Another model: Simple regressions + Basic Principles

[Jedi Master Spock]

This can be viewed in part as a sequel to this thread, in which I presented a model for estimating the capabilities of SW and ST ships from basic principles and a single well-studied baseline.

Here, our assumptions and technique are slightly different. Instead of assuming that firepower and acceleration should have a certain type of relationship, we take two baseline values and fit a power relationship to them. I've started with the "Volumetrics" data from ST-v-SW.net here.

This is the list of basic parameters fed into the model, with some "default" values filled in, and an explanation of how each is used:

Code: Select all

Fuel energy/L 1.00E+14
Fuel fraction	0.1
Fuel density (SW)	0.84

I'm assuming SW uses unimaginably efficient fusion on something that smells suspiciously like heavy decane.

Code: Select all

Watts, firepower, X-Wing	1.00E+012
Watts, firepower, ISD	5.00E+017

These figures are generally high. On the main website, I list an estimate range of 23 TW - 84 PW for the ISD based on a documentarian-style analysis. However, I chose to illustrate more generous parameters. Obviously some are less generous (ST-v-SW)

For comparison purposes, Saxton on SWTC has estimated 500 exawatts, which figure Sarli has estimated to be about a thousand times too high (500 petawatts) on the Wizards boards. Wong actually gave a figure of 8-600 petawatts on the SDN website. 500 petawatts can be considered a generous figure.

For the purpose of the model, I'm assuming that Star Wars firepower is dependent solely on surface area, but is not necessarily linear with surface area. For the above figures, we end up with firepower being proportionate to S^1.37.

Code: Select all

Ion engine efficiency	0.9

This is the percentage of energy that can be translated in the reactor to ejecta. I've assumed, in other words, that SW ships use incredibly potent ion engines with c-fractional ejecta.

Code: Select all

Acceleration, X-Wing	1153.74
Acceleration, ISD	254.05

These are the geometric means of the accelerations cited on the main websites, more or less some rounding error. I've assumed acceleration is related strictly to total volume.

Code: Select all

Density (X-Wing)	0.9
Density (Venator)	0.5

Both of these craft have been seen landing. This is actually the dry density omitting fuel; thus, I'm assuming that the X-Wing is almost neutral bouyancy, while the Venator is a lot more full of empty space. We're assuming density sans fuel is proportionate to volume raised to some power (here, about .96).

Given the cramped nature of smaller craft and the spacious large interior areas in larger craft, this seems reasonable.

Code: Select all

Hyperdrive limit (planetary radii)	6.5

Here, I'm assuming that SW ships can crank sufficient juice through their hyperdrives to displace themselves directly away from an Earthlike planet at c from six planetary diameters out. The generally accepted range for this parameter is 1.5-6.5 (1-6 planetary diameters from the surface of an Earthlike planet).

Code: Select all

Fuel energy/L (ST)	1.48E+016
Fuel density (ST)	0.16

Deuterium/antideuterium slush.

Code: Select all

Density, ST (body)	0.09
Density, ST (nacelle)	18.44
Density, ST (mixed composition)	2.18

These parameters were derived from comparing Voyager and the Enterprise A and estimating total mass from nacelle and body size. If nacelle volume was not given, we assume a "moderate" density of 2.18.

This isn't to say that nacelles actually mass 18.44 g/cc, but that we're assuming that denser, more CCS-like ships have larger nacelles than lighter, more ICS-like ships.

Warp limit (m/s^2) 274
Firepower fraction (ST) 0.01

I'm assuming that at peak power production, a TNG-era ST ship is able to displace itself at c directly away from the surface of our Sun.

Shield ratio 1000

Shields are still being estimated directly from surface area. Here we have Shield strength = Peak Power Production * Shield Ratio / Surface Area. 1000 was chosen as a value that worked well for the GCS.

The same parameter is used for both SW and ST.

Code: Select all

Shield advancement (ST)	2
Weapon advancement (ST)	1.45
Warp drive advancement (ST)	1.15
Base generation (ST)	4

One of the primary differences between ST ships is how advanced they are. I've assumed that with each "generation" of 25 years, shields double in efficiency ("Yesterday's Enterprise"), firepower increases by 1.45 ("Genesis"), and warp engine power overall increases by 1.15 ("Flashbacks").

Here, everything is based on TNG as a starting point. Thus, we're assuming that all but the newest ST ships use substantially less efficient shields than SW ships.

[Jedi Master Spock]

Mass:

When we say that mass is linear with respect to nacelle size and overall size, the GCS is estimated at just shy of 11 million tons - a fairly massive ship. The ISD is 38 million; the GCS is actually projected to be more massive than the VSD.

Our assumption of decreasing "dry" density with a constant percentage of volume devoted to fuel creates a "natural" tendency for larger SW ships to look more like flying fuel tanks. Extending the model all the way up to the Death Stars, for example, we expect them to be very light overall with close to a third of their mass being in fuel.

Power:

By actually computing the power requirements for our hypothetical super-efficient ion-fusion engine, something very interesting becomes visible: Our default parameters are actually within a "changeover" area where our theoretical minimum STL and FTL power requirements overlap.

They also indicate that SW fighters should only be able to maintain maximum output for a few hours before running out of fuel - something we suggested earlier - and that virtually all ST ships are in the same boat.

Acceleration:

It's interesting to note that if you put in the values I computed for ISD and X-Wing acceleration, you get out values in the range I've suggested the Death Stars accelerate.

Firepower and shields:

With a relatively heavy GCS and using the full "peak" power generation value necessary to warp orthogonal to a sun's surface, even being able to apply 1% of that value to offensive firepower results in what I consider to be a relatively high estimate - several gigatons per second.

What's very interesting, though, is that simply by continuing to relate shields directly to surface area, this model suggests just as much as the last one that as SW ships get larger, their shields shouldn't actually improve all that much.

Indeed, using the exact same equation for shield strength, SW ships are estimated to have absolutely terrible shield strength. Using the parameters above, the USS Stargazer is expected to have less than half the firepower of the Executor - and over 100 times the shields.

We need substantially less increase in firepower with size to see any real change in this phenomenon - for example, if we use the SFJ official "low end" documentarian estimate of 23 TW, and a not too unreasonable 10 GW for the X-Wing, we get shield strengths that go up with size.

[Jedi Master Spock]

(I would recommend downloading the sheet and playing around with the parameters to see what I'm talking about.)

Anyway, that was a little more time burned looking at how consistent - or inconsistent - I could make things look.

[Praeothmin]

A few remarks:
SW ships do not go at c, but they go at a few thousand km/h at STL, and then switch to Hyperspace for FTL travel, so I think estimating power for c is too generous... Especially considering Einstein posited that to go to c one would need infinite power... :)

How many times more volume in a GCS then an Intrepid?
Voyager masses 700 000 tons, and since the GCS is from the same time period, I would estimatge its density as closer to that of Voyager then, say, the E-Nil...

[Jedi Master Spock]

A few remarks:
SW ships do not go at c, but they go at a few thousand km/h at STL, and then switch to Hyperspace for FTL travel, so I think estimating power for c is too generous... Especially considering Einstein posited that to go to c one would need infinite power... :)

Well, it's not the energy for moving at lightspeed, it's for displacing mysteriously at a rate of lightspeed. The theory here is that if you turned off the hyperdrive, or warp drive, suddenly after achieving lightspeed/warp, you'd have displaced yourself at a speed roughly equal to lightspeed. (Presumably it gets faster later on).

It's a slick trick that assumes that the ship isn't pulling energy out of subspace/hyperspace - that might not be a warranted assumption, but it's the only one I can make to guess with.

How many times more volume in a GCS then an Intrepid?
Voyager masses 700 000 tons, and since the GCS is from the same time period, I would estimatge its density as closer to that of Voyager then, say, the E-Nil...

Here is your go-to reference for that.

An Intrepid density GCS would be 6.5 million tons - that's the "low" density quoted on ST-v-SW. An Enterprise (A) density GCS would mass 25 million tons. So the regression based on nacelle size is really putting the GCS much closer to the ICS than the CCS; however, I can give off the top of my head one good reason why the GCS is denser:

Voyager is primarily constructed of duranium; Enterprise (D) is primarily constructed of tritanium, which seems to be tougher stuff. I think the projected mass really makes a lot of sense.

Actually, the most surprising result of the regression is one I think I forgot to mention: The original Enterprise is actually projected to be slightly more massive than the new one. Also: If we assume uniform density, there's this sharp disconnect in UFP classes:

Constitution-0: 1.00
Miranda: 1.03
Constitution-A: 1.11
Constellation: 3.01
Excelsior: 4.13

That's a huge jump. However, if I plug in the TMP-Constitution nacelles onto the Miranda and Constellation (which has four), I get these masses (in millions of tons) to the nearest hundredth:

Constitution-0: 1.04
Miranda: 1.00
Constitution-A: 1.00
Constellation: 2.02
Excelsior: 2.23

The Constellation and Excelsior are suddenly much closer to their predecessor classes in mass.

[Praeothmin]

But both FTL drives do indeed use funky effects to get them above Light Speeds:
They both "open" a passage to another space "layer", where our knowledge of conservation of energy and c speed requirements are funked up...
So assuming they can go to c or appear to be when they clearly are not is wrong, IMO, because as soon as both drives are turned off, both universes see their ships go back to their original speeds...


As for the mass, where is it mentioned the Voyager is mostly Duranium and the GCS Tritanium?

[Jedi Master Spock]

But both FTL drives do indeed use funky effects to get them above Light Speeds:
They both "open" a passage to another space "layer", where our knowledge of conservation of energy and c speed requirements are funked up...
So assuming they can go to c or appear to be when they clearly are not is wrong, IMO, because as soon as both drives are turned off, both universes see their ships go back to their original speeds...

That's what I'm assuming - they're not actually going c, they simply happen to have displaced about the right distance when you turn off the engines. Obviously the number goes up as you get out there, but the steepest gravitational potentials are generally in-system.

As for the mass, where is it mentioned the Voyager is mostly Duranium and the GCS Tritanium?

It's not actually certain that this is the case. Consider it informed speculation. We know one, but the comparison is actually speculation.

See, we do know that both ships contain both substances. We know that both ships use tritanium bulkheads ("Where Silence Has Lease," "Year of Hell"). We know the GCS uses duranium in the cargo bay ("A Matter of Perspective"). We know that the shuttles used on the GCS have tritanium hulls ("Rascals").

We do hear explicitly that the hull of Voyager is duranium ("Drone"). We also know that Voyager's newer class 8 shuttles use duranium alloy hulls instead of tritanium hulls ("Initiations") though the older class 2s use tritanium alloy, and that it carries spare duranium sheeting ("Alice.")

This suggests that Starfleet has been moving towards more duranium construction. At the same time, we know that tritanium is incredibly tough ("Obsession" and "Arsenal of Freedom") - almost certainly tougher than duranium, which can actually be damaged by hand phasers.

So why? Probably because it's lighter and easier to work with, since we also know that ship densities are going down and manufacturing volume is going way up. Think of it as being like the difference between aluminum and titanium; titanium is the "superior" metal in terms of toughness, but aluminum is much cheaper and much easier to work with