Basic principles and a model

[Jedi Master Spock]

The big picture: Ballparks and benchmarks

It's been a little while since I did a "big picture" post and explained just what it is that I see as the most plausible picture from the canon based on analysis from first principles. That is, we try to figure out what is underlying the mechanisms seen, and then determine the most reasonable capabilities based on that.

Building a model We assume the general case of L^6 ~ S^3 ~ V^2 ~ M^2 when data not available on st-v-sw.net and otherwise assume ISD-like proportions for SW ships based on available dimensional data, GCS-like proportions for a ST ship.

In Star Wars, highly efficient fusion is the name of the game. Larger ships require S (approximate surface area) greater area in shielding, which means that their shield strength increases per V/S with a V^1 investment in shield generators. Although they have V^1 times the fuel, they only have S~V^(2/3) times the surface area and a similar density of weapon emplacements. It would be reasonable to assume a typical designed mission duration proportionate to V^(1/3), which would complement a ~V^(2/3) rate of consumption. There are some problems associated with this, but I believe they can be accounted for using additional tactical factors and remain pernicious problems for any account of Star Wars.

EU support for these propositions: In the EU, we have the explicit baseline of combat power scaling per V^(1/3) and cost per V^(2/3) per the Strike Cruiser and similar fluff; we do indeed also have mission duration specifications scaling roughly on V^(1/3) - days to weeks for fighters, months to years for capital ships.

We will assume that Star Wars ships are fueled with heavy hydrocarbons producing 100 terajoules per liter in a fusion reaction of staggering efficiency. Hydrocarbon fuels burned with essentially magical fusion efficiencies remain, IMO, the best explanation for Star Wars technology on the highest level of canon. Alternate power sources may well exist, but are overall similarly effective.

We now consider sublight maneuverability. With the use of ion engines, the primary limiting factor of forward acceleration is more reactant mass than power. We will assume thrust scales with V. Thus, maximum linear acceleration will be presumed constant, in keeping with the TESB chase. Angular momentum, however, is V*L^2. Thus, rotational acceleration (in degrees per second squared) will decrease with L^2 (roughly).

We also apply a similar model to Star Trek. Several of our assumptions should be modified. Star Trek ships do not scale combat or mission endurance noticeably with size. A Constitution class seems to have a similar refuel and refit cycle as a Galaxy class. Thus, base firepower will scale directly with V. We will begin with the base case of the Galaxy class. We will assume that weapons output is 1% of maximum power output normally (we will consider some special cases, later). We will assume that 10% of the volume of a starship is given to fuel storage in both cases.

Baseline cases:

Take the iconic ship of Star Wars: The X-Wing starfighter. The total potential fuel capacity of the X-Wing is then 2700 liters, and the X-Wing carries fuel with a total energy value of 270 petajoules. Launching from and leaving an Earthlike planet at an Earthlike orbit around a Sunlike star requires only 0.1% of its fuel capacity. We assume, based on the lower hyperspace limit and a density like water, that the X-Wing is capable of putting out 10 terawatts at peak consumption. The X-Wing thus has fuel for 7.5 hours of maximum consumption. We will assume that 10% of peak instantaneous output may be directed towards weapons after accounting for system inefficiencies. This estimate then exceeds even the Wongian VFX-based overestimate of 600 GW, but is not unreasonable given the presumed power requirements of hyperdrive and the fuel capacity of the vehicle. We assume that a device providing 1 terajoule is capable of broaching the shields. (A VFX-based approach should fall two orders of magnitude lower.) We estimate turning speed generously at 180 degrees/sec^2, which represents the ability to perform a hard 180 in 2 seconds flat.)

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X-Wing: 
Length: 12.5m
Effective weapon output: 1 TW
Endurance @ maximum power: 7.5 hours
Shielding: 1 TJ
Maximum rotational acceleration: 180 deg/sec^2

For Star Trek, we begin with the best studied ship, the Galaxy class. Assume 580 million liters of M/AM storage at 14.2 PJ/L. This gives us 8.3 YJ of capacity, which lasts less than 6 hours at maximum power (this actually does not seem strange given the Enterprise's apparent ability to push itself to the breaking point in minutes when drawing maximum power from the warp coils). We take the minimum energy to breach the shields and deal bleed-through damage as 200 petajoules, i.e., a lower-end SB.com calculation for a photon torpedo. This is not at all realistic for what will bring down the shields, but it's worth making the point of comparison.

Is this fair? I think so. While the X-Wing would be able to drain its fuel with weapons in 75 hours, all Star Trek ships are then assumed to be able to do so in 575 hours; Star Trek ships seem to exhaust themselves more easily (see the E-E running out of torpedoes in its fight with the Scimitar). I think it is about as reasonable to place the GCS firepower at 4 EW as an X-Wing at 1 TW; both are generous given a VFX-based approach, but perfectly reasonable from first principles, and could be justified via reference to proton torpedoes and high end phaser drilling/photon torpedo spread incidents.

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Galaxy class:
Length: 642m
Effective weapon output: 4 EW
Shielding: 200 PJ
Maximum rotational acceleration: 22.5 deg/sec^2

Model predictions:
Now, we examine the results of the model. Our model will provide general predictions - obviously, there are more complex factors in play. The obvious ship to check next is the Falcon:

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Millenium Falcon:
Length: 35m
Effective weapon output: 18 TW
Shielding: 8 TJ
Maximum rotational acceleration: 23 deg/sec^2

The turn rate is a little low, but the Falcon is an exceptionally nimble ship for its size. We now dip into the EU, to consider the Victory Star Destroyer that starfighters keep bringing down in the EU books:

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Victory Star Destroyer:
Length: 900m
Effective weapon output: 4.5 PW
Shielding: 79 TJ
Maximum rotational acceleration: 0.03 deg/sec^2

Given a proton torpedo yield of ~1 kiloton, it would take close to twenty proton torpedoes detonating in roughly the same place at roughly the same time to take down the Victory class's shields. Note that the Victory class is able to put that sort of energy out in a fraction of a second. Under this model, we have to assume that tactical factors prevent capital ships from effectively focusing firepower to take down each other's shields - it may be a question of the angular precision of weapons turrets and the use of many small weapons with distinct firing cycles, but it's a problem that needs to be considered in any version of the Star Wars universe that gives capital ships incredible firepower while still allowing fighters to threaten them.

Armor and structural durability should actually be quite significant in the Star Wars universe. One possibility that comes up frequently is the idea Star Wars shields are particularly vulnerable to torpedoes, due either to the very short time in which a proton torpedo detonates (microseconds) or due to the torpedo/fragments physically passing through shields designed to stop ray sections. Another is that capital ships' shields are somewhat diffuse and fighters actually fly through/under them when making attack runs. For the moment, though, we will leave the figures as they are.

Rotation is a more serious problem. While we should expect these larger ships to have far more trouble turning, they don't. Either their mass and thrusters are far better distributed, or they invest much more effort in being able to maneuver. We'll note this is a similar problem in Star Trek. Let's check the ISD, though:

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Imperial Star Destroyer:
Length: 1600m
Effective weapon output: 14 PW
Shielding: 140 TJ
Mission endurance (relative to X-Wing): 125

Here, the ISD is beyond the reach of a single squadron of Rebel fighters. The firepower falls on the higher end of the range I outlined originally on my website based on the movies and VFX, although definitely within it. This is well above the firepower estimated for an ISD on ST-v-SW.net and well below the firepower estimated for an ISD on SDN. I've included for reference what V^(1/3) looks like about now - the ISD is supposed to be around 125 times as effective, overall, as the X-Wing, and is supposed to carry fuel and supplies for around a hundred times the mission duration. We now compare briefly to the MCC:

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Mon Calamari Cruiser:
Length: 1200m
Effective weapon output: 3.4 PW
Shielding: 196 TJ

Here, our model has done something very clever that anticipates the EU's treatment of the ship. The SWRPG, for example, gives the MCC 20% more shields, which then regenerate twice as quickly; our model simply gives the MCC 40% more shields. The SWRPG gives the MCC 20 dice of turbolasers versus the ISD's 95, and 35 total dice of weapons vs the ISD's 107, i.e., 20-33% of the total firepower. Our model gives the MCC 24% of the total firepower.

The MCC has less surface area relative to its volume; our model interprets that as emphasizing shields over firepower. I still think the game statistics and similar statistics shortchange the MCC compared to its treatment in fiction, but this model happening to line them up is interesting. Now, we'll look at the Executor. Using the current "official" 19 km length, we would guess these to be its capabilities, from its baseline:

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Super Star Destroyer:
Length: 19 km
Effective weapon output: 784 PW
Shielding: 751 terajoules

Almost 200 kilotons to take the shields down. In the EU, 300 proton torpedoes take down the Lusankya's shields and start damaging it; I think the firepower seems high based on its failure to blow up tons of Rebel ships in ROTJ, but it would be perfectly reasonable to assume firepower like that based on first principles. The shields may seem exceptionally fragile, but not unusually so if each little section is shielded independently.

Now we look at a few Star Trek ships. First, we take the Defiant and key its weapons up to 15% of its reactor power, rather than 1%:

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Defiant:
Length: 120m
Effective weapon output: 640 PW
Shielding: 55 petajoules
Turn rate: 644 deg/s^2

Here, we see two things. First, the turn rate estimation - which worked out to be proportionate to 1/L^2, since moment of inertia was ~ ML^2 and thrust ~M - is completely absurd for Star Trek, just as it is for Star Wars. Smaller ships invest less in turning ability, larger ships more, and it breaks down rapidly. Second, the Defiant's firepower is actually pretty respectable. We'll compare it with Voyager:

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Voyager:
Length: 344m
Effective weapon output: 430 PW
Shielding: 109 petajoules

Here we see just how amazing the Defiant is, pound for pound. Voyager is ten times the size, but if you can put 15% of your warp plasma towards weapons, the amount of firepower you can bring to the party goes up sharply. The Defiant carries more torpedoes, if anybody is counting - quantum torpedoes, at that - so Voyager getting the short end of the firepower comparison makes sense. The Defiant's shields are probably also overjuiced a little - probably not by a factor of fifteen, but they only need to be doubled from the strength expected of a "typical" ship their size and shape to match what we expect of Voygager's. For those of you putting photon torpedoes around 100 megatons, this puts Voyager's peak fighting output at ~1 photon torpedo per second, and the Defiant's at ~1.5.

Probably the most commonly appearing non-flagship class is the Excelsior, with 60 distinct appearances listed on Memory Alpha; it's also about average size for 24th century Federation starships, as far as we can tell. ST-v-SW.net gives two different models, one a little larger and bulkier:

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Excelsior:
Length: 467-469m
Effective weapon output: 600-680 PW
Shielding: 42-43 petajoules

For ~100 MT photon torpedoes that might be acceptable on, say, SB.com, that's 3 photon torpedoes every two seconds. Which is actually about what we see Excelsior class ships doing, in some scenes. However, our model predicts they are more fragile than the compact Defiant. Let's look at the Danube to see how this model extends for the smallest starships:

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Danube:
Length: 23m
Effective weapon output: 40 PW
Shielding: 4.7 petajoules

Now, compare and contrast to the Nebulon-B:

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Nebulon-B:
Length: 300m
Effective weapon output: 300 TW
Shielding: 23 terajoules

Even if the Nebulon was designed to blast through its fuel as quickly as the X-Wing, you'd still have less than 7 PW of effective weapon output. Fusion power is simply that anemic compared to antimatter power. Under a model that takes that into account, only the largest Star Wars ships can provide the firepower necessary to threaten a Star Trek ship - and the smallest of Star Trek ships is capable of pulling out photon torpedoes and blowing through any shields that a proton torpedo can threaten.

Analysis

These are all, of course, "first principles" ballpark estimates. It is reasonable to go back through and adjust specifically based on the balance of shielding to firepower to maneuverability - perhaps the Executor needs to invest more in maneuvering thrusters and less in firepower. Perhaps the Excelsior should go down in firepower and up in shielding. Some of the older ships may be more or less powerful across the board. The Sovereign class and Ambassador class are about the same overall size, but I'm pretty sure they don't have the same reactor rating. The Trade Federation battleship is clearly outclassed by ships a fraction of its size, so our first order estimate of its capabilities from first principles wouldn't be accurate at all.

There are assumptions in this model of Star Wars and Star Trek ships that are not "fair." That is, they seem to heavily penalize larger ships. At the same time, all of this makes sense in the EU and in the movies. A Saxtonian model where Star Destroyers wield proportionately similar or even more firepower than fighters simply cannot make sense of small attack craft. It cannot make sense of Rogue Squadron, and such a view also cannot make sense of the battles in ROTJ and ROTS. Or even TPM, for that matter.

It's all perfectly reasonable, and perfectly robust. You could perfectly reasonably place the shields higher for both franchises, and the firepower lower. Drop the ST firepower by more than an order of magnitude, and you start running into trouble with photon torpedoes. Raise the SW firepower by more than an order of magnitude, and you're going well beyond what proton torpedoes can provide for fighters (as well as very dramatically exceeding the VFX) - do both, and we have ISDs with firepower somewhere around the neigborhood of an Akira or Ambassador.

It's a problem. You can justify higher power generation by introducing exotic matter systems, but then you still have thermonuclear proton torpedoes. VFX problems may plague everyone, but at least Trek's VFX problems allow for multi-megaton firepower by its principal ships.

In Star Wars, it requires a great leap of faith to squeeze 600 GW out of an X-Wing shooting at the Death Star, or any more than a kiloton out of an exploding proton torpedo. If you squeeze hard, you can reasonably justify Star Destroyers competing with Klingon battlecruisers in bombardment capabilities. You can justify a Star Destroyer powerful enough to turbolaser a planetary civilization into oblivion. It's not hard, actually. But you can't justify a Star Destroyer that can ignore fighters freely, and because of that, you can't justify a Star Destroyer that can survive getting in a fight with a Galaxy class.

[2046]

This post is gorgeous. However, how far can you get on it without the SW EU? From the first look, I'd say that some of it might seem to break down without EU support.

[Mr. Oragahn]

Wow, I'm still trying to digest your posts in the cubaton thread, and you drop that. It will have to wait a week or so.

[Mike DiCenso]

This makes me think of the YAWCF story: with numbers like that, how do you seriously expect a Venator cruiser to take on even a moderately damaged Ambassador?
-Mike

[2046]

Lest the post end up being given short shrift, I wish to play devil's advocate for this post, and make counterpoints:

Building a model We assume the general case of L^6 ~ S^3 ~ V^2 ~ M^2 when data not available on st-v-sw.net and otherwise assume ISD-like proportions for SW ships based on available dimensional data, GCS-like proportions for a ST ship.

Yes, ST-v-SW.Net is highly reliable.

(What?!? I'm playing devil's advocate! ;-) )

Incidentally, your notation is a bit unique. In logic, that ~ would be sometimes used for negation. Informally, it's often used to mean "about" or "around". I assume it refers to equivalence in your usage, but this presumption sometimes appears to break down given the apparent context. Can you clarify?

In Star Wars, highly efficient fusion is the name of the game. Larger ships require S (approximate surface area) greater area in shielding, which means that their shield strength increases per V/S with a V^1 investment in shield generators. Although they have V^1 times the fuel, they only have S~V^(2/3) times the surface area and a similar density of weapon emplacements. It would be reasonable to assume a typical designed mission duration proportionate to V^(1/3), which would complement a ~V^(2/3) rate of consumption. There are some problems associated with this, but I believe they can be accounted for using additional tactical factors and remain pernicious problems for any account of Star Wars.

So here we have the mathematical derivation, though it's not quite clear at first. A good background is here: http://www.st-v-sw.net/G-volumetrics-bhmm.html

Generally speaking, a ship of equivalent shape (e.g. a Star Destroyer shape, a cube, or whatever) with its length increased by X will have its volume increased by X^3 and its surface area increased by X^2.

For example, using the volume basics page, the volume coefficient of an Imperial Star Destroyer is 0.01317. If we double the length of a 1600m Imperial Star Destroyer to 3200 meters to create the Wank Class Star Destroyer, its volume will increase from the listed 53,942,400 cubic meters to 431,539,200 cubic meters . . . a factor of 8.

However, the surface area of the ship does not increase by a factor of 8. It only increases by a factor of 4, or about 17,000,000 m^2 in this case from the original 4.3 million.

Your statements above, if I am translating correctly, argue that the Wank Class will thus have four times as much area in need of shielding, but also eight times as much space to put shield generators in, so for the purposes of the model you are assuming larger ships are commensurately better shielded for the surface area. However, gun density on the hull does not increase with volume, it appears (the ISD and Venator both have similar gun counts, as a matter of fact -- it just looks bigger on the Venator). The gun density is thus presumed to remain more or less constant in relation to surface area. So, if the ISD has 60 guns, we might expect the Wank Class to be capable of fielding 240.

Is that a fair translation, or did I miss something?

We now consider sublight maneuverability. With the use of ion engines, the primary limiting factor of forward acceleration is more reactant mass than power. We will assume thrust scales with V. Thus, maximum linear acceleration will be presumed constant, in keeping with the TESB chase.

This part of the model confuses me. If I read you right, you're suggesting that the TESB chase shows that the ISD and the Falcon are basically capable of the same acceleration rate. Although that's by no means insane given how often the Falcon has an ISD hanging on her tail, I always took it to be the result of excessive evasion maneuvers on the part of the Falcon, as required by the ISD's proximity. To be sure, the ISD is no slouch, and I believe her to be particularly quick with her antigravs, but it would never occur to me to suggest that the SSD could keep up with the ISD in a drag race.

We also apply a similar model to Star Trek. Several of our assumptions should be modified. Star Trek ships do not scale combat or mission endurance noticeably with size. A Constitution class seems to have a similar refuel and refit cycle as a Galaxy class. Thus, base firepower will scale directly with V.

This might need more basis. For instance, we have little idea of the refuel cycle of a Galaxy in normal operation, and no idea of the Constitution, save for Kirk's "it regenerates". We know the resupply of the Constitution, give or take (Kirk had food for 430 for five years as of "The Mark of Gideon"[TOS3]).

We know Voyager ran out of deuterium at some point, but there's no indication they ever ran out of antimatter. Of course, antimatter appears to be created onboard assuming they have the same tech as the Enterprise-D ("Liaisons"[TNG7] refers to the "mass flow rate of the antimatter replenishment stream to the containment pods", whereas "Night"[VOY5] refers to residual antimatter from the reactor being broken down by other means, so the replenishment stream is, as we would expect, evidently not from the reactor ... not that we'd expect residual antimatter anyway).

However, Excelsior did not appear to be four times the asskicker of the B-type Constitution Class (e.g. the Enterprise-A), at least in torpedo output, though her reserves may have been that much greater. And, true, she did have five of the TMP era emitters per saucer side compared to three. But still, from a power perspective, unless we assume more powerful phasers in addition to the extra emitters (they may be larger, which would help), I'm not sure we can get the Excelsior to be four times as powerful.

Similarly, there was the Klingon ship in the Delta Quadrant that Voyager had a tangle with. Voyager won, but not by as much as she should've considering she's got three times the volume of a TOS Connie and a century higher tech. That might be an outlier, though, given Voyager's condition.

We will begin with the base case of the Galaxy class. We will assume that weapons output is 1% of maximum power output normally (we will consider some special cases, later). We will assume that 10% of the volume of a starship is given to fuel storage in both cases.

I know the above is the result of past threads, but it remains emotionally unsatisfying ... certainly the writers always seemed to think that much of the ship's energy was devoted to weapons in combat situations, but that yes (per BoBW) the reactor put out significantly more than the weapons. But rather than go through that again, I just wanted to note that a full account might involve detail here.

Take the iconic ship of Star Wars: The X-Wing starfighter. The total potential fuel capacity of the X-Wing is then 2700 liters, and the X-Wing carries fuel with a total energy value of 270 petajoules. Launching from and leaving an Earthlike planet at an Earthlike orbit around a Sunlike star requires only 0.1% of its fuel capacity. We assume, based on the lower hyperspace limit and a density like water, that the X-Wing is capable of putting out 10 terawatts at peak consumption. The X-Wing thus has fuel for 7.5 hours of maximum consumption. We will assume that 10% of peak instantaneous output may be directed towards weapons after accounting for system inefficiencies. This estimate then exceeds even the Wongian VFX-based overestimate of 600 GW, but is not unreasonable given the presumed power requirements of hyperdrive and the fuel capacity of the vehicle.

I don't necessarily agree with these values, per the page-in-progress here (specifically this section). Indeed, I think the fact that you came in over Wong with it is indicative of the problem. But that's a discussion for another thread.

Is this fair? I think so. While the X-Wing would be able to drain its fuel with weapons in 75 hours, all Star Trek ships are then assumed to be able to do so in 575 hours; Star Trek ships seem to exhaust themselves more easily (see the E-E running out of torpedoes in its fight with the Scimitar).

This seems an unusual outcome. The X-Wing I can kinda roll with, given that we're basically pondering the thing sitting dead in space but shooting for 75 hours. Given that it has to maneuver, enter hyperspace, power shields, and so on, it seems reasonable that once all those factors are taken into account the ship's endurance falls tremendously. So I can live with that.

But the 575 hours for the Galaxy? I suppose it's possible given the whole dead-in-space-but-shooting idea, but it seems a weirdly high value. Ah well, nevermind.

Now, we examine the results of the model. Our model will provide general predictions - obviously, there are more complex factors in play. The obvious ship to check next is the Falcon:

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Millenium Falcon:
Length: 35m
Effective weapon output: 18 TW
Shielding: 8 TJ
Maximum rotational acceleration: 23 deg/sec^2

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X-Wing:
Length: 12.5m
Effective weapon output: 1 TW
Endurance @ maximum power: 7.5 hours
Shielding: 1 TJ
Maximum rotational acceleration: 180 deg/sec^2

I took the liberty of moving the X-Wing beside the Falcon. As I see it, the X-Wing could knock out her own shields in one second, and the Falcon's in eight, at maximum output and with aim that wasn't made of ass. The Falcon, meanwhile, could take out X-Wing shields in 1/18th of a second . . . which I would think would translate to somewhere in the neighborhood of a shot or two.

In any case, the model seems reasonable, accounting for the atrocious aim we usually see in Star Wars. However, I think we've done something odd in comparing the Falcon to a fighter. She's capable of some self-defense, yes, and probably has great shields for her size. However, I would not expect her to have beam weaponry capable of more than fighter-level firepower. A dedicated warship of that size, perhaps, but she's perhaps 2-3 times an X-Wing at best. But that's not necessarily a failure of the model generally . . . just in this case.

(And yes, I know you mentioned missile weapons, and yes, the Falcon could carry way more than a fighter, but missile weapons seem seldom used in Star Wars.)

Under this model, we have to assume that tactical factors prevent capital ships from effectively focusing firepower to take down each other's shields - it may be a question of the angular precision of weapons turrets and the use of many small weapons with distinct firing cycles, but it's a problem that needs to be considered in any version of the Star Wars universe that gives capital ships incredible firepower while still allowing fighters to threaten them.

While technically plausible, it seems that someone would've figured this out already and designed a computer-based primary firing control. That is to say, it wouldn't make a good excuse.

While we should expect these larger ships to have far more trouble turning, they don't. Either their mass and thrusters are far better distributed, or they invest much more effort in being able to maneuver.

There is, I think, a distinction between maneuvering with antigrav support and maneuvering in open space. An ISD still lumbers in open space, as seen during the emergency evasive before the TESB collision. Some sort of emergency rocket is not out of the question in such a case. But even then, I don't see any indication that they are super-quick. However, you're correct in that the 0.03 deg/sec^2 seems too little.

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Imperial Star Destroyer:
Length: 1600m
Effective weapon output: 14 PW (14000TW)
Shielding: 140 TJ
Mission endurance (relative to X-Wing): 125

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Millenium Falcon:
Length: 35m
Effective weapon output: 18 TW
Shielding: 8 TJ
Maximum rotational acceleration: 23 deg/sec^2

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X-Wing:
Length: 12.5m
Effective weapon output: 1 TW
Endurance @ maximum power: 7.5 hours
Shielding: 1 TJ
Maximum rotational acceleration: 180 deg/sec^2

The model has here produced a peculiar situation, wherein an ISD weapon output is worth 14,000 X-Wings, and could defeat its own shields in 1/100th of a second.

Granted, aim is still bad for Star Wars (ships were missing at point-blank and standing still in RotJ), but I don't think mainliine cruiser battles are usually measured in seconds. And assuming maximum output from the Falcon model, it could defeat an ISD's shields in just under 8 seconds. That seems off.

In TCW, a Y-Wing squadron is considered capable of defeating the shields of the Malevolence and breaching the bridge with proton torpedoes. However, a fierce cannonade by three Venators cannot breach the aft hull.

Meanwhile, as seen over Ryloth, a squadron of Y-Wings are also capable of using their beam weapons alone to defeat six Munificents. And, from "Downfall of a Droid"[TCW1], we see that Republic tanks can smash the hull of a Munificent.

Quoting from my "Downfall of a Droid" analysis: "Grievous is attacking with six Munificents against three Republic Venators, and Ahsoka says they're outgunned. Compare with the prior episode, however, when nine Munificents had six Venators in front of them and Grievous complained that he was outgunned. Apparently 1.5 Munificents to 1 Venator is a clear Venator win, but 2 Munificents to 1 Venator is considered good for the Munificents. That seems like an awfully narrow swing."

There are two things to get from this:

1. Munificents are much less voluminous than Venators, since much of the superstructure's volume is literally empty space. The very pretty Google SketchUp model I measured to within 5% gave me a volume of 2,137,120 cubic meters. A simple Venator model at the same accuracy nets me 10,616,929 cubic meters . . . a difference of almost five times, despite the ships being only 1130 vs. 830 meters (the Muni's shorter). (For reference, the Muni's volume is less than a Sovereign Class Federation starship, and she's 130 meters longer . . . we all know how sleek and spindly the Sovereigns are.)

Given that much of the Venator volume is composed of carrier-related space, though, she's really a big empty ship. If we assume half of her volume is dedicated to fighters, then the ship's only about 2.5 times the volume of the Muni, which gets us closer to understanding the combat ratio. Factor in crew quarters and life support needs versus droid facilities and we can easily get to 1.5 to 2 Munis per Venator.

2. Scary as it is, several Y-Wing fighter-bombers can take down Munis without much problem. This is bound to blow your model's mind. No doubt part of it can be ascribed to accuracy, somehow, but there was no evidence of proton torpedo use at Ryloth. The Munis simply got torn up by bombers that didn't even drop bombs.

So the concept of warships being untouchable by fighters just can't survive . . . any model must take that into account. Good luck with that. ;)

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Super Star Destroyer:
Length: 19 km
Effective weapon output: 784 PW
Shielding: 751 terajoules

Almost 200 kilotons to take the shields down. In the EU, 300 proton torpedoes take down the Lusankya's shields and start damaging it; I think the firepower seems high based on its failure to blow up tons of Rebel ships in ROTJ, but it would be perfectly reasonable to assume firepower like that based on first principles.

True, but the prediction still suggests they wouldn't have needed the Death Star in that battle with that thing flying around. It's literally got the firepower of 56 ISDs, in the view above.

I'll split my Wars and Trek related messages here. Next up, Trek ships.

[2046]

Oh yeah, I forgot to mention something with the Star Wars post. As I've noted elsewhere, the idea that reactor power and weapon power are related is rather less certain than is classically assumed, thanks to the use of shells by Separatist ships and presumably others as well. This presents quite a problem in regards to Star Wars scaling of firepower by reactors, though theoretically ammo volume could be similar per unit volume.

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Galaxy class:
Length: 642m
Effective weapon output: 4 EW
Shielding: 200 PJ
Maximum rotational acceleration: 22.5 deg/sec^2

Just so we have that above. Now:

Now we look at a few Star Trek ships. First, we take the Defiant and key its weapons up to 15% of its reactor power, rather than 1%:

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Defiant:
Length: 120m
Effective weapon output: 640 PW
Shielding: 55 petajoules
Turn rate: 644 deg/s^2

Here, we see two things. First, the turn rate estimation - which worked out to be proportionate to 1/L^2, since moment of inertia was ~ ML^2 and thrust ~M - is completely absurd for Star Trek, just as it is for Star Wars. Smaller ships invest less in turning ability, larger ships more, and it breaks down rapidly. Second, the Defiant's firepower is actually pretty respectable.

Sure, with all that extra percentage. But the percentage makes sense, since the Defiant's phaser power is such that, transferred to warp, they can go quite a bit faster.

However, the weapon output of over half of a Galaxy Class seems off. The Defiant is something like 1/100th the volume of a Galaxy, and although she's a stripped down warship compared to a luxury liner like the Galaxy, I can't imagine it's that superior, pound for pound.

The Lakota, for instance, is about 1/6th of a Galaxy, and after being upgraded to maximum whoopass potential she and the Defiant in a disabling-fight fought to a draw, but the Lakota never used her quantums. The Defiant seemingly did fire at least one aft photon at close range, though the sound effect for that shot suggested a phaser pulse instead.

Point being, in a phaser fight to the death I'd bank on a Galaxy before the Lakota.

We'll compare it with Voyager:

Code: Select all

Voyager:
Length: 344m
Effective weapon output: 430 PW
Shielding: 109 petajoules

Here we see just how amazing the Defiant is, pound for pound. Voyager is ten times the size, but if you can put 15% of your warp plasma towards weapons, the amount of firepower you can bring to the party goes up sharply. The Defiant carries more torpedoes, if anybody is counting - quantum torpedoes, at that - so Voyager getting the short end of the firepower comparison makes sense.

Defiant in wartime carried more torpedoes, but I'd be willing to bet that Voyager, which according to Paris in "The Thaw" was built for combat performance, could carry more when not simply being sent to muck about in the Badlands looking for some wimpy Maquis ship.

Probably the most commonly appearing non-flagship class is the Excelsior, with 60 distinct appearances listed on Memory Alpha; it's also about average size for 24th century Federation starships, as far as we can tell. ST-v-SW.net gives two different models, one a little larger and bulkier:

The B-type Excelsior is literally the B-type . . . Enterprise-B, specifically. The type designation is based on "B-type Warbird" and other similar uses, which I take to refer to different variations in the same class ship. The TMP Constitution is the B-type Constitution in this view, but I refrain from calling the TOS Connie A-type because that would just get confusing.

Code: Select all

Excelsior:
Length: 467-469m
Effective weapon output: 600-680 PW
Shielding: 42-43 petajoules

For ~100 MT photon torpedoes that might be acceptable on, say, SB.com, that's 3 photon torpedoes every two seconds. Which is actually about what we see Excelsior class ships doing, in some scenes. However, our model predicts they are more fragile than the compact Defiant.

That's iffy. Two phaser shots from Lakota holed the Defiant's port shields to the tune of 40%. Then the Defiant finally started to unload, and the two fought roughly to a draw, though the assessment on the Defiant was that the Lakota was worse off. So your mileage may vary here.

Let's look at the Danube to see how this model extends for the smallest starships:

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Danube:
Length: 23m
Effective weapon output: 40 PW
Shielding: 4.7 petajoules

A weakish point in the shields of a Jem'Hadar battlebug were penetrated by concentrated fire from a Danube, quickly resulting in the ship's destruction. But the Danube's shields have often been shown to withstand at least a couple of hits. Character shields probably, but still something that a model would need to account for, and I'm not sure this did.

The Trade Federation battleship is clearly outclassed by ships a fraction of its size

Really?

At the same time, all of this makes sense in the EU and in the movies. A Saxtonian model where Star Destroyers wield proportionately similar or even more firepower than fighters simply cannot make sense of small attack craft. It cannot make sense of Rogue Squadron, and such a view also cannot make sense of the battles in ROTJ and ROTS. Or even TPM, for that matter.

This is the crux of the whole post, right here, and makes all the rest worthwhile. All my nitpicking aside, this is where the whole exercise pays off.

Put simply, this rough sketch model of Star Wars vessel relative strengths is far superior to the Saxtonite understanding. In the Saxton model, fighters should hardly be capable of scratching ship windows. The model you've presented is at least a helluva lot closer in that regard, if still imperfect.

It's all perfectly reasonable, and perfectly robust. You could perfectly reasonably place the shields higher for both franchises, and the firepower lower. Drop the ST firepower by more than an order of magnitude, and you start running into trouble with photon torpedoes. Raise the SW firepower by more than an order of magnitude, and you're going well beyond what proton torpedoes can provide for fighters (as well as very dramatically exceeding the VFX) - do both, and we have ISDs with firepower somewhere around the neigborhood of an Akira or Ambassador.

It's a problem. You can justify higher power generation by introducing exotic matter systems, but then you still have thermonuclear proton torpedoes. VFX problems may plague everyone, but at least Trek's VFX problems allow for multi-megaton firepower by its principal ships.

In Star Wars, it requires a great leap of faith to squeeze 600 GW out of an X-Wing shooting at the Death Star, or any more than a kiloton out of an exploding proton torpedo. If you squeeze hard, you can reasonably justify Star Destroyers competing with Klingon battlecruisers in bombardment capabilities. You can justify a Star Destroyer powerful enough to turbolaser a planetary civilization into oblivion. It's not hard, actually. But you can't justify a Star Destroyer that can ignore fighters freely, and because of that, you can't justify a Star Destroyer that can survive getting in a fight with a Galaxy class.

Again, gorgeous. Devil's advocacy be damned, the points above are generally correct.

And that doesn't even take into account the massive weapon range disparity.

[Khas]

Oh yeah, I forgot to mention something with the Star Wars post. As I've noted elsewhere, the idea that reactor power and weapon power are related is rather less certain than is classically assumed, thanks to the use of shells by Separatist ships and presumably others as well. This presents quite a problem in regards to Star Wars scaling of firepower by reactors, though theoretically ammo volume could be similar per unit volume.

Wait. Shells as in projectile weapons? (Sorry, hardly seen any of TCW. What I did see was mostly crap though. Save for the episode where the droids infiltrate that clone base on planet Whats-its-name.)

[2046]

Oh yeah, I forgot to mention something with the Star Wars post. As I've noted elsewhere, the idea that reactor power and weapon power are related is rather less certain than is classically assumed, thanks to the use of shells by Separatist ships and presumably others as well. This presents quite a problem in regards to Star Wars scaling of firepower by reactors, though theoretically ammo volume could be similar per unit volume.

Wait. Shells as in projectile weapons? (Sorry, hardly seen any of TCW. What I did see was mostly crap though. Save for the episode where the droids infiltrate that clone base on planet Whats-its-name.)

Sorry, I was being too quick in posting.

There's some sort of canister thingy that they put in the guns and which is ejected when the bolt is fired. The canisters themselves are highly explosive. So presumably, it's basically turbolaser ammo. Or a battery. Who knows? But in any case, it isn't like the warship is powering the whole shebang directly, but something supplemental is going on.

[Mike DiCenso]

It's interesting that RoTS introduced the "canister shell" concept since in ANH during the Battle of Yavin, the small AA batteries on the Death Star do not make use of anything like this. Maybe he larger, slower anti-capship towers still work that way, but unfortunately we did not get to see what was going on inside them while they were firing.
-Mike

[2046]

Well, the guns on the first Death Star are referred to as having to "wind up their turbine generators to create sufficient power" in the script. Perhaps instead of individual cartridges they pipe it in.

[Mike DiCenso]

In that case it might explain why those AA batteries were constantly venting that steam-like gas, if they were having to pump in some kind of gas instead of having the AA crews try to keep up by manually inserting individual containers. Which would be a necessity given the fairly rapid rate of fire they demonstrated compared to their larger counterparts.
-Mike

[Mr. Oragahn]

I must confess, JMSpock, I find your article hard to digest. I'm not sure about the rules and nomenclature you're using. I'm probably missing a small thing that would unlock the whole picture, but what's going on with:

We assume the general case of L^6 ~ S^3 ~ V^2 ~ M^2 when data not available on st-v-sw.net and otherwise assume ISD-like proportions for SW ships based on available dimensional data, GCS-like proportions for a ST ship.

In Star Wars, highly efficient fusion is the name of the game. Larger ships require S (approximate surface area) greater area in shielding, which means that their shield strength increases per V/S with a V^1 investment in shield generators. Although they have V^1 times the fuel, they only have S~V^(2/3) times the surface area and a similar density of weapon emplacements. It would be reasonable to assume a typical designed mission duration proportionate to V^(1/3), which would complement a ~V^(2/3) rate of consumption. There are some problems associated with this, but I believe they can be accounted for using additional tactical factors and remain pernicious problems for any account of Star Wars.

EU support for these propositions: In the EU, we have the explicit baseline of combat power scaling per V^(1/3) and cost per V^(2/3) per the Strike Cruiser and similar fluff; we do indeed also have mission duration specifications scaling roughly on V^(1/3) - days to weeks for fighters, months to years for capital ships.

[Jedi Master Spock]

I must confess, JMSpock, I find your article hard to digest. I'm not sure about the rules and nomenclature you're using. I'm probably missing a small thing that would unlock the whole picture, but what's going on with:

Here's the key that might unlock it: "L" is length. "M" is mass. "S" is surface area. "V" is volume. So what I'm doing in this is I'm guessing how ships might behave just based on their size and their shape compared to a benchmark ship of a similar techbase.

This makes me think of the YAWCF story: with numbers like that, how do you seriously expect a Venator cruiser to take on even a moderately damaged Ambassador?
-Mike

Personally, I don't. I think that if you push it far enough, you might be able to give them similar firepower without breaking beyond the bounds of reason, but even then, the tactical factors - by which I mean such things as accuracy, effective range, and maneuvering ability - give the Ambassador an advantage.

[Jedi Master Spock]

Incidentally, your notation is a bit unique. In logic, that ~ would be sometimes used for negation. Informally, it's often used to mean "about" or "around". I assume it refers to equivalence in your usage, but this presumption sometimes appears to break down given the apparent context. Can you clarify?

It's not really unique per se. Precisely, I'm using it in the sense of "is proportionate to"/"is approximately."

Your statements above, if I am translating correctly, argue that the Wank Class will thus have four times as much area in need of shielding, but also eight times as much space to put shield generators in, so for the purposes of the model you are assuming larger ships are commensurately better shielded for the surface area. However, gun density on the hull does not increase with volume, it appears (the ISD and Venator both have similar gun counts, as a matter of fact -- it just looks bigger on the Venator). The gun density is thus presumed to remain more or less constant in relation to surface area. So, if the ISD has 60 guns, we might expect the Wank Class to be capable of fielding 240.

Is that a fair translation, or did I miss something?

A fair translation.

This part of the model confuses me. If I read you right, you're suggesting that the TESB chase shows that the ISD and the Falcon are basically capable of the same acceleration rate. Although that's by no means insane given how often the Falcon has an ISD hanging on her tail, I always took it to be the result of excessive evasion maneuvers on the part of the Falcon, as required by the ISD's proximity. To be sure, the ISD is no slouch, and I believe her to be particularly quick with her antigravs, but it would never occur to me to suggest that the SSD could keep up with the ISD in a drag race.

Approximately the same. If I were to, say, assume that speed is ~V^(-1/3) in keeping with its longer endurance, I would have a Falcon with over twenty times the linear acceleration.

Presumably the ISD is trading some of its potential linear acceleration for maneuvering thrust.

This might need more basis. For instance, we have little idea of the refuel cycle of a Galaxy in normal operation, and no idea of the Constitution, save for Kirk's "it regenerates". We know the resupply of the Constitution, give or take (Kirk had food for 430 for five years as of "The Mark of Gideon"[TOS3]).

Well, there's the basis. We have absolutely no idea, but every ship seems capable of very long-term operation.

However, Excelsior did not appear to be four times the asskicker of the B-type Constitution Class (e.g. the Enterprise-A), at least in torpedo output, though her reserves may have been that much greater. And, true, she did have five of the TMP era emitters per saucer side compared to three. But still, from a power perspective, unless we assume more powerful phasers in addition to the extra emitters (they may be larger, which would help), I'm not sure we can get the Excelsior to be four times as powerful.

Similarly, there was the Klingon ship in the Delta Quadrant that Voyager had a tangle with. Voyager won, but not by as much as she should've considering she's got three times the volume of a TOS Connie and a century higher tech. That might be an outlier, though, given Voyager's condition.

There's something very important, canonically, that we know about the CCS. Power should actually be proportionate to M, but in the case of all the other ships I cited, we only have V, so I basically didn't include any discussion of mass except to say it's generally proportionate to volume. The CCS is about four times as dense as the Intrepid class - 40% more massive. If Voyager were twice as powerful per unit mass (based on "Flashbacks" giving twice the speed for VOY vs TOS-era ships) we would only expect it to be 40% more powerful than a TOS-era CCS. We might expect the technology gap to be even higher, but it's also quite possible that the CCS is much closer to a warship design than the ICS.

Similarly, if the Excelsior class has density closer to Voyager, and puts by design a greater emphasis on shields (necessary given its larger size) and speed (by description), then its relative firepower would suffer as a consequence.

But the 575 hours for the Galaxy? I suppose it's possible given the whole dead-in-space-but-shooting idea, but it seems a weirdly high value. Ah well, nevermind.

Well, phasers don't use much power relative to the peak consumption. The important piece to highlight is that the GCS is expected to burn through its entire fuel store in less than six hours at maximum warp.

While technically plausible, it seems that someone would've figured this out already and designed a computer-based primary firing control. That is to say, it wouldn't make a good excuse.

Our main other option is to scale firepower in lockstep with shielding - per V^(1/3). That would fit more closely with your estimates and TCW.

The model has here produced a peculiar situation, wherein an ISD weapon output is worth 14,000 X-Wings, and could defeat its own shields in 1/100th of a second.

Granted, aim is still bad for Star Wars (ships were missing at point-blank and standing still in RotJ), but I don't think mainliine cruiser battles are usually measured in seconds. And assuming maximum output from the Falcon model, it could defeat an ISD's shields in just under 8 seconds. That seems off.

Well, the estimate is more for point failure or bleedthrough than for gross shield destruction, but it seems a little off to me, too, even considering that.

However, if theoretically an ISD is able to put out up to 16 bolts per second, it would only be able to direct 8 on target. Each individual bolt would be less than one petajoule, and be attenuated by the sectional shields over each individual site, which might or might not fail. Then we would be estimating the damage to the armor based on how much energy got through the shields.

If the theoretical maximum output of the ISD was 100 similar-strength bolts per second - again, something the ISD would not be able to direct all to the same target, due to the way the ship is laid out - each individual bolt would be in an energy range the shields might be able to handle. It's still problematic, though.

Meanwhile, as seen over Ryloth, a squadron of Y-Wings are also capable of using their beam weapons alone to defeat six Munificents. And, from "Downfall of a Droid"[TCW1], we see that Republic tanks can smash the hull of a Munificent... Scary as it is, several Y-Wing fighter-bombers can take down Munis without much problem.

Yeah, that's a problem. If several Y-Wings can take down a ship that can hold up to the fire of a cruiser, SW capital ships simply have very weak firepower relative to their size.

True, but the prediction still suggests they wouldn't have needed the Death Star in that battle with that thing flying around. It's literally got the firepower of 56 ISDs, in the view above.

As a first order estimate. The Executor needs to invest more in maneuvering thrusters in order to be able to turn at all, and then we also should take into account the size of its hangars, storage spaces, and generally empty non-fighting areas.

It is an argument for using the L~V^(1/3) scale of firepower based on the Strike Cruiser's description (and, IIRC, that would probably fit with game mechanics), but I can't justify that one from first principles. It's instead necessary to look back at actual incidents to justify that.

[Jedi Master Spock]

Oh yeah, I forgot to mention something with the Star Wars post. As I've noted elsewhere, the idea that reactor power and weapon power are related is rather less certain than is classically assumed, thanks to the use of shells by Separatist ships and presumably others as well. This presents quite a problem in regards to Star Wars scaling of firepower by reactors, though theoretically ammo volume could be similar per unit volume.

Well, I'm really not caring whether or not firepower comes directly from the reactor. In fact, if hyperdrive/warp drive is the limiting factor for peak power output, this model is actually predicting that larger ships allocate a smaller amount of "peak" reactor power, or carry capacitor banks or something to let them hop into hyperspace, or have to get further away from planets to make it into hyperspace.

Sure, with all that extra percentage. But the percentage makes sense, since the Defiant's phaser power is such that, transferred to warp, they can go quite a bit faster.

15% is actually taken directly from "For the Uniform," in which we have the order "15% of plasma to phaser banks." "The Sound of Her Voice" does seem to confirm that.

However, the weapon output of over half of a Galaxy Class seems off. The Defiant is something like 1/100th the volume of a Galaxy, and although she's a stripped down warship compared to a luxury liner like the Galaxy, I can't imagine it's that superior, pound for pound.

Double check that. I put the GCS at 4 exawatts - 4,000 petawatts. That would put the Defiant around 1/6 the firepower...

The Lakota, for instance, is about 1/6th of a Galaxy, and after being upgraded to maximum whoopass potential she and the Defiant in a disabling-fight fought to a draw, but the Lakota never used her quantums.

Which fits, when we correct for that.

Point being, in a phaser fight to the death I'd bank on a Galaxy before the Lakota.

Definitely. Me too.

A weakish point in the shields of a Jem'Hadar battlebug were penetrated by concentrated fire from a Danube, quickly resulting in the ship's destruction. But the Danube's shields have often been shown to withstand at least a couple of hits. Character shields probably, but still something that a model would need to account for, and I'm not sure this did.

Well, this version of the model used fairly pessimistic shield figures. 50 MT for the GCS? It's the yield intended to match the lowest end for bleed-through damage.

We have other benchmarks that we could use, which I'll demonstrate next.

Really?

Really. The first order model's estimates are that they would chew through Republic attack cruisers like pixie sticks.