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Old October 4 2013, 07:29 PM   #1
Nob Akimoto
Location: The People's Republic of Austin
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Sorry Johnny, your ship's too small...

The Excelsior scaling thread had me going back to look at some of my volumetrics notes from ages ago. (And let me tell you, digging around for half-written short form memos on harddrives from a decade ago isn't fun)

Specifically I wanted to look at the comparative internal volumes of the Sovereign, Galaxy, Akira and Nebula classes. (Along with older ships like Excelsiors and Ambassadors).

The Galaxy and Nebula have a substantial advantage when it comes to overall internal volume clocking in at 5.8 and 4.5 million m respectively. The next largest Starfleet design is Ambassador at 2.9 million m. The Sovereign when scaled at the John Eaves length of 2248' comes into a mere 2.4 million m.

First, we need to subtract the usable volume by getting rid of the warp nacelles.

Interestingly despite appearances, the Galaxy-class nacelles are fairly more voluminous due to their substantially greater beam. (Their heights are equivalent, while the Sovereign nacelles are longer by about a 20%. Sizes are about 250x50x30 for the GCS, and 320x30x30 for the SCS) Modelled volume is about 280,000 m while rougher calculations with cylinders of comparable dimensions yield a range of between 250,000 m - 290,000 m. Two nacelles gives us about 500,000 - 580,000 m. SCS nacelle volume estimates range from about 190,000 - 220,000 m giving us a total volume of 380,000 - 440,000 m.

So habitable volume on each ship becomes: 5.3 million m on the Galaxy, 4 million m on the Nebula and ~2 million m on the Sovereign.

Conservatively let's assume the TNG:TM is correct and about 35% of the Galaxy-class is empty space in her initial configuration circa 2365. And being even more conservative, let's subtract that as a total volume of the ship, not simply of habitable volume. That works out to 2 million m of empty space leaving us with 3.3 million m of volume used for things like systems, components, etc.

We can subtract some volume based on what we know of the crew complement of the Enterprise-D. As of Rascals she had a complement of 1,012. Allocating single occupancy quarters of 110 square meters per person, and allowing for triple redundancy (*guest quarters, evacuation limit, troops, etc.) we get a volume of about 1,018,000 m used for crew quarters. (Assumption is 110 m quarters * 3.3m average deck height giving us a roughly 363 m crew quarter module). So we're now left with 2.2 million m of usable volume.

For the sake of maximizing Sovereign-class internal systems, let's say she has a crew of 400 with crew quarters that are about half the area of a Galaxy-class ship and only double redundancy. (The quarters in the TNG movies are IIRC, redresses of the Voyager sets, which were in fact smaller for most quarters except the Captain's.) So 55 m and a deck height of 3.5 m (87m height divided by 24 decks, ignoring for the moment the deck 26 by Daniels in FC and 29 in NEM) giving us 192.5 m multiplied by 800 for 154,000 m total for crew quarters. This leaves the ship with 1.85 million m.

Next we go with fuel. Again, let's work with the TNG:TM's numbers for the GCS. 66,000 m is dedicated for the deuterium and anti-deuterium tanks, which is supposedly good for a 3 year cruise at warp 6. Basically the volume is a rounding error compared to total volume. I see nothing wrong with giving the same volume to the Sovereign.

Therefore if we assume the Galaxy's remaining internal volume is perhaps dedicated 75:25 to scientific vs. tactical systems (overly conservative, again), we get a payload capacity for equipment of 575,000 m.

If we decide that the Sovereign is fully loaded AND has internal volume almost totally dedicated to warfare instead of science (again, a dubious proposition) with the inverse proportion of systems dedication as the Galaxy we do get a more powerful tactical suite of 1.4 million m.

We know at least the intention was for the Enterprise-E to be a more powerful ship than her predecessor, given the STFC script describes her as "Starfleet's newest and most powerful vessel".(Emphasis added)

The internal features suggest Sovereign is a more powerful ship. For example scaling the warp core using Data as a benchmark (he crawls on top of the Enterprise-D core at one point and then he stands basically right next to the coolant pod in First Contact in this scene.) The coolant pods seem to be about the same diameter (or perhaps a smidge larger) than the Enterprise-D warp core. The Enterprise-E's warp core "nodes" are each about 2/3rds the diameter of the coolant pods. Somewhat conservatively we'll assume the coolant pods and the E-D core are 1.5m in diamater. We get a cross-section area of 1.8 m for the E-D core, and 1 m per "node" in the E-E. (A lower end estimate for this by the way is a 75cm diameter node instead and a cross-section area of 0.785 m) If the E-E warp core has only 6 nodes (without the central one shown in cutaways) that gives us a total area of 4.71~ 6 m. If the heights are equal to deck height then the respective cylinders have a volume of 75.6 m (1.8 m x 12 decks of 3.5 m each) and 230.8 ~ 294.2 m (14 decks of 3.5 m each x 4.71 ~ 6). Reaction chamber sizes are a bit harder to measure, but the Galaxy chamber appears to be about 1.5m tall while the Sovereign one is a bit taller at around 2m. The chamber sizes are therefore about: 2.7 m vs 9.41 ~ 12 m. Meaning the Sovereign's warp core is anywhere between 3x to 3.85x the total size of a Galaxy's. Reaction chamber size is closer to 4-5x. In which case this is all good, right? Sovereign more powerful than Galaxy case closed...

The problem of course becomes when we start chipping away at the assumptions made in the volume calcs above.

First, is it reasonable that the Sovereign would have such a small crew? We know the Intrepid-class has a crew complement of approximately 150, with a total internal volume of 625,000 m. Galaxy with a volume 9.3x that of Intrepid has approximately 6.7x the complement. So we know the scaling of crew size isn't necessarily linear with volume. OTOH Intrepid-class ships are state of the art, brand new with computer systems that are bleeding edge circa 2371. Since the Enterprise-E is roughly the same vintage, it's probably safest to assume a similar crew density, particularly since unlike the Enterprise-D circa 2367, she (presumably) doesn't have an enormous amount of empty volume. In fact, accounting for that empty space actually makes the Enterprise-D crew density HIGHER than Voyager at 0.26 people/1,000 m vs 0.24 people/1,000 m. At Voyager level crew densities, the Enterprise-E would have a complement of 574, while at the same density as her predecessor, we get a complement of 624. Since the senior staff is essentially unchanged from her predecessor, we might surmise the E-E has a similar crew complement (sans civilians).

Double redundancy in capacity in this case gives us a total of 1,300 or so quarters and a total use of 250,000 m or so. Of course we're told in Treklit and tech publications that Enterprise's complement is closer to 800 and she has an evacuation capacity for something like 9,800, so perhaps she, too has triple redundancy in accommodations, which would bring us to about 500,000 m of total internal volume dedicated to crew quarters.

Finally on the accommodations front, are the quarters really THAT much smaller than on the Galaxy? We know Riker's quarters at least has a full sized bath tub, a separate bedroom/office area in addition to the living room, so isn't all that much smaller than those on the E-D. Picard's quarters were a redress of Janeway's, which were in turn I think a redress of Picard's original quarters. Even using the Fact Files cutaway, we get something in the order of 60 m for the living area, plus an unspecified size for the other rooms (bedroom + bathroom). In which case quarters of 80 m to the original GCS spec of 110 m are perhaps more reasonable. This of course substantially increases the amount of space taken up by crew quarters. (672,000 - 924,000 m vs our original estimate of 154,000 m) This would significantly reduce the available space for other uses. The new range of available systems volume goes down to 1,076,000 - 1,328,000 m. Recalculating our tactical systems at 75% of those volumes gives us: 807,000 - 996,000 m.

Second, should we assume Sovereign is completely biased toward tactical goals? We know that Picard seems annoyed at being sent out to put out diplomatic brush fires, and that she's finally assigned to do some exploring at the end of NEM. Presumably the ship is capable of serving some scientific functions and exploratory functions. Using our revised available volume figures, this gives us payload of 403,500 m to 498,000 m which, uh oh, puts us under the Galaxy. Even the old payload volume of 75% of hull volume sans living quarters looks pretty low, too as we're talking 605,250 - 747,000 m.

Further, is pegging the Galaxy class tactical systems at a mere 15.5% of her total internal volume reasonable? What if we set the volume percentage at 25% of total internal volume instead? We get a rather much larger volume of 1.45 million m, or something equal to our original (vastly inflated) Sovereign estimates or nearly twice that of our revised (and still inflated) estimates. (Coincidentally or not, 1.45 million m is roughly the same as the internal volume sans nacelles of the Galaxy-class battle section.)

This is a bit of a problem. We see suggestions in the DS9TM that Starfleet was more than capable of building "mostly empty" Galaxy-class hulls with just their tactical suites. Assuming that most or all Starfleet technology is modular, it makes no sense to build a Sovereign when you could build an equally or even superior Galaxy-class hull for the same effort. This is even more the case when you consider that in terms of long-term expandability and usability the latter hull is vastly, vastly superior.

Further the raise d'etre of the Sovereign becomes murkier still when we see that there's already a "reduced size" modern ship of similar, but not quite capability as the Galaxy in the Nebula. At 3.5 million m internal volume, a stripped down Nebula could be equipped with more spartan living quarters and given a similar or superior tactical payload. what's the point of a 2.4 million m Sovereign? Is her warp geometry that much more superior? It's a possibility given that ships similar to it in length/width ratio seem to have substantially improved warp speed performance over much beamier ships. Voyager has a "maximum cruising speed" of warp 9.975 according to Caretaker, and Prometheus was doing warp 9.9 without much trouble. On the other hand, Bonchune (or whatever that Nebula in Message in a Bottle is named) was catching up to the fleeing Prometheus so perhaps the performance advantage isn't quite as pronounced as we're given to think.

But what if we scale the Sovereign to a slightly greater size? We can either work from a 2370s average deck height of 4m x 24 decks (ignoring the deck 26 and 29 references) or stick with a 3.5m deck height but increase deck count to 29. In either case we end up with an increase of volume of about 1.331 - 1.56x giving us a more comfortable range of 3.12 - 3.75 million m. Nacelle volume now ranges from 247,000 - 343,000 m which might reasonably give us a superior performing set of nacelles over the Galaxy. For the sake of compromise, let's take the mid-point between the really big figures and posit a 3.435 million m Sovereign for the remainder of this post. (This would give us a ship length of 775m or so...)

Such ship would have a nacelle volume of 295,000 m and a total usable volume of 2,845,000 m. Assuming more modest accomodations than the Galaxy of 80 m with a deck height of 4.1m (roughly equal to Intrepid and Defiant dimensions and rather incidentally equal to the deck scaling in the Sovereign MSDs) and 2,000 quarters gives us 656,000 m of accomodations leaving us with 2,189,000 m of payload volume. With a 75:25 split of tactical/scientific volume, we then get a mission payload of 1,641,750 m for tactical systems and 547,250 m for everything else, which actually compare rather favorably to our 25% total volume tactical Galaxy's 1,450,000 m tactical and 750,000 m scientific facilities. Contrasting to a Nebula with a similar loadout ratio as a Galaxy yields 1,125,000/585,000 m which compares very favorably to our bigger Sovereign. (Of course our "maximum possible" Sovereign based on dialogue and internal arrangements would have 29 decks with Intrepid style 4m decks given cooridor size/Jefferies Tubes arrangements and would have a volume damn near approaching a Galaxy, but let's not go there)

If you then combine much more favorable warp geometry (official sources range from warp 9.8 to 9.985 for Sovereign-class top speed) and perhaps better distribution of tactical systems, this then becomes a ship that actually is more powerful and perhaps more useful to build than upgunned or upgraded Galaxy or Nebula-class ships.

It's all a bit speculative, of course, but perhaps we misread the size comparison in First Contact. Maybe the Defiant wasn't scaled down, and it's simply that Enterprise is bigger than the various setting drawings. Perhaps Jean-Luc was just talking about the length of the ship itself (sans nacelles?) when describing her to Lily. Both are a bit of a stretch, of course, but the ship being only 2.4 million m in volume is also a stretch.

Last edited by Nob Akimoto; October 4 2013 at 08:46 PM.
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