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At least 1,711 records · Page 95

Computed voltage distribution around Solar Electric Propulsion spacecraft

The paper uses the NASCAP computer code to compute voltage distributions around a Solar Electric Propulsion (SEP) spacecraft as it encounters an idealized geomagnetic substorm environment. Consideration is given to both a standard operating voltage and direct-drive voltage configuration. The computations are presented without thruster operations as well as with a simplified, simulated thruster-on representation for direct-drive configuration only. Finally, it is stressed that the computations seeking possible areas of concern in the spacecraft design are exploratory.

Stevens, N. J.↗

Space station propulsion technology: Space station propulsion system test bed test plan

Testing of the hydrogen/oxygen Space Station Propulsion System will demonstrate the technology readiness for the IOC application. To facilitate early demonstration of this technology and to allow demonstration of maturing technology, this testing will be performed with the components installed on a test bed which simulated the Space Station Structure. The test plan contains a description of the test bed, test objective, instrumentation plan, and controls plan. Each of these is discussed in detail.

Briley, G. L.↗

Summary of Rocketdyne Engine A5 Rocket Based Combined Cycle Testing

Rocketdyne Propulsion and Power (RPP) has completed a highly successful experimental test program of an advanced rocket based combined cycle (RBCC) propulsion system. The test program was conducted as part of the Advanced Reusable Technology program directed by NASA-MSFC to demonstrate technologies for low-cost access to space. Testing was conducted in the new GASL Flight Acceleration Simulation Test (FAST) facility at sea level (Mach 0), Mach 3.0 - 4.0, and vacuum flight conditions. Significant achievements obtained during the test program include 1) demonstration of engine operation in air-augmented rocket mode (AAR), ramjet mode and rocket mode and 2) smooth transition from AAR to ramjet mode operation. Testing in the fourth mode (scramjet) is scheduled for November 1998.

Ketchum. A.↗

Spacecraft Formation Flying Maneuvers Using Linear-Quadratic Regulation with No Radial Axis Inputs

Regarding multiple spacecraft formation flying, the observation has been made that control thrust need only be applied coplanar to the local horizon to achieve complete controllability of a two-satellite (leader-follower) formation. A formulation of orbital dynamics using the state of one satellite relative to another is used. Without the need for thrust along the radial (zenith-nadir) axis of the relative reference frame ' propulsion system simplifications and weight reduction may be accomplished. Several linear-quadratic regulators (LQR) are explored and compared based on performance measures likely to be important to many missions, but not directly optimized in the LQR designs. Maneuver simulations are performed using commercial ODE solvers to propagate the Keplerian dynamics of a controlled satellite relative to an uncontrolled leader. These short maneuver simulations demonstrate the capacity of the controller to perform changes from one formation geometry to another. This work focusses on formations in which the controlled satellite has a relative trajectory which projects onto the local horizon of the uncontrolled satellite as a circle. This formation has potential uses for distributed remote sensing systems.

Starin, Scott R.↗

Combustion Devices CFD Simulation Capability Roadmap

The objective of this roadmap is to enable the use of CFD for simulation of pre-burners, ducting, thrust chamber assembly and supporting infrastructure in terms of performance, life, and stability so as to affect the design process in a timely fashion. To enable flange to exit analysis of real(3D) propulsion hardware within the last 5 years (2008). To meet this objective all model problems must be sufficiently mastered.

West, Jeff↗

Cryogenic Selective Surfaces

There are many challenges involved in deep-space exploration, but several of these can be mitigated, or even solved, by the development of a coating that reflects most of the Sun’s energy, yet still provides far-infrared heat emission. Such a coating would allow non-heat-generating objects in space to reach cryogenic temperatures without using an active cooling system. This would benefit deep-space sensors that require low temperatures, such as the James Webb Telescope focal plane array. It would also allow the use of superconductors in deep space, which could lead to magnetic energy storage rings, lossless power delivery, or perhaps a large-volume magnetic shield against galactic cosmic radiation. However, perhaps the most significant enablement achieved from such a coating would be the long-term, deep space storage of cryogenic liquids, such as liquid oxygen (LOX). In our Phase I NIAC study, we realized that a combination of scattering particles and a silver backing could yield a highly effective, very broadband, reflector that could potentially reflect more than 99.9% of the Sun’s irradiant power. We developed a sophisticated model of this reflector and theoretically showed that cryogenic temperatures could be achieved in deep space at one astronomical unit (1 AU) from the Sun. We showed how this new reflector could minimize heat conduction into the cryogenic tanks by coating the tank support struts. We then modelled a strawman architecture for a mission to Mars, using a coated LOX tank, coated struts, and infrared shields, to show that with our new coating it would be possible to maintain liquid oxygen passively. As a result of this work a patent application was generated and a paper published in Optics Letters. Our Phase II NIAC study had two primary goals, to develop a rigid version of the cryogenic selective surface proposed in Phase I and to test its performance in a simulated deep space environment. During the first year of the project the work concentrated on developing rigid tiles of BaF2, leading to tiles as large as 4 inches in diameter that transmitted very little visible light. In addition, during the first year a simulated deep space environment was created using a vacuum chamber and cryocooler. Using this facility, we showed that our BaF2 tiles absorbed less than ¼% of 375 nm radiation, a significant milestone for the work. During the second year of the project, we continued to develop the BaF2 tiles and we put significant effort into the construction of a deep space environment where we could project simulated solar radiation onto a sample. In the spring of 2018, we conducted our first solar simulator test with BaF2 and saw about 3.6% absorption. This is better than the state-of-the-art, but disappointing since predictions were for much lower absorption. We, erroneously, attributed this absorption to water retention by the BaF2, and decided to change materials. We considered several oxides and settled on yttrium oxide (Y2O3) for further development, because it is broadband, lightweight, has high index, and is hydrophobic. In July 2018 we conducted our first test of a rigid tile of Y2O3 in the simulated deep space environment and saw significant absorption again. We then realized that the issue was not water, but mid-wave radiation passing through the tile and being absorbed by the temperature sensor and the varnish used to hold it in place. We wrapped the sensor in silver foil, re-ran the test, and saw much lower absorption; only 1.1%. We then re-ran the BaF2 tile and saw 1.4% absorption. These values are almost adequate to maintain LOX in deep space, but we suspect that there are still issues in our test apparatus; we suspect thermocouple wires may be absorbing radiation. Further, post-NIAC, testing will better determine the performance of our new solar reflector. In order to restrict the size of this report, we will only briefly describe topics that we have previously published, allowing us to devote more time to new material. So minimal material will be devoted to modeling the material and deep space cryogenic storage, while longer sections will cover our material development, simulated deep space testing, and new applications. The Launch Service Program (LSP) requested that we explore ways to use this new coating to maintain LOX in low Earth Orbit and that work is described. In addition, the Nuclear Thermal Propulsion (NTP) Program asked us to explore ways to reduce the heat load for liquid hydrogen, resulting in the development of a spray-on version of the coating that should significantly improve in-space multi-layer insulation performance.

Robert C. Youngquist,↗

Simulations of the Modular Axisymmetric Scramjet Test Rig Under Reacting Flow Conditions

Simulations of the Air Force Research Laboratory (AFRL) Modular Axisymmetric Scramjet Test Rig (MASTeR) are presented. MASTeR is a parametric test article capable of investigating various scramjet cavity flameholder designs and fueling strategies with the goal to characterize and optimize flameholding capability. In the current work, three cavity aspect ratios, and two fueling strategies (upstream and in-cavity) with ethylene at a nominal facility pressure and temperature condition are evaluated. The reacting simulations are performed, and the resulting flow characteristics are discussed. For each configuration and fueling strategy, cavity residence time, entrainment rate, and fuel-air equivalence ratio are computed. The MASTeR geometry is defined in Engineering Sketch Pad (ESP) and the simulations use a sketch-to-solution (S2S) automated unstructured grid adaptation tool in VULCAN-CFD. This tool automatically generates a simulation grid from the ESP geometry and systematically adapts it to the numerical solution based on the Hessian error estimate of a specified flow field parameter. Reynolds averaged simulations (RAS) are used with a two-equation linear eddy viscosity and diffusivity model. The resulting database can be compared with the experimental data as those become available, and explored to develop models for cavity performance for scramjet propulsion design applications.

hypersonics↗

Simulations of the Modular Axisymmetric Scramjet Test Rig Under Reacting Flow Conditions

Simulations of the Air Force Research Laboratory (AFRL) Modular Axisymmetric Scramjet Test Rig (MASTeR) are presented. MASTeR is a parametric test article capable of investigating various scramjet cavity flameholder designs and fueling strategies with the goal to characterize and optimize flameholding capability. In the current work, three cavity aspect ratios, three depths, and two fueling strategies (upstream and in-cavity) with ethylene at a nominal facility pressure and temperature conditions are evaluated. The simulations are performed for mixing-only and reacting flows, and the resulting flow characteristics are compared. For each configuration and fueling strategy, cavity residence time, entrainment rate, and fuel-air equivalence ratio are computed. The MASTeR geometry is defined in the Engineering Sketch Pad (ESP) and the simulations use a sketch-to-solution (S2S) automated unstructured grid adaptation tool in VULCAN-CFD. This tool automatically generates a simulation grid from the ESP geometry and systematically adapts it to the numerical solution based on the Hessian error estimate of a specified flow field parameter. Reynolds averaged simulations (RAS) are used with typical two-equation linear eddy viscosity and diffusivity model. The resulting database can be compared with the experimental data as those becomes available and explored to develop models for cavity performance for scramjet propulsion design applications.

hypersonics↗

Transition Aero-Propulsive Analysis of a Tilt-Wing eVTOL Aircraft Using a Surface-Vorticity Solver

This work uses FlightStream, a surface-vorticity solver, to perform an aero-propulsive analysis on the NASA LA-8 aircraft through the transition flight regime. Aerodynamic force and moment coefficient predictions for forward and transition flight of the airframe without propulsors are compared with wind tunnel data. Powered transition cases are simulated using Conway actuator disks to model the propellers and results are compared with response surface equations derived from wind tunnel data. The approach described in the paper provides mid-fidelity solutions at a reduced computational cost compared to volumetric CFD, which allows for rapid transition flight analyses and optimization in the early design stages. The best prediction results were observed in forward flight and high-speed transition. Mid-transition results were not as close in magnitude but the trends exhibited reasonable agreement with experimental data.

Advanced Air Mobility↗

Enabling Architecture Trades and Design Exploration for Nuclear Electric Propulsion

Recent renewed interest in Nuclear Electric Propulsion (NEP) at NASA has driven the need for design space exploration and analysis of alternative architectures to evaluate performance and feasibility of NEP concepts. It has been over a decade since NASA last invested in Nuclear Electric Propulsion development efforts, and the landscape has shifted in both mission objectives and technology readiness levels. This also means that many of the engineering analyses and design frameworks tailored to NEP date back to the Jupiter Icy Moons Orbiter (JIMO) days of the early 2000s. Thus, a need was identified for updating and modernizing the modeling and simulation toolsets for NEP. This paper will detail the development efforts in the Marshall Space Flight Center’s Advanced Concepts Office, with a particular focus on the development of the NEP stage of the NEP-Chem vehicle. The paper will cover the various models used, and their current development status, as well as provide an overview of the integrated vehicle model and plans for further development.

Nuclear↗

Computational Analysis of a Chevron Nozzle Uniquely Tailored for Propulsion Airframe Aeroacoustics

A computational flow field and predicted jet noise source analysis is presented for asymmetrical fan chevrons on a modern separate flow nozzle at take off conditions. The propulsion airframe aeroacoustic asymmetric fan nozzle is designed with an azimuthally varying chevron pattern with longer chevrons close to the pylon. A baseline round nozzle without chevrons and a reference nozzle with azimuthally uniform chevrons are also studied. The intent of the asymmetric fan chevron nozzle was to improve the noise reduction potential by creating a favorable propulsion airframe aeroacoustic interaction effect between the pylon and chevron nozzle. This favorable interaction and improved noise reduction was observed in model scale tests and flight test data and has been reported in other studies. The goal of this study was to identify the fundamental flow and noise source mechanisms. The flow simulation uses the asymptotically steady, compressible Reynolds averaged Navier-Stokes equations on a structured grid. Flow computations are performed using the parallel, multi-block, structured grid code PAB3D. Local noise sources were mapped and integrated computationally using the Jet3D code based upon the Lighthill Acoustic Analogy with anisotropic Reynolds stress modeling. In this study, trends of noise reduction were correctly predicted. Jet3D was also utilized to produce noise source maps that were then correlated to local flow features. The flow studies show that asymmetry of the longer fan chevrons near the pylon work to reduce the strength of the secondary flow induced by the pylon itself, such that the asymmetric merging of the fan and core shear layers is significantly delayed. The effect is to reduce the peak turbulence kinetic energy and shift it downstream, reducing overall noise production. This combined flow and noise prediction approach has yielded considerable understanding of the physics of a fan chevron nozzle designed to include propulsion airframe aeroacoustic interaction effects.

Massey, Steven J.↗

Integrated Approach to the Dynamics and Control of Maneuvering Flexible Aircraft

This work uses a fundamental approach to the problem of simulating the flight of flexible aircraft. To this end, it integrates into a single formulation the pertinent disciplines, namely, analytical dynamics, structural dynamics, aerodynamics, and controls. It considers both the rigid body motions of the aircraft, three translations (forward motion, sideslip and plunge) and three rotations (roll, pitch and yaw), and the elastic deformations of every point of the aircraft, as well as the aerodynamic, propulsion, gravity and control forces. The equations of motion are expressed in a form ideally suited for computer processing. A perturbation approach yields a flight dynamics problem for the motions of a quasi-rigid aircraft and an 'extended aeroelasticity' problem for the elastic deformations and perturbations in the rigid body motions, with the solution of the first problem entering as an input into the second problem. The control forces for the flight dynamics problem are obtained by an 'inverse' process and the feedback controls for the extended aeroservoelasticity problem are determined by the LQG theory. A numerical example presents time simulations of rigid body perturbations and elastic deformations about 1) a steady level flight and 2) a level steady turn maneuver.

Waszak, Martin R.↗

Planetary Protection Bioburden Analysis Program

This program is a Microsoft Access program that performed statistical analysis of the colony counts from assays performed on the Mars Science Laboratory (MSL) spacecraft to determine the bioburden density, 3-sigma biodensity, and the total bioburdens required for the MSL prelaunch reports. It also contains numerous tools that report the data in various ways to simplify the reports required. The program performs all the calculations directly in the MS Access program. Prior to this development, the data was exported to large Excel files that had to be cut and pasted to provide the desired results. The program contains a main menu and a number of submenus. Analyses can be performed by using either all the assays, or only the accountable assays that will be used in the final analysis. There are three options on the first menu: either calculate using (1) the old MER (Mars Exploration Rover) statistics, (2) the MSL statistics for all the assays, or This software implements penetration limit equations for common micrometeoroid and orbital debris (MMOD) shield configurations, windows, and thermal protection systems. Allowable MMOD risk is formulated in terms of the probability of penetration (PNP) of the spacecraft pressure hull. For calculating the risk, spacecraft geometry models, mission profiles, debris environment models, and penetration limit equations for installed shielding configurations are required. Risk assessment software such as NASA's BUMPERII is used to calculate mission PNP; however, they are unsuitable for use in shield design and preliminary analysis studies. The software defines a single equation for the design and performance evaluation of common MMOD shielding configurations, windows, and thermal protection systems, along with a description of their validity range and guidelines for their application. Recommendations are based on preliminary reviews of fundamental assumptions, and accuracy in predicting experimental impact test results. The software is programmed in Visual Basic for Applications for installation as a simple add-in for Microsoft Excel. The user is directed to a graphical user interface (GUI) that requires user inputs and provides solutions directly in Microsoft Excel workbooks. This work was done by Shannon Ryan of the USRA Lunar and Planetary Institute for Johnson Space Center. Further information is contained in a TSP (see page 1). MSC- 24582-1 Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program Lyndon B. Johnson Space Center, Houston, Texas Commercially, because it is so generic, Enigma can be used for almost any project that requires engineering visualization, model building, or animation. Models in Enigma can be exported to many other formats for use in other applications as well. Educationally, Enigma is being used to allow university students to visualize robotic algorithms in a simulation mode before using them with actual hardware. This work was done by David Shores and Sharon P. Goza of Johnson Space Center; Cheyenne McKeegan, Rick Easley, Janet Way, and Shonn Everett of MEI Technologies; Mark Manning of PTI; and Mark Guerra, Ray Kraesig, and William Leu of Tietronix Software, Inc. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24211-1 Spitzer Telemetry Processing System NASA's Jet Propulsion Laboratory, Pasadena, California The Spitzer Telemetry Processing System (SirtfTlmProc) was designed to address objectives of JPL's Multi-mission Image Processing Lab (MIPL) in processing spacecraft telemetry and distributing the resulting data to the science community. To minimize costs and maximize operability, the software design focused on automated error recovery, performance, and information management. The system processes telemetry from the Spitzer spacecraft and delivers Level 0 products to the Spitzer Science Center. SirtfTlmProc is a unique system with automated error notification and recovery, with a real-time continuous service that can go quiescent after periods of inactivity. The software can process 2 GB of telemetry and deliver Level 0 science products to the end user in four hours. It provides analysis tools so the operator can manage the system and troubleshoot problems. It automates telemetry processing in order to reduce staffing costs. This work was done by Alice Stanboli, Elmain M. Martinez, and James M. McAuley of Caltech for NASA's Jet Propulsion Laboratory. For more information, contact iaoffice @jpl.nasa.gov. This software is available for commercial licensing. Please contact Dan Broderick at Daniel.F. Broderick@jpl.nasa.gov. Refer to NPO-47803. NASA Tech Briefs, September 2013 29 This rapid response computer program predicts Orbiter Wing Leading Edge (WLE) damage caused by ice or foam impact during a Space Shuttle launch (Program "IMPACT2"). The program was developed after the Columbia accident in order to assess quickly WLE damage due to ice, foam, or metal impact (if any) during a Shuttle launch. IMPACT2 simulates an impact event in a few minutes for foam impactors, and in seconds for ice and metal impactors. The damage criterion is derived from results obtained from one sophisticated commercial program, which requires hours to carry out simulations of the same impact events. The program was designed to run much faster than the commercial program with prediction of projectile threshold velocities within 10 to 15% of commercial-program values. The mathematical model involves coupling of Orbiter wing normal modes of vibration to nonlinear or linear springmass models. IMPACT2 solves nonlinear or linear impact problems using classical normal modes of vibration of a target, and nonlinear/ linear time-domain equations for the projectile. Impact loads and stresses developed in the target are computed as functions of time. This model is novel because of its speed of execution. A typical model of foam, or other projectile characterized by material nonlinearities, impacting an RCC panel is executed in minutes instead of hours needed by the commercial programs. Target damage due to impact can be assessed quickly, provided that target vibration modes and allowable stress are known. This work was done by Robert Clark, Jr., Paul Cotter, and Constantine Michalopoulos of The Boeing Company for Johnson Space Center. For further information, contact the JSC Innovation Partnerships Office at (281) 483-3809. MSC-24988-1 Wing Leading Edge RCC Rapid Response Damage Prediction Tool (IMPACT2) Lyndon B. Johnson Space Center, Houston, Texas (3) the MSL statistics for only the accountable assays. Other options on the main menu include a data editing form and utility programs that produce various reports requested by the microbiologists and the project, and tools to generate the groupings for the final analyses. The analyses can be carried out in three ways: Each assay can be treated separately, the assays can be collectively treated for the whole zone as a group, or the assays can be collected in groups designated by the JPL Planetary Protection Manager. The latter approach was used to generate the final report because assays on the same equipment or similar equipment can be assumed to have been exposed to the same environment and cleaning. Thus, the statistics are improved by having a larger population, thereby reducing the standard deviation by the square root of N. For each method mentioned above, three reports are available. The first is a detailed report including all the data. This version was very useful in verifying the calculations. The second is a brief report that is similar to the full detailed report, but does not print out the data. The third is a grand total and summary report in which each assay requires only one line. For the first and second reports, most of the calculations are performed in the report section itself. For the third, all the calculations are performed directly in the query bound to the report. All the numerical results were verified by comparing them with Excel templates, then exporting the data from the Planetary Protection Analysis program to Excel.

Beaudet, Robert A.↗

ENABLING ARCHITECTURE TRADES AND DESIGN EXPLORATION FOR NUCLEAR ELECTRIC PROPULSION

Recent renewed interest in Nuclear Electric Propulsion (NEP) at NASA has driven the need for design space exploration and analysis of alternative architectures to evaluate performance and feasibility of NEP concepts. It has been over a decade since NASA last invested in Nuclear Electric Propulsion development efforts, and the landscape has shifted in both mission objectives and technology readiness levels. This also means that many of the engineering analyses and design frameworks tailored to NEP date back to the Jupiter Icy Moons Orbiter (JIMO) days of the early 2000s. Thus, a need was identified for updating and modernizing the modeling and simulation toolsets for NEP. This paper will detail the development efforts in the Marshall Space Flight Center’s Advanced Concepts Office, with a particular focus on the development of the NEP stage of the NEP-Chem vehicle. The paper will cover the various models used, and their current development status, as well as provide an overview of the integrated vehicle model and plans for further development.

Nuclear↗

Hybrid Propulsion Emulation Rig (HyPER)

HyPER is a hardware-in-the-loop laboratory that was designed specifically to investigate the dynamic interactions between turbomachinery, the electric power system, and the constantly varying loads of electrified aircraft. It is a small-scale lab capable of rapid reconfiguration through software. This allows the emulation of new engines using simulation models that are easily replaced and then appropriately scaled for power and inertia to the test hardware.

Control↗

Quasi 1D Modeling of Mixed Compression Supersonic Inlets

The AeroServoElasticity task under the NASA Supersonics Project is developing dynamic models of the propulsion system and the vehicle in order to conduct research for integrated vehicle dynamic performance. As part of this effort, a nonlinear quasi 1-dimensional model of the 2-dimensional bifurcated mixed compression supersonic inlet is being developed. The model utilizes computational fluid dynamics for both the supersonic and subsonic diffusers. The oblique shocks are modeled utilizing compressible flow equations. This model also implements variable geometry required to control the normal shock position. The model is flexible and can also be utilized to simulate other mixed compression supersonic inlet designs. The model was validated both in time and in the frequency domain against the legacy LArge Perturbation INlet code, which has been previously verified using test data. This legacy code written in FORTRAN is quite extensive and complex in terms of the amount of software and number of subroutines. Further, the legacy code is not suitable for closed loop feedback controls design, and the simulation environment is not amenable to systems integration. Therefore, a solution is to develop an innovative, more simplified, mixed compression inlet model with the same steady state and dynamic performance as the legacy code that also can be used for controls design. The new nonlinear dynamic model is implemented in MATLAB Simulink. This environment allows easier development of linear models for controls design for shock positioning. The new model is also well suited for integration with a propulsion system model to study inlet/propulsion system performance, and integration with an aero-servo-elastic system model to study integrated vehicle ride quality, vehicle stability, and efficiency.

Kopasakis, George↗

In-Situ Propellant Production on Mars: A Sabatier/Electrolysis Demonstration Plant

An efficient, reliable propellant production plant has been developed for use on Mars. Using a Sabatier reactor in conjunction with a water electrolysis system, a complete demonstration plant has produced methane and liquid oxygen from simulated Martian atmosphere. The production plant has demonstrated high efficiency, extended duration production and autonomous operations. This paper presents the results and conclusions relating to eventual use in a Mars sample return mission. This work was funded by the Jet Propulsion Laboratory (JPL). The production plant was built and tested at the Propulsion Center of Lockheed Martin at the Denver Colorado facility.

Clark, David L.↗

Experimental Demonstration of Microwave Signal/Electric Thruster Plasma Interaction Effects

An experiment was designed and conducted in the Electric Propulsion Laboratory of NASA Lewis Research Center to assess the impact of ion thruster exhaust plasma plume on electromagnetic signal propagation. A microwave transmission experiment was set up inside the propulsion test bed using a pair of broadband horn antennas and a 30 cm 2.3 kW ion thruster. Frequency of signal propagation covered from 6.5 to 18 GHz range. The stainless steel test bed when enclosed can be depressurized to simulate a near vacuum environment. A pulsed CW system with gating hardware was utilized to eliminate multiple chamber reflections from the test signal. Microwave signal was transmitted and received between the two hours when the thruster was operating at a given power level in such a way that the signal propagation path crossed directly through the plume volume. Signal attenuation and phase shift due to the plume was measured for the entire frequency band. Results for this worst case configuration simulation indicate that the effects of the ion thruster plume on microwave signals is a negligible attenuation (within 0.15 dB) and a small phase shift (within 8 deg.). This paper describes the detailed experiment and presents some of the results.

Zaman, Afroz J.↗