Author Topic: Impact Physics  (Read 9343 times)

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Offline byron

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Impact Physics
« on: January 26, 2012, 04:59:22 PM »
I met with Dr. Schonberg today, and learned the following:
First, we have very little data on long rods (which I presume NA is using) at anything above ordnance velocities.  This is for two reasons.  First, it's difficult to run those tests.  Second, nobody is launching long rods, and the chances of an object randomly functioning as one are very low.
That said, a couple things to add to the standard wisdom of atomic rockets.
While a projectile hitting a whipple shield will fragment, unshocked projectile will remain unitary and continue to penetrate.  Long rods thus could go through multiple compartments, shedding length each time and destroying whatever is inside.
At velocities above about 30 km/s, the projectile begins to turn to plasma after impact.  This could decrease penetration, as the plasma cloud will hit over a much larger area then a fragment of a projectile.  This would tend to reduce penetration at these velocities, provided sufficient standoff is allowed.  What that is, I don't know.  Armor is effective against the plasma cloud.  However, the same thing that was mentioned above could also occur, with multiple compartments penetrated.
To achieve either of the above, the long rod must hit straight on.  Otherwise, the entire thing will disintegrate on the whipple shield.
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Offline Mel Vixen

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Re: Impact Physics
« Reply #1 on: January 26, 2012, 10:17:39 PM »
Quote
First, we have very little data on long rods (which I presume NA is using) at anything above ordnance velocities.  This is for two reasons.  First, it's difficult to run those tests.  Second, nobody is launching long rods, and the chances of an object randomly functioning as one are very low.

There is only one way to find out! Just donate me half a billion Dollars on my paypal account and ...

In all seriousness now isnt there some kind of Simulation-software for this kind of stuff? I know that some meteor-simulators allow to choose a form but i guess thats not compare-able.
I am not really convinced that Steves Railguns use Javelin like ordinance.

 ^^ maybe someone has contacts to the US Navy could get the info - after all they are building that Railgun prototypes for years now.
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Offline byron

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Re: Impact Physics
« Reply #2 on: January 27, 2012, 12:00:06 AM »
There is only one way to find out! Just donate me half a billion Dollars on my paypal account and ...

In all seriousness now isnt there some kind of Simulation-software for this kind of stuff? I know that some meteor-simulators allow to choose a form but i guess thats not compare-able.
I am not really convinced that Steves Railguns use Javelin like ordinance.

 ^^ maybe someone has contacts to the US Navy could get the info - after all they are building that Railgun prototypes for years now.
That's not the problem.  The thing is that there is just no data to plug into the models.  The Navy's railgun works at Mach 4-6, while we're talking Mach 25 and up.  It's a completely different physical realm.  And no, a meteor sim is not going to work.
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Offline UnLimiTeD

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Re: Impact Physics
« Reply #3 on: January 27, 2012, 06:14:50 AM »
So, the interesting question remaining is:
How much will turning into plasma decrease the effective velocity of the projectile?
Because the impact speeds are more likely to be in the range of 100km/s, so we can expect that to happen often.
Will it expand spherical? Aka, half the projectile will slow down significantly?
Will it disintegrate from front to back, thus significantly slowing down the rest of the matter?
We don't know.
 

Offline byron

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Re: Impact Physics
« Reply #4 on: January 27, 2012, 07:49:28 AM »
So, the interesting question remaining is:
How much will turning into plasma decrease the effective velocity of the projectile?
Because the impact speeds are more likely to be in the range of 100km/s, so we can expect that to happen often.
Will it expand spherical? Aka, half the projectile will slow down significantly?
Will it disintegrate from front to back, thus significantly slowing down the rest of the matter?
We don't know.
Not that much.  Plasma is what happens when the front of the projectile is under a couple hundred gigapascals or more that then go away.
No, because momentum is conserved, most of it will go into the ship.  I'm not sure what the random velocity in plasma is, but it's not that high.
I think that it will not slow down the back significantly.  The pressures involved are too high for the material to withstand as a solid, so the back section will probably be largely unaffected.
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Online Steve Walmsley

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Re: Impact Physics
« Reply #5 on: January 27, 2012, 11:17:28 AM »
I haven't rally given much thought to the projectile shape. I assumed something like those fired by the US Navy Railgun, or a modern day APDS round

Steve
 

Offline Mel Vixen

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Re: Impact Physics
« Reply #6 on: January 27, 2012, 11:46:39 AM »
Well one can make some assumptions right? You [edit: i mean byron] say at high enough velocities our projectile turns to plasma, wouldnt that have a initial damage-profile compare-able to a very intense laserpulse due to the energy imparted on projectile and targed? Iirc some kind of Shockwave traveling through the matter or something?
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Offline fcharton

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Re: Impact Physics
« Reply #7 on: January 27, 2012, 12:12:56 PM »
If the projectile turns to plasma, then you could consider that most of its kinetic energy is turned into heat and consider most/all damage results from two causes : electromagnetic shock and heatwave.

I'm not sure how one would calculate the electromagnetic shock, but we discussed the heat aspect with Yonder in the NA thread. Assuming a specific heat for the projectile and a speed will provide an impact temperature. Heat transfer equations would then define an expanding sphere of decreasing temperature, which, if you cut it to some "tolerable level" would sort of define the radius of the "hole" the projectile would melt in the ship.

This said, I wonder whether the "turn into plasma over 30 km/s" rule applies in space. Air friction, and pressure, play a considerable role in heating fast moving objects. Would the same happen in space?

Francois
 

Offline byron

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Re: Impact Physics
« Reply #8 on: January 27, 2012, 01:21:06 PM »
If the projectile turns to plasma, then you could consider that most of its kinetic energy is turned into heat and consider most/all damage results from two causes : electromagnetic shock and heatwave.

I'm not sure how one would calculate the electromagnetic shock, but we discussed the heat aspect with Yonder in the NA thread. Assuming a specific heat for the projectile and a speed will provide an impact temperature. Heat transfer equations would then define an expanding sphere of decreasing temperature, which, if you cut it to some "tolerable level" would sort of define the radius of the "hole" the projectile would melt in the ship.
Yes and no.  The projectile is likely to turn into plasma on the whipple shield, which would reduce damage because the plasma would spread out before it hit the main armor.  I think that the remaining momentum of the plasma and fragments would do the most damage, not heat transfer.  Also, specific heat is not constant for a situation like this.

Quote
This said, I wonder whether the "turn into plasma over 30 km/s" rule applies in space. Air friction, and pressure, play a considerable role in heating fast moving objects. Would the same happen in space?

Francois
Absolutely.  The plasma is not due to atmospheric heating.  It's what happens when something is under pressure in the gigapascal-terapascal range that then gets released.

Well one can make some assumptions right? You [edit: i mean byron] say at high enough velocities our projectile turns to plasma, wouldnt that have a initial damage-profile compare-able to a very intense laserpulse due to the energy imparted on projectile and targed? Iirc some kind of Shockwave traveling through the matter or something?

Maybe.  The problem is that the plasma is produced at the whipple shield, then expands to hit the hull itself.  So it's less like a laser pulse, and more like a conventional explosion.

I haven't rally given much thought to the projectile shape. I assumed something like those fired by the US Navy Railgun, or a modern day APDS round

Steve
That would be a long rod.  As an addendum, the projectile virtually has to be guided.  If it doesn't hit straight on, then it loses most of its penetration.
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Offline fcharton

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Re: Impact Physics
« Reply #9 on: January 27, 2012, 02:04:41 PM »
Hi Byron

The projectile is likely to turn into plasma on the whipple shield, which would reduce damage because the plasma would spread out before it hit the main armor.  I think that the remaining momentum of the plasma and fragments would do the most damage, not heat transfer.  Also, specific heat is not constant for a situation like this.

How would the whipple shield work, then? I mean, for what I understand, modern day shields work for very light objects, with speeds in the tens of km per second. We're talking here of something weighing about a kilogram, colliding at a speed ranging from 100 to 1000 km/s.

At 100km/s, energy is 5 GJ, at 100, 500 GJ. Which means even if one percent of energy turns into heat, we get temperatures around a hundred of thousand kelvins, probably even millions for the faster projectiles... Wouldn't the whipple shield need to be very far from the ship to protect it from this kind of thermal shock?

I was asking that because it seems to me that over a certain energy, radiation output dominates (because its strength increases as a large power of the temperature, fourth if memory serves, and because it moves at lightspeed).

I might also be totally wrong (this wouldn't be the first time).

Francois
 

Offline Sudragon2k3

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Re: Impact Physics
« Reply #10 on: January 28, 2012, 05:36:55 AM »
If I may cite research done by MIT in to a similar problem?

from http://www.mit.edu/people/daveg/Humor/ravioli_as_gas

> There was still one aspect of the whole concept of a ravioli-loaded
> railgun type wepon which we, lolling about late on a weeknight, with
> only a few neurons randomly firing, could not resolve.  Would a chunk
> of metal (can of ravioli) impacting another, larger, rest mass
> structure (star destroyer) produce an "explosion" effect, or simply
> punch an appropriately shaped hole as it passed through?  Bill?

What am I, the neighborhood blast physicist???  Well, maybe... :-)

It all depends on speed of impact versus the speed of sound in the target
(what is called the Mach number, where Mach 1 means the speed of sound,
Mach 2 is twice the speed of sound, etc), and the speed of the ravioli
versus the speed of light in the target (which I'll call the Cerenkov
number, where Cerenkov 1 is the speed of light in anything; Cerenkov 1.3
is the speed of high-energy protons in a water-cooled reactor (that's why
you get that nifty blue glow), and you can get up to Cerenkov 2.4 using
diamonds and nuclear accellerators.  In the late 40's people used to talk
about Cerenkov numbers, but they don't anymore.  Pity.).  Lastly, there's
the ravioli velocity expressed as a fraction of the speed of light in a
vacuum (that is, as a fraction of "c").  "C" velocities are always between
0 and 1.

At low speeds (REAL low) the ravioli will simply flow over the surface,
yielding a space-cruiser with a distinctly Italian paint job.

Faster (still well below speed-of-sound in the target) the metal of the
space-cruiser's skin will distort downward, making what we Boston drivers
call a "small dent".

Faster still, you may have a "big dent" or maybe even a "big dent with a
hole in the middle", caused by the ravioli having enough energy to push
the dent through, stretching and thinning the hull metal till the metal
finally tears in the middle of the dent.

Getting up past Mach 1 (say, 5000 feet/sec for steel), you start to get
punch-a-hole-shaped-like-the-object effects, because the metal is being
asked to move faster than the binding forces in the object can propagate
the "HEY!  MOVE!" information.  (After all, sound is just the binding
forces between atoms in a material moving the adjacent atoms -- and the
speed of sound is how fast the message to "move" can propagate.)  From
this, we see that WileE Coyote often reached far-supersonic speeds because
he often punched silhouette-type holes in rocks, cliffs, trucks, etc.

Around Mach 4 or so, another phenomenon starts -- compressive heating.
This is where the leading edge of the ravioli actually starts being heated
by compression (remember PV=nRT, the ideal gas law?)  Well, ravioli isn't
a gas, but under enough pressure, ravioli behaves as a gas.  It is
compressed at the instant of impact and gets hot -- very hot.  Likewise,
the impact point on the hull is compressed and gets hot.  Both turn to
gasses -- real gasses, glowing-white-hot gasses.  The gasses expand
spherically, causing crater-like effects, including a raised rim and a
basically parabolic shape.  In the center of the crater, some material is
vaporized, then there's a melt zone, then a larger "bent" zone, and the
raised rim is caused because the gas expansion bubble center point (the
bending force) is actually *inside* the hull plate.  If the hull plate
isn't thick enough, then the gas-expansion bubble pushes through to the
other side, and you get a structural breach event (technically speaking,
a "big hole") in the side of the space-cruiser.

Compressive heating really hits the stride up around 20,000 feet/sec (Mach
4 in steel, Mach 15 in air) and continues as a major factor all the way
up to the high fractional Cerenkov speeds, where nuclear forces begin to
take effect.

Aside: the "re-entry friction heating" that spacecraft endure when the
reenter the atmosphere is NOT friction.  It's really compressive heating
of the air in the path.  As long as the spacecraft is faster than Mach 1,
the air can't know to get out of the way, so it bunches up in front of
the spacecraft.  When you squeeze any gas, it gets hot.  So, the glowing
"reentry gas" is really just squeezed air, which heats the spacecraft heat
shield by conduction and infrared.  The hypersonic ravioli can be expected
to behave similarly.

As we increase speed from the high Mach numbers (about 10 miles/sec) all
the way up to about 150,000 miles/sec, not much different happens except
that the amount of kinetic energy (which turns into compressive heat)
increases.  This is a huge range of velocity, but it's uninteresting
velocity.

At high fractional Cerenkov speeds, the ravioli is now beginning to travel
at relativistic velocities.  Among other things, this means that the
ravioli is aging more slowly than usual, and the ravioli can looks
compressed in the direction of travel.  But that's really not important
right now.

As we pass Cerenkov 1.0 in the target, we get a new phenomenon -- Cerenkov
radiation.  This is that distinctive blue glow seen around water-cooled
reactors.  It's just (relatively) harmless light (harmless compared to
the other blast effects, that is).  I mention it only because it's so
nifty...

At around .9 c (Cerenkov 1.1) , the ravioli starts to perceptibly weigh
more.  It's just a relativistic mass increase -- all the additional weight
is actually energy, available to do compressive heating upon impact.  The
extra weight is converted to heat energy according to the equation E=mc^2;
it looks like compressive heating but it's not.

[Here's where I'm a little hazy on the numbers; I'm at work and
 don't have time to rederive the Lorentz transformations.]

At around .985 c (Cerenkov 1.2 or so), the ravioli now weighs twice what
it used to weigh. For a one pound can, that's two pounds... or about sixty
megatons of excess energy.  All of it turns to heat on impact.  Probably
very little is left of the space-cruiser.

At around .998 c, the impacting ravioli begins to behave less like ravioli
and more like an extremely intense radiation beam.  Protons in the water
of the ravioli begin to successfully penetrate the nuclei of the hull
metal.  Thermonuclear interactions, such as hydrogen fusion, may take
place in the tomato sauce.

At around .9998 c, the ravioli radiation beam is still wimpy as far as
nuclear accellerator energy is concerned, but because there is so much of
it, we can expect a truly powerful blast of mixed radiation coming out of
the impact site.  Radiation, not mechanical blast, may become the largest
hazard to any surviving crew members.

At around .9999999 c, the ravioli radiation may begin to produce
"interesting" nuclear particles and events (heavy, short-lived particles).

At around .999999999999 c, the ravioli impact site may begin to resemble
conditions in the original "big bang"; equilibrium between matter and
energy; free pair production; antimatter and matter coexisting in
equilibrium with a very intense gamma-ray flux, etc.[1]

Past that, who knows?  It may be possible to generate quantum black holes
given a sufficiently high velocity can of ravioli.

     --Bill

[1]According to physicist W. Murray, we may also expect raining frogs,
   plagues of locusts, cats and dogs living together, real Old Testament
   destruction.  You get the idea...
 

Offline UnLimiTeD

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Re: Impact Physics
« Reply #11 on: January 28, 2012, 09:12:14 AM »
Very useful post. Damn, I'd like some ravioli right now.
Sadly not happening.
 

Offline sublight

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Re: Impact Physics
« Reply #12 on: January 28, 2012, 10:39:35 AM »
Very interesting, very informative, but still not a whole lot I can see as usefull for Newtonian Aurora.
A much simplified explanation: At hypervelocity speeds material strength becomes negligible, so only density, distance, and energy need be considered.

According to one approximate equation I found, penetration depth is proportional to the projectile length time the square root of the density ratios.

I'd hypothesize that a whipple shield functions by creating a composite 'material' of greater thickness at lower densities. So, spreading the same material across a greater thickness gives more protection per mass: very important in space.

As further hypothetical musings, lets consider Mr. Satellite with 3mm aluminum shielding, and 2mm Mr. Iron Splinter. Mr. Satellite and Mr. Iron meet at orbital velocity (say, 7,000 m/s.) 2mm * (7.86g/cm / 2.7g/cm)^.5 = 3.41 mm penetration. Since the impact energy, comparable to a .45 handgun round, hasn't vanished, the remaining energy might be modeled as a small 1 kJ explosion at that depth. This could be BAD since it is now on the wrong side of the shielding with vital circuitry.

However, if Mr. Satellite has 1mm aluminum shell plus 10 mm thick whipple shielding with 2mm equivalent thickness aluminum, then the penetration is 2mm * (7.86g/cm3 / 0.54g/cm3)^.5 = 7.86 mm. The resulting impact detonation now occurs inside the whipple shielding and outside the inner hull.

I'm sure real life whipple shielding is even more effective, but this might be simple enough to start building a Newtonian Aurora approximation.

Considering the 1kg 4800 MJ railgun: if it was an 8.9 g/cm3 copper sphere then it will be about 6cm in diameter, with an average thickness of 4cm any way it impacts.

The Emperial Ship Luckless has 5cm High Density Duranium Armor. According to the rules section, this absorbs 80MJ/cm and has 1g/cm3 density. The Railgun round has a maximum penetration of 4cm *(8.9/1)^.5 = 11.9 cm. Unfortunately, the luckless only has 5cm armor. The High Density Duranium absorbs 400 MJ. The remaining 4400 MJ expand into a plasma cloud gutting the ship. I'd propose modeling this by having the remaining dissipate like a conventional missile explosion against the opposite hull. Half the energy, 2200 MJ, exploding outwards to make an impressive exit wound. The other 2200 MJ exploding inward to make friends with the internal components.

Now lets say there are 'specialty armor' tech lines that can be optionally applied. Ablative armor to reduce laser and nuke thermal penetration (X effective multiplier against those, but damage depth is rounded up instead of down). Whipple Armor to reduce Kinetic Impact (lower density, greater thickness. same dmg rating). The Luckless_v2 might have (40% density, 5x thickness) whipple armor applied.

The same rail gun impact here penetrates 4cm *(8.9/0.4)^.5 = 18.9 cm. This penetrates 3 armor layers, and releases the remaining energy explosively between 3rd and 4th. (4800 - 3*80)/2 = 2280 MJ each direction. Looking at the Aurora Contact-Missile Explosion rules, 977 MJ seems to leak through the remaining two armor layers inward while the outbound energy goes to work widening the entry hole. Better, but still pretty bad. If the luckless had had 8 unit thicknesses of armor rather than 5 she might have survived with minimal casualties.

It isn't supper accurate, but given how little practical knowledge there is I think it might still be a place to start for Newtonian modeling.
« Last Edit: January 28, 2012, 10:44:47 AM by sublight »
 

Offline jseah

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Re: Impact Physics
« Reply #13 on: January 28, 2012, 12:12:58 PM »
Muzzle velocity of 4800 kJ railgun: 97km/s - 1kg projectile
Expected speeds (1/8 of delta v budget): Geosurvey Vessel - 3kkm/s
Expected closing speeds: 0.1kkm/s (firing up the engines) to 6.1kkm/s (head on collision)
Expected kinetic energy: 4.8GJ to 243GJ  (note: quadratic scale, mid point is roughly 60.9GJ)

So we are looking at something around an order of magnitude higher energy than what you are assuming. 

Making the projectile explode on impact will destroy any ship that isn't just a ball of armour. 

Note that missiles set to ram will be many thousands of times heavier and move much much faster. 
 

Offline sublight

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Re: Impact Physics
« Reply #14 on: January 28, 2012, 02:53:16 PM »
A 1kg 3k km/s has 4.5 TJ. With the mass disparity between a projectile and a ship, a 6.1k km/s head on collision is probably upwards of 18 TJ.

Anyway, the thread topic seems to be "What happens at 30 km/s+." I just thought mentioning 3,000 km/s+ effects might be overstepping and overkill.

So yes, a direct hit from two objects traveling head-on is probably death. Even with cookie cutter.

If cookie-cutter does happen, then at 3k km/s the previously mentioned copper sphere would punch 28.3 cm3 out of a single 1-cm layer of armor. By conservation of momentum, it would slow to 2,917 km/s releasing 125 GJ of energy in the process. I think this is where ravioli compression comes in. If this energy is transferred to the ship, the ship is probably doomed. If this is contained by the projectile, the ship is probably still doomed. Using constant 300K thermal heat capacity as an approximation seems to put the copper sphere at thermonuclear temperatures if it contains all 125 GJ.

At 2,917 km/s speed, the coper and compressed armor would have 17µs to expand while crossing a small 50m diameter ship. However, at 350 MK thermonuclear temperatures, radiative heat transfer dominates so completely that 17µs is plenty of time to cook the ship's interior. Simple lumped capacitance modeling shows GJs of radiative thermal energy transfer by the femtosecond. No, I don't believe that, but there is still going to be lots of hot death for cookie-cutter.
« Last Edit: January 28, 2012, 03:03:45 PM by sublight »
 

 

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