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NASA NTRS2015

Fracture Toughness of Carbon Fiber Composites Containing Various Fiber Sizings and a Puncture Self-Healing Thermoplastic Matrix

Ongoing efforts at NASA Langley Research Center (LaRC) have resulted in the identification of several commercially available thermoplastic resin systems which self-heal after ballistic impact and through penetration. One of these resins, polybutylene graft copolymer (PBg), was selected as a matrix for processing with unsized carbon fibers to fabricate reinforced composites for further evaluation. During process development, data from thermo-physical analyses was utilized to determine a processing cycle to fabricate laminate panels, which were analyzed by photo microscopy and acid digestion. The process cycle was further optimized based on these results to fabricate panels for mechanical property characterization. The results of the processing development effort of this composite material, as well as the results of the mechanical property characterization, indicated that bonding between the fiber and PBg was not adequate. Therefore, three sizings were investigated in this work to assess their potential to improve fiber/matrix bonding compared to previously tested unsized IM7 fiber. Unidirectional prepreg was made at NASA LaRC from three sized carbon fibers and utilized to fabricate test coupons that were tested in double cantilever beam configurations to determine GIc fracture toughness.

Cano, Roberto J.↗
NASA NTRS2013

Determine ISS Soyuz Orbital Module Ballistic Limits for Steel Projectiles Hypervelocity Impact Testing

A new orbital debris environment model (ORDEM 3.0) defines the density distribution of the debris environment in terms of the fraction of debris that are low-density (plastic), medium-density (aluminum) or high-density (steel) particles. This hypervelocity impact (HVI) program focused on assessing ballistic limits (BLs) for steel projectiles impacting the enhanced Soyuz Orbital Module (OM) micrometeoroid and orbital debris (MMOD) shield configuration. The ballistic limit was defined as the projectile size on the threshold of failure of the OM pressure shell as a function of impact speeds and angle. The enhanced OM shield configuration was first introduced with Soyuz 30S (launched in May 2012) to improve the MMOD protection of Soyuz vehicles docked to the International Space Station (ISS). This test program provides HVI data on U.S. materials similar in composition and density to the Russian materials for the enhanced Soyuz OM shield configuration of the vehicle. Data from this test program was used to update ballistic limit equations used in Soyuz OM penetration risk assessments. The objective of this hypervelocity impact test program was to determine the ballistic limit particle size for 440C stainless steel spherical projectiles on the Soyuz OM shielding at several impact conditions (velocity and angle combinations). This test report was prepared by NASA-JSC/ HVIT, upon completion of tests.

Lyons, Frankel↗
NASA NTRS2013

Micrometeoroid and Orbital Debris (MMOD) Shield Ballistic Limit Analysis Program

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.

Ryan, Shannon↗
NASA NTRS2012

Processing and Damage Tolerance of Continuous Carbon Fiber Composites Containing Puncture Self-Healing Thermoplastic Matrix

Research at NASA Langley Research Center (NASA LaRC) has identified several commercially available thermoplastic polymers that self-heal after ballistic impact and through-penetration. One of these resins, polybutadiene graft copolymer (PB(sub g)), was processed with unsized IM7 carbon fibers to fabricate reinforced composite material for further evaluation. Temperature dependent characteristics, such as the degradation point, glass transition (T(sub g)), and viscosity of the PBg polymer were characterized by thermogravimetric analysis (TGA), differential scanning calorimetry (DSC), and dynamic parallel plate rheology. The PBg resin was processed into approximately equal to 22.0 cm wide unidirectional prepreg tape in the NASA LaRC Advanced Composites Processing Research Laboratory. Data from polymer thermal characterization guided the determination of a processing cycle used to fabricate quasi-isotropic 32-ply laminate panels in various dimensions up to 30.5cm x 30.5cm in a vacuum press. The consolidation quality of these panels was analyzed by optical microscopy and acid digestion. The process cycle was further optimized based on these results and quasi-isotropic, [45/0/-45/90]4S, 15.24cm x 15.24cm laminate panels were fabricated for mechanical property characterization. The compression strength after impact (CAI) of the IM7/pBG composites was measured both before and after an elevated temperature and pressure healing cycle. The results of the processing development effort of this composite material as well as the results of the mechanical property characterization are presented in this paper.

Grimsley, Brian W.↗
NASA NTRS2013

International Space Station (ISS) Soyuz Vehicle Descent Module Evaluation of Thermal Protection System (TPS) Penetration Characteristics

The descent module (DM) of the ISS Soyuz vehicle is covered by thermal protection system (TPS) materials that provide protection from heating conditions experienced during reentry. Damage and penetration of these materials by micrometeoroid and orbital debris (MMOD) impacts could result in loss of vehicle during return phases of the mission. The descent module heat shield has relatively thick TPS and is protected by the instrument-service module. The TPS materials on the conical sides of the descent module (referred to as backshell in this test plan) are exposed to more MMOD impacts and are relatively thin compared to the heat shield. This test program provides hypervelocity impact (HVI) data on materials similar in composition and density to the Soyuz TPS on the backshell of the vehicle. Data from this test program was used to update ballistic limit equations used in Soyuz TPS penetration risk assessments. The impact testing was coordinated by the NASA Johnson Space Center (JSC) Hypervelocity Impact Technology (HVIT) Group [1] in Houston, Texas. The HVI testing was conducted at the NASA-JSC White Sands Hypervelocity Impact Test Facility (WSTF) at Las Cruces, New Mexico. Figure

Davis, Bruce A.↗
NASA NTRS1981

Aerodynamic mission concepts for the Mars sample return mission

Future plans for the continued exploration of Mars call for a sample return mission. This plan proposes bringing a distributed, selected sample of Mars material from several locales on Mars back to earth. The mission options studied to date utilize an extensive number of aerodynamic concepts not previously planned in past planetary exploration programs. These include various modes of orbit modification using atmospheric braking, aeromaneuvering to effect precision surface landing, very low ballistic entry for a network of surface penetrators, low flying hydrazine powered airplanes, balloons, ascent vehicles and direct entry of the samples on return to earth. This paper will discuss the concepts and their feasibility along with technology problems associated with them as surveyed from the reference material. The paper focuses primarily on the aerocapture technique as it relates to Mars orbit modification. Remaining orbit modification techniques are also discussed briefly for comparison.

Cruz, M. I.↗
NASA NTRS2011

Micrometeoroid and Orbital Debris Threat Assessment: Mars Sample Return Earth Entry Vehicle

This report provides results of a Micrometeoroid and Orbital Debris (MMOD) risk assessment of the Mars Sample Return Earth Entry Vehicle (MSR EEV). The assessment was performed using standard risk assessment methodology illustrated in Figure 1-1. Central to the process is the Bumper risk assessment code (Figure 1-2), which calculates the critical penetration risk based on geometry, shielding configurations and flight parameters. The assessment process begins by building a finite element model (FEM) of the spacecraft, which defines the size and shape of the spacecraft as well as the locations of the various shielding configurations. This model is built using the NX I-deas software package from Siemens PLM Software. The FEM is constructed using triangular and quadrilateral elements that define the outer shell of the spacecraft. Bumper-II uses the model file to determine the geometry of the spacecraft for the analysis. The next step of the process is to identify the ballistic limit characteristics for the various shield types. These ballistic limits define the critical size particle that will penetrate a shield at a given impact angle and impact velocity. When the finite element model is built, each individual element is assigned a property identifier (PID) to act as an index for its shielding properties. Using the ballistic limit equations (BLEs) built into the Bumper-II code, the shield characteristics are defined for each and every PID in the model. The final stage of the analysis is to determine the probability of no penetration (PNP) on the spacecraft. This is done using the micrometeoroid and orbital debris environment definitions that are built into the Bumper-II code. These engineering models take into account orbit inclination, altitude, attitude and analysis date in order to predict an impacting particle flux on the spacecraft. Using the geometry and shielding characteristics previously defined for the spacecraft and combining that information with the environment model calculations, the Bumper-II code calculates a probability of no penetration for the spacecraft.

Christiansen, Eric L.↗
NASA NTRS1985

Effect of low-velocity or ballistic impact damage on the strength of thin composite and aluminum shear panels

Impact tests were conducted on shear panels fabricated from 6061-T6 aluminum and from woven fabric prepreg of Du Pont Kevlara fiber/epoxy resin and graphite fiber/epoxy resin. The shear panels consisted of three different composite laminates and one aluminum material configuration. Three panel aspect ratios were evaluated for each material configuration. Composite panels were impacted with a 1.27-cm (0.05-in) diameter aluminum sphere at low velocities of 46 m/sec (150 ft/sec) and 67 m/sec (220 ft/sec). Ballistic impact conditions consisted of a tumbled 0.50-caliber projectile impacting loaded composite and aluminum shear panels. The results of these tests indicate that ballistic threshold load (the lowest load which will result in immediate failure upon penetration by the projectile) varied between 0.44 and 0.61 of the average failure load of undamaged panels. The residual strengths of the panels after ballistic impact varied between 0.55 and 0.75 of the average failure strength of the undamaged panels. The low velocity impacts at 67 m/sec (220 ft/sec) caused a 15 to 20 percent reduction in strength, whereas the impacts at 46 m/sec (150 ft/sec) resulted in negligible strength loss. Good agreement was obtained between the experimental failure strengths and the predicted strength with the point stress failure criterion.

Farley, G. L.↗
NASA NTRS1991

Single wall penetration equations

Five single plate penetration equations are compared for accuracy and effectiveness. These five equations are two well-known equations (Fish-Summers and Schmidt-Holsapple), two equations developed by the Apollo project (Rockwell and Johnson Space Center (JSC), and one recently revised from JSC (Cour-Palais). They were derived from test results, with velocities ranging up to 8 km/s. Microsoft Excel software was used to construct a spreadsheet to calculate the diameters and masses of projectiles for various velocities, varying the material properties of both projectile and target for the five single plate penetration equations. The results were plotted on diameter versus velocity graphs for ballistic and spallation limits using Cricket Graph software, for velocities ranging from 2 to 15 km/s defined for the orbital debris. First, these equations were compared to each other, then each equation was compared with various aluminum projectile densities. Finally, these equations were compared with test results performed at JSC for the Marshall Space Flight Center. These equations predict a wide variety of projectile diameters at a given velocity. Thus, it is very difficult to choose the 'right' prediction equation. The thickness of a single plate could have a large variation by choosing a different penetration equation. Even though all five equations are empirically developed with various materials, especially for aluminum alloys, one cannot be confident in the shield design with the predictions obtained by the penetration equations without verifying by tests.

Hayashida, K. B.↗
NASA NTRS2005

Orbital Debris Shape and Orientation Effects on Ballistic Limits

The SPHC hydrodynamic code was used to evaluate the effects of orbital debris particle shape and orientation on penetration of a typical spacecraft dual-wall shield. Impacts were simulated at near-normal obliquity at 12 km/sec. Debris cloud characteristics and damage potential are compared with those from impacts by spherical projectiles. Results of these simulations indicate the uncertainties in the predicted ballistic limits due to modeling uncertainty and to uncertainty in the impactor orientation.

Evans, Steven W.↗
NASA NTRS1998

Calculation of Area Loss Due to Meteoroid Penetration

Simple Monte Carlo methods have been applied to the calculation of meteoroid penetration of spacecraft surfaces to account for the distributions of impact angle and velocity on the impact mechanics. Both single sheet and double sheet surfaces have been modeled. The model has been applied to several spacecraft and spacecraft concepts to evaluate light leakage into optical instruments or through sunshades. Results indicate that surfaces are less likely to be penetrated - or will be penetrated less often - than indicated by simply assuming an "average" velocity and normal impact. The reduction is typically about 40 percent. This effect is caused by the angular dependence of the penetration mechanics. However, the probability distribution of penetrating particles is relatively broad and indicates a peak above the ballistic limit particle size associated with the average velocity case.

Cooke, William J., Jr.↗
NASA NTRS2008

Micro-Structural Response of DP 600 to High Strain Rate Deformation

The object of this study was to investigate the micro-structural response of DP 600 subjected to high strain rate, ballistic impact tests. The ballistic tests were conducted using normal impact of a hardened steel penetrator into a 2 mm thick sheet of DP 600. The average strain rates produced from this test method are on the order of 10(exp 5)/s. Electron microscopy was used to investigate the microstructure before and after high strain rate deformation. A variation in material response was observed between tests conducted at 0.8 x 105 and 25 x 10(exp 5)/s.

Hamburg, Brian↗
NASA NTRSDate not supplied

Overview of Micrometeoroid and Orbital Debris Analysis Process for Mars Sample Return Earth Entry System

Introduction: Micrometeoroid and orbital debris (MMOD) risk analyses for the Mars Sample Return (MSR) Earth Entry System (EES) have been significantly more rigorous than previously flown missions because of its categorization as a Class V restricted return mission. This means the returned samples present significant concern for biogenic contamination. These analyses seek to determine if a micrometeoroid or orbital debris strike would result in loss of containment assurance and are summarized in the flowchart in Fig. 1. Methodology: The mission is considered in two MMOD phases: a pre-release phase where the EES is protected by a Micrometeoroid Protection System (MMPS) and a post-release phase called “free-flight” where the EES is exposed directly to the MMOD environment. These phases correspond to interplanetary cruise and imminent re-entry, respectively. To inform the MMPS design, a 30-shot high velocity impact testing (HVIT) series on candidate configurations at NASA White Sands Test Facility was completed in the summer of 2022. Sample post-shot images are shown in Fig 2 [1]. These data are used to baseline the MMPS design and to tune the hydrocode simulations. ALE3D, CTH, and SPHC are the hydrocodes that simulate physics of high-speed impacts [2]. Results generated with these populate a penetration depth versus energy space beyond the testable velocity regime of HVIT (~7 km/s). The penetration depth versus energy space data are used to define a critical projectile diameter function called a Ballistic Limit Equation (BLE), where the projectile “criticality” is determined by zone dependent failure criteria defined a-priori [3]. For example, the nose of the heatshield has a failure criterion of 50% TPS penetration, assigned because the landing loads are concentrated on that region and no substructure damage is permitted. The BLEs for each vehicle material zone are input into the BUMPER 3 code, along with the vehicle surface mesh and the corresponding space environment model, to calculate a probability of penetration or number of penetrations. The environment models, MEM3 for MM and ORDEM 3.2 for OD, simulate the meteoroid environment from 0.2 to 2 au based on the Grün flux equation, and the debris environment up to 40,000 km altitude from Earth surface, respectively [4,5]. Presentation Focus: The presentation or poster will present the results to-date focusing on the full risk analysis process flow seen in Fig. 1. Details on the derivation of the failure criteria will be discussed, along with HVIT results and how these influenced the MMPS configuration baseline decision. Further, results of hydrocode simulations will be presented and the tuning to HVIT outputs will be described. Finally, the strategies that direct the BLE formulation will be reviewed, specifically, for the EES elements that are most exposed to the MMOD environment.

mmod↗
NASA NTRS2009

Characteristics of Whipple Shield Performance in the Shatter Regime

Between the onset of projectile fragmentation and the assumption of rear wall failure due to an impulsive load, multi-wall ballistic limit equations are linearly interpolated to provide reasonable yet conservative predictions of perforation thresholds with conveniently simple mathematics. Although low velocity and hypervelocity regime predictions are based on analytical expressions, there is no such scientific foundation for predictions in the intermediate (or shatter) regime. As the debris flux in low earth orbit (LEO) becomes increasingly dominated by manmade pollution, the profile of micrometeoroid and orbital debris (MMOD) risk shifts continually towards lower velocities. For the International Space Station (ISS), encounter velocities below 7 km/s now constitute approximately 50% of the penetration risk. Considering that the transition velocity from shatter to hypervelocity impact regimes described by common ballistic limit equations (e.g. new non-optimum Whipple shield equation [1]) occurs at 7 km/s, 50% of station risk is now calculated based on failure limit equations with little analytical foundation. To investigate projectile and shield behavior for impact conditions leading to projectile fragmentation and melt, a series of hypervelocity impact tests have been performed on aluminum Whipple shields. In the experiments projectile diameter, bumper thickness, and shield spacing were kept constant, while rear wall thickness was adjusted to determine spallation and perforation limits at various impact velocities and angles. The results, shown in Figure 1 for normal and 45 impacts, demonstrated behavior that was not sufficiently described by the simplified linear interpolation of the NNO equation (also shown in Figure 1). Hopkins et al. [2] investigated the performance of a nominally-identical aluminum Whipple shield, identifying the effects of phase change in the shatter regime. The results (conceptually represented in Figure 2) were found to agree well with those obtained in this study at normal incidence, suggesting that shielding performance in the shatter regime could be well described by considering more complex phase conditions than currently implemented in most BLEs. Furthermore, evidence of these phase effects were found in the oblique test results, providing the basis for an empirical description of these effects that can be applied in MMOD risk assessment software. In this paper, results of the impact experiments are presented, and characteristics of target damage are evaluated. A comparison of intermediate velocity impact failure mechanisms in current BLEs are discussed and compared to the findings of the experimental study. Risk assessment calculations have been made on a simplified structure using currently implemented penetration equations and predicted limits from the experimental program, and the variation in perceived mission risk is discussed. It was found that ballistic limit curves that explicitly incorporated phase change effects within the intermediate regime lead to a decrease in predicted MMOD risk for ISS-representative orbits. When considered for all Whipple-based shielding configurations onboard the ISS, intermediate phase change effects could lead to significant variations in predicted mission risk.

Ryan, Shannon↗
NASA NTRS1997

Striations, Polish, and Related Features from Clasts in Impact-Ejecta Deposits and the "Tillite Problem"

Proximal ejecta deposits related to three large terrestrial impacts, the 14.8-Ma Ries impact structure in Germany (the Bunte Breccia), the 65-Ma Chicxulub impact structure in the Yucatan (the Albion and Pook's Hill Diamictites in Belize) and the mid-Tertiary Azuara impact structure in Spain (the Pelarda Fm.) occur in the form of widespread debris-flow deposits most likely originating from ballistic processes. These impact-related diamictites typically are poorly sorted, containing grain sizes from clay to large boulders and blocks, and commonly display evidence of mass flow, including preferred orientation of long axes of clasts, class imbrication, flow noses, plugs and pods of coarse debris, and internal shear planes. Clasts of various lithologies show faceting, various degrees of rounding, striations (including nailhead striae), crescentic chattermarks, mirror-like polish, percussion marks, pitting, and penetration features. Considering the impact history of the Earth, it is surprising that so few ballistic ejecta, deposits have been discovered, unless the preservation potential is extremely low, or such materials exist but have been overlooked or misidentified as other types of geologic deposits . Debris-flow diamictites of various kinds have been reported in the geologic record, but these are commonly attributed to glaciation based on the coarse and poorly sorted nature of the deposits and, in many cases, on the presence of clasts showing features considered diagnostic of glacial action, including striations of various kinds, polish, and pitting. These diamictites are the primary evidence for ancient ice ages. We present evidence of the surface features on clasts from known proximal ejecta debris-flow deposits and compare these features with those reported in diamictites. interpreted as ancient glacial deposits (tillites). Our purpose is to document the types of features seen on clasts in diamictites of ejecta origin in order to help in the interpretation of the origin of ancient diamictites. The recognition of characteristic features in clast populations in ancient diamictites may allow identification and discrimination of debris-flow deposits of various origins (e.g., impact glacial, tectonic) and may shed light on some climatic paradoxes, such as inferred Proterozoic glaciations at low paleolatitudes.

Rampino, M. R.↗
NASA NTRS2009

Performance of Whipple Shields at Impact Velocities above 9 km/s

Whipple shields were first proposed as a means of protecting spacecraft from the impact of micrometeoroids in 1947 [1] and are currently in use as micrometeoroid and orbital debris shields on modern spacecraft. In the intervening years, the function of the thin bumper used to shatter or melt threatening particles has been augmented and enhanced by the use of various types and configurations of intermediate layers of various materials. All shield designs serve to minimize the threat of a spall failure or perforation of the main wall of the spacecraft as a result of the impact of the fragments. With increasing use of Whipple shields, various ballistic limit equations (BLEs) for guiding the design and estimating the performance of shield systems have been developed. Perhaps the best known and most used are the "new" modified Cour-Palais (Christiansen) equations [2]. These equations address the three phases of impact: (1) ballistic (<3 km/s), where the projectile is moving too slowly to fragment and essentially penetrates as an intact projectile; (2) shatter (3 to 7 km/s), where the projectile fragments at impact and forms an expanding cloud of debris fragments; and (3) melt/vaporization (>7 km/s), where the projectile melts or vaporizes at impact. The performance of Whipple shields and the adequacy of the BLEs have been examined for the first two phases using the results of impact tests obtained from two-stage, light-gas gun test firings. Shield performance and the adequacy of the BLEs has not been evaluated in the melt/vaporization phase until now because of the limitations of launchers used to accelerate projectiles with controlled properties to velocities above 7.5 km/s. A three-stage, light-gas gun, developed at the University of Dayton Research Institute (UDRI) [3], is capable of launching small, aluminum spheres to velocities above 9 km/s. This launcher was used to evaluate the ballistic performance of two Whipple shield systems, various thermal protection system materials, and other spacecraft-related materials to the impact of 1.6-mm- to 2.6-mm-diameter, 2017-T4 aluminum spheres at impact velocities ranging from 8.91 km/s to 9.28 km/s. Test results, details of the shield systems, and nominal ballistic limits for the two Whipple shields are shown in Figures 1 and 2.

Christiansen, Eric L.↗
NASA NTRS1973

Impact resistance of fiber composite blades used in aircraft turbine engines

Resistance of advanced fiber reinforced epoxy matrix composite materials to ballistic impact was investigated as a function of impacting projectile characteristics, and composite material properties. Ballistic impact damage due to normal impacts, was classified as transverse (stress wave delamination and splitting), penetrative, or structural (gross failure). Steel projectiles were found to be gelatin ice projectiles in causing penetrative damage leading to reduced tensile strength. Gelatin and ice projectiles caused either transverse or structural damage, depending upon projectile mass and velocity. Improved composite transverse tensile strength, use of dispersed ply lay-ups, and inclusion of PRD-49-1 or S-glass fibers correlated with improved resistance of composite materials to transverse damage. In non-normal impacts against simulated blade shapes, the normal velocity component of the impact was used to correlate damage results with normal impact results. Stiffening the leading edge of simulated blade specimens led to reduced ballistic damage, while addition of a metallic leading edge provided nearly complete protection against 0.64 cm diameter steel, and 1.27 cm diameter ice and gelatin projectiles, and partial protection against 2.54 cm diameter projectiles of ice and gelatin.

Friedrich, L. A.↗
NASA NTRS1995

Penetration experiments in aluminum 1100 targets using soda-lime glass projectiles

The cratering and penetration behavior of annealed aluminum 1100 targets, with thickness varied from several centimeters to ultra-thin foils less than 1 micrometer thick, were experimentally investigated using 3.2 mm diameter spherical soda-lime glass projectiles at velocities from 1 to 7 km/s. The objective was to establish quantitative, dimensional relationships between initial impact conditions (impact velocity, projectile diameter, and target thickness) and the diameter of the resulting crater or penetration hole. Such dimensional relationships and calibration experiments are needed to extract the diameters and fluxes of hypervelocity particles from space-exposed surfaces and to predict the performance of certain collisional shields. The cratering behavior of aluminum 1100 is fairly well predicted. However, crater depth is modestly deeper for our silicate impactors than the canonical value based on aluminum projectiles and aluminum 6061-T6 targets. The ballistic-limit thickness was also different. These differences attest to the great sensitivity of detailed crater geometry and penetration behavior on the physical properties of both the target and impactor. Each penetration experiment was equipped with a witness plate to monitor the nature of the debris plume emanating from the rear of the target. This plume consists of both projectile fragments and target debris. Both penetration hole and witness-plate spray patterns systematically evolve in response to projectile diameter/target thickness. The relative dimensions of the projectile and target totally dominate the experimental products documented in this report; impact velocity is an important contributor as well to the evolution of penetration holes, but is of subordinate significance for the witness-plate spray patterns.

Horz, Friedrich↗