Starfleet Jedi

TEYLA: Wait!

(She forces herself to continue her probe of the Queen's mind, and sees a red light begin to pulse on the control panel of the cruiser.

Teyla raises her head, her eyes open.)

TEYLA: She has activated the self-destruct device of the Wraith cruiser. It is set to detonate within two hours.

(The Queen looks round at John and grins.)

SHEPPARD: So – *not* an empty threat.

Me wrote:
I'm looking at three webpages for the moment:

Wong's Calculator, to see how much energy this system estimates will be necessary to break the crust.
This thread, which suggests that the fragmentation part of Wong's calculator may be well under what's correct.
The Golevka test was based on a detonation of a 10 MT nukes, and it didn't shatter the asteroid down to 10 meters wide fragments.
The calculator says that only 148.9 kilotons are necessary for a 530 meters wide rocky asteroid. Wong's number is 67.16 times inferior to what the test returned, and the asteroid was not shattered at all.
Then, I suppose that as it always happens with energy figures when you account for volume and radii, the thicker the asteroid, the bigger the ratio would be.
Then, I look at Mount St Helens' eruption, which indicates a total energy release of 24 megatons thermal energy (7 by blast, rest through release of heat), for 401 m of matter removed (height comparison at the top of the table).
If anything, the Golevka test points to a range much closer to St Helens's figures than Wong's estimations.

Then, let's think about the crust thickness that that depth. Earth's crust has a minimal thickness of 5 km.
So let's say that the bomb is planted in an asteroid being 10 km wide.
Wong's calc says:

Fragmentation energy: 1 gigaton.
Ok, we're already in the gigaton range.
Now, using the former ratio, the figure would already be around 67.16 gigatons, and a final yield a thousand times bigger than that.
That's for using a ratio which could likely be inferior, possibly by one order of magnitude, to what the real ratio would be in the end.

It's funny to look at wikipedia's comparison between the Richter scale and the TNT equivalence.

The ratio could, and would probably need to be a hell lot bigger, if the resulting explosion would be expected to defeat water pressure, because I suppose much of the water actually help keeping a huge pressure on that layer of rock.
I've recently seen an interesting documentary, showing how the ice cap melting, increasing the volume of liquid water, would increase the pressure on zones of seismic activity, for examples in zones near Seattle and Tokyo, because of the presence of the Ring of Fire, increasing the rate and magnitude of earthquakes.

Meaning that where there's no such a rift (there's no sign of submarine mountain range, nor any volcano as far as I can remember in the episode), the pressure is logically going to homogeneously compress the rock layer and keep the lava underneath.
Which means that a good deal of energy will be needed to let the lava burst, and have the eruption multiply the initial blast by a thousand (which, of course, is a figure they totally made up).

Finally, you were quite right, in january, when you considered that something could be obtained from this episode, and we could really be looking at something really big.

Now, I may have done a few things wrong, but I can't tell for the moment, so if you feel like giving it a look.

Other person wrote:
Some interesting thoughts here to be sure. A lot of people use Wongs calculator assuming it infallible but I would say something like St. Helen's is a much more reliable benchmark for this type of event since it, you know, actually happened.

Your bringing up the water pressure also got me to thinking, and if I'm on the right track here get ready for the numbers to shoot WAY up.

They say that the cruiser blowing up will also pose a serious threat to, if not outright destroy Atlantis?

How?

Blowing a hole in the bottem of the ocean wouldn't do it, unless we're talking about a hole big enough to basically flash boil most of the water under the city in an allmighty explosion. Or by creating one with enough energy to send rocks and shit up through however many miles of ocean to physically blow the city apart.


So we're looking at a few more potential numbers here.

Warsie style High end

The crusier exploding will destroy atlantis by itself: This would require that the cruiser's reactor be able to vaporise god knows how many square miles of seawater to be able to create a convincing, and fast, enough blast wave to actually destroy or badly damage the city resting on the surface.

More reasonable interpretation

The cruiser will cause enough damage to the planet to make it do this: I'm not sure if this is even physically possible or not, though I'm leaning toward not. The dialog says it is though so we'll roll with it I guess, in the interest of a lower estimate. Basically the cruiser will have to open up such a massive fissure in the ocean floor that the energy released from it will do basically what I wrote about above. Also the actual reactor explosion shouldn't be less than roughly 1/1000 of the energy required to do this.




Another thing to consider here as well is the city shields. I can't remember if they have them available at this point but if they do they increase the numbers further.

To destroy the city with its shields up you're going to either have to create such a powerful blast that the city is destroyed almost instantly, before they can be raised to protect it. This will mean that a slow moving "depth charge" type wave wouldn't be viable as they could raise the shields when detecting the initial explosion long before the wave made it to the surface. It would basically mean that flash vaporization of mass quanties of ocean would be required, either to destroy most of the interveening water and shorten the distance the shockwave would have to travel, or to just blow the city up with raw energy despite the interveening water.

Now I don't know much about how undersea explosions actually work so I might be completely off and wrong about things like the shockwaves but I think we've hit on something important here.

When estimating how much energy this is going to take we must keep in mind that the blast, either from the cruiser or planet, is going to have to also be capable of reaching and damaging or destroying atlantis, likely before it can raise its shields.

Here's the dialog from the episode that's relevant.

So it won’t just be us that’s affected.
ZELENKA: No. Atlantis will be affected as well. It’s well within the blast radius.
WEIR: And we have no way to warn them?
McKAY: They’d never even see it coming.

So they think it's going to happen fast enough that Atlantis will "never see it coming" and also that it's going to be well within the blast radius, which probably means destruction is likely rather than just damage.

If we can take a reasonable low end estimate for the depth of the ocean and then calculate a hemispherical region of water to boil/vape this can probably be calced.

Me wrote:

Some interesting thoughts here to be sure. A lot of people use Wongs calculator assuming it infallible but I would say something like St. Helen's is a much more reliable benchmark for this type of event since it, you know, actually happened.

Your bringing up the water pressure also got me to thinking, and if I'm on the right track here get ready for the numbers to shoot WAY up.

Could be, yeah, but I'm fairly sure that breaking the crust is a very low end, at least. I figure a reasonable middle end would be like cracking the crust open to let the thermal energy shoot out rather dramatically.

They say that the cruiser blowing up will also pose a serious threat to, if not outright destroy Atlantis?
How?

Well, they don't say what type of danger. They don't say the city will be destroy, just that it will affected. Well, a fish fifty kilometers away would be affected as well. Make that vague. :)
That said, it's probably sarcastic, cause Sheppard use the word affected for them as well.

Blowing a hole in the bottem of the ocean wouldn't do it, unless we're talking about a hole big enough to basically flash boil most of the water under the city in an allmighty explosion. Or by creating one with enough energy to send rocks and shit up through however many miles of ocean to physically blow the city apart.

The cruiser was already one kilometer away from the thermoplant. I don't know where the plant was, in relation to Atlantis, but I know that the plant is mounted on threads, so it can obviously be moved around.

TEYLA: She has activated the self-destruct device of the Wraith cruiser. It is set to detonate within two hours.

(The Queen looks round at John and grins.)

SHEPPARD: So – *not* an empty threat.


CONTROL ROOM. John and Elizabeth walk in.

McKAY: How's Teyla?

WEIR: She's resting. I think it took a lot more out of her than she's willing to admit.

SHEPPARD: What's the news?

McKAY: OK, well, it looks like the Ancients chose this section of the ocean floor because the planet's crust is remarkably thin right below us, allowing them to drill directly into the magma and maximise the geothermal power output.

SHEPPARD: OK ...

ZELENKA: Which means there's a great deal of potential energy directly beneath this station.

SHEPPARD: That's the news? That this place works as advertised?

McKAY: No. No, the news is that if they were to detonate, say, the self-destruct of a Wraith cruiser on just such a wafer-thin crust ...

WEIR: Oh my God.

ZELENKA: ... all that thermal energy directly beneath us will be released all at once.

SHEPPARD: So, bad news.

McKAY: Yeah. The initial explosion will be magnified a thousand times. We're talking catastrophic.

SHEPPARD: So it won't just be us that's affected.

ZELENKA: No. Atlantis will be affected as well. It's well within the blast radius.

WEIR: And we have no way to warn them?

McKAY: They'd never even see it coming.

SHEPPARD: So we disarm the self-destruct.

McKAY: That's brilliant, but we still need to get there.

WEIR: And how do we do that without the Jumper?

SHEPPARD: We're way behind schedule. They're gonna send a rescue Jumper any minute now.

McKAY: Even if they've left already – I mean the *moment* we were overdue ...

ZELENKA: No, they won't make it in time.

SHEPPARD: How far is the cruiser?

ZELENKA: Um, less than a kilometre.

SHEPPARD: She swam that far?! What *is* she?!

ZELENKA: A formidable enemy.

McKAY: I have an idea.

So we're looking at a few more potential numbers here.

Warsie style High end

The crusier exploding will destroy atlantis by itself: This would require that the cruiser's reactor be able to vaporise god knows how many square miles of seawater to be able to create a convincing, and fast, enough blast wave to actually destroy or badly damage the city resting on the surface.

More reasonable interpretation

The cruiser will cause enough damage to the planet to make it do this: I'm not sure if this is even physically possible or not, though I'm leaning toward not. The dialog says it is though so we'll roll with it I guess, in the interest of a lower estimate. Basically the cruiser will have to open up such a massive fissure in the ocean floor that the energy released from it will do basically what I wrote about above. Also the actual reactor explosion shouldn't be less than roughly 1/1000 of the energy required to do this.

That's a curious thing. I can't picture how the bomb's yield could be multiplied a thousand times. There's pressure underneath, but there can't be that much pressure.
But there's probably something to dig...

Another thing to consider here as well is the city shields. I can't remember if they have them available at this point but if they do they increase the numbers further.

I suppose. They had a ZPM since The Return if I'm right.

To destroy the city with its shields up you're going to either have to create such a powerful blast that the city is destroyed almost instantly, before they can be raised to protect it.

Yes, and you know my stance on the shields, from the moment you plug a ZPM in there.

This will mean that a slow moving "depth charge" type wave wouldn't be viable as they could raise the shields when detecting the initial explosion long before the wave made it to the surface. It would basically mean that flash vaporization of mass quanties of ocean would be required, either to destroy most of the interveening water and shorten the distance the shockwave would have to travel, or to just blow the city up with raw energy despite the interveening water.

Well, that's the problem.
If the city is close to the powerplant, creating a tsunami would be enough to threaten the city, and damage it.

Now I don't know much about how undersea explosions actually work so I might be completely off and wrong about things like the shockwaves but I think we've hit on something important here.

When estimating how much energy this is going to take we must keep in mind that the blast, either from the cruiser or planet, is going to have to also be capable of reaching and damaging or destroying atlantis, likely before it can raise its shields.

Here's the dialog from the episode that's relevant.

So it won’t just be us that’s affected.
ZELENKA: No. Atlantis will be affected as well. It’s well within the blast radius.
WEIR: And we have no way to warn them?
McKAY: They’d never even see it coming.

So they think it's going to happen fast enough that Atlantis will "never see it coming" and also that it's going to be well within the blast radius, which probably means destruction is likely rather than just damage.

If we can take a reasonable low end estimate for the depth of the ocean and then calculate a hemispherical region of water to boil/vape this can probably be calced.

I can't figure out what the blast radius means. The amount of water being displaced itself could be enough to be considered this being the blast radius, if it's akin to air blast radii when we speak of nuclear bombs.

Yet, I'm looking at supervolcanos, but the yields aren't that formidable: 1 GT for Toba (2,800 km³ of matter ejected).
There's "La Garita Caldera, Colorado, United States - Source of the truly enormous eruption of the Fish Canyon Tuff 27.8 million years ago (~5,000 km³)", but I can't numbers for that one.
I found two sources which apparently reference LaGarita, but we need to pay.

However, an interesting article is the wiki page about the indonesian earthquake.

It has "hot stuff":

Energy released by the earthquake

The energy released on the earth's surface only, MEwhich is the seismic potential for damage, by the 2004 Indian Ocean earthquake and tsunami was estimated at 1.1×10^17 joules or 26.3 megatons of TNT. This energy is equivalent to over 1502 times that of the Hiroshima atomic bomb, but less than that of Tsar Bomba, the largest nuclear weapon ever detonated. However, this is but a tiny fraction of the total work done MW (and thus energy) by this quake, 4.0×10^29 ergs (40 ZJ), the vast majority underground. This equates to 4.0×10^22 J, over 363 thousand times more than its ME. This is a truly enormous figure, equivalent to 9,560 gigatons of TNT equivalent (550 million times that of Hiroshima), or about 370 years of energy use in the United States at 2005 levels of 1.08×10^20 J.

The only earthquakes ever with a larger MW were the 1960 Chilean and 1964 Alaskan quakes, with 2.5×10^30 ergs (250 ZJ) and 7.5×10^29 ergs (75 ZJ) respectively. Please see USGS:Measuring the size of earthquakes.

The earthquake generated seismic oscillation of the Earth's surface of up to 20–30 cm (8–12 in), equivalent to the effect of the tidal forces caused by the Sun and Moon. The shock waves of the earthquake were felt across the planet; as far away as the U.S. state of Oklahoma, where vertical movements of 3 mm (0.12 in) were recorded.

Because of its enormous energy release and shallow rupture depth, the earthquake generated remarkable seismic ground motions around the globe, particularly due to huge Rayleigh (surface) elastic waves that exceeded 1 cm in vertical amplitude everywhere on Earth. The record section plot below displays vertical displacements of the Earth's surface recorded by seismometers from the IRIS/USGS Global Seismographic Network plotted with respect to time (since the earthquake initiation) on the horizontal axis, and vertical displacements of the Earth on the vertical axis (note the 1 cm scale bar at the bottom for scale). The seismograms are arranged vertically by distance from the epicenter in degrees. The earliest, lower amplitude, signal is that of the compressional (P) wave, which takes about 22 minutes to reach the other side of the planet (the antipode; in this case near Ecuador). The largest amplitude signals are seismic surface waves that reach the antipode after about 100 minutes. The surface waves can be clearly seen to reinforce near the antipode (with the closest seismic stations in Ecuador), and to subsequently encircle the planet to return to the epicentral region after about 200 minutes. A major aftershock (magnitude 7.1) can be seen at the closest stations starting just after the 200 minute mark. This aftershock would be considered a major earthquake under ordinary circumstances, but is dwarfed by the mainshock.

The shift of mass and the massive release of energy very slightly altered the Earth's rotation. The exact amount is not yet known, but theoretical models suggest the earthquake shortened the length of a day by 2.68 microseconds, due to a decrease in the oblateness of the Earth. It also caused the Earth to minutely "wobble" on its axis by up to 2.5 cm (1 in) in the direction of 145° east longitude, or perhaps by up to 5 or 6 cm (2.0 to 2.4 in). However, because of tidal effects of the Moon, the length of a day increases at an average of 15 µs per year, so any rotational change due to the earthquake will be lost quickly. Similarly, the natural Chandler wobble of the Earth, which in some cases can be up to 15 m (50 ft), will eventually offset the minor wobble produced by the earthquake.

More spectacularly, there was 10 m (33 ft) movement laterally and 4–5 m (13–16 ft) vertically along the fault line. Early speculation was that some of the smaller islands south-west of Sumatra, which is on the Burma Plate (the southern regions are on the Sunda Plate), might have moved south-west by up to 36 m (118 ft), but more accurate data released more than a month after the earthquake found the movement to be about 20 cm (7.9 in). Since movement was vertical as well as lateral, some coastal areas may have been moved to below sea level. The Andaman and Nicobar Islands appear to have shifted south-west by around 1.25 m (4.1 ft) and to have sunk by 1 m (3.28 ft).

In February 2005, the Royal Navy vessel HMS Scott surveyed the seabed around the earthquake zone, which varies in depth between 1,000 m and 5,000 m (3,300 ft and 16,500 ft). The survey, conducted using a high-resolution, multi-beam sonar system, revealed that the earthquake had made a huge impact on the topography of the seabed. 1,500-meter (5,000 ft) high thrust ridges created by previous geologic activity along the fault had collapsed, generating landslides several kilometers wide. One such landslide consisted of a single block of rock some 100 m high and 2 km long (300 ft by 1.25 mi). The momentum of the water displaced by tectonic uplift had also dragged massive slabs of rock, each weighing millions of tons, as far as 10 km (7 mi) across the seabed. An oceanic trench several kilometres wide was exposed in the earthquake zone.

The TOPEX/Poseidon and Jason 1 satellites happened to pass over the tsunami as it was crossing the ocean. These satellites carry radars that measure precisely the height of the water surface; anomalies of the order of 50 cm (20 in) were measured. Measurements from these satellites may prove invaluable for the understanding of the earthquake and tsunami. Unlike data from tide gauges installed on shores, measurements obtained in the middle of the ocean can be used for computing the parameters of the source earthquake without having to compensate for the complex ways in which close proximity to the coast changes the size and shape of a wave.

Me wrote:
Based on this, I'd go for a thickness of 10 km.

Ok, so then, it really gets crazy. Really crazy.

Here's the elements of important I spotted:

The energy released on the earth surface only was around 26 megatons. That's, I suppose, spread and divided across all shockwaves and the tsunami.
You can see a picture of the tsunami, and we're a far cry from the freak wave that threatened Atlantis more than two years ago.
The amount of work done on the seabed, and mainly underground, is rated at "4.0 e29 ergs (40 ZJ), the vast majority underground. This equates to 4.0 e22 J, over 363 thousand times more than its ME. This is a truly enormous figure, equivalent to 9,560 gigatons of TNT equivalent."

9.56 teratons.

This, again, wasn't the most powerful earthquake... the most powerful one is rated at 250 ZJ, 59.751 teratons.

Now, let's get the other elements clarified:

Here is the page used to calculate energies from earthquakes. Just to get an idea what the stuff they calc means.

The biggest earthquake was the chilian one in 1960, which released roughly 59.75 teratons of energy.

In February 2005, the Royal Navy vessel HMS Scott surveyed the seabed around the earthquake zone, which varies in depth between 1,000 m and 5,000 m (3,300 ft and 16,500 ft).

That's far from the 10 km which concern us.

The survey, conducted using a high-resolution, multi-beam sonar system, revealed that the earthquake had made a huge impact on the topography of the seabed. 1,500-meter (5,000 ft) high thrust ridges created by previous geologic activity along the fault had collapsed, generating landslides several kilometers wide.

1.5 km deep ridges would be very short of the 5 km figure we worked from.

If we reduced the crust of that alien planet to something like 1.5 km, we'd have to equally add that amount of water above.

One such landslide consisted of a single block of rock some 100 m high and 2 km long (300 ft by 1.25 mi). The momentum of the water displaced by tectonic uplift had also dragged massive slabs of rock, each weighing millions of tons, as far as 10 km (7 mi) across the seabed. An oceanic trench several kilometres wide was exposed in the earthquake zone.

It only moved bits of rock sideways, over a max distance of 10 km.

and Jason 1 satellites happened to pass over the tsunami as it was crossing the ocean. These satellites carry radars that measure precisely the height of the water surface; anomalies of the order of 50 cm (20 in) were measured.

An anomaly of 50 cm. Okay, I don't really get what this anomaly relates to, as I'd rather say that the anomaly is the tsunami, but the tsunami itself might be a sideeffect of the wave nearing the coast, and thus due to pressure, increasing the height of the wave.

That said, if the 50 cm is what you get on the surface, at the apogee of the earthquake focus point, that's rather underwhelming. Considering the size of Atlantis, anything below several many dozens of meters would be laughable.
And, of course, nowhere do we get anything ressembling the description of a convincing and instantaneous blast radius. None of these yet powerful events created anything looking an explosion. No thermal energy, being the primary concern of Rodney McKay, was significantly liberated here.

Now, we're not talking about an earthquake, but a sudden explosion, so we have to be steady here as well. A violent, single explosion, would have a much higher magnitude, and logically push the water far above the anomaly reference above. The earthquakes release their energy over several seconds.

But I think we can consider that the explosion may be tickling the feet of the petaton range, but not confortably twiddling its toes in that field, as a high end.

We may be looking at an event that would blow a piece of the seabed off and significantly fuck up an Atlantis floating at at least 10 km of water above. The water, of course, acting as a cushion.

That said, the numbers are not precise enough, but the consideration that we would be dealing with, at least, a high gigaton figure seems rather logical.

If anything, I feel safe at assuming that for the process to work, several gigatons would be needed to break the crust.
How the pressure underneath could shoot up, I don't know.

On Earth, there's some uranium stuff in the lava layer. It's not concentrated enough to be worth a chain reaction, but it might add a bit if the initial reaction is powerful enough.

That said, you're right on the blast thing. They clearly won't have time to react, and I wish I could figure out to calc the energy needed to move the necessary amount of water to threaten Atlantis.
We'd probably have to consider the energy loss over distance. So if the city is 1 km away from the vertical point above the explosion center, maybe we'd have to consider the energy to move a water column of a diameter of 1 meter, and a depth of 10 km, up to a height of, well, 10 meters at least. And with that energy, we'd do an inverse square law, based on a distance of 1000 m.

Other person wrote:
The cruiser must generate enough energy in its initial blast to at the bare minimum blast a hole through the planetary crust. Some low end number like 10km can be assigned for that.

That's not all that needs to be done to determine the energy released though, and the other parts are a lot harder to pin down. Those parts are how much of a threat the city is under from this event and how the energy that's supposed to be liberated from the planet itself will factor into everything.

In regards to damaging the city I would say that a Tsunami type wave is not going to be ideal. Not only do I think it's actually impossible to form such a wave in the middle of the ocean but it will be rendered moot by the city's shields and detected on sensors long before it hits.

It is possible to detect an incoming tsunami even with modern methods in enough to to raise the shields on the city.

For the method of damage to the city we need to select something that, as the quote says, they would "never see coming" so that the city can be damaged before someone can put the shields up.

We should also keep in mind to take into account that the city will be "well within" the blast radius of this event. With this in mind any estimates on blast size should account for a blast that would still be capable of damaging the city even if it were further away than it actually was in the episode.

I also wonder how much value underwater nuclear testing data might be to working this out. You seem to have a talent for finding actual useful information like this so that's one direction I would definately look in.

See if we can find out how big of an effect radius a nuke of a given yeild has under water, how fast blast waves travel and then try to compare that information with information pertaining to the same yeilds in atomsphere.

So for example if we can determine that a nuke of X yeild above water has an effective radius of 1km for smashing structures like buildings and only .5km under water to do similar, then we can arrive at something of a crude conversion method.

Me wrote: I've seen a few video tests of nuclear weapons detonated underwater with kiloton yields, and it's not threatening.
You're right about tsunami detection, and it's not a meagre five or ten meters tall wave that's going to pose problem to the city.