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In Star Trek: The Next Generation, we see type 2 hand phasers used as the primary firearm used by most Starfleet officers, citizens of the federation, and basically anybody who could lay their hands (or tentacles, claws etc) on one.

In the following pictures (which I got from Google, and claim no right to), we see how the phaser beam often comes out at different angles to hit the target:

Commander Riker firing a phaser

Deanna Troi firing a phaser

Both Riker and Data firing phasers at the same time, using the same model phaser,  but with the beams coming out at different angles

A beam at a completely different angle to the phaser

This would imply that these phasers have an automatic target-acquiring system, that changes the angle of the beam depending on what angle it is being held.

However, we also see phasers being fired, and the beam coming out in a straight line (i.e in the same plane as the nozzle, for want of a better word, of the phaser). On these occasions, and again, using the same type of phaser, the beam will miss by a matter of centimetres (as seen in these photos, which I again found on Google, and a photo from Netflix, to which I claim no rights):

Chief O'Brien firing a phaser beam in the same plain as the gun

A very close miss

The same effect is also observable on Cardassian and Romulan weapons.

My question is: do phasers (or disruptors) have an automatic targeting mode?

An in-universe answer is preferable, but any out-of-universe answer would also be appreciated.

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    Shoot! I was hoping you were a Star Trek writer and could make a sincere claim to the pictures. Everyone knows that the pictures don't belong to the fans. Don't worry. You won't be sent to the brig today. – Ham Sandwich Jul 25 '17 at 0:04
  • @T-1000'sSon Haha, thanks for reassuring me, I just wanted to make sure!😂 – Captain J.L Picard Jul 25 '17 at 0:05
  • They sometimes miss, so I would think not - where the beam is at a different angle to the phaser I'd put down to a special effects failure. I can't recall the auto-targeting ever being mentioned on the show, though the ship's phasers do have this feature. – colmde Jul 28 '17 at 11:24
  • @colmde Thanks for the reply, good answer😊 – Captain J.L Picard Jul 28 '17 at 12:13
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In a word, yes. On 'away missions' the Type 1 and Type 2 (handheld) phaser are merely a point 'n' shoot device. When they're tied into the ship's sensors, however (and typically when they're on board the ship) they're a slightly smarter piece of kit, capable of being automatically limited to stun and with the beam targeted by the ship.

Voyager Technical Manual

How to use [Hand Phasers]: Just point and shoot. Phasers are normally set to "stun," but have controls which permit adjustment to other settings and power levels.

TNG Technical Manual

Downstream from the power cell are three interconnected control modules: the beam control assembly, safety interlock, and subspace transceiver assembly (STA). The beam control assembly includes tactile interface buttons for configuring the phaser beam width and intensity, and a firing trigger. The safety interlock is a code processor for safing the power functions of the phaser and for personalizing a phaser for limited personnel use. Key-press combinations of beam width and intensity controls are used to configure the phaser's safety condition. The STA is used as part of the safety system while aboard Starfleet vessels. It maintains contact between the phaser and the ship computers to assure that power levels are automatically restrained during shipboard firings, usually limited to heavy stun. Emergency override commands may be keyed in by the beam controls. The STA adapted for phaser use is augmented with target sensors and processors for distant aiming functions.

We learn in DS9 that Type 3 Phaser-rifles are capable of independent targeting despite having much the same control system as Type 1 and 2 Hand-phasers.

KIRA: This is a standard issue, Cardassian phase-disruptor rifle. It has a four point seven megajoule power capacity, three millisecond recharge two beam settings.

ZIYAL: How do you know so much about Cardassian weapons?

KIRA: We captured a lot of them during the occupation. It's a good weapon, solid, simple. You can drag it through the mud and it'll still fire. Now this. [holds up a Federation phaser rifle.] This is an entirely different animal. Federation standard issue. It's a little less powerful, but it's got a more options. Sixteen beam settings. Fully autonomous recharge, multiple target acquisition, gyro stabilised, the works. It's a little more complicated, so it's not as good a field weapon. Too many things can go wrong with it.

DS9: Return to Grace

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    Note that writers weren't held to this fact. Hand-phasers are as accurate or as inaccurate as the script requires. – Valorum Jul 25 '17 at 0:18
  • That definitely makes sense as an out-of-universe plot device, thank you! – Captain J.L Picard Jul 25 '17 at 0:23
  • Thanks for answering, this definitely clears things up! Although, in-universe, does this extend to on planets, such as the third photo of Riker and Data on a planet's surface, and also to the fourth picture, which appears to be off of the Enterprise? – Captain J.L Picard Jul 25 '17 at 0:25
  • @CaptainJ.LPicard - I refer you to my earlier comment. Phasers do whatever the writers want them to do. – Valorum Jul 25 '17 at 0:37
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    @Valorum In many cases, I think it's less about the writers and more about the special effects department. I don't imagine many scripts specifying where every phaser beam lands unless the plot requires them to hit or miss something very specific. SFX, on the other hand, would try their best to make sure the beam hits whatever its supposed to hit. If the script says "Beam hits <character>", they just think "Where's the beam coming from, and where's it going? Draw a line between those two points". Everything else, like how the actor holds the device, is fairly irrelevant. – DisturbedNeo Jul 25 '17 at 9:28

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