Penetration dynamics

Vehicles that use their kinetic energy of arrival at a planetary surface to emplace a payload at depth are called penetrators (sometimes called kinetic-energy penetrators or KEPs). In contrast to other landers, the kinetic energy is intended to be dissipated mostly in the surface material rather than the structure of the landing vehicle. While planetary landers reach the surface at speeds of the order of 1-10ms~1 penetrators arrive at speeds ranging from 60-300ms~x, depending on factors such as the desired depth, the mass and geometry of the penetrator, the expected surface mechanical properties, the shock resistance of internal components, and constraints imposed by the entry and descent from orbit or interplanetary trajectory. A number of concepts for hypervelocity penetrators, arriving at speeds in excess of 1kms~1, have been studied but have not yet flown.

At the time of writing, the only examples launched so far in planetary exploration are the Mars 96 penetrators and the Deep Space 2 Mars Microprobes. Details of these and other projects are given in Chapter 19. Here we discuss briefly the impact and penetration dynamics of such vehicles, which is a key aspect of their design. Accelerometry measurements of the penetration event can also be of scientific interest, in that they probe the mechanical properties of the sub-surface material.

The field of impact penetration testing and modelling was reviewed briefly by Lorenz and Ball (2001). The relevant literature is distributed across a wide range of fields including planetary science, soil mechanics, impact engineering, military and aerospace sources. In the development of planetary penetrators, both modelling and testing play essential roles. Modelling can be used at an early stage to evaluate the performance of candidate configurations, and to access regimes that may be prohibitively expensive to reproduce many times in the laboratory, if it can be done at all. Much time can be saved by modelling, however while it is easy to obtain output, much attention needs to be paid to how the target properties are modelled. Moreover, planetary surface/sub-surface mechanical properties are both subject to uncertainty as well as small-scale variations, so a wide range of cases has to be modelled. For example, the surface material may be cohesive (either hard or soft), granular (e.g. sand or reoglith), icy or even a mixture of these.

Models of penetration may be divided into several categories, and can be applied both to predictions of a given penetrator design's behaviour in a specified target, and to constrain target properties from actual penetration measurements. The first category of model is purely empirical, namely fits of penetration depth against projectile and target properties. The work of Young (1969, 1997) is widely cited, although it does not build up from the underlying physical processes and lacks dimensional consistency, and so is perhaps more distracting than useful for interpreting measurements. It can be usefully applied to initial calculations of penetration depth, however.

The second type of model is purely physical - by making an idealised model of the forces on a penetrator, the dynamic behaviour can be predicted. This type of model is the oldest for which good records exist; the Robins-Euler, Poncelet and Resal equations dating from the 18th and 19th centuries are examples of these, with deceleration being related to a constant term, or a linear combination of a constant term and velocity raised to the first or second power. More recent models often use a 'cavity expansion' technique to model the forces (e.g. Yew and Stirbis, 1978; Forrestal and Luk, 1992).

Beyond the simple algebraeic/analytic models of penetration, various levels of numerical sophistication can be applied to penetration models - at one end of the spectrum the SAMPLL code, developed by Young to apply his empirical penetration equations stepwise to layers, is a trivial example. At the other end of the complexity spectrum are full 2- and 3-dimensional finite-element models and smooth particle hydrocodes. Many examples exist (e.g. Autodyn) although are often restricted in access.

The penetration process can be divided conceptually into three phases: initial impact, 'free flight' and the terminal phase. The initial impact may be complicated by the partial immersion of the projectile tip in the target as well as ejection of material from the target to form a crater. The second phase (which may in fact be vanishingly short in duration) is a more or less steady state (near-constant deceleration), although when shaft friction is of interest then the phase may be subdivided according to whether or not the shaft has completely penetrated. Finally, in the third phase the projectile comes to a halt. In some cases this may be indistinguishable from the free-flight phase, but in others elastic phenomena in the target lead to a final peak in the deceleration history as the target 'grabs' the projectile.

Penetration dynamics can be further complicated if the penetrator is of the forebody/aftbody design (as opposed to bullet-shaped), in which case the interaction of both parts with the ground, and indeed with each other, must be studied. An important constraint on the design is to achieve clean and reliable separation of the two parts and ensure that they do not subsequently hit each other as the forebody comes to a halt. The aftbody must also be made to stay close to the surface, to ensure communications and proper deployment of surface components such as cameras, meteorological sensors and solar cells. To achieve clean separation it is necessary for the mass/area ratio of the forebody to be at least a factor of several (~4) higher than that of the aftbody.

There is no substitute for sooner or later embarking upon a series of impact penetration tests. These may be performed on a range of development models from simple 'boilerplate' structural models to instrumented prototypes and engineering models. Acceleration techniques include dropping under Earth gravity (whether by hand, drop rig, helicopter or aircraft), conventional 'powder' guns and airguns. Gas guns are usually too energetic for this field, although they are widely used to study hypervelocity impacts. A novel technique was used for acceleration of the Mars 96 penetrators, where a sideways velocity component due to strong Martian winds had to be considered. A penetrator was suspended and dropped from a parasail pulled by a car. The Mars 96 programme also used elastic 'bungee' cord acceleration to afford higher impact speeds than could be achieved from a simple drop tower. The impact testing phase is usually performed as a moving test article decelerates in a target; however, 'reverse' techniques are also used. For example, a target sample can be accelerated and impacted onto a stationary penetrator, or shock tests can be performed with an airgun/piston system, which applies a well-characterised acceleration pulse to an initially stationary test article.

One aspect of testing that is important for the design of a penetrator is the robustness to internal shear forces on components, and non-zero angle of impact and/or angle of attack. While many internal components may be highly resistant to shock, this is usually only for acceleration along a particular axis. Solutions to improve shock resistance, as part of careful structural design, include 'potting' materials that encase components in a block of material or glass microspheres. Susceptibility to non-zero angle of attack may be tested using spinning guns, such as that used for the Lunar-A project (Shiraishi et al., 2000).

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