Thursday, January 21, 2010

Star Destroyer Mass and Density Guesstimate

While working on an old unfinished page I'd forgotten about, I realized that I really needed a decent estimate of Star Destroyer mass.   Despite not having much to really go on, I decided to make a guesstimate.  

Unless and until we get more information, it's as good as anything else:

So, let us assume that a Star Destroyer is 1600 meters in length.   Now we need an estimate of their density.   We have options here.

1.  We can attempt to use the density of Star Trek vessels.   Star Trek vessels like the Intrepid Class, for instance, have a density of over 1100 kg/m³.  However, we know that the vessels are constructed of different materials and so on, so this is a somewhat dangerous assumption.  There's also the fact that the Constitution Class ships had a far higher density of over 4300 kg/m³.   However, given that the Intrepid can land as most Star Destroyer classes seem able to, the Intrepid density seems the safer (albeit still dangerous) assumption.

2.  We can attempt to use the density of real-world spacecraft.   This is also dangerous, of course, since real-world spacecraft are hardly military vessels.  They are designed to allow people to get to space for a brief period of time, but can hardly be expected to withstand even a single hostile bullet or other decent-velocity impact.

Now, it happens that when Star Trek guru Rick Sternbach was designing the Intrepid Class for Star Trek: Voyager, he intentionally based their stated mass off of an estimate of the ship's volume, calculating the mass via a density derived from an estimate of the Apollo capsule command module.  And indeed, the Intrepid density is within about 10-20% of that value, assuming the Intrepid model used on this site for the estimate is basically the same as his.   However, the command module was basically just the crew compartment and heat shield for re-entry, a single part of the combined Command/Service Module (CSM), with the service module featuring the large engine bell and other machinery that enabled Earth-Moon transit.

Taking that combined vehicle which masses 30 tonnes and ballparking her volume based on her 4m diameter and 8m length (she's actually 11 meters, but between the rear engine bell and conical front section a 'shave' is not out of order for determining ballpark density), the CSM volume is 100m³ and her density is thus 298kg/m³.

That seems a bit light, so we can also compare to the space shuttle orbiter.  Empty, a newer shuttle like Endeavour weighs about 70 tonnes, and she's about 105 tonnes when full.   At about 37.25m long, 23.75m wide, and 17.25 meters tall, she's a big girl.   Determining her density is a little bit of a trick, though, since much of her total empty mass . . . not to mention her width and height . . . is nothing more than wing surfaces.   But since we're ballparking, we can simply take the fuselage as a cylinder and tack on a couple of extra meters for the eyeballed volume of the various atmospheric control surfaces.

So, per estimation from this site, we have the total length of 37.25 meters.   A smidgen of that is the vertical stablizer (the tail fin), but we'll just roll with that figure.  Given that the shuttle fuselage is roughly cylindrical, the height and width values of about 6 meters are sufficient for diameter (the crew area and payload bay are below six meters, the rear fuselage with the engines is over six).   So if we ballpark a 40x6 cylinder, we come up with a total volume of 1130m³.  Given her empty and full masses, the density ranges between 62 and 93kg/m³.

Well, now.   It seems that Rick Sternbach's choice was rather on the heavy side, after all.  The space shuttle tops out at around 100kg/m³, the Apollo CSM 300kg/m³, and the Apollo command module with heat shield by itself is near 1000kg/m³.  And yet the Constitution Class still came in four times more dense than that, and about 40 times denser than the space shuttle!

So where should we attempt to put the Star Destroyers?   Considering that large warships of the Clone Wars era seem to be largely hollow (e.g. the Venators with their extensive landing bay areas, the Malevolence with its massive open center railway areas, and so on), I hardly feel comfortable comparing it to an Intrepid Class ship that has very little empty space by comparison.

On the other hand, given the extensive use of simple steel even for external towers on the Death Star (per the ANH novelization), Coruscant buildings, and similar, it seems unlikely that durasteel or steelcrete will be superdense.   After all, given that a natural stone on Yavin was so dense that no weapon was thought capable of penetrating it, we could be forgiven in believing that Star Wars ships are built strong but as light as possible.

That said, I figure Star Destroyer density probably falls somewhere in the 500-1000kg/m³ range.

Given a calculated volume of about 54,000,000m³ for Star Destroyers at 1600m length, and a density range of 500-1000kg/m³, the mass of a Star Destroyer should fall somewhere between 27,000,000,000 and 54,000,000,000 kilograms.   That's 27 to 54 million metric tonnes.  

If one wants a specific estimate, I'd guess a density of 750kg/m³ and an ISD mass of 40,000,000 tonnes.

Using this density figure elsewhere would give us the following masses:

VesselMass in KilogramsMass in Tonnes (est.)
DS1 (@120km):678525000000000000680 trillion
DS2 (@160km):16080000000000000001.6 quadrillion
Super SD:94844250000009.5 billion
Home One:253978500000250 million
Trade Fed:15208125000001.5 billion
Nebulon-B:138729000140,000
Tantive IV:4856400050,000
X-Wing:2025020
TIE:1125011
Imp. Shuttle:357750360
Millennium Falcon:29377503000

Actual figures could vary significantly, of course, and my rounding above was somewhat haphazard.   I would say that this is especially the case with smaller vessels, but interestingly the X-Wing mass is almost identical to the empty mass of an F-14 Tomcat.  Once missiles and fuel are added, though, an F-14 can mass 33 tonnes.

Also, I don't have volume figures for the Venator or Acclamator.  I'd guesstimate the former at 15 million tonnes and the latter around 8-10, but I really have no clue as to the proper value.  This is just a complete pulled-from-the-posterior guess from memory.

2 Comments:

Anonymous Anonymous said...

Interesting guesses. Although isn't the F-14 alot bigger at 19.1m while the X-Wing is alot smaller at 12.5m ?

Thu Jan 21, 09:32:00 PM 2010  
Blogger G2k said...

Yes.

Thu Jan 21, 10:46:00 PM 2010  

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