Friday, April 24, 2009

A Problem With Math

According to the Eve Ship Chart the length of a Hyperion is 1700 meters which seems reasonable in a game where a Rifter frigate is reportedly the size of a 747 jumbo jet (58 meters on the chart). The Hyperion is a big ship.

According to the Eve item database the mass of the Hyperion is 100,200,000 kg and its volume is 513,000 m3. That means its average density is 195 kg per m3 which seems reasonable.

The problems arise when you compare length to volume.

Volume is simply length times width times height and we know the length is 1700 meters. That means the rough width times height of the Hyperion is about 301 meters squared. That number seem low to you? It should.

Basically if the Hyperion was a rectangular block 1700 meters long and a volume of 513,000 m3 then it would be about 30 meters wide and 10 meters high. In essence, a Hyperion would look like this:
That is a profile of a rectangle 30m x 10m x 1700m. More like a rod I'd say. Let's review what a Hyperion actually looks like, shall we?

Its immediately obvious that a Hyperion is vastly more than 30 meters wide and 10 meters high even at its thinnest. So either the length is wrong or the volume is wrong. Since the volume comes from Eve itself, we must question the length. What if the length was half as much, merely 850 meters? Then the profile would jump to 30 meters by 20 meters! Look at that picture again... you think it being 20 meters high is a likely possibility?

No, in order for the proportion of the Hyperion to match the volume, I'm thinking that if the length is A then the average height is about one fifth the length and I'll go with the same for width, treating it like a square. So solve for A:

A x A/5 x A/5 = 513,000

A^3/25 = 513,000

A^3 = 12,825,000

A = ~234 meters

Length of 234 meters, width of 46.8 meters, height of 46.8 meters. Roughly. Ok, maybe that is the right length then, right?

Only one problem. If the Hyperion, one of the largest battleships in the game, is 236 meters than the Rifter is correspondingly 8 meters long, the size of a fighter jet. With a Eve db volume of 27,289 m3, the length of 8 meters means its height times width value is in the range of 3411 m2 which if you think of it another way... a Rifter would be 8 meters long, 34 meters high, and 100 meters wide. Obviously that will just not work.

The point I'm trying to make is that the volumes are completely off for ships, drones, modules, ... and carrier ship maintenance arrays.

A typical carrier has a Ship Maintenance array capacity of 1,000,000 m3 which sounds big... until you realize that if you assume its 1000 meters long than its about 100 meters wide and 10 meters high. Its the Hyperion-rod all over again! Drop it down to only 500 meters long and you can bump the height up to 20 meters. And that's ignoring the fact that the model for the Hyperion would not fit in a Nyx much less a Thanatos.

Volumes for everything in Eve have practically no actual relation to reality by any stretch of the imagination. Better to call it Eve-Size-Factor and measure it in Hooligans cubed rather than meters. I know that comparing anything in a game to reality is chocked full of disaster but the simple mathematics of volume to dimensions should not be that hard manage. Simply start with a stated fact like "a Rifter is 60 meters long" and go from there to calculate the dimensions of all ships based on how many Rifter-length they are, and then CALCULATE the volumes from the approximate dimensions. Its not even a complicated calculation. Then adjust ship maintenance array capacities to match the corrected volumes.

While the Hyperion would still look like it would never fit in a mothership, at least the math would match up.

14 comments:

  1. Perhaps the structure of ships in EVE are very porous. Kinda like a spounge or like a honeycomb. This would take up a lot of room for very little displacement volume.

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  2. Well, how else do you get a large standard container that takes up 650m3 but you can fit 780m3 inside it? EVE Math is special, or are we using Tardis technology here? :D

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  3. But the containers specifically have lore stating they generate extra-dimensional space using "Planck bubble stabilizers". You'll see the 404 error message(and the other error messages) for the Eve website say "Something happened to the Planck bubble stabilizers" when something is wrong on the website. That's why all of the containers fit more volume than they take. ^^

    As for being, porous, I'm afraid that when you're talking about volumes of displacement you always act as if the inside of the container doesn't count as extra volume. F.ex. A 1m cube cardboard box that's hollow on the inside is considered to take up 1m3, not some infinitesimally small volume that the cardboard actually occupies.

    What it does mean is that the ship would be lighter than it's volume would imply. Unfortunately, for Kirith's example of the Hyperion, it's displacement volume, assuming it has empty spaces like, floor decks, halls, rooms, cargo bays, etc (a reasonable assumption, I think. ^^) would imply a lighter mass than the reasonable 195kg/m3 that Kirith has calculated. This can, of course, be easily explained away by stating that the materials in Eve are rather dense, so even though the Hyperion is a honeycomb it is made of heavy wax. ^^

    As for the numbers: It's a game, and to keep things balanced(especially because mass and volume have direct impact on game mechanics) you simply have to sacrifice realism in the calculations in order to make sure everything works. It would be far too easy for everything to break otherwise, or else it would be far too finicky to ever be proper.

    Fly Safe
    -Az

    (I should totally just start my own flipping blog. >>)

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  4. lol, this amused my inner pedant, well done :D

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  5. I'm not sure where the chart numbers came from, but if they are based on the "long axis" count on the in game "eyeball" view on the info page, then that means that a number of these are based purely on the artists guess-timates. For example the Tristan's long axis come in at close to 80m, which is obviously its height. How does one, from there, deduce that its profile length is 29m?

    But the point is well taken, the mass estimates are clearly off no matter how you slice it.

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  6. Problems arise when you start to match up the ingame volume attribute with the actual volume of the model. The model sizes/volumes are vastly different from one another in the same class, for example Scorpion is tiny for a bs, almost the same size as the Prophecy on the ship chart. The Apoc, on the other hand, is massive approaching carrier sizes.
    Also the progression of size isn't very accurate, like Abaddon being smaller then Apoc and so on.
    If volume would correlate better to size progression using the actual volume for maintenance arrays would make more sense.
    Final thing, cargo sizes are pretty small I'd think, think of a EMP L slug that is supposed to fit in a 1400mm artillery gun, to have that diameter on the shell the length would have to be thickness of a dime.

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  7. The thickness is not really the issue on ammo, what really does your head in is the fact that how does the ammo fit into 650mm guns and 1400mm guns.

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  8. And to add to the confusion just that extra bit, how does one unit off ammo fill all the barrels of a quad 650mm anyways?

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  9. well, it could be something like metal storm(http://www.youtube.com/watch?v=kRJqt629QFA),
    I don't know, but even if that would be so the bullet volume is really really tiny relative to bore sizes on even the railguns =p

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  10. Looks like Eve is facing some of the same math problems David Weber encountered in his Honor Harrington series. Although I don't know if they're really problems. As long as you don't crash into anything, you're doing okay, right?

    I don't even play Eve and I found this fascinating.

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  11. Wow... Lots of time, eh Kirith? ;)

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  12. Actually, it took me only an hour to write up but I had been thinking a long time on it once I thought about how big 25m3 was to add to the drone bay of the Rokh.

    For the record, 25m3 is like a room 2.9 meters on height, length, and width. Tell me that they can't find that much space on a kilometer long battleship!

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  13. Hey I checked in game, and I don't know where the EVE chart you linked gets its numbers, but the in game number for the length of the Hyperion is *not* 1700. Look up the Hyperion, hit show info, and then click the red eye next to the picture and name. It will give you full pan control to look at the ship and tell you the length of its longest axis - in this case, its clear that the long axis of the Hyperion is its length, and the game lists that at 500 meters.

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  14. I'll check that out, but its still twice as long as it needs to be to match the volume.

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