www.ditl.org

In First Contact it is shown that four quantum torpedo's is enough to destroy a borg sphere. According to the DITL specs page it has a diameter of 600 meters. This would give a volume of about 113097335 m^3.

A borg cube would have a volume of 27983710656 m^3. Assuming an equal density it would take 990 quantum torpedo's to destroy a cube. However a transphasic torpedo has been shown to be able to destroy a borg cube with one shot.

Grahams Torpedo Yields Article lists quantum torpedo's as 50 isotons. 50*990=49500 so a transphasic torpedo would have a yield of fourty-nine thousand five hundred isotons, or approximately 122760 megatons.

There's a very large flaw in your logic - you assume that Borg ships are inert objects, and that the number of torpedoes required to destroy one is therefore proportional to their mass. This is not the case - they're ships. Ships which carry antimatter. All you need to to do to destroy one, therefore, is to inflict sufficient damage to disable whatever system is containing said antimatter. In the case of the Borg specifically, their ships are designed to self-destruct if any key technology is seriously damaged, as we saw in Dark Frontier, making their destruction even easier, provided you hit them in the right place.

Spheres are ships too, are they not?

Correct. So?

The flaw is that a ship ten times as large doesn't necessarily take ten times the firepower.

For one, even assuming the firepower scaled, it might be the case that the attack on the sphere was overkill. If I shoot a puppy with a bazooka it will die. Does it therefore follow that to shoot an elephant a thousand times bigger than the puppy I need something a thousand times bigger than a bazooka? Of course not.

For another, as Seafort pointed out, ships tend to have explosive stuff in them. In World War II the Hood and the Bismark were two ships that were comparable in size and armament. Yet one salvo from Bismark sent Hood to the bottom. When Bismark was finally tracked down two battleships pounded her for well over an hour, firing more than 700 shells in the process, and she still didn't sink until a cruiser put a couple of torpedoes into her. With no ideas of what strengths and vulnerabilities Spheres and Cubes might have there's no real way to compare them.

GrahamKennedy wrote:When Bismark was finally tracked down two battleships pounded her for well over an hour, firing more than 700 shells in the process, and she still didn't sink until a cruiser put a couple of torpedoes into her.

That, I think, is the best explanation for the obvious superiority of transphasics over PTs and QTs (which the Borg can soak up by the dozen or hundred) - they're able to bypass their defences. Whether or not they're also more powerful, explaining why a couple of TTs could do what it needed at least a dozen QTs/PTs plus several phaser blasts to do it FC, or whether they're simply more effective, is an entirely different question.

We can only really guess, but I'd say that's a pretty good guess. "Phasing" has often been used in Trek for that funky cloaking effect where the phased object is invisible and can pass through unphased matter, so I'd guess that a transphasic torpedo can pass through shields and/or hull and detonate inside the enemy ship.

Hell, it might even be LESS powerful than a photon for all we know.

Nice reasoning. Different tech but same idea than those chronaton torpedoes the krenim had.