Gurney equations, Explosively formed penetrators and kinetic energy

[LaCroix]

Is this a physical limit? Can we go faster? Is this efficiency the result of lab tests or theoretical limits? Even 5% of a megaton yield can push a 1 ton projectile to 647km/s.

They use "reportedly", which means someone has done tests on it. They talk about small nuclear devices - most likely, a BIG nuclear device is not feasible for this. But if you want to know more, ask the people who wrote the paper. They have actually built and detonated such devices. Or just read the paper - it seems you haven't, or just do not like the results in there. They even have put their math in the footnotes for you to use.

I cannot tell you anything about it that isn't in it, for I didn't have time to play aroudn with nuclear devices in my backyard, obviously.

[matterbeam]

I think I see where the confusion over the 85% is coming from. That's the efficiency of the Orion pulse units, and the Casaba charges described in this paper have a different design from the Orion units. It looks like the design described in the paper is attempting to shape the actual burn wave to converge on the projectile liner as in a conventional shaped charge, whereas Orion pulse units get very high efficiencies by focusing the radiation products of the detonation instead.

If you were to use an Orion charge with the right propellant material you can get a beam with a 5.7 degree cone-angle, much better than the 22.5 degree cone of the standard charge but not as focused as the design described in the paper, so you would lose in range for gains in overall efficiency.

Matterbeam, the section from the paper that appears to be the most helpful to you would be this footnote:

‡ The energy fluence per beam, E in J/m2, is approximately ηY/(NbR2θ2), where η is the fraction of overall yield transferred to the pellets, Y is the bomb yield (1 kiloton is equivalent to 4.2 × 1012 joules), Nb is the number of individual beams being driven by one bomb, R is the distance to the target, and θ is the individual full-beam divergence angle. A maneuvering target could accelerate out of the path of the beam if amR/vf2 > θ, where am is the magnitude of the target's average acceleration, vf is the particle velocity, and τ = R/vf is the particle fly-out time. (For comparison, the average acceleration of ICBMs is about 40 m/s2.) To deliver this energy requires a total mass per beam of Mb = 2E(Rθ)2/vf2.

I don't know how accurate this would be to apply to an Orion-derived device, though, since the two designs rely on very different operating mechanisms.

The NEFP design I'm considering is simply a thin metal plate placed above the Orion pulse unit. A flat plate, wide enough to capture the entirety of the pulse unit's propellant streams' plasma. Through momentum transfer, it will be accelerate outwards.

Imagine it as an Orion drive, but without the suspension and the spaceship on top.

How fast will the plate go?

In the configuration, the determinants of efficiency are how well the nuclear energy is converted into the propellant's energy, and how well the propellant's energy is absorbed by the plate.

Nothing else, such as convergence radians, beam focus, Monroe effect, cone angle and so on matter. The plate is wide enough to capture everything the pulse unit produces.

An extremely simplistic approximation would be to use a momentum equivalency. In the Orion 4000t proposal, I know that a 5 kiloton device was supposed to accelerate is by 12m/s. If we remove the spaceship and reduce the plate mass to a single-use minimum of maybe 1000kg, shouldn't the plate be accelerated to 48km/s? Energy conservation does not agree with me.

[jwl]

As I said, if E is energy density, you didn't plug that in, you plugged in energy on its own. Although actually energy density would fail dimensional analysis too, what wouldn't would be specific energy.

[matterbeam]

As I said, if E is energy density, you didn't plug that in, you plugged in energy on its own. Although actually energy density would fail dimensional analysis too, what wouldn't would be specific energy.

Would you like me to continuously update the original post to reflect the ongoing discussion?

[jwl]

As I said, if E is energy density, you didn't plug that in, you plugged in energy on its own. Although actually energy density would fail dimensional analysis too, what wouldn't would be specific energy.

Would you like me to continuously update the original post to reflect the ongoing discussion?

Oh, you are factoring it in now? Never mind then.

[Simon_Jester]

As I said, if E is energy density, you didn't plug that in, you plugged in energy on its own. Although actually energy density would fail dimensional analysis too, what wouldn't would be specific energy.

Would you like me to continuously update the original post to reflect the ongoing discussion?

Edit privileges on this forum are extremely restricted, so I'd be pleasantly surprised if it were possible to do so.

The NEFP design I'm considering is simply a thin metal plate placed above the Orion pulse unit. A flat plate, wide enough to capture the entirety of the pulse unit's propellant streams' plasma. Through momentum transfer, it will be accelerate outwards.

Imagine it as an Orion drive, but without the suspension and the spaceship on top.

How fast will the plate go?

In the configuration, the determinants of efficiency are how well the nuclear energy is converted into the propellant's energy, and how well the propellant's energy is absorbed by the plate.

Nothing else, such as convergence radians, beam focus, Monroe effect, cone angle and so on matter. The plate is wide enough to capture everything the pulse unit produces.

Other key questions- is the plate's material dispersed laterally into an expanding cone? Given that it's vaporized, this can result in huge losses of efficiency. All or most of the energy of the nuclear device hits the plate, but not all of the plate hits the thing you're trying to accelerate.

An extremely simplistic approximation would be to use a momentum equivalency. In the Orion 4000t proposal, I know that a 5 kiloton device was supposed to accelerate is by 12m/s. If we remove the spaceship and reduce the plate mass to a single-use minimum of maybe 1000kg, shouldn't the plate be accelerated to 48km/s? Energy conservation does not agree with me.

Nuclear detonations produce specific things- a big one being X-rays. A four thousand ton spacecraft with a pusher plate massing in the hundreds of tons will catch all the X-rays that strike it and absorb momentum from them, plus some degree of material being ablated off the plate and therefore acting as propellant (analogous to laser launch).

Slim your plate down to a ton or so, and a significant fraction of the X-ray output of the nuclear device may well shine right through the plate and out the other side. Have you calculated the thickness of your notional one-ton plate?

[matterbeam]

Edit privileges on this forum are extremely restricted, so I'd be pleasantly surprised if it were possible to do so.

Sorry, was being sarcastic.

Other key questions- is the plate's material dispersed laterally into an expanding cone? Given that it's vaporized, this can result in huge losses of efficiency. All or most of the energy of the nuclear device hits the plate, but not all of the plate hits the thing you're trying to accelerate.

The propulsion unit detonates a nuclear device. This devices emits 80% or so of its energy as X-ray. These X-rays are absorbed by a beryllium filler. Beryllium is opaque to X-rays and heats up to incredible temperatures. The beryllium plasma expands and drives a propellant material into a narrow cone. This propellant material was tungsten in the original proposal, polyethylene in later examples.

This cloud of propellant impinges on the drive plate and transfers most of its momentum in a non-elastic collision.

In the design I am looking at, the drive plate is replaced by a thin sheet of tungsten. That is the only modification. The metal plate, which becomes the flyer in this case, is not supposed to melt, only reaching superplastic temperatures while remaining intact.

Nuclear detonations produce specific things- a big one being X-rays. A four thousand ton spacecraft with a pusher plate massing in the hundreds of tons will catch all the X-rays that strike it and absorb momentum from them, plus some degree of material being ablated off the plate and therefore acting as propellant (analogous to laser launch).

Slim your plate down to a ton or so, and a significant fraction of the X-ray output of the nuclear device may well shine right through the plate and out the other side. Have you calculated the thickness of your notional one-ton plate?

[/quote][/quote]

The 4000 ton Orion has a 10m plate that intercepts most of the propellant cloud. The propellant cloud starts off at 67000K, but cools down to 14000K by the time it reaches the plate. Further testing revealed that even a very thin layer of oil could reduce the ablation rate to a couple of micrometers per pulse.

A 1000kg metal plate made of tungsten, would be 0.65mm thick. This is thick enough to not be bothered by the ablation of a single pulse. No X-rays are expected to leak from the pulse unit in the direction of the plate.

[Simon_Jester]

In the design I am looking at, the drive plate is replaced by a thin sheet of tungsten. That is the only modification. The metal plate, which becomes the flyer in this case, is not supposed to melt, only reaching superplastic temperatures while remaining intact.

Things made out of atoms do not remain intact when heated to tens of thousands of degrees. When the energy per atom is large compared to the binding energies tying the atoms together, they will fly apart, one way or another.

The 4000 ton Orion has a 10m plate that intercepts most of the propellant cloud. The propellant cloud starts off at 67000K, but cools down to 14000K by the time it reaches the plate. Further testing revealed that even a very thin layer of oil could reduce the ablation rate to a couple of micrometers per pulse.

A 1000kg metal plate made of tungsten, would be 0.65mm thick. This is thick enough to not be bothered by the ablation of a single pulse. No X-rays are expected to leak from the pulse unit in the direction of the plate.

Do you seriously think that a plate two thirds of a millimeter thick is going to fully absorb the X-ray pulse of a nuclear weapon? What's the tenth-value (or half-value, or whatever) thickness for X-rays in tungsten?

You're doing the thing where you make way too many simplifying assumptions again. This allows you to do calculations using basic formulas... but it also makes the results of the calculations meaningless because you've committed oversimplifications on the order of "I have the answer, but it only works for spherical elastic cows in a vacuum."

[Imperial528]

Do you seriously think that a plate two thirds of a millimeter thick is going to fully absorb the X-ray pulse of a nuclear weapon? What's the tenth-value (or half-value, or whatever) thickness for X-rays in tungsten?

All x-ray emissions in an Orion pulse unit are absorbed by the beryllium filler, vaporizing the filler, and the resulting plasma then vaporizes the propellant material launching it outwards in a conical plasma jet that strikes the pusher plate.

What matterbeam wants to do is replace the full-sized pusher plate and spacecraft with the minimal thickness of plating that wouldn't be completely vaporized by ablation and use that as a projectile.

I don't know enough about the physics myself to say for sure, but I suspect that without the larger backing mass of a full pusher plate, matterbeam's plate will undergo significant warping or buckling during the pulse from any uneven areas of ablation, thus either throwing it off aim at best or fracturing/disintegrating the plate at worst.

[matterbeam]

Things made out of atoms do not remain intact when heated to tens of thousands of degrees. When the energy per atom is large compared to the binding energies tying the atoms together, they will fly apart, one way or another.

Oh, the plate itself does not reach the temperature of the plasma pushing against it. The plasma cools down to 14000K before contact, but only touches the plate for a few microseconds, so with its poor heat conductivity on top, it won't heat up anything in that timescale.

The USAF 10m Orion proposal had the pusher plate heat up by 0.07 degrees C per pulse.

Do you seriously think that a plate two thirds of a millimeter thick is going to fully absorb the X-ray pulse of a nuclear weapon? What's the tenth-value (or half-value, or whatever) thickness for X-rays in tungsten?

No, the beryllium in the channel filler inside the pulse unit absorbs the X-rays. The tungsten only comes in contact with the cloud of propellant, which is actually emitting UV.

You're doing the thing where you make way too many simplifying assumptions again. This allows you to do calculations using basic formulas... but it also makes the results of the calculations meaningless because you've committed oversimplifications on the order of "I have the answer, but it only works for spherical elastic cows in a vacuum."

In this case, I'm using the maths and figures of people far better than me - real aerospace engineers who were a hair away from convincing the USAF to fund their project. The only thing I'm bringing to the project is cutting out the spacecraft.

[Simon_Jester]

Do you seriously think that a plate two thirds of a millimeter thick is going to fully absorb the X-ray pulse of a nuclear weapon? What's the tenth-value (or half-value, or whatever) thickness for X-rays in tungsten?

All x-ray emissions in an Orion pulse unit are absorbed by the beryllium filler, vaporizing the filler, and the resulting plasma then vaporizes the propellant material launching it outwards in a conical plasma jet that strikes the pusher plate.

My apologies for the fuzzy thinking, BUT...

What matterbeam wants to do is replace the full-sized pusher plate and spacecraft with the minimal thickness of plating that wouldn't be completely vaporized by ablation and use that as a projectile.

I don't know enough about the physics myself to say for sure, but I suspect that without the larger backing mass of a full pusher plate, matterbeam's plate will undergo significant warping or buckling during the pulse from any uneven areas of ablation, thus either throwing it off aim at best or fracturing/disintegrating the plate at worst.

As you note, there is still a problem.

[The following is NOT me lecturing you directly, it is simply me talking about what you have said, to the general audience]

Basically, if you take a four thousand ton system and try to replace its heaviest component with a one ton object, removing the entire rest of the system... The resulting system is not going to respond in a simple or linear fashion. One cannot simply say "this accelerates four thousand tons by X meters per second, so it should accelerate one ton by 4000X meters per second."

A large, abrupt force that is sufficient to cause large delta-V in a four thousand ton object is very likely to destroy a one ton object. Just as a force large enough to accelerate a two-ton pickup truck will probably destroy a one-pound object that is placed so as to get run over or crushed by the truck.

We had long-lasting cyclic problems of this nature with matterbeam's orbital tether concept thread, for instance- because he kept designing systems without paying attention to how much force they would be subjected to. This resulted in a huge array of variations on the original design concept, all of which had the same fundamental flaw, namely that at some point some part of the system had to be accelerated to tremendous forces. Forces great enough to accelerate a large payload from (relative) rest to 7 km/s, in a short amount of time. While the exact result ("which part of the system gets torn apart") varied from version to version, the broad outlines of the problem with the plan were fairly consistent.

And the fundamental insight that kept getting dodged by repeated attempts to design around the problem was, well... "kicking something from zero to seven kilometers per second in a matter of a couple of minutes is hard, and most things will break if you try to kick them that forcefully."

This is not an especially difficult insight, but it's easy to miss the insight if one is getting bogged down in the weeds of trying to model and re-model and re-re-model the same system over and over using freshman physics equations on systems that don't apply to very well.

The same thing seems to be an issue here.

Linear extrapolation can be a good model for engineering systems when you are scaling the system up or down by 10%, or 20%, or even by a factor of two or something. They are almost never a good model when you scale things up or down by a factor of a thousand.

[matterbeam]

Basically, if you take a four thousand ton system and try to replace its heaviest component with a one ton object, removing the entire rest of the system... The resulting system is not going to respond in a simple or linear fashion. One cannot simply say "this accelerates four thousand tons by X meters per second, so it should accelerate one ton by 4000X meters per second."

A large, abrupt force that is sufficient to cause large delta-V in a four thousand ton object is very likely to destroy a one ton object. Just as a force large enough to accelerate a two-ton pickup truck will probably destroy a one-pound object that is placed so as to get run over or crushed by the truck.

We had long-lasting cyclic problems of this nature with matterbeam's orbital tether concept thread, for instance- because he kept designing systems without paying attention to how much force they would be subjected to. This resulted in a huge array of variations on the original design concept, all of which had the same fundamental flaw, namely that at some point some part of the system had to be accelerated to tremendous forces. Forces great enough to accelerate a large payload from (relative) rest to 7 km/s, in a short amount of time. While the exact result ("which part of the system gets torn apart") varied from version to version, the broad outlines of the problem with the plan were fairly consistent.

And the fundamental insight that kept getting dodged by repeated attempts to design around the problem was, well... "kicking something from zero to seven kilometers per second in a matter of a couple of minutes is hard, and most things will break if you try to kick them that forcefully."

This is not an especially difficult insight, but it's easy to miss the insight if one is getting bogged down in the weeds of trying to model and re-model and re-re-model the same system over and over using freshman physics equations on systems that don't apply to very well.

The same thing seems to be an issue here.

Linear extrapolation can be a good model for engineering systems when you are scaling the system up or down by 10%, or 20%, or even by a factor of two or something. They are almost never a good model when you scale things up or down by a factor of a thousand.

The 4000 ton/ 1 ton comment was to illustrate the effect I was looking for. It is not what I expect to happen (hence my mentioning the kinetic energy inequality), and I am more interested in discussing the ways it won't work and if they are realistically solvable.

Apparently, looking at Voitenko Compressors, thin disks can handle extreme accelerations much more gracefully than thick disks of equal mass.

[LaCroix]

The paper you posted was talking about the apparatus creating a beam of fragments, millions of them, after the nuclear device had shattered the plate.

Now, the only relatively small object (900kg) that I know to been driven by a nuclear bomb the way you want to is the infamous "manhole cover in orbit" * after that one test, but this one was not directly next to the blast, but was hit with the blast wave travelling through a pipe.

(*) Spoiler: it's not...

Also, a bit of correction on the orion data that is thrown around, which is most likely the basis for why you think this would work:

The plasma would cool to 14,000 °C as it traversed the 25 m distance to the pusher plate and then reheat to 67,000 °C as, at about 300 microseconds, it hits the pusher plate and is recompressed.

The cooldown to 14000 degrees is after a travel through 25m of air or vacuum... Not quite applicable here - the bomb touches the whole assembly.
To quote Soo, Jason. "Atomic Education." Enscquire. 7, 4 (September 1995): 10.

Within 17 meters, the explosion temperature was 300,000 degrees Celsius. Within 50 meters it was
9,000-11,000 degrees, and at ground level beneath hypocenter the temperature exceeded 6,000 degrees.

Data for temperature right at the center is in the 106 to 107 degree range. This is something completely different than what we have been talking about.

Same for pressure wave and radiation exposure. This is all completely different when you reduce the range.

Especially sinde the 4000t Orion ship was supposed to use 0.14 kt nukes, not 1kt!

To see the data for a 1kt bomb consider using http://stardestroyer.net/Resources/Calc ... sions.html with .001 megatons

[matterbeam]

The paper you posted was talking about the apparatus creating a beam of fragments, millions of them, after the nuclear device had shattered the plate.

Now, the only relatively small object (900kg) that I know to been driven by a nuclear bomb the way you want to is the infamous "manhole cover in orbit" * after that one test, but this one was not directly next to the blast, but was hit with the blast wave travelling through a pipe.

The fragments is only one option, but I would be happy to work out how the energy of the device, the mass of the fragments and their velocity is related.

(*) Spoiler: it's not...

Also, a bit of correction on the orion data that is thrown around, which is most likely the basis for why you think this would work:

The plasma would cool to 14,000 °C as it traversed the 25 m distance to the pusher plate and then reheat to 67,000 °C as, at about 300 microseconds, it hits the pusher plate and is recompressed.

The cooldown to 14000 degrees is after a travel through 25m of air or vacuum... Not quite applicable here - the bomb touches the whole assembly.
To quote Soo, Jason. "Atomic Education." Enscquire. 7, 4 (September 1995): 10.

Within 17 meters, the explosion temperature was 300,000 degrees Celsius. Within 50 meters it was
9,000-11,000 degrees, and at ground level beneath hypocenter the temperature exceeded 6,000 degrees.

Data for temperature right at the center is in the 106 to 107 degree range. This is something completely different than what we have been talking about.

Why would a device for use in space not be able to exploit the same configuration and spacing as the original Orion drive? I think it would be simpler if we start off with as many things similar to the Orion drive as possible, specifically the 4000t 10m USAF design that called for 5kt devices, 25m spacing and 22.5 degree cone of propellant imparting 12m/s per pulse.

Same for pressure wave and radiation exposure. This is all completely different when you reduce the range.

Especially sinde the 4000t Orion ship was supposed to use 0.14 kt nukes, not 1kt!

To see the data for a 1kt bomb consider using http://stardestroyer.net/Resources/Calc ... sions.html with .001 megatons

I believe the 0.14kt charges were for takeoff.

[LaCroix]

Why would a device for use in space not be able to exploit the same configuration and spacing as the original Orion drive? I think it would be simpler if we start off with as many things similar to the Orion drive as possible, specifically the 4000t 10m USAF design that called for 5kt devices, 25m spacing and 22.5 degree cone of propellant imparting 12m/s per pulse.

Not aware of this design - I refer to Dyson's work, and all calculations for a 4000t ship popint to .14kt yield. 5kt devices might be feasible for bigger ships in the million ton ranges, with a pusher plate of appropriate size, but a 4000t ship would most likely not survive that blast at 20m distance, if we take nuclear tests and the effects on armored warships far further away into consideration.

And it won't be able to exploit the "same confiburation" because it's _not_ the same device - orion called for 20-25 m distance between plate and detonation, your model has them touching.

Or did you change your design in the meantime?

[Imperial528]

https://web.archive.org/web/20070704104 ... 085619.pdf

This paper mentions using 1kt units with the 10m design, and does have a thrust table for up to 100kt units. The highest specific yield I could find in the paper was in a section on plutonium requirements, which was as follows:

The range of yields required of the nuclear devices (less than 1 KT to approximately 15 KT), assuming current technology devices are used, reportedly do not change the amount of fissionable material required.

The paper is difficult to search through and I can't find any other mention of a 15kt device via text searching, but I imagine that range of yields was chosen for a reason, and given that the paper only mentions the 10m and 20m design studies, the authors must have expected the higher yields to be compatible with at least the larger design.

[LaCroix]

I've been reading (skimming, mostly) that document (thank you Imperial528), and I think I'm getting why matterbeam is talking about "similar configuration". We are not talking about a weaponized pulse unit, as the diagram leads to assume. This talk about ablation and stuff leaves me to think you want to use the pusher plate as the projectile?

First of all, you need to correct the relative sizes of filler and propellant - a pulse unit uses a 1:4 ratio of filler to propellant (tungsten in this case) to achieve radiation absorption and instant propellant vaporization. Your proposition and calculation uses a 1:1 ratio. I can't find the weights of the parts, but it's most likely in the tens of kg for each of the two components, given the total mass of the unit.(140kg)
So 40kg tungsten for 10kg beryllium oxide for your config. And still, the tungsten gets vaporized or even turned into plasma.

So, assuming you want to use the tungsten as projectile, you might need calculate the amount of tungsten needed to have at least some of it not vaporize, in order to create a molten or solid slug leaving the unit. I can't do that. It would also only be quite wasteful, for only that non- vaporized part is left as projectile, the high-speed vapor is lost.

A rough calculation of the pusher plate results in at least 60 tons mass, for the whole dry drive it states 90 tons. (I think this is for a nominal 3g maximum) So the pusher plate as projectile is not feasible, unless you scale it way down. You probably will want to use a pipe and convert this into a cannon, driving a slug,

3.5×106N is the magic number. that's what the propellant thrust amounts to. You now only need a barrel where either the superheated tungsten slug or the vapor driven projectile is driven through.

I'm pretty sure you can rearrange and hack that into these formulas for smoothbore ballistics : http://www.arc.id.au/CannonBallistics.html