground signatures, and loudness levels on the ground were compared with that of mean values from other workshop participants. The effect of three flux-limiters on the accuracy of nearfield pressure signature prediction was investigated and results were compared with that of mean values from other workshop participants. The effect of using wall-function models for predicting nearfield pressure signatures was also evaluated. Results showed that the overpressure signatures extracted from the wall-modeled simulations and the wall-resolved simulations are in good agreement. The use of wall functions (wall-modeled simulations) allowed for approximately 23% savings in the time to solution and yielded comparable perceived loudness levels on the ground to the wall-resolved Reynolds-averaged Navier Stokes simulations.

Supersonics↗

Molecular dynamics simulation of a piston driven shock wave in a hard sphere gas

Molecular dynamics simulation is used to study the piston driven shock wave at Mach 1.5, 3, and 10. A shock tube, whose shape is a circular cylinder, is filled with hard sphere molecules having a Maxwellian thermal velocity distribution and zero mean velocity. The piston moves and a shock wave is generated. All collisions are specular, including those between the molecules and the computational boundaries, so that the shock development is entirely causal, with no imposed statistics. The structure of the generated shock is examined in detail, and the wave speed; profiles of density, velocity, and temperature; and shock thickness are determined. The results are compared with published results of other methods, especially the direct simulation Monte-Carlo method. Property profiles are similar to those generated by direct simulation Monte-Carlo method. The shock wave thicknesses are smaller than the direct simulation Monte-Carlo results, but larger than those of the other methods. Simulation of a shock wave, which is one-dimensional, is a severe test of the molecular dynamics method, which is always three-dimensional. A major challenge of the thesis is to examine the capability of the molecular dynamics methods by choosing a difficult task.

Woo, Myeung-Jouh↗

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.↗

USM3D Simulations for the Third Sonic Boom Prediction Workshop (SBPW-3)

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases include a nearfield biconvex shock-plume interaction wind tunnel model, and the C608 Low Boom Flight Demonstrator. Numerical simulations were conducted on the mixed-element and tetrahedral grids provided by the workshop committee, as well as a family of grids generated by an in-house approach for sonic boom analyses known as BoomGrid. The near-field pressure signatures were extracted, propagated to the ground and the perceived loudness levels on the ground were computed. The USM3D near-field pressure signatures, corresponding ground signatures, and loudness levels on the ground are compared with that of mean values from other workshop participants. The effect of three flux-limiters on the accuracy of near-field pressure signatures prediction was investigated and results are compared with that of mean values from other workshop participants. The effect of using wall function grids in accurately predicting near-field pressure signatures was also evaluated.

Supersonics↗

Numerical simulations of the flow in the HYPULSE expansion tube

Axisymmetric numerical simulations with finite-rate chemistry are presented for two operating conditions in the HYPULSE expansion tube. The operating gas for these two cases is nitrogen and the computations are compared to experimental data. One test condition is at a total enthalpy of 15.2 MJ/Kg and a relatively low static pressure of 2 kPa. This case is characterized by a laminar boundary layer and significant chemical nonequilibrium in the acceleration gas. The second test condition is at a total enthalpy of 10.2 MJ/Kg and a static pressure of 38 kPa and is characterized by a turbulent boundary layer. For both cases, the time-varying test gas pressure predicted by the simulations is in good agreement with experimental data. The computations are also found to be in good agreement with Mirels' correlations for shock tube flow. It is shown that the nonuniformity of the test gas observed in the HYPULSE expansion tube is strongly linked to the boundary layer thickness. The turbulent flow investigated has a larger boundary layer and greater test gas nonuniformity. In order to investigate possibilities of improving expansion tube flow quality by reducing the boundary layer thickness, parametric studies showing the effect of density and turbulent transition point on the test conditions are also presented. Although an increase in the expansion tube operating pressure level would reduce the boundary layer thickness, the simulations indicate that the reduction would be less than what is predicted by flat plate boundary layer correlations.

Wilson, Gregory J.↗

Mechanical environmental test program for the Communications Technology Satellite

This paper describes the spacecraft and subsystem level mechanical environmental test program which was developed for the Communications Technology Satellite (CTS). At the spacecraft level it includes sine and random vibration, static loading, centrifuge loading, pyrotechnic and separation shock simulation and (tentatively) acoustics. At the subsystem level it entails the same type of environmental exposure as applicable. Matrices of system and subsystem tests are presented showing type, level and hardware status for each major test.

Buckingham, R.↗

Electron acceleration at nearly perpendicular collisionless shocks. I - One-dimensional simulations without electron scale fluctuations

Under certain conditions electrons can be reflected and effectively energized at quasi-perpendicular shocks. This process is most prominent close to the point where the upstream magnetic field is tangent to the curved shock. A theoretical explanation of the underlying physical mechanism has been proposed which assumes conservation of magnetic moment and a static, simplified shock profile are performed. Test particle calculations of the electron reflection process in order to examine the results of the theoretical analysis without imposing these restrictive conditions. A one-dimensional hybrid simulation code generates the characteristic field variations across the shock. Special emphasis is placed on the spatial and temporal length scales involved in the mirroring process. The simulation results agree generally well with the predictions from adiabatic theory. The effects of the cross-shock potential and unsteadiness are quantified, and the influence of field fluctuations on the reflection process is discussed.

Krauss-Varban, D.↗

Experimental program for real gas flow code validation at NASA Ames Research Center

The experimental program for validating real gas hypersonic flow codes at NASA Ames is described. Ground based test facilities used include ballistic ranges, shock tubes and shock tunnels, arcjet facilities and heated air hypersonic wind tunnels. Also included are large scale computer systems for kinetic theory simulations and benchmark code solutions. Flight tests consist of the Aeroassist Flight Experiment, the Space Shuttle, Project Fire 2, and planetary probes such as Galileo, Pioneer Venus and PAET.

Deiwert, George S.↗

Measured pressure distributions, aerodynamic coefficients and shock shapes on blunt bodies at incidence in hypersonic air and CF4

Pressure distributions, aerodynamic coefficients, and shock shapes were measured on blunt bodies of revolution in Mach 6 CF4 and in Mach 6 and Mach 10 air. The angle of attack was varied from 0 deg to 20 deg in 4 deg increments. Configurations tested were a hyperboloid with an asymptotic angle of 45 deg, a sonic-corner paraboloid, a paraboloid with an angle of 27.6 deg at the base, a Viking aeroshell generated in a generalized orthogonal coordinate system, and a family of cones having a 45 deg half-angle with spherical, flattened, concave, and cusp nose shapes. Real-gas effects were simulated for the hperboloid and paraboloid models at Mach 6 by testing at a normal-shock density ratio of 5.3 in air and 12 CF4. Predictions from simple theories and numerical flow field programs are compared with measurement. It is anticipated that the data presented in this report will be useful for verification of analytical methods for predicting hypersonic flow fields about blunt bodies at incidence.

Miller, C. G., III↗