ST VI: TUC torpedo calculations...

[Mike DiCenso]

That second example is not a very good example, Oragahn. In particular it is different than the one being described earlier in this thread, mostly due to the fact that Voyager has been the recipient of Borg technology. The first example is from before the Borg alliance, and clearly shows the ship being smacked around so hard that she flips end-over-end. We also see a full shield bubble in the first example, where in the second the shields have been knocked down by numerous hits.

The Voyager is also just barely getting underway in the first example, and moving fairly slowly, suggesting the mass-lightening effect is not fully in play here. It takes about 10-15 seconds to overcome the imparted KE, and escape at warp.
-Mike

[Mike DiCenso]

Jedi Master Spock wrote:
Anything qualitatively known about the biobeams, or in particular how fast they propagate?

For composition, no. If I understand you correctly on the second question we see them travel across several km or more in under a few seconds. But like phasers and turbolasers, we see them travel at different speeds, and they are quite visible.
-Mike

[Mr. Oragahn]

That second example is not a very good example, Oragahn. In particular it is different than the one being described earlier in this thread, mostly due to the fact that Voyager has been the recipient of Borg technology. The first example is from before the Borg alliance, and clearly shows the ship being smacked around so hard that she flips end-over-end. We also see a full shield bubble in the first example, where in the second the shields have been knocked down by numerous hits.

The Voyager is also just barely getting underway in the first example, and moving fairly slowly, suggesting the mass-lightening effect is not fully in play here. It takes about 10-15 seconds to overcome the imparted KE, and escape at warp.
-Mike

Ok. But it does not explain why the ship got spinning the wrong way round, suggesting that what made it spin wasn't directly due to the impact.
Possibly a mechanical issue, and seeing that it took them between 10 and 15 seconds to actually stop the ship spinning, which is quite very long, it would support that the engines, or something related to directional engines or closely related mechanisms, are more responsible of the strange spin than any KE transmitted by a beam of unknown composition and amking the ship spin against physics.

As for the engines not being pushed at full, it's rather odd and unbelievable, as they were facing an unknown ship, largely assumed as being a threat, possibly part of a fleet, that destroyed 15 Borg Cubes.
Tell me Janeway didn't plan to get her ass off this zone ASAP! :)

Jedi Master Spock wrote:
Anything qualitatively known about the biobeams, or in particular how fast they propagate?

For composition, no. If I understand you correctly on the second question we see them travel across several km or more in under a few seconds. But like phasers and turbolasers, we see them travel at different speeds, and they are quite visible.
-Mike

So assuming anything like or closely similar to photons would be a mistake.

[Mike DiCenso]

Mr. Oragahn wrote:
Ok. But it does not explain why the ship got spinning the wrong way round, suggesting that what made it spin wasn't directly due to the impact.
Possibly a mechanical issue, and seeing that it took them between 10 and 15 seconds to actually stop the ship spinning, which is quite very long, it would support that the engines, or something related to directional engines or closely related mechanisms, are more responsible of the strange spin than any KE transmitted by a beam of unknown composition and amking the ship spin against physics.

Um, no. When we see the crew trying to regain control of the ship, they're struggling against the forces (as though in a giant centrifuge) to reach the controls and stablize the ship. There is also no dialog whatsoever indicating that the ship's engines and stabilizers are off-line.

As for the engines not being pushed at full, it's rather odd and unbelievable, as they were facing an unknown ship, largely assumed as being a threat, possibly part of a fleet, that destroyed 15 Borg Cubes.
Tell me Janeway didn't plan to get her ass off this zone ASAP! :)

Actually, as you haven't seen the episode, you must not know that once they stablize the ship, they immediately jump the ship to warp, not full impulse. Given some of the extremely fast accelerations seen in Trek, the slow initial acceleration of Voyager was probably due to a lack of mass-lightening for the impulse engines, otherwise they'd have (literally) rocketed out of there like a bat out of hell. Here's the dialog:

TORRES: I've got them.
JANEWAY: A skeletal lock, huh? We'll have to add that one to the Transporter manual.
PARIS: Captain, the bio-ship is powering up, like it's charging some kind of weapon.
JANEWAY: Mister Paris, get us out of here. Maximum warp!
PARIS: The alien ship is not pursuing.

Nothing about full impulse.

So assuming anything like or closely similar to photons would be a mistake.

But the assumption here is that we're dealing with the S8472 weapon in the same manner as the militant pro-Wars people do in assuming a photon-based TL.
-Mike

[Mr. Oragahn]

Mr. Oragahn wrote:
Ok. But it does not explain why the ship got spinning the wrong way round, suggesting that what made it spin wasn't directly due to the impact.
Possibly a mechanical issue, and seeing that it took them between 10 and 15 seconds to actually stop the ship spinning, which is quite very long, it would support that the engines, or something related to directional engines or closely related mechanisms, are more responsible of the strange spin than any KE transmitted by a beam of unknown composition and amking the ship spin against physics.

Um, no. When we see the crew trying to regain control of the ship, they're struggling against the forces (as though in a giant centrifuge) to reach the controls and stablize the ship. There is also no dialog whatsoever indicating that the ship's engines and stabilizers are off-line.

1. Has the Voyager seen being able to rotate that fast under controlled conditions?
2. If my suggestion above doesn't work, then one has to be found, other than the ship was poked by a solid sudden gigaton flux or whatever particles, because this doesn't add up as far as simple physics are concerned.

As for the engines not being pushed at full, it's rather odd and unbelievable, as they were facing an unknown ship, largely assumed as being a threat, possibly part of a fleet, that destroyed 15 Borg Cubes.
Tell me Janeway didn't plan to get her ass off this zone ASAP! :)

Actually, as you haven't seen the episode, you must not know that once they stablize the ship, they immediately jump the ship to warp, not full impulse. Given some of the extremely fast accelerations seen in Trek, the slow initial acceleration of Voyager was probably due to a lack of mass-lightening for the impulse engines, otherwise they'd have (literally) rocketed out of there like a bat out of hell. Here's the dialog:

TORRES: I've got them.
JANEWAY: A skeletal lock, huh? We'll have to add that one to the Transporter manual.
PARIS: Captain, the bio-ship is powering up, like it's charging some kind of weapon.
JANEWAY: Mister Paris, get us out of here. Maximum warp!
PARIS: The alien ship is not pursuing.

Nothing about full impulse.

If there's no proof that they were at full impulse, there's no support to claim that there was a lack of mass-lightening because of their low escape velocity.
So the "speed" was rather low. Ok, so they were suicidal, and instead of going at max warp ASAP, just as soon as Janeway ordered it, they rather sailed away on moderate cruise with a ship's about to blast their asses off the sky, like it did to those Borg Cubes.
If there had been a quantum singularity forbidding a warp jump, then all the more a reason to fly at full impulse away from the bioship and that singularity altogether.

So assuming anything like or closely similar to photons would be a mistake.

But the assumption here is that we're dealing with the S8472 weapon in the same manner as the militant pro-Wars people do in assuming a photon-based TL.
-Mike

We know that their assumption is a mistake. So are you guys just doing a test, to see what would happen if you used the same flawed assumption?
There are people on the first page who actually took it for granted, being quick to relate those gigatons of KE to shielding.

[Jedi Master Spock]

Shows the ship getting hit.

A few questions now.

What's the composition of the bioship's beams?

Unknown.

What's the real mass lightening factor?

IMO, that's irrelevant. In general, it's either present at somewhere around 0.99+, or not at all. If there's any significant mass lightening effects, we have absolutely nothing to work with... so we may as well assume there isn't, because otherwise we have no data to work with.

However, it's perfectly reasonable to assume that they aren't present for in-universe reasons (more on that later).

Is the hull able to withstand tens of gigatons (~70 GT) of firepower (see this clip, at 2:21, to view the unshielded Voyager getting hit by a bioship's beam)?

Potentially, depending on various other sources for firepower. Although it is possible those are different bioship beam settings, AFAIK.

If I get it correctly, the idea is that the beam imparted like 70 GT of kinetic energy, right.
Well, then there might be a problem, because of the impact angle. The beam's coming from behind, and is almost horizontal to Voyager's horizon plate. It hits the superior hemisphere of the shield, above the stern, off axis on the left, actually above the portside nacelle.
Considering the ship's center of gravity, with a hit coming kilometers away from behind, wouldn't that make the ship spin the other way round, and slower?

I'm not quite sure you're right, here. I'd want a better clip that I can frame-by-frame at full rate to be sure where that beam is impacting. It could very easily - from what I can tell from that clip - be impacting the right way to cause Voyager to spin that direction (i.e., clipping Voyager from "below" at an oblique angle.)

More important is the fact that we have little reason to assume the bioship's beam is very close to lightspeed. As you and Mike and correctly brought up, the scenario is analagous to the Millenium Falcon hit; you can pull some nice figures out of a hat if and only if you make a batch of assumptions that can't be backed up very well.

So the "speed" was rather low. Ok, so they were suicidal, and instead of going at max warp ASAP, just as soon as Janeway ordered it, they rather sailed away on moderate cruise with a ship's about to blast their asses off the sky, like it did to those Borg Cubes.

"Full impulse" is pretty fast, so we can be sure that they weren't going full impulse. Note, however, that mass lightening effects are tied to warp fields in any case. If warp systems are offline, there are no mass lightening effects in play.

What I'm seeing here is that they needed to dump the angular momentum before going to warp. Remember, active warp fields lighten to a miniscule fraction of effective mass. Ramp up a warp field while you're spinning, and you'll spin faster and faster. Turn off a warp field while you're spinning under one, and you'll stop spinning instantly.

More interesting, IMO, is the music video you posted - the point from that (2:24) shows an almost direct hit on Voyager's tail, only slightly angled, but it still causes Voyager to swerve a little in response. If I had those two clips at full speed and resolution in an editable file format, I should be able to give you a very good estimation of the momentum those suckers transmit per shot - to, at worst, +/- half an order of magnitude.

Unfortunately, I am not a great fan of Voyager, and so do not have those clips immediately on hand.

[Mr. Oragahn]

That second example is not a very good example, Oragahn. In particular it is different than the one being described earlier in this thread, mostly due to the fact that Voyager has been the recipient of Borg technology.

Do we have proof that the modifications, whatever that is supposed to represent, enhanced hull toughness?
This would be a good explanation, but I need concrete data for that.
Otherwise, you're just seeing the bare hull withstand a direct shot, from a bioship which is, for all intents and purposes, trying to destroy it.
The slaughter of the 15 Cubes armada would largely suggest that they don't seem to care that much about whatever kind of technology assimilation or personnal captures. So that's less reasons to expect a dialed down attack.

The first example is from before the Borg alliance, and clearly shows the ship being smacked around so hard that she flips end-over-end. We also see a full shield bubble in the first example, where in the second the shields have been knocked down by numerous hits.

Probably worn out after a couple of hits. You've just observed that the shields were down. Eventually, you come with a reasonable explanation for that.
Thus, in the lack of an explanation for the hull's feat, you're facing a case where the shieldless Voyager gets hit by a beam, logically dialed at a yield sufficient to destroy the ship, but the ship survives.

The Voyager is also just barely getting underway in the first example, and moving fairly slowly, suggesting the mass-lightening effect is not fully in play here. It takes about 10-15 seconds to overcome the imparted KE, and escape at warp.
-Mike

Which is funny to notice that while the Voyager could potentially be able to charge her shields up (no matter the magnitude), its engines need a 10-15 seconds timeframe to compensate, without ML tech activated.
Of course, one would wonder why capacitors, apparently used to support shields (they're charged, right?), can't also be used to keep extra power in reserve for evasive manoeuvers and warp jump on the volley. There's obviously the problem due to inertia and how much impulse drives can pump out for linear acceleration straight ahead, which is largely favoured over manoeuverability, with the Voyager being a "sprinter", while the Defiant seems to be more of a "dancer".

Unknown.

So this clearly defines the nature of the calculations here, as they're just a "what if". Nothing more.

What's the real mass lightening factor?

IMO, that's irrelevant. In general, it's either present at somewhere around 0.99+, or not at all. If there's any significant mass lightening effects, we have absolutely nothing to work with...

Mike seems to say that it's not all that black and white. Even the OP assumes a 10% reduction.

...so we may as well assume there isn't, because otherwise we have no data to work with.

And that would be bad how? If there's nothing to work from, that's about it, just that. There's no point running on wild on asumptions and eventually flawed premises, just to create a foam of numbers, if it can't demonstrate anything reliable.

Is the hull able to withstand tens of gigatons (~70 GT) of firepower (see this clip, at 2:21, to view the unshielded Voyager getting hit by a bioship's beam)?

Potentially, depending on various other sources for firepower. Although it is possible those are different bioship beam settings, AFAIK.

I'd beg to see other pieces of evidence to corroborate this. I can't picture a hull being hit by whatever type of particle and withstanding tens of gigatons of firepower (and that's a number which could, in fact, be dramatically lower or higher), if the same ship can loose a nacelle because of some rough ride after "crashing" on an ice planet. And "crashing" is a big word. Yes, the ship landed hard on the ground, but it's snow and ice, with rocks located at an unknown depth, and likely deep considering the environment, and above all the angle of impact wasn't that sharp.
Now, I know that Trek ships use fiels to enhance their structural integrity.
So are there other elements to compare this to?

I'm not quite sure you're right, here. I'd want a better clip that I can frame-by-frame at full rate to be sure where that beam is impacting. It could very easily - from what I can tell from that clip - be impacting the right way to cause Voyager to spin that direction (i.e., clipping Voyager from "below" at an oblique angle.)

Actually, the beam swipes over the shield. It starts behind the nacelle, as a faint glare, but the main impact flare is clearly above the portside nacelle, and seems to be locked on this point until the beam stops. It's hard to pause videos on youtube, but with a bit of luck and enough double clicks, you can get the right frame that shows it.

If the beam deals KE, the overall direction of the beam is important. It's like what happens when you poke a ball floating in a zero g field.

More important is the fact that we have little reason to assume the bioship's beam is very close to lightspeed. As you and Mike and correctly brought up, the scenario is analagous to the Millenium Falcon hit; you can pull some nice figures out of a hat if and only if you make a batch of assumptions that can't be backed up very well.

So we agree. But that's what I don't get either. Why this thread? It sounds more like a source of mockery, disguised under scientific virtues such observation, physical principles and calculations.

"Full impulse" is pretty fast, so we can be sure that they weren't going full impulse. Note, however, that mass lightening effects are tied to warp fields in any case. If warp systems are offline, there are no mass lightening effects in play.

Ah. Someone else on page one suggested that ML systems were tied to impulse, instead.

What I'm seeing here is that they needed to dump the angular momentum before going to warp. Remember, active warp fields lighten to a miniscule fraction of effective mass. Ramp up a warp field while you're spinning, and you'll spin faster and faster. Turn off a warp field while you're spinning under one, and you'll stop spinning instantly.

I agree. However, it doesn't explain why they waited so long to engage warp, contrary to Janeway's orders. The navigation guy was lucky it was not Cain who was in command of the Voyager.

More interesting, IMO, is the music video you posted - the point from that (2:24) shows an almost direct hit on Voyager's tail, only slightly angled, but it still causes Voyager to swerve a little in response. If I had those two clips at full speed and resolution in an editable file format, I should be able to give you a very good estimation of the momentum those suckers transmit per shot - to, at worst, +/- half an order of magnitude.

I've seen many videos on youtube where we see Trek ships being hit by beams, and when those beams trigger explosions, no matter their yield, they rock the ships to various extents, which is logical.
A beam reacting with a hull is likely to cause some kind of material reaction, unless the hull can perfectly withstand everything the beam is made of and contains as energy, of any form.
Besides, if the beam itself, which is like a lightning bolt, relies a lot on EM fields, it could actually shake ships just out of sheer virtue that it's a story about an EM field hitting a metallic hull, and messing around with navigational systems.
But we do see that there was an explosion, precisely at 2:24.
The video, to check out.
Just like nearby flak burst rocks SW ships.

Unfortunately, I am not a great fan of Voyager, and so do not have those clips immediately on hand.

A thing I noticed, is how die hard fans of Trek dislike Voyager, while as a guy who's quite detached from Trek, I have watched several episodes and the show was good, character wise and action wise. Plus the VFX are neat.

[Mike DiCenso]

That second example is not a very good example, Oragahn. In particular it is different than the one being described earlier in this thread, mostly due to the fact that Voyager has been the recipient of Borg technology.

Do we have proof that the modifications, whatever that is supposed to represent, enhanced hull toughness?
This would be a good explanation, but I need concrete data for that.
Otherwise, you're just seeing the bare hull withstand a direct shot, from a bioship which is, for all intents and purposes, trying to destroy it.
The slaughter of the 15 Cubes armada would largely suggest that they don't seem to care that much about whatever kind of technology assimilation or personnal captures. So that's less reasons to expect a dialed down attack.

If you watch the two parter in full, you will see that the Borg resistance to the S8472 beam becomes greater over time, though is still not 100%. But it's entirely possible that the Borg structures on Voyager also give the ship greater toughness (especially since they have the Voyager crew to make adjustments based on experiance), as well as fire the modified nanoprobe torpedo weapons.

As seen here:

http://voy.trekcore.com/gallery/display ... 57&pos=154

http://voy.trekcore.com/gallery/display ... 57&pos=156

The damage is very significantly less than when the two factions first met:


http://voy.trekcore.com/gallery/display ... m=56&pos=3

http://voy.trekcore.com/gallery/display ... m=56&pos=4

The first example is from before the Borg alliance, and clearly shows the ship being smacked around so hard that she flips end-over-end. We also see a full shield bubble in the first example, where in the second the shields have been knocked down by numerous hits.

Probably worn out after a couple of hits. You've just observed that the shields were down. Eventually, you come with a reasonable explanation for that.
Thus, in the lack of an explanation for the hull's feat, you're facing a case where the shieldless Voyager gets hit by a beam, logically dialed at a yield sufficient to destroy the ship, but the ship survives

.

The ship probably survived (and didn't tumble) because it was Borgified up to hell. It was not, however, invunerable, and if it had not been for the nanoprobes doing their thing, the ship and crew would not have survived very long.

The Voyager is also just barely getting underway in the first example, and moving fairly slowly, suggesting the mass-lightening effect is not fully in play here. It takes about 10-15 seconds to overcome the imparted KE, and escape at warp.
-Mike

Which is funny to notice that while the Voyager could potentially be able to charge her shields up (no matter the magnitude), its engines need a 10-15 seconds timeframe to compensate, without ML tech activated.
Of course, one would wonder why capacitors, apparently used to support shields (they're charged, right?), can't also be used to keep extra power in reserve for evasive manoeuvers and warp jump on the volley. There's obviously the problem due to inertia and how much impulse drives can pump out for linear acceleration straight ahead, which is largely favoured over manoeuverability, with the Voyager being a "sprinter", while the Defiant seems to be more of a "dancer".

I don't quite buy that, we've seen Voyager "dance" when she needs to. The dodging of the 15 Borg cubes, for instance.
-Mike

[Mr. Oragahn]

If you watch the two parter in full, you will see that the Borg resistance to the S8472 beam becomes greater over time, though is still not 100%. But it's entirely possible that the Borg structures on Voyager also give the ship greater toughness (especially since they have the Voyager crew to make adjustments based on experiance), as well as fire the modified nanoprobe torpedo weapons.

Though I don't need to insist on the point I was trying to get through, the shots showing teh maximum damage actually are from Scorpion part I, the episode which feature a rather low to execute officer behind the nav console.
Now, those shots finely outline how far the upgrades went.

Which is funny to notice that while the Voyager could potentially be able to charge her shields up (no matter the magnitude), its engines need a 10-15 seconds timeframe to compensate, without ML tech activated.
Of course, one would wonder why capacitors, apparently used to support shields (they're charged, right?), can't also be used to keep extra power in reserve for evasive manoeuvers and warp jump on the volley. There's obviously the problem due to inertia and how much impulse drives can pump out for linear acceleration straight ahead, which is largely favoured over manoeuverability, with the Voyager being a "sprinter", while the Defiant seems to be more of a "dancer".

I don't quite buy that, we've seen Voyager "dance" when she needs to. The dodging of the 15 Borg cubes, for instance.
-Mike

To some extent, yes. Voyager's just been making curves to avoid the Cubes, nothing really fancy like battle rolls and else.
What puzzles me is just how something like 13 seconds were actually needed to stop the ship spinning. Above all, shouldn't be there some sort of auto-adjust function, especially when a ship's about to enter Warp?

[Praeothmin]

Mr. Oragahn wrote:

Why this thread? It sounds more like a source of mockery, disguised under scientific virtues such observation, physical principles and calculations.

Actually, no it isn't.
At least, not from my part.
When I started the thread, I really thought that we could get an estimate of the firepower from that biobeam.
I was positive it was a high end figure, and it was nagging at me that everytime we talked about the high end Trek firepower, that example wasn't mentioned.
I still think we can.
I feel that from the angle of the hit, Voyager could have been swung the way it was.
I never heard of the mass-lightening being used during impulse in any episode or movies, so I don't really think it is used for Impulse travel.
So I really think that, by knowing the angular speed of Voyager from that instant, and with its canon mass being 700 000 metric tons, that the number derived from that incident would be a good calculated estimate.

A thing I noticed, is how die hard fans of Trek dislike Voyager, while as a guy who's quite detached from Trek, I have watched several episodes and the show was good, character wise and action wise. Plus the VFX are neat.

I must not be a die hard fan then, because I did like a lot of the episodes, and I watched all I could of Voyager.
I just got tired of all the Alien-of-the-week-that-look-like-humans-but-aren't.

[Jedi Master Spock]

Mike seems to say that it's not all that black and white. Even the OP assumes a 10% reduction.

IMO, you're pretty much never going to see a 10% reduction, nor are you going to see any significant mass reduction without either warp engines active, or impulse running for a long time. Warp fields involve enormous amounts of energy, even for a 10% reduction. Besides, as I pointed out (and you agreed):

What I'm seeing here is that they needed to dump the angular momentum before going to warp. Remember, active warp fields lighten to a miniscule fraction of effective mass. Ramp up a warp field while you're spinning, and you'll spin faster and faster. Turn off a warp field while you're spinning under one, and you'll stop spinning instantly.

I agree. However, it doesn't explain why they waited so long to engage warp, contrary to Janeway's orders. The navigation guy was lucky it was not Cain who was in command of the Voyager.

As far as "so long," it was "enough time to stop the ship from spinning and then apply warp field." Ramping up a full strength warp field from nothing takes a lot of energy (see here for discussion of that) and usually at least the better part of a second. I wouldn't say that it took a long time.

I'd beg to see other pieces of evidence to corroborate this. I can't picture a hull being hit by whatever type of particle and withstanding tens of gigatons of firepower (and that's a number which could, in fact, be dramatically lower or higher), if the same ship can loose a nacelle because of some rough ride after "crashing" on an ice planet. And "crashing" is a big word. Yes, the ship landed hard on the ground, but it's snow and ice, with rocks located at an unknown depth, and likely deep considering the environment, and above all the angle of impact wasn't that sharp.
Now, I know that Trek ships use fiels to enhance their structural integrity.
So are there other elements to compare this to?

Exactly. You never really have "naked" hull. However, we do happen to have some estimates for how much energy tritanium can take, and it's pretty high. I see I need to flesh out some of the relevant pages, but in general, tritanium's near indestructability is one of the many items suggesting low gigaton firepower for the TNG era.

It's hard to pause videos on youtube, but with a bit of luck and enough double clicks, you can get the right frame that shows it.

I refuse to spend that much time. As I said... give me an editable file with full framerate and resolution, and I'll do much more.

But we do see that there was an explosion, precisely at 2:24.
The video, to check out.
Just like nearby flak burst rocks SW ships.

I see the swerve start just before the explosion, although again, I'm not sure with a YouTube clip (see above) - the explosion, incidentally, tells us the hull was penetrated.

[Mr. Oragahn]

As far as "so long," it was "enough time to stop the ship from spinning and then apply warp field." Ramping up a full strength warp field from nothing takes a lot of energy (see here for discussion of that) and usually at least the better part of a second. I wouldn't say that it took a long time.

I'm talking about the time between the moment Janeway passes her order, and the moment the ship gets hit.
Trek used me, for all I've seen, to engage warp rather faster than that.

I refuse to spend that much time. As I said... give me an editable file with full framerate and resolution, and I'll do much more.

I can't do better than that. I'm afraid you'll have to find videos on your own then.
Needless to say, I stay firm on my claim that the ship is spinning in the wrong way, and thus it can't be due to a shock, so there's no point calculating kinetic transfers.

I see the swerve start just before the explosion, although again, I'm not sure with a YouTube clip (see above) - the explosion, incidentally, tells us the hull was penetrated.

Well, at least, a layer of the armour was destroyed. We don't know how deep. Plus, it could be particles from the beam splashing against the hull.

[Jedi Master Spock]

I'm talking about the time between the moment Janeway passes her order, and the moment the ship gets hit.
Trek used me, for all I've seen, to engage warp rather faster than that.

Often. However - particularly in TOS - warp engines sometimes need a bit of warm-up time if they're not being kept ready. "The Naked Time," for example, gives us a 30 minute standard "warm up" time from cold nacelles to active warp drive.

We don't see that in the TNG era much, but a little variability is not unexpected.

Well, at least, a layer of the armour was destroyed. We don't know how deep. Plus, it could be particles from the beam splashing against the hull.

It's a little late to be splash, but it's true that we don't know the extent of the damage.

[Who is like God arbour]

As for the engines not being pushed at full, it's rather odd and unbelievable, as they were facing an unknown ship, largely assumed as being a threat, possibly part of a fleet, that destroyed 15 Borg Cubes.
Tell me Janeway didn't plan to get her ass off this zone ASAP! :)

I'm talking about the time between the moment Janeway passes her order, and the moment the ship gets hit.
Trek used me, for all I've seen, to engage warp rather faster than that.

I don't see the problem.
Voyager was, as you can see in the clip from YouTube - and as far as I can remember from seeing the episode - within an expanse of debris of the destroyed borg cubes.
Before going to warp, they had to maneuver the ship out of this field.

As you can see in the picture, which shows the moment, Voyager is hit, there is still debris in the background.

__________

That's why Voyager couldn't go to warp immediately after Janeway has given her order.

The dialog in the episode suggests that the bioship was still in the stages of powering up when it fired. On top of that, Tuvok at an earlier point notes that the same ship suffered damage from a Borg disruptor fire. So this is what a powering up, damaged S8472 vessel can do.

And that could be the reason, why the bioship's beam was not at full strength. A moment later, Yoyager would have left the debris field and would have gone to warp. The pilot of the bioship had to fire in this moment at the latest, if he would have wanted to hit Voyager, regardless that his weapons were still in the stages of powering up.