Momentum Enhancement in Hypervelocity Impacts: Parameters for Space Debris and Meteoroid Perturbations

Transcription

1 Momentum Enhancement in Hypervelocity Impacts: Parameters for Space Debris and Meteoroid Perturbations Abstract J.A.M. McDonnell Open University, Milton Keynes, Walton Hall MK7 6AA UK The impulse to space structures from meteoroids and debris is enhanced above the incident particle momentum by hypervelocity impact processes namely cratering or penetration. Although laboratory experiments reproduce only the lower range of desired calibration (up to some 9 kms -1 for mm particles) sensors flown near Comet Halley on the Giotto spacecraft (at 68 kms -1 ) provide data at velocities up to the fastest meteoroids in space. We review experimental data, and formulations thereof, introducing theoretical considerations where applicable. Special effects for thin target marginal perforation such as Solar Arrays apply but de-rating for very thin targets is derived, again based on space data from the Giotto mission. Introduction Interaction of meteoroids or space debris with a spacecraft necessarily involves velocities generating pressures in excess of material strengths. The regime, termed Hypervelocity Impact (HVI) attracted early attention from the aspect of spacecraft survival and reliability primarily regarding penetration (e.g. [1] ); significant experiments on momentum (e.g. [12] ) were also performed which now need review to apply to perturbations experienced on space platforms stabilised by pointing systems. Critical HVI damage has not been a significant driver for unmanned satellite design but, more recently, the impact scene has been identified as more critical because of three reasons: 1. the increased flux of space debris, now exceeding the background meteoroids at micron sized and at millimetre dimensions 2. the advent of permanently manned Space Stations, now making critical, what were previously acceptable failure risks 3. the increased area, and longer lifetime, of spacecraft leads not only to a higher accumulation of impacts at a particular size but also increased probability of encounter of a larger particle. The level of space debris flux is conveniently referred to the local meteoroid flux experienced; this is generally an unavoidable natural hazard and has been well determined [6] from many sources from micron to millimetre dimensions. It provides a reference flux at 1 Astronomical unit heliocentric distance, away from the Earth s gravitation, but can be transformed to particular near Earth situations. For a given area-time product, (A.t, m 2 s), in LEO Earth orbit, this flux distribution has been used to generate a useful engineering formula for the maximum mass M

2 Kg of meteoroid encountered and the penetrated thickness Fmax (mm) of 6064 T6 aluminium [11]: M (kg) = 10-3.(( At) ( At) ) (1) Fmax (mm) = 10-3.((1340 At) ( At)-0.620) (2) The velocity of meteoroids averages 21.4 kms -1 for this population but we take a value representative of the normal component of the assumed isotropic influx for penetration aspects; we can identify typical values for an area of 100m 2 over a period of 10 years. The product A.t = m 2 s and the maximum mass, from eq 1, is kg. This corresponds to a particle diameter of 0.94 mm and penetrated thickness of space grade aluminium (from Eq 2) of 5.78 mm. Given that the consequent damage from this particle is within the design limits of an element we can see, from the size distribution of the meteoroid distribution at this mass, that the frequency of smaller masses increases as (mass). In the range of m p above Kg the flux decreases as a = and for these masses, which will crater or partially penetrate the spacecraft, we can calculate the increasing number of smaller perturbations in the spacecraft due to the momentum imparted by the incident meteoroids or space debris. The flux of potentially perturbing 100 micron diameter particles, which can cause a crater of near 1 mm diameter, is 716 over 1 year. This review focuses on the impulse reaction to this cratering where the ejected mass well exceeds that of the incident particle but at lower velocities. Momentum is conserved in all processes, but since ejecta pattern is dependent on the impacting particle and target configuration, momentum enhancement cannot be given a fixed value. Masses of particles and ejecta for a typical scenario we consider are: Entity Mass Velocity Particle mass (m p ) Spacecraft mass (M) Ejected crater mass or spallation fragment mass (M ej ) Kg to10-6 Kg 10 3 Kg to10 5 Kg Kg to10-3 Kg Meteoroids: 21.4 kms -1 (14.3 kms -1 effective); Debris: 9.5kms -1. (V)=0 (c.f. impactors) v ej =1 ms -1 (spall) to over 5 kms -1 (liquid ejecta) Table 1 - Typical parameters considered for momentum exchange with a spacecraft; the incident particle has high energy and small momentum. On impact it is rarely absorbed entirely; contrarily, crater ejecta is generated causing enhanced reaction of the spacecraft.

3 The overall momentum enhancement is E = total target momentum/particle momentum (P target /P particle ) but from the physics of the process, and continuity relationships across the low and high velocity range, we may prefer to formulate the effect as: P target = P particle (1 + e(v)) where e(v) is the ratio of target eject to particle ejecta which kicks in as ejecta or fragments are released above a critical velocity on entering the HVI regime. This gives e = 0 and E = 1 at low velocity if the particle sticks but without rebound or fails to detach material. We examine theory and experimental measurements; both are needed for providing best estimates of the effect, which involves complex and varying processes occurring throughout the different stages of impact and generally occurs at velocities beyond laboratory calibration. Target Configurations For semi-infinite thick ductile targets, laboratory data is largely uncontroversial, although the velocity range in the laboratory only marginally extends to that of space debris and certainly not to meteoroids for particles of visible dimensions e.g. mm scale impactors and above. We review this data but first show the need to identify other impact configurations which lead to differing perturbations; these are of increased importance in large structures involving extensive areas of thin arrays (e.g. solar array panels). Looking at the thin target configuration, we see that momentum will not be absorbed completely and hence the reaction is not potentially so great as that of a thick target. A de-rating factor needs to be generated, corresponding to either 1) the reduced back-splashed ejecta or 2) forward ejected spall fragments. The de-rating or negative enhancement will be dependent on target thickness relative to the maximum target penetration limit Fmax. We review theoretical and experimental data on this also, but especially useful is that from momentum sensitive detectors on the Giotto spacecraft [10] where the velocity exceeds that of all debris and almost all meteoroids (68.4 kms -1 ). A special extension of this thin target situation we raise here, is the case where part of a thin target may be detached from the spacecraft (e.g. in an unsecured thermal blanket or the cover glass of a solar cell); this provides opportunity for greater momentum enhancement than the fluid flow cratering of ductile targets. The limiting case would be where the particle penetrates a thin layer covering the spacecraft and, in the intermediate region, dissipates its energy. If the enclosed region remains as such, then the net momentum will tend to that of the particle, without enhancement (the particle is absorbed). If, however, part of the layer is detached, its reaction during energy dissipation may provide significant enhancement of the spacecraft momentum. It is a piston engine effect, where the reactive pressure from heating behind the penetrated layer (from target evaporation) accelerates away the ejecta fragment; work is performed on both surfaces and we can estimate the momentum reaction from the energy input. The momentum impulse to the spacecraft is the maximum impulse which the energy of the particle

4 imparts to the fragment. Large, low velocity, fragments are shown (below) to offer more scope for enhancement than the hypervelocity ejecta from simple craters. If the energy of the small incoming particle, mass m, could (by a hypothetical process) be transferred wholly to a spacecraft of mass M leading to a reaction velocity V sc, we could establish an upper limit for any conceivable ejecta process, namely: ½ MV sc 2 < ½ m p v p 2 rearranging to find the spacecraft momentum MV sc : MV sc < m p v p (M/m p ) 1/2 the enhancement E relative to the incident momentum is simply (M/m p ) 1/2. If M is a tonne (a small spacecraft) and m p a microgramme where we could find (M/m p ) 1/2 = But we have no reference frame in space to work against, thus finding that we cannot convert the energy so efficiently. This is a hypothetical limit. If, by a clearly non-hypothetical situation, the damage leads to the detachment of a part of a shield, thermal blanket of mass M ej, the reaction of the spacecraft can be found by replacing M by M ej in equation 3 leading to an enhancement (M ej /m p ) 1/2 yielding 10 3 for a detached fragment of 1 gram or (10 3 ) 1/2 = 32 even for a milligram particle. This exceeds the ductile cratering estimates and may account for anomalous reactions in space; certainly the need to consider in design. Certainly, realistic and frequently encountered enhancements may be attained if we take a M ej to be a fragment typically detached from a solar array, a cover cell fragment: with area 5 mm square and thickness 30 microns the mass is M ej = 45 mg and some 600 craters were catalogued on the HST solar array. We find an enhancement of (45) 0.5 = 6.71 for a 1 mg incident particle mass. Higher energy particles could perforate a thin structure and create this effect on the reverse side. For ductile targets with little spallation but hydrodynamic flow, very low net momentum will be transferred if the ejecta cloud were to be comparable on both entrance and exit sides. The space calibrations provide evidence on this effect. Velocity dependence for thick ductile targets There is a fairly narrow range of velocities available in the laboratory for studying the velocity dependence of enhancement. Two main laboratory workhorses provide quantitative tools for study, namely the two stage light gas gun and the electrostatic microparticle accelerator. With the exception of elastic rebound at very low velocities, HVI enhancement commences at velocities where hydrodynamic cratering excavation is effective; for common engineering materials, this is about 1 kms. We shall call this the onset velocity V ons and the exponent of functional velocity dependence for the increase of ejecta enhancement relative to the particle g, i.e. of the form e = k V. Noting that the upper limit for the light gas gun is around 10 kms -1 we see that the dynamic velocity range is modest; the independent

5 determination of V ons and g is, therefore, restricted by the possible trade off between the parameters, although the value of e at the highest velocity may be well determined in the same data. The exponent g is, however, needed to extrapolate to higher meteoroid velocities. We have two additional approaches: theory and space measurement data. Theoretical considerations commence from the well observed functional dependence of cratering volumes, related to particle parameters, albeit few observations determine the velocity distributions needed of the ejecta. Regarding the total ejecta volume, most empirical formulae for HVI cratering are close to the relationship of a constant crater volume per particle energy; if the reaction momentum is considered to scale linearly as crater volume, namely as V p, the enhancement e will scale as V p with g = 1 and hence a form E = 1+ kv p. This scaling, at constant particle mass, provides a useful bound to speculation, but does rely on an assumed characteristic ejecta velocity regarding the momentum integral which is independent of velocity. Experimental Data and Measurements Most convincing and least subject to misinterpretation is provided by ballistic pendulum measurements, in a series performed under NASA contracts [12]. Reported there are the first, but perhaps still best, cratering measurements from light gas guns; momenta were measured e.g. for 3.2 mm aluminium spheres and nylon spheres impacting at up to 8.1 kms ; both thick targets and thin targets were studied and, especially, the threshold for spallation and ejecta cloud formation giving insight into the energy and momentum balances we now understand and exploit. In extensions of the ballistic approach [2] small flyer plates were placed in the path of ejecta clouds following the penetration by 3.17 mm spheres of thin (0.79mm) aluminium plates to determine the angular distribution of ejecta within the cloud. Nysmith and Denardo found V ons of 0.55 kms and a dependence of e a (V-V ons ) /V over a wide velocity range. Similar values were found for the onset [15] namely 0.65 kms ; we use the two values he measured of e =.36 at 1 kms, e =.72 at 2 kms to support the Denardo-Nysmith formulation. Microscale Measurements In accord with the onset of ejecta in ductile targets, the values for the onset velocity are reasonable but are in contrast to the higher values found in microscale momenta studies e.g. 2.0 kms [14] We cannot ascribe differences in momenta as due to size scaling because the cratering processes are well studied in both domains and lead to a very weak scaling of the crater depth at constant particle velocity, namely as (diameter). Rembor s microscale data supporting the Giotto momentum measurements, used a technique of piezo-electric ultrasonic transducers mounted to a plate; it was first used on captured V2 rockets, launched into space by the US. The measurement of the pulse voltage (amplitude) is related linearly to the

6 deformation of a diaphragm or a surface wave amplitude transmitted from the impulse to the detecting element. Because there is a linear relationship between to the injection of momentum surrounding an impact and the amplitude of the surface or bending wave generated, the system is momentum sensitive [9]. This technique has since been applied to numerous space detectors [8] and to [7] including position sensitive measurements on the Giotto dust shield. Rembor s observations of an apparently higher onset velocity may leads to a need for a higher coefficient to factor in a velocity dependence which he derives very ingeniously from cratering process considerations. He shows that e = C Vp where C is independent of velocity and finds, with this form, that the data yields a relationship compatible with best fit values in: E = (V-2.0). The data extend to some 7 kms only. Thereafter it decreases to the measurement noise level and, because of fluctuations from shot to shot of 3:1, a bias towards recording the higher results at that velocity always remains. Using a higher performance Van de Graaff 5 MV accelerator and a capacitor microphone at Los Alamos, data has been extended to some 20kms [17]. Although, quantitatively, not in conflict with trends of the velocity dependence from other considerations, it does not define the onset velocity. Other microscale data from Slattery and Roy [16] reviewed in the same publication, indicating an onset velocity of 5 kms, adding further doubt to the findings of Rembor regarding a piezo-electric sensing system being fully momentum sensitive at low velocities. There may be other propagation modes and shock waves which affect the mode of stimulation of the sensing element and hence distort the true velocity-momentum trend. Thin Target Momentum transfer For millimetre scale projectiles (causing centimetre scale craters) the thin targets of Denardo and Nysmith showed clearly the different regimes as penetration increased. Spallation was surprisingly high in their targets, indicating the choice of a very brittle material and onset effects particularly strong; for this targets (t/d = 0.315) they found the target momentum less than some 2 % of the peak enhanced momentum when t/d = at 5 kms. The 2% retained corresponds to a mass of 897 times the marginally penetrating mass and we can use this data to compare to formulations of de-rating effects for thin targets. The need for significant derating and momentum retention in very thin targets arose in the Giotto mission where the momentum sensors were on the 1 mm dust shield, part of the Whipple bumper protecting the spacecraft. Micron scale cometary particulates, even at 68.4 kms -1 did not penetrate and the thick ductile target relationship was applied to the calibration of dust grains but the size spectrum extended to a maximum mass of 1 gram. The in-situ dust mass distribution, measurements from the Giotto encounter with Comet Halley [13] were able to be compared to a variety of other techniques such as impact plasma generation, optical reflectance of the grains and the integrated deceleration of the spacecraft.

7 It was found, when extrapolating available penetration data from 1 to 16 kms -1, that the minimum penetrating mass m ) for 1mm Aluminium would be Kg at ( pen 68.4 kms -1 but needed to calibrate the sensors was the effect of momentum passing through the shield but still contributing to the spacecraft deceleration. It was proposed (Wallis 1986) that p p [ m] thick Ë m = Ì Í m pen Û Ü Ý where = pthick is the momentum induced on a thick target where m>>m pen At the velocity 68.4 kms -1 for penetrating particles, for the large particles intercepted (1 g) Perry investigates the effect of g in this de-rating. He minimises the error, between other data, on the inferred mass distribution and finds, for convergence with the total spacecraft deceleration, that a value of g = 0.4 gives best agreement. This is essentially a cross calibration with a ballistic technique. Application of the space results to the data ballistic pendulum data would indicate a retention of 6.5 percent of the maximum enhancement at 5 kms-1 compared to the 2% figure inferred from the data of Nysmith and Denardo. Differences are smaller than the substantial uncertainties involved and assumptions, but we cannot say that the data are in conflict. Perry finds that the momentum going through shield is: Relationships for Enhancement Î Ë mpen Û p = mvï1 - Ì Ü ÏÐ Í m Ý For ductile targets we accept the onset velocity of the truly ballistic experiments and the continued scaling with velocity of the form e a (V-V ons ) /V because of its comparability with HVI cratering onset. We see that at high velocities the formula converges towards a scaling V scaling commensurate with energy considerations and the findings of Rembor. Yet, in needing to extend the velocity range of the formula, we find a coefficient for the functionality from fitting the function to the highest velocity data reported at 25 kms [17, 16] yielding e = 3.44 and E = The formula is given by: 0.4 Þ ß ßà E= (V-0.55) /V Values of the formula are tabulated in table 2 for critical values where experimental data is available. We see the enhancement at Giotto s encounter speeds is in line with the value of E = 11 used for decoding of the scientific data but lower than that predicted from the more limited velocity range of Rembor.

8 Velocity E: Rembor E: Nysmith - kms -1 Denardo (fitted to 25kms -1 ) Applicability Space Debris Meteoroids MV accelerator data Giotto Table 2 - Momentum enhancement for the preferred relationship of Nysmith and Denardo, adjusted for later calibration and space data. For fragile targets where a mass is detached at low velocity we find enhancements of up to a factor of 10 above these enhancements but, because the situation is target configuration sensitive, a ready formula cannot be offered. For marginally thin targets we should refer to the data of Nysmith and Denardo who found the enhancement could cancel the impulse entirely and, by rear surface spall, make the impulse negative. For very thin targets, thickness f, compared to a maximum penetration Fmax we take experience from the Giotto data and suggest a modified form of equation 7, namely: E = (1 + (0.144 (V-0.55) /V)).(f/Fmax) ) References [1] Cour Palais, B.G., The Meteoroid Environment Model Near Earth to Lunar Surface 1969, NASA SP 8013, [2] Cunningham, J.H., Momentum Distribution in the Debris Cloud Produced by Hypervelocity Perforation of Thin Plates, Technical Report AFML-TR , [3] Denardo, B.P., Measurement of Momentum Transfer from Plastic Projectiles to massive Aluminium Targets at Speeds up to 25,600 Feet per Second, NASA-TN-D-1210, [4] Denardo, B.P. & Nysmith, C.R., Momentum Transfer and Cratering Phenomena Associated with the Impact of Aluminium Spheres Into Thick Aluminium Targets at Velocities to 24,000 Feet Per Second, AGARDograph 87, The Fluid Dynamic Aspects of Space Flight, Vol.1, pp , [5] Drolshagen, G., McDonnell, J.A.M., Stevenson, T.J., Aceti, R. and Gerlach, L., Postflight Measurements of Meteoroid/Debris Impact Features on

9 EURECA and the Hubble Solar Array, Advances in Space Research, Vol.16, No. 11, pp. (11)85-(11)89), [6] Grun, E., Fechtig, H., Giese, R. H., Zook, H. A., Collisional balance of the meteoritic complex, Icarus pp , [7] Leese, M.R., McDonnell, J.A.M., Burchell, M.J., Green, S.F. Jolly, H.S., Ratcliff, P.R. and Shaw, H.A. DEBIE A low Resource Dust Environment Monitor, Proceedings of the 1st Symposium on the Utilisation of ISS, ESA SP 385, pp , [8] McDonnell, J.A.M., Detection of Meteoritic Dust from a Sounding Rocket, Journal of Geophysical Research, Vol. 72, No. 23, p , [9] McDonnell, J.A.M., Calibration Studies on a Piezoelectric Sensing Diaphragm for the Detection of Micrometeorites in Space, Journal of Scientific Instruments (Journal of Physics E), Series 2, Vol.2, pp , [10] McDonnell, J.A.M., Alexander, W.M., Burton, W.M., Bussoletti, E., Clark, D.H., Evans, G.C. Evans, S.T., Firth, J.G., Grard, R.J.L., Grün, E., Hanner, M.S., Hughes, D.W. Igenbergs, E., Kuczera, H., Wallis, M.K., Lindblad, B.A., Littler, A.N., Massonne, L., Olearczyk, R.E., Pankiewicz, G.S.A., Mandeville, J.-C., Minafra, A., Schwehm, G.H., Stevenson, T.J., Sekanina, Z., Turner, R.F. and Zarnecki, J.C., Dust Density and Mass Distribution Near Comet Halley from Giotto Observations, Nature, Vol. 321, No. 6067, pp , [11] McDonnell, J. A. M., McBride, N., Green, S. F., Ratcliff, P. R., Gardner, D., Griffiths, A. D., Near Earth Environment, Interplanetary Dust, Eds E. Grün et al,springer, pp , [12] Nysmith, C.R. & Denardo, B.P., Experimental Investigation of the Momentum Transfer associated with Impact into thin Aluminium Targets, NASA-TN-D-5492, [13] Perry, C.H., In-situ Dust Mass Distribution Measurements from the Giotto encounter with Comet P/Halley, PhD Dissertation, University of Kent at Canterbury, UK, [14] Rembor, K.-M., An Application of the UKC Van-de-Graaff Accelerator: Momentum Exchange at Particle Impacts - a Calibration Study for the Giotto/DIDSY Momentum Sensors, Report on the research project in Physics, Submitted to Universitat Karlsruhe & University of Kent at Canterbury, UK, 1993.

10 [15] Rosen, F. D., Scully, C. N. and Wrinkle, W. W. North American Aviation Report SID , [16] Slattery, J. C. and Roy, N. L., Investigations of Hypervelocity Microparticle Impact Phenomena; NASA CR-66872, [17] Stradling, G.L, Idzadorek, G. C., Keaton, P. W. and Studebaker, J. K., Searching for the Momentum Enhancement in Hypervelocity Impacts, International Journal of Impact Engineering, Vol 10, pp , [18] Wallis, M.K., Planetary and Space Science, Vol.34, No.11, pp , 1986.