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NASA NTRS2002

Constellation X-Ray Mission and Support

This is the Third Annual Report of work performed by the Smithsonian Astrophysical Observatory (SAO) for NASA Goddard Space Flight Center (GSFC) under Cooperative Agreement NCC5-3681. The Agreement is entitled 'Constellation X-ray Mission Study and Support.' Work performed through January 31, 2001 was reported in a supplement to the Second Annual Report. That supplemental report was submitted in order to obtain funding subsequent to March 2001 which has, as the result of prior funding actions, become the de facto beginning of the funding year under the Agreement. This report covers the balance of the third year of the Agreement from February 1, 2001 through September 30, 2001. The Agreement as currently configured runs for two more years. When funding is significantly different from the originally approved amounts, SAO submits a revised budget. One such revision was submitted last year and was the basis for funding a portion of the work reported here. This report summarizes the main areas of SAO activity. Most of the work has been performed jointly with personnel from GSFC and Marshall Space Flight Center (MSFC). Consequently, we do not claim that such activities were carried out exclusively by SAO. Rather, we describe SAO participation in these efforts. Under the Agreement, SAO performed work in seven major areas of activity. These areas related to: (1) Constellation X-ray Mission Facility Definition Team and Study Management; (2) Science Support; (3) Spectroscopy X-ray Telescope (SXT); (4) Systems Engineering; (5) Travel; and (6) In-house Management and Coordination.

Tananbaum, H.↗
NASA NTRS2003

A Multi-Use Airborne Research Facility

Much of our progress in understanding the Earth system comes from measurements made in the atmosphere. Aircraft are widely used to collect in situ measurements of the troposphere and lower stratosphere, and they also serve as platforms for many remote sensing instruments. Airborne field measurement campaigns require a capable aircraft, a specially trained support team, a suite of basic instrumentation, space and power for new instruments, and data analysis and processing capabilities (e.g. Veal et al., 1977). However, these capabilities are expensive and there is a need to reduce costs while maintaining the capability to perform this type of research. To this end, NASA entered a Cooperative Agreement with the University of North Dakota (UND) to help support the operations of the UND Cessna Citation research aircraft. This Cooperative Agreement followed in form and substance a previous agreement. The Cooperative Agreement has benefited both NASA and UND. In part because of budget reductions, the NASA Airborne Science Office has elected to take advantage of outside operators of science research platforms to off-load some science requirements (Huning, 1996). UND has worked with NASA to identify those requirements that could be met more cost effectively with the UND platform. This has resulted in significant cost savings to NASA while broadening the base of researchers in the NASA science programs. At the same time, the Agreement has provided much needed support to UND to help sustain the Citation research facility. In this report, we describe the work conducted under this Cooperative Agreement.

Poellot, Michael R.↗
NASA NTRS2014

Comparison of Knee and Ankle Dynamometry between NASA's X1 Exoskeleton and Biodex System 4

Pre- and post-flight dynamometry is performed on International Space Station crewmembers to characterize microgravity-induced strength changes. Strength is not assessed in flight due to hardware limitations and there is poor understanding of the time course of in-flight changes. PURPOSE: To assess the reliability of a prototype dynamometer, the X1 Exoskeleton (EXO) and its agreement with a Biodex System 4 (BIO). METHODS: Eight subjects (4 M/4 F) completed 2 counterbalanced testing sessions of knee extension/flexion (KE/KF), 1 with BIO and 1 with EXO, with repeated measures within each session in normal gravity. Test-retest reliability (test 1 and 2) and device agreement (BIO vs. EXO) were evaluated. Later, to assess device agreement for ankle plantarflexion (PF), 10 subjects (4 M/6 F) completed 3 test conditions (BIO, EXO, and BIOEXO); BIOEXO was a hybrid condition comprised of the Biodex dynamometer motor and the X1 footplate and ankle frame. Ankle comparisons were: BIO vs. BIOEXO (footplate differences), BIOEXO vs. EXO (motor differences), and BIO vs. EXO (all differences). Reliability for KE/KF was determined by intraclass correlation (ICC). Device agreement was assessed with: 1) repeated measures ANOVA, 2) a measure of concordance (rho), and 3) average difference. RESULTS: ICCs for KE/KF were 0.99 for BIO and 0.96 to 0.99 for EXO. Agreement was high for KE (concordance: 0.86 to 0.95; average differences: -7 to +9 Nm) and low to moderate for KF (concordance: 0.64 to 0.78; average differences: -4 to -29 Nm, P<0.05). BIO vs. BIOEXO PF concordance ranged from 0.89 to 0.92 and mean differences ranged from -9 to +3 Nm (BIO < BIOEXO). BIOEXO vs. EXO PF concordance ranged from 0.73 to 0.80 while mean differences were -18 to -36 Nm (BIOEXO < EXO, P<0.05). PF concordance for BIO vs. EXO was slightly lower (0.61 to 0.84) and mean differences were greater (-27 to -33 Nm; BIO < EXO, P<0.05). CONCLUSION: BIO and EXO were similarly reliable for KE and KF. KE measures produced high agreement between devices; KF did not. For ankle PF, torque differences due to the two footplates were small. However, the X1 motor reports greater torques than the Biodex motor during PF. This first prototype provides proof of concept for a reliable, robotic-based exoskeleton to perform portable dynamometry for large muscle groups of the lower body.

English, K. L.↗
NASA NTRS1989

The 27-28 October 1986 FIRE IFO Cirrus case study: Comparison of radiative transfer theory with observations by satellite and aircraft

Observations of cirrus and altocumulus clouds during the First International Satellite Cloud Climatology Project Regional Experiment (FIRE) are compared to theoretical models of cloud radiative properties. Three tests are performed. First, LANDSAT radiances are used to compare the relationship between nadir reflectance ot 0.83 micron and beam emittance at 11.5 microns with that predicted for model calculations using spherical and nonspherical phase functions. Good agreement is found between observations and theory when water droplets dominate. Poor agreement is found when ice particles dominate, especially using scattering phase functions for spherical particles. Even when compared to a laboratory measured ice particle phase function, the observations show increased side scattered radiation relative to the theoretical calculations. Second, the anisotropy of conservatively scattered radiation is examined using simultaneous multiple angle views of the cirrus from LANDSAT and ER-2 aircraft radiometers. Observed anisotropy gives good agreement with theoretical calculations using the laboratory measured ice particle phase function and poor agreement with a spherical particle phase function. Third, Landsat radiances at 0.83, 1.65, and 2.21 microns are used to infer particle phase and particle size. For water droplets, good agreement is found with King Air FSSP particle probe measurements in the cloud. For ice particles, the LANDSAT radiance observations predict an effective radius of 60 microns versus aircraft observations of about 200 microns. It is suggested that this descrepancy may be explained by uncertainty in the imaginary index of ice and by inadequate measurements of small ice particles by microphysical probes.

Wielicki, Bruce A.↗
NASA NTRS1990

The 27-28 October 1986 FIRE IFO cirrus case study - Comparison of radiative transfer theory with observations by satellite and aircraft

Observations of cirrus and altocumulus clouds during the FIRE are compared to theoretical models of cloud radiative properties. Three tests are performed. First, radiances are used to compare the relationship between nadir reflectance ot 0.83 micron and beam emittance at 11.5 microns with that predicted for model calculations using spherical and nonspherical phase functions. Good agreement is found between observations and theory when water droplets dominate. Poor agreement is found when ice particles dominate, especially using spherical-particle phase functions (SPPFs). Even when compared to a laboratory-measured ice-particle phase function (IPPF), the observations show great side-scattered radiation than the theoretical calculations. Second, the anisotropy of conservatively scattered radiation is examined using simultaneous multiple angle views of the cirrus from Landsat and ER-2 aircraft radiometers. Observed anisotropy gives good agreement with theoretical calculations using the laboratory IPPF and poor agreement with an SPPF. Third, Landsat radiances at 0.83, 1.65, and 2.21 microns are used to infer particle phase and size. For water droplets, good agreement is found with particle-probe measurements in the cloud. For ice particles, the Landsat radiance observations predict an effective radius of 60 microns versus aircraft observations of about 200 microns. It is suggested that this discrepancy may be explained by uncertainty in the imaginary index of ice and by inadequate measurements of small ice particles by microphysical probes.

Wielicki, Bruce A.↗
NASA NTRS1999

Aerospace Human Factors

The following contains the final report on the activities related to the Cooperative Agreement between the human factors research group at NASA Ames Research Center and the Psychology Department at San Jose State University. The participating NASA Ames division has been, as the organization has changed, the Aerospace Human Factors Research Division (ASHFRD and Code FL), the Flight Management and Human Factors Research Division (Code AF), and the Human Factors Research and Technology Division (Code IH). The inclusive dates for the report are November 1, 1984 to January 31, 1999. Throughout the years, approximately 170 persons worked on the cooperative agreements in one capacity or another. The Cooperative Agreement provided for research personnel to collaborate with senior scientists in ongoing NASA ARC research. Finally, many post-MA/MS and post-doctoral personnel contributed to the projects. It is worth noting that 10 former cooperative agreement personnel were hired into civil service positions directly from the agreements.

Jordan, Kevin↗
NASA NTRS1999

Mission Study and Optics Development Support for Constellation X

This document is the Final Report for NASA Cooperative Agreement NCC5-268 between NASA Goddard Space Flight Center (GSFC) and the Smithsonian Astrophysical Observatory (SAO). The Agreement is entitled "Constellation X-ray Mission Study and Optics Development." The report is required by the terms of the Agreement. There were four modifications to the Agreement. The period of performance was from February 1, 1998 through March 31, 1999. The report summarizes the main areas of SAO activity. Other than the design and analysis related to the SXT Mirror (see Section 4.0), most of the work was carried out jointly with personnel from GSFC and Marshall Space Flight Center (MSFC). Consequently, we do not mean to imply that such activities were carried out exclusively by SAO. Rather, we have tried to describe the SAO participation in these efforts.The report summarizes the main areas of SAO activity. Other than the design and analysis related to the SXT Mirror (see Section 4.0), most of the work was carried out jointly with personnel from GSFC and Marshall Space Flight Center (MSFC). Consequently, we do not mean to imply that such activities were carried out exclusively by SAO. Rather, we have tried to describe the SAO participation in these efforts. As is appropriate to a Cooperative Agreement, SAO worked with GSFC in an integrated team mode. SAO was involved in the mission management, technology development, and mission definition. The organization is shown in Figure 1. While overall management responsibility resided with GSFC, scientific lead and subordinate responsibilities were shared between GSFC and SAO.

Tananbaum, H.↗
NASA NTRS2002

Constellation X-Ray Mission and Support

This Fourth Annual Report summarizes work performed by the Smithsonian Astrophysical Observatory (SAO) for NASA Goddard Space Flight Center (GSFC) under Cooperative Agreement NCC5-368. The Agreement is entitled Constellation X-ray Mission Study and SAO continues to perform work under the overall direction of Dr. Harvey Tananbaum, the SAO Principal Investigator for the program. Mr. Robert Rasche is the SAO Program Manager and is responsible for day-to-day program management at SAO and coordination with GSFC. The report summarizes the main areas of SAO activity. Most of the work has been done jointly with personnel from GSFC and Marshall Space Flight Center (MSFC). We describe SAO participation in these efforts. As is appropriate to a Cooperative Agreement, SAO continued to work with GSFC in an integrated team mode. SAO was involved in the overall mission management, technology development, scientific direction, and mission definition. While formal overall management responsibility resides with GSFC, scientific lead and subordinate responsibilities continue to be shared by GSFC and SAO. The work performed by SAO is consistent with the SAO proposal 'Constellation X-ray Mission Study and Optics Development' dated September 1997, which was the basis for establishing the Cooperative Agreement under which SAO is currently funded. Over time, the scope of the effort has expanded somewhat to accommodate the needs of the project. Work, except for meeting support and high priority program tasks, has been at a level of effort. Priorities and work progress have been closely coordinated with the Constellation-X Project Formulation Manager at GSFC. Funding limitations constrained the work accomplished during this period. Nonetheless, a significant amount of work was accomplished. Under the Agreement, SAO performed work in seven major areas of activity. These areas related to: Constellation X-ray Mission Facility Definition Team and Study Management; Science Support; Spectroscopy X-ray Telescope (SXT); Systems Engineering; Travel in Support of the Work Effort; In-house Management and Coordination.

Grady, Jean↗
NASA NTRS1998

Ab Initio Calculations of Water Line Strengths

We report on the determination of a high quality ab initiu potential energy surface (PES) and dipole moment function for water. This PES is empirically adjusted to improve the agreement between the computed line positions and those from the HITRAN 92 data base with J less than 6 for H2O. The changes in the PES are small, nonetheless including an estimate of core (oxygen 1s) electron correlation greatly improves the agreement with experiment. Using this adjusted PES, we can match 30,092 of the 30,117 transitions in the HITRAN 96 data base for H2O with theoretical lines. The 10,25,50,75, and 90 percentiles of the difference between the calculated and tabulated line positions are -0.11, -0.04, -0.01, 0.02, and 0.07 l/cm. Non-adiabatic effects are not explicitly included. About 3% of the tabulated line positions appear to be incorrect. Similar agreement using this adjusted PES is obtained for the oxygen 17 and oxygen 18 isotopes. For HDO, the agreement is not as good, with root-mean-square error of 0.25 l/cm for lines with J less than 6. This error is reduced to 0.02 l/cm by including a small asymmetric correction to the PES, which is parameterized by simultaneously fitting to HDO md D2O data. Scaling this correction by mass factors yields good results for T2O and HTO. The intensities summed over vibrational bands are usually in good agreement between the calculations and the tabulated results, but individual lines strengths can differ greatly. A high temperature list consisting of 307,721,352 lines is generated for H2O using our PES and dipole moment function.

Schwenke, David W.↗
NASA NTRS2005

Constellation X-Ray Mission and Support

This Final Report summarizes work performed by the Smithsonian Astrophysical Observatory (SAO) for NASA Goddard Space Flight Center (GSFC) under Cooperative Agreement NCC5-368. The Agreement is entitled "Constellation X-ray Mission Study and Support." The report covers the full duration of the Agreement which ran from October 1,1998 to October 14,2004. Included in the report is a description of previously unreported work that was performed between October 2003 and the end of the Agreement. For convenience, the previously unreported work is covered first in Section 2.0. Then, an overall summary of all work performed under the Agreement is presented in Section 3. Section 4.0 contains a list of all formal reports that SAO has submitted to GSFC along with publications and presentations at various conferences.

Tananbaum, H.↗
NASA NTRS2009

Water Vapor Measurements by Howard University Raman Lidar during the WAVES 2006 Campaign

Retrieval of water vapor mixing ratio using the Howard University Raman Lidar is presented with emphasis on three aspects: i) performance of the lidar against collocated radiosondes and Raman lidar, ii) investigation of the atmospheric state variables when poor agreement between lidar and radiosondes values occurred and iii) a comparison with satellite-based measurements. The measurements were acquired during the Water Vapor Validation Experiment Sondes/Satellites 2006 field campaign. Ensemble averaging of water vapor mixing ratio data from ten night-time comparisons with Vaisala RS92 radiosondes shows on average an agreement within 10 % up to approx. 8 km. A similar analysis of lidar-to-lidar data of over 700 profiles revealed an agreement to within 20 % over the first 7 km (10 % below 4 km). A grid analysis, defined in the temperature - relative humidity space, was developed to characterize the lidar - radiosonde agreement and quantitatively localizes regions of strong and weak correlations as a function of altitude, temperature or relative humidity. Three main regions of weak correlation emerge: i) regions of low relative humidity and low temperature, ii) moderate relative humidity at low temperatures and iii) low relative humidity at moderate temperatures. Comparison of Atmospheric InfraRed Sounder and Tropospheric Emission Sounder satellites retrievals of moisture with that of Howard University Raman Lidar showed a general agreement in the trend but the formers miss a lot of the details in atmospheric structure due to their low resolution. A relative difference of about 20 % is usually found between lidar and satellites measurements.

Adam, M.↗
NASA NTRSDate not supplied

Comparison between Hayabusa 2 Spectral Measurements and Simulations

Recent Hayabusa 2 spectral measurements are compared with state-of-the-art shock-layer radiation simulations resulting from the LAURA/HARA code suite. These simulations include coupled ablation, which accounts for the injection of ablation products into the flowfield, and coupled radiation, which accounts for radiative energy loss in the flowfield. To enable the cou- pled ablation simulations, a best-estimate model is developed for Hayabusa’s carbon-phenolic ablator based on available published information. The comparison between the simulations and measurements focuses on three atomic nitrogen lines, two atomic oxygen lines, one atomic hydrogen line, and the CN Violet band system. Parametric uncertainties are evaluated for these features using a recently developed capability in LAURA/HARA. These uncertainties capture the impact of flowfield and radiation modeling uncertainties on the observed radiation simulations, and include the impact of coupled radiation and ablation product emission. The resulting parametric uncertainties range from 50 to over 100% for the atomic lines, and 80% for CN Violet. Uncertainties in flowfield kinetics and non-Boltzmann modeling provide the dominant contribution to these uncertainties. For the atomic nitrogen and oxygen lines, com- parisons between the nominal simulations and measurements show agreement well within these simulation uncertainty bounds, with the measurements within 20% of the nominal simulation over most of the trajectory, and within 10% at peak emission. This excellent agreement is un- precedented for observed radiation measurements of atomic lines, where previous Stardust and Hayabusa 1 comparisons were significantly worse. The improved agreement for these Hayabusa 2 comparisons is both the result of improved measurement quality and enhanced flowfield and radiation modeling. For the ablation product emission from the 656 nm atomic hydrogen line, the agreement between measurements and simulations is within ±20% for all trajectory points except one outlier. This good comparison is surprising considering this species depends on the ablation rate and is shown to have strong wake contribution, which both contribute to the large ≈±70% parametric uncertainty. For the ablation product emission from CN Violet, the simulations over-predict the measurements by over a factor of two early in the trajectory, with the comparison improving later in the trajectory. This disagreement for CN Violet is consistent with the ≈±80% parametric uncertainty bounds evaluated for the simulations. To utilize the excellent agreement between the atomic line simulations and measurements in the assessment of the radiative heating margin for a future flight vehicle, the flowfield property binning (FPB) approach is applied. Using the Mars Sample Return (MSR) Earth Entry System (EES) as an example, the combination of the excellent Hayabusa comparisons and the FPB analysis justify nearly a 10% reduction in the radiative heating margin from an assumed baseline margin of 30%. This direct quantitative link between observed radiation measurements and the radia- tive heating margin of future flight vehicles demonstrates the value of these observed radiation measurements.

Shock-Layer Radiative Heating↗
NASA NTRS2024

Antarctic polar stratospheric cloud composition as observed by ACE, CALIPSO and MIPAS

The composition of polar stratospheric clouds (PSCs) in the Antarctic is measured by infrared absorption spectroscopy by the Atmospheric Chemistry Experiment (ACE) satellite and compared to lidar (CALIPSO) and emission spectroscopy (MIPAS) results. ACE observations are compared first to CALIPSO for the period 2006–2020, then to MIPAS for the period 2005–2011, and then a set of triple coincidences is studied. In both CALIPSO-ACE and MIPAS-ACE comparisons, nitric acid trihydrate (NAT) detections are in excellent agreement (∼80 % of coincident compositions is found). Supercooled ternary solution (STS) detections are in good agreement for CALIPSO-ACE (∼60 %) but in poor agreement for MIPAS-ACE (39 %). This contrasts with ice detections, in poor agreement for CALIPSO-ACE (∼30 %) and in better agreement for MIPAS-ACE (45 %). Triple coincidences show that ACE STS detections are more reliable than MIPAS STS detections. The comparison between ACE observations and homogeneous CALIPSO PSCs shows that for 11 events, CALIPSO reports STS rather than supercooled nitric acid (SNA) clouds.

Atmospheric Chemistry Experiment↗
NASA NTRS1972

An experimental investigation of turbulent boundary layers at high Mach number and Reynolds numbers

Skin friction, heat transfer and pressure measurements were obtained in laminar, transitional and turbulent boundary layers on flat plates at Mach numbers from 7 to 13 at wall-to-free stream stagnation temperature ratios from 0.1 to 0.3. Measurements in laminar flows were in excellent agreement with the theory of Cheng. Correlations of the transition measurements with measurements on flight vehicles and in ballistic ranges show good agreement. Our transition measurements do not correlate well with those of Pate and Schueler. Comparisons have been made between the skin friction and heat transfer measurements and the theories of Van Driest, Eckert and Spalding and Chi. These comparisons reveal in general that at the high end of our Mach number range (10-13) the theory of Van Driest is in best agreement with the data, whereas at lower Mach numbers (6.5-10) the Spalding Chi theory is in better agreement with the measurements.

Holden, M. S.↗
NASA NTRS1974

Boundary layer integral matrix procedure code modifications and verifications

A summary of modifications to Aerotherm's Boundary Layer Integral Matrix Procedure (BLIMP) code is presented. These modifications represent a preliminary effort to make BLIMP compatible with other JANNAF codes and to adjust the code for specific application to rocket nozzle flows. Results of the initial verification of the code for prediction of rocket nozzle type flows are discussed. For those cases in which measured free stream flow conditions were used as input to the code, the boundary layer predictions and measurements are in excellent agreement. In two cases, with free stream flow conditions calculated by another JANNAF code (TDK) for use as input to BLIMP, the predictions and the data were in fair agreement for one case and in poor agreement for the other case. The poor agreement is believed to result from failure of the turbulent model in BLIMP to account for laminarization of a turbulent flow. Recommendations for further code modifications and improvements are also presented.

Evans, R. M.↗
NASA NTRS1976

Heat-transfer distributions on a 0.013-scale shuttle solid rocket booster at Mach 3.70 and angles of attack from 0 deg to 180 deg

An experimental investigation was conducted in the Langley Unitary Plan wind tunnel to estimate the peak aerodynamic heating on the space shuttle solid rocket booster during the descent phase of its flight. Heat transfer measurements were obtained using 0.013 scale models instrumented with thermocouples at a Mach number of 3.70, Reynolds number per meter of 11.48 million, and angles of attack from 0 to 180 deg. At angles of attack of 0 and 180 deg, heat transfer measurements on the cylindrical section of the model between the conical nose and ring interaction region were in good agreement with flat plate strip theory for laminar and turbulent flow. At angles of attack up to 30 deg, measurements on this section of the model were in good agreement with laminar swept-cylinder theory, whereas at angles of attack from 120 to 180 deg, the measurements were in good agreement with turbulent swept-cylinder theory. The good agreement with turbulent theory indicated that large flow disturbances created by the nozzle and afterbody flare at these large angles of attack influenced the downstream heating primarily by promoting boundary layer transition. Measurements obtained at 90 deg angle of attack were indicative of laminar flow.

Lamb, M.↗
NASA NTRS1984

Air-Sea Interaction During Cold Air Outbreaks

The NOAA P-3 1-sec and 20 Hz gust probe data, dropsonde measurements, and lidar data were combined to study the organized convection and the effects of the coastal shape and the sea surface temperature (SST) pattern on the development of the marine atmospheric boundary layer (MABL) during cold air outbreaks. The preliminary analysis indicated that the SST pattern and the coastal shape caused the MABL to deepen eastward and southward, which is in good agreement with the suggestion of Atlas et al. (1983). Also, good agreements were found between the lidar data and the NOAA P-3 and dropsonde date, e.g., the boundary heights, the dominant scales of motion, and the heat flux ratio between the top of MABL and the sea surface. The planetary boundary layer (PBL) height measured by lidar was found to be in good agreement with that measured by the dropsonde temperature profile. Assuming a linear heat flux profile in the clear PBL, the heat flux ratio between the PBL top and the surface may be estimated from the ratio of the entrainment zone to the completely mixed boundary layer height. The heat flux ratio estimated by lidar measurements was found to be in good agreement with that derived from the gust probe data.

Chou, S.↗
NASA NTRS1985

Analysis of turbulent underexpanded jets. II - Shock noise features using SCIPVIS

SCIPVIS, the computational model discussed by Dash et al. (1985), is assessed in predicting the complicated flow structure associated with shock-containing plumes. In addition, the analysis in this study examines this code's applicability as a basic part of a program for estimating broadband shock noise radiation. The results of this study show that excellent agreement exists between predicted and measured static pressure distributions for both underexpanded and overexpanded flow cases considered. Of the three turbulence closure models incorporated in the SCIPVIS code, the kW model of Spalding produces the most uniform agreement with measurement. The k-epsilon-2 model of Launder consistently overestimates plume spreading for supersonic jets with exit Mach numbers in the 1-2 range. Dash's (1983) k-epsilon-2-cc, compressibility-corrected version of Launder's model underestimates plume spreading. Good qualitative agreement was also obtained between the measured longitudinal turbulence intensity and that predicted by the code for the same trial case. Comparison of measured and predicted broadband shock noise spectrum peak values were found to be in excellent agreement. This utilized a variant of the Harper-Bourne and Fisher (1973) phase-array model: the effective shock spacing was reinterpreted as the value of the end of the plume potential core, determined herein by the SCIPVIS code.

Seiner, J. M.↗