Kinetic bombardment - how destructive?

[adam_grif]

By this badly worded line, I'll assume you mean "as large and fast as it needs to be in order to still have a mass of 20kg and velocity of 0.013c when it hits the ground."

Huh?

as large and fast as it needs to be in order to have a mass of exactly 20 KG and a velocity of 1.3% of C when it hits the ground.

What about it was poorly worded? "1.3% of C"?

So, let's suppose instead that the ship has some kind of magic forcefield technology to make a vacuum column through the atmosphere, all the way down to ground level.

Eh, don't bother going to any effort justifying it, you can just say "I'm ignoring air resistance". We're discussing spherical cows in a vacuum here, it ain't like I'm going to go write a fan fic about it.

The problem is that anything so massive would do far more damage than the mere 36 kT figure derived from a simple ½mv² calculation.

Well, you can discuss that in detail if you want. Would the mass burned up before it strikes something solid create a big tunnel of expanding fire or something on the way down?

That looks like a downward-firing rocket. It wouldn't be going anywhere near 0.013c, and it could also fire its rockets the whole time, so its velocity wouldn't peak until its hits the ground. Still, such a device will have far greater energy per kg than a chemical explosive would, so at the least you should get a nice big explosion.

Getting a nuclear fireball, however, requires nuclear yield. At a much smaller yield, you'd get something more like a conventional explosion.

Yeah I know the scales are nowhere near the scenario discussed here. I shouldn't be surprised though, it's not like the Ubisoft cutscene department is world renowned for it's scientific accuracy...

[Darth Wong]

What about it was poorly worded? "1.3% of C"?

Sorry, when I first saw it I thought you had accidentally said it was doing 1.3c. My mistake.

Well, you can discuss that in detail if you want. Would the mass burned up before it strikes something solid create a big tunnel of expanding fire or something on the way down?

I think you have to keep in mind that for an object moving that quickly, it might as well be striking something solid when it hits the atmosphere. It's sort of like the way they say a terminal-velocity impact with water feels like you're hitting a solid wall. So what you're really talking about is an elongated impact, with the tip just barely reaching the city. The amount of energy involved in this impact would kill everyone in the city even if the impact didn't; the sheer radiation from it would cook anything in a line of sight.

Yeah I know the scales are nowhere near the scenario discussed here. I shouldn't be surprised though, it's not like the Ubisoft cutscene department is world renowned for it's scientific accuracy...

Not to mention the stupidity of having a fancy high-tech holographic gameboard control system for giving orders to your soldiers electronically, and then putting your HQ right on the front lines

[adam_grif]

Not to mention the stupidity of having a fancy high-tech holographic gameboard control system for giving orders to your soldiers electronically, and then putting your HQ right on the front lines

Which is funny, because in the actual game, the whole point is that it recognizes standardized voice commands that you give on the fly through your headset. No holographic displays in sight. Those bunker things aren't command centers in-game either, they're some kind of satellite nodes that control the missile shield as it intercepts shit in that local area? Not entirely sure why they're needed.

Sorry, when I first saw it I thought you had accidentally said it was doing 1.3c. My mistake.

1.3c? Yeah, that'd probably leave a bit more of a mark than 1.3% of c would

[The Yosemite Bear]

no it would travel through time, open a wormhole and miss the planet entirely....

[adam_grif]

Don't be absurd. Time travel only occurs with objects going 88 miles per hour, and that have multi-jiggawatt power reactors.

[Ford Prefect]

Instead, the column will be more cylindrical, and much of the plasma will shoot right back up to the ship.

Wouldn't this only be the case if the ship was within the atmosphere? You could sit out at the moon and take potshots without having to worry about it, I would presume. How close do you think you would actually have to be for this to be an issue?

[Darth Wong]

In Grif's example, he asked what would happen if the ship were only a few hundred metres above the city. If it were in space, the projectile would burn up in the atmosphere before it ever touched the city.

[Ford Prefect]

Well that shows how much I'm paying attention, I didn't even realise this thread had two pages. I wonder how effective blunt-body impactors might be for bombardment purposes. Obviously not at 1.3% of the speed of light, at which point it becomes irrelevant, but perhaps at lower velocities? Though at the same time deliberately increasing your air resistance on a kinetic impactor seems kind of silly from a 'common sense' perspective. I'm also not really sure how effective it would be in protecting the slug from the heat once you hit a few hundred km/s.

[Sky Captain]

My thoughts

Dense projectiles would have better chance penetrating the atmosphere than less dense ones. Right?. So if you could manufacture your 20 kg bullet out of some super dense and strong unobtanium making it only few millimeters in size it theoretically could penetrate atmosphere and still deliver most of it`s energy into groundburst explosion?

[takemeout_totheblack]

It should be less destructive than a ground-burst nuke of the same yield. Some of the fireball energy goes up the column and this means that less of it remains near ground level. Also, you won't have the same nasty nuclear material fallout.

Fascinating! It's literally a weapon that flips its victims the bird!
What kind of damage are we looking at in the Killing Star? Are they over rated or does the description above sound about right? What does 'living room sized' mean? Would R-bomb bombardment over cities leave the planet's ecosystem and resources relatively intact or turn the continent into a plasma cooker?
R-bombs and other relativistic weapons fascinate me but they're almost never used in popular sci-fi except for Andromeda, which is kind of sad!

[Darth Wong]

What kind of damage are we looking at in the Killing Star? Are they over rated or does the description above sound about right? What does 'living room sized' mean?

Go measure your living room. Let's say it's 20 feet square, with a 10 foot ceiling. That's 4000 cubic feet, or 111 cubic metres. If the object is solid iron, then it should have a mass of nearly 900 metric tonnes. The Newtonian KE for a 900 metric ton object moving at 0.92c would be roughly 3.4E+22 J (8 million megatons), while the more accurate relativistic KE would be roughly 1.3E+23 J (equivalent to 31 million megatons).

Would R-bomb bombardment over cities leave the planet's ecosystem and resources relatively intact or turn the continent into a plasma cooker?

Everything in a line of sight (pretty much the whole hemisphere) would probably be cooked by the radiation.

R-bombs and other relativistic weapons fascinate me but they're almost never used in popular sci-fi except for Andromeda, which is kind of sad!

Halo uses them a lot. They're perceived as being more "hard sci-fi" than rayguns, even though they are no more plausible. If you were to mount a cannon on a ship which was capable of that kind of acceleration, it would hurl the ship backwards unless it is capable of generating enough thrust to compensate, and its material structure can withstand the enormous stresses involved.

[Serafina]

In Grif's example, he asked what would happen if the ship were only a few hundred metres above the city. If it were in space, the projectile would burn up in the atmosphere before it ever touched the city.

So, what would that heat do?
Would there be some kind of shockwave, or any other effects from the sudden release of a lot of heat in the atmosphere?

[Teleros]

So, what would that heat do?
Would there be some kind of shockwave, or any other effects from the sudden release of a lot of heat in the atmosphere?

Assuming you mean the heat from burning up in the atmosphere... tiddly-squat, unless (as in the Killing Star example) it's a particularly massive missile. I think someone noted on the previous page that Earth's atmosphere eats kiloton-yield asteroid impacts fairly frequently.

[Korvan]

I thought I'd take a stab at working out some numbers for the original scenario which is a 20 kg iron mass hitting atmosphere at 0.013 c or about 3.9 million m/s. There's a lot of variables to deal with such as increasing atmospheric pressure, decreasing mass of the projectile as it's outer layers boil off, etc, but I will be making a number of simplifications to bring a measure of sanity to the equations.

For the atmosphere I will be assuming constant pressure out to 100 km. I'll be using a simple average of the pressure giving a value of 1/2 atmospheres (about 50 kPa). We will be ignoring the effect of gravity on the shell and further make the assumption that the shell's trajectory is constant and is perpendicular to the planet's surface.

From a naval site I got the following formula for drag on a shell: 0.5*r*V2 * S * Cd
where r is density of air, V is velocity, S is surface area of the shell and Cd is the drag coefficient.

Cd is going to be tricky to deal with as it is either,
1. determined experimentally,
2. calculated using fluid flow equations, or
3. determined numerically using supercompters

I'm going to go with the ever popular option 4 and pull a number out of my ass, say 0.3. (which is a reasonable value for a spherical projectile)

Given that the density of pure iron is 7870 kg/m³, 20 kgs gives us 0.00254 m³ which makes a nice sphere of 0.0847 m radius (~8.5 cm). This gives us a cross sectional area of 0.0225 m2.

That just leaves the density of air, which at 1/2 atmosphere is 0.602 kg/m2.

So the drag force = 0.5*(0.602 kg/m2)*(3.9 million m/s)2*(0.0225 m2)*0.3 = 30.1 GN (giga Newtons).

Since energy is Force * distance, over the 100 km, the atmosphere will do negative work on the shell, slowing it down (we are ignoring this slowdown as it greatly complicates the drag equation), and the difference is energy is converted into heat. This energy works out to be (30.1 GN)*(100 km) = 3.01 e-15 Joules. This value is very large and exceeds the kinetic energy of the shell (1.52 e-14 Joules) which can't happen so my assumption of constant velocity is bogus. But we'll say the shell's entire KE gets converted into heat and made a further assumption that all the heat goes into heating and vaporising the iron.

The specific heat of iron is 0.46 (kJ/kg K), the boiling point is 2750.0 °C (3023.15 K) and the heat of vaporization is 349.60 kJ /mol. We'll say the iron's initial temperature is 4 K (background temperature of space, perhaps the shell has been traveling a while) so the energy to raise the 20kg of iron to 3023 K is about 28 MJoules and the energy to vaporize the iron is 125 MJoules, giving us a grand total of 153 Mjoules (1.53 e-8 Joules). This is such a small fraction of the heat going into the iron, even if a large amount of heat is carried away by the atmosphere, there is plenty left over to vaporize the iron. That was a lot of work to come up the answer that everyone else has been giving in the thread so far, but it was a fun exercise and it was interesting to see the orders of magnitudes involved.

One final note, heat transfer and vaporization are not instantaneous, they do take a finite amount of time. I would conjecture that even a small projectile moving fast enough may have enough time to hit the planet's surface before losing the majority of it's mass. Working out what that speed would be is beyond my capabilities.

[Darth Wong]

...

So the drag force = 0.5*(0.602 kg/m2)*(3.9 million m/s)2*(0.0225 m2)*0.3 = 30.1 GN (giga Newtons).

Since energy is Force * distance, over the 100 km, the atmosphere will do negative work on the shell, slowing it down (we are ignoring this slowdown as it greatly complicates the drag equation), and the difference is energy is converted into heat. This energy works out to be (30.1 GN)*(100 km) = 3.01 e-15 Joules. This value is very large and exceeds the kinetic energy of the shell (1.52 e-14 Joules) which can't happen so my assumption of constant velocity is bogus. But we'll say the shell's entire KE gets converted into heat and made a further assumption that all the heat goes into heating and vaporising the iron.

The specific heat of iron is 0.46 (kJ/kg K), the boiling point is 2750.0 °C (3023.15 K) and the heat of vaporization is 349.60 kJ /mol. We'll say the iron's initial temperature is 4 K (background temperature of space, perhaps the shell has been traveling a while) so the energy to raise the 20kg of iron to 3023 K is about 28 MJoules and the energy to vaporize the iron is 125 MJoules, giving us a grand total of 153 Mjoules (1.53 e-8 Joules). This is such a small fraction of the heat going into the iron, even if a large amount of heat is carried away by the atmosphere, there is plenty left over to vaporize the iron. That was a lot of work to come up the answer that everyone else has been giving in the thread so far, but it was a fun exercise and it was interesting to see the orders of magnitudes involved.

One final note, heat transfer and vaporization are not instantaneous, they do take a finite amount of time. I would conjecture that even a small projectile moving fast enough may have enough time to hit the planet's surface before losing the majority of it's mass. Working out what that speed would be is beyond my capabilities.

Interesting work. I like the amount of effort.

Mind you, 30 GN applied to a 0.085m radius circle is more than 1.3TPa, or 13 million bars. 2Mbars is enough to create a shockwave inside the iron which would melt it completely, so you have three mechanisms of heating:

1) Frictional
2) Shock heating
3) Radiation

A quickie back-of-envelope calculation gives me a shockwave speed of roughly 19.7 km/s for 1.3TPa pressure (hopefully I didn't get careless with the Hugoniot relation). In other words, if you were to suddenly apply 1.3TPa pressure to a 17cm wide sphere, the shockwave would go through the entire sphere in less than 9 microseconds.

[Korvan]

Interesting work. I like the amount of effort.

Mind you, 30 GN applied to a 0.085m radius circle is more than 1.3TPa, or 13 million bars. 2Mbars is enough to create a shockwave inside the iron which would melt it completely, so you have three mechanisms of heating:

1) Frictional
2) Shock heating
3) Radiation

A quickie back-of-envelope calculation gives me a shockwave speed of roughly 19.7 km/s for 1.3TPa pressure (hopefully I didn't get careless with the Hugoniot relation). In other words, if you were to suddenly apply 1.3TPa pressure to a 17cm wide sphere, the shockwave would go through the entire sphere in less than 9 microseconds.

Thanks! I'm actually back in school doing a refresher of first year science (been 20 years since I was last in first year) and we covered drag a while back, so I thought I'd give it a go and see what I came up with. First year physics only gets you so far with a problem like this though and my last time through the system, I only got as far as 2nd year physics before switching off to computer science.

That shockwave is definitely interesting, in 9 microseconds, even if the shell was moving close to c, it wouldn't get further than 3 km. Of course now there's relativistic mass to deal with so at large fractions of c, the shell could get through, but thinking a bit more, with length contraction, wouldn't the shockwave go through the (now flattened) sphere a lot quicker?

[Darth Wong]

Fast-moving objects become longer, not shorter. But that's just from the perspective of an outside observer; in their own frame of reference their size has, of course, not changed at all. But since time is moving slower for them, I suppose that would mean that the propagation would take a bit longer from an outside perspective. Then again, if the shell were moving close to c, the pressure would also be much greater, and the shockwave much faster.

I think the shockwave figure is useful just because it graphically demonstrates what I mentioned earlier: at very high velocities, hitting the atmosphere is like hitting a solid object. An armour-piercing shell meets less resistance punching through six inches of armour plate than such a high-velocity projectile would encounter from hitting the atmosphere.

[Nyrath]

The Newtonian KE for a 900 metric ton object moving at 0.92c would be roughly 3.4E+22 J (8 million megatons), while the more accurate relativistic KE would be roughly 1.3E+23 J (equivalent to 31 million megatons). ... snip ...

They're perceived as being more "hard sci-fi" than rayguns, even though they are no more plausible.

Yes, the writers who flunked Physics 101 fail to realize that in order to get 31 million megatons out of a kinetic energy projectile, you have to put 31 million megatons into the projectile in the first place in order to accelerate it. Which has implications for the plausibility of the weapon.

[takemeout_totheblack]

The Newtonian KE for a 900 metric ton object moving at 0.92c would be roughly 3.4E+22 J (8 million megatons), while the more accurate relativistic KE would be roughly 1.3E+23 J (equivalent to 31 million megatons). ... snip ...

They're perceived as being more "hard sci-fi" than rayguns, even though they are no more plausible.

Yes, the writers who flunked Physics 101 fail to realize that in order to get 31 million megatons out of a kinetic energy projectile, you have to put 31 million megatons into the projectile in the first place in order to accelerate it. Which has implications for the plausibility of the weapon.

Well, I haven't read The Killing Star myself, and I'm just playing blind advocate here, but is it possible that there's some unobtainium application involved to pecker-slap physics a bit? I guess not, considering it's on Atomic Rocket as a fairly realistic portrayal of the effects of an R-Bomb, but again I haven't read the thing so I dunno.
Could someone who has read it attest to the hardness of The Killing Star?

[Simon_Jester]

Well, other examples are welcome in the thread too. But of course Nyrath's wasn't related to the ME example.

It's a good illustration of the high-velocity end, with relativistic or ultra-relativistic bombardment, where the effects approximate those of a nuclear explosion, only with less radioactivity. At the low-velocity end you get Meteor Crater- something that, mechanically, looks a lot like dropping a rock into a sandbox, only scaled up.

At 0.01c, you're somewhere in the middle.

I haven't determined anything; I have zero experience in such matters.

One of the reasons I decided to ask was that in the MEverse specifically, there is a treaty about the construction of the ships with mainguns firing these 20 KG @ .013 C slug, because they carry so much energy. It's not outright stated, but heavily implied, that it's referring to the bombardment of cities and planetary colonies.

Again, not outright stated, but heavily implied that it would do significant damage to a city.

In effect, you'd be peppering the airspace many kilometers above the city with small nuclear airbursts at high altitude; it really shouldn't do very much damage.

Eh, don't bother going to any effort justifying it, you can just say "I'm ignoring air resistance". We're discussing spherical cows in a vacuum here, it ain't like I'm going to go write a fan fic about it.

The problem is that for low mass kinetic weapons in the kiloton energy range, the "no air resistance" case is totally different from the "air resistance" case. Bombarding the Moon, or even Mars (in its current state) with such weapons would be far more effective than bombarding Earth with them, because of the lack of air.

Fascinating! It's literally a weapon that flips its victims the bird!

Yes, but the drawback is that the middle finger is aimed straight up your gunport. And is on fire.

They're perceived as being more "hard sci-fi" than rayguns, even though they are no more plausible.

Yes, the writers who flunked Physics 101 fail to realize that in order to get 31 million megatons out of a kinetic energy projectile, you have to put 31 million megatons into the projectile in the first place in order to accelerate it. Which has implications for the plausibility of the weapon.

Or, failing that, the capabilities of whoever built the thing. Though anything capable enough to put 31 teratons into a living room sized projectile is probably outside the bounds of hard science fiction, even if you're pumping those Dyson spheres as hard as you can.

[dragon]

link has a good info on what even a small object hitting at high speeds can do.
A 1m in diameter chunk of of something with density of iron traveling at 12kps will leave a crater 41.7m in diameter and 8.9m deep.
link

Cool think about the website is you can scale up to large scale or very fast or both. THey also talk about thermal effects and all sorts of other tidbits.

[Ford Prefect]

Could someone who has read it attest to the hardness of The Killing Star?

I can't actually remember whether it is explained how they launched the r-bombs, but the alien that is encountered at the end of the story talks about how the catalyst for the attack was humanity achieving relatavistic starships, and given that the aliens themselves were not that far behind their projectiles, I got the impression that they just dumped them off their ships before they began deceleration burns. The design of the starships in the book is based on one of the author's theoretical work (with another physicist) on relatavistic space travel, called Valkyrie, which is theoretically capable of reaching 93% of the speed of light.

Also, I hear that the big spaceship in Avatar was based on that design.

EDIT: on second thought some of the claims about the fuel needed for Valkyrie are pretty silly. It's some ridiculously low amount of antimatter.

[Simon_Jester]

Yeah. An object traveling at .9c is carrying kinetic energy greater than its own rest mass-energy. Which means that even assuming a perfectly efficient drive you need to burn a matter/antimatter mix with total mass greater than the ship's dry (unfueled) weight to get it moving. And you'll have to do it again to slow down, unless I'm doing my seat-of-the-pants math badly wrong.

[adam_grif]

Yes, but I get the impression that there are other ways to slow down, such as mag sails to generate friction. The RKV's the aliens were using didn't slow down, so it is in essence more plausible that such RKVs could be developed than transports that achieve those speeds then slow down to nothing.

If you have a ship that can reach 0.7C one way then slow down again, if you try to turn it into a missile you can just dump all the fuel into acceleration instead of slowing down, and achieve a far greater velocity (~twice the energy).

This more speaks to the implausiblities involved with high relativistic velocities than it does with the plausibility of RKVs as weapons, mind you.

[Simon_Jester]

Agreed on all counts. You're not going to get high relativistic speeds with reaction drives unless you have some form of efficient matter-to-energy as the power source; otherwise you just don't have the power to weight ratio for it. Fission bombs, for example, are probably not going to cut it.