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NASA NTRS1997

Hypersonic Flight Experimentation - Status and Shortfalls

For some 50 years, man has flown, very successfully, in and through the hypersonic flow regime up to Mach Number 35 and beyond with very few "surprises." In general, hypersonic vehicles have performed successfully with good-to-excellent comparisons between flight, ground facility extrapolations and computations being the norm. A consistent and glaring shortfall to date is in the boundary layer transition arena, due primarily to the dominance for flight vehicles of roughness induced transition where the roughness characteristics are extremely vehicle specific and dictated by either vehicle operational exigencies such as antennas, handling plugs, and field joints, etc. or characteristics of the thermal protection system. Emerging shortfalls for future systems which require research flight tests include transition and air-breathing propulsion-related technology for both cruise and space access. Specific flight test recommendations include "systems demonstrations" for various air-breathing propulsion options and efforts to correct a pervasive lack of adequate analysis of the existing, and very expensive to replicate, hypersonic flight data base.

Bushnell, Dennis M.↗
NASA NTRS1978

Comparisons of measured and calculated potential magnetic fields

Photospheric line-of-sight and transverse-magnetic-field data obtained, with a vector magnetograph system for an isolated sunspot are described. A study of the linear polarization patterns and of the calculated transverse field lines indicates that the magnetic field of the region is very nearly potential. The H-alpha fibril structures of this region as seen in high-resolution photographs corroborate this conclusion. Consequently, a potential-field calculation is described using the measured line-of-sight fields together with assumed Neumann boundary conditions; both are necessary and sufficient for a unique solution. The computed transverse fields are then compared with the measured transverse fields to verify the potential-field model and assumed boundary values. The implications of these comparisons for the validity of magnetic-field extrapolations using potential theory are discussed.

Hagyard, M. J.↗
NASA NTRS2017

Volatile Content of 4-Vesta: Evidence from Unequilibrated Eucrites

Eucrites are a class of basaltic meteorites that, along with the howardites and diogenites, likely derive from the asteroid 4-Vesta. This asteroid is depleted in moderately volatile elements relative to the Earth and carbonaceous chondrites. Extrapolation of this depletion trend predicts that bulk silicate 4-Vesta (BSV) contains at most 250-1000 μg/g H2O, which is approximately a factor of two lower than the H2O content of Earth. To obtain more accurate H2O and F estimates for BSV, we examined four unequilibrated antarctic meteorites, Yamato(Y)-793548, Y-82210, Y-75011, and Y-74450, by EPMA and SIMS. Pyroxenes contain MgO-rich cores and FeO-rich rims, consistent with primary magmatic zoning. Volatile concentrations generally follow patterns expected for growth zoning with lower values in the cores and higher in the rims. These features indicate that thermal metamorphism and other post-crystallization processes did not significantly perturb the volatile contents of these unequilibrated eucrite pyroxenes. We used these data to derive best estimates for the BSV H2O and F content based on experimentally determined pyroxene-melt partition coefficients and models for magma generation on Vesta. In addition, we measured D/H in the early crystallizing pyroxenes and late crystallzing apatites. We find that the D/H of pyroxene and apatite are within error of one another as well as previous measurements of apatite in equilibrated eucrites. These results imply that degassing was minimal or did not fractionate D/H. Degassing may have been limited if eucrites were shallowly emplaced sills or dykes, or the total H2O content of the magmas was too low for vapor saturation. An alternative mechanism for limited D/H fractionation is that degassing did occur, but the H2/H2O of the exsolved vapor was approximately 15:85, as predicted from experiments.

Sarafian, A. R.↗
NASA NTRS2007

The Remarkable X-ray Spectrum of the Broad-Line Radio Galaxy 3C 445

The nearby (z=0.057) radio-loud source 3C 445, optically classified as a Broad-Line Radio Galaxy, exhibits an X-ray spectrum strongly reminiscent of an obscured AGN, suggesting we are seeing this source at a relatively large angle from the radio jet. Here we present an archival 15 ks XMM-Newton observation of 3C 445 which confirms the remarkable complexity of its X-ray emission. The X-ray emission is described by a power law continuum with GAMMA approximately equal to 1.4, absorbed by several layers of cold gas, plus strong cold reflection. A narrow, unresolved Fe Kalpha emission line is detected, confirming previous findings, with EW approximately equal to 400 eV. A soft excess is present below 2 keV over the extrapolation of the hard X-ray power law, which we model with a power law with the same photon index and absorbed by a column density N(sub H)5 approximately equal to 10(sup 20) cm(sup -2) in excess to Galactic. Remarkably, a host of emission lines are present below 2 keV, confirming previous indications from ASCA, due to H- and He-like O, Mg, and Si. The detection of two features at 0.74 and 0.87 keV, identified with OVII and OVIII Radiative Recombination Continuum features, suggest an origin of the lines from a photoionized gas, with properties very similar to radio-quiet obscured AGN. Two different ionized media, or a single stratified medium, are required to fit the soft X-ray data satisfactorily. The similarity of the X-ray spectrum of 3C 445 to Seyferts underscores that the central engines of radio-loud and radio-quiet AGN similarly host both cold and warm gas.

Sambruna, R. M.↗
NASA NTRS1997

The High-Energy Continuum Emission of the Gamma-Ray Blazar PKS 0528+134

We present Advanced Satellite for Cosmology and Astrophysics (ASCA) observations of the gamma-ray blazar PKS 0528 + 134, obtained at two separate epochs in 1994 August and 1995 March. These data represent the first measurement of the X-ray continuum emission of this source in the medium-hard X-ray band. Both ASCA spectra are consistent with a single power law with photon index GAMMA approximate 1.7-1.8 and column density N(sub H) approximately 5 x 10(exp 21) /sq cm, higher than Galactic. The X-ray flux increased by a factor of 4 in approximately 7 months without appreciable change of the spectral shape. During the lower state of 1994 August, PKS 0528 + 134 was observed simultaneously in the optical, X-rays, and at gamma-ray energies with EGRET. The gamma-ray intensity is the faintest detected thus far in the source, with a steep spectrum (GAMMA approximately 2.7). The extrapolation of the X-ray continuum to the gamma-ray range requires a sharp spectral break at approximately 10(exp 22) Hz. We discuss the radio through gamma-ray spectral energy distribution of PKS 0528 + 134, comparing the low state of 1994 August with the flare state of 1993 March. We show that in PKS 0528 + 134, a non-negligible contribution from the external radiation field is present and that, although synchrotron self-Compton scenarios cannot be ruled out, inverse Compton upscattering of thermal seed photons may be the dominant cooling process for the production of the high-energy continuum in this blazar.

Sambruna, Rita M.↗
NASA NTRS2002

New CERES Data Examined for Evidence of Tropical Iris Feedback

New data products are available from the CERES instrument, a part of the NASA Earth Observing System. The Single Scanner Footprint (SSF) product combines radiative fluxes with extensive information on the cloud conditions in the footprint, which are retrieved using the co-orbiting imager instrument. These data have been analyzed to more accurately define the radiative properties for the various regions of the recently-proposed adaptive infrared Iris. A variety of ways of defining the cloudy moist region were examined. According to CERES, the net radiative flux for the cloudy moist region ranges between 28 and 54 W/m2 depending on the specific definition used. This is in contrast to the value of 123 W/m2 which was somewhat subjectively assigned by LCH. This simple model may miss many feedbacks in the climate system, but it should provide a rough range of the climate variations if the physics of the Iris is correct. There is some question whether the change in cloudy moist area with cloud-weighted SST actually represents a useful quantity, and whether extrapolating it from a regional variation to a global response to warmer climate is appropriate. Regardless, the current results show that the proposed Iris feedback is very much weaker when objectively-determined radiative properties are used in the model.

Chambers, Lin H.↗
NASA NTRS1999

The spacing of the interstellar 6.2 and 7.7 micron emission features as an indicator of polycyclic aromatic hydrocarbon size

A database of astrophysically relevant, infrared spectral measurements on a wide variety of neutral as well as positively and negatively charged polycyclic aromatic hydrocarbons (PAHs), ranging in size from C10H8 through C48H20, is now available to extend the interstellar PAH model. Beyond simply indicating general characteristics of the carriers, this collection of data now makes it possible to conduct a more thorough interpretation of the details of the interstellar spectra and thereby derive deeper insights into the nature of the emitting material and conditions in the emission zones. This Letter is the first such implementation of this spectral database. The infrared spectra of PAH cations, the main PAH form in the most energetic emission zones, are usually dominated by a few strong features in the 1650-1100 cm-1 (6.1-9.1 microns) region that tend to cluster the vicinity of the interstellar emission bands at 1610 and 1320 cm-1 (6.2 and 7.6 microns), but with spacings typically somewhat less than that observed in the canonical interstellar spectrum. However, the spectra in the database show that this spacing increases steadily with molecular size. Extrapolation of this trend indicates that PAHs in the 50-80 carbon atom size range are entirely consistent with the observed interstellar spacing. Furthermore, the profile of the 1610 cm-1 (6.2 microns) interstellar band indicates that PAHs containing as few as 20 carbon atoms contribute to this feature.

Extraterrestrial Environment↗
NASA NTRS2014

Convective and Diffusive O2 Transport Components of Peak Oxygen Uptake Following Long-duration Spaceflight

Spaceflight reduces aerobic capacity and may be linked with maladaptations in the O2 transport pathway. The aim was to 1) evaluate the cardiorespiratory adaptations following 6 months aboard the International Space Station and 2) model the contributions of convective (Q (raised dot) O2) and peripheral diffusive (DO2) components of O2 transport to changes in peak O2 uptake (V (raised dot) O2PEAK). To date, 1 male astronaut (XX yrs) completed an incremental exercise test to measure V (raised dot) O2PEAK prior to and 2 days post-flight. Cardiac output (Q (raised dot) ) was measured at three submaximal work rates via carbon dioxide rebreathing. The Q (raised dot) :V (raised dot) O2 relationship was extrapolated to V (raised dot) O2PEAK to determine Q (raised dot) PEAK. Hemoglobin concentration was measured at rest via a venous blood sample. These measurements were used to model the changes in Q (raised dot) O2 and DO2 using Fick's principle of mass conservation and Law of Diffusion as established by Wagner and colleagues (Annu. Rev. Physiol 58: 21-50, 1996 and J. Appl. Physiol. 73: 1067-1076, 1992). V (raised dot) O2PEAK decreased postflight from 3.72 to 3.45 l min-1, but Q (raised dot) PEAK increased from 24.5 to 27.7 l min-1. The decrease in V (raised dot) O2PEAK post-flight was associated with a 21.2% decrease in DO2, an 18.6% decrease in O2 extraction, but a 3.4% increase in Q (raised dot) O2. These preliminary data suggest that long-duration spaceflight reduces peripheral diffusing capacity and that it largely contributes to the post-flight decrease in aerobic capacity.

Ade, Carl J.↗
NASA NTRS2010

Dispersion and Lifetime of the SO2 Cloud from the August 2008 Kasatochi Eruption

Hemispherical dispersion of the SO2 cloud from the August 2008 Kasatochi eruption is analyzed using satellite data from the Ozone Monitoring Instrument (OMI) and the Goddard Trajectory Model (GTM). The operational OMI retrievals underestimate the total SO2 mass by 20-30% on 8-11 August, as compared with more accurate offline Extended Iterative Spectral Fit (EISF) retrievals, but the error decreases with time due to plume dispersion and a drop in peak SO2 column densities. The GTM runs were initialized with and compared to the operational OMI SO2 data during early plume dispersion to constrain SO2 plume heights and eruption times. The most probable SO2 heights during initial dispersion are estimated to be 10-12 km, in agreement with direct height retrievals using EISF algorithm and IR measurements. Using these height constraints a forward GTM run was initialized on 11 August to compare with the month-long Kasatochi SO2 cloud dispersion patterns. Predicted volcanic cloud locations generally agree with OMI observations, although some discrepancies were observed. Operational OMI SO2 burdens were refined using GTM-predicted mass-weighted probability density height distributions. The total refined SO2 mass was integrated over the Northern Hemisphere to place empirical constraints on the SO2 chemical decay rate. The resulting lower limit of the Kasatochi SO2 e-folding time is approx.8-9 days. Extrapolation of the exponential decay back in time yields an initial erupted SO2 mass of approx.2.2 Tg on 8 August, twice as much as the measured mass on that day.

Krotkov, N. A.↗
NASA NTRS2012

Earth Radiation Imbalance from a Constellation of 66 Iridium Satellites: Climate Science Aspects

The "global warming hiatus" since the 1998 El Nino, highlighted by Meehl et al., and the resulting "missing energy" problem highlighted by Trenberth et al., has opened the door to a more fundamental view of climate change than mere surface air temperature. That new view is based on two variables which are strongly correlated: the rate of change of ocean heat content d(OHC)/dt; and Earth Radiation Imbalance (ERI) at the top of the atmosphere, whose guesstimated range is 0.4 to 0.9 Watts per square meters (this imbalance being mainly due to increasing CO2). The Argo float array is making better and better measurements of OHC. But existing satellite systems cannot measure ERI to even one significant digit. So, climate model predictions of ERI are used in place of real measurements of it, and the satellite data are tuned to the climate model predictions. Some oceanographers say "just depend on Argo for understanding the global warming hiatus and the missing energy", but we don't think this is a good idea because d(OHC)/dt and ERI have different time scales and are never perfectly correlated. We think the ERB community needs to step up to measuring ERI correctly, just as oceanographers have deployed Argo to measure OHC correctly. This talk will overview a proposed constellation of 66 Earth radiation budget instruments, hosted on Iridium satellites, that will actually be able to measure ERI to at least one significant digit, thus enabling a crucial test of climate models. This constellation will also be able to provide ERI at two-hourly time scales and 500-km spatial scales without extrapolations from uncalibrated narrowband geostationary instruments, using the highly successful methods of GRACE to obtain spatial resolution. This high time resolution would make ERI a synoptic variable like temperature, and allow studies of ERI's response to fast-evolving phenomena like dust storms and hurricanes and even brief excursions of Total Solar Irradiance. Time permitting, we will also discuss the emerging view of clear vs. cloudy and its implications for the traditional ERB approach.

Wiscombe, W.↗
NASA NTRS1997

The High-energy Continuum Emission of the Gamma-Ray Blazar PKS 0528+134

We present Advanced Satellite for Cosmology and Astrophysics (ASCA) observations of the gamma-ray blazar PKS 0528 + 134, obtained at two separate epochs in 1994 August and 1995 March. These data represent the first measurement of the X-ray continuum emission of this source in the medium-hard X-ray band. Both ASCA spectra are consistent with a single power law with photon index GAMMA approx. = 1.7-1.8 and column density N(sub H) approx. = 5 x 10(exp 21)/ sq cm, higher than Galactic. The X-ray flux increased by a factor of 4 in approx. 7 months without appreciable change of the spectral shape. During the lower state of 1994 August, PKS 0528 + 134 was observed simultaneously in the optical, X-rays, and at gamma-ray energies with Energetic Gamma Ray Experiment Telescope (EGRET). The gamma-ray intensity is the faintest detected thus far in the source, with a steep spectrum (GAMMA approx. = 2.7). The extrapolation of the X-ray continuum to the gamma-ray range requires a sharp spectral break at approx. 10(exp 22) Hz. We discuss the radio through gamma-ray spectral energy distribution of PKS 0528 + 134, comparing the low state of 1994 August with the flare state of 1993 March. We show that in PKS 0528 + 134, a non-negligible contribution from the external radiation field is present and that, although synchrotron self-Compton scenarios cannot be ruled out, inverse Compton upscattering of thermal seed photons may be the dominant cooling process for the production of the high-energy continuum in this blazar.

Sambruna, Rita M.↗
NASA NTRS1998

The Spacing of the Interstellar 6.2 Microns and 7.7 Microns Emission Features as an Indicator of PAH Size

A database of astrophysically relevant, infrared spectral measurements on a wide variety of neutral as well as positively and negatively charged polycyclic aromatic hydrocarbons ranging in size from C10H8 through C48H20 is now available to extend the interstellar PAH model. Beyond simply indicating general characteristics of the carriers, this collection of data now makes it possible to conduct a more thorough interpretation of the details of the interstellar spectra and thereby derive deeper insights into the nature of the emitting material and conditions in the emission zones. This paper is the first such implementation of this spectral database. The infrared spectra of PAH cations, the main PAH form in the most energetic emission zones, are usually dominated by a few strong features in the 1650 - 1100 per centimeter (6.1 - 9.1 microns) region which tend to cluster in the vicinity of the interstellar emission bands at 1610 per centimeter and 1320 per centimeter (6.2 and 7.6 microns) but with spacings typically somewhat less than that observed in the canonical interstellar spectrum. However, the spectra in the database show that this spacing increases steadily with molecular size. Extrapolation of this trend indicates that PAHS in the 50 to 80 carbon atom size range are entirely consistent with the observed interstellar spacing. Furthermore, the profile of the 1610 per centimeter (6.2 microns) interstellar band indicates that PAHS containing as few as 20 carbon atoms contribute to this feature.

Hudgins, Douglas M.↗
NASA NTRS1972

Comparative cut-bar thermal conductivity apparatus.

Construction details, error analysis, and typical data for a rapid comparative device for thermal conductivity measurements are presented. The apparatus consists of a comparative cut-bar arrangement contained in a bell-jar. The cylinder shaped specimen is placed between two ARMCO-iron meter bars of the same diameter. The upper bar is equipped with a heater, while the lower one is terminated in a heat sink. The temperature gradient along the bars is measured with a series of copper/constantan microthermocouples, spot welded to them. The assembly is held together by loading the bars to a desired pressure, via a pneumatic cylinder. Contact resistance at the boundaries between the specimen and the meter bars is minimized by using a Hg/In/Ga alloy film at the interface and sufficient loading force. The gradients determined for the meter bars then may be extrapolated to the boundaries yielding the temperature drop along the specimen. Using two different length specimens, the magnitude of the temperature drop across the interface can be computed, or the true gradient along the specimen can be obtained from the difference in overall temperature drops and lengths.

Gaal, P. S.↗
NASA NTRS2022

Energy Landscape, and Structural and Spectroscopic Characterization of Diazirine and Its Cyclic Isomers

Identifying new nitrogenated hydrocarbon molecules in the interstellar medium (ISM) is challenging due to the lack of comprehensive spectroscopic data from experiments. In this computational work, we focus on investigating the structures, relative energies, spectroscopic constants, and energy landscape of the cyclic isomers of diazirine (c-CH2N2) using ab initio quantum chemical methods. Density functional theory (DFT) methods and coupled cluster theory with singles and doubles including perturbative triples [CCSD(T)] and CCSD(T) with the explicitly correlated F12 b correction [CCSD(T)-F12b] were employed for this purpose along with large correlation consistent cc-pVTZ, cc-pVQZ, and cc-pV5Z basis sets. Harmonic vibrational frequencies, infrared vibrational intensities, rotational constants, and dipole moments are reported. An harmonic vibrational fundamentals along with centrifugal distortion constants, and vibration-rotation interaction constants are also reported for all the cyclic isomers. The energies computed with the CCSD(T) and CCSD(T)-F12b methods were extrapolated to the one-particle complete basis set (CBS) limit following a three-point formula. At the CCSD(T)-F12b/CBS level of theory the 3,3H-diazirine (c-CH2N2) is the lowest energy cyclic isomer followed by 1,3H-diazirine, (E)-1,2H-Diazirine, and (Z)-1,2H-diazirine which are 20.1, 47.8, and 51.3kcal mol-1above the 3,3H-Diazirine, respectively. Accurate structures and spectroscopic constants that are reported here could be useful for future identification of these cyclic nitrogenated organic molecules in the interstellar medium or circumstellar disks.

Energy Landscape↗
NASA NTRS2009

Gaussian and Lognormal Models of Hurricane Gust Factors

A document describes a tool that predicts the likelihood of land-falling tropical storms and hurricanes exceeding specified peak speeds, given the mean wind speed at various heights of up to 500 feet (150 meters) above ground level. Empirical models to calculate mean and standard deviation of the gust factor as a function of height and mean wind speed were developed in Excel based on data from previous hurricanes. Separate models were developed for Gaussian and offset lognormal distributions for the gust factor. Rather than forecasting a single, specific peak wind speed, this tool provides a probability of exceeding a specified value. This probability is provided as a function of height, allowing it to be applied at a height appropriate for tall structures. The user inputs the mean wind speed, height, and operational threshold. The tool produces the probability from each model that the given threshold will be exceeded. This application does have its limits. They were tested only in tropical storm conditions associated with the periphery of hurricanes. Winds of similar speed produced by non-tropical system may have different turbulence dynamics and stability, which may change those winds statistical characteristics. These models were developed along the Central Florida seacoast, and their results may not accurately extrapolate to inland areas, or even to coastal sites that are different from those used to build the models. Although this tool cannot be generalized for use in different environments, its methodology could be applied to those locations to develop a similar tool tuned to local conditions.

Merceret, Frank↗
NASA NTRS1979

On the lack of absorption of 1 keV diffuse X-rays by the Small Magellanic Cloud

The contribution to the diffuse X-ray background near 1 keV cosmic (extragalactic) origin is poorly known. Data from a slow scan across the Small Magellanic Cloud by the Wisconsin soft X-ray experiment on OSO 8 are analyzed to search for absorption of a possible cosmic component to the diffuse flux. No indication of an X-ray shadow near 1 keV is found, setting an upper limit to the intensity of the flux originating beyond the SMC that is inconsistent with a cosmic spectrum of 11 E to the -1.4 photons per (sq cm s sr keV), even allowing for depletion of the absorbing elements in the SMC. Unless emission by the SMC or an upward fluctuation in the galactic or cosmic diffuse flux at the position of the SMC has canceled out the expected absorption, the contribution to the diffuse flux at 1 keV from beyond the SMC must be less than 50% of that expected for an extrapolated E to the -1.4 source spectrum.

Bunner, A. N.↗
NASA NTRS2002

The Anisotropy of the Microwave Background to l=3500: Mosaic Observations with the Cosmic Background Imager

Using the Cosmic Background Imager, a 13-element interferometer array operating in the 26-36 GHz frequency band, we have observed 40 deg (sup 2) of sky in three pairs of fields, each approximately 145 feet x 165 feet, using overlapping pointings: (mosaicing). We present images and power spectra of the cosmic microwave background radiation in these mosaic fields. We remove ground radiation and other low-level contaminating signals by differencing matched observations of the fields in each pair. The primary foreground contamination is due to point sources (radio galaxies and quasars). We have subtracted the strongest sources from the data using higher-resolution measurements, and we have projected out the response to other sources of known position in the power-spectrum analysis. The images show features on scales approximately 6 feet-15 feet, corresponding to masses approximately 5-80 x 10(exp 14) solar mass at the surface of last scattering, which are likely to be the seeds of clusters of galaxies. The power spectrum estimates have a resolution delta l approximately 200 and are consistent with earlier results in the multipole range l approximately less than 1000. The power spectrum is detected with high signal-to-noise ratio in the range 300 approximately less than l approximately less than 1700. For 1700 approximately less than l approximately less than 3000 the observations are consistent with the results from more sensitive CBI deep-field observations. The results agree with the extrapolation of cosmological models fitted to observations at lower l, and show the predicted drop at high l (the "damping tail").

Pearson, T. J.↗
NASA NTRS1996

Theoretical Basis for Finite Difference Extrapolation of Sonic Boom Signatures

Calculation of sonic boom signatures for aircraft has traditionally followed the methods of Whitham' and Walkden. The wave disturbance generated by the vehicle is obtained by area rule linearized supersonic flow methods, which yield a locally axisymmetric asymptotic solution. This solution is acoustic in nature, i.e., first order in disturbance quantities, and corresponds to ray acoustics. Cumulative nonlinear distortion of the signature is incorporated by using this solution to adjust propagation speed to first order, thus yielding a solution second order in disturbance quantities. The effects of atmospheric gradients are treated by Blokhintzov's method of geometrical acoustics. Both nonlinear signature evolution and ray tracing are applied as if the pressure field very close to the vehicle were actually that given by the source term (the 'F-function') of the asymptotic linearized flow solution. The viewpoint is thus that the flow solution exists at a small radius near the vehicle, and may be treated as an input to an extrapolation procedure consisting of ray tracing and nonlinear aging. The F-function is often regarded as a representation of a near-field pressure signature, and it is common for computational implementations to treat it interchangeably with the pressure signature. There is a 'matching radius' between the source function and the subsequent propagation extrapolation. This viewpoint has been supported by wind tunnel tests of simple models, and very typically yields correct results for actual flight vehicles. The assumption that the F-function and near-field signature are interchangeable is generally not correct. The flowfield of a vehicle which is not axisymmetric contains crossflow components which are very significant at small radii and less so at larger distances. From an acoustical viewpoint, the crossflow is equivalent to source diffraction portions of the wave field. Use of the F-function as a near field signature effectively assumes that the diminution of the crossflow/diffraction component may be applied all at once at the matching radius noted above. This approximation, though not rigorously validated, is responsible for the usual correct far-field results. On the other hand, if an actual near-field signature (either from wind tunnel or CFD data) is used at a starting point rather than one based on th effective source distribution, the predicted far-field signature is generally wrong.

Plotkin, Kenneth J.↗