Rise: have we underestimated torpedoes?

[Moff Tarquin]

This little calculation came from fairly early on when I was into Star Wars vs Star Trek stuff. I initially rejected it because, well, it seemed kind of wanky. Like, "The-Die-is-Cast-had-a-baby-with-the-antimatter-bomb-from-Obsession-level" wanky. Then I discovered this board.

I discovered that the Enterprise-D was capable of dragging around neutron stars (TNG: The Masterpiece Society). That's at least 1e27 J right there. (assumptions: the neutron star was ~5 km in diameter, had the stated density of 1e17 kg/m^3, and its delta-V was changed by less than 1 m/s)

I discovered that a "technologically primative" species was capable of turning a significant chunk of its own planet into an asteroid field (TNG: Booby Trap). 1e30 J or more. (assumptions: 1% of the planet's mass was launched into space, forming the asteroid field we saw)

I discovered that the Defiant would have been capable of destroying the ocean-like great link while being escorted by multiple dominion vessels (DS9: Broken Link). Harder to gauge, but could be as high as 1e24 J. (assumptions: the great link takes up a volume comparable to that of the Mediterranean sea, it takes half as much energy to sterilize the great link as it would take to heat the Mediterranean sea from 4 degrees Celsius to boiling).

Suddenly, the numbers I was getting seemed to have plenty of company in Star Trek canon. Since I now know they won't find themselves alone, I will release these numbers to the world!

This whole thing is based on what Kim said about what should have happened when they shot the asteroid: there shouldn't have been any fragments larger than a centimeter in diameter.

Now, contrary to most of what passes for "scientific analysis" in this debate, it is nearly impossible to "vaporize" an asteroid. A nuke or a weaponized laser will deliver all of its energy to a relatively thin layer on the surface of the asteroid. If the layer is heated faster than it can exchange heat with the rest of the asteroid, said layer vaporizes. If it vaporizes fast enough, it can blow the rest of the asteroid apart. Adding more power doesn't necessarily make the layer any thicker, it just makes it explode more violently. The only way I can picture large-scale vaporization occurring is if the necessary energy is imparted at a very low power (when compared to the power of a weaponized laser), allowing the heated region to exchange heat with its surroundings. Such a method would be impossible if said energy were being delivered via a nuke - or an antimatter explosive for that matter.

Incidentally, similar considerations apply to particle beams. Only instead of a layer of vaporized material heated by photons, you get a conical region heated by a cascade of collision products. But I digress.

What is required to gauge the effectiveness of a photon torpedo is not an analysis in terms of the heat capacity of the asteroid, but in terms of the energy it would take to reduce the 100+ meter asteroid down to 1 cm fragments.

Which is where this study comes in. There's a lot of fun stuff in there, but on page 703, there's an interesting equation:

log(Ml/Mt) = a - B*log(Ei)

where Ml is the mass of the largest fragment, Mt is the mass of the target asteroid, Ei is the energy density in J/kg, and "a" and "B" are empirically determined constants.

In short, if we know the mass of an asteroid before it goes boom, and we know the mass of the largest piece left after it goes boom, we can figure out how big the boom was in the first place.

It's actually fairly easy to manipulate logarithms, but with all the [sup] and [sub] tags*, it's easier for me just to skip to the final product:

Ei = ((Mt/Ml)^(1/B)) * 10^(a/B)

(*in the first version of this post, I had attempted to use superscript and subscript tags to get rid of all those messy carats and parentheses. Unfortunately, those tags don't appear to work on this forum. So all superscript and subscript have been edited out as of 1/11/2016.)

Fortunately for us, they provide values for a and B on page 702 (I just now realize how quickly I'm moving, but this post is monstrously long already, so I'm counting on being able to clarify in the comments section).

For basalt, a = 1.29, and B = 0.77. We're going to assume that the asteroid is basalt-like, as assuming that it's tuff-like would inflate our result by more than two orders of magnitude.

Throwing in those numbers, our new equation is:

Ei = 9(Mt/Ml)^1.30) * 10^1.68

Darkstar has a calculation on his site indicating that the asteroid is more than 300 meters long, and some 200 meters wide, but we'll assume it's a 100 meter sphere for our purposes. Assuming the largest fragment that should have been left would have been a 0.01 meter sphere, we get a value of 1e12 for Mt/Ml.

Plugging that in, Ei = 1.91e17 J/kg. A 100 m wide spherical asteroid would have a volume of some 5.24e5 m^3, and basalt has a density of 2900 kg/m^3, giving us a total of 2.9e26 J. That's about the same amount of energy as was released by the Kirk-bomb from Obsession.

Like I said, ludicrously high. Though there may be some mitigating factors. First and foremost, the study got its numbers by shooting steel bullets at rock targets. The velocities involved were substantially less than one kilometer per second, and the targets were (with only one exception) never heavier than a kilogram. The highest energy densities were in the tens of thousands of Joules per kilogram. So we may have a simple issue of pushing an otherwise accurate model further than it was meant to go.

But there are lesser factors to consider. Note that the asteroid in Rise was apparently nickel-iron, not basalt. If the comparison of basalt to tuff is anything to go by, a harder asteroid actually reduces the amount of energy required. In the case of basalt and tuff, the difference is some two orders of magnitude. A tuff-like asteroid would have required an energy density of 5.25e19 J/kg, compared to the 1.91e17 kg required by the basalt-like asteroid. If iron is to basalt as basalt is to tuff, then the energy density required to fragment an iron-nickel asteroid could be as low as 10e15 J/kg. That still gives us a good 1e24 J, but that's actually pretty much in line with Garak's expectations (reducing the planet to a "smoking cinder" and obliterating the ocean-like great link) of what the Defiant could do with only a minute's worth of pulse phasers and maybe two volleys of torpedoes.

For that matter, putting the maximum yield of a photon torpedo in the hundreds of teratons (1 TT = 4e21 J) fits in well with the "primative" planet destroyers from Booby Trap, the planetary bombardment from TDiC, and the Kirk-bombs in Obsession and The Immunity Syndrome. Plus there's the fact that Voyager's shields were capable of surviving explosions that demolished planets in episodes like Think Tank. Why have shields that can tank teratons if you don't expect to face weapons that can deliver teratons?

High yield torpedoes also explain why ships that can fight at ranges in the light-seconds often choose to fight at ranges in the tens of kilometers at most: if you get that close, the enemy can't one-shot you without one-shotting himself as collateral damage.

That still might not be enough to convince you. Heck, I'm not 100% convinced myself. But the more I read this forum's archives, things like TDiC look less and less like outliers and more and more like expected upper limits. Before discovering StarFleetJedi, I thought I had misapplied the math. Now? My weird numbers seem to fit into a surprising pattern.


EDIT I: Is it possible to do subscripts and superscripts on this forum? If so, how?

EDIT II: Evidently it is not possible. All superscript and subscript tags have been removed.

[Goper]

Hi, I only joined shortly before you, but welcome to the forums all the same :D

Someone else also did calculations for the neutron star episode on narutoforums, and I'm not sure if he used different values or not, but he ended up with a total output (this term is quoted) of around 10^38 J. I didn't really look at his calculations, but you can see them here if you are interested: http://www.narutoforums.com/blog.php?bt=193924.

Also, the script of "Booby Trap" suggests that the entire planet had been turned into an asteroid field, which likely requires even more energy than 10^30 J (it doesn't help that the debris from the planet didn't clump back together after a thousand years, which suggests that the debris were originally quite far apart). So I agree that there are instances in Star Trek where extremely powerful weapons are implied.

[Moff Tarquin]

Hi, I only joined shortly before you, but welcome to the forums all the same :D

Thanks!

Someone else also did calculations for the neutron star episode on narutoforums, and I'm not sure if he used different values or not, but he ended up with a total output (this term is quoted) of around 10^38 J. I didn't really look at his calculations, but you can see them here if you are interested: http://www.narutoforums.com/blog.php?bt=193924.

Whoa, I may be a fan of inflated numbers on all sides, but that's just in-freaking-sane!

I got my number from this thread here: http://www.starfleetjedi.net/forum/view ... f=8&t=6651

359 gets his numbers about the speed of the neutron star from the visuals of the episode ("willyvereb" made assumptions, reasonable as they may have been, based on general astronomical considerations that put the neutron star at relativistic velocities), and he estimated the total energy requirements at ~2e29 J, and the power requirements at ~1.66e27 W.

Connections to TOS:
On 359's calculations, the entire process would have consumed some billion tons of antimatter, and an equal amount of matter. Given that the Enterprise likely weighs less than twenty-five million tons, and given that most of its space appears to be human-inhabitable (every time we see a schematic, it looks like the entire thing is taken up by easily accessible decks!), it seems nearly impossible for antimatter in the Trek-verse to be the same as real world antimatter.

If, however, antimatter in Star Trek has the energy density implied by TOS episode "Obsession," only 35 kg of antimatter and an equal amount of matter would be required to accomplish the task. Much more reasonable.

But if willyvereb's calculations are correct, some thirty million tons of "Obsession"-style antimatter would be required, in addition to an equal amount of matter. Once again, the Enterprise D isn't big enough to carry that much antimatter.

Personally, I think it could be argued that something in between the two figures would be reasonable, provided we have hyper-antimatter a la Obsession.

Also, the script of "Booby Trap" suggests that the entire planet had been turned into an asteroid field, which likely requires even more energy than 10^30 J (it doesn't help that the debris from the planet didn't clump back together after a thousand years, which suggests that the debris were originally quite far apart).

Yeah, well, I was trying to be conservative with all of the estimates.

So I agree that there are instances in Star Trek where extremely powerful weapons are implied.

Yeah, there's plenty of good stuff all through the archives of this forum.

If you're interested, the Voyager tanking an exploding planet can be found here: http://www.starfleetjedi.net/forum/view ... 4&start=30

That and the "Masterpiece Society" calculation are what really convinced me that my "absurd" numbers might not be as absurd as they look.

A couple of questions:
1. Do you know whether or not subscript and superscript tags work on this forum? Because if they don't, I'm probably going to have to edit that monster of an original post.

2. Do you have any thoughts about my asteroid calculations? I really would appreciate any feedback/critique you care to offer.

[2046]

Enormous yields immediately beside an inhabited planet make me nervous.

[Mr. Oragahn]

Enormous yields immediately beside an inhabited planet make me nervous.

Wet and pink cheeks nervous or chill in toilets nervous?

[Moff Tarquin]

Enormous yields immediately beside an inhabited planet make me nervous.

Well, if I have to be refuted in one sentence, I guess it's a good thing for that sentence to be delivered by one of the most knowledgeable STvSW debaters on the net. Reduces the humiliation by a pretty substantial factor.

Later I'll post some numbers about how much energy would have been deposited on the planet by a blast releasing 2.9e26 J.

Out of curiousity, do you know if subscript and superscript tags work on these forums?

[359]

Nervous indeed, but if that's the data then that's the data. And this is some well done and solid data.



Those tags do not appear to work, and I have yet to see them anywhere either, so I doubt they are on. Instead you could format the equation using lower-case for subscripts, or even darken the subscript text to make it distinct. And for powers I use standard carrot symbol "^", which works sufficiently well (Until you get into superscript notation such as with atomic numbers, but that probably won't be needed here). And for degrees there is an ASCII character (char 248); on Macs it's SHIFT + OPTION + 8 and on Windows it should be ALT + (NUM0→NUM1→NUM7→NUM6). That or find the character somewhere and copy-paste copy-paste. So E[sub]i[/sub] = (M[sub]t[/sub]/M[sub]l[/sub])[sup]1/B[/sup] * 10[sup]a/B[/sup] could be written as Ei = ((Mt / Ml)^(1/B)) * 10^(a/B).



But back to the main topic. This is a very nice piece of work. However I would think that some of the kinetic energy of the event would be converted to thermal energy through mechanical losses, thus creating more vaporized material due to the energy level of the event. This would in turn make it easier to demolish down into smaller chunks. In detail, each 'step' or 'layer' in the demolition would be heated by the mechanical work being done to it, as well as simple conduction from the super-hot gas that is impacting it and doing work unto it. This should cause a significant chunk of the asteroid to be vaporized by the end, making it easier to reduce the outer chunks, but adding thermal work.

Unfortunately this specific calculation is outside my knowledge of material mechanics, so I don't know by how much this would affect the result. It certainly wouldn't drop it by half its orders of magnitude. It should drop a couple, but still your number should be reasonably close. However I could be totally wrong ...this warrants further research when time permits...

[Mike DiCenso]

eah, there's plenty of good stuff all through the archives of this forum.

If you're interested, the Voyager tanking an exploding planet can be found here: viewtopic.php?f=8&t=6564&start=30

That and the "Masterpiece Society" calculation are what really convinced me that my "absurd" numbers might not be as absurd as they look.

"The Masterpiece Society" tractor beam against the stellar fragment and "Think Tank" planetoid explosion are covered in the old Slave Ship and ICS thread from a few years ago.

Warning: long thread and lots of SWST trolling.
-Mike

[Mr. Oragahn]

But back to the main topic. This is a very nice piece of work. However I would think that some of the kinetic energy of the event would be converted to thermal energy through mechanical losses, thus creating more vaporized material due to the energy level of the event. This would in turn make it easier to demolish down into smaller chunks. In detail, each 'step' or 'layer' in the demolition would be heated by the mechanical work being done to it, as well as simple conduction from the super-hot gas that is impacting it and doing work unto it. This should cause a significant chunk of the asteroid to be vaporized by the end, making it easier to reduce the outer chunks, but adding thermal work.

Unfortunately this specific calculation is outside my knowledge of material mechanics, so I don't know by how much this would affect the result. It certainly wouldn't drop it by half its orders of magnitude. It should drop a couple, but still your number should be reasonably close. However I could be totally wrong ...this warrants further research when time permits...

This is where Wong's expertise, for all the flaws in his premises, would come handy. He has, after all, been the one largely exposing the effects of excessive material stress on asteroids, assuming a considerable initial energetic input. Basically, the energy imparted to a side of the asteroid (target) is immense enough to generate a pressure wave of such magnitude that the sheer compression that passes through the material heats it up, capable of reaching boiling levels in a flash.
That said, it would probably be affected by the compound. The age of hard monolumps of matter are quite bygone, many asteroid types being seen as agglomerates of smaller pieces. Meaning the entire structure would count many fault lines which might prevent the pressure from passing through the entire asteroid as efficiently as if it were one solid piece.

[Moff Tarquin]

Nervous indeed, but if that's the data then that's the data. And this is some well done and solid data.

Thanks, but as good as my data may be, it's only based on the dialogue. And plot beats dialogue, just like dialogue beats visuals.

Of course, that just means that I have to address Darkstar's concerns. We do have several examples of nuclear tests that occurred in the upper atmosphere. There was Hardtack Teak, a 4 megaton bomb set off 77 kilometers straight up. It lit up the sky like the sun and caused a hell of an EMP. A 1.7 teraton (7e21 J) bomb set off at 50,000 km (just above geosynchronous orbit, and a rough eyeball estimate of the height of the Rise asteroid above the surface of the planet) would produce a comparable intensity on the ground. There would be no fallout, just the initial flash. I can't imagine that a weapon five times as powerful would do too much beyond make the flash five times brighter and make the EMP five times more severe. It wouldn't set random objects on the planet's surface on fire or anything - it would take a blast some twenty percent more powerful to do that. If the Nisu knew about the asteroid and Voyager's planned method of demolition, they could easily have told everybody to stay indoors and keep all electronics in the basement (or just exchange the use of the electronics for the continued habitability of the planet) on that day. Keep local fire departments at the ready, just in case the yield of the torpedo is a bit greater than expected, and there's not all that much to be nervous about even if the torpedo's yield was as high as 8.5 teratons (3.5e22 J). Such a yield, therefore, would be consistent with the goals of Voyager in using the torpedo in the first place, as well as with the way the craft tanked an exploding planet in Think Tank, the way the Defiant was expected to be capable of destroying the Great Link in Broken Link, etc. etc.

It's four orders of magnitude shy of what the math says it would have to be, but I think it's safe to assume that the math is overestimating energy requirements by at least that much anyways.

Those tags do not appear to work, and I have yet to see them anywhere either, so I doubt they are on. Instead you could format the equation using lower-case for subscripts, or even darken the subscript text to make it distinct. And for powers I use standard carrot symbol "^", which works sufficiently well (Until you get into superscript notation such as with atomic numbers, but that probably won't be needed here). And for degrees there is an ASCII character (char 248); on Macs it's SHIFT + OPTION + 8 and on Windows it should be ALT + (NUM0→NUM1→NUM7→NUM6). That or find the character somewhere and copy-paste copy-paste. So E[sub]i[/sub] = (M[sub]t[/sub]/M[sub]l[/sub])[sup]1/B[/sup] * 10[sup]a/B[/sup] could be written as Ei = ((Mt / Ml)^(1/B)) * 10^(a/B).

Thanks! I've edited my post accordingly.

But back to the main topic. This is a very nice piece of work. However I would think that some of the kinetic energy of the event would be converted to thermal energy through mechanical losses, thus creating more vaporized material due to the energy level of the event. This would in turn make it easier to demolish down into smaller chunks. In detail, each 'step' or 'layer' in the demolition would be heated by the mechanical work being done to it, as well as simple conduction from the super-hot gas that is impacting it and doing work unto it. This should cause a significant chunk of the asteroid to be vaporized by the end, making it easier to reduce the outer chunks, but adding thermal work.

Unfortunately this specific calculation is outside my knowledge of material mechanics, so I don't know by how much this would affect the result. It certainly wouldn't drop it by half its orders of magnitude. It should drop a couple, but still your number should be reasonably close. However I could be totally wrong ...this warrants further research when time permits...

If you find anything good, be sure to tell all of us!

[2046]

Sorry, my intent was not to refute or otherwise dismiss. I was simply making a general point.

Put another way: There are calculations seemingly good or bad in favor of various universes which purport to show megauberyottajoule events occurring immediately beside unaffected tissue-paper, as it were, and that detail must be accounted for or else the calculation is invalid.

I am not suggesting yours is invalid . . . indeed, I haven't had adequate time to review it, and apologize for not giving it due time yet. But, it is a point to ponder.

[Moff Tarquin]

Sorry, my intent was not to refute or otherwise dismiss. I was simply making a general point.

Put another way: There are calculations seemingly good or bad in favor of various universes which purport to show megauberyottajoule events occurring immediately beside unaffected tissue-paper, as it were, and that detail must be accounted for or else the calculation is invalid.

I am not suggesting yours is invalid . . . indeed, I haven't had adequate time to review it, and apologize for not giving it due time yet. But, it is a point to ponder.

Fair enough. However, from my perspective - as the person who offered the calculation in the first place - your general point was sufficiently pointy to serve as a defeater for my calculation. A defeater that could itself be defeated, sure, but a defeater nonetheless.

[Moff Tarquin]

This is where Wong's expertise, for all the flaws in his premises, would come handy. He has, after all, been the one largely exposing the effects of excessive material stress on asteroids, assuming a considerable initial energetic input. Basically, the energy imparted to a side of the asteroid (target) is immense enough to generate a pressure wave of such magnitude that the sheer compression that passes through the material heats it up, capable of reaching boiling levels in a flash.

Would you happen to have any links to discussions of such pressure waves? Anything to refine the calculation would come in handy.

In particular, I'm interested in knowing how the energy input required to cause such a pressure wave compares to the energy a lower-power heat ray would expend while slowly melting and then boiling the asteroid (the latter is the value one gets by using Wong's asteroid destruction calculator to figure out how much energy it takes to "vaporize" an asteroid).

[Moff Tarquin]

eah, there's plenty of good stuff all through the archives of this forum.

If you're interested, the Voyager tanking an exploding planet can be found here: viewtopic.php?f=8&t=6564&start=30

That and the "Masterpiece Society" calculation are what really convinced me that my "absurd" numbers might not be as absurd as they look.

"The Masterpiece Society" tractor beam against the stellar fragment and "Think Tank" planetoid explosion are covered in the old Slave Ship and ICS thread from a few years ago.

Warning: long thread and lots of SWST trolling.
-Mike

In the last post on the fourth page, you mention a calculation you did based on warp core breaches. Do you still have the link to that calculation?

For that matter, any links to substantive technical calculations or discussions would be greatly appreciated if you have the time to dig them up. If you don't have the time, then don't worry about it. I'll find them eventually.

[Mike DiCenso]

The calculations were done in the Phaser/Warp Power thread. Click on the link here, if you want to go right to them.
-Mike