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DSG2k

Star Wars Vessel Densities

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Ooh, I like this editor.   It allowed for perfectly good copy and paste without a lot of manual modification.  Nice.  But, rather than copy and paste the long posts, I'll simply summarize below.

 

Anyway, given that there is not a great deal of overlap between communities currently, and given that ASVS is a bit slow at the moment, I thought it might be worthwhile to post this here for additional feedback.

 

To summarize, "Water War"[TCW4] points toward vessel engine densities in the 500-1000 kg/m^3 range, and the newly-canon TCW novelization points to vessel and fuel densities that are far less still in the case of the Twilight.   Even if we presume the Twilight's design was not known by Traviss owing to the greater lead time required for novelization-work versus production-work (and thus that the specifics as applied to the Twilight might not be valid), there is still the point that the fuel itself is not especially weighty.

 

Put simply, then, I see no obvious way to maintain the claim of super-dense ships.  The X-Wing suddenly sinking in muck on Dagobah certainly doesn't point to super-dense fightercraft.  The X-Wing sinks all of the sudden . . . it sat on the ground beneath the not-terribly-deep water from the time of unsoft-landing until the middle of the stone-stacking exercise. Then R2 freaks because all of the sudden the thing is almost submerged.

Presumably the ground beneath both it and the water gave way somehow, since not only did it sink all of the sudden but also turn by about 30 degrees, as well, given the apparent orientation of the guns versus the ship's prior orientation (with the big tree nearby as a guide). Perhaps the thing that tried to eat R2 had an underwater lair that collapsed? Who knows.

But in any case, I'd say that's more a test of the ground pressure of the lake bottom.

 

So do we have any canon evidence of massive ships that I'm missing?   

 

There's the crash of the Trade Federation core ship in AotC . . . assuming a 700m sphere that vessel's volume is 179,600,000 cubic meters, suggesting a probable mass of 90 million tonnes or less.  I haven't worked the scene to get crash speed and whatnot, but I don't get the sense that it was hypervelocity.   At 200 meters per second, for instance, the kinetic energy would work out to less than half a megaton, which doesn't seem too off from the scene as I remember it (and bearing in mind that not all of an impact like that would be in the form of air blast, owing to the comparatively low impact velocity, the fact that it was a strike on the deformable ground by a deformable ship, et cetera).

 

What else is left?

 

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So do we have any canon evidence of massive ships that I'm missing?  

 

The Death Star.  Minimum average density in excess of 5000 tons/m^3, just to fuel the Alderaan shot.  However, it may be a slight outlier in this regard, given that scaling the DS power generation capabilties to capship size produces numbers one or two orders of magnitude above their actual capabilties.

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Welcome to the Forum DSG2K 

These ships can accelerate to and from relativistic velocities, and such requires a huge quantity of fuel. To be successful the fuel carried would have to outmass the ship by ~10 times, otherwise you would run out of fuel long before achieving such velocities. The example in the novel is inconsistent with these other [onscreen] examples where ships easily achieve very high velocities orders of magnitude faster than the speed of sound, such as the X-wings very fast navigation past the diameter of a gas giant named Yavin, before decelerating to "combat velocities" and remaining relative to the moving Death Star. 

 

The Rebels tac-display also demonstrates that the Death Star massively accelerated within the last five minutes of its navigation around the planet. Strangely, but clearly, it's speed had remained constant for the entire trips duration before those final five minutes. This is further evidence for very high acceleration. 

 

http://www.galacticempirewars.com/starship-hulls-and-anti-grav

 

http://www.scifights.net/ics5.m4v

 

The ships sink rapidly to the bottom of oceans. They are not superlight. They are dense. 

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The Death Star.  Minimum average density in excess of 5000 tons/m^3, just to fuel the Alderaan shot.

That estimate requires a set of assumptions about the operation of the Death Star that seem rather unsupportable. Assumptions do not trump canon. Here we have direct measurements and direct statements that correspond to all other direct indications insofar as the behavior of the assorted liquid fuels and hoses observed.

 

And, of course, there are competing views insofar as the Death Star's operation are concerned. But,rather than wind up derailed on that discussion, allow me to simply thank you for your post.

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That estimate requires a set of assumptions about the operation of the Death Star that seem rather unsupportable.

 

The only assumption it requires is that the energy density of hypermatter is limited to 9E16J/kg.  The dimensions of the Death Star are provided in the original ICS, and the energy requirements to destroy Alderaan can be determined from the visuals, both from the rate of expansion of the debris field and the momentum recoil of the planet.

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Well, as the ICS is no longer canon, we can't really say HOW big the Death Stars were.  The only canon information now is from SW.com, which simply says "size of a small moon".

 

(Which is odd, considering it gives exact measurements for every other ship.)

 

And I'm not doing one of those "Higher Canon Tiers" things.  Ever since Disney implemented the new canon policy, ALL books save for adaptations of the movies and cartoons have been moved to the non-canon, or "Legends".  Even the ICS was dumped there, according to Wookieepedia.

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Well, as the ICS is no longer canon, we can't really say HOW big the Death Stars were.  The only canon information now is from SW.com, which simply says "size of a small moon".

 

Plus the film itself of course, which gives a diameter between 125 and 190 km - the 160km figure I used is bang in the middle of that.

 

And I'm not doing one of those "Higher Canon Tiers" things.  Ever since Disney implemented the new canon policy, ALL books save for adaptations of the movies and cartoons have been moved to the non-canon, or "Legends".  Even the ICS was dumped there, according to Wookieepedia.

 

Huh.  My understanding was that they'd simply binned everything below G-canon, which included the ICSes.

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"Legends" pretty much means "non-canon, but authors can use stuff there as a resource."  The movies, TCW, Rebels, and their adaptations are canon.  Everything else is "Legends".

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The only assumption it requires is that the energy density of hypermatter is limited to 9E16J/kg.  The dimensions of the Death Star are provided in the original ICS, and the energy requirements to destroy Alderaan can be determined from the visuals, both from the rate of expansion of the debris field and the momentum recoil of the planet.

 

Well, I prefer to confine my examinations to the canon, so I will simply thank you again.

 

I am aiming specifically for direct indications of supermassive ships, with evidence on par with the sinking and direct statements, as opposed to if-this-then-that-and-if-that-then-that-there scenarios.   For example, a guy being unable to lift a small hull plate would be good.  A ship with spindly legs sinking into the ground would be nice.   That sort of thing.

 

Instead, what I find are references to hydrofoamed permacrete and other weight-saving measures of that nature as I have mentioned elsewhere, such as http://dsg2k.blogspot.com/2014/02/permacrete.html

 

That kind of thing doesn't make a lot of sense under the dense ship arguments.  Certainly a Death Star with a steel exterior (at least in the docking port areas per the ANH novelization) could have been made of something more robust instead if the entire vessel density is about a thousand times more than steel anyway.  In biggaton-land that's just asking for trouble.

 

I don't bring that up to derail but to point out the consistency of "normal", accessible, authentic values, because I'm here to seek the hardest available counter-evidence, since none came to mind for me.  And, with apologies, a number of assumptions about the Death Star and how it works which result in extraordinary density just don't make that cut for me.  To my way of thinking, if a chain of assumptions, when reasoned out, results in severe and repetitive disagreement with the canon (which in this case it certainly seems to), then perhaps the reasoning is flawed.

 

But again, thanks for pointing that out.

 

As for the Death Star size, my old DVD-era work comes to 120km for DS1, which corresponds nicely with some of the old popular values.  It was DS2 that came out to 160.

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Well, I prefer to confine my examinations to the canon

 

I'm glad to hear it, hence why I refer you to dimensions and power requirements derived directly from ANH.

 

 Certainly a Death Star with a steel exterior (at least in the docking port areas per the ANH novelization) could have been made of something more robust instead if the entire vessel density is about a thousand times more than steel anyway.  In biggaton-land that's just asking for trouble.

 

Steel's robust enough to do the job it needs to for that part of the station. It's a docking port, not the main belt, no why use something fancy when you don't need to?  Indeed, I wouldn't be surprised if DS armour protection is considerably less than a typical warship - it's designed to withstand capital ship attack, and its shields can withstand energy releases sufficient to destroy planets.  Why waste resources with high grade armour?

 

I don't bring that up to derail but to point out the consistency of "normal", accessible, authentic values, because I'm here to seek the hardest available counter-evidence, since none came to mind for me.  And, with apologies, a number of assumptions about the Death Star and how it works which result in extraordinary density just don't make that cut for me.  To my way of thinking, if a chain of assumptions, when reasoned out, results in severe and repetitive disagreement with the canon (which in this case it certainly seems to), then perhaps the reasoning is flawed.

 

 

Actually there are very few assumptions involved here - we saw Alderaan explode, violently, and we saw that the planet had been knocked back, hard.  The energy requirements for the event are based on hard physics.  The only area where there's a lack of hard numbers is in the size of the Death Star, and based on your figures the uncertainty there seem to tend towards a smaller, and therefore even more dense, vessel.

 

As for the Death Star size, my old DVD-era work comes to 120km for DS1, which corresponds nicely with some of the old popular values.  It was DS2 that came out to 160.

 

The relevent calculations are here if you'd like to have a look.

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Welcome to the Forum DSG2K 

 

These ships can accelerate to and from relativistic velocities, and such requires a huge quantity of fuel.

Other than the conclusion that this is how the Falcon got from Anoat to Bespin, do we have any other evidence for relativistic velocity from the sublight engines, i.e. not when making the jump into or out of hyperspace?

 

Also, on the canon point I made with Seafort, if we use the ICS and hypermatter as I understand it, we get tachyonic fuel with complex mass used to alter the ship's real mass to cheat the requirements for infinite energy to get to lightspeed. In other words, it brings mass lightening to the table, making all mass calculations suspect, and even rendering moot acceleration values as a guide to fuel density. So, I will skip the non-canon and with it contradictions, though this may be something you would like to address.

 

The example in the novel is inconsistent with these other [onscreen] examples where ships easily achieve very high velocities orders of magnitude faster than the speed of sound, such as the X-wings very fast navigation past the diameter of a gas giant named Yavin, before decelerating to "combat velocities" and remaining relative to the moving Death Star.

I have the rough sketch outline of a differing opinion of that example and the other time-to-orbit claims. I will elucidate them more thoroughly in a future post when I have time to sit and do screenshots and write it up properly. Suffice it to say for the time being that none of them hold up very well.

 

Also, for what it's worth, I have heard it argued that antigravs only serve to remove 1g of acceleration. This is not accurate, as they serve to boost per the ANH novelization:

 

"Docking bay ninety-four, Luke noted, was no different in appearance from a host of other grandiosely named docking bays scattered throughout Mos Eisley. It consisted mostly of an entrance rampway and an enormous pit gouged from the rocky soil. This served as clearance radii for the effects of the simple antigrav drive which boosted all spacecraft clear of the gravitational field of the planet.

The mathematics of spacedrive were simple enough even to Luke. Antigrav could operate only when there was a sufficient gravity well to push against-like that of a planet-whereas supralight travel could only take place when a ship was clear of that same gravity. Hence the necessity for the dual-drive system on any extrasystem craft."

 

The Rebels tac-display also demonstrates that the Death Star massively accelerated within the last five minutes of its navigation around the planet. Strangely, but clearly, it's speed had remained constant for the entire trips duration before those final five minutes. This is further evidence for very high acceleration.

This concept was addressed circa 2002: http://st-v-sw.net/STSWdsaccel.html

 

Suffice it to say that the Rebel screen is contradicted by the Imperial screen of the same event.

 

Indeed, something I've been considering lately is whether or not there's any evidence of a powered orbit in that case at all. I have yet to run the numbers regarding orbital mechanics to determine that. So far as I'm aware, the only other evidence is the note about "orbiting the planet at maximum velocity" given early in the scene (which suggests antigrav use), which itself is a second contradiction to the acceleration claim based on the Rebel screen.

 

Yes, I've seen that you're using my "established volumes". Please do me the courtesy of a link to the Volumetrics page or at least a mention of ST-v-SW.Net. Even if your use is somehow not covered by the creative commons licensing stuff, attribution would at least be polite.

  

The ships sink rapidly to the bottom of oceans. They are not superlight. They are dense.

Actually, the "Water War" example is the exact same example you use. Obviously it does not support super-dense ships. The other video example you use is of a sneaky invasion attempt, intentionally dropping parts intended to sink into the planet below and emit droids. Even if it suggests greater sinking velocity (which I don't know), it is not a 'natural' debris example and thus one should be wary using it for such.

 

And besides which, if ships are averaging somewhere in the neighborhood of 750 kilograms per cubic meter (assuming the engines are the most dense components), they hardly qualify as superlight. They qualify as pretty "normal" and comprehensible in a universe of fusion and steel.

 

And that really fits in with the more authentic Star Wars realism perspective that was prevalent before fusion and steel became re-imagined as hypermatter and neutronium in recent years.

 

The TPM novelization refers to Coruscant as steel alloys and glass. The ascension cables were steel-clawed. The ANH script refers to the door sealing the chasm that Luke and Leia swing over as steel. The ANH novelization refers to the Death Star exterior as steel and references its "steely horizon". The RotJ novelization refers to Boba as "steel-masked" and Luke's hand as being made of steel. The floor of the Emperor's room in the Death Star is made of steel. The Imperial shuttle has a "steely hull", and its landing ramp is described as chilly steel. The bunker corridors are made of steel. Melted steel floats amongst the debris of the final battle.

 

And, of course, there's the hydrofoamed permacrete and other weight-saving measures of that nature as I've mentioned before and will no doubt mention repeatedly.

 

These bits don't support super-dense ships, but instead point toward more readily-comprehensible densities and masses.

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Actually there are very few assumptions involved here - we saw Alderaan explode, violently, and we saw that the planet had been knocked back, hard.

 

The planet's still in the same place when the secondary blast occurs. 

 

Polarani.gif

 

polarcollapse.gif

 

This recent claim of Alderaan being blown back is incorrect, and, I would think, physically unlikely.  What's the claim, that it was knocked back at a million g or something?   I think it seriously unlikely that a planet would hold any shape at all even if you were very careful with your million-g acceleration effort.

 

The energy requirements for the event are based on hard physics.

The yield of the event is based on hard physics. The energy requirements you argue inasmuch as what the Death Star provided and what its reactor generated are based on assumptions.

 

If I watch a Dirty Harry movie, I can calculate that, to blow a hole in the badguy of such-and-such size, a projectile of a certain energy and certain characteristics was used.  However, if I have no understanding of gunpowder or clockwork-style mechanics, I may end up making assumptions that require Dirty Harry's trigger finger to be capable of twitching at that energy level in order to throw the projectile using the trigger as a simple lever.  

 

Naturally, I would be mistaken.

 

Similarly, if most all other direct evidence -- such as observing sinking parts, reading direct statements of vessel and fuel mass, pondering the materials from which the vessels are constructed, noting that ships are built with weight-saving measures -- points toward normal densities for fuel and vessels, the notion of a superdense Death Star . . . drawn as a conclusion from assumptions . . . suggests that the assumptions that led you to that conclusion are wrong.

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The second Death Star can't possibly be less than hundreds of kilometres in diameter otherwise the curvature of the horizon in the Executor crash scene would have been far more dramatic. 

Executor%20to%20Death%20Star%20size%20sc

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The planet's still in the same place when the secondary blast occurs.

 

Compare the position of the planet and the center of mass of the debris field in the last frame and there's a clear offset.  Brian has demonstrated this repeatedly in his videos.

 

 

This recent claim of Alderaan being blown back is incorrect, and, I would think, physically unlikely.  What's the claim, that it was knocked back at a million g or something?   I think it seriously unlikely that a planet would hold any shape at all even if you were very careful with your million-g acceleration effort.

 

It's far from recent - SWTC has referenced the planet's recoil and the minimum yield required to impart that momentum for over fifteen years.  As for the planet holding together under that acceleration, I agree that its unlikely.  I trust you will likewise agree with my observation that it didn't hold together.

 

If I watch a Dirty Harry movie, I can calculate that, to blow a hole in the badguy of such-and-such size, a projectile of a certain energy and certain characteristics was used.  However, if I have no understanding of gunpowder or clockwork-style mechanics, I may end up making assumptions that require Dirty Harry's trigger finger to be capable of twitching at that energy level in order to throw the projectile using the trigger as a simple lever.

 

You would, however, draw the conclusion that Harry had the capability to impart the requistite KE to the bullet, and therefore would have to store that energy on his person until the bullet was fired.  While you would mistakenly conclude that it was stored as body fat rather than propellant in the round, the fundamental conclusion is accurate. Likewise, the Death Star must store mass-energy before projecting it at a planet, even if the precise mechanism is unknown.

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Other than the conclusion that this is how the Falcon got from Anoat to Bespin, do we have any other evidence for relativistic velocity from the sublight engines, i.e. not when making the jump into or out of hyperspace?

Han's journey is a pretty solid example, but there are a couple more. 

 

Brian uses examples from TCW which you may have seen. A ship flies past a star in a matter of seconds before flying to a planet in the goldilocks zone within moments. The ship then decelerates to relatively mundane velocities just before they reach theplanets atmosphere. Both scenes are shot in real time, yet they were clearly moving at sub light according to dialogue and plot. The effects of time dilation at high percentages of lightspeed mean that those seconds could actually have been minutes, which is the only logical way to explain how they could have reached the goldilocks zone so very quickly. Even if the star was very small. 

 

If Endor is smaller than Earth (which it is based on comparison to the DS II) then the Rebel fleet was traveling at sublight speeds after exiting the hyperspace effects. The ships would have been traveling at a high percent of lightspeed in those few seconds as the moon rapidly multiplies in size in the cockpit view. They decelerate after having left hyperspace, which would have required thousands of g's in order to halt before crashing into the DSII or the planet. Similarly there is nothing to suggest that the Imperial fleet made tactical hyperspace jumps to flank the rebels.

Rebel%20fleet%20drops%20out%20of%20hyperWithing%20a%20second%20Endor%20appears%2Withing%20the%20next%20four%20seconds%20

 

 

 

And besides which, if ships are averaging somewhere in the neighborhood of 750 kilograms per cubic meter (assuming the engines are the most dense components), they hardly qualify as superlight. They qualify as pretty "normal" and comprehensible in a universe of fusion and steel.

How do you arrive at <1 ton per cubic meter? Why do ship debris sink so rapidly to the bottom of oceans is they are less dense than water? If ships only massed 1 ton per cubic meter (including fuels) then they would not have enough energy to achieve relativistic velocities. They would run out of fuel. Same with the high accelerations, those require extraordinary power and fuel. With such little density and so little energy they could not achieve such feats. This only makes sense if you think that ships in SW are limited to only single or double digit G's, but the Battle of Yavin would cease to make any sense if that were true, and the Battle of Endor would be more difficult to explain. The trip to the goldilocks zone in what is perceived as seconds at sublght would be flat out impossible. 

 

This concept was addressed circa 2002: http://st-v-sw.net/STSWdsaccel.html

 
Suffice it to say that the Rebel screen is contradicted by the Imperial screen of the same event.
 
Indeed, something I've been considering lately is whether or not there's any evidence of a powered orbit in that case at all. I have yet to run the numbers regarding orbital mechanics to determine that. So far as I'm aware, the only other evidence is the note about "orbiting the planet at maximum velocity" given early in the scene (which suggests antigrav use), which itself is a second contradiction to 

The rebel tac screen clearly shows that the speed had been constant until the last five minutes of the journey. Then the DS accelerated with at least 100 G's (probably hundreds) to cover the final length of the journey. So what does the Imperial tac screen show? What is the distance moved over time and what is the potent contradiction.

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I think there are a couple of inconsistently-scaled DS2 shots, yes. The better shots, including scaling against people rather than ships which themselves are of unclear size, point lower.

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Compare the position of the planet and the center of mass of the debris field in the last frame and there's a clear offset. Brian has demonstrated this repeatedly in his videos.

And I have demonstrated that the planet was in the same place when the secondary blast began, a blast which began to the left and above-center albeit still within the planet's pre-beam area.

 

Polarani.gif

 

AlderaanBlastg2k-0+25.jpg

 

That hardly seems to match the momentum viewpoint given that the beam struck above and to the right, unless the superlaser beam speaks billiards English. Even the second ring is only offset to the left by a smidgen . . .

 

Aldsecondring.jpg

 

. . . which follows the whole aspect of planar effects being at the center of mass . . .

 

DS2ringoffset.jpg

 

. . . with consideration of the violence of Alderaan's primary blast.

 

Moreover, the so-called debris field in the final frame hardly seems to contain the majority of debris . . . the large dark chunks which blast away and seemingly disappear, for instance, seem to come from the approximate location of the planet pre-beam. In other words, in which image do you think you see the most significant portion of the remnant mass?

 

AlderaanBlastg2k-0+60.jpg

 

AlderaanBlast-end.jpg

 

Some small portion of debris or a gas cloud or whatever it is being the focus of attention at the expense of the big dark chunks hardly seems a worthwhile argument, and certainly proves very little in regards to the Death Star's fuel density requirement.

 

It's far from recent - SWTC has referenced the planet's recoil and the minimum yield required to impart that momentum for over fifteen years.

Yep, it has been there for years. I stand corrected. It has, however, been the subject of a lot more than a passing paragraph recently, becoming a centerpiece of inflationary Death Star arguments, as you yourself demonstrated earlier.

 

However, I don't find it particularly relevant. Its relevance is only in the context of . . . and I hate to say it again, but it is what it is . . . a certain set of assumptions which I do not share.

 

Put quite simply, the inflationist viewpoint on the Death Star is to take the yield of a single event based only on a small smattering of its details (ignoring all the rest, which I consider a big no-no), give that yield exclusively to the superlaser (effectively treating it like a laser despite evidence to the contrary, which I consider a big hot mess of assumption at the expense of canon), and then assign that value with a short time-average to the Death Star reactor (a la Dirty Harry's finger, which I consider to be a bad idea).

 

I think a far more logical way of going about it is to gather all the information about the Death Star and its firing events first (plus obviously-related events such as DS explosions), and only then to start deciding what is or isn't going on based on a comparison of events and a reasonable synthesis of the evidence.  I rather think the good Sherlock Holmes would prefer the latter technique to the former, especially if he's being confronted with (to him) quasi-magical technologies he knows little about.

 

Or, in other words, ST-v-SW.Net and the Death Star Research Project.

 

So no, I don't view the superlaser destruction of Alderaan as evidence of an ultra-massive Death Star or fuel for it, and as it seems we're not likely to get anywhere on that point at the moment, we'll simply have to agree to disagree that it is a useful example in that context.

 

As for the planet holding together under that acceleration, I agree that its unlikely. I trust you will likewise agree with my observation that it didn't hold together.

That rather depends . . . looks like the planet was in place and still relatively round until the secondary blast. After that, not so much.

 

You would, however, draw the conclusion that Harry had the capability to impart the requistite KE to the bullet, and therefore would have to store that energy on his person until the bullet was fired. While you would mistakenly conclude that it was stored as body fat rather than propellant in the round, the fundamental conclusion is accurate. Likewise, the Death Star must store mass-energy before projecting it at a planet, even if the precise mechanism is unknown.

Well, you have at least conceptually acknowledged that the reactor (body) may not necessarily have had the energy itself via its fuel (food) to do the deed, but that instead it could have been a release of energy stored elsewhere (gunpowder).

 

Now, let us also ponder an explosion that completely destroys the badguy Dirty Harry fired upon, going off like a multiton bomb. And we ponder this in the context of how we now know about muscle, fat, guns, gunpowder, and bullets, and densities thereof.

 

Most would agree that continuing to insist that Dirty Harry was storing that explosive energy on or in his person and transmitting it via the bullet seems a rather noteworthy assumption, at the very least.

 

In any case, it is fairly apparent that we are not going to agree on the Death Star topic. I prefer to take the canon for what it says and shows from the rings to the reactor, whereas your arguments are based on trying to override the canon using what you believe to be scientific assumptions (though this is debatable, to put it mildly), thereby modifying Star Wars. Thus, I am talking about Star Wars and you are talking about something else, so we aren't really talking about the same thing.

 

But still, thanks again for the merry go-round.

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Just a quick note for Vince, re:

 

"How do you arrive at <1 ton per cubic meter? Why do ship debris sink so rapidly to the bottom of oceans is they are less dense than water?"

 

I arrived at that from the opening link I gave.

 

As for ship densities and sinking, I hope you are aware that a section of a modern ship will sink despite having less density than water just as is the case with the rest of the ship as a whole . . . if it is a section of the ship that is not airtight, it will fill with water then go down.    If we're talking about a hull plate instead and there's no air or what-have-you allowing for buoyancy, it will drop like the steel that it is, albeit perhaps at a slow rate if it is not exactly the most hydrodynamic shape.

 

Take the Titanic, for instance, whose forward section apparently went down in a unique "bouncy" manner with the nose pitching up and down, altering the speed as she went.

 

In "Water War", we see hull plates and frame sections also going down . . . they do not go down any faster than the engines.

 

More later.

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