Response to "Geometric Complexity: Warp Nacelle Combinations
Good explainations, Nob.
Here's my view on those subjects:
Regarding the hull configuration:
In addition to your points, I always wondered what purpose the "neck" section serves.
In TNG, we can see diagrams of the Enterprise inside the warp bubble on computer screens several times. The interesting thing is that the boundary between the two warp field lobes runs through the neck.
As I see it, the reason for the neck is that this boundary should run through the narrowest part of the ship. This configuration increases warp field efficiency and stability (meaning higher possible velocities) and is the reason why the best Starfleet ship classes (the Enterprises) have a neck.
Of course there are ships with wider necks or even without one.
The Excelsior for example has a wider neck because of her transwarp drive. Stress produced by the new engine lead to sturdiness being of higher priority.
That the Sovereign has no neck may have different reasons:
She may be built for combat so a neck would be a weak point (the USS Odyssey was rammed into the neck I think). This, among other things, could explain her big warp nacelles and warp core compensating the inferior hull configuration. This explanation would also work for other, more tactically oriented ship classes.
The "weak point"-explanation would also work for the Sovereign being built for superior impulse maneuverability. Speaking for that are the huge impulse engines.
The Nova and Intrepid have no neck because they're supposed to be able to land, meaning a sturdy hull design is needed.
The Akira is fast with her relatively thin "necks" but because there are two of them, she's also sturdy enough for combat.
The Defiant, as we know, has severe problems with warp speeds higher than warp 9. This could be explained by the absence of a neck, meaning that the boundary of the field lobes runs straight through the ship resulting in a highly unstable warp field that stresses the hull tremendously. Only an extremely powerful propulsion system (as we know from dialogue she has) could make her fast enough.
Most other ship designs could also be explained this way.
Alternatively, at least from the Akira and Sovereign on, Starfleet has found a way to make a neck section redundant. If I remember correctly the problems of the Defiant were solved at some time in the series, so maybe that would speak for this too.
Regarding single nacelle starships:
In addition to bad maneuverability and slow speed, another reason for only one nacelle could be saving ressources. I believe to remember that the stuff from which warp coils are made (verterium cortenide) cannot be replicated, so if Starfleet needs as many ships as possible, a one nacelle configuration is the way to go.
Regarding four nacelle starships:
In my view, four-nacelled ships are the fastest and the most maneuverable, or, when only using two nacelles, the most endurable.
The downside is, as you said, that the warp field requires substantially more tuning, so the complexity of the engine and susceptibility to nacelle imbalance are keeping Starfleet from using this configuration.
Aditionally, verterium cortenide shortages and, maybe, higher fuel consumption would be a factor.
Regarding two nacelle starships:
They would simply be the best of both worlds, being faster and more maneuverable than one nacelle and easier to operate and more economical than four nacelles.
Regarding the odd three nacelle starships:
Alternatively, the third nacelle could be a kind of booster. It would make an ordinary two-nacelled ship faster, but in return makes the warpfield more inefficient and more unstable raising fuel consumption, increasing hull stress and reducing warp maneuverability. Also, to explain the "fifth wheel" remark, the boost gained from the third nacelle could also be accomplished with only two nacelles (modification of the warp coils or the ship's hull, for example), but it is easier to simply stick another one on the ship.
Nob Akimoto wrote:
However, quad nacelle configurations offer superior warp maneuverability, particularly in unorthodox pitch and roll maneuvers, making the ships well suited to eluding pursuit or exploring regions of space "off-axis" on the galactic plane.
Are you saying that most starships have problems flying up and down on the galactic plane?