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Warp Maneuverability

I do not see the problem in the Alcubierre metric being able to allow you to maneuver as you need to by changing the shape of the space-time. It is another matter as to practicality of it and its related metric solutions to GR.
 
The rationale I cannot think up yet is the one that explains why there are few or no BVR engagements - ones where the attacker fires very long range weapons from a distance.
As I've had to work out lately for fanfic work, the most likely reason is that determining a target's position over distances of more than, say, 1000km is just not feasible in most situations. Anything that can scan for them quickly is going to have a very wide cross section, and anything that can pinpoint their exact position will take some time to work it all out. The closer you get, the faster your sensors can work out a firing solution and the better your chances of putting all your weapons on the target.

BVR weapons might exist with some very special equipment; my speculative JJ-D7 has a disruptor cannon in the nose capable of hitting targets up to a light minute away, but it requires such an incredibly precise targeting fix that the Klingons invariably distribute small probes throughout the battlespace, connected to the mother ship via subspace radio, that can act as spotters and tell that cannon where to point. Since the disruptor beam itself would travel at high warp (about warp 16, I reckon) this gives the ship a kind of "sniper-ship" capability that can be used effectively at long strategic ranges. But even so, most battles would still take place at closer ranges where less sophisticated sensors could obtain faster and more dynamic firing solutions and give their commanders more defensive/evasive options.

Torpedoes should be capable of this
Depends on what drives them. I no longer believe photon torpedoes have any real warp capability, but quantum torpedoes are vague enough that they might. In their case, though, I would have to reimagine them as disembodied warp nacelles that get fired out of a tube and then take off at warp one or warp two to chase down a target and then intentionally crash into it.
 
I do not see the problem in the Alcubierre metric being able to allow you to maneuver as you need to by changing the shape of the space-time. It is another matter as to practicality of it and its related metric solutions to GR.

Sure, but once again, the Alcubierre Metric would be useable at ANY speed, even modest sublight velociies; warp engines would be able to function as a starship's sole means of propulsion and would eliminate the need for impulse engines altogether (and starships would simply resort to maneuvering thrusters when moving near space stations or performing orbit changes). That impulse engines still exist, and that they are still used for almost all sublight maneuvers--indicates that warp drive is either incapable of use or very difficult to use below light speed, where most combat is going to take place anyway.
 
The rationale I cannot think up yet is the one that explains why there are few or no BVR engagements - ones where the attacker fires very long range weapons from a distance.

Well, first, if you go by dialogue most battles would be BVR. Several times it's been shown that combat occurs at hundreds or thousands of kilometers.

Torpedoes should be capable of this, even if phasers are more comparable to 17th century cannon, and the tactics should be useful against slow or stationary targets
Torpedos, like an AMRAAM (or anything created since the Falcon missile), would be less effective the longer the range. MaxRange for an AAM is a probability curve based on the speed of the missile at launch, target speed and heading, and target reaction time and ability (turn radius, but usually acceleration). Reaction time and ability is most critical, because as range and reaction ability increases, certainty of where a target will be at time of impact (ToI) decreases.

A modern fighter, if faced with an incoming missile fired at its maximum range, usually just has to change its heading by 90 degrees and accelerate to dodge, not make any kind of hard turn. The missile is on a ballistic flight path, and because of its finite propellant load and velocity, that path is aimed at where it and the pilot thinks the fighter will most likely by at ToI, which is some 20-40 seconds in the future. 40 seconds can be the difference of 10 miles and that's a lot more than a missile can overcome, so it misses.

On the other hand, if you fire a missile at MaxRange, you can have a reasonably good idea of where that plane is going to go once it detects the incoming fire, and you can bracket him with another missile targeted on that location. Alternatively, while the enemy jet is dodging your missile, you can close range and fire another missile, which because it has a shorter flight time, can better adapt to changes in course because the missile has both higher velocity (and therefore greater range of motion) and the enemy has less time to get out of the way.

Tactically, a torpedo barrage would be used the same way. Since a PT has a finite speed and run time, its MaxRange isn't its straight-line range, but a probability curve based on the speed and reaction time of the target, like a missile, but several orders of magnitude higher. You're left with the same two basic tactics, either bracket the enemy with larger numbers of torpedoes, or use the torpedo spread to force the opponent into a course that's tactically favorable to you.

This thinking also forces certain necessary abilities a PT must have to be effective. 1) It must be faster than a probable target. The probable target would be a defined specification set during a weapon's design. 2) It must have the range to close to impact the probable target while said target is at high speeds from most headings. This high speed isn't necessarily (though it would ideally be) the targets maximum speed. 3) It must be able to react quicker than the probable target. Ideally in all performance measurements (acceleration, turn radius), but one would suffice for a practical, though not a particularly good, weapon. 4) It must meet all above specifications while delivering a large enough payload to achieve considerable damage to the target. Ideally, this payload would be enough to destroy the target in one shot under any condition, but with capital ship weapons this usually isn't practical.

Also, given the way PT are supposed to work, you could sacrifice payload for range. So you have a ship killer at close ranges, but also something that has the legs and just enough kick to knock out small fighters or escorts and long range.

Phasers are more simple. Their range is limited by how quickly they can reach the target before it can react and break lock. At extreme range, a small reaction would make a phaser miss. At close range, a phaser will carve you up like tomorrows turkey.

We see high speed strafing runs in TOS, and an attack against a stationary target in DS9, but the weapons are fired at point blank ranges. Why? Elsewhere, we assuredly see torps and comparable probes moving at warp and crossing great distances.
We see that, because no one on the shows or movies actually sat down and pondered what tactics would be in a starship fight. It would probably be less like sailing ship combat (under most conditions) and more like hand to hand martial combat. By that, I mean it's not a smart idea to have a knock-down slug-fest at close quarters. It's hit and dodge. Fire phasers, back away, preferably at warp. It would take external circumstances to have large fleets engage for prolonged times at sublight speeds. It would be most common, at least in open space and especially during the skirmishes most commonly seen on screen, to have ships fire on each other (or one on the other) and warp away before the other ship could react, or at least before weapons impact becomes inevitable. This would, of course, be a lot more boring to watch on TV than ST:FC or DS9 style melees.

Ironically, all the scenes showing the Defiant dodging phaser beams left and right are more realistic only if we're looking at ranges over thousands, if not tens of thousands of kilometers. Again, longer the range of engagement the less drastic your maneuvering has to be to avoid getting hit.
 
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