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All sourcesNASA NTRSDOE OSTI
NASA NTRS1999

Human Mars Mission: SEP Architecture Crew Taxi Propulsion Stage Study and Design and Technology for Reaction and Control System

The Mars exploration is a candidate pathway to expand human presence and useful activities in the solar system. There are several propulsion system options being considered to place the Mars payload on its inter-planetary transfer trajectory. One propulsion option is the use of Solar Electric Propulsion (SEP) to spiral out with the Mars payload from an initial Low Earth Orbit (LEO) to an elliptical High Earth Orbit (HEO). This report, presented in annotated facing page format, describes the work completed on the design of a crew taxi propulsion stage used in conjunction with the SEP. Transportation system/mission analysis topics covered in this report include sub-system analysis, trajectory profile description, mass performance and crew taxi stage sizing, stage configuration, stage cost, and Trans-Mars Injection (TMI) launch window. The high efficiency of SEP is used to provide the major part of the TMI propulsion maneuver. Orbital energy is continuously added over a period of approximately twelve months. The SEP and Mars payload follow a spiral trajectory from an initial LEO to a final elliptical HEO. A small chemical stage is then used to provide the final part of the TMI. The now unloaded SEP returns to LEO to repeat another spiral trajectory with payload to HEO. The spiral phase of the SEP's trajectory takes several months to reach HEO, thus significantly increasing the exposure time of the crew to zero-gravity. In order to minimize the long zero-gravity effects, a high thrust chemical stage delivers the crew to the SEP's HEO. The crew rendezvous with the Mars payload in HEO. After a checkout period the Mars payload with the crew is injected onto a Trans-Mars Trajectory by a small chemical stage.

Young, Archie↗
NASA NTRS1999

Human Mars Mission: SEP Architecture, Crew Taxi Propulsion Stage Study and Design and Technology for Reaction and Control System

The Mars exploration is a candidate pathway to expand human presence and useful activities in the solar system. There are several propulsion system options being considered to place the Mars payload on its interplanetary transfer trajectory. One propulsion option is the use of Solar Electric Propulsion (SEP) to spiral out with the Mars payload from an initial Low Earth Orbit (LEO) to an elliptical High Earth Orbit (HEO). This report, presented in annotated facing page format, describes the work completed on the design of a crew taxi propulsion stage used in conjunction with the SEP. Transportation system/mission analysis topics covered in this report include sub-system analysis, trajectory profile description, mass performance and crew taxi stage sizing, stage configuration, stage cost, and Trans-Mars Injection (TMI) launch window. The high efficiency of SEP is used to provide the major part of the TMI propulsion maneuver. Orbital energy is continuously added over a period of approximately twelve months. The SEP and Mars payload follow a spiral trajectory from an initial LEO to a final elliptical HEO. A small chemical stage is then used to provide the final part of the TMI. The now unloaded SEP returns to LEO to repeat another spiral trajectory with payload to HEO. The spiral phase of the SEP's trajectory takes several months to reach HEO, thus significantly increasing the exposure time of the crew to zero-gravity. In order to minimize the long zero-gravity effects, a high thrust chemical stage delivers the crew to the SEP's HEO. The crew rendezvous with the Mars payload in HEO. After a checkout period the Mars payload with the crew is injected onto a Trans-Mars Trajectory by a small chemical stage.

Young, Archie↗
NASA NTRS1973

Free-Flight Test Results of Scale Models Simulating Viking Parachute/Lander Staging

This report presents the results of Viking Aerothermodynamics Test D4-34.0. Motion picture coverage of a number of Scale model drop tests provides the data from which time-position characteristics as well as canopy shape and model system attitudes are measured. These data are processed to obtain the instantaneous drag during staging of a model simulating the Viking decelerator system during parachute staging at Mars. Through scaling laws derived prior to test (Appendix A and B) these results are used to predict such performance of the Viking decelerator parachute during staging at Mars. The tests were performed at the NASA/Kennedy Space Center (KSC) Vertical Assembly Building (VAB). Model assemblies were dropped 300 feet to a platform in High Bay No. 3. The data consist of an edited master film (negative) which is on permanent file in the NASA/LRC Library. Principal results of this investigation indicate that for Viking parachute staging at Mars: 1. Parachute staging separation distance is always positive and continuously increasing generally along the descent path. 2. At staging, the parachute drag coefficient is at least 55% of its prestage equilibrium value. One quarter minute later, it has recovered to its pre-stage value.

Polutchko, Robert J.↗
NASA NTRS2008

Ares I Crew Launch Vehicle Upper Stage Element Overview

This viewgraph presentation gives an overview of NASA's Ares I Crew Launch Vehicle Upper Stage Element. The topics include: 1) What is NASA s Mission?; 2) NASA s Exploration Roadmap What is our time line?; 3) Building on a Foundation of Proven Technologies Launch Vehicle Comparisons; 4) Ares I Upper Stage; 5) Upper Stage Primary Products; 6) Ares I Upper Stage Development Approach; 7) What progress have we made?; 8) Upper Stage Subsystem Highlights; 9) Structural Testing; 10) Common Bulkhead Processing; 11) Stage Installation at Stennis Space Center; 12) Boeing Producibility Team; 13) Upper Stage Low Cost Strategy; 14) Ares I and V Production at Michoud Assembly Facility (MAF); 15) Merged Manufacturing Flow; and 16) Manufacturing and Assembly Weld Tools.

McArthur, J. Craig↗
NASA NTRS2011

COMPASS Final Report: Enceladus Solar Electric Propulsion Stage

The results of the NASA Glenn Research Center (GRC) COllaborative Modeling and Parametric Assessment of Space Systems (COMPASS) internal Solar Electric Propulsion (SEP) stage design are documented in this report (Figure 1.1). The SEP Stage was designed to deliver a science probe to Saturn (the probe design was performed separately by the NASA Goddard Space Flight Center s (GSFC) Integrated Mission Design Center (IMDC)). The SEP Stage delivers the 2444 kg probe on a Saturn trajectory with a hyperbolic arrival velocity of 5.4 km/s. The design carried 30 percent mass, 10 percent power, and 6 percent propellant margins. The SEP Stage relies on the probe for substantial guidance, navigation and control (GN&C), command and data handling (C&DH), and Communications functions. The stage is configured to carry the probe and to minimize the packaging interference between the probe and the stage. The propulsion system consisted of a 1+1 (one active, one spare) configuration of gimbaled 7 kW NASA Evolutionary Xenon Thruster (NEXT) ion propulsion thrusters with a throughput of 309 kg Xe propellant. Two 9350 W GaAs triple junction (at 1 Astronomical Unit (AU), includes 10 percent margin) ultra-flex solar arrays provided power to the stage, with Li-ion batteries for launch and contingency operations power. The base structure was an Al-Li hexagonal skin-stringer frame built to withstand launch loads. A passive thermal control system consisted of heat pipes to north and south radiator panels, multilayer insulation (MLI) and heaters for the Xe tank. All systems except tanks and solar arrays were designed to be single fault tolerant.

Oleson, Steven R.↗
NASA NTRS2014

Space Launch System Upper Stage Technology Assessment

The Space Launch System (SLS) is envisioned as a heavy-lift vehicle that will provide the foundation for future beyond low-Earth orbit (LEO) exploration missions. Previous studies have been performed to determine the optimal configuration for the SLS and the applicability of commercial off-the-shelf in-space stages for Earth departure. Currently NASA is analyzing the concept of a Dual Use Upper Stage (DUUS) that will provide LEO insertion and Earth departure burns. This paper will explore candidate in-space stages based on the DUUS design for a wide range of beyond LEO missions. Mission payloads will range from small robotic systems up to human systems with deep space habitats and landers. Mission destinations will include cislunar space, Mars, Jupiter, and Saturn. Given these wide-ranging mission objectives, a vehicle-sizing tool has been developed to determine the size of an Earth departure stage based on the mission objectives. The tool calculates masses for all the major subsystems of the vehicle including propellant loads, avionics, power, engines, main propulsion system components, tanks, pressurization system and gases, primary structural elements, and secondary structural elements. The tool uses an iterative sizing algorithm to determine the resulting mass of the stage. Any input into one of the subsystem sizing routines or the mission parameters can be treated as a parametric sweep or as a distribution for use in Monte Carlo analysis. Taking these factors together allows for multi-variable, coupled analysis runs. To increase confidence in the tool, the results have been verified against two point-of-departure designs of the DUUS. The tool has also been verified against Apollo moon mission elements and other manned space systems. This paper will focus on trading key propulsion technologies including chemical, Nuclear Thermal Propulsion (NTP), and Solar Electric Propulsion (SEP). All of the key performance inputs and relationships will be presented and discussed in light of the various missions. For each mission there are several trajectory options and each will be discussed in terms of delta-v required and transit duration. Each propulsion system will be modeled, sized, and judged based on their applicability to the whole range of beyond LEO missions. Criteria for scoring will include the resulting dry mass of the stage, resulting propellant required, time to destination, and an assessment of key enabling technologies. In addition to the larger metrics, this paper will present the results of several coupled sensitivity studies. The ultimate goals of these tools and studies are to provide NASA with the most mass-, technology-, and cost-effective in-space stage for its future exploration missions.

Holladay, Jon↗
NASA NTRS2012

Aero-Assisted Pre-Stage for Ballistic and Aero-Assisted Launch Vehicles

A concept of an aero-assisted pre-stage is proposed, which enables launch of both ballistic and aero-assisted launch vehicles from conventional runways. The pre-stage can be implemented as a delta-wing with a suitable undercarriage, which is mated with the launch vehicle, so that their flight directions are coaligned. The ample wing area of the pre-stage combined with the thrust of the launch vehicle ensure prompt roll-out and take-off of the stack at airspeeds typical for a conventional jet airliner. The launch vehicle is separated from the pre-stage as soon as safe altitude is achieved, and the desired ascent trajectory is reached. Nominally, the pre-stage is non-powered. As an option, to save the propellant of the launch vehicle, the pre-stage may have its own short-burn propulsion system, whereas the propulsion system of the launch vehicle is activated at the separation point. A general non-dimensional analysis of performance of the pre-stage from roll-out to separation is carried out and applications to existing ballistic launch vehicle and hypothetical aero-assisted vehicles (spaceplanes) are considered.

access to space↗
NASA NTRS2018

SLS Block 1-B and Exploration Upper Stage Navigation System Design

The SLS Block 1B vehicle is planned to extend NASA's heavy lift capability beyond the initial SLS Block 1 vehicle. The most noticeable change for this vehicle from SLS Block 1 is the swapping of the upper stage from the Interim Cryogenic Propulsion stage (ICPS), a modified Delta IV upper stage, to the more capable Exploration Upper Stage (EUS). As the vehicle evolves to provide greater lift capability and execute more demanding missions so must the SLS Integrated Navigation System to support those missions. The SLS Block 1 vehicle carries two independent navigation systems. The responsibility of the two systems is delineated between ascent and upper stage flight. The Block 1 navigation system is responsible for the phase of flight between the launch pad and insertion into Low-Earth Orbit (LEO). The upper stage system assumes the mission from LEO to payload separation. For the Block 1B vehicle, the two functions are combined into a single system intended to navigate from ground to payload insertion. Both are responsible for self-disposal once payload delivery is achieved. The evolution of the navigation hardware and algorithms from an inertial-only navigation system for Block 1 ascent flight to a tightly coupled GPS-aided inertial navigation system for Block 1-B is described. The Block 1 GN&C system has been designed to meet a LEO insertion target with a specified accuracy. The Block 1-B vehicle navigation system is designed to support the Block 1 LEO target accuracy as well as trans-lunar or trans-planetary injection accuracy. This is measured in terms of payload impact and stage disposal requirements. Additionally, the Block 1-B vehicle is designed to support human exploration and thus is designed to minimize the probability of Loss of Crew (LOC) through high-quality inertial instruments and Fault Detection, Isolation, and Recovery (FDIR) logic. The preliminary Block 1B integrated navigation system design is presented along with the challenges associated with meeting the design objectives. This paper also addresses the design considerations associated with the use of Block 1 and Commercial Off-the-Shelf (COTS) avionics for Block 1-B/EUS as part of an integrated vehicle suite for orbital operations.

Oliver, T. Emerson↗
NASA NTRS2022

The Hyper-inflation Stage in the Coronal Mass Ejection Formation: A Missing Link That Connects Flares, Coronal Mass Ejections, and Shocks in the Low Corona

We analyze the formation and three-dimensional (3D) evolution of two coronal mass ejections (CMEs) and their associated waves in the low corona via a detailed multi-viewpoint analysis of extreme-ultraviolet observations. We analyze the kinematics in the radial and lateral directions and identify three stages in the early evolution of the CME: (1) a hyper-inflation stage, when the CME laterally expands at speeds of ∼1000 km/s, followed by (2) a shorter and slower expansion stage of a few minutes and ending with (3) a self-similar phase that carries the CME into the middle corona. The first two stages coincide with the impulsive phase of the accompanying flare, the formation and separation of an EUV wave from the CME, and the start of the metric type II radio burst. Our 3D analysis suggests that the hyper-inflation phase may be a crucial stage in the CME formation with wide-ranging implications for solar eruption research. It likely represents the formation stage of the magnetic structure that is eventually ejected into the corona, as the white-light CME. It appears to be driven by the injection of poloidal flux into the ejecting magnetic structure, which leads to the lateral (primarily) growth of the magnetic flux rope. The rapid growth results in the creation of EUV waves and eventually shocks at the CME flanks that are detected as metric type II radio bursts. In other words, the hyper-inflation stage in the early CME evolution may be the "missing" link between CMEs, flares, and coronal shocks.

Solar coronal waves↗
NASA NTRS2017

A CFD Case Study of a Fan Stage with Split Flow Path Subject to Total Pressure Distortion Inflow

This report is the documentation of the work performed under the Hypersonic Project of the NASA's Fundamental Aeronautics Program. It was funded through Task Number NNC10E444T under GESS-2 Contract NNC06BA07B. The objective of the task is to develop advanced computational tools for the simulation of multi-stage turbomachinery in support of aeropropulsion. This includes work elements in extending the TURBO code and validating the multi-stage URANS (Unsteady Reynolds Averaged Navier Stokes) simulation results with the experimental data. The unsteady CFD (Computation Fluid Dynamics) calculations were performed in full wheel mode with and without screen generated total pressure distortion at the computational inflow boundary, as well as in single passage phase lag mode for uniform inflow. The experimental data were provided by NASA from the single stage RTA (Revolutionary Turbine Accelerator) fan test program.Significant non-uniform flow condition at the fan-face of the aeropropulsion system is frequentlyencountered in many of the advanced aerospace vehicles. These propulsion systems can be eithera podded or an embedded design employed in HWB (Hybrid Wing Body) airframe concept. It isalso a topic of interest in military applications, in which advanced air vehicles have already deployedsome form of embedded propulsion systems in their design because of the requirementsof compact and low observable inlets. Even in the conventional airframe/engine design, the fancould operate under such condition when the air vehicle is undergoing rapid maneuvering action.It is believed that a better understanding of the fan’s aerodynamic and aeromechanical responseto this type of operating condition or off design operation would be beneficial to designing distortiontolerant blades for improved engine operability.The objective for this research is to assess the capability of turbomachinery code as an analysistool in understanding the effects and evaluating the impact of flow distortion on the aerodynamicand aeromechanical performance of the fan in advanced propulsion systems. Results from thetesting of an advanced fan stage released by NASA are available and will be used here for CFDcode validation. The experiment was performed at NASA’s high speed compressor facility aspart of the RTA (Revolutionary Turbine Accelerator) demonstration project, a joint effort ofNASA Glenn Research Center and GE Aircraft Engines in developing an advanced Mach 4TBCC (Turbine Based Combined Cycle) turbofan/ramjet engine for access to space. Part of thetest was to assess the aerodynamic performance and operability of the fan stage under nonuniforminflow condition. Various flow distortion patterns were created at the fan-face by manipulatingsets of screens placed upstream of the wind tunnel. Measurements at the fan-face willprovide the necessary distortion flow information as the inflow boundary condition for the CFDin a full wheel simulation. Therefore the purpose of this work is to demonstrate the NASA supportedmulti-stage turbomachinery code, TURBO [1-5], in the aerodynamic performance analysisof a modern fan design operating under off design condition, and in particular to validate theCFD results with the RTA fan test data.A brief description of the RTA fan rig configuration is given in the next section, explaining onhow flow distortion were measured in the test and constructed for the CFD at the fan-face. It isfollowed by a section summarizing previous CFD work performed at NASA relevant to the currentfan configuration. A short description of the TURBO code is given next, followed by detailsin the computational model of the fan rig, the required computing resources, and the numericalprocedure for the simulations. The CFD results are presented in the discussion section and finallyconcluding remarks are summarized.

Fan Stage↗
NASA NTRSDate not supplied

Control System Development for A Zero Boil-Off Hydrogen Storage Demonstration With Two-Stage Active Cooling

A NASA team is designing and building a test article to demonstrate the long duration storage of liquid hydrogen via active cooling (cryocoolers) while implementing a two-stage cooling approach. This activity is one of a large portfolio of NASA’s Space Technology Mission Directorate funded activities which focuses on the technology maturation needed for long duration storage of cryogenic liquid in-space. The current state-of-the-art for liquid hydrogen storage on-orbit is on the order of hours while NASA’s planned missions require storage for months, or even years. To enable such a long duration, Zero Boil-Off conditions must be achieved which requires passive technologies to minimize environmental heat loads, but also active cooling to intercept and reject the remaining heat to deep space. The implementation of active cooling results in a significant amount of dry mass added to the vehicle. Utilizing a Two-Stage Cooling approach, analysis and testing to date indicates the Zero Boil-Off of liquid hydrogen can be achieved with less mass and electrical power relative to a single-stage cooling approach where only one cryocooler is used. This activity will demonstrate the fully integrated suite of technologies needed to enable the Two-Stage Cooling approach which includes Multi-Layer Insulation blankets, Low Conductivity Structures, a Tube-On-Tank Heat Exchanger, Tube-On-Shield Heat Exchanger and a Two-Stage Cryogenerator (both 90 Kelvin and 20 Kelvin) with each stage having an independently controlled circulation loop. The bulk of the heat load is intercepted by the 90 Kelvin loop via a thin foil heat exchanger internal to the insulation blankets (also known as a Broad Area Cooling Shield), with the remainder removed at cryofluid temperature (20 Kelvin) by tubes directly welded to the outer tank surface. In this paper, we examine the challenges of controlling the system, and describe the development of control algorithms and software for future testing with liquid hydrogen. The interactions between the cryofans which control circulation loop mass flow rates, electrical heaters which vary the cryocooler lift to simulate the operation of variable-lift flight units, tank heaters which can vary the overall heat load, and the effects of changes in circulation loop pressure as temperatures change, can be complex and must be well understood to maintain steady-state propellant conditions and achieve Zero Boil-Off. Parallel PID loops and watchdog programs implemented on the user interface system will help bring the systems to steady state operation and keep them at selected operating points within acceptable error, while avoiding runaway feedback loops.

cryogenics↗
NASA NTRSDate not supplied

Green Run Modal Test of the NASA Space Launch System Core Stage

The Core Stage of the new NASA Space Launch System (SLS) is a 212-foot-tall rocket assembly—consisting primarily of two cryogenic propellant tanks, an engine section, and four RS-25 rocket engines—that will send crew and large payloads to the moon and beyond for NASA’s Artemis program. Prior to SLS assembly, the Core Stage completed a series of structural and functional tests in the B-2 Test Stand at Stennis Space Center, designated Green Run. The goal of Green Run was to verify analytical models, confirm proper subsystem operation, and test-fire all four RS-25 engines of the Core Stage. In January 2020, Green Run testing began with an experimental modal analysis test, performed by the Marshal Space Flight Center modal test team. A free-boundary test condition of the Core Stage was simulated as close as possible by suspending the massive launch vehicle from the B-2 Test Stand crane. Modal excitation was provided by a pair of 250-lb electro-dynamic shakers for multi-shaker random vibration testing, as well as a 12-pound instrumented hammer for impact testing. Modal response was measured with 550 accelerometer channels distributed on both the Core Stage and the B-2 Test Stand derrick crane. Following one very long day of testing, frequency response functions were calculated from the measured time histories in the target mode frequency range of 5 Hz to 15 Hz, and mode shapes, frequencies, and damping values were successfully estimated. The case-study presented in this paper will discuss Green Run, the SLS Core Stage, the modal test setup and execution, as well as a brief overview of the test results. Challenges associated with testing such a large, suspended structure in an outdoor environment will be discussed as well.

Space Launch System↗
NASA NTRS1972

Upper stage technology evaluation studies

Studies to evaluate advanced technology relative to chemical upper stages and orbit-to-orbit stages are reported. The work described includes: development of LH2/LOX stage data, development of data to indicate stage sensitivity to engine tolerance, modified thermal routines to accommodate storable propellants, added stage geometries to computer program for monopropellant configurations, determination of the relative gain obtainable through improvement of stage mass fraction, future propulsion concepts, effect of ultrahigh chamber-pressure increases, and relative gains obtainable through improved mass fraction.

Source record↗
NASA NTRS1973

Performance of a 1.20 pressure ratio STOL fan stage at three rotor blade setting angles

A model of a short takeoff and landing (STOL) fan stage was testedin a single-stage compressor research facility. Surveys of the airflow conditions ahead of the rotor, between the rotor and stator, and behind the stator were made over the stable operating range of the stage. At the design speed of 213.3 meters per second and a weight flow of 31.2 kilograms per second, the stage pressure ratio of 1.15 was less than the design value of 1.2. The stage was tested with the rotor blades reset for more flow. Design pressure ratio was achieved and surpassed with the minus 5 deg and minus 7 deg resets, respectively. The stage efficiency was 0.88 for the minus 5 deg reset and 0.85 for the minus 7 deg reset.

Lewis, G. W., Jr.↗
NASA NTRS1975

The effect of initial flow nonuniformity on second-stage fuel injection and combustion in a supersonic duct

The effects of flow nonuniformity on second-stage hydrogen fuel injection and combustion in supersonic flow were evaluated. The first case, second-stage fuel injection into a uniform duct flow, produced data indicating that fuel mixing is considerably slower than estimates based on an empirical mixing correlation. The second-case, two-stage fuel injection (or second-stage fuel injection into a nonuniform duct flow), produced a large interaction between stages with extensive flow separation. For this case the measured wall pressure, heat transfer, and amount of reaction at the duct exit were significantly greater than estimates based on the mixing correlation. Substantially more second-stage fuel burned in the second case than in the first case. Overall effects of unmixedness/chemical kinetics were found not to be significant at the exit for stoichiometric fuel injection.

Russin, W. R.↗
NASA NTRS1976

Noise comparisons of single and two stage demonstrator fans for advanced technology aircraft

A high-speed single-stage and a low-speed two-stage fan were designed, fabricated, and tested to demonstrate their predicted low noise performance for an advanced 0.85-0.90 cruise Mach number aircraft requiring a 1.8-1.9 pressure ratio fan. Acoustic tests were made with both unsuppressed and suppressed configurations. The two-stage fan demonstrated that quiet fan technology developed for low-speed single-stage fan is applicable to two-stage designs. The unsuppressed high-speed single-stage fan demonstrated that significant reductions in inlet noise can be achieved from the sonic blockage caused by supersonic flow in the rotor blading. Both fans demonstrated suppressed inlet noise levels with treated sonic inlets that met advanced technology goals.

Heidmann, M. F.↗
NASA NTRS1981

Core compressor exit stage study, volume 6

Rear stage blading designs that have lower losses in their endwall boundary layer regions were studied. A baseline Stage A was designed as a low-speed model of stage 7 of a 10-stage compressor. Candidate rotors and stators were designed which have the potential of reducing endwall losses relative to the baseline. Rotor B uses a type of meanline in the tip region that unloads the leading edge and loads the trailing edge relative to the baseline rotor A designs. Rotor C incorporates a more skewed (hub strong) radial distribution of total pressure and smoother distribution of static pressure on the rotor tip than those of rotor B. Candidate stator B embodies twist gradients in the endwall region. Stator C embodies airfoil sections near the endwalls that have reduced trailing edge loading relative to stator A. The baseline and candidate bladings were tested using four identical stages to produce a true multistage environment. Single-stage tests were also conducted. The test data were analyzed and performances were compared. Several of the candidate configurations showed a performance improvement relative to the baseline.

Wisler, D. C.↗
NASA NTRS1981

The excavation stage of basin formation - A qualitative model

One of the most complex problems in planetary geology and geophysics is the determination of the nature of the impact cratering processes at scales of tens to thousands of kilometers that produce the complex morphological structures of multiring basins. The cratering process is frequently considered to be divided into three stages, including a short high-pressure stage of initial contact between the projectile and the planetary crust, a longer excavation or cratering flow stage culminating in the formation of a transient crater, and a still longer modification stage during which the transient crater is modified into the observed final geologic form. The transient crater may be considered as the initial boundary condition of the modification stage. In the present investigation, the nature of the transient crater is indicated by the cratering flow field determined from numerical simulations of the excavation stage. Attention is given to empirical and theoretical scaling.

Croft, S. K.↗