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Detailed inspections of LDEF surfaces, performed by members of the LDEF M&D SIG, have resulted in an excellent benchmark data set of craters resulting from hypervelocity impacts of both natural meteoroids and man-made orbiting debris iparticles. This data set has been used to check and update mathematical M&D environment models. The comparisons of the LDEF data with model predictions presented here were made by POD Associates, Inc. under contract to NASA (NAS9-17900, SC-02N0165768, Project No. 960-12-171).
The LDEF observations revealed data on crater numbers (and fluxes) as a function of crater size, surface orientations relative to the spacecraft orbiting velocity vector, and surface materials. LDEF exposed most of the materials that are of interest to spacecraft designers - materials ranging from 6061-T6 aluminum, other metals, polymers, composites, ceramics and glasses. Many of the exposed surfaces also had various coatings and paints applied. The cratering comparisons presented here, however, are limited to aluminum surfaces.
The individual craters observed on LDEF were carefully documented with regard to their exact position LDEF; each crater was also documented with regard to size, lip dimensions, and any associated cracking or delamination features. These data were reduced to impact fluxes (impacts per unit area) versus crater diameter for various surface orientations. These measured fluxes were then compared with model flux predictions.
For meteoroids, the Cour-Palais et al. model ( Ref. 1) was used with the Kessler-Erickson velocity distribution as described by Zook (Ref. 2), while for orbital debris, the Kessler model (Ref. 3) was used. Both the Cour-Palais and Kessler model's predict impact fluxes as a function of particle diameters. The following equation was used to relate particle diameters to crater diameters for comparison with the LDEF data:
where Dc is the crater diameter, Dp is the particle diameter, dp and dt are the particle and target densities, V is the impact velocity normal to the surface, and the constant is determined by laboratory impact experiments (Ref. 4 and 5).
POD Associates developed a PC-based computer code SPENV (SPace ENVironment) which incorporates these models to predict the cratering on LDEF (Ref. 6). The comparisons of the cratering predictions for different locations on LDEF relative to the ram direction (velocity vector) with the observed craters is presented in the following plot. Other plots were generated which include comparisons for every 30 degrees on the LDEF structure.
A comparison of the number of craters with diameters equal to or greater than 50 µm, 100 µm, 250 µm, and 500 µm observed on LDEF as a function on the degrees from the ram direction with the numbers of craters the models predict were prepared. The following figure presents the 50 µm results:
In general, the model crater predictions agree with the LDEF crater observations within a factor of 2 to 3 for surfaces in the ram direction. The agreement for the trailing surfaces is worse by a factor of 4 or more. Kessler's debris model overpredicts the number of small craters (~0.005 cm diameter), while the Cour-Palais meteoroid model underpredicts the craters in this size range.
The comparisons presented herein demonstrate the relative applicability of the environment models for first-order engineering design purposes. They also illustrate the need for improvements in the models to predict the smaller craters - craters that are of concern in determining the expected spacecraft degradation.
In particular, the models fail to predict the fact that debris exist in elliptical orbits. The models also fail to predict the short period (days) dynamics in the impact fluxes of small particles that were observed by the active M&D experiment that flew on LDEF. The data from this experiment, the Interplanetary Dust Experiment, in presented in the following chart. As can be noted, the impact fluxes varied by orders of magnitude from day to day and in various positions along the LDEF orbit.
It must be remembered that the man-made debris environment is also dynamic over long periods of time. Debris is generated by every space mission, thus the debris population is a function of the frequency of spacecraft traffic.
References
(1) Cour-Palais, B. G. et al. (1969) Meteoroid Environment Model - 1969 (Near Earth to Lunar Surface), NASA SP-8013.
(2) Zook, H. A. (1990) Meteoroid Directionality on LDEF and Asteroid Versus Cometary Surfaces (abstract). In Lunar and Planet. Sci. Conf. XXII, Lunar and Planetary Institute, Houston, TX, pp. 1385-1386.
(3) Kessler, D. J., Reynolds, R. C., and Anz-Meador, P.D. (1988) Orbital Debris Environment for Spacecraft Designed to Operate in Low Earth Orbit, NASA TM-100471.
(4) Watts, A. J., Atkinson, D.R., and Rieco, S.F. (1992) LDEF Penetration Assessment: Final Report Prepared for Nichols Research Corporation, Dayton, OH.
(5) McDonnell, J. A. M. et al. (1984) An Empirical Penetration Equation for Thin Metallic Films Used in Capture Cell Techniques. Nature, 309, pp. 237-240. Updates with K. Sullivan, private communication, 1991.
(6) Atkinson, D., Watts, A., and Crowell, L. (1991) Final Report: Spacecraft Microparticle Impact Flux Definition. Prepared for; LLNL, Univ. of Calif.
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