'Under the Dome' on CBS HD - Page 16 - AVS Forum
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post #451 of 2120 Old 07-10-2013, 10:02 AM
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Raise your right hand Otto and repeat after me.. You have the job..

That being the case then, I think I need to arrest the newspaper editor and perform a complete strip search biggrin.gif
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post #452 of 2120 Old 07-10-2013, 10:04 AM
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Originally Posted by HDTVChallenged View Post

Correct. Although, I'm not sure how you would actually go about finding a tangent to the circle with any degree of accuracy at a single point. wink.gif This is why you need three points A, B and C, from which you construct two perpendicular bisectors, one bisecting the line AB and another bisecting line BC ... or you could even do AB and AC, etc, etc. (If the line is perpendicular to the line AB, it will also be perpendicular to the circle where they intersect - from this point you *could* go ahead and construct the tangent line(s,) but that's just extra busy work.) The intersection of the two bisectors is the center of the circle. And BOOM ... all three unknowns solved for at once. The rest is just clean up.

Of course, this assumes that any difference in physical elevation between the three plotted points is minimal compared to the radius of the dome. (See original analysis of the plane crash.)

To determine a circle (as a minimum) you need know either:

1a) The center point and the radius.

1b) The center point and one point on the circle.

-or-

2) Three points that lie *on* the circle.

All other cases are non-determinate. (Unless you have more than three points on the circle, etc ...)

PS: In this case, we don't know the radius or the center point, so as Elrond would say, "You have only one choice" from which to proceed.

To continue the nerd fest, I certainly agree with the perpendicular bisector method. However, another alternative is to treat the three points as the vertices of a triangle. Measure the lengths of the three sides, then solve directly for the radius of the circumscribed circle. The solution is in many math references eg CRC Standard mathematical Tables:
1) From three sides, a, b, c, calculate s = 0.5*(a + b +c)
2) Area K = sqrt(s*(s-a)*(s-b)*(s-c)) Heron's formula
3) R = 0.25*a*b*c/K

Alternatively, use law of cosines to solve for the angle opposite any side, then R = 0.5*c/sin C (this is related to the law of sines). This method works (by measuring the chords) even if there is no map on which to do the graphical construction, but involves more math.

What the kid did seems totally useless. I had not seen a previous screen grab of it. The screen grab of the map is taken from an oblique angle, it is therefore an ellipse in the screen grab and the perpendicular bisector method works poorly. However, there is no scale, and the oblique angle would cause variable scale, so I think we are not in a position to calculate it correctly.
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post #453 of 2120 Old 07-10-2013, 10:18 AM
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To continue the nerd fest, I certainly agree with the perpendicular bisector method. However, another alternative is to treat the three points as the vertices of a triangle. Measure the lengths of the three sides, then solve directly for the radius of the circumscribed circle. The solution is in many math references eg CRC Standard mathematical Tables:
1) From three sides, a, b, c, calculate s = 0.5*(a + b +c)
2) Area K = sqrt(s*(s-a)*(s-b)*(s-c)) Heron's formula
3) R = 0.25*a*b*c/K

Alternatively, use law of cosines to solve for the angle opposite any side, then R = 0.5*c/sin C (this is related to the law of sines). This method works (by measuring the chords) even if there is no map on which to do the graphical construction, but involves more math.

I'll take your word for it ... I suspected there might be a more "robust" method, that I didn't remember ... Lot's of brain atrophy on my part ... no doubt related to all the adult beverages. biggrin.gif

Point being, you'd expect that a "whiz kid," with the ambition to tackle the problem, would actually be able to follow through correctly, since theoretically the knowledge should be "fresh" from his perspective.
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post #454 of 2120 Old 07-10-2013, 10:34 AM
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Originally Posted by HDTVChallenged View Post

RE: The Radio Station

There are some indicators that the dome may absorb EMF rather than reflect it. *If* that's the case, then radio should operate "normally" inside the dome, if not just add it to the list ... smile.gif

OTOH, exploding pacemakers and overheated flashlights might indicate the opposite ...

Eh .... whatever the script needs, I guess ...

The town's radio station is inside the dome, why wouldn't it work? People inside the dome can pick it up.

The radio station tower can pickup, once in awhile, the broadcast of the military just outside the dome. They talked about this in the premiere episode how the lady was able to modify her equipment and get it to faintly pick it up at times but takes a lot of fine tuning.

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post #455 of 2120 Old 07-10-2013, 10:42 AM
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Originally Posted by WilliamR View Post

The town's radio station is inside the dome, why wouldn't it work? People inside the dome can pick it up.
Because the multipath from all those reflections off the dome should make the signal very diificult to lock onto for many of the people. Instead of one solid signal from pretty much one direction, now the signal is bouncing around and you'd pick it up from multiple directions - some of which could put the signal completelty out of phase.

Now, the earlier theory that the dome absorbs the signal could be sound in that it would prevent all those reflections. The only issue then remains as to why something that can blow up pacemakers and flashlights doesn't interfere with the radio signal, which would likely be sent out closer to the dome for best reach of the broadcast area.
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post #456 of 2120 Old 07-10-2013, 11:07 AM
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Originally Posted by HDTVChallenged View Post

I'll take your word for it ... I suspected there might be a more "robust" method, that I didn't remember ... Lot's of brain atrophy on my part ... no doubt related to all the adult beverages. biggrin.gif

Point being, you'd expect that a "whiz kid," with the ambition to tackle the problem, would actually be able to follow through correctly, since theoretically the knowledge should be "fresh" from his perspective.

I only remembered there WAS another method. I had to look it up. I would have been hard pressed to recreate from basic principles. I remember and frequently use the law of sines. I had forgotten the ratio is the diameter of the circumscribed circle. So at least a couple of us are ready for a math-off with whiz-kid. Teach him to respect his elders. smile.gif
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post #457 of 2120 Old 07-10-2013, 11:08 AM
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Because the multipath from all those reflections off the dome should make the signal very diificult to lock onto for many of the people. Instead of one solid signal from pretty much one direction, now the signal is bouncing around and you'd pick it up from multiple directions - some of which could put the signal completelty out of phase.

Now, the earlier theory that the dome absorbs the signal could be sound in that it would prevent all those reflections. The only issue then remains as to why something that can blow up pacemakers and flashlights doesn't interfere with the radio signal, which would likely be sent out closer to the dome for best reach of the broadcast area.

So since the town can hear the signal the dome must be absorbing the signal. The dome only interferes in close proximity so I can buy that it absorbs the signal and those that get close can be interrupted. We are talking about an invisible dome that dropped in from somewhere, controlled by something. Is it so hard to now believe the dome can absorb the radio and interfere with a pace maker. Its not like we can explain what is happening with our level of technology/understanding, it is a massive invisible force field like dome, we have no clue how to do this/sustain it with our level of technology, so we have to suspend our beliefs and go along for the sci-fi ride and drama this show is suppose to be.

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post #458 of 2120 Old 07-10-2013, 11:22 AM
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Originally Posted by WilliamR View Post

Its not like we can explain what is happening with our level of technology/understanding, it is a massive invisible force field like dome, we have no clue how to do this/sustain it with our level of technology, so we have to suspend our beliefs and go along for the sci-fi ride and drama this show is suppose to be.

 

I agree. However they are giving us virtually no reason to take the ride and plenty of reasons not to... smile.gif I can never find the quote but Roget Ebert wrote such... as long as they don't break their own universe's rules you have to go along... you can't judge it based on ours.

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post #459 of 2120 Old 07-10-2013, 11:35 AM
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Originally Posted by WilliamR View Post

So since the town can hear the signal the dome must be absorbing the signal. The dome only interferes in close proximity so I can buy that it absorbs the signal and those that get close can be interrupted. We are talking about an invisible dome that dropped in from somewhere, controlled by something. Is it so hard to now believe the dome can absorb the radio and interfere with a pace maker. Its not like we can explain what is happening with our level of technology/understanding, it is a massive invisible force field like dome, we have no clue how to do this/sustain it with our level of technology, so we have to suspend our beliefs and go along for the sci-fi ride and drama this show is suppose to be.
Sure, it could be absorbing the waves, preventing them from reflecting.

Then, the problem becomes, how are the signals from outside leaking in?

Think about it: the radio station is likely several thousand watts coming off a tower inside the dome and it isn't be screwed up by reflecting off the dome. That calls for a lot of absorbing, considering something like brick can block radio waves, but wiull also reflect them. Now we have little hand-held radios leaking in and not being absorbed, despite maybe putting out 3 watts - tops (compare to a cell phone which uses less than a watt).

On the other hand, other radio and TV stations putting out 10, 20 or even 50 thousand watts seem to be blocked, this despite the dome being semi-permeable (it let water leak in).

Further, if water can leak in, air can get in (and out). That means sound should be able to enter and escape - at the very least, with enough amplication, it should allow you to be heard on the other side.

However, the one thing that bugs me is that most of the people don't know the dome is semi-pemeable. Why does that matter? Well, if I were one of the residents, I'd be insisting everyone stop driving cars and doing other things that might eat up all the oxygen without knowing if any more can be had than what's in the dome.

I get that it's a big giant mysterious dome. However, there are ways of portraying that and still taking into account the science behind it.
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post #460 of 2120 Old 07-10-2013, 01:17 PM
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Originally Posted by NetworkTV View Post

Sure, it could be absorbing the waves, preventing them from reflecting.

Then, the problem becomes, how are the signals from outside leaking in?

Think about it: the radio station is likely several thousand watts coming off a tower inside the dome and it isn't be screwed up by reflecting off the dome. That calls for a lot of absorbing, considering something like brick can block radio waves, but wiull also reflect them. Now we have little hand-held radios leaking in and not being absorbed, despite maybe putting out 3 watts - tops (compare to a cell phone which uses less than a watt).

On the other hand, other radio and TV stations putting out 10, 20 or even 50 thousand watts seem to be blocked, this despite the dome being semi-permeable (it let water leak in).

Further, if water can leak in, air can get in (and out). That means sound should be able to enter and escape - at the very least, with enough amplication, it should allow you to be heard on the other side.

However, the one thing that bugs me is that most of the people don't know the dome is semi-pemeable. Why does that matter? Well, if I were one of the residents, I'd be insisting everyone stop driving cars and doing other things that might eat up all the oxygen without knowing if any more can be had than what's in the dome.

I get that it's a big giant mysterious dome. However, there are ways of portraying that and still taking into account the science behind it.

What about it absorbs almost all of the signal, some passes through, the rest absorbs, it could absorb more in the beginning then once it builds up it has to leak some through. This applies to both ways. This would explain the intermittent radio signals being picked up. Also, perhaps, it is different from the outside in then the inside out. Anything could really explain it since we don't know how to make this and it appears to be alien/advanced beyond our current means.

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post #461 of 2120 Old 07-10-2013, 01:19 PM
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I gave up believing when they had the house catch on fire. The smoke from the house was producing deadly toxins. More than enough to have killed them all if the were in a sealed dome. The fire would have consumed a lot of their usable oxygen also. If any of you have ever seen or had a house fire near the first thing you smell or remember is the faint odor of something burning.
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post #462 of 2120 Old 07-10-2013, 01:58 PM
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To summarize the math lessons... We seem to have two possible conclusions:

1. The Whizkid is really an idiot... but such an idiot wouldn't bother pretending to fake that kind of math... so he isn't acting according to character.

2. Whizkid is smart, but the people making the show are not.

Meanwhile... to this point we also have only seen things from inside the dome perspective... Do we "know" yet that everything works the same way outside? By which I mean... people inside cannot hear or receive transmissions from outside... but do we "know" for sure that people outside cannot hear them?

For all we know, given what has unfolded thus far... the dudes outside the dome might be hearing them perfectly well...

Yeah baby!  It's Halloween!
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post #463 of 2120 Old 07-10-2013, 02:13 PM
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Originally Posted by Sharp1080 View Post

I gave up believing when they had the house catch on fire. The smoke from the house was producing deadly toxins. More than enough to have killed them all if the were in a sealed dome. The fire would have consumed a lot of their usable oxygen also. If any of you have ever seen or had a house fire near the first thing you smell or remember is the faint odor of something burning.
My reaction to the house fire was:

a) the stuff in that house was really, really extra flammable. I mean, those curtains went up faster than anything I've ever seen.

b) The undertaker got trapped in there as fast as he did, with the house going up as quick as it was, yet the cop kicks in the door (without a singkle flame behind it) and is able to go in and get him without any protection.
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post #464 of 2120 Old 07-10-2013, 03:03 PM
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Originally Posted by HDTVChallenged View Post

PS: Be careful, it so happens that the equation for a circle looks suspiciously like the equation described by the Pythagorean Theorem ... so much so that there's an entire branch of mathematics devoted to that happy "coincidence." wink.gif
If you like that, then I suggest doing some research into the Tau constant, aka 2*Pi!!! Probably one of my favorite alternative math-related discussions. When you replace "2*Pi" in many mathematical formulas with "tau", they begin to exhibit "happy coincidences" much like the above.

For example, the formula for area of a circle would become 1/2*tau*r^2, which is similar to momentum (1/2*mv^2) and gravity in a medium (1/2*gt^2).
Euler's Identity simplifies to e^(i*tau) = 1.
sin(x + tau) = sin(x)
cos(x + tau) = cos(x)
The radians for a complete circle would be easier to translate to degrees, i.e. 90 degrees (a quarter turn of a circle) would be 1/4*tau, 180 degrees (half turn) would be 1/2*tau, and a complete turn would be tau.

My other favorite alternative math-related discussion is metric time, where the day is subdivided into 10 hours of 100 minutes and 100 seconds. The value of a second would be recalibrated to 86.4% of it's current value (making it shorter, and there would be more seconds in a day) but it would be easier to keep track of time related activities.

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post #465 of 2120 Old 07-10-2013, 05:42 PM
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Originally Posted by NetworkTV View Post

My reaction to the house fire was:

a) the stuff in that house was really, really extra flammable. I mean, those curtains went up faster than anything I've ever seen.

b) The undertaker got trapped in there as fast as he did, with the house going up as quick as it was, yet the cop kicks in the door (without a singkle flame behind it) and is able to go in and get him without any protection.


I was rolling my eyes when the door was "kicked in". The story was all over the place including the usual "smokeless fire". Can't see the actors faces with smoke in the scenes. Of course none of that would happen that way in the real world.
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post #466 of 2120 Old 07-10-2013, 05:55 PM
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I was rolling my eyes when the door was "kicked in". The story was all over the place including the usual "smokeless fire". Can't see the actors faces with smoke in the scenes. Of course none of that would happen that way in the real world.
So Hank.. er Big Jim rolling in with the backhoe knocking down the fully involved house fire in his Sunday jacket and polyester slacks was BS too biggrin.gif

"I say we take off and nuke the entire site from orbit. It's the only way to be sure...."

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post #467 of 2120 Old 07-10-2013, 06:00 PM
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I try to turn off my brain when watching TV but this show is circling the shark.

The surviving cop, alone at the station, enters the cell of an obviously crazy prisoner. Then she goes alone into the woods with a pistol to chase the same who has an assault rifle. This is beyond stupid, it is attempted suicide.

Our Barbie has a car which has a trunk so he leaves his pack on top of the bed where a female reporter will check it out. Of course the thing closest to the top of the pack is a map with the spot marked "X". Is he even dumber than the cop?

Sweetie in chains encourages the nutcase to go into a dangerous, possibly fatal mine. Is she that desperate for a long-term zero-calorie diet?

Our inquiring reporter follows the nutcase into a mine without a flashlight. Did you ever try to do anything or go more than a few feet with wooden matches? Try it, you won't like it. Ditto for following someone in the dark when they are far in front of you.

I must stop thinking. I must stop thinking. This is a Stephen King-based show. Strike One! And Spielburg influenced. Strike Two! One more episode and then ???

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post #468 of 2120 Old 07-10-2013, 06:16 PM
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Originally Posted by humbug2 View Post

Sweetie in chains encourages the nutcase to go into a dangerous, possibly fatal mine. Is she that desperate for a long-term zero-calorie diet?

Our inquiring reporter follows the nutcase into a mine without a flashlight. Did you ever try to do anything or go more than a few feet with wooden matches? Try it, you won't like it. Ditto for following someone in the dark when they are far in front of you.
For what it's worth, if crazy boyfriend disappears, perhaps his dad would try to find him and perhaps check the bunker to see if maybe he was there, since he saw him poking about earlier.

Granted, the kid told his dad it was flooded, but I would hope he would check it anyway, especially after he said Barbie attacked him. I'd want to make sure he wasn't dead and stashed down there.

As far as the reporter, don't forget two things:

1) She didn't know where he was going. She saw him head out and followed with no time to collect any gear.

2) She was following him in the dark and he had a flashlight. She couldn't use one without him spotting her. She was likely relying on following his path. Once his flashlight was destroyed, then she had to resort to the matches (though who actually carries matches verses a lighter?).

The rest of what you said was spot on.
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post #469 of 2120 Old 07-10-2013, 07:41 PM
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At the Dome edge:
Pacemaker: Pow!
Flashlight: Pow!
Cop gal's HT when she's trying to talk to her husband through the dome: nothing unusual. Motorola must be good stuff!
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post #470 of 2120 Old 07-10-2013, 09:06 PM
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Cop gal's HT when she's trying to talk to her husband through the dome: nothing unusual. Motorola must be good stuff!
Mine is indestructible, and I've dropped it from very high places.

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post #471 of 2120 Old 07-11-2013, 04:43 AM
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I gave up believing when they had the house catch on fire. The smoke from the house was producing deadly toxins. More than enough to have killed them all if the were in a sealed dome. The fire would have consumed a lot of their usable oxygen also. If any of you have ever seen or had a house fire near the first thing you smell or remember is the faint odor of something burning.

The fire would not of used up all the oxygen and put enough toxins in the air to kill them inside a dome 10 miles wide and who knows how tall. Plus, they clearly showed that some stuff is getting through the dome like water, in a smaller form, so some air is getting in to replenish the air supply, and some would probably be leaving then too.

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post #472 of 2120 Old 07-11-2013, 05:55 AM
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The fire would not of used up all the oxygen and put enough toxins in the air to kill them inside a dome 10 miles wide and who knows how tall. Plus, they clearly showed that some stuff is getting through the dome like water, in a smaller form, so some air is getting in to replenish the air supply, and some would probably be leaving then too.

Probably closer to 20 miles wide. I figured around 15-20 or so as I read the book just from how distances were described. (There is a tendency to underestimate the size of the dome on this thread.) If it's 20 miles wide, then the height would be 10 miles - it is a dome from the surface upward, after all. Underneath the ground, the assumption is that the sides go straight down to some indeterminate depth based on the thin cut at the surface (a curved surface below the ground would necessarily evidence itself on the surface). That part, at least, is consistent with the book. You're correct in assuming that one small house fire would not degrade the air inside the dome to any appreciable degree. One of these SmartGuys like "HDTVChallenged" could probably estimate the cubic volume of air in the dome based on these assumptions. wink.gif Would have to be many, many millions of cubic feet....

Correct also that there is some small amount of air & water that can diffuse through on both sides - that's been shown. They appear to have ret-conned nearly everything else about the dome for this series.
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post #473 of 2120 Old 07-11-2013, 06:41 AM
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By which I mean... people inside cannot hear or receive transmissions from outside... but do we "know" for sure that people outside cannot hear them?

Well, yes and no. In the underground scene, Junior was shown from the outside yelling and pounding on the dome, and no sound was heard, not even from the impact on the dome itself. It appeared the inside of the dome was flexing while the outside was unperturbed, consistent with complete absorption of a pressure wave.

Otoh, perhaps we shouldn't assume the dome's properties are uniform...

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they clearly showed that some stuff is getting through the dome like water, in a smaller form, so some air is getting in to replenish the air supply, and some would probably be leaving then too.

There had better be some water leaving, too, else we should soon have an episode called "The Flood"...

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post #474 of 2120 Old 07-11-2013, 07:23 AM
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I still want to see those scenes on the lake down south to see what's happening there, maybe one on that river up north.

The pink part on the map is supposed to be the county right? or the town is 10 miles radius sized?

RIP Mom, we always love you 8/18/13
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post #475 of 2120 Old 07-11-2013, 08:20 AM
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Originally Posted by archiguy View Post

Probably closer to 20 miles wide. I figured around 15-20 or so as I read the book just from how distances were described. (There is a tendency to underestimate the size of the dome on this thread.) If it's 20 miles wide, then the height would be 10 miles - it is a dome from the surface upward, after all.
It's not necessarily true that the dome is half as tall as it is wide. That entirely depends on if a) the dome itself is actually a sphere partially buried under the Earth, and b) where the dome/sphere bisects the Earth.

If the dome does bisect the Earth at the point where the tangent of the curve is orthogonal to the surrounding ground level, and the curvature of the dome is spherical, then yes, the height would be 10 miles (or whatever the radius of the sphere is). But it could just as easily be less.

~Tighr: Not helping the situation since 1983

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post #476 of 2120 Old 07-11-2013, 08:47 AM
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^^^That's my assumption from both the book and the series - a perfect semi-sphere from the ground upward. The beginning of the curve is precisely at ground level, with straight sides underneath. It would look something like this (thanks to "Uncle Willie" from post 253 in this thread):

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post #477 of 2120 Old 07-11-2013, 09:03 AM
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Thanks for the credit, arch .. cool.gif .. I have the same impression of the dome structure ..

When the plane hits the "wall" on episode One, had the dome not been structured as the PIC shows, the plane debris would have landed farther inside ..

Uncle Willie


Oddball: Why don't you knock it off with them negative waves? Why don't you dig how beautiful it is out here? Why don't you say something righteous and hopeful for a change?
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post #478 of 2120 Old 07-11-2013, 09:08 AM
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The one thing that bugged me and my wife during this last episode is that it has now been a day, yet people are going out to eat at the dinner, they are driving their cars, etc. They know they are not being rescued as it is a dome and they hear the broadcasts from the radio station. When does human nature kick in and people start hording things and start conserving/rationing??

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post #479 of 2120 Old 07-11-2013, 09:40 AM
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I have not read the book, but I was imagining it to look more like this:



If the spherical dome perfectly bisects the Earth at it's center, then the radius of the dome would be equal to the height.

If the spherical dome bisects the Earth at some point higher up on the arc, the radius of the dome would be greater than it's height.

~Tighr: Not helping the situation since 1983

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post #480 of 2120 Old 07-11-2013, 10:21 AM
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Quote:
Originally Posted by tighr View Post

I have not read the book, but I was imagining it to look more like this:



If the spherical dome perfectly bisects the Earth at it's center, then the radius of the dome would be equal to the height.

If the spherical dome bisects the Earth at some point higher up on the arc, the radius of the dome would be greater than it's height.

If a perfect sphere, like that, had crashed down, it would have crushed the entire town. Everything and everyone in it would be smushed into a concave half sphere in the ground. In fact, if it had any curvature whatsoever underneath the surface (assuming it was open ended on the bottom), then whatever that x-axis dimension was would be reflected in the width of the slash in the earth where the Dome now sits. But it's just a narrow opening, enlarged somewhat for a dramatic television perspective as we discussed ad nauseum back in the first pages of this thread. (I still maintain the Dome, being an energy field, has no appreciable thickness at all.)

Everything we've seen thusfar indicates a cylindrical surface underneath the ground with a spherical dome above it as the drawing provided in post 476 illustrates.
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