Impact Physics

[Paul M]

At high velocities the atmosphere is largely treated as a solid.  In reality compression would occur that would make a material with the number of atoms of the column of air equal to the missiles diameter.  Essentially once the missile's transit time through the atmosphere is shorter than the ability of the air to move away from it the air is simply compressed.  Pretty much as happens with a piston.  The temperature rise is such the molecules disassociate into atoms.  This heat is conducted into the missile body but again due to the short time involved...(at 0.1c 50 km requires 1.7 ms) only the upper fraction of the missile would convert into plasma but the plasma would have the same mass, and momentum (hence kinetic energy) of the original missile.  The energy required to compress that air column would be lost to the missile but I suspect that it is not enough to slow the missile down significantly.

When the missile strikes the ground the entire mass of the missile (plus the air column) is then converted into kinetic energy and dispersed via the shock wave and in large part transferred to all the debris thrown up.  In principle though everything within a reasonable distance of the missile strike would be converted into plasma by the energy contained in the missile and only once the fireball expanded and cooled would you start seeing debris thrown upwards.

Note the ground shock wave would be extremely powerful.  But even the air shock would be considerable...the missile impact probably is causing an outward going pressure shock front that would meet the inbound atmosphere from the vacuum left by its passage with ugly results.

There is no need for warheads on missiles that can achieve even low fractional C velocities.

The plasma is no less dangerous then a metal bar.  It is fully capable of transmitting shock and energy to a material.  HEAP rounds convert a titanium cone to a directed plasma jet to slice through armour, and plasma cutting is a standard way to cut thick metal.  Any oxyacetylene torch is a plasma as well.

A plasma strike is what does damage in a nuclear blast in space.  It is the warhead/missile being converted into plasma that is doing the damage as there is no atmosphere to transmit the energy.  All the other energy is contained in particles and photons...which are not negligible but follow a r2 law so they loss energy rapidly with range.

An impact of a 20 tonne object moving at speeds were relativistic corrections become important (v>>0.75c) would be very nasty.  Luckily most planets are massive enough (earth is 6x10^24 kg) that outright destruction is hard to produce...but for environment I'd say that is a different situation.  You would need to accumulate a total mass of 10^7 kg of material in the missile plasma before the velocity of the plasma would drop from 10^8 m/s to 10 m/s or so.  Not completely accurate but assuming the plasma remains around 4 m in diameter that only takes 150 m for a planet of the density of the earth 5.5tonne per m3...so the missile impact depth is around 150 m, in water it would be something like 1 km.  At this point the plasma is roughly stationary and transfers its energy to the surroundings...which promptly sublimate and then the shockwaves from that spread.

[bean (OP)]

I'm not sure about that.  Sorium is more abundant than anything else now (eg. Tritium for warheads) and mines faster than anything else. 

And fuel is ridiculously energy dense; which can be packed into a high speed projectile by a high speed ship shooting a high delta-v missile, all without increasing the missile's weight. 
Even if the missile turns into plasma in the upper atmosphere (I think you mentioned 50km?), the resulting nuclear fireball could be big enough to reach the ground. 

I don't disagree with this.  I was commenting on a proposal to allow the use of asteroids as weapons.  And for that, you tend to go for mass over velocity.  And it would break up well above 50 km.  I just chose to find dynamic pressure there.

I would agree with byron that a relatively slow missile that can transit the atmsphere is going to be more effective that one that is basically trying to shove it out the way.

I'm now wondering if the best planetary defense would actually just be a bunch of terraformers that busily pumped up the atmosphere density to the maximum tolerances of my inhabitants.

Not a bad idea.  However, it really wouldn't do much to mitigate the damage.  All this does is make it impossible to physically hit ground-level targets.

At high velocities the atmosphere is largely treated as a solid.  In reality compression would occur that would make a material with the number of atoms of the column of air equal to the missiles diameter.  Essentially once the missile's transit time through the atmosphere is shorter than the ability of the air to move away from it the air is simply compressed.  Pretty much as happens with a piston.  The temperature rise is such the molecules disassociate into atoms.  This heat is conducted into the missile body but again due to the short time involved...(at 0.1c 50 km requires 1.7 ms) only the upper fraction of the missile would convert into plasma but the plasma would have the same mass, and momentum (hence kinetic energy) of the original missile.  The energy required to compress that air column would be lost to the missile but I suspect that it is not enough to slow the missile down significantly.

When the missile strikes the ground the entire mass of the missile (plus the air column) is then converted into kinetic energy and dispersed via the shock wave and in large part transferred to all the debris thrown up.  In principle though everything within a reasonable distance of the missile strike would be converted into plasma by the energy contained in the missile and only once the fireball expanded and cooled would you start seeing debris thrown upwards.

Note the ground shock wave would be extremely powerful.  But even the air shock would be considerable...the missile impact probably is causing an outward going pressure shock front that would meet the inbound atmosphere from the vacuum left by its passage with ugly results.

There is no need for warheads on missiles that can achieve even low fractional C velocities.

Really?  The projectile will begin heating and suffering aerodynamic stresses somewhere above 150 km, which is three times what you estimated.  Also, what's stopping it from breaking up under the load?  Just curious.

The plasma is no less dangerous then a metal bar.  It is fully capable of transmitting shock and energy to a material.  HEAP rounds convert a titanium cone to a directed plasma jet to slice through armour, and plasma cutting is a standard way to cut thick metal.  Any oxyacetylene torch is a plasma as well.

No, that's not how HEAT rounds work.  The copper liner stays in metallic form the entire time, but behaves like a liquid under the pressure.  And neither an oxyacetylene torch cuts by heating the metal, not by momentum transfer.  So does a plasma torch for that matter.

A plasma strike is what does damage in a nuclear blast in space.  It is the warhead/missile being converted into plasma that is doing the damage as there is no atmosphere to transmit the energy.  All the other energy is contained in particles and photons...which are not negligible but follow a r2 law so they loss energy rapidly with range.

No, that's not what does the damage.  The damage is done by the X-rays from the bomb itself.  The casing is fairly negligible. 

[jseah]

I don't disagree with this.  I was commenting on a proposal to allow the use of asteroids as weapons.  And for that, you tend to go for mass over velocity.  And it would break up well above 50 km.  I just chose to find dynamic pressure there.

I looked up hypervelocity weapons on that atomic rockets site.  They calculate that the ideal energy point of an accelerating missile is when it's speed is equal to exhaust velocity.  Beyond that, burning more fuel reduces KE since your fuel's mass is worth more energy. 

Given that I calculated the exhaust velocity of the Geosurvey vessel as 19100 km/s, that would mean that kinetic missiles will be travelling at 19kkm/s... at starting tech. 

Naive conservation of momentum indicates to me that your missile will need to be 50% fuel to achieve this. 

EDIT: for obvious reasons, your ships launching missiles should have their own velocity and hence some buffer should be added.  Say 55% fuel and 45% engine.  The missile would accelerate to exhaust velocity and then start evasive course changes using the extra 5%. 

[bean (OP)]

Given that I calculated the exhaust velocity of the Geosurvey vessel as 19100 km/s, that would mean that kinetic missiles will be travelling at 19kkm/s... at starting tech. 

That assumes that the engine has the same exhaust velocity.  I know that's obvious, but I for one expect the missile to have a considerably lower exhaust velocity.  Particularly early in the game, I'm not going to build missiles to kill planets.

Naive conservation of momentum indicates to me that your missile will need to be 50% fuel to achieve this. 

Naive indeed.  No offense.  And you really should read all of atomic rockets.  It's a great site.  And now for some rocket science:
For delta-V to equal exhaust velocity, the mass ratio is actually going to be about 2.7.  The mass ratio is defined as the ratio of loaded mass to empty mass.  Delta-V is calculated from the rocket equation: DV=Ve*ln(Ml/Me) DV is delta-V, Ve is exhaust velocity, ln is the natural log, and Ml and Me are the loaded and empty masses respectively.  Note that loaded and empty only refer to the fuel tanks.  Anything else is factored into both.

[jseah]

Hm, 2.7 doesn't sound all that much.  Certainly affordable at least. 

Still, 20kkm/s does not make a planet-killer.  It makes a very good ship killer though (although for AS work, you'd probably want more smaller missiles at a lower velocity)

[ollobrains]

an interesting strategic element for terraformers against fast moving missiles burn em up versus having them hit.  Sorium perhaps could be needed if u wanted a guided missile.

And the affordable factor versus perhaps a higher manufacture cost and was to intercept them as well.  From an impact physics point of view something to consider, steve seems to have been offline for a week waiting to see what he thinks of some of these new ideas whenever he graces his presense again

[procyon]

At high velocities the atmosphere is largely treated as a solid.  In reality compression would occur that would make a material with the number of atoms of the column of air equal to the missiles diameter.

I think most folks are looking at this backward.  This missile won't reach the ground intact.  It is easier to look at it in reverse.

Instead of wondering if the missile will punch through that much air and reach the ground at this velocity,  try to imagine hitting the missile with this amount of particles at this velocity and it surviving.  It won't.

The atmosphere is going to act like a solid.  A diffuse one, but a solid.  One that when slammed into the missile will disintegrate it.  Big high altitude air burst.  If it will reach the ground is totally a function of its energy.  A lot of it is going to be reflected into the upper atmosphere again as it rebounds off of the tropopause, etc in the different layers of the atmosphere, just like sonar echos off the thermocline.

[bean (OP)]

I think most folks are looking at this backward.  This missile won't reach the ground intact.  It is easier to look at it in reverse.

Instead of wondering if the missile will punch through that much air and reach the ground at this velocity,  try to imagine hitting the missile with this amount of particles at this velocity and it surviving.  It won't.

The atmosphere is going to act like a solid.  A diffuse one, but a solid.  One that when slammed into the missile will disintegrate it.  Big high altitude air burst.  If it will reach the ground is totally a function of its energy.  A lot of it is going to be reflected into the upper atmosphere again as it rebounds off of the tropopause, etc in the different layers of the atmosphere, just like sonar echos off the thermocline.

The first part is entirely correct, but I'm not so sure about the last part of your statement.  Momentum in this situation is almost negligible.  Once the projectile breaks up, the sectional density goes way down, dumping energy/momentum even faster.  Almost all movement in this case is going to come from the heated air, which will be moving in all directions.  I don't see it "rebounding" at all.
And I'm even more skeptical of the person you quoted, given that he got just about everything else completely wrong.

[jseah]

The question of course is whether your missile going at c-fractional speeds (coz 60kkm/s is 20% of c) will generate an airburst large enough for that to affect the ground. 

Given the kind of energies we are throwing around at even early-mid game, I'd say the shockwave alone should do plenty of damage on the ground under the atmosphere entry site.  It certainly won't destroy all the biosphere, but you didn't want to do that anyway. 

[bean (OP)]

The question of course is whether your missile going at c-fractional speeds (coz 60kkm/s is 20% of c) will generate an airburst large enough for that to affect the ground. 

Given the kind of energies we are throwing around at even early-mid game, I'd say the shockwave alone should do plenty of damage on the ground under the atmosphere entry site.  It certainly won't destroy all the biosphere, but you didn't want to do that anyway. 

The answer depends heavily on the size of the projectile.  Even at .999c, 1 gram isn't going to do more then maybe make a flash when viewed from ground level (454 kilotons).  A few kilograms might make me nervous, except that the burst altitude is probably over 100 km, which makes it somewhat less of a threat.  Once past that, it gets very dangerous, very fast.
The airburst will form a shockwave.  Nuclear weapons produce shockwaves because they heat the air around them to incredibly high temperatures.  The same thing happens here.

[jseah]

We probably won't get 99.9% c. 

I have seriously doubts about the practicality of acheving 90+% c anyway.  100kkm/s ought to be enough to kill anything you hit. 
EDIT: I reserve the right to build yatches that go that fast at end-game.  Simply for the lulz.  =)

A 5ton missile at 100kkm/s could doable by midgame (Steve said that late game fuel efficiency was just under c?).  That's... what, 25E18 J?  Or about 6 gigatons?
Even with an additional 5-10% fuel weight for maneuvering and spreading out attack vectors to avoid interception, the missile shouldn't reach much more than 20tons in total. 

Even if it's a 100km high airburst, that's got to do *something* rather nasty. 

[Arwyn]

All that being said, isn't atmospheric density an issue there as well? Trace atmospheres don't have a 1atm density, so conceivably you could have an actual surface kinetic strike.

Flip side to that, when you have higher density atm, say 3 or 4, the high altitude dissipation is greater, but the overpressure wave for anything that gets down the air column is going to be... nasty...

[ollobrains]

All that being said, isn't atmospheric density an issue there as well? Trace atmospheres don't have a 1atm density, so conceivably you could have an actual surface kinetic strike.

Flip side to that, when you have higher density atm, say 3 or 4, the high altitude dissipation is greater, but the overpressure wave for anything that gets down the air column is going to be... nasty...

Atomospheric conditions being stirred up by quite a bit in this situation could be well very nasty indeed to what specific data sets im not sure but a consideration on this point yes

[bean (OP)]

All that being said, isn't atmospheric density an issue there as well? Trace atmospheres don't have a 1atm density, so conceivably you could have an actual surface kinetic strike.

Flip side to that, when you have higher density atm, say 3 or 4, the high altitude dissipation is greater, but the overpressure wave for anything that gets down the air column is going to be... nasty...

This is true.  However, there are several factors at play here.  First, the fact that a planet with lower gravity is going to suffer less.  Why?  The depth of the atmosphere is a function of the gravity of the planet.  At some altitude, Mars had a denser atmosphere then that of Earth.  For a given velocity, a projectile will break up at a given density, so for constant surface pressure, you're better off on a low-G world.  Note that this is for a given sea-level pressure.
I don't know terribly much about shockwave propagation, but based on a little research (Effects of nuclear weapons) it appears that for a given blast, overpressure is directly proportional to ambient pressure.  I'm not sure how various losses would effect the shockwave at different pressures.

[procyon]

The first part is entirely correct, but I'm not so sure about the last part of your statement.  Momentum in this situation is almost negligible.  Once the projectile breaks up, the sectional density goes way down, dumping energy/momentum even faster.  Almost all movement in this case is going to come from the heated air, which will be moving in all directions.  I don't see it "rebounding" at all.
And I'm even more skeptical of the person you quoted, given that he got just about everything else completely wrong.

Didn't worry about anything else in the post, just saves on typing to copy what is right.

And as for the rebound (actually reflection) of the shockwave, it will happen.  There aren't any studies of it for high energy shockwaves in atmosphere, but lots of them for the shockwave of sound as it travels in water and hits the different temps/densities.  Tracking something with sonar depends alot on where it is in the layers of water.

The tropopause should reflect a fair amount of energy back into the high atmosphere as the low density air above it runs into the much higher density air below.  But what percentage is reflected is anyones guess.

This is true.  However, there are several factors at play here.  First, the fact that a planet with lower gravity is going to suffer less.  Why?  The depth of the atmosphere is a function of the gravity of the planet.  At some altitude, Mars had a denser atmosphere then that of Earth.  For a given velocity, a projectile will break up at a given density, so for constant surface pressure, you're better off on a low-G world.  Note that this is for a given sea-level pressure.

Only to a degree does gravity impact density of atmosphere.  Titan (moon of Saturn) has only a fraction of Earth gravity but its atmosphere is actually denser than Earth's.  It is about 40% more dense as I remember.
But as a general rule, it is true that lower gravity will have lower atm density.

I don't know terribly much about shockwave propagation, but based on a little research (Effects of nuclear weapons) it appears that for a given blast, overpressure is directly proportional to ambient pressure.  I'm not sure how various losses would effect the shockwave at different pressures.

How it propagates is anyone's guess on this one.  The thought of how dense the atmosphere will have to be to stop a projectile could be a nightmare.  A rare atm might disrupt the missile but still be thin enough to allow the plasma to reach the surface.  This one is way over my head...