Volumetric Confirmations

(The below was originally written in 2022 and not quite polished for publication.)

"Ilithi Dragon" recently commented that some of the entries in the Starship Volumetrics section might be off, based on experiences with deriving volumes for different models being employed as part of a large game mod effort.  I was, of course, suitably horrified, but having just done a little confirmatory experiment with a Galaxy Class warp nacelle, I didn't panic.   

Much.

The reason for the nacelle maneuver was that someone did a 2-D side view comparison of the Enterprise-D nacelle and the Titanic, which was cool.  But, of course, I knew that this was missing the difference of width and other factors, so I naturally put together a quick little video of the Titanic atop a warp nacelle and, also an art deco-inspired poster version as a follow-up, though of course it would be much better if SketchUp did lit internally objects properly, natively . . . 

The part that gave me pause was that, although I was pretty sure I'd calculated the Titanic volume before, I couldn't find where I'd posted it.   So, rather than reinvent the wheel, I did a quick search and saw where some Titanic website had a volume of 400,000 cubic meters or so.   I freaked out because an entire Galaxy nacelle ought to come out to around 280,000 cubic meters, per the old reckoning, so how the devil could that thing be another third of a nacelle when it was scarcely longer, no taller, and like half as wide?

After finding a nacelle, cleaning it out, and doing some testing, I became convinced that the nacelle figure was right . . . and in further looking, that Titanic website's estimate for the Titanic was wildly over the line.  The Titanic was 269 meters long, a maximum of 29.2 wide, and from keel to the top of the smokestacks was 53.3 meters ... if you treat that as a rectangular box, that's 404,000m³, but the ship was most assuredly not a box.   (Alas, I never did find my Titanic calcs . . . I think maybe I'd started some for this post?  I don't know.)

 

So the nacelle was fine . . . but what about the rest of the ship?   Dragon's statement was that not just the Galaxy, but the Nebula and the Sovereign also were off.   I trust that Dragon, so how borked is my stuff?

Well, I think I'm actually good*.   It's become harder to find models available for use now that 3-D printers exist.   That's because these models can have a purpose other than doing your own renders or being a volume-minded dork, so a bunch of folks are keen on trying to sell their models, no matter the quality or lack thereof.   However, if you're persistent, you can still find ways to acquire them.   

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* What does "good" mean, here?

Let's ponder our terms for a moment.   There will never be a perfect value for the Galaxy Class starship's volume, for various reasons.   Most notable among those reasons is the question:  which one?    I don't mean Enterprise versus Venture or Yamato versus Challenger.   I simply mean that there are a surprising number of models that have represented the ship.   Most people know about the graceful original six foot model and the chonky-boi "bulldog" four-footer with beefier lines and thicker paneling, putting my opinion of it nicely here.   That's all bad enough.   However, there was another small two-foot physical model in service from the start, and let's not forget the various ones blown up in that time-loop episode, and the special crashed saucer, the CGI versions . . . well, suffice it say, the list is extensive.

 So at that point, which one are we using?   That big fat shuttlebay on the back of the crash saucer is going to have an effect on volume, as will the more muscular upper secondary hull of the four-foot Bulldog, not to mention the thickened saucer.    Needless to say, there will be variation.   How much?   Certainly up to several percent.  After all, if we're dealing with a simple circular saucer a hundred meters across and ten meters thick, we have a total volume of 78,500 cubic meters, thanks to v=hπr².   Adding one percent to the thickness (taking it up to 10.1 meters) will only add about one percent to the volume, now 79,300m³.   But, if we instead add one percent to the diameter (101 meters, or 50.5 radius), that'll get squared, and our final volume will be 80,100m³, or two percent different.  Doing both gets us up by three percent.   That may not sound like much, but remember that we're only dealing with flat pancake shape, here.  If you imagine the Enterprise-D saucer as a set of flat pancakes for volume calculation purposes, then having many rather wider than they might otherwise be (as would be the case for a bulldog-esque saucer) and having more of them (for a vertically thicker saucer) will make differences add up pretty dang fast.

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I've selected a particularly svelte Galaxy Class, most closely resembling the six foot model as she appeared in Star Trek: Generations.  Let's run through all the steps, here, from conversion to the final confirmation of the volume reading.

First, a note that my old technique for Bridge Commander model use doesn't work anymore, generally proving my idea that software gets crappier over time, but there is an alternative technique available, and BC models have improved greatly in quality as computer hardware has improved.   As I mention in the linked Twitter thread, I don't need pretty, well-textured models for my purposes.   Indeed, my personal favorite models to use are of the style of modeler "Fort Opus" from the SketchUp 3-D Warehouse.   These are not and never will be photorealistic, and that isn't the goal.   What you see, though, is what you get . . . there are no textures being used to fake detail.   (There are some really, really crappy models out there that have great crappiness-hiding textures.)    Every window you see is a cut into the hull.   Every detail is a detail.  Every colored surface is a real colored surface, not just a texture wrap hiding a blank piece of digital cardboard.   This is, in short, the good stuff, even if it does look a tad cartoonish.

That said, few modelers cater to my needs . . . and by that I mean "zero".

So, let's take the aforementioned Bridge Commander: Remastered Enterprise-D.   I'll be covering the process of model conversion in another post, but suffice it to say that one can get a model from STBC to SketchUp 7 with only a minor amount of torment.

So now we have a SketchUp 7 model, ready for use with our SketchUp 7 volume integration tool.  The tool basically works by making slices of the model a certain number of times and calculating volume based on those slices.  By analogy, if you didn't know how to calculate the volume of a sphere, you could cut it into a hundred slices, do the volume of the hundred really short cylinders you made (with some fudging for the edge angles), and come up with a figure that was at least relatively close to a sphere's actual volume.   Obviously, this technique is useful for complex shapes like starships, too, but as with many things (even the Bridge Commander game) it requires that the object volume not have openings or gaps in the outer surface.  Additionally, you really don't want any extraneous geometry on the inside, either, since you end up with an 'outer wall' on the inside, which just confuses the thing.

Being impatient, I tend not to give the models a once-over at this point and instead just run the volume tool at "5% accuracy" (20 slices) and see what happens, 'cause sometimes I get lucky.    In this case, however, I don't.   As you can see from the pic to the right, it took  . . . oh, a few tries.

If you'll pardon me for going all Sybok, here's the part where I share my pain so we gain strength from the sharing:

I ran through a few iterations, changes of angle, and so on, and never did get what seemed to me to be a complete volume based on the visual feedback of the slices and their absence.   That is why I adore the volume plugin I use, though, and refuse to use one that doesn't feature that sort of feedback.

The first attempt resulted in a figure of 4.27 millon cubic meters, which is much lower than the 5.8 million I have on the Volumetrics page.

As you can see, there's a big section around the center of the saucer missing, another down around deck 39ish, and a few other things going on, like the upper neck . . . oh, and the nacelle pylons are completely missing.   Oops.   I tried again at different accuracy and did worse.

Before you go in ready to start hacking away at the model, there are other things to try.  This plugin is oriented to the 'world' of the modeling space, not the model.   That is to say, if you change the orientation of the model, the slices remain level to the 'ground', which can help you get around problems sometimes.   I generally tend to raise the nose 90 degrees and try again, which is basically what I did here.

That resulted in 5.2 million cubic meters at 2%, but with some obvious missing bits at the nacelles.  

Honestly, I could stop here and declare the 5.8 million figure basically verified.  Perhaps as much as half of each nacelle's volume is missing, which by itself puts us at 5.5 millionish, and if there's any other large gap or set of small gaps then we're within a point or two.   However, I tend to be a perfectionist, and at this point I am thinking the "Received Wisdom" model was probably rather bulldog-like and I'd love to know a more graceful, Probert-esque figure.

I decided to try rolling the model instead, which in this case didn't do a bit of good.

I landed at 4.6 million, with big obvious chunks of saucer missing, seemingly along the saucer impulse engines . . . suggesting there's probably an 'open' in those areas where they join the rest of the saucer.   There was also a strange gap along the entire saucer midline, as if the bridge might have a problem, and a separate smaller issue on the secondary hull.    I decided to try going straight up again but with a rotation, and while it did much better, it was still imperfect.

So at this point, it seemed as if a nacelle root repair job might do the trick.  I switched to a special "style" which colors the outside faces yellow and the inner faces red as a quick way to see if there are any reversed faces or internal issues causing problems.   Sure enough, the nacelle pylons intruded into the nacelles, and there was a 'cap' of sorts blocking things off.   

Looking forward from behind the port pylon

Starboard nacelle, extended pylon visible

Starboard pylon interior looking up at 'cap'

I cleared out one and just decapped the other and tried again.   This helped, but no changes I tried to accuracy or vessel angle would solve the fact that there remained an underlying issue.  

Finally, it dawned on me that this model could separate, with finished stardrive "cobra-head" and saucer aft cradle.   I decided to separate the ship and do it that way.   I had the saucer happy enough, I thought, but the drive section was still being a punk.   

(The above being a "5% accuracy" try, I re-ran the saucer at 0.5% and got almost exactly 3.7 million with no apparent gaps, though I expected more to show up (see below).   That's a 5.9% difference.   Mileage can vary.)    

So, I cleared out the other nacelle, and discovered that it was my lazy experiment of leaving the intrusion that was jacking up both nacelles.  Once I finished the cleanout process on the starboard nacelle, everything was great:

Being a glutton for punishment, I then manually docked the sections (gaining new respect for Riker in the process), and had "just one more" go at a volume for the combined ship.   

Needless to say, I found an issue:

Those saucer impulse engines and/or the stardrive battle bridge and/or the deflector dish were still taking a chunk out of the ship.   With her vertical and nose-up, you can see the gap going all through the neck and secondary hull.   So, even though I'd landed at about 5.5 million cubic meters with the nacelles fixed (as predicted, woot), my perfectionist tendencies were intensifying even as the thought of tackling the problems horrified me.  

So, I returned the ship to normal orientation, then pitched the nose up just thirty degrees, hoping the problem around the saucer impulse deck would be quite minimized at that angle, unable to affect the secondary hull at all.   Unfortunately, this revealed two other problem spots . . . something's still wrong at the nacelle roots, and there's (still) a mid-saucer problem, with all of these forcing me back down to 5.27 million cubic meters.

The good part about this outcome is that it cured my perfectionism regarding this model.   The way I see it, the six foot graceful Enterprise-D model probably runs around 5.6 or 5.65 million cubic meters, compared to the 5.82 million of the four foot Bulldog.  Sure, that's like an entire starship's worth of variation, but (a) that's what happens with a big ship, and anyway (b) it's a 3% or maybe up to 4% difference, which ain't bad.  

I can live with it.  

Figure confirmed.