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At least 973 records · Page 54

A Framework for Evaluating Distributed Electric Propulsion on the SUSAN Electrofan Aircraft

This work presents a framework for evaluating models and algorithms for Distributed Electric Propulsion (DEP) on the SUSAN Electrofan Aircraft. Throughout the development of the SUSAN aircraft, the performance of various configurations of the aircraft will need to be analyzed. However, the static behavior alone is not sufficient to describe the performance of these configurations. Therefore, simulation with fully integrated subsystem models is required. The proposed framework considers the vehicle aerodynamic, propulsion, and control subsystems. The presented framework automatically generates control laws for any vehicle configuration in response to changes in these subsystems. To compare these different vehicle configurations, various time and frequency domain performance metrics are compared. Three different system modifications are used as cases to evaluate this framework. The first modification integrates the propulsion control system with the flight controller to enable differential thrust without stalling the main engine. This evaluation case is used to validate the framework for aircraft configurations with coupled subsystems. The second modification compares the effect of the vertical tail size on open and closed loop performance. This evaluation case is used to validate the framework for controlling different configurations and tuning towards comparable closed loop performance despite changes to the aircraft's aerodynamic model. The third modification implements two different control allocation schemes. This evaluation case demonstrates the framework's ability to evaluate allocation modifications needed to take advantage of DEP. The first evaluation case is used to show that controller integration enables differential thrust, improving realized wingfan bandwidth by up to 40\% in simulation. The second evaluation case demonstrates that the framework can stabilize the reduced tail size aircraft with closed loop control. The third evaluation case demonstrates that a pseudoinverse control allocation scheme improves lateral velocity settling time by approximately 17~seconds over a symmetric-thrust allocation. These cases show that the framework is useful for evaluating the performance of integrated system designs, enabling analyses of new models and algorithms for the SUSAN distributed electric propulsion vehicle.

Nicholas C Ogden↗

Estimation of attitude sensor timetag biases

This paper presents an extended Kalman filter for estimating attitude sensor timing errors. Spacecraft attitude is determined by finding the mean rotation from a set of reference vectors in inertial space to the corresponding observed vectors in the body frame. Any timing errors in the observations can lead to attitude errors if either the spacecraft is rotating or the reference vectors themselves vary with time. The state vector here consists of the attitude quaternion, timetag biases, and, optionally, gyro drift rate biases. The filter models the timetags as random walk processes: their expectation values propagate as constants and white noise contributes to their covariance. Thus, this filter is applicable to cases where the true timing errors are constant or slowly varying. The observability of the state vector is studied first through an examination of the algebraic observability condition and then through several examples with simulated star tracker timing errors. The examples use both simulated and actual flight data from the Extreme Ultraviolet Explorer (EUVE). The flight data come from times when EUVE had a constant rotation rate, while the simulated data feature large angle attitude maneuvers. The tests include cases with timetag errors on one or two sensors, both constant and time-varying, and with and without gyro bias errors. Due to EUVE's sensor geometry, the observability of the state vector is severely limited when the spacecraft rotation rate is constant. In the absence of attitude maneuvers, the state elements are highly correlated, and the state estimate is unreliable. The estimates are particularly sensitive to filter mistuning in this case. The EUVE geometry, though, is a degenerate case having coplanar sensors and rotation vector. Observability is much improved and the filter performs well when the rate is either varying or noncoplanar with the sensors, as during a slew. Even with bad geometry and constant rates, if gyro biases are independently known, the timetag error for a single sensor can be accurately estimated as long as its boresight is not too close to the spacecraft rotation axis.

Sedlak, J.↗

Radiation Beamline Testbeds for the Simulation of Planetary and Spacecraft Environments for Human and Robotic Mission Risk Assessment

The Center for Radiation Engineering and Science for Space Exploration (CRESSE) at Prairie View A&M University, Prairie View, Texas, USA, is establishing an integrated, multi-disciplinary research program on the scientific and engineering challenges faced by NASA and the international space community caused by space radiation. CRESSE focuses on space radiation research directly applicable to astronaut health and safety during future long term, deep space missions, including Martian, lunar, and other planetary body missions beyond low earth orbit. The research approach will consist of experimental and theoretical radiation modeling studies utilizing particle accelerator facilities including: 1. NASA Space Radiation Laboratory (NSRL) at Brookhaven National Laboratory; 2. Proton Synchrotron at Loma Linda University Medical Center; and 3. Los Alamos Neutron Science Center (LANSCE) at Los Alamos National Laboratory. Specifically, CRESSE investigators are designing, developing, and building experimental test beds that simulate the lunar and Martian radiation environments for experiments focused on risk assessment for astronauts and instrumentation. The testbeds have been designated the Bioastronautics Experimental Research Testbeds for Environmental Radiation Nostrum Investigations and Education (BERT and ERNIE). The designs of BERT and ERNIE will allow for a high degree of flexibility and adaptability to modify experimental configurations to simulate planetary surface environments, planetary habitats, and spacecraft interiors. In the nominal configuration, BERT and ERIE will consist of a set of experimental zones that will simulate the planetary atmosphere (Solid CO2 in the case of the Martian surface.), the planetary surface, and sub-surface regions. These experimental zones can be used for dosimetry, shielding, biological, and electronic effects radiation studies in support of space exploration missions. BERT and ERNIE are designed to be compatible with the experimental areas associated with the above facilities. CRESSE has broad expertise in space radiation in the areas of space radiation environment modeling, Monte-Carlo radiation transport modeling, space radiation instrumentation and dosimetry, radiation effects on electronics, and multi-functional composite shielding materials. The BERT and ERNIE testbeds will be utilized in individual and collaborative research incorporating this expertise. The research goal is to maximize the technical readiness level (TRL) of radiation instrumentation for human and robotic missions, optimizing the return value of CRESSE for NASA exploration and international co-operative missions. Outcomes and knowledge from research utilizing BERT and ERNIE will be applied to a variety of scientific and engineering disciplines vital for safe and reliable execution of future space exploration missions, which can be negatively impacted by the space radiation environment. The testbeds will be central to a variety of university educational activities and educational goals of NASA. Specifically, BERT and ERNIE will enhance educational opportunities in science, technology, engineering and mathematics (STEM) disciplines for engineering and science students at PVAMU, a historically black college/university. Preliminary data on prototype testbed configurations, including simulated lunar regolith (JSC-1A stimulant based on Apollo 11 samples), regolith/polyethylene composites, and dry ice, will be presented to demonstrate the usefulness of BERT and ERNIE in radiation beam line experiments.

Wilkins, Richard↗

The direct numerical simulations of the turbulent wakes of axisymmetric bodies

Results of direct numerical simulations of turbulence are compared with both laboratory data and self-similarity theory for the case of the turbulent wakes of towed, axisymmetric bodies. In general, the agreement of the simulation results with both the laboratory data and the self-similarity theory is good, although the comparisons are hampered by inadequate procedures for initializing the numerical simulations.

Riley, J. J.↗

Comparison of in-flight and ground-based simulator derived flying qualities and pilot performance for approach and landing tasks

For the case of an approach-and-landing piloting task emphasizing response to the landing flare, pilot opinion and performance parameters derived from jet transport aircraft six-degree-of-freedom ground-based and in-flight simulators were compared in order to derive data for the flight-controls/flying-qualities engineers. The data thus obtained indicate that ground simulation results tend to be conservative, and that the effect of control sensitivity is more pronounced for ground simulation. The pilot also has a greater tendency to generate pilot-induced oscillation in ground-based simulation than in flight.

Grantham, William D.↗

Intermittency and Cessation of Vortex Shedding in the Wake of a Thin Flat Plate with a Circular Trailing Edge

The near and very near wake of thin flat plates with both sharp and circular trailing edges (TEs) are investigated with direct numerical simulations (DNSs). The TE is circular in two of the cases (IN & NS) and sharp in one of them (ST). The separating boundary layers are turbulent in all cases. The objectives of this study are twofold. The first is to explore the effect of significantly reducing Re(sub D) (Reynolds number based on circular TE diameter, D) on the flow in the TE region, and the shedding process (Cases IN and NS). The second is to better understand the reasons underlying the findings of an earlier experimental wake investigation (sharp TE) where (1) the center-line values in normal intensity, and the peak in shear stress profiles in the cross-stream direction, were found to first increase in the streamwise direction (x), from that obtained at the TE, before diminishing further downstream, and (2) a broadband peak was observed in centerline cross-stream velocity (v) spectra (indicating quasi-periodicity, possibly due to vortices or wave-like motions). Case ST from the present study showed a near wake instability resulting in spanwise vortices (with a streamwise component). The instability is intermittent and contributes to both the broadband peak in the v spectrum and the initial increases in normal intensity and shear stress (as in the experiment). Case NS, with the lower value of ReD is an "essentially" non-shedding case where the flow in the TE region continually changes direction (upward/downward) because of turbulence. Case IN, with twice the value of ReD as Case NS, also exhibits a swaying motion in the TE region. In addition, vortex shedding is initiated during periods when the flow direction changes rapidly. Shedding in this case is intermittent. It results in a peak in the v spectrum obtained at the centerline (x/D = 1.0).

direct numerical simulations↗

Assessments of a Turbulence Model Based on Menter's Modification to Rotta's Two-Equation Model

The main objective of this paper is to construct a turbulence model with a more reliable second equation simulating length scale. In the present paper, we assess the length scale equation based on Menter s modification to Rotta s two-equation model. Rotta shows that a reliable second equation can be formed in an exact transport equation from the turbulent length scale L and kinetic energy. Rotta s equation is well suited for a term-by-term modeling and shows some interesting features compared to other approaches. The most important difference is that the formulation leads to a natural inclusion of higher order velocity derivatives into the source terms of the scale equation, which has the potential to enhance the capability of Reynolds-averaged Navier-Stokes (RANS) to simulate unsteady flows. The model is implemented in the PAB3D solver with complete formulation, usage methodology, and validation examples to demonstrate its capabilities. The detailed studies include grid convergence. Near-wall and shear flows cases are documented and compared with experimental and Large Eddy Simulation (LES) data. The results from this formulation are as good or better than the well-known SST turbulence model and much better than k-epsilon results. Overall, the study provides useful insights into the model capability in predicting attached and separated flows.

Abdol-Hamid, Khaled S.↗

Characterizing Wheel-Soil Interaction Loads Using Meshfree Finite Element Methods: A Sensitivity Analysis for Design Trade Studies

A wheel experiencing sinkage and slippage events poses a high risk to planetary rover missions as evidenced by the mobility challenges endured by the Mars Exploration Rover (MER) project. Current wheel design practice utilizes loads derived from a series of events in the life cycle of the rover which do not include (1) failure metrics related to wheel sinkage and slippage and (2) performance trade-offs based on grouser placement/orientation. Wheel designs are rigorously tested experimentally through a variety of drive scenarios and simulated soil environments; however, a robust simulation capability is still in development due to myriad of complex interaction phenomena that contribute to wheel sinkage and slippage conditions such as soil composition, large deformation soil behavior, wheel geometry, nonlinear contact forces, terrain irregularity, etc. For the purposes of modeling wheel sinkage and slippage at an engineering scale, meshfree nite element approaches enable simulations that capture su cient detail of wheel-soil interaction while remaining computationally feasible. This study implements the JPL wheel-soil benchmark problem in the commercial code environment utilizing the large deformation modeling capability of Smooth Particle Hydrodynamics (SPH) meshfree methods. The nominal, benchmark wheel-soil interaction model that produces numerically stable and physically realistic results is presented and simulations are shown for both wheel traverse and wheel sinkage cases. A sensitivity analysis developing the capability and framework for future ight applications is conducted to illustrate the importance of perturbations to critical material properties and parameters. Implementation of the proposed soil-wheel interaction simulation capability and associated sensitivity framework has the potential to reduce experimentation cost and improve the early stage wheel design proce

terramechanics↗

Noise of a model counterrotation propeller with simulated fuselage and support pylon at takeoff/approach conditions

Two modern high-speed advanced counterrotation propellers, F7/A7 and F7/A3 were tested in the NASA Lewis Research Centers's 9- by 15-foot Anechoic Wind Tunnel at simulated takeoff/approach conditions of 0.2 Mach number. Both rotors were of similar diameter on the F7/A7 propeller, while the aft rotor diameter of the F7/A3 propeller was 85 percent of the forward propeller to reduce tip vortex-aft rotor interaction. The two propellers were designed for similar performance. The propellers were tested in both the clean configuration, and installed configuration consisting of a simulated upstream nacelle support pylon and fuselage section. Acoustic measurements were made with an axially translating microphone probe, and with a polar microphone probe which was fixed to the propeller nacelle and could make both sideline and circumferential acoustic surveys. Aerodynamic measurements were also made to establish propeller operating conditions. The propellers were run at blade setting angles (fron angle/rear angle) of 41.1/39.4 deg for the F7/A7 propeller, and 41.1/46.4 deg for the F7/A3 propeller. The forward rotors were tested over a range of tip speeds from 165 to 259 m/sec (540 to 850 ft/sec), and both propellers were tested at the maximum rotor-rotor spacing, based on pitch change axis separation, of 14.99 cm (5.90 in.). The data presented in this paper are for 0 deg propeller axis angle of attack. Results are presented for the baseline, pylon-alone, and strut + fuselage configurations. The presence of the simulated fuselage resulted in higher rotor-alone tone levels in a direction normal to the advancing propeller blade near the fuselage. A corresponding rotor-alone tone reduction was often observed 180 deg circumferentially from this region of increased noise. A significant rotor-alone increase for both rotors was observed diametrically opposite the fuselage. In some cases, interaction tone levels were likewise affected by the simulated installation.

Woodward, Richard P.↗

Noise of a model counterrotation propeller with simulated fuselage and support pylon at takeoff/approach conditions

Two modern high-speed advanced counterrotation propellers, F7/A7 and F7/A3 were tested in the NASA Lewis Research Centers's 9- by 15-foot Anechoic Wind Tunnel at simulated takeoff/approach conditions of 0.2 Mach number. Both rotors were of similar diameter on the F7/A7 propeller, while the aft rotor diameter of the F7/A3 propeller was 85 percent of the forward propeller to reduce tip vortex-aft rotor interaction. The two propellers were designed for similar performance. The propellers were tested in both the clean configuration, and installed configuration consisting of a simulated upstream nacelle support pylon and fuselage section. Acoustic measurements were made with an axially translating microphone probe, and with a polar microphone probe which was fixed to the propeller nacelle and could make both sideline and circumferential acoustic surveys. Aerodynamic measurements were also made to establish propeller operating conditions. The propellers were run at blade setting angles (front angle/rear angle) of 41.1/39.4 deg for the F7/A7 propeller, and 41.1/46.4 deg for the F7/A3 propeller. The forward rotors were tested over a range of tip speeds from 165 to 259 m/sec (540 to 850 ft/sec), and both propellers were tested at the maximum rotor-rotor spacing, based on pitch change axis separation, of 14.99 cm (5.90 in.). The data presented in this paper are for 0 deg propeller axis angle of attack. Results are presented for the baseline, pylon-alone, and strut + fuselage configurations. The presence of the simulated fuselage resulted in higher rotor-alone tone levels in a direction normal to the advancing propeller blade near the fuselage. A corresponding rotor-alone tone reduction was often observed 180 deg circumferentially from this region of increased noise. A significant rotor-alone increase for both rotors was observed diametrically opposite the fuselage. In some cases, interaction tone levels were likewise affected by the simulated installation.

Woodward, Richard P.↗

Monte Carlo computer simulations of Venus equilibrium and global resurfacing models

Two models have been proposed for the resurfacing history of Venus: (1) equilibrium resurfacing and (2) global resurfacing. The equilibrium model consists of two cases: in case 1, areas less than or equal to 0.03 percent of the planet are spatially randomly resurfaced at intervals of less than or greater than 150,000 yr to produce the observed spatially random distribution of impact craters and average surface age of about 500 m.y.; and in case 2, areas greater than or equal to 10 percent of the planet are resurfaced at intervals of greater than or equal to 50 m.y. The global resurfacing model proposes that the entire planet was resurfaced about 500 m.y. ago, destroying the preexisting crater population and followed by significantly reduced volcanism and tectonism. The present crater population has accumulated since then with only 4 percent of the observed craters having been embayed by more recent lavas. To test the equilibrium resurfacing model we have run several Monte Carlo computer simulations for the two proposed cases. It is shown that the equilibrium resurfacing model is not a valid model for an explanation of the observed crater population characteristics or Venus' resurfacing history. The global resurfacing model is the most likely explanation for the characteristics of Venus' cratering record. The amount of resurfacing since that event, some 500 m.y. ago, can be estimated by a different type of Monte Carolo simulation. To date, our initial simulation has only considered the easiest case to implement. In this case, the volcanic events are randomly distributed across the entire planet and, therefore, contrary to observation, the flooded craters are also randomly distributed across the planet.

Dawson, D. D.↗

FUN3D Analyses in Support of the 1st AIAA Stability and Control Prediction Workshop

The 1st AIAA Stability and Control Prediction Workshop was created to establish best practices for the prediction of stability & control derivatives using computational fluid dynamics and assess the limitations of these computational methods when those best practices are applied. The inaugural workshop considers the ONERA version of the NASA/Boeing Common Research Model(CRM), which includes the wing, body, horizontal tail, and a vertical tail designed by ONERA. Wind tunnel tests have been conducted for this configuration with longitudinal tests having been previously published, in addition to unpublished data at small sideslip angles that will serve as ‘blind’ data for workshop data comparisons. Participants were provided a ‘family’ of unstructured grids for the full-span ONERA CRM model with the wind-tunnel sting included. This family of mixed-element grids consists of 5 levels of refinement (tiny, coarse, medium, fine, and extra fine) with surface and volume mesh scaling, resulting in a size range of 14.6 to 53.4 million nodes. In addition, a medium refinement mesh has been provided for the ONERA CRM configuration without a sting to evaluate the sting’s impact on static longitudinal stability characteristics. In addition to these workshop-provided grids, the present work also considers an equivalent ‘family’ of computational grids generated using Heldenmesh™, a rapid grid generation software by Helden Aerospace Corporation for creating high-quality, three-dimensional, mixed-element unstructured meshes. Because of the authors’ familiarity with this software, these additional grids were generated as a comparison to the workshop-provided grids and to better understand the implications of using volume-mirrored grids for stability and control predictions. The present work will contribute to the workshop with test case data generated using the NASA FUN3D code, a parallelized, unstructured, node-based, finite-volume discretization, Reynolds-averaged Navier-Stokes flow solver. Numerical simulations will be conducted using the Quadratic Constitutive Relationship (QCR) version of the Spalart-Allmaras (SA) turbulence model with negative turbulence variable provisions. Both steady and2nd-order, time-accurate simulation results are to be generated and compared for select test cases, as time permits, to investigate their impact on FUN3D predictions. The present work will consider the three primary workshop test cases: (1) grid convergence study, (2) Mach number effect on static stability, and (3) wind tunnel sting increments. Additionally, data will be provided for the two optional test cases, which include:(1) static stability derivative calculations and (2)sideslip angle sweeps. In each of the test cases, the vehicle is stationary, and the body is assumed to be rigid, where vehicle deformation has been accounted for in the model configuration geometry. For all test cases, longitudinal and lateral force and moment aerodynamic coefficients will be provided for the total configuration, in addition to a component-level breakdown that includes the port wing, starboard wing, fuselage, and tail.

CFD↗

USM3D Simulations for Third Sonic Boom Workshop

The NASA USM3D flow solver was used to compute test cases for the Third AIAA Sonic Boom Prediction Workshop (SBPW3). The test cases include an axisymmetric equivalent area body, a near field biconvex shock-plume interaction wind tunnel model, and the C608 Low Boom Flight Demonstrator. Numerical simulations were conducted on the mixed element grids and the tetrahedral grids provided by the workshop committee, as well as a family of grids generated by an in-house approach for sonic boom analyses known as Boom Grid. The near-field pressure signatures were extracted, propagated to the ground and the perceived loudness levels on the ground was computed. The USM3D near-field pressure signatures,corresponding ground signatures, and loudness levels on the ground are compared with mean values from other workshop participants.

Supersonics↗

Colored noise effects on batch attitude accuracy estimates

The effects of colored noise on the accuracy of batch least squares parameter estimates with applications to attitude determination cases are investigated. The standard approaches used for estimating the accuracy of a computed attitude commonly assume uncorrelated (white) measurement noise, while in actual flight experience measurement noise often contains significant time correlations and thus is colored. For example, horizon scanner measurements from low Earth orbit were observed to show correlations over many minutes in response to large scale atmospheric phenomena. A general approach to the analysis of the effects of colored noise is investigated, and interpretation of the resulting equations provides insight into the effects of any particular noise color and the worst case noise coloring for any particular parameter estimate. It is shown that for certain cases, the effects of relatively short term correlations can be accommodated by a simple correction factor. The errors in the predicted accuracy assuming white noise and the reduced accuracy due to the suboptimal nature of estimators that do not take into account the noise color characteristics are discussed. The appearance of a variety of sample noise color characteristics are demonstrated through simulation, and their effects are discussed for sample estimation cases. Based on the analysis, options for dealing with the effects of colored noise are discussed.

Bilanow, Stephen↗

Gain-Scheduled Fault Tolerance Control Under False Identification

An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

Shin, Jong-Yeob↗

Development of a Test Facility for Air Revitalization Technology Evaluation

An active fault tolerant control (FTC) law is generally sensitive to false identification since the control gain is reconfigured for fault occurrence. In the conventional FTC law design procedure, dynamic variations due to false identification are not considered. In this paper, an FTC synthesis method is developed in order to consider possible variations of closed-loop dynamics under false identification into the control design procedure. An active FTC synthesis problem is formulated into an LMI optimization problem to minimize the upper bound of the induced-L2 norm which can represent the worst-case performance degradation due to false identification. The developed synthesis method is applied for control of the longitudinal motions of FASER (Free-flying Airplane for Subscale Experimental Research). The designed FTC law of the airplane is simulated for pitch angle command tracking under a false identification case.

Lu, Sao-Dung↗

Simulator for concurrent processing data flow architectures

A software simulator capability of simulating execution of an algorithm graph on a given system under the Algorithm to Architecture Mapping Model (ATAMM) rules is presented. ATAMM is capable of modeling the execution of large-grained algorithms on distributed data flow architectures. Investigating the behavior and determining the performance of an ATAMM based system requires the aid of software tools. The ATAMM Simulator presented is capable of determining the performance of a system without having to build a hardware prototype. Case studies are performed on four algorithms to demonstrate the capabilities of the ATAMM Simulator. Simulated results are shown to be comparable to the experimental results of the Advanced Development Model System.

Malekpour, Mahyar R.↗

Investigating Premature Ignition of Thruster Pressure Cartridges by Vibration-Induced Electrostatic Discharge

Pyrotechnic thruster pressure cartridges (TPCs) are used for aeroshell separation on a new NASA crew launch vehicle. Nondestructive evaluation (NDE) during TPC acceptance testing indicated that internal assemblies moved during shock and vibration testing due to an internal bond anomaly. This caused concerns that the launch environment might produce the same movement and release propellant grains that might be prematurely ignited through impact or through electrostatic discharge (ESD) as grains vibrated against internal surfaces. Since a new lot could not be fabricated in time, a determination had to be made as to whether the lot was acceptable to fly. This paper discusses the ESD evaluation and a separate paper addresses the impact problem. A challenge to straight forward assessment existed due to the unavailability of triboelectric data characterizing the static charging characteristics of the propellants within the TPC. The approach examined the physical limitations for charge buildup within the TPC system geometry and evaluated it for discharge under simulated vibrations used to qualify components for launch. A facsimile TPC was fabricated using SS 301 for the case and surrogate worst case materials for the propellants based on triboelectric data. System discharge behavior was evaluated by applying high voltage to the point of discharge in air and by placing worst case charge accumulations within the facsimile TPC and forcing discharge. The facsimile TPC contained simulated propellant grains and lycopodium, a well characterized indicator for static discharge in dust explosions, and was subjected to accelerations equivalent to the maximum accelerations possible during launch. The magnitude of charge generated within the facsimile TPC system was demonstrated to lie in a range of 100 to 10,000 times smaller than the spark energies measured to ignite propellant grains in industry standard discharge tests. The test apparatus, methodology, and results are described in this paper.

Woods, Stephen S.↗