Upper Limit Naquadah Reactor Power [Stargate]

[NecronLord]

There would be lots of lavishly illustrated screenshots from Lost City and Solitudes in here, but my DVD drive on the computer has packed up and refuses to even open.

In Lost City, O’Neill modifies a set of goa’uld transport rings to bore a hole through the ice of Antarctica to reach a buried outpost below. We can presume, as the characters do, that this is near McMurdo station, and the original location of the second stargate - presumably, given that it was within 50 miles of McMurdo, somewhere on the Ross Ice Shelf. The ancient outpost under the ice was, however, on land, and anchored to it by a mid sized tower. This, along with the mountains in the background, leads me to think it’s in the vicinity of the Transantarctic Range, where I believe the ice to be around 1 to 2 kilometres thick.

As I’m trying to derive an upper limit, I’ll use 2000 meters as the depth of the hole that was bored. This is rather more than the quip in the story ‘a mile of ice,’ too.

The hole down to the facility (which, according to the commentary, the original script called for, amusingly, the team to rappel down into) was burnt over – in screentime, from when it starts, to when O’Neill shuts the reactor off – 103 seconds. It appears to be somewhat wider than the transmission beam itself, so for radius of the column of evaporated ice, I will use two meters diameter.

π1² = 3.14159 m²
3.14159 m²*2,000m=6,283.19m³
6,283,185 Kg of ice.
Latent heat of fusion = 6,283,185*334,000 J = 2,098,583,790,000 J
Other Increase = 6,283,185*418,680 J = 2,630,643,895,800 J
Latent Heat of vaporisation = 6,283,185*2,260,000 J = 14,199,998,100,000 J
2,098,583,790,000+2,630,643,895,800+14,199,998,100,000 = 18,929,225,785,800 J / 103 sec =
183,778,891,124 W =~ 184 GW

Personally, I'm quite impressed, given that this is a reactor you can hold under your arm. That's, using my previous calculations, about 1/200,000th of a ZPM.

This is an upper limit because it discounts any contribution made by the cargo ship hosting the transport rings, which, in order to rapidly reach escape velocity, assuming a mass of around ten tons, must be able to generate about the same output, possibly more, and uses a generous depth of ice and radius.

So… Comments or rebuttals?

[Keevan_Colton]

You can get the energy of the beam, but that doesnt really give an upper limit for the naquadah reactor, just a decent benchmark for its power output. There are various factors that might mean the reactor is not able to direct 100% of its output into Oniell's jury rigged drill...which means while you can establish the power required to operate the drill, that doesnt mean that it is the power of the reactor.

After all, you can run a hand drill on a shop bought battery pack, or on the mains from a nuclear reactor...and still it uses the same power, that doesnt establish an upper limit for the reactor or the batteries, only a lower one.

To establish a hard upper limit you need to find something it cant do. Anything it can do establishes a lower limit, anything it proves incapable of provides an upper bound, in that the power of it must be above what it's shown to be capable of and below what it cant do. You need to find the lowest possible value for the upper limit and the highest possible one for the lower limit to establish the bounds properly.

So, good work on the calcs there, but it's not really an upper limit for the reactor, plus as you point out there is the unknown of the contribution of the cargo ship to the process, it can give a good ballpark figure for the power though.

[NecronLord]

I'm fairly certain it's piped directly into the ring platform, and that most of the rest of the stuff was simply to make the rings do something they weren't designed to do. While the capacity of the wires used there is a limit, as you say, it's the same wiring as they always use to plug those things into anything. Still, I suppose you're right that the rings themselves are likely to be a limit on the amount of power that can be directed. Damn. It's always something obvious that you miss.

[Chris OFarrell]

Uh my impression from the episode was always that the matter stream effectively was being used to 'dematerialize' the ice like a ring transporter does in normal operations (if on a much more controlled and smaller scale) probably dissipating the matter as some kind of energy (neutrino radiators anyone?) It was very clearly NOT vaporizing its way down, that much ice vaporizing should have cause a gigantic steam plume to scream up at very high speed, completely engulfing the cargo ship as a matter of course. All you got was a very tiny and gentle bit of steam wafting, the beam might have had some tiny thermal component after all...

I mean hey, its basically a cheap Asgard 'go somewhere' beam, he DID have the frigen Database in his head after all.

It also explains the lack of a horribly hot Ancient outpost at the bottom of the shaft, the expected flood of water from ice that melted rather then vaporized and the almost perfectly smooth hole made.

I mean I'm not a geologist but I'm pretty sure that vaporizing your way through a kilometer or two of ice in a matter of minutes is going to cause the walls of said shaft to fracture and break down from the heat.

Still. Removing that much ice that fast, there must be some kind of thermodynamic issues which can be used to calculate power consumption.

[NecronLord]

Fair point, but the results from it being able to dematerialise many many tons per second would be laughable, though. As in 'A ZPM powered weapon should bounce off a Tel'tak, which can re-radiate vastly more energy'

I'd rather write the small amount of steam off as an effects/watchability issue than try to rationalise the tel'tak being able to somehow safely dump over a teraton per second into its enviroment. The effects do make an effort to acknowledge a heating effect, after all.