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The problem with basing any analysis on phasers is the NDF effect - it's far less effective against dense materials like metal, and can't be treated as a simple DET calculation.

We know how powerful the Galaxy class phasers are

Do we? Keep in mind that official statements on the power are incredibly different from what we actually see.

I'd go with the official figures. If thats what they say they are thats good enough for me unless blatantly contridicted on screen.

The problem is that they are blatantly contradicted on screen. The guys working on the show clearly didn't have a clue about how to calc these things.

it all started off so simply...now, I feel like you're speaking arabic.

Now we've gone into the mystical land of physics...

I don't think they were conridicted to much. Phasers can be used at different power settings. So long as they didnt go over the maximum it still stands.

The problem with phasers is that they're described as anywhere from low-Gigawatt range (The Survivors) to low-Terawatt range (A Matter of Time). Moreover, their method of operation is based on a chain reaction, possibly conversion into neutrinos, that seems to be adversly affected by increasing material density. We can't use formula that assume direct energy transfer to calaculate phaser firepower, as the result would only apply to that particular material.

Thank you Seafort, thats exactly the problem. Phasers are shown at being great against something like rock, but much weaker against metal.
As such, its difficult to get any hard figures. I should note that we have never seen power levels as described in the official figures, even when it would have been advantageous to use them.

Remember that these metals are not what we think of - even the strongest ones like titanium, it's all this duranium and tritanium, it's probably several order of magnitides stronger than anything we know, then there's the specific metals made for armour such as the ablative stuff.

As phasers do seem to vapourise, it would be possible to get the strength of the phasers in each hit (assuming "decent" special effects), based on the latent heat capacity, the latent heat of vapourisation, etc. We know that of our modern day rocks (specifically granite was mentioned in the episode with Tasha Yar), and we could find out the boiling temperature of these other metals.

I think it boils down to bad physics/chemistry in the special effects department

Remember that these metals are not what we think of - even the strongest ones like titanium, it's all this duranium and tritanium, it's probably several order of magnitides stronger than anything we know, then there's the specific metals made for armour such as the ablative stuff.

True, but we can establish low-end calculations from these events. And in some cases the dialogue specificaly states what power the weapons are at, thus allowing us to find a lot of information from a single effects scene.

As phasers do seem to vapourise, it would be possible to get the strength of the phasers in each hit (assuming "decent" special effects), based on the latent heat capacity, the latent heat of vapourisation, etc.

Phasers do not vapourise things. If it were vapourisation every one in the room would be badly burned, if not killed, by the boiling vapour produced. This is what vapourisation is, litteraly turning something into vapour. Since there is no vapour it clearly is some other unknown mechanism making people dissapear. Most likely, it is some type of chain reaction, this explains how it take the same amount of power to "vapourise" a klingon as it does a human.

I think it boils down to bad physics/chemistry in the special effects department

And pure ignorance on behalf of the 'experts' working on the show.

They do call it vapourisation, so whether or not that corresponds to what we know as vapourisation we don't know. We'd assume that it doesn't due to the boiling effects, however in the Trek universe those high settings on a phaser are "vapourise". I will grant that the most likely explanation does seem to be that any matter which is hit by a phaser on vapourise, is changed chemically, quite possibly broken down into its elements, which are then released as a vapour. We must assume though, at some point, the matter with which a phaser (whether it be a hand or ship one) is hit is turned to a gas, but with such advanced equipment it might not necessarily mean that it has boiled or gone to an extreme temperature.

They do call it vapourisation, so whether or not that corresponds to what we know as vapourisation we don't know.

It does not correspond even the slightest to vapourisation.

We'd assume that it doesn't due to the boiling effects, however in the Trek universe those high settings on a phaser are "vapourise".

We know it dosen't. The very deffinition of vapourisation is being turned into vapour. If there is no vapour it is not vapourisation. Its that simple.

I will grant that the most likely explanation does seem to be that any matter which is hit by a phaser on vapourise, is changed chemically, quite possibly broken down into its elements, which are then released as a vapour.

This would be a good theory, if there was any vapour. But there clearly isn't.

We must assume though, at some point, the matter with which a phaser (whether it be a hand or ship one) is hit is turned to a gas, but with such advanced equipment it might not necessarily mean that it has boiled or gone to an extreme temperature.

How could you possibly turn something into vapour without it being heated?

It can't be vapourisation of any sort, since the person hit never turns into a pillar of steam, and there are none of the overpressure effects that would inevitably be associated with turning a person of a given volume into a gas of tens of times that volume. The most likely explanation I've seen suggested is that the target is somehow turned into neutrinos, which would pass through light years of matter without hitting anything. Unfortunately, modern physics doesn't have a formula for turning stuff into neutrinos, so we can't calculate anything.

The neutrino idea could work, perhaps vapourisation referring to matter being changed into neutrinos