Materials science

[Libertarian666]

I have an idea for an invention but I don't know enough about materials science to tell if it makes sense. Maybe someone here can help.

Basically, the question is: what would an object massing several hundred kilograms have to be made out of for it to withstand a hit by a 1-gram solid metallic ball traveling at 4 km/sec without severe damage to the object?

My initial calculations suggest that this would produce an energy pulse in the terawatt range, which would seem to suggest vaporizing a fair quantity of almost any material, but as I said, this isn't one of my areas of expertise.

[Mark Leavy]

Great question.

I'll try to help you out some more if you can provide more information.

The "damage" aspect is crucial.

A tank of water (or better, ballistic gel) immediately answers your question - but I don't think that is what you are looking for.

[Mark Leavy]

What you are really talking about is absorbing 8000 joules of energy via a projectile impact.
[Correction from Desert - I forgot the 0.5 multiplier...]

That is just slightly less than a 50 caliber BMG round from a sniper rifle.  They use these to disable truck engines from a mile away...

The only way to handle that much energy is to swallow it (i.e. ballistic gel) or to let it pass through you (cardboard) or to reflect it (I don't know what you would use. Neither marble or Tungsten would be enough )

Realistically, your only option is to absorb it.

It looks like 32" of Ballistic Gel is not enough.
https://www.youtube.com/watch?v=5J9hCDr21mo

Can you put 3 to 4 feet of sand as the outside layer of your object?  If my life depended on it, I wouldn't trust anything less.

[Tyler]

It depends -- how badass are your Jules?

[Pointedstick]

There are all kinds of things that can easily absorb an 8,000 joule impact. Enough high-grade steel alone could do it, but various NATO militaries armor their tanks with something called Chobham armor that withstands anti-tank rounds with an impact energy of considerably higher power, whose composition is secret but that is widely believed to be made out of a composite of metal, ceramic, and polymer.

Convert joules to foot-pounds and you have the compressive strength PSI rating (5,900 PSI) to withstand this impact for something with a one square inch cross-section. Such compressive strength ratings are trivial to achieve with a variety of materials, but the rub is that such a small projectile as a 1-gram sphere acts as a multiplier to the strength value needed since it would undoubtedly be smaller than one square inch. The smaller the cross-section of the projectile, the higher the strength of the material needed to absorb the impact.

If the metal chosen for the projectile is lithium (the lightest metal), then a 1 gram ball would occupy 1.87 cubic centimeters, which can fit into a 1.52 cm diameter sphere, which has a cross-section at its widest part of 1.81 square centimeters which is 0.28 square inches, which means you would multiply a PSI value by 3.57, which means that the 1-gram lithium ball traveling at 4km/sec could be absorbed by a material with a compressive strength value of 21,000 PSI, which is not ridiculous, as normal steel can have a compressive strength rating of 43,000 PSI.

If the metal is iron, then the material needs to have a compressive strength of 126,609 PSI. I have no idea what Chobham can absorb but a variety of ceramics have extremely high compressive strength rating sufficient to absorb this, such as lab-grown sapphire, with a compressive strength of 350,000 PSI. Other manufactured ceramics can have PSI ratings up to 500,000 or higher.

Tungsten would probably be the best, and re

Finally, keep in mind that a 1-gram pellet would have a limited accurate range because it would be strongly affected by the wind.

Finally times two, all my math could be completely wrong. At school I was a C student in the sciences and virtually everything I know on the subjects now is inexpertly self-taught.

[Libertarian666]

Thanks for the replies so far!

The ball would be made out of something hard and dense. Tungsten would probably be the best but might not be cost-effective, as we would need quite a few of the balls, probably on the order of several million per "use".

Wind would not be a problem, as this impact would occur in space.

Anyone want to guess what the application is at this point? 

[Libertarian666]

Thanks for the replies so far!

The ball would be made out of something hard and dense. Tungsten would probably be the best but might not be cost-effective, as we would need quite a few of the balls, probably on the order of several million per "use".

Wind would not be a problem, as this impact would occur in space.

Anyone want to guess what the application is at this point? 

Defending the world against an alien horde?

Not quite, but sort of on the right track...

[Libertarian666]

Ok, here's another hint. How could you improve the gun described at https://en.wikipedia.org/wiki/Paris_Gun with modern materials, to provide a higher maximum altitude and larger payload?

[Tyler]

Anyone want to guess what the application is at this point? 

Asteroid deflection?

[dualstow]

Satellite shield?

[l82start]

it both shoots and needs defense against fast moving steel/tungsten balls?

some kind of post apocalyptic Dystopian  death game machine?

[Pointedstick]

I'm guessing orbital space debris vaporizer.

[Libertarian666]

Closer but still not right.

Next clue:

Imagine dozens or hundreds of large guns around every major city in the USA, capable of shooting dozens or hundreds of shells containing millions of BB-sized tungsten balls to altitudes of 100 miles or so in a few minutes. When the shells get to their designated altitude, which takes several minutes for each shell, they open up, spewing the balls in all directions. The balls are dispersed to an average density of about 250 thousand per cubic kilometer. Obviously they start falling as soon as their upward momentum is exhausted, but they have a fairly long hang time before they re-enter the atmosphere and slow down.

What potential threat would be defanged by such a mechanism?

[Pointedstick]

Ballistic missiles?

[Libertarian666]

Ballistic missiles?

Yep. Is there any reason it wouldn't work?

[l82start]

Ballistic missiles?

Yep. Is there any reason it wouldn't work?

https://en.wikipedia.org/wiki/Celebratory_gunfire  possibly this...
not so much that it wouldn't kill missiles but what happens to the people - property under the falling (giant shotgun) blast?

[Libertarian666]

Ballistic missiles?

Yep. Is there any reason it wouldn't work?

https://en.wikipedia.org/wiki/Celebratory_gunfire  possibly this...
not so much that it wouldn't kill missiles but what happens to the people property under the falling (giant shotgun) blast?

Small enough balls won't have very high terminal velocities.
Or they could be made out of something that would burn up or otherwise disintegrate on re-entry.
Also, the dispersal would be very thin, so no one piece of property would get more than a few balls at most.

But since people would probably want to take cover to protect against a possible high-altitude explosion anyway, I'm not sure that would be a big problem...

[Mountaineer]

Have you calculated reentry velocity for a tungsten ball of that size?  A low drag, high density projectile does not sound like something I would desire to hit my bald head.  But I get it now, you are developing an umbrella that will resist the falling balls.  Eliminate one problem, create another, develop protection product - similar to umbrella insurance policies. 

... M

[dualstow]

I thought we were trying to stop missles with a



but your idea is very intriguing!

[Pointedstick]

Basically you're envisioning an anti-missile flak gun. These were dominant against aircraft until the age of rocketry, and for good reason: guided missiles proved superior in nearly every way except for cost. Nowadays the only direct-fire anti-missile weapons are automated minigun turret type things (CIWS) that protect military ships from anti-shipping missiles, but these systems have a very short range--in the order of just a few miles--not at all suitable for protection from a ballistic missile, and are used because of their lower cost, higher versatility (can be fired at small incoming vessels and aircraft too), and lower first-shot firing time compared to a launched missile.

The way I see it, your idea has the following potential advantages over the status quo of anti-missile missiles launched from ships, aircraft, and land-based silos:
- Lower per-interception cost
- Unguided projectiles are unjammable
- Flak is more difficult for a smart missile to evade than a single large guided projectile

It also has the following drawbacks:
- Untested and unproven; doesn't exist yet
- Intercepts the missile much closer to the target city than anti-missile missiles can
- The longer the distance to the incoming missile, the more difficult it would be to actually hit it with an unguided projectile; may actually be close to impossible
- Anti-aircraft gunnery is a lost art in the age of missile weapons; reinventing the wheel is inevitable to a certain extent
- Fixed ground installations more vulnerable to sabotage or destruction than ship- and air-based launching platforms

[Libertarian666]

Basically you're envisioning an anti-missile flak gun. These were dominant against aircraft until the age of rocketry, and for good reason: guided missiles proved superior in nearly every way except for cost. Nowadays the only direct-fire anti-missile weapons are automated minigun turret type things (CIWS) that protect military ships from anti-shipping missiles, but these systems have a very short range--in the order of just a few miles--not at all suitable for protection from a ballistic missile, and are used because of their lower cost, higher versatility (can be fired at small incoming vessels and aircraft too), and lower first-shot firing time compared to a launched missile.

The way I see it, your idea has the following potential advantages over the status quo of anti-missile missiles launched from ships, aircraft, and land-based silos:
- Lower per-interception cost
- Unguided projectiles are unjammable
- Flak is more difficult for a smart missile to evade than a single large guided projectile

It also has the following drawbacks:
- Untested and unproven; doesn't exist yet
- Intercepts the missile much closer to the target city than anti-missile missiles can
- The longer the distance to the incoming missile, the more difficult it would be to actually hit it with an unguided projectile; may actually be close to impossible
- Anti-aircraft gunnery is a lost art in the age of missile weapons; reinventing the wheel is inevitable to a certain extent
- Fixed ground installations more vulnerable to sabotage or destruction than ship- and air-based launching platforms

Fairly good analysis except that you are missing one vital point: my guns would not be aimed at missiles. What they would do is to put up a fountain of particles that the missiles would have to cross on their way to the target area. Let's call the particles "BBs" for short.

Assume the following:

Payload of each shell: 250 kg, or 250,000 BBs.
Cross section of the missile: 1 m^2.
Speed of the missile: 4 km/sec.
Height of curtain: 50 km, starting at 75 km and going to 125.
Thickness of curtain: 4 km.
Width of curtain: 100 km, probably semicircular, as we don't expect missiles to come from the south, but this is obviously adjustable.
Number of cubic km to be covered: 50*4*100, or 20,000, per city.
Firing rate of gun: 1/sec.
Number of guns: about 1000 per city.

Obviously the BBs will follow a trajectory rather than hanging in one place. If they have a vertical velocity of 100 m/sec when they are released, it will take roughly 10 seconds for gravity to slow that velocity to 0, then another 10 seconds for the velocity to get to -100 m/sec. During the ascent, they will cover 500 m, and the same for the descent, so they will be in the same vertical 500 m section for about 20 seconds, which should be plenty of time for the gun(s) covering that vertical section of the fountain to provide the next batch.

So let's suppose that we can maintain an average density of 1 million BBs per cubic kilometer. We can calculate the volume of the space that the missile will pass through in each second as 1 m^2 * 4 km/sec, or 4000 m^3. There are 10^9 cubic meters in a cubic kilometer, which means that the trajectory of the missile occupies 1/250,000 of one cubic kilometer. That amount of space contains an average of 4 BBs.

As far as I can tell, no reasonably conceivable countermeasures can protect the missile from BB strikes that use its own velocity to provide the kinetic energy that destroy its functionality.

[Pointedstick]

Again, you're essentially describing an updated version of an anti-aircraft flak gun. These clearly worked; they were mature technology at the point where they were replaced by missiles because of their greater range and power.

1,000 guns firing one round per second for only one second means a total of 1,000 rounds fired per interception. These rounds are fairly sophisticated; they're flak canisters filled with super-dense projectiles that are fired into the stratosphere. $2,000 per fired round is probably a huge understatement considering that a conventional dumb artillery round that only goes a dozen or two miles can cost $1,500 or more, but it seems like a good starting point. $2,000 per round for 1,000 rounds = 2 million bucks per missile interception. That's a little bit more than the cost of a Tomahawk cruise missile, but compares favorably with the RIM-161 anti-ballistic missile that the U.S. currently uses, which costs $10-14 million a pop (these numbers become ridiculous). The cost per interception goes down if it's intercepting a MIRV weapon since the barrage could probably destroy multiple warheads, but only the Soviet union and China have those and I don't think they've ever actually been used in battle, like most modern weapons, interestingly enough.

So it seems like this could work economically if it does its job technically. But that's the real trick, isn't it? Additionally, the Israeli Arrow 3 anti-ballistic missile should only cost about $2 or 3 million per use as well, so as the cost of anti-missile missiles declines, the cost advantage of your idea would correspondingly fall unless its per-interception cost could be similarly reduced. And if you need multiple seconds of firing or the cost per round is higher than my random guess, the economics fail pretty quickly.

[Libertarian666]

Again, you're essentially describing an updated version of an anti-aircraft flak gun. These clearly worked; they were mature technology at the point where they were replaced by missiles because of their greater range and power.

1,000 guns firing one round per second for only one second means a total of 1,000 rounds fired per interception. These rounds are fairly sophisticated; they're flak canisters filled with super-dense projectiles that are fired into the stratosphere. $2,000 per fired round is probably a huge understatement considering that a conventional dumb artillery round that only goes a dozen or two miles can cost $1,500 or more, but it seems like a good starting point. $2,000 per round for 1,000 rounds = 2 million bucks per missile interception. That's a little bit more than the cost of a Tomahawk cruise missile, but compares favorably with the RIM-161 anti-ballistic missile that the U.S. currently uses, which costs $10-14 million a pop (these numbers become ridiculous). The cost per interception goes down if it's intercepting a MIRV weapon since the barrage could probably destroy multiple warheads, but only the Soviet union and China have those and I don't think they've ever actually been used in battle, like most modern weapons, interestingly enough.

So it seems like this could work economically if it does its job technically. But that's the real trick, isn't it? Additionally, the Israeli Arrow 3 anti-ballistic missile should only cost about $2 or 3 million per use as well, so as the cost of anti-missile missiles declines, the cost advantage of your idea would correspondingly fall unless its per-interception cost could be similarly reduced. And if you need multiple seconds of firing or the cost per round is higher than my random guess, the economics fail pretty quickly.

Hmm, I would think that the projectiles would actually be less complicated and expensive than normal artillery shells, as they wouldn't contain any explosives or detonation mechanism. They would be spin-stabilized and just open up at their intended altitude. So they would need some sort of timing mechanism but that's about it.

And of course the entire system would be a lot less complicated than systems that attempt to hit an incoming missile by aiming at it, and wouldn't be affected by course changes or the like.

What am I missing?

[Pointedstick]

Hmm, I would think that the projectiles would actually be less complicated and expensive than normal artillery shells, as they wouldn't contain any explosives or detonation mechanism. They would be spin-stabilized and just open up at their intended altitude. So they would need some sort of timing mechanism but that's about it.

And of course the entire system would be a lot less complicated than systems that attempt to hit an incoming missile by aiming at it, and wouldn't be affected by course changes or the like.

What am I missing?

This pellet cloud would need to be generated pretty close to the missile itself, which suggests perfect calculation on the ground or a proximity fuze, which will add a lot to the cost. The launcher itself will be expensive, too, and some of that cost needs to be amortized into the per-shot price. A gun that can fire projectiles into the mesosphere would not be cheap, nor would the launching charge to actually propel it up to that height. Also, tungsten isn't cheap. Steel balls would be cheaper but probably less effective. Finally, there is also the military-industrial complex mark-up to contend with. Something that would be manufactured for $10 inevitably reaches a final price of $200 after its component parts have been separately built in all 50 states and shipped to China for final assembly.

Bottom line: I think $2,000 to shoot a high-tech flak shell almost into space is a very reasonable price--probably too reasonable given all the real-world complications. If the price per shot was much lower than this, it would be pretty sweet.

[Tyler]

This pellet cloud would need to be generated pretty close to the missile itself, which suggests perfect calculation on the ground or a proximity fuze, which will add a lot to the cost. The launcher itself will be expensive, too, and some of that cost needs to be amortized into the per-shot price. A gun that can fire projectiles into the mesosphere would not be cheap, nor would the launching charge to actually propel it up to that height.

My first reaction was to ditch the gun and make it satellite based.  Use the economy of scale to launch all of the pellets into space, and let the military satellites already tracking the missiles handle distribution back into the atmosphere.  At that point it's a matter of accuracy and response time.