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At least 811 records · Page 45

Temperature stabilization of microwave ferrite devices

Thin-film heating element for strip-line circulator is sandwiched between insulation and copper laminations. Disks conform to shape of circulator ferrite disks and are installed between copper-clad epoxy ground planes. Heater design eliminates external cartridges and reduces weight by approximately one-third.

Kaminsky, R.↗

Exact finite elements for conduction and convection

An approach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions.

Thornton, E. A.↗

High spectral and spatial resolution observations of the 12.28 micron emission from H2 in the Orion molecular cloud

The pure rotational S(2) line of molecular hydrogen at 12.28 microns was looked for in 44 positions in the Orion moleular cloud with 6 in. beams and 35 km/s spectral resolution; it was detected in 27 positions. Emission was observed over a velocity range of + or - 100 km/s. The lines are approximately symmetric, and have full widths at half maximum ranging from 100 km/s down to the resolution limit. The distribution of intensities and line shapes is largely consistent with that seen in the 2 micron hydrogen transitions. However, unexpectedly complex line profiles and point-to-point variations in linear shapes appear, particularly in the region near IRc9.

Beck, S. C.↗

Exact finite elements for conduction and convection

An appproach for developing exact one dimensional conduction-convection finite elements is presented. Exact interpolation functions are derived based on solutions to the governing differential equations by employing a nodeless parameter. Exact interpolation functions are presented for combined heat transfer in several solids of different shapes, and for combined heat transfer in a flow passage. Numerical results demonstrate that exact one dimensional elements offer advantages over elements based on approximate interpolation functions. Previously announced in STAR as N81-31507

Thornton, E. A.↗

Neptune radio emission - Predictions based on planetary scaling laws

In this paper a prediction is advanced concerning Neptune's low-frequency radio emission based on the radiometric Bode's law for radio planets in combination with the magnetostrophic scaling law for magnetized planets. The total emitted radio power is predicted to be about 1.6 x 10 to the 7th W, very nearly the same as that predicted and observed for Uranus. Possible emission spectral shapes, based on Saturn and earth-like models, are shown. Using these models, the radio emission frequency range is predicted to extend from approximately 100 to just over 1000 kHz, with a spectral peak between 350 and 500 kHz. If radiation is beamed approximately in the sunward direction, Neptune should be detectable by the planetary radio astronomy experiment onboard the Voyager spacecraft sometime between 45 and 90 days before closest approach. This detection is likely to represent the first direct evidence of a Neptune magnetic field. Possible implications for Neptune's magnetosphere with regard to the time of first detection are discussed.

Desch, Michael D.↗

Problems in determining the surface density of the Galactic disk

A new method is presented for determining the local surface density of the Galactic disk from distance and velocity measurements of stars toward the Galactic poles. The procedure is fully three-dimensional, approximating the Galactic potential by a potential of Staeckel form and using the analytic third integral to treat the tilt and the change of shape of the velocity ellipsoid consistently. Applying the procedure to artificial data superficially resembling the K dwarf sample of Kuijken and Gilmore (1988, 1989), it is shown that the current best estimates of local disk surface density are uncertain by at least 30 percent. Of this, about 25 percent is due to the size of the velocity sample, about 15 percent comes from uncertainties in the rotation curve and the solar galactocentric distance, and about 10 percent from ignorance of the shape of the velocity distribution above z = 1 kpc, the errors adding in quadrature. Increasing the sample size by a factor of 3 will reduce the error to 20 percent. To achieve 10 percent accuracy, observations will be needed along other lines of sight to constrain the shape of the velocity ellipsoid.

Statler, Thomas S.↗

Measured and predicted shock shapes for AFE configuration at Mach 6 in air and in CF4

Shock shapes and stand-off distances were obtained for the Aeroassist Flight Experiment configuration from Mach 6 tests in air and in CF4. Results were plotted for an angle-of attack range from -10 to 10 degrees and comparisons were made at selected angles with inviscid-flow predictions. Tests were performed in the Langley Research Center (LaRC) 20 inch Mach 6 Tunnel (air) at unit free-stream Reynolds numbers (N sub Re, infinity) of 2 million/ft and 0.6 million/ft and in the LaRC Hypersonic CF4 Tunnel at N sub Re, infinity = 0.5 million/ft and 0.3 million/ft. Within the range of these tests, N sub Re, infinity did not affect the shock shape or stand off distance, and the predictions were in good agreement with the measurements. The shock stand-off distance in CF4 was approximately half of that in air. This effect resulted from the differences in density ratio across the normal shock, which was approximately 12 in CF4 and 5 in air. In both test gases, the shock lay progressively closer to the body as angle of attack decreased.

Wells, William L.↗

Comments on the statistical analysis of excess variance in the COBE differential microwave radiometer maps

Cosmic anisotrophy produces an excess variance sq sigma(sub sky) in the Delta maps produced by the Differential Microwave Radiometer (DMR) on cosmic background explorer (COBE) that is over and above the instrument noise. After smoothing to an effective resolution of 10 deg, this excess sigma(sub sky)(10 deg), provides an estimate for the amplitude of the primordial density perturbation power spectrum with a cosmic uncertainty of only 12%. We employ detailed Monte Carlo techniques to express the amplitude derived from this statistic in terms of the universal root mean square (rms) quadrupole amplitude, (Q sq/RMS)(exp 0.5). The effects of monopole and dipole subtraction and the non-Gaussian shape of the DMR beam cause the derived (Q sq/RMS)(exp 0.5) to be 5%-10% larger than would be derived using simplified analytic approximations. We also investigate the properties of two other map statistics: the actual quadrupole and the Boughn-Cottingham statistic. Both the sigma(sub sky)(10 deg) statistic and the Boughn-Cottingham statistic are consistent with the (Q sq/RMS)(exp 0.5) = 17 +/- 5 micro K reported by Smoot et al. (1992) and Wright et al. (1992).

Wright, E. L.↗

First-Generation Jet Propulsion Laboratory "Hockey-Puck" Free-Flying Magnetometers for Distributed In-Situ Multiprobe Measurement of Current Density Filamentation in the Northern Auroral Zone: Enstrophy Mission

The sub-orbital rocket mission was a collaborative project between the University of New Hampshire, Cornell University, and the Jet Propulsion Laboratory (JPL) to study filamentation phenomena in the northern Auroral zone. The Enstrophy mission test flies the JPL Free-Flying Magnetometer (FFM) concept. The FFM technology development task has been funded by NASA develop miniaturized, low-power, integrated "sensorcrafts". JPL's role was to design, integrate, test, and deliver four FFMs for deployment from the sounding rocket, allowing a unique determination of curl-B. This provides a direct measurement of magnetic-field-aligned current density along the rocket trajectory. A miniaturized three-axis fluxgate magnetometer was integrated with a 4-channel 22-bit sigma-delta Analog to Digital Converter (ADC), four temperature sensors, digital control electronics, seven (Li-SOCl2) batteries, two (4 deg x 170 deg field of view) sun-sensors, a fan-shaped-beam laser diode beacon, a (16 MHz) stable Temperature Compensated Crystal Oscillator (TCXO) clock, Radio Frequency (RF) communication subsystem, and an antenna for approximately 15 minutes of operation where data was collected continuously and transmitted in three (3) bursts (approximately 26 seconds each) to ground station antennas at Poker Flat, Alaska. FFMs were stowed within two trays onboard the rocket during the rocket launch and were released simultaneously using the spinning action of the rocket at approximately 300 km altitude (approximately 100 sec. into the flight). FFMs were deployed with spin rate of approximately 17 Hz and approximately 3 m/sec linear velocity with respect to the rocket. For testing purposes while the rocket was in the launch pad and during flight prior to release of FFMs from the rocket, commands (such as "power on", "test", "flight", "power off', and clock "Reset" signal) were transmitted via a infrared Light Emitting Diode to an infrared detector in the FFM. Special attention was paid to low magnetic signature electronic design and choice of materials in packaging. The miniaturized fluxgate magnetometers had a range of 1-60000 nT with 0.1% full-scale linearity. The frequency range of interest for magnetic measurement was 10 mHz - 50 Hz. Digital data from the magnetometer's three axes were placed in a 4MB Static Random Access Memory (SRAM) in data packages (frames) formatted together with time tags and frame ID. After a specified time was elapsed, the data were Viterbi encoded and transmitted at a rate of 100 kbps (BPSK). Each of the four FFMs transmitted at different frequency. These carrier frequencies were in the range of 2200-2300 MHz. The antenna was a single patch on a high dielectric constant substrate covering one end-plate of the hockey-puck-sized unit. The local clocks aboard the FFMs were reset at the start of the mission and stayed synchronized within 3 msec during the mission. Position of each FFM with respect to the rocket is calculated by the knowledge of its release velocity (measured at exit point of the FFM launcher tract) providing an accuracy of 1 m over the maximum range of 3 km. Spatial and temporal nature of observants can be separated to within 3 m in space or 3 msec time interval.

Javadi, H.↗

A Proposed Landing Site for the 2001 Lander in a Hematite-Rich Region in Sinus Meridiani

The Thermal Emission Spectrometer (TES) instrument on the Mars Global Surveyor (MGS) mission has identified an accumulation of crystalline hematite (alpha-Fe2O3) that covers an area with very sharp boundaries approximately 350 by 350-750 km in size centered near 2 S latitude between 0 and 5 W longitude (Sinus Meridiani). The depth and shape of the hematite fundamental bands in the TES spectra show that the hematite is relatively coarse grained (> 5-10 microns). The spectrally-derived areal abundance of hematite varies with particle size from approx. 10% for particles > 30 microns in diameter to 40-60% for unpacked 10 micron powders. The hematite in Sinus Meridiani is thus distinct from the fine-grained (diameter < 5-10 microns), red, crystalline hematite considered, on the basis of visible and near-IR data, to be a minor spectral component in Martian bright regions. A map of the hematite index has been constructed using TES data from 11 orbits, including the six in which hematite was detected and five orbits that passed nearby that showed no evidence of hematite. The boundaries of the hematite-rich region are sharp at spatial scales of about 10 km. Within this region there are spatial variations in spectral band depth of a factor of two to three. At the present time the hematite-rich region has not been completely mapped. However, by using the bounding orbits to the east and west in which hematite was not detected, we can establish that this region covers an area that is between 350 and 750 km in length and over -350 km in width (1.2 x 10(exp 5) to 2.6 x 10(exp 5 sq km). The hematite-rich surface discovered by TES closely corresponds with smooth-surfaced unit ('sm') that appears to be the surface of a layered sequence. The presence of small mesas superposed on 'sm' and the degraded nature of the small impact craters suggests that material has been removed from this unit. These layered materials do not appear to be primary volcanic products (i.e., lava flows) because there are no associated lava flow lobes, fronts or pressure ridges; there are no fissures or calderae, nor any other features that can be interpreted as volcanic within 'sm'. Bowl-shaped depressions in 'sm' and the remnant mesas on top of a portion of this unit suggest that deflation has removed material that was once above the present surface of 'sm'. The most likely cause of the deflation is wind, which suggests that the layered materials are relatively friable. In summary, Sinus Meridiani hematite is closely associated with a smooth, layered, friable surface that is interpreted to be sedimentary in origin.

Christensen, Philip R.↗

Aerodynamics of Stardust Sample Return Capsule

Successful return of interstellar dust and cometary material by the Stardust Sample Return Capsule requires an accurate description of the Earth entry vehicle's aerodynamics. This description must span the hypersonic-rarefied, hypersonic-continuum, supersonic, transonic, and subsonic flow regimes. Data from numerous sources are compiled to accomplish this objective. These include Direct Simulation Monte Carlo analyses, thermochemical nonequilibrium computational fluid dynamics, transonic computational fluid dynamics, existing wind tunnel data, and new wind tunnel data. Four observations are highlighted: 1) a static instability is revealed in the free-molecular and early transitional-flow regime due to aft location of the vehicle s center-of-gravity, 2) the aerodynamics across the hypersonic regime are compared with the Newtonian flow approximation and a correlation between the accuracy of the Newtonian flow assumption and the sonic line position is noted, 3) the primary effect of shape change due to ablation is shown to be a reduction in drag, and 4) a subsonic dynamic instability is revealed which will necessitate either a change in the vehicle s center-of-gravity location or the use of a stabilizing drogue parachute.

Mitcheltree, R. A.↗

Joining and Assembly of Bulk Metallic Glass Composites Through Capacitive Discharge

Bulk metallic glasses (BMGs), a class of amorphous metals defined as having a thickness greater than 1 mm, are being broadly investigated by NASA for use in spacecraft hardware. Their unique properties, attained from their non-crystalline structure, motivate several game-changing aerospace applications. BMGs have low melting temperatures so they can be cheaply and repeatedly cast into complex net shapes, such as mirrors or electronic casings. They are extremely strong and wear-resistant, which motivates their use in gears and bearings. Amorphous metal coatings are hard, corrosion-resistant, and have high reflectivity. BMG composites, reinforced with soft second phases, can be fabricated into energy-absorbing cellular panels for orbital debris shielding. One limitation of BMG materials is their inability to be welded, bonded, brazed, or fastened in a convenient method to form larger structures. Cellular structures (which can be classified as trusses, foams, honeycombs, egg boxes, etc.) are useful for many NASA, commercial, and military aerospace applications, including low-density paneling and shields. Although conventional cellular structures exhibit high specific strength, their porous structures make them challenging to fabricate. In particular, metal cellular structures are extremely difficult to fabricate due to their high processing temperatures. Aluminum honeycomb sandwich panels, for example, are used widely as spacecraft shields due to their low density and ease of fabrication, but suffer from low strength. A desirable metal cellular structure is one with high strength, combined with low density and simple fabrication. The thermoplastic joining process described here allows for the fabrication of monolithic BMG truss-like structures that are 90% porous and have no heat-affected zone, weld, bond, or braze. This is accomplished by welding the nodes of stacked BMG composite panels using a localized capacitor discharge, forming a single monolithic structure. This removes many complicated and costly fabrication steps. Moreover, the cellular structures detailed in this work are among the highest- strength and most energy-absorbent materials known. This implies that a fabricated structure made from these materials would have unequaled mechanical properties compared to other metal foams or trusses. The process works by taking advantage of the electrical properties of the matrix material in the metal-matrix composite, which in this case is a metallic glass. Due to the random nanoscale arrangement of atoms (without any grain boundaries), the matrix glass exhibits a near-constant electrical resistivity as a function of temperature. By placing the composite panels between two copper electrode plates and discharging a capacitor, the entire matrix of the panel can be heated to approximately 700 C in 10 milliseconds, which is above the alloy s solidus but below the liquidus. By designing the geometry of the panels into the shape of an egg box, the electrical discharge localizes only in the tips of each pyramidal cell. By applying a forging load during discharge, the nodes of the panels can be fused together into a single piece, which then dissipates heat through radiation back into a glassy state. This means that two panels can be metallurgically fused into one panel with no heat-affected zone, creating a seamless connection between panels. During the process, the soft metal particles (dendrites) that are uniformly distributed in the glassy matrix to increase the toughness are completely unaffected by the thermoplastic joining. The novelty is that a truss (or foam-like) structure can be formed with excellent energy- absorbing capabilities without the need for machining. The technique allows for large-scale fabrication of panels, well-suited for spacecraft shields or military vehicle door panels. Crystalline metal cellular structures cannot be fabricated using the thermoplastic joining technique described here. If metal panels were te assembled into a cellular structure, they would either have to be welded, brazed, bonded, or fastened together, creating a weak spot in the structure at each connection. Welded parts require a welding material to be added to the joint and exhibit a soft and weak heat-affected zone. Brazing and bonding do not form a metallurgical joint and thus exhibit low strengths, especially when the panels are pulled apart and fasteners require high-stress-concentration holes to be drilled. No equivalent rapid heating method exists for assembling metal panels together into cellular structures, and thus, those parts must be foamed, machined, or investment cast if they are to form a monolithic structure. If the crystalline panels were to be joined using capacitive discharge, as with a spot welder, their bond would be very weak, and the panels would have to be extremely thin. In contrast, the strength of joined BMG parts has been demonstrated to have strength comparable to the parent material. This technique opens up the possibility of using large-scale BMG hardware in spacecraft, military, or commercial applications.

Hofmann, Douglas C.↗

Further Development Of Aperture: A Precise Extremely Large Reflective Telescope Using Re-Configurable Elements: NASA Innovative Advanced Concepts (NIAC) - Phase II

One of the pressing needs for space ultraviolet-visible astronomy is a design to allow larger mirrors than the James Webb Space Telescope primary. The diameter of the rocket fairing limits the mirror diameter such that all future missions calling for mirrors up to 16 meters in diameter or larger will require a mirror that is deployed post-launch. In response to the deployment requirement, we address the issues of this concept called "A Precise Extremely Large Reflective Telescope Using Reconfigurable Elements (APERTURE) with both hardware experiments and software simulations... We designed and built several fixtures with O-rings to hold a membrane. We established a coating process to make a membrane that was coated on one side with Cr and the other side with Cr-Terfenol-D-NiCo. The Terfenol-D (T-D hereafter) is the MSM (Magnetic Smart Memory) we use. We bought and established a procedure for measuring a deformation over time and purchased a Shack Hartmann system from Imagine Optic (https://www.imagine-optic.com). The first substrate we used was DuPont (TM) Kapton® polyimide film. Due to material creep, we found the stability over a 48-hour period with a Kapton substrate was not as good as desired (greater than 1 micron). We then switched to CP1 Polyimide. We found the CP1 much more stable to creep, being stable from about 3 hours to 48 hours to within a measurement error to below approximately 0.1 micron. We produced a 13 micron maximum deviation on a 50-millimeter-diameter piece of CP1 (25 microns thick). The T-D coating was about 2 microns, and the other layers, about 10 nanometers. The magnetic field at the base was about 0.1 teslas. We can make the T-D film at least 5 times thicker and the magnetic field at least 5 times stronger, and hence make deformations as much as 25 times larger. We have a formed a collaboration produced at the NIAC (NASA Innovative Advanced Concepts) mid-term review with Dr. Ron Shiri of Goddard Space Flight Center (GSFC) to explore making controlled deviations on lambda/14-lambda/20 scales which are required to bring a surface to the diffraction limit. We carried out only preliminary work on Si using a Coordinate Measuring Machine (CMM), which produced deviations on the 1 micron level. We are still working on a program to bring to GSFC a flat enough (radius of curvature greater than 10 microns) -coated a Si piece with Cr, T-D, NiCo. Then we plan to carry out tests with an interferometer. Further, we formed a new collaboration with Prof. Rajan Vaidyanathan of the University of Central Florida to replace the CP1 with a shape memory alloy (SMA). With his collaboration, we acquired new Federal funding outside of NASA to explore the use of SMAs (we use NiTi). Our preliminary results indicate that we can produce deformations greater than 1 micron on approximately 100 microns thick. Furthermore we have shown that the NiTi can deploy to better than 1 micron of its set original and then trained shape.

Re-Configurable Elements↗

Radar Observations of Asteroid 1620 Geographos

Goldstone radar observations of Geographos from August 28 through September 2, 1994 yield over 400 delay-Doppler images whose linear spatial resolutions range from approximately 75 - 151 m, and 138 pairs of dual-polarization (OC, SC) spectra with one-dimensional resolution of 103 m. Each data type provides thorough rotational coverage. The images contain an intrinsic north/south ambiguity, but the equatorial view allows accurate determination of the shape of the radar-facing part of the asteroid's pole-on silhouette at any rotation phase. Sums of co-registered images that cover nearly a full rotation have defined the extremely elongated shape of that silhouette (S. J. Ostro, K. D. Rosema, R. S. Hudson, R. F. Jurgens, J. D. Giorgini, R. Winkler, D. K. Yeomans, D. Choate, R. Rose, M. A. Slade, S. D. Howard, and D. L. Mitchell 1995, Nature 375, 474-477). Here we present individual images and co-registered sums over approximately 30 deg of rotation phase that show the silhouette's structural characteristics in finer detail and also reveal numerous contrast features "inside" the silhouette. Those features include several candidate craters as well as indications of other sorts of large-scale topographic relief, including a prominent central indentation. Protuberances at the asteroid's ends may be related to the pattern of ejecta removal and deposition caused by the asteroid's gravity field. The asteroid's surface is homogeneous and displays only modest roughness at centimeter-to-meter scales. Our estimates of radar cross section and the currently available constraints on the asteroid's dimensions are consistent with a near-surface bulk density between 2 and 3 g/cc. The delay-Doppler trajectory of Geographos' center of mass has been determined to about 200 m on August 28 and to about 100 m on August 31, an improvement of two orders of magnitude over pre-observation ephemerides.

Ostro, Steven J.↗

A Communication Channel Density Estimating Generative Adversarial Network

Autoencoder-based communication systems use neural network channel models to backwardly propagate message reconstruction error gradients across an approximation of the physical communication channel. In this work, we develop and test a new generative adversarial network (GAN) architecture for the purpose of training a stochastic channel approximating neural network. In previous research, investigators have focused on additive white Gaussian noise (AWGN) channels and/or simplified Rayleigh fading channels, both of which are linear and have well defined analytic solutions. Given that training a neural network is computationally expensive, channel approximation networks— and more generally the autoencoder systems—should be evaluated in communication environments that are traditionally difficult. To that end, our investigation focuses on channels that contain a combination of non-linear amplifier distortion, pulse shape filtering, intersymbol interference, frequency-dependent group delay, multipath, and non-Gaussian statistics. Each of our models are trained without any prior knowledge of the channel. We show that the trained models have learned to generalize over an arbitrary amplifier drive level and constellation alphabet. We demonstrate the versatility of our GAN architecture by comparing the marginal probability density function of several channel simulations with that of their corresponding neural network approximations

Smith, Aaron↗

Equivalent plate structural modeling for wing shape optimization including transverse shear

A new technique for structural modeling of airplanes wings is presented taking transverse shear effects into account. The kinematic assumptions of first-order shear deformation plate theory in combination with numerical analysis, where simple polynomials are used to define geometry, construction, and displacement approximations, lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps, and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of wing modeling techniques based on classical plate theory are discussed, and the improved accuracy of the new equivalent plate technique is demonstrated through comparison with finite element analysis and test results. Expressions for analytical derivatives of stiffness, mass, and load terms with respect to wing shape are given. Based on these, it is possible to obtain analytic sensitivities of displacements, stresses, and natural frequencies with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗

Equivalent Plate Structural Modeling for Wing Shape Optimization Including Transverse Shear

A new technique for structural modeling of airplane wings is presented taking transverse shear effects into account. The kinematic assumptions of first-order shear deformation plate theory In combination with numerical analysis, where simple polynomials are used to define geometry, construction, and displacement approximations, lead to analytical expressions for elements of the stiffness and mass matrices and load vector. Contributions from the cover skins, spar and rib caps, and spar and rib webs are included as well as concentrated springs and concentrated masses. Limitations of wing modeling techniques based on classical plate theory are discussed, and the Improved accuracy of the new equivalent plate technique is demonstrated through comparison with finite element analysis and test results. Expressions for analytical derivatives of stiffness, mass, and load terms with respect to wing shape are given. Based on these, it is possible to obtain analytic sensitivities of displacements, stresses, and natural frequencies with respect to planform shape and depth distribution. This makes the new capability an effective structural tool for wing shape optimization.

Livne, Eli↗

An approximate viscous shock layer technique for calculating chemically reacting hypersonic flows about blunt-nosed bodies

An approximate axisymmetric method was developed which can reliably calculate fully viscous hypersonic flows over blunt nosed bodies. By substituting Maslen's second order pressure expression for the normal momentum equation, a simplified form of the viscous shock layer (VSL) equations is obtained. This approach can solve both the subsonic and supersonic regions of the shock layer without a starting solution for the shock shape. The approach is applicable to perfect gas, equilibrium, and nonequilibrium flowfields. Since the method is fully viscous, the problems associated with a boundary layer solution with an inviscid layer solution are avoided. This procedure is significantly faster than the parabolized Navier-Stokes (PNS) or VSL solvers and would be useful in a preliminary design environment. Problems associated with a previously developed approximate VSL technique are addressed before extending the method to nonequilibrium calculations. Perfect gas (laminar and turbulent), equilibrium, and nonequilibrium solutions were generated for airflows over several analytic body shapes. Surface heat transfer, skin friction, and pressure predictions are comparable to VSL results. In addition, computed heating rates are in good agreement with experimental data. The present technique generates its own shock shape as part of its solution, and therefore could be used to provide more accurate initial shock shapes for higher order procedures which require starting solutions.

Cheatwood, F. Mcneil↗