I was able to successfully calculate the energy of an object hitting the ground from an airdrop of 40,000’, but the physics of how to calculate the friction of an object travelling through concrete or sand elude me.
For the purposes of this question, let us assume that the object in question is a tungsten cylinder with a cone on the “fore” end, 16" in diameter, and 9 feet in length. If necessary, let us also assume that this object weighs 500lbs.
The initial research says it will hit the ground (in a vacuum) travelling 1600fps. However, once it hits the ground, it will rapidly stop. If we were to assume that it could continue to travel at 1600fps, how would we calculate its friction? How long would it take before we reached the melting point of tungsten (eg 6500F)?
Are there other materials (uranium?) which may have higher melting points, such as alloys which might allow deeper penetration?
As much as I’d like to think the RNEP would actually be a feasible concept, the notion of it being necessary to penetrate 50 to 100+ feet of sand or concrete make it seem most impossible.
50-100 ft of concrete is a cinch for high speed penetrators. the 1600 fps figure is a little low for sometign with that kind of capability. But penetrators of the same weight class have been around for a while that can go through that much concrete. Think impact speeds of more like 3-4000 fps.
I can’t cite anything that you can find online. I speak from familiarity with plenty of Army and Air Force tech reports by my defense researcer colleagues.
And the methods for calculating what you want are far too complex for “back of the envelope” figuring. Think CFD-like simulations, with codes that require mucho CPU power. There aren’t a lot of simplifying assumptions that will do anything useful for you.
4,000 feet per second would liquefy tungsten. You’re going to have to come up with something better than that. I was personally thinking that such a device would not have to be simply gravity propelled, but rocket aided.
Kinetic energy and the tensile strength of reinforced concrete are declassified. I have held a TS, and nobody’s ever mentioned a munition that is capable of penetrating 100 feet of concrete. Much less it being a cinch.
Now, if you read the article, penetrating 100 feet of concrete explosively would be simple. So you’d have a sort of double-munition. A conventional shaped charge that was designed to create a 100-200 feet deep channel and a following charge designed to create shockwaves and destroy the facility. That’s feasible, in my book. But something travelling through 100 feet of concrete or sand would incur so much friction – heat – that no material I’ve ever seen or heard of could sustain it. Like I said, what are the formulas?
When we talk about reinforced concrete, the Army usually has 2 kinds, 3,000psi tensile strength and 5,000psi.
I’m approaching this with an open mind, but an engineer’s open mind.
Well, 4000 fps certainly does not liquefy tungsten. And that’s mainy because it’s not moving any slower. Remember that, to a certain point, going faster is easier than going slower. If you go fast enough, the solid material fluidizes, and flows around the nose of the penetrator. The flow separation induced by the fluid’s inability to hug the nose means that a large portion of the penetrator is never actually in contact with the concrete. Usually just the very extreme tip and the back half of the body. Penetrators recovered after plowing through 50 ft of concrete generally have no visible gouges over most of the front half of their length. And even the parts that are gouged look pretty good (all things considered). All post-test high speed penetrators I’ve seen look like they could easily be reused.
There’s a range of speeds for any given penetrator construction where it can go deeper than it could above or below that range. Take a 500-lb tungsten ogive-nosed penetrator, and it may have an optimum around 3500 fps. Hit the ground at 800 fps, and you get a tungsten pancake with a shallow crater. Hit at 10000 fps, and you get a cloud of tungsten and concrete vapor, and an expansion cavity just a few feet into the concrete. The bright side is you don’t have to try to retrieve the penetrator.
As far as the heat generated… Remember how quickly this deceleration takes place. Milliseconds. That’s not enough time for the material to absorb the heat of friction and ablate. The top couple millimeters may be removed from melting/ablation/abrasion. But the heat can’t soak in fast enough to affect the other 99.9% of the metal. Yet another reason why faster is better. Of course, go too fast and you’re left with the problem I mentioned above. But in that case the disintegration is initially caused by mechanical failure of the material—the compression stress of the initial impact exceeds the material’s limits—then all hell breaks loose.
I don’t know how things change when the thing is rocket assisted. I’m not even sure it would help penetration depth.
The reports I mentioned aren’t classified (most of them). But their only repository is the part of the DoD tech library available to Government and Contractors. Not everything unclassified is publicly available.