WatchingStar Trek I've observed that phasers and photon torpedos are used interchangeably, often seemingly at random. I know that writers probably didn't think/care but I look for explanations in-universe.
The presence of two weapons in single vehicle is usually justified by different targets and uses, say a machine gun for soft targets (infantry) and a main gun for hard ones (other tanks). Otherwise it only increase problems (incompatible ammunition, increased maintenance cost etc.).
One is energy-based (phasers) and the other is matter-based (torpedoes) with an explosive yield. I remember reading once that it in a confrontational situation, the phasers would typically be used to weaken another ship's shields and then the torpedoes would finish the target off.
Also the phasers were used more to disable ships than to destroy them, as they could target more precisely.
According to the Technical Manual phasers are constrained to the speed of light so are of less use in confrontations that are taking place under warp drive. Photon torpedoes have warp capability (though not full warp drives) and so can go faster than light speed and engages ships also doing so.
I suspect there is a desire on the part of the writers to have an analogy to pre aircraftcarrier battleship fighting. Phasers are like deck guns, and torpedos, are like their namesake. One has longer range, and is quicker to aim, and the other is slower, but does more damage. Most spacewar stuff, wants to reenact war world two battles, either naval, or bombers versus fighter planes.
Another good reason to use them differently is that torpedoes can track a target where as a phaser is fired directly. If it misses, it misses. If you recall, one of the movies, a Klingon ship is cloaked but leaking particles (photons was it?) and they modified a torpedo to run the particles down to the source to kill the ship.
Phasers and torpedoes are, as was mentioned, much like deck guns and torpedoes in WWII-era naval warfare. The idea of the Klingon and Romulan warbirds being able to cloak and thus be hidden was a direct analog to the German U-boats.
Tactically speaking, you want as many types of weapons as you can get when you're in a fight. This applies virtually across the board, in all situations. If one weapon doesn't suit the situation, you bring another. It's why police officers don't just have guns, but batons, tasers and pepper spray as well.
Back in-universe, phasers are the go-to weapon. Phasers are energy-based, meaning as long as you have sufficient power you can continue to fire them. They are very powerful against most unshielded targets, and can be brought to bear from nearly 360 degrees (provided all phaser banks are operating nominally). Lastly, being a beam, they can usually be aimed and fired pretty quickly at a target at almost any renge at which the weapon is effective (even right up close). However, depending on the race's level of technological advancement, phasers often have minimal effect on shields or even ship hulls. They are also limited by the speed of light, so they cannot be used while travelling at warp.
Torpedoes are the Star Trek equivalent to the same weapons in naval combat, or to anti-ship missiles like the Harpoon or Exocet. Get hit with one of these with your shields down and your ship has a big gaping hole in it. The explosion also requires a lot of shield power to repel and can cause damage even with shields up. They also require minimal power to fire, making them the principal weapon of cloaked ships like the Klingon Bird of Prey, and they can be used while the ship is travelling at warp, as they maintain a "warp bubble" generated by the firing ship. However, they are an expendable weapon; it is implied that torpedoes are too complex a machine to replicate, even without their antimatter payload. They are also, for the most-part, non-seeking; they must be given their initial guidance from the firing ship, and if the "sight picture" changes (the ship radically changes course or speed) the torpedo can miss. Torps have a maximum rate of turn and come out of the launcher along the fore-to-aft axis of most ships in the universe (there are a few turreted launchers such as the ones mounted on DS9), meaning their effectiveness in a "broadside" confrontation is reduced. This makes torpedoes a weapon you use in head-on combat when you are pretty confident that you will hit your target, usually meaning relatively close range.
It is mentioned several times in Voyager that photon torpedoes are irreplaceable. Although fans have counted the number of photon torpedoes fired throughout the entire series and found it to be much higher than the number given explicitly in one of the first episodes, it nonetheless provides an in-universe reason not to want to waste them.
I know this a technical discussion about different capabilities, but phasers have become progressivly less powerful as the series progressed from Star Trek to Voyager. In the original series, where the plots were written by classic sf writers from the golden age of sf, and as such were dense with new sf concepts, there is some discussion about how vastly powerful they are. I don't know the episode, but it is about two humans who crash landed and were badly damaged and the aliens allow them to be viewed as complete and unbroken.
In that episode, they need to break into the underground fortress (it was the episode with the lift underground); they use a tripod phaser, which is really powerful. They say that it 'should have blown the hill in seconds' even though the telepathic aliens are generating an image in the crew's minds of an unbroken hill at that point.
The point is, Kirk discusses firing the phasers from space, but they're worried (if you read the script) that the phasers are going to really destroy everything, cutting into the planet down to the core, and even destroying it, cutting it in half. Those were super power cutting beams that are vastly powerful, unimaginably fed by antimatter engines.
A well designed and maneuverable ship controlled by a deft captain and crew could let out a continuous fire of Phasers by rotating their ship and corkscrewing around their opponents path while constantly rotating the shields presented their foe.
A well designed and fast ship could stay out of range of the enemy and let out a slow but steady barrage of photon torpedoes. Forcing the enemy ships to flee or be destroyed without dealing any return damage.
The alpha strike is the concept of charging all a ships weapons and then waiting until point blank range and unleashing them all at once or in quick succession. For a Federation ship to manage this full charge they often needed to reduce their maximum speed or run the risk of damaging their engines.A well executed Alpha Strike could strip a shield sector by using all phasers, and then unload overloaded photon torpedoes (adjusted to increase damage but decrease accuracy) through that downed shield and destroy or cripple most ships of similar class.
Lead with photon torpedoes to take out almost all shields, and then unleash targeted phasers and you could cripple a ship with precision, cutting out warp drives or weapons, but keeping ship, crew and contents intact.
Photon torpedoes came along late in the first season of Trek. If you remember BALANCE OF TERROR, the phasers were fired using "proximity blasts;" these probably led to the writers coming up with a different sounding weapon that lent believability to the show. The torpedoes seemed harder to hit a target with, but apparently were capable of diabling/destroying another vessel with just a few hits. It also seemed many writers were apparently unaware of the photon torpedoes--in the DOOMSDAY MACHINE, phasers were used exclusively where torpedoes might have proven more effective without having Decker & the Constellation sacrificed. Both weapons had the coolest sound effects audible from the bridge when firing.
Phasers are much more effective against shields than torpedoes are. If against a ship's shields a phaser hit and a torpedo hit do about the same damage, wouldn't you rather use the one you can keep spamming?
The shield absorbs, blocks, and reflects most of the energy and redistributes it across its whole. If any energy gets through then its something the shield normally wouldnt block anyway (eg, certain kinds of radiation, and shots which are modulated to bypass and match the shield's frequency). Any damage the ship takes from a hit to the shields is probably buffeting from the Shield pushing on the Shield Emitters which then transfers some of that energy into the ship superstructure (sorta like blunt force trauma on a ship level).
Against an un-shielded ship, Phasers do decent damage to a ship by themselves but a Torpedo hits so strong it can severely cripple or destroy the ship in one shot. Of course this depends on the size of the ship - A Borg Assimilation Cube is 6000 meters size per side, and it regenerates, but at least it doesn't have shields.
(though it makes me wonder why not just make the Warp Capable Torpedoes hit the borg ship At Warp Speed or something close to C... then the explosive power of it pales in comparison to the kinetic striking power. But oh well).
Torpedoes can also be useful if you're having problems hitting the target, but I think using the torpedoes in this way is unrealistic and was used for theatric performance in the show. The idea of firing a spread of torpedoes would be to get at least one of the torpedoes close enough to the offender so that it gets hit with an energy-shockwave.
But... if it can take more than one shot to blow up a de-shielded ship on a Direct Hit (or even with an internal explosion in some cases) then we aren't exactly talking about NUCLEAR YIELDS here, contrary to what some star trek theorists claim.
If a torpedo is listed as having a 25 Isoton Yield then im saying thats probably more like 25 Tons of modern High Explosives. Thats like 10 modern day cruise missiles in one hit, and the torpedo itself is a fraction of its size. An admirably strong weapon for a warhead you can probably carry in a suitcase. But its not a briefcase nuke by any measure. Its somewhere in that gray area between conventional explosives and nuclear.
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