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Dear Grandpa,

When very high speed "missiles" penetrate targets, e.g. a "rail gun" cube of paper against a steel block, or even a meteor in space, does the very hard steel surface of the block give way simply due to the high degree of kinetic energy of the missile, or is there another set of "surface adhesion physics" that take over at high speeds which, in effect, softens the surface of the target?  If not, how can the softer paper cube penetrate the harder steel surface.

This question has haunted me for several years, and I'm hoping for a reply.

Thanks, Holland
 

 

Holland -

 

Running rocket sled tests for several years, certain properties of materials became clear, and in particular, a kind of "hardness."

There are hardness scales we use. On most of these scales, diamond is listed as the hardest naturally occurring substance. Our finger nail is used as one of the levels on some of these scales. These are about "static" hardness, and your question is really about more than that. A more complex term, the "Coefficient of Restitution" has to do with how fast something regains its shape after having it changed. It's the elasticity. There is another attribute which has to do with resistance to shape change. This can be viewed as hardness also, but this is "dynamic" hardness and is related to speed. In general, everything is harder the faster we try to change its shape.

Some things are soft at one speed and hard at a faster speed. In fact, the dynamic hardness of all things is dependent on how fast we try to change the shape. Dynamic hardness is actually the time-resistance to shape-change. Even glass is soft if moved slowly enough. Over many years, you could bend a pane of glass without breaking it.

You have played with silly putty. That stuff is quite hard if you throw it fast against a wall. It shatters like glass. Yet when moved slowly, it stretches like chewing gum. Slow, it is very soft; fast, it is quite hard. Silly putty is an extreme example, and it requires only a little speed for its hardness to be noticeably increased. Even stretching it fast, it will break instead of stretching. Try hitting it against a hard surface with a hammer. If you throw it against a wall, when it comes back, it will still have its shape. It did get a flat spot when it hit the wall, but like a golf ball, it regained its shape to spring back. Push it slowly against the wall, and it will mash down and keep its new shape.

If you make taffy, it is this way too. Pull it and it stretches - hit it with a table knife, and it breaks.

Now some interesting examples:

At 3000 feet per second, water is harder than most steel. Steel is still malleable at this speed, while water is more non-giving. A quarter-inch thick plate of steel will be dented by a drop of water if they collide at this speed. The water will change its shape also, but not as fast as the steel. The steel will be dented before the water drop collapses. A bird got in the way of one of our rocket sleds at about this speed and left a bird-shaped imprint in the steel. Since steel is an alloy, not all steel is the same - other steels could act differently, but this was ordinary cold-rolled steel making up the body of the sled.

Lead, at this speed in collision, is also harder than most steel. Using a high-powered rifle, fire a lead bullet into a steel plate, and the plate is likely to be dented. The lead will splatter too, but a little more slowly. It takes extremely sophisticated and fast photography to "see" this happen, but the end result tells the story. The lead will be nowhere to be found or it will be flat and thin on the steel, but the steel will have a dent. We all know that when no speed is involved, lead is much softer than steel.

By experimenting with materials, we can make them more and more penetrating for given other materials. To be sure, we need to know the properties of both materials, the "bullet" and the target.

The shape of the bullet also will determine what is being required about shape change. A point requires the target to change more slowly as the bullet penetrates. Pushing against a piece of wood with your finger, you may find it hard, yet with a needle, it may feel soft.

If you have ever belly-flopped on the water from a high-dive, you know that water gets "hard" with only a little speed. When an airplane hits water at a very high speed, it might just as well have hit concrete. The airplane will disintegrate before the water can change its shape very much. Entering slowly, the airplane would not change shape at all, and the water would change its shape instead. Slow, the water is soft.

Strictly speaking, "hardness" is not the correct term for this attribute of materials. Still, this is the term used by most people for this. A hardball (baseball) and a softball may have the same leather cover (and therefore the same hardness), but one gives more easily on being hit or caught. The hardness scales are about that actual surface, while here, we're talking about shape change and how fast it happens.

This was an interesting question, Holland.

 

 - Grandpa