Legacy & Inheritance: phaser drills

[Mr. Oragahn]

Continued from here.

There's something important to note.
Where does this 12% increase come from?
I've seen it in a script, but not in the episode in question.

Notice, that if this increase was mentionned in a longer variant of the episode - and we see that the cut is a bit blunt at this point in the episode - it would mean that the average drilling rate of 10 km / 19 s (~520 m/s) is above the rate when they increase the yield by 12%, that is, 2 km / 5 s (400 m/s).
There's no way to work around this. In the script I had found, the 12% increase is immediately followed by the drilling through the last two kilometers, and there's no evidence that they would have reduced the power - especially a second after pumping it up.

This would show that once again, someone screwed up.

So really, I'd like to know what's correct about the 12% increase.

No, they have had to drill through the crust and a huge part of the mantle to a magma pocket that was shortly above the core, they wanted to "restart". An earthlike planet assuming, that would be round about 2'800 kilometers and accidentally that was what Geordi has shown in the briefing:

• 

Even if they wouldn't have increased the power it would be still circa 2'800 kilometers in 19 seconds - minus the last 2 kilometers in 5 from these 19 seconds.

I think you didn't understand my point.
The screw up does exist if the 12% increase is in anyway canon.

2800 kilometers in 19 seconds, which would be an averaged rate, would mean 147,368 m/s.
2798 km/14 s means 199,857 m/s (the whole lenght, minus the 2 last km and the 5 last seconds).

2 km in 5 seconds, that's only 400 m/s. This latest phase was, according to the script with the 12% reference, precisely happening immediately after the 12% increase.

The point is fairly simple. They boost the drilling power by 12%... and the drilling speed comes down by 3 orders of magnitude.

This is simply why I asked if there was any canonical reference about the 12% boost. There better not.
The only way to rationalize this would be that the weapon lost efficiency to such a degree that it would mean that either it was going through some hard material, or that the phasers' quality was suddenly degraded.

[Mike DiCenso]

Here's the relevent dialong from "Inheritence":



DATA
(continuing)
These scans indicate that the
magma pockets where we plan to set
up the infusion units are somewhat
unstable.

She acknowledges and sits near him.

JULIANA
I'm going to monitor the density
of the rock layers and adjust the
strength of the particle beam as
we go. That should minimize the
seismic stress we generate while
we're drilling.

Geordi approaches from another part of Engineering.

GEORDI
(to Data)
I've configured the phasers to
create the most highly focused
particle beam possible.

DATA
Thank you, Geordi.



DATA
(off console)
The beam has penetrated eight
kilometers beneath the surface...

JULIANA
Once it's through the crust, we'll
boost phaser intensity by twelve
percent.

WORF
Standing by.

STAR TREK: "Inheritance" - 09/27/93 - ACT TWO 17.

10 CONTINUED:

After a moment.

JULIANA
Now...

Worf works the console.

11 EXT. SPACE - THE ENTERPRISE (OPTICAL)

the beam changes in intensity.

12 RESUME ENGINEERING/BRIDGE INTERCUT

JULIANA
The mantle is less resistant than
I thought it would be --

DATA
We are within two kilometers of
the magma pocket.

JULIANA
Another five seconds should do it.
(beat; off console)
We've broken through --

WORF
(works)
Terminating beam.

Juliana studies the console for a moment, then allows
herself a small smile.

JULIANA
The pocket seems stable...

DATA
I detect no increase in stress
levels in the surrounding magma.

RIKER
Good work. I don't think we could
have gotten in any cleaner.



They are mostly concerned with the stablity of the rock they are drilling through, not necessarily with power or efficency.
-Mike

[Mr. Oragahn]

Yes, I know this script. My question is, does the part with the phaser boosting by 12% appear in a later DVD version of the episode? Because it is clearly not present in the version I have.

[Mike DiCenso]

I'd have to check, but what difference does it make if it does appear in any version of the filmed episode?
-Mike

[Mr. Oragahn]

It makes the difference I've been describing here and there, in that a boost of intensity by 12%... reduces the drilling rate by three orders of magnitude.

[Mike DiCenso]

I must have missed something in one of your essays, Oragahn, but how does boosting the intensity of the phaser beam result in such signficant reduction in drilling rate?
-Mike

[Mr. Oragahn]

I must have missed something in one of your essays, Oragahn, but how does boosting the intensity of the phaser beam result in such signficant reduction in drilling rate?
-Mike

You have to ask that to the guy who wrote the script! :D

Really, it's not that complicated.

Either we make an average drilling speed from the total planned lenght (2,800 km according to first posts), or from the one minus the last two kilometers after the boost.

Removing the last two kilometers, and thus the five seconds which were spent during these last two kilometers, this will provide a drilling speed of 199,857 meters per second.

Then, phaser intensity is boosted by 12%, and Juliana estimates that 5 seconds will be necessary, then, to cut through the last two kilometers.
The computer actually bips at each second. 5 bips.

That's 400 meters per second.

Do you agree or not?

[Mike DiCenso]

Okay, there are a number of possibilities; but given the uncertainty of the 12% quote anyway, it's moot until I or someone else can dig up their copies of the actual as-filmed episode to compare the script to.

For instance, the drilling was intended to be done in such a manner as not to disturb the potentially unstable layers of rock the phaser beam had to drill through. Thus we could have had multiple instances throughout the drilling where the beam drill rate was reduced and then increased, perhaps very incrementally, then the last 2 km required the more sigifi cant 12% increase.

At any rate, "Inheritence" only shows us a lower probable limit since the goal was simply to drill through the crust and mantle of a "dying" planet, not to blast chunks of it indiscriminately.

The drilling done in "Legacy" is another similar example, though the depth drilled down to is much more specific (1,600 meters).
-Mike

[AFT]

You guys are impossible, but I guess that don’t surprise me anymore, I mean you really enjoy nitpicking small details and that’s not bad in itself since it could possible be of significance like in this example but I suggest you stop relaying on non-definitive screenplays and watch the actual episodes. So, here, the actual episode goes like this:

DATA
(continuing)
These scans indicate that the
magma pockets where we plan to set
up the infusion units are somewhat
unstable.

She acknowledges and sits near him.

JULIANA
I'm going to monitor the density
of the rock layers and adjust the
strength of the particle beam as
we go. That should minimize the
seismic stress we generate while
we're drilling.

Geordi approaches from another part of Engineering.

GEORDI
(to Data)
I've configured the phasers to
create the most highly focused
particle beam possible.

DATA
Thank you, Geordi.

RIKER
Mr. Worf.

WORF
Phasers lock on target.

RIKER
Fire when ready.

The E-D fires on the planet below.

DATA
We are within two kilometers of
the magma pocket.

JULIANA
Another five seconds should do it.
(beat; off console)
We've broken through --

WORF
(works)
Terminating beam.

Juliana studies the console for a moment, then allows
herself a small smile.

JULIANA
The pocket seems stable...

DATA
I detect no increase in stress
levels in the surrounding magma.

RIKER
Good work. I don't think we could
have gotten in any cleaner.

See? You actually argued over nothing as there is no mention whatsoever of “phaser intensity boosted by 12%“ and 5 seconds of drilling after that. If anything they decreased the phaser intensity for those two last kilometers seeing how concerned they were with the seismic stress and whatnot. So, please, someone can tell me that all this was worthwhile and provide an actual estimation for firepower from this example?

P.D. I’ll keep the episode until this matter is settled so if anyone wants any other details feel free to ask.

[Mike DiCenso]

You beat me to it. I watched the episode, and it is as AFT tells it. There is no 12% anything mentioned anywhere in the episode, and so it is a moot point after all.
-Mike

[AFT]

You beat me to it. I watched the episode, and it is as AFT tells it. There is no 12% anything mentioned anywhere in the episode, and so it is a moot point after all.
-Mike

Well Mike, it’s all good and everything but is there a calculation coming? A figure of firepower perhaps? Something? I’m just asking…

[Mr. Oragahn]

You guys are impossible, but I guess that don’t surprise me anymore, I mean you really enjoy nitpicking small details and that’s not bad in itself since it could possible be of significance like in this example but I suggest you stop relaying on non-definitive screenplays and watch the actual episodes. So, here, the actual episode goes like this:

...


See? You actually argued over nothing as there is no mention whatsoever of “phaser intensity boosted by 12%“ and 5 seconds of drilling after that. If anything they decreased the phaser intensity for those two last kilometers seeing how concerned they were with the seismic stress and whatnot. So, please, someone can tell me that all this was worthwhile and provide an actual estimation for firepower from this example?

P.D. I’ll keep the episode until this matter is settled so if anyone wants any other details feel free to ask.

Gosh, it actually helps to *read*.
There is nothing impossible about it.

If you're going to use dialogue and visuals to get solid numbers, up to the point where you're going to argue about what the characters mean, and many pixels and joules this or that means, you'll have to accept that level of nitpicking, which it hardly is, btw.

Secondly, I have repeatedly asked if this 12% reference was mentionned on the DVD. I repeatedly said, here and in the TDIC thread, that the version of the episode I have does not have such a reference.

With the lack of the 12% boost, there's no issue.
We can safely claim that they slowed down the drilling, which explains the drop in speed.

[Mike DiCenso]

Both the offical VHS as well as DVD versions of "Inheritance" just happen to be the uncut "as aired" version of the episode, and they are essentially identical. In neither version is the whole script thing of the drilling through 8 km, then the 12% boost during the last 2 km. Like a lot of things in scripts versus the final as-filmed version, it was probably cut to save time and money for the episode.
-Mike

[Mike DiCenso]

You beat me to it. I watched the episode, and it is as AFT tells it. There is no 12% anything mentioned anywhere in the episode, and so it is a moot point after all.
-Mike

Well Mike, it’s all good and everything but is there a calculation coming? A figure of firepower perhaps? Something? I’m just asking…

Kind of hard to judge firepower off of this episode since the goal was to drill a tunnel with as narrow a beam as possible, as carefully as possible to avoid disrupting the unstable rock layers. One factor that needs to be addressed:

* How wide was the tunnel? Certainly not as wide as would be the case in a straight forward blasting-the-crust-to-smitherins scenario.

* The narrowest beam fired that we know of from the E-D appears to be ~6 meters.

* Assuming an even numbered depth of 3,000 km, that means the phaser was drilling some 150 km a second on average!

If we assume a clean, straight drilling by the phaser, then we can calculate by treating it as a cylinder where 3 meters is the radius, and the height is 3,000,000 meters. Thus 84,823,001.64 m^3 should be the volume of rock vaporized by the E-D phasers. Dividing that by 20 seconds we get approximately 4,241,150 m^3 a second. That's roughly the same as vaporizing a 93 meter wide sphere of solid rock every second! Again, we should remember that this is a delicate, highly controlled drilling. But even for this operation, the ship is putting out every second the equivalent of 3.1 megatons of energy each second, assuming solid granite rock layers.

So, bearing in mind the context of the drilling and that at no point is the ship's energy reserves are strained, we can assume this to be a lower limit example.
-Mike

[Kane Starkiller]

If you fire a 3.1Mt/s beam into the ground there is no way you'll end up with a cleanly drilled 6m wide tunnel that's for sure.
You'll get a huge fireball at the surface and end up with a huge crater that will continue to grow as you pump in more energy until it at last turns into a huge tunnel probably kilometers wide.

Furthermore how can a 6m wide hole keep itself from collapsing once you drill through many kilometers of rock? That episode has more issues than a news stand.