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According to the StarCraft-wikia, it did have this ability, but that was later removed.
Twelve days later. It was a mechanics fart: unpleasant but over quickly.
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The Anti-Air-firing-rate of the Thor is almost equal, and the anti-air-damage of the Thor is also similar (10x4, +4 damage against light each shot), whereas the Viking does (10x2, +10 damage against massive each shot).
... What? How is 10x4 + 4 vs. Light AoE "similar" to 10x2 + 10 vs. Massive? The only things similar are that they are multi-attacks with a base value of 10, which is coincidence at best.
The Thor is clearly better against light armored units, particularly those that cluster together (hence the AoE). Vikings are better, cost for cost, against massive units and single-targets.
And no, they don't fire at about the same rate. Vikings are notably faster on the attack.
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Cost-wise, the Thor does seem to beat 3-4 Vikings on the ground.
Against what? Even if we assume they fire at the same speed, 2 Vikings cost slightly less than a Thor. Two Vikings deliver equal firepower to a single target as a Thor. And they fly, thus they can chase targets down. Against massive targets (Viking specialty), one Viking can keep pace with a Thor's damage.
And while a Thor isn't susceptible to AtA, Vikings aren't susceptible to AtG. So Banshees and Brood Lords are mere prey for the Viking, whereas either unit is a major pain for Thors.
Yes, if you get clusters of the Thor's preferred targets together, the Thor is better. But it should be better. Vikings and Thors handle different situations.
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Personaly, I don't see the use of a ground-based terran battlecruiser
People keep trying to call the Thor a "something else." It's a modified Siege Tank or a big Goliath or a walking Battlecruiser or some other nonsense. The fact is that it's none of these. It's a Thor. It has its own designation, and its own unique nature. It is not a slightly modified version of any other Terran unit.
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Can all 6 laser batteries fire at one time? From the video it seems only 2 at a time, but at the same time...is it possible that each weapon has an limited angle range in which it can fire? I don't really know how best to describe what I mean...the weapon platform firing the laser may have a limited field (like line of sight) in which it could fire. The mothership does rotate rather quickly
What good would that be? The Mothership doesn't rotate that quickly. And in order for it to be used as you suggest, it would have to be surrounded. Which is probably not the place you want your expensive and unique Mothership to be.