Impact Physics

[ollobrains]

SHoemaker levy into jupiter serves as a real world example though they were much larger and falling into a gas atmosphere

[Paul M]

Thermal conduction limites the rate at which the missile will be destroyed, and coversion of the missile into a plasma strike in the atmosphere is irrelevent to the planet underneath it the energy contained in the missile will arrive on the surface as its momentum is so great, it will not "bounce."  The atmosphere is not a factor (unless you live in a gas giant).  The missile plasma is the equivelent of a high energy particle beam weapon in this case.

This is true for anything moving at 0.1c and upwards.  At that speed a missile hitting a ship is an instant kill of the vessel struck.  Even a ship of 100,000 tonnes hit by a 20 tonne missile moving at 0.1c will be destroyed instantly.  The missile and ship will merge and the resulting body will be instantly (in under 0.1 ms) be accelerated to the velocity of (20*30,000 km/s)/(100000+20)= 6 km/s.  6000 m/s/0.1 ms is an acceleration of 6x10^7 m/s2...or 6 million gravities.  The ship collapses structurally and the crew is rendered into paste.  In reality I would assume the missile blows through the ship and the amount of energy and momentum transfered to the target ship is less but it probably bends like a pretzel and the crew is again rendered into paste by the 1000 G's or so.

Normal planetary velocities are under 50 km/s.  And asteroid strikes and such are probably at a velocity that is lower since the object is usually moving in a spiral rather than directly inwards and it becomes a case of relative velocity (which can make it worse for head on collisions).

For a working newtonian motion system you probably could look at the game "Attack Vector: Tactical" by Ad Astra.  They have a set of full newtonian rules.

[bean (OP)]

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.

When I wrote that, I was thinking about the physical projectile, not the shockwave.  So yes, some would be reflected.

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.

That was not my point.  My point was that a low-gravity world with the same sea-level pressure will have a thicker atmosphere.  And if the world in question is terraformed to match earth at sea level, then it will absolutely have the same density. 

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...

I'm not sure either.  Maybe in a few years...

SHoemaker levy into jupiter serves as a real world example though they were much larger and falling into a gas atmosphere

Also, not traveling at remotely the same speed.  No comparison.

Thermal conduction limites the rate at which the missile will be destroyed, and coversion of the missile into a plasma strike in the atmosphere is irrelevent to the planet underneath it the energy contained in the missile will arrive on the surface as its momentum is so great, it will not "bounce."  The atmosphere is not a factor (unless you live in a gas giant).  The missile plasma is the equivelent of a high energy particle beam weapon in this case.

Every one of these statements is false.  First off, the missile is likely to be destroyed by physical stress, not just heating.  Dynamic pressures on the order of terapascals.  In the upper atmosphere.  Secondly, the amount of heat released is so large that I'm going to assume that it will be destroyed by heating unless you can show me the calculations that prove otherwise.  Thirdly, the momentum is not great at all.  The kinetic energy to momentum ratio is absurdly high, and that's what matters.  Technically, it does have a lot of momentum, but that's like claiming that an artillery shell has a lot of momentum, so after it goes off, the gas cloud should still be able to penetrate things.  Lastly, the plasma will want to expand out the sides.  Nothing is stopping it.  Maybe I should put this another way.  I've done the math (a page or two back) to support my position.  Do the math to support yours.  Things like heat transfer, and why it doesn't just break up.  Also, why the plasma doesn't expand into a cloud, which rapidly dumps its momentum into the atmosphere.

This is true for anything moving at 0.1c and upwards.  At that speed a missile hitting a ship is an instant kill of the vessel struck.  Even a ship of 100,000 tonnes hit by a 20 tonne missile moving at 0.1c will be destroyed instantly.  The missile and ship will merge and the resulting body will be instantly (in under 0.1 ms) be accelerated to the velocity of (20*30,000 km/s)/(100000+20)= 6 km/s.  6000 m/s/0.1 ms is an acceleration of 6x10^7 m/s2...or 6 million gravities.  The ship collapses structurally and the crew is rendered into paste.  In reality I would assume the missile blows through the ship and the amount of energy and momentum transfered to the target ship is less but it probably bends like a pretzel and the crew is again rendered into paste by the 1000 G's or so.

That's a good point, but I'm not totally sure how true it is.  Anything under 6 million Gs will probably fail.  And that includes the parts adjacent to the impact.  Those pull off, and go spinning through the ship sowing destruction, but also sharply increasing the momentum transfer time.  On the other hand, it's a good reason not to use armor.  On the gripping hand, 30 tons is very, very big for an antiship weapon under these circumstances,

Normal planetary velocities are under 50 km/s.  And asteroid strikes and such are probably at a velocity that is lower since the object is usually moving in a spiral rather than directly inwards and it becomes a case of relative velocity (which can make it worse for head on collisions).

For a working newtonian motion system you probably could look at the game "Attack Vector: Tactical" by Ad Astra.  They have a set of full newtonian rules.

Asteroid strikes generally are under 50 km/s, but so is everything else.  I'm sure I could find a velocity distribution if I really wanted to, but those operate in an entirely different realm.
And I own a copy of AV:T.

[jseah]

I posted a thread about this particular problem on XKCD fictional science. 

Wardraft's post there includes some lower bound estimates on how much the projectile would expand outwards (5tons at 60kkm/s relative)

http://forums.xkcd.com/viewtopic.php?f=59&t=80213#p2888555

Obviously, his estimates are riddled with assumptions but he errs on the side of greater penetration so the projectile ought to explode somewhere above where he puts it. 
The conclusion is that the projectile will not reach the surface. 

Is there any kind of test on how high-altitude nuke-like explosions work?  Especially focusing on how the shockwave propagates downwards?

[bean (OP)]

Nothing on this scale.  None of the nuclear weapons tests that I know of were at the right size and altitude.  Only a few were high-altitude, and those were too high.  I'm looking up more data. 
The analysis you posted agrees with my gut.  It's simply not going to reach the ground.  I need to figure out how the expansion rate would be calculated.  Someone around here has to know.

[sublight]

My gut ration is to agree that the missile won't reach the ground, but if the expansion rate was limited by the speed of sound then a heavy enough missile could actually do it.

The speed of sound in a solid seems to range from 3,000 m/s to 5,000 m/s. A 30 ton missile (50% fuel mass burned to accelerate) has a target cross section radius of 2.78 m.

To figure out what would happen if this 0.1c missile broke up at 90 km and was limited to a 4 km/s expansion rate, I dumped the problem into a spread sheet for a discrete method solution with 5-10km steps. The resulting mass didn't slow to less than the expansion rate until 2km above sea level. If it had hit a 6 km tall mountain, it would have been a 138m radius mass of mostly supper heated compressed air moving at 29 km/s with 0.1% of the original kinetic energy (6.5PJ)

A slower expansion rate would have hit the ground. A faster expansion rate or earlier break up wouldn't hit any mountains.

If anyone wants a planet killer, they'll probably need the mass and momentum of an entire suicide-ship, and not just a fast missile.


I can't remember seeing anyone's math on structural acceleration-related failure, so for what they're worth here are my "yes, it will pancake" calculations.
Acceleration = F/m. Force/area = stress. mass=density*volume. Max_Accell = Ultimate_Stress/(density*length)
Also
Acceleration = ?V/?T. ?V = V*?m/mass -> accell = V*m'/mass. m'=area*air_density*speed, so A=V^2/(density*length)
Equate the two accelerations, material density and length cancel, and Vmax = sqrt(ultimate_stress/air_density)
A strong solid metal alloy (400 MPa) vs 1g/m3 air will squash itself at anything above 633 km/s even without the help of heating. A trans-Newtonian alloys sold slug 25x stronger will shatter against the atmosphere at impacts over 3200 km/s.

[bean (OP)]

I'm going to try to get a better handle on the expansion speed, or at least the speed of sound.  First off, I'm using c=sqrt(1.6667 R*T /M).  Now, for the first instant.  Assuming that all of the iron is instantly converted to plasma, and assuming the xkcd numbers and all of the energy dumped into the iron particles as kinetic energy, the temperature should be 4.8e6 K.  Assuming all of that, the speed of sound comes out to 34,660 m/s.  I have no doubt that the above analysis is riddled with errors, but it should be accurate to within a factor of two or so (I hope).  I'm not sure how it would change with time.  As the projectile slows, it picks up particles, but releases energy.  After the next 10 km (using his numbers), and hoping I've done the math correctly, it should have a speed of sound of somewhere between 1,964 km/s (density of iron) and 1,389 km/s (half the density of iron).  Based on that, I think the expansion will be significantly faster then previously expected, at least at first.
Oh, and I did the acceleration-related failure earlier in the thread.  I can up with something around (I think) 2 TPa at 50 km for .2 c, which will pulverize anything, regardless of heating.

Edit:
Looking more at high-altitude nukes, I'm starting to think that, for smaller objects, the fireball might well be the biggest contributor to damage.  It's going to be very, very hot, and radiation from that will start fires and such.  The blast wave from all of the various high-altitude tests appears to have been negligible.  None of them were in the same region as we're looking at.  The closest were Hardtack Oak, Orange, and Yucca.

[jseah]

Bluegill Triple Prime was 410kt at 48km altitude.  Caused retinal burns on 2 unshielded workers. 
And that Orange event you mentioned was 3.8mt at 43km altitude, producing 3 cal/cm^2 thermal radiation at ground zero. 

Source: (search for Wednesday, March 29, 2006)
http://glasstone.blogspot.com/2006/03/checkmate-detonation-as-seen-from.html

Doesn't tell you much though.  You can't just simply scale it up to the hundred megaton range that would be expected of most anti-planet kinetic weapons.  Atmospheric absorption is certainly going to be different at the kind of temperatures a kilocal/cm^2 radiation level would cause

[bean (OP)]

Bluegill Triple Prime was 410kt at 48km altitude.  Caused retinal burns on 2 unshielded workers. 
And that Orange event you mentioned was 3.8mt at 43km altitude, producing 3 cal/cm^2 thermal radiation at ground zero. 

Source: (search for Wednesday, March 29, 2006)
http://glasstone.blogspot.com/2006/03/checkmate-detonation-as-seen-from.html

Doesn't tell you much though.  You can't just simply scale it up to the hundred megaton range that would be expected of most anti-planet kinetic weapons.  Atmospheric absorption is certainly going to be different at the kind of temperatures a kilocal/cm^2 radiation level would cause

Oops, I guess I missed that one.  However, I'm not certain that atmospheric absorption will be all that different.  Why would it be?  For one thing, the overall situation is similar, and we have data on propagation of those sorts of flux.  It's just from bombs closer to the ground.  Secondly, for all intents and purposes the atmosphere is transparent at the frequencies in question.  Yes, they might not propagate perfectly, but this isn't a laser.

[jseah]

But that much energy being dumped might cause the air to breakdown into plasma, ala laser blooming effect.  's why anti-ship lasers don't work against planets, even if the frequency was changed to microwaves. 

Oh but then again...

Nvm, found a neat source:
http://nuclearweaponarchive.org/Nwfaq/Nfaq5.html

Haven't read it all, but it might appear that getting these bits:
- the size of the shockwave when at 5psi as a function of yield
- % energy in thermal radiation and length of pulse (to calculate wattage per cm^2 at specific ranges)

And then back calculating the yield (and hence KE) of the kinetic missile to get the minimum parameters for:
1) Thermal energy under impact site to destroy wood/concrete/iron
2) Shockwave to reach ground

Would go a long way to estimating the relative damage of kinetic missiles.  Assuming we can take a burst height of ~50km?

EDIT:
Found this under 5.6.1.1 Thermal Injury:

Convenient scaling laws to allow calculation of burn effects for any yield are:
r_thermal_1st = Y^0.38 * 1.20
r_thermal_2nd = Y^0.40 * 0.87
r_thermal_3rd = Y^0.41 * 0.67
Range is in km, yield is in kt; the equations are accurate to within 10% or so from 1 kt to 20 Mt.

[bean (OP)]

Maybe.  However, I'm fairly certain that any equation that gives you pressure as a function of burst radius or vice versa will assume that both are at or near sea level unless it mentions otherwise.
For an authoritative source on the subject, try: http://www.fourmilab.ch/etexts/www/effects/.

[Beersatron]

How does the http://en.wikipedia.org/wiki/Tunguska_event relate to your calculations? (directed to everybody)

I realize it was most likely going slower than the kind of projectiles you folks are talking about, but if it really was only tens of meters across then my thought would be to just drop a smeg ton of them out of a ship and then let gravity do the rest. Obviously the slower the object the easier it is to intercept, but dumping a couple hundred of them could start to get dicey for the defenders, no?

I am not a mathematician, so feel free to tell me I am orders of magnitude outisde the conversation

[bean (OP)]

How does the http://en.wikipedia.org/wiki/Tunguska_event relate to your calculations? (directed to everybody)

I realize it was most likely going slower than the kind of projectiles you folks are talking about, but if it really was only tens of meters across then my thought would be to just drop a smeg ton of them out of a ship and then let gravity do the rest. Obviously the slower the object the easier it is to intercept, but dumping a couple hundred of them could start to get dicey for the defenders, no?

I am not a mathematician, so feel free to tell me I am orders of magnitude outisde the conversation

Pretty much.

Nobody is claiming that Tunguska-type weapons are useless.  The current discussion is about objects going three orders of magnitude faster, which puts them in an entirely different range of energies, which leads to different altitudes and burst effects.  However, if you just want to flatten an area, a nuke is easier and cheaper then moving a few hundred or thousand tons of rock.  (Yes, I understand about sorium's energy density.  The problem is how deep and fast you can get something without it blowing up.  And moving asteroids is very difficult.  Someone posted "rocks are not free, citizen" early in the main thread.)  And remember that a few tens of meters may not sound like much, but given that volume is equal to length cubed, and we're dealing with something more dense then water, it adds up fast.

[UnLimiTeD]

I'd just dump a tanker in the atmosphere and let it rain fire.^^
Psych ftw. 

As a more serious question, what would a "Planetkiller" weapon try to achieve?
Deal serious damage on the ground?
Kill the Atmosphere?
Kill all inhabitants?
Or actually damaging the planet?

[procyon]

As a more serious question, what would a "Planetkiller" weapon try to achieve?
Deal serious damage on the ground?
Kill the Atmosphere?
Kill all inhabitants?
Or actually damaging the planet?

Guess it would depend on your goals.  And how much you were willing to invest in 'rebuilding' or if you were willing to write it off for the safety of your race.

If the race isn't a major threat, damaging them enough that they have no ability to resist you would be enough.

If they could push you into extinction, then you had better beat them to the punch.

On the thought of killing a planet...I doubt the game has ever even addressed what it would take to be a 'crust buster' or such.  Rendering orbital bodies into debris is a pretty tall order....