Rehabilitating The Die is Cast
Posted: Tue Feb 02, 2016 2:34 am
This thread is right what it says on the tin. My program has three stages, which are (in descending order of difficulty): 1) explanation of discrepancies between different pieces of dialogue, 2) explanation of "discrepancies" between dialogue and visuals, 3) demonstration that the episode is in good company with the rest of Trek.
So, as we all know, the initial projection is that it will take one hour to destroy the crust and five hours to destroy the mantle. Then, when they get to the planet, after about five seconds of firing, the Romulan chick reports that 30% of the planet's crust has been destroyed. At that rate, some seventeen seconds of continuous fire would have destroyed the entirety of the crust. In other words, the demolition appears to have been going two hundred times faster than anticipated. This is actually the easy problem to solve: it would take an hour to melt or vaporize the crust (necessary in order to get at the mantle), but in those five seconds, they managed to substantially fragment 30% of it. The issue is equivocation.
The real difficulty comes in trying to figure out why it would take one hour to destroy the thirty kilometer thick crust, but only five hours to destroy the three thousand kilometer thick mantle. The mantle makes up 67% of earth's mass, the crust only makes up 0.5%. The second phase of the operation thus appears to be 26.8 times as effective per unit time. My own suggestion is that they never actually attempted to destroy the crust directly: it was merely collateral damage during the destruction of the mantle. We know that torpedoes are capable of drilling deep into rock, and we also know that they are capable of surviving the temperatures and pressures of stars with some modification, so it's hardly unreasonable to expect the fleet to set them off deep within the mantle from the get-go.
Which brings us to the visuals: if the torpedoes are going off hundreds or even thousands of kilometers underground, we wouldn't expect to see fireballs, we wouldn't expect to see debris launched into orbit, and we wouldn't expect to see gigantic glowing craters. We'd expect to see magnitude 11+ earthquakes. What would a magnitude 12 earthquake look like from orbit? Maybe we'd see a butt-load of dust kicked up into the atmosphere, maybe we'd see shockwaves moving across the planet's surface, but we wouldn't see much else at first. Maybe if we waited a while, we'd see some magma seeping up between newly-formed cracks in the crust, but it wouldn't happen instantly, and we wouldn't even see that if the crust was underwater - instead, we'd see massive clouds of steam.
Now, combine the "everything was underwater" hypothesis that has already been discussed ad nauseum over the course of the debate with the "all torpedoes were set off hundreds or thousands of kilometers underground" hypothesis: we'd expect to see vapor kicked up into the atmosphere, shockwaves traveling across the planet's surface, and possibly massive clouds of steam. All of which are consistent with the odd ring-like effects we see onscreen.
Here's my own personal hypothesis as to what the Tal-Shiar timeline would have looked like:
0:00 - Open fire on Dominion homeworld. Disruptors either a) boil away large portions of the oceans (producing large amounts of steam), killing millions of founders directly, or b) fire upon faultlines in the planet's crust, accelerating destruction of the crust and increasing the violence of earthquakes. Torpedoes are fired and set off 500 km below sea level or deeper, at positions selected to produce maximal seismic devastation. The appearance of the planet for the first few minutes will be more or less unaffected.
0:15 - Either as a result of disruptor fire or magma moving upwards through cracks in the crust, the entirety of the ocean has now been vaporized. Through gaps in the now almost total cloud-cover, the glow of magma can be seen. Disruptors and torpedoes are fired more or less indiscriminantly. Disruptors target remaining pieces of the crust, torpedoes are still detonated in the depths of the mantle.
1:00 - The few solid portions of the crust are gone, having melted in the magma covering the planet or having been blown to bits/vaporized/disappeared by disruptors. The water-based clouds have been replaced by an atmosphere of vaporized mantle material - silica vapor is produced as torpedoes explode, then is displaced as the hollow detonation region collapses. The radius of the planet has been noticeably reduced.
6:00 - Bits of slag float on an ocean of molten metal under a very dense atmosphere of silica vapor. The Great Link has been destroyed - and then some.
As far as I know, this timeline is entirely consistent with everything we see and hear, as well as with the physics of the situation. It would take on the order of 1e30 J to pull off - that's some 250 exatons of TNT. Over a period of six hours, that's on the order of ten petatons every second from the entire fleet, or 500 teratons per second per ship worth of firepower.
"But Tarquin," You're saying. "Isn't that completely beyond anything else we ever see in Star Trek?" The short answer: no. For the long answer, hold on for another couple of paragraphs.
From TNG: Booby Trap:
Now, it's probably the case that the authors intended to imply that almost the entirety of Orelious Nine was destroyed in the conflict, but let's assume that only a portion of the planet was blown into space. In fact, let's assume that it was only the crust that was launched into space. That would take 1.5e30 J.
Now let's assume that the two armies had a combined fleet of 1000 capital ships, each of which was capable of carrying 1000 "primitive weapons," and each of which made 1000 bombing runs during the "decisive conflict." Each of those bombs would have to have a yield of 1.5e21 J.
These weapons would have had yields of over 350 gigatons each, and Data is looking down his nose at them. That has to say something about the heavy ordnance the Alpha-quadrant powers are capable of bringing to bear. But it doesn't say anything specific. For that, we need another concrete incident.
The other incident comes from the episode Broken Link in DS9.
Note that the Defiant was being escorted by as many as seven battlebugs:
The Defiant would last, at most, five minutes. Probably closer to thirty seconds, really.
To sterilize all of earth's oceans (heat them to boiling) - which amount to some 1.335e9 cubic kilometers - it would take some 6.6e26 J. So the question is, just how big is the Great Link?
If it's the size of the Baltic sea (2.1e4 cubic kilometers) it would "only" take 1.0e22 J. If it's the size of the Pacific ocean (6.6e8 cubic kilometers) it would take a whopping 3.3e26 J.
Sterilizing the Pacific ocean in thirty seconds would require some 1.1e25 W - 2.7 petatons per second. Sterilizing the Baltic sea in five minutes 3.5e19 W - 8.7 gigatons per second. The geometric mean of the two - a reasonable "middle ground" - is 2.0e22 W - 4.9 teratons per second. More than enough to turn the planet into a smoking cinder, and about 1/100 of the power observed in TDiC - which, given that the Defiant is about 1/400 the volume of a D'deridex and 1/20 the size of a Galor, is entirely reasonable.
So both times planetary bombardment of the founders was discussed in DS9, it is implied that warships are capable of putting out out planet-busting levels of firepower. Which is impressive consistency for Star Trek.
So, as we all know, the initial projection is that it will take one hour to destroy the crust and five hours to destroy the mantle. Then, when they get to the planet, after about five seconds of firing, the Romulan chick reports that 30% of the planet's crust has been destroyed. At that rate, some seventeen seconds of continuous fire would have destroyed the entirety of the crust. In other words, the demolition appears to have been going two hundred times faster than anticipated. This is actually the easy problem to solve: it would take an hour to melt or vaporize the crust (necessary in order to get at the mantle), but in those five seconds, they managed to substantially fragment 30% of it. The issue is equivocation.
The real difficulty comes in trying to figure out why it would take one hour to destroy the thirty kilometer thick crust, but only five hours to destroy the three thousand kilometer thick mantle. The mantle makes up 67% of earth's mass, the crust only makes up 0.5%. The second phase of the operation thus appears to be 26.8 times as effective per unit time. My own suggestion is that they never actually attempted to destroy the crust directly: it was merely collateral damage during the destruction of the mantle. We know that torpedoes are capable of drilling deep into rock, and we also know that they are capable of surviving the temperatures and pressures of stars with some modification, so it's hardly unreasonable to expect the fleet to set them off deep within the mantle from the get-go.
Which brings us to the visuals: if the torpedoes are going off hundreds or even thousands of kilometers underground, we wouldn't expect to see fireballs, we wouldn't expect to see debris launched into orbit, and we wouldn't expect to see gigantic glowing craters. We'd expect to see magnitude 11+ earthquakes. What would a magnitude 12 earthquake look like from orbit? Maybe we'd see a butt-load of dust kicked up into the atmosphere, maybe we'd see shockwaves moving across the planet's surface, but we wouldn't see much else at first. Maybe if we waited a while, we'd see some magma seeping up between newly-formed cracks in the crust, but it wouldn't happen instantly, and we wouldn't even see that if the crust was underwater - instead, we'd see massive clouds of steam.
Now, combine the "everything was underwater" hypothesis that has already been discussed ad nauseum over the course of the debate with the "all torpedoes were set off hundreds or thousands of kilometers underground" hypothesis: we'd expect to see vapor kicked up into the atmosphere, shockwaves traveling across the planet's surface, and possibly massive clouds of steam. All of which are consistent with the odd ring-like effects we see onscreen.
Here's my own personal hypothesis as to what the Tal-Shiar timeline would have looked like:
0:00 - Open fire on Dominion homeworld. Disruptors either a) boil away large portions of the oceans (producing large amounts of steam), killing millions of founders directly, or b) fire upon faultlines in the planet's crust, accelerating destruction of the crust and increasing the violence of earthquakes. Torpedoes are fired and set off 500 km below sea level or deeper, at positions selected to produce maximal seismic devastation. The appearance of the planet for the first few minutes will be more or less unaffected.
0:15 - Either as a result of disruptor fire or magma moving upwards through cracks in the crust, the entirety of the ocean has now been vaporized. Through gaps in the now almost total cloud-cover, the glow of magma can be seen. Disruptors and torpedoes are fired more or less indiscriminantly. Disruptors target remaining pieces of the crust, torpedoes are still detonated in the depths of the mantle.
1:00 - The few solid portions of the crust are gone, having melted in the magma covering the planet or having been blown to bits/vaporized/disappeared by disruptors. The water-based clouds have been replaced by an atmosphere of vaporized mantle material - silica vapor is produced as torpedoes explode, then is displaced as the hollow detonation region collapses. The radius of the planet has been noticeably reduced.
6:00 - Bits of slag float on an ocean of molten metal under a very dense atmosphere of silica vapor. The Great Link has been destroyed - and then some.
As far as I know, this timeline is entirely consistent with everything we see and hear, as well as with the physics of the situation. It would take on the order of 1e30 J to pull off - that's some 250 exatons of TNT. Over a period of six hours, that's on the order of ten petatons every second from the entire fleet, or 500 teratons per second per ship worth of firepower.
"But Tarquin," You're saying. "Isn't that completely beyond anything else we ever see in Star Trek?" The short answer: no. For the long answer, hold on for another couple of paragraphs.
From TNG: Booby Trap:
WESLEY: This was the final battle, wasn't it?
DATA: Neither side intended Orelious Nine to be the decisive conflict.
WESLEY: There's not much left, is there.
DATA: The destruction is remarkable considering the primitive weapons of the period.
Now, it's probably the case that the authors intended to imply that almost the entirety of Orelious Nine was destroyed in the conflict, but let's assume that only a portion of the planet was blown into space. In fact, let's assume that it was only the crust that was launched into space. That would take 1.5e30 J.
Now let's assume that the two armies had a combined fleet of 1000 capital ships, each of which was capable of carrying 1000 "primitive weapons," and each of which made 1000 bombing runs during the "decisive conflict." Each of those bombs would have to have a yield of 1.5e21 J.
These weapons would have had yields of over 350 gigatons each, and Data is looking down his nose at them. That has to say something about the heavy ordnance the Alpha-quadrant powers are capable of bringing to bear. But it doesn't say anything specific. For that, we need another concrete incident.
The other incident comes from the episode Broken Link in DS9.
Garak thinks that, even surrounded by Dominion warships, the Defiant has a chance at obliterating the ocean-like Great Link.WORF: Garak. Just as I thought.
GARAK: Don't tell me. I overlooked one of the security monitors.
WORF: You were trying to override the launch controls for the quantum torpedoes.
GARAK: I was hoping to gain control of the phasers as well. I just hadn't got around to it yet. Don't you see? We have an opportunity here. A chance to end the Dominion threat once and for all. We have enough firepower on this ship to turn that planet into a smoking cinder. Personally, I think that would be a very good thing.
WORF: And what about Odo, and Captain Sisko and Doctor Bashir?
GARAK: They'll die. And once the Jem'Hadar ships realise what we're doing, so will we. But what are our lives compared to saving the entire Alpha Quadrant?
WORF: We are not here to wage war.
GARAK: I'm not talking about war. What I'm proposing is wiping out every Founder on that planet. Obliterating the Great Link. Come now, Mister Worf, you're a Klingon. Don't tell me you'd object to a little genocide in the name of self-defence?
WORF: I am a warrior, not a murderer.
GARAK: What you are is a great disappointment.
(They fight. Worf finally gets the upper hand.)
WORF: You fight well for a tailor.
Note that the Defiant was being escorted by as many as seven battlebugs:
The Defiant would last, at most, five minutes. Probably closer to thirty seconds, really.
To sterilize all of earth's oceans (heat them to boiling) - which amount to some 1.335e9 cubic kilometers - it would take some 6.6e26 J. So the question is, just how big is the Great Link?
If it's the size of the Baltic sea (2.1e4 cubic kilometers) it would "only" take 1.0e22 J. If it's the size of the Pacific ocean (6.6e8 cubic kilometers) it would take a whopping 3.3e26 J.
Sterilizing the Pacific ocean in thirty seconds would require some 1.1e25 W - 2.7 petatons per second. Sterilizing the Baltic sea in five minutes 3.5e19 W - 8.7 gigatons per second. The geometric mean of the two - a reasonable "middle ground" - is 2.0e22 W - 4.9 teratons per second. More than enough to turn the planet into a smoking cinder, and about 1/100 of the power observed in TDiC - which, given that the Defiant is about 1/400 the volume of a D'deridex and 1/20 the size of a Galor, is entirely reasonable.
So both times planetary bombardment of the founders was discussed in DS9, it is implied that warships are capable of putting out out planet-busting levels of firepower. Which is impressive consistency for Star Trek.