Author Topic: Impact Physics  (Read 7943 times)

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Offline sublight

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Re: Impact Physics
« Reply #120 on: November 14, 2012, 07:27:50 AM »
Nice to see this thread's final conclusion receive 3rd party confirmation from xkcd.

A 100ft diamater diamond would mass roughly 50kTons. Six posts ago jseah speculated that 10kTons moving at 0.33c would be needed to crack the crust. If the Xkcd numbers are good, then cracking planets is even harder than our dreadnought-sized missile assumptions.
 

Offline Paul M

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Re: Impact Physics
« Reply #121 on: November 14, 2012, 08:03:28 AM »
Kinetic kill weapons are as precise as the delivery mechanism.  You can use them at the level of taking out a city or removing an artillary position.  Brute force weapons such as asteroids are different matters but kinetic rods, or webs don't need to be all that large as the kinetic energy causes shock waves to radiate outwards.

The weapon speeds used in bog standard aurora don't need warheads the shock from one of them impacting on a ship would cause it to crumple and kill every living thing on it from blunt force trauma as they get hurled around inside.

Lets do the mass for the diamond:  100 ft = 30 m = 15 m radius volume = 14100 m3.  density is 3.5 g/cm3 or 3.5x10^3 kg/m3 mass = 49.4x10^6 kg.

At 0.01c we can ignore relativity and taking mass of planet as earth's mass you have a resulting velocity change of 3E6 m/s *49.4E6/6E24 = 24E-12 m/s (so the planet barely noticed this impact).  The K.E. is 9E12*25E6 or 1725E18 joules.  This is 1725 Gigaton's worth of explosive force.  However I found a nice web site the covered this and basically the results for 3,000 km/s impact as a non event at 1000 km from ground 0 since they think the object will break up in the air at a high altitude.

As a comparison a 1 km diameter iron asteroid at 17 km/s...  1000 m = 500 m radius volume = 522x10^6 m3 density of iron is 8000 kg/m3 giving a mass of 4176x10^9 kg.  negligable velocity change from impact.  The K.E. is 290x10^6*2075x10^9 = 6x10^20 J or about 1/3 of the above.  The effect on the earth would be significantly more castrophic as the object would strike the earth not break up in the air.

At .99c we get a resulting mass of the diamond projectile of 49.4x10^6*SQRT(1/1-(.99)^2)) or 350x10^6 kg.  Not quite enough to do to anything to the earths orbit as the momentum is only 10x10^16 so a change in the earths velocity of 10^-8 m/s...still the K.E. is 175E6*3E16 or 5E24 J (basicialy 5 million gigatons) and that is...well pretty impressive.  Assuming it can impact on the planet anyway.  Lets take 0.9 kJ/kg-K and see what the means...5E21J/(6E24*0.9) = an overall temperture rise of the planet by 0.001 K.  Lets consider instead 100 m diameter x 1000 m of rock (density 5.52x10^3 kg/m^3) = 43x10^9 kg of rock....so 5E21/(43E9*0.9) = well ok...that will certainly penetrate the crust.  After that I imagine half the planet becomes unlivable rather fast.  The object is moving to fast to fragment in the atmosphere I'd think so its energy loss there will likely be rather small.  The planet itself though is going to be there..probably with a new axial tilt and a lot of siesmic activity.

Consider also just for fun the impact of a 1000 kg missile moving at 6000 km/s on a 6000 tonne ship at rest.  The ship's new velocity would be 6000 km/s*1000 kg/(6000*1000)kg = 1 km/s assume this occurs in 10 ms.  The acceleration of the ship is 1000 m/s/0.01 s or 100,000 m/s^2 or 10,000 G.  The ship crumples around the impact point, and the crew is dead.  Warheads are pointless at these sort of velocities.
 

Offline swarm_sadist

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Re: Impact Physics
« Reply #122 on: November 14, 2012, 10:16:51 AM »
Just thinking of some ways to counter long range mass driver attacks while I wait. Some attributes of mass drivers:
-They need a large 'runway' to get moving
-It's target is fairly small
-A larger rock has more volume to burn than surface area to burn
-At very high speeds, p->kE

I notice:
-That a rock can be intercepted as it's accelerating, due to the large thermal signal it would generate
-That, if broken into smaller pieces, a rock is easier to both vaporize and move
-A tug could alter the course of even the most massive rocks at quite a distance
-Because mass approaches infinity near light, destroying mass is just as effective at reducing kE
-Even a slight deviation from course will cause a miss if far enough away
 

Offline byron

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Re: Impact Physics
« Reply #123 on: November 14, 2012, 11:31:23 AM »
Kinetic kill weapons are as precise as the delivery mechanism.  You can use them at the level of taking out a city or removing an artillary position.  Brute force weapons such as asteroids are different matters but kinetic rods, or webs don't need to be all that large as the kinetic energy causes shock waves to radiate outwards.
No, there is a limit on the minimum size of kinetic projectiles.  They have to be long enough to penetrate the atmosphere, and the diameter is set by the structural requirements of the projectile.  Also, the damage of a kinetic depends on its shape.  A long-rod will do most of its damage to what it hits, not to the surrounding area.  To get area damage, the projectile needs to have about the same length and width, which in turn drives mass up significantly.  The minimum size for such a projectile is likely to be about 20 tons.  Or you could break up the projectile above the surface, which would produce a fireball and shockwave.
Also, the projectile can't have terminal guidance, unless it dumps a lot of energy so that the plasma sheath goes away.

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The weapon speeds used in bog standard aurora don't need warheads the shock from one of them impacting on a ship would cause it to crumple and kill every living thing on it from blunt force trauma as they get hurled around inside.
No, it wouldn't.  The material they hit would shear off, and the projectile would probably go straight through.  Most of the damage would be from the ship's structure bouncing around.  This is not an inelastic collision by any stretch of the imagination.

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Consider also just for fun the impact of a 1000 kg missile moving at 6000 km/s on a 6000 tonne ship at rest.  The ship's new velocity would be 6000 km/s*1000 kg/(6000*1000)kg = 1 km/s assume this occurs in 10 ms.  The acceleration of the ship is 1000 m/s/0.01 s or 100,000 m/s^2 or 10,000 G.  The ship crumples around the impact point, and the crew is dead.  Warheads are pointless at these sort of velocities.
Warheads are pointless, but not because they turn the crew into jelly.  Think about it.  If the ship is designed to stand maybe 10Gs of acceleration, anything substantially above that will cause the structure to fail.  The vessel would still be dead because of spalling, but that's not the point.
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Offline Paul M

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Re: Impact Physics
« Reply #124 on: November 14, 2012, 01:29:46 PM »
If the rod is designed to punch through the atmosphere and can survive the heat of re-entry it does not need to be 20 tons.  And impacting at hypersonic speed it will make a nice hole in the ground.  20 tons is absurdly high.  There is no physical reason for such a number.  We aren't talking about an arbitrary potatoe shaped object striking the atmosphere but a guided projectile.  Most of the energy is lost in the atmosphere and the end velocity of the projectiles is low, the less energy you give to the atmosphere (a more direct approach, a better areodynamic shape) the higher the impact velocity the lower the mass needs to be.  What it has to do is not disintigrate in the upper atmosphere like most meteors do.

The material of the missile would vaporize on impact at those speeds, the plasma shock front of that would expand through the ship and tear it appart even if only a fraction of the momentum (1-10%) is transfered.  Thousand of KPS you don't gain by a warhead.  It doesn't need to be perfectly in-elastic since the ship is going to crumple around that impact point anyway, even if the plasma ball that used to be a missile punches through it the ship will be rendered mission killed since every human onboard will be reduced to so much thin paste.  Getting slamed into a wall at 100G isn't something you survive.  The point is putting a fusion bomb on a kinetic weapon moving at thousands of KPS is needless.  At those speeds you don't get spalling, or anything...6000 kps is 6,000,000 m/s that goes through a 100 m of ship in tens of microseconds.  Nothing can move out of the way of that, that is faster than the scale at which molecules move.  It might even be energetic enough to exceed the columb barrier but that is more akin to a particle beam hitting a material objec then what is normally considered an impact of two physical objects.
 

Offline sublight

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Re: Impact Physics
« Reply #125 on: November 14, 2012, 02:42:17 PM »
The classic weaponized long rod is designed for relatively low retry speeds, astronomically speaking. Say, 10 km/s. Add a couple zeros, and the mechanical forces of atmospheric deceleration will lead to structural failure in even a sold metal object. Once breakup starts retry heating adds insult to injury and transforms the object into an expanding ball of plasma. 20 tons at 10 km/s might hit the ground depending on shape and composition. 20 tons at 1,000 km/s won't.


I think Byron's point on jellifying the crew isn't that crew won't be jelly but rather that an impact that large is overkill since the ship could be broken apart by an impact an order of magnitude smaller.
 

Offline byron

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Re: Impact Physics
« Reply #126 on: November 14, 2012, 04:52:49 PM »
If the rod is designed to punch through the atmosphere and can survive the heat of re-entry it does not need to be 20 tons.
Yes.  If it's a rod.  I was speaking of a projectile designed to make a crater and do surface damage.  Which has to be about the same in length and width.

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And impacting at hypersonic speed it will make a nice hole in the ground.
A rod will do little else.

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20 tons is absurdly high.  There is no physical reason for such a number.
It is somewhat high.  I made a mistake, and the actual number is more like 2.1 tons for tungsten.  It will be higher for other objects.
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We aren't talking about an arbitrary potatoe shaped object striking the atmosphere but a guided projectile.  Most of the energy is lost in the atmosphere and the end velocity of the projectiles is low, the less energy you give to the atmosphere (a more direct approach, a better areodynamic shape) the higher the impact velocity the lower the mass needs to be.  What it has to do is not disintigrate in the upper atmosphere like most meteors do.
Please do not lecture me on atmospheric entry and hypervelocity impact physics.  I've read far more about it that you have.  I know this because what you keep saying is wrong.  And I'm also willing to share the source of my insights.  For a basic background, check out Space Weapons, Earth wars. http://www.rand.org/pubs/monograph_reports/MR1209.html


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The material of the missile would vaporize on impact at those speeds, the plasma shock front of that would expand through the ship and tear it appart even if only a fraction of the momentum (1-10%) is transfered.  Thousand of KPS you don't gain by a warhead.
That's pretty much what I've been saying, although I think you vastly overestimate the amount of momentum transferred.  Stuff will break before it passes much on, and become part of the shrapnel cloud. 

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It doesn't need to be perfectly in-elastic since the ship is going to crumple around that impact point anyway, even if the plasma ball that used to be a missile punches through it the ship will be rendered mission killed since every human onboard will be reduced to so much thin paste.  Getting slamed into a wall at 100G isn't something you survive.
 
You've been doing the math as if the collision was perfectly inelastic (the objects stuck together).
But you still are ignoring my arguments as to why the momentum transfer won't kill the ship.  So I'll lay them out simply. 
First, the projectiles you keep using are ludicrously large compared to the target ship, particularly given their speed.  An Iowa-class was 33,333 times the size of its projectile at light load. 
Second, the ship's structure will not be able to take the forces involved in 100G acceleration.  The structure might be rated for 10G, but that's only from the engine.  From any other direction, it will fail under much lower loads.  The area that gets hit will behave more or less as a liquid, rip free very close to the projectile and turn into shrapnel (which is what I meant when I referred to spalling.)  The total momentum transferred to the rest of the ship will be minor.  The same goes for any other bulkheads it hits along the way, and the projectile goes out the other side as a cloud of plasma. 

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The point is putting a fusion bomb on a kinetic weapon moving at thousands of KPS is needless.  At those speeds you don't get spalling, or anything...6000 kps is 6,000,000 m/s that goes through a 100 m of ship in tens of microseconds.  Nothing can move out of the way of that, that is faster than the scale at which molecules move.  It might even be energetic enough to exceed the columb barrier but that is more akin to a particle beam hitting a material objec then what is normally considered an impact of two physical objects.
Not even close.  Particle beams operate close to c, which is 300,000 kps.  You're still a long way short of that.
And again, look at what happens here.  Force is equal to the change in momentum (impulse) times the change in time.  The time is very small (.000017 seconds).  The impulse available is simply too small to have a serious effect on the motion of either the projectile or the ship.  So no jelly.  Burned and lacerated humans, but not jellied.
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