Analyzing the Death Star more rigorously (ANH and ROTJ)

[Jedi Master Spock]

Reflecting on the Death Stars, I've frequently had cause to change my mind. I'm no longer very attached to the notion that superlasers and phasers are the same. Frankly, I'm now thinking the superlaser is a more powerful type of weapon by principle.

So far, while the new Death Star novel seems interesting, I'm a little worried about its overall consistency as a source, and reminded just how much information actually is present in the films and novelizations - especially remembering how much energy was released in their destruction.

I'm going to present a few calculations on this topic and see if I can't come up with a hard and fast set of figures - for reactor wattage and yield - I can defend without using the novel Death Star (and therefore can justify "publishing" on my website, as I will only publish on the website proper analysis whose epistemic basis is independent of the stated dispute between movie purists and EU completists) even if largely inspired by the Death Star.

[Jedi Master Spock]

First, I think it's clear to me that the best assumption is to conclude that the Death Stars use a non-volatile or nearly non-volatile fuel for the purpose of measuring the immediate yield of the Death Star's destruction. This assumption is compatible with the model of pulling energy out of nowhere (hyperspace) as well as the fusion reactor models. Implosion effects are presumed to be the effect of some side effect of the destruction of the reactor.

Second, it's also clear that at the time of their demises, both Death Stars were both prepared to fire. Jerjerrod was no more than 30 seconds away from pressing the button on the second Death Star, and Tarkin was similarly only moments away from firing on the first. Both, therefore, had fully charged superlasers.

However, the destructive effects of both were limited. In the case of the DS2, peak velocity of debris is commonly estimated to be in the area of 40 km/s (Sarli) to 80 km/s (Saxton); the primary difference between these two models being the presumed size of the second Death Star, and Saxton presuming a large DS2 for the purposes of his figures, 40 km/s is preferred. Some chunks are faster. We will assume 40 km/s to be the average velocity; this could be considered a compromise figure.

The kinetic energy of debris will constitute one reasonable estimate. Assuming the second Death Star to be, as Sarli does, 270 km in diameter (one of the highest figure which can be justified from the novelization), and assuming the average density of the second Death Star to be a somewhat plausible 5 g/cm^3, and the station half complete by mass, the mass could readily be 3e19 kg. Accelerating this mass to an average speed of 40 km/s gives an initial kinetic energy of 2e28 joules.

A quick scaling off the back of the envelope on poorly resolved frames suggests similar speeds for the DS1 if the DS1 is 160 km (again, a reasonable figure by all standards, if higher than some and lower than others, and one of the more popular ones). Using the same figures, we wind up with a kinetic energy of 9e27 joules - about half as much - although it's worth rounding up to 1e28 joules due to the fairly energetic ring seen.

However, a passage in the novelization suggests that brilliant illumination accompanied this. Specifically, that for several seconds, the light was blinding enough that nobody could look directly at it. Let us consider the possibililites for this.

I will assume this to be a flux of luminous energy that is at least 1 kW/m^2, and has a total energy of less than 300 kJ/m^2, from the perspective of things liiving on Yavin IV. Since it is brighter than the sun for several seconds but probably remains bright for a while, I will assume that, on the lower bound averages 1 kW/m^2 over the first thirty seconds -i.e., deposits 30-300 kJ/m^2 at a ~200,000 km radius. This will be 1.5e22-23 joules. The atmosphere can be expected to block around 90% of this radiation; however, the e24 joule range remains significantly lower than the kinetic energy of the Death Stars, which is then dominant in terms of the short-term energy burst released by the charged (but not firing) superlaser.

So, in conclusion, we expect around 2e28 J for a full power shot from DS1, and 4e28 J for a full power shot from DS2.

How long does it take to charge for a full power shot? It's not completely clear from the movies, particularly with low power shots being fired in ROTJ. We expect - generally - that the charging time is probably no more than a day (Alderaan and Yavin could easily be this close in time) and probably no less than the thirty minutes it took the Death Star to move into position.

The geometric mean of this is around 3-4 hours*, giving 7e23 W and 1.5e24 W for our power estimates.

*Coincidentally, this matches the Death Star novel.

[2046]

Interesting approach. Two details are missing, however:

1. Both film-only analysis and the new EU novel both suggest that the Death Stars were destroyed by a catastrophic chain reaction of the same type which the superweapons employ to annihilate worlds.

2. Material disappearance is also observable in both film and EU studies.

Both of those elements will seriously affect any attempt to gauge reactor output via the means you've used. The first virtually negates the idea of using the Death Star destructions to get reactor energy . . . the second specifically causes trouble for the use of debris kinetic energy figures.

I'm not sure how to append these to the approach you've used in a constructive manner.

[Jedi Master Spock]

Interesting approach. Two details are missing, however:

1. Both film-only analysis and the new EU novel both suggest that the Death Stars were destroyed by a catastrophic chain reaction of the same type which the superweapons employ to annihilate worlds.

2. Material disappearance is also observable in both film and EU studies.

Both of those elements will seriously affect any attempt to gauge reactor output via the means you've used. The first virtually negates the idea of using the Death Star destructions to get reactor energy . . . the second specifically causes trouble for the use of debris kinetic energy figures.

I'm not sure how to append these to the approach you've used in a constructive manner.

If you wish, think of this as a maximalist ballpark - what would the Death Star explosions mean if they weren't chain reaction effects? However, there's a lot of solid instinct between my choice of a model here, aside from the fact that it does provide a fairly good "bound" as far as traditional VS debaters may be concerned. (If anything, that seems like a remarkably low upper bound as far as I'm concerned; scaling down to ISDs puts us 2 orders of magnitude below what I like to claim for peak ISD reactor capabilities.)

I'm hinging my assumptions on the notion that the primary effect for the first few moments is going to be a simple explosion with the force of a superlaser hit. It's not necessary, but the implosion curve of the DS2 suggests that the explosion starts off looking fairly normal, and then diverges. By gauging the apparent normal part, I can attempt to gauge the "normal" yield minus any superlaser effect.

It's also worth taking into account one source of both disappearance and additional reaction energy - a presumed open rift into hyperspace. If you open a rift into hyperspace deep within an object, it'll collapse inward on itself unless the rift pours a lot of energy out.

Let's say open a rift in the middle of a planet and implode all its material through hyperspace into a region 1 km across. (We know implosion is involved from the ANH novelization as well as the ROTJ FX.) You pick up on the order of ~e36 joules of energy along the way.

Now, open the same rift in the middle of a Death Star. You pick up barely e24 joules along the way because of matter collapsing inward.

We'd generally expect similar phenomena with any chain reaction fueled by matter; a Death Star will fuel far less reaction than planet, meaning its explosion should (initially) behave reasonably simply.

[Mr. Oragahn]

People staring that the DS2 blowing up in high orbit... and partying later on.

About radiations only... what kind of initial energy can we estimate, considering that the victorious people down there didn't suffer at all, and that no major atmospheric disturbance could be spotted?

Besides, that could cap DS1's max output, as the DS2 was more powerful. Twice, in fact.

I think the figure we'd obtain that way would be way too low, and would require an extravagant explanation to explain the low amount of radiations poured on Endor.

Besides, how much do you rate the energy that generates the first explosion occuring on Alderaan?