An assessment of the NASA explosion fragmentation model to 1 mm characteristic sizes

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Abstract

The current NASA explosion model, as utilized by EVOLVE and LEGEND, is predicated upon observations of on-orbit fragmentation debris arising from the explosion of rocket bodies and payloads, and ground-based laboratory tests. This model results in a good comparison with the environment observed and cataloged by the US Space Command's Space Surveillance Network (SSN), assumed to be complete to a limiting size on the order of 10 cm. However, the hazard posed by debris in the size range from 1 mm to 10 cm is paramount in terms of personnel and spacecraft protection; thus, there is a need for a fragmentation model validated down to characteristic sizes of 1 mm. This paper summarizes current NASA efforts to validate the explosion model in this size range by utilizing both on-orbit data (collected by the SSN, Haystack, and Haystack Auxiliary (HAX) radars) and ground-test data, and presents the mathematical formalisms describing the model as a function of mass and size. A comparison of the explosion model to individual explosive fragmentations occurring in the 1990s and observed by the Haystack and HAX radars was made. The consequences for the future debris environment are discussed.

Introduction

A fundamental component of any orbital debris environment evolution model is the satellite breakup model. This component model is itself composed of sub-component modules which, in the NASA codes EVOLVE and LEGEND, comprise a model of the ballistic properties of debris fragments, and a model describing the change in velocity of debris fragments (the “delta-v”). This last model may also describe the directionality of debris in a fragmentation event. These models must be applicable to explosions, low-speed collisions, and high-speed (hypervelocity) collisions for both rocket bodies and spacecraft.

Historically, the breakup model has been predicated upon observations of the space environment by ground-based sensors or systems, laboratory experiments and, to a limited extent, the examination and analysis of surfaces returned from space. These approaches tended to produce results which were in good agreement with the tracked and cataloged on-orbit population (generally assumed to be approximately 10 cm in characteristic size and larger in low Earth orbit), was “anchored” in the small debris sizes by the in-situ results (generally less than 300 μm), and could display considerable variability between these sizes, if indeed considered at all. In an effort to better understand the small particle environment down to 1 mm characteristic sizes, NASA has sponsored this effort to examine available on-orbit and ground-based laboratory data in order to characterize the number/size/mass distribution, the area-to-mass ratio (A/m) distribution function, and the separation velocity (“delta-v”) and directionality distributions. This effort, begun in Fiscal Year 2002, has yielded several results of interest to the modeling and environment characterization communities.

This paper is a progress report on that effort. The objective of this analysis shall concentrate on those components of the analysis which have been completed: the number/size distribution function for explosions and the area-to-mass ratio distribution function for explosions and collisions. The delta-v and directionality models shall be discussed in future papers.

Section snippets

Data sources

Primary sources of data utilized in this study are the data products of the US Space Command's Space Surveillance Network (SSN), the NASA Haystack and Haystack Auxiliary (HAX) radar observation campaigns, and the Satellite Orbital Debris Characterization Impact Test (SOCIT), a ground-based hypervelocity impact test against a realistic satellite target. SSN products include both the Two-Line Element (TLE) set data for debris objects on-orbit as well as the Radar Cross-Section (RCS) catalogs. The

The number/size distribution

The CBERS-1/SACI-1 rocket booster (Long March 4B) debris cloud was examined in order to ascertain the best fit functional form appropriate to the cloud. The Tsyklon rocket booster debris cloud, though more difficult to discern in the data, was used as a check to the method and function form derived from the Long March cloud.

Two methods were utilized to perform the non-linear least squares fitting of the trial function defined byN(Lc)=SF·[F1(Lc)+F2(Lc)],whereF1(Lc)=a5·Lca6,andF2(Lc)=a1·Lca2·exp−a

The area-to-mass ratio distribution

The area-to-mass (A/m) ratio distribution function is derived from both SSN and SOCIT test data. In the case of the SSN data, TLEs for every member of a given debris cloud are used to estimate the appropriate A/m (assuming a constant drag coefficient of 2.2) ensemble via Brent's Method of inverse parabolic interpolation (Press et al., 1987, pp. 283–286). For the SOCIT data set, the point estimate 〈A〉/m is used to approximate the A/m ratio for each debris fragment. The average cross-sectional

Number/size distribution function

As may be seen in Fig. 1, this function fits the entire Long March 4B rocket body fragmentation data spectrum well with the exception of large (d>∼2 m) objects. The “eyeball” fit coefficients, when utilized, tended to fit these objects better, but fit the size range 0.1–0.5 m less well. Therefore, the recommended ensemble of fit coefficients is {160,−0.43,2.9,0.75,0.001,−3.2}. In order to scale this somewhat more prolific fragmentation to a generic or nominal explosion (approximately 240 pieces

Conclusions

This paper has described NASA efforts to validate the breakup model down to 1 mm characteristic sizes. In particular, two components of the breakup model have been described: the number/size distribution function and the A/m distribution function. In the case of the number/size distribution function, Haystack and HAX radar data have been utilized for the first time to image the small particle component of an on-orbit breakup event. While limited in scope, this offers tantalizing prospects for

Acknowledgements

The authors wish to acknowledge the significant contributions to the present work by Dr. Doyle Hall (Hernandez Engineering). Dr. Hall performed the original analysis of the A/m distribution data (Liou et al., 2001), which was confirmed as being representative of the A/m for small (<0.1 m) particles by the effort reported upon in this work.

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