The RDA can't do physics - Tree of Souls - An Avatar Community Forum
 Tree of Souls - An Avatar Community Forum The RDA can't do physics
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#1
08-18-2011, 08:22 PM
 Karyu Clarke wants his own Avatar. Join Date: Jul 2011 Location: Scotland, 140 years too early Posts: 1,330
 The RDA can't do physics permalink

Because, among other things, rocketry does not work the way James Cameron thinks it does.

To demonstrate this, I managed to dig out an equation that relates a rocket's velocity change to its fuel-to-payload ratio. This page says,
$\bg_black \Delta v = c \cdot tanh(\frac{I_{sp}}{c}ln\frac{m_0}{m_1})$
where Δv is the ISV's total velocity change, 0.75c.
c is the speed of light. (300,000,000 m/s)
m0 is the mass of fuel and payload combined, before accelerating anywhere.
and m1 is the mass of the payload. (i.e. what we actually want to get to Alpha Centuari.)

That last figure, I(sp) is "specific impulse", the efficiency of the fuel. Since nobody knows the practical figure for antimatter, I'm trusting this page that I(sp)/c is roughly 0.25.

If we actually put in the things we know, we get:
$\dpi{120} \bg_black \\ 0.75c = c \cdot \tanh(0.25 \times \ln\frac{m_0}{m_1}) \\ 0.75 = \tanh(0.25 \times \ln\frac{m_0}{m_1}) \\ \tanh^{-1}(0.75) = 0.25 \times \ln\frac{m_0}{m_1} \\ 4\tanh^{-1}(0.75) = \ln\frac{m_0}{m_1} \\ \ln\frac{m_0}{m_1} = 4\tanh^{-1}(0.75) \\ {\color{Cyan} \frac{m_0}{m_1} = e^{4\tanh^{-1}(0.75)} = 49 }$

That is, any rocket trying to get up to (or down from. Everything is relative. ) 3/4 of light-speed requires 49 times as much fuel as it has cargo. Specifically, it needs to carry 49 times as much antimatter as it has cargo. This poses a problem: antimatter can't be harvested from anywhere in macroscopic quantity. You might have heard about antimatter being discovered in Earth's magnetic field; that was measured in billionths of a gram, which is a far cry from the 49,000g we need to transport 1kg of stuff to Alpha Centuari.

And that means the RDA need to build it themselves. Imagine, as a vast exaggeration, that the RDA rules the world, and the world of 2154 produces 200 times as much power as the USA did in 2001, which was 1.3x10^19J. That means the RDA produces 2.6×10^21 J per year. The energy-equivalent of 49kg of antimatter is 4.4×10^18 J. Dividing the two, it takes the RDA 14.5 hours to produce the fuel for 1kg of stuff, using all of its resources. That's not a lot, right?

Jake weighs, say, 80kg. That means that he, alone, requires just under 7 weeks of the entire world's power output for a one-way ticket to Pandora. (That's all he'll be using, but the RDA have every way in the world of predicting that no way of knowing that.) There are more than 100 people going to Pandora on any given ship. 100 80kg people take 13 years' worth of fuel to transport, all one-way. This is forgetting that the empty ISV itself weighs far more than those 100 people. If we take a rough estimate and say the full ship itself weighs 50 tons, then fueling it with the full capacity of a super-industrial Earth takes... 80 years.

That is a lot. Especially since the RDA don't control the world, and don't have a 100% efficient antimatter creation process. (Such a thing is impossible.) If they're antimatter creation process is as unimaginably high as 50% efficient, that means every single timespan in the last paragraph doubles. Oops.
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Last edited by Clarke; 08-18-2011 at 08:25 PM.
#2
08-18-2011, 10:29 PM
 Needs Moar Neytiri Icu Back from the dead? Join Date: Jun 2010 Location: Shack Posts: 411

It's not that they can't do physics, it's that they're making a movie and don't quite care enough.

Besides, I'm sure they can just invent some "in the future....." line that takes care of everything, as cheap as that is.

But I guess this is bad news for anyone wanting to go to a "Pandora" in the near future.
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#3
08-18-2011, 10:33 PM
 Pamtseo Vitra Fkeu'itan hasn't been here in years. Join Date: Mar 2010 Location: Aberystwyth, Wales. Posts: 2,562

There's a little thing called 'artistic lisence'...

Still, pretty interesting, I guess.
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#4
08-18-2011, 11:11 PM
 Tsulfätu Tsyal Makto glad to be home! Join Date: Mar 2010 Location: Body - Chicago, Spirit - Pandora Posts: 1,873

^ That.

I wonder how a hydrogen ramjet would work, though? Use another energy source to get the craft up to a speed at which interstellar hydrogren concentration becomes high enough for sustained fusion?
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Last edited by Tsyal Makto; 08-18-2011 at 11:27 PM.
#5
08-18-2011, 11:18 PM
 Olo'eyktan tm20 has no status. Join Date: May 2010 Posts: 2,751

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#6
08-18-2011, 11:57 PM
 Hapxìtu EywaBlessMe Disillusioned Tawtute (but you can call me Vawmpay) Join Date: May 2010 Location: under cover, ducking the bullets Posts: 182

Really? You mean there is no way that a sci-fi pic has the facts right, and blows logic? Wow, I suppose next you'll tell me that no Terminator came back in time to kill John Conner and there is no guy in Gotham in tight black leather calling himself "batman" and fighting crime.
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#7
08-19-2011, 12:43 AM
 Ikran Makto Ashen Key is writing Join Date: Aug 2010 Posts: 796

The joy of science-fiction! Also, why I put Avatar in the space-fantasy/cyberpunk corner and roll with it.

(On this issue, anyway - on other things, I bash my head against the world-building. But the physics I just roll with because that's what you get for playing in a sci-fi world)
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#8
08-19-2011, 12:44 AM
 Old Guard Isard -- Wait, you do hear the voices right? Join Date: Mar 2010 Posts: 3,416

iirc, ISV's use laser batteries to get up to speed.
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#9
08-19-2011, 01:16 AM
 Dandy Lion Moco Loco is a lion in a low place Join Date: Jun 2011 Location: New Orleans Posts: 2,911

OHOHO, wait until HNM sees THIS. I saw all that up in IRC yesterday, and if I recall correctly, he put you to shame on the claim that unobtanium can be synthesized on Earth. I know this specifically was more about antimatter, but it gets around to whether the cargo being retrieved is worth the trip.
#10
08-19-2011, 01:27 AM
 Mother Falcon Advent is feeling bittersweet Join Date: May 2010 Location: Somewhere home Posts: 2,972

It's science fiction, you can't expect everything to be entirely up to scratch. Though Cameron did make Avatar seem like a very realistic movie.
Suppose we'll see if he's fixed things up a bit in the sequel.
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#11
08-19-2011, 01:59 AM
 Tsamsiyu mikkowilson has no status. Join Date: Apr 2011 Location: Juneau, Alaska (Not Kansas, any more) Posts: 661

Lets see how well I remember by Avatar Universe cannon...

The first trips to Pandora where much slower, and bought back Unobtanium as fuel for the faster ISV's.

ISV's are accelerated from Earth (and decelerated to Earth) via a laser sail over a period of 6 months.

ISV's use a matter-antimatter fission reaction to decelerate to and accelerate from Pandora, using Unobtanium as fuel.

On Pandora Unobtanium is cheap. It's getting it to Earth that's the expensive part.

Each ISV leaves Pandora with enough Unobtanium to decelerate on it's *next* trip *to* Pandora, plus the actual product for sale, PLUS the (larger) amount as fuel for the acceleration from Pandora.

I don't believe the currently released information goes into detail about the ratios; but that's irrelevant.

Just as a boat may require more fuel than it can carry cargo; doesn't mean it's impossible, or even impractical if the cargo is valuable enough.

That fact that the ISV's fuel and extremely valuable cargo are the same substance is mere ironic coincidence. But not really that surprising as all sources of energy & fuels require energy / fuel to move them. Oil tankers are fueled by oil, even if the first trip to get to the oil had to be made in a sail boat.

- Mikko
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#12
08-19-2011, 02:41 AM
 Tsamsiyu Sempu has no status. Join Date: May 2010 Location: Pacific NorthWest Posts: 579

Robert Forward did some calculations on antimatter production; I'm too lazy to look for them right now. But I'll bet he came up with some ways of producing more. I was at a talk he gave once on antimatter propelled spacecraft and he enumerated the world's current antimatter production (picograms/year I think), then said he wanted, I think it was about a ton of it. And worked out how. Don't remember the details. Might have been a sunlight pump on or in the orbit of Mercury. With the Sun converting 4 million tons of matter to energy per second IIRC there's a lot of energy available if you can harvest it.
#13
08-19-2011, 07:49 AM
 Nawmtu Helicoradian nope...no status Join Date: Mar 2010 Location: Washington Posts: 1,220

Perhaps the RDA found a way to produce or harvest antimatter without expending a massive amount of energy? That would allow them to produce more of it given a set amount of energy available for production.

But the first few trips to Pandora would have been a real challenge, because the early ISV's were so much more massive due to using low-temperature superconductors instead of Unobtanium. They would have had to carry much more fuel...
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#14
08-19-2011, 01:23 PM
 Karyu Clarke wants his own Avatar. Join Date: Jul 2011 Location: Scotland, 140 years too early Posts: 1,330

Quote:
 Originally Posted by Fkeu'itan There's a little thing called 'artistic lisence'... Still, pretty interesting, I guess.
It'd be nice if the artistic license didn't shoot itself in the foot.

Quote:
 Originally Posted by Tsyal Makto ^ That. I wonder how a hydrogen ramjet would work, though? Use another energy source to get the craft up to a speed at which interstellar hydrogren concentration becomes high enough for sustained fusion?
That speed is larger than 0.75c, AFAIK.

Quote:
 Originally Posted by Isard iirc, ISV's use laser batteries to get up to speed.
...And down again? You don't want to crash into Pandora at 0.75c. (Or possibly you do. It's the only way to be sure, after all. )

Quote:
 Originally Posted by Moco Loco OHOHO, wait until HNM sees THIS. I saw all that up in IRC yesterday, and if I recall correctly, he put you to shame on the claim that unobtanium can be synthesized on Earth. I know this specifically was more about antimatter, but it gets around to whether the cargo being retrieved is worth the trip.
I'm actually surprised he hasn't said anything, considering how defensive he was on IRC. Avatar most definitely has internal logic problems, despite Cameron's attempts to avoid them.

Quote:
 Originally Posted by mikkowilson Lets see how well I remember by Avatar Universe cannon... The first trips to Pandora where much slower, and bought back Unobtanium as fuel for the faster ISV's. ISV's are accelerated from Earth (and decelerated to Earth) via a laser sail over a period of 6 months. ISV's use a matter-antimatter fission reaction to decelerate to and accelerate from Pandora, using Unobtanium as fuel. On Pandora Unobtanium is cheap. It's getting it to Earth that's the expensive part. Each ISV leaves Pandora with enough Unobtanium to decelerate on it's *next* trip *to* Pandora, plus the actual product for sale, PLUS the (larger) amount as fuel for the acceleration from Pandora. I don't believe the currently released information goes into detail about the ratios; but that's irrelevant.
Unobtanium can't be used for an antimatter reaction on its own. It needs an exactly equal mass of antimatter to react with. Unobtanium isn't antimatter itself, because if it was, the chunk on Selfridge's desk would have vaporized Hell's Gate. (And the surrounding miles of forest.)

Quote:
 Just as a boat may require more fuel than it can carry cargo; doesn't mean it's impossible, or even impractical if the cargo is valuable enough
It does if the fuel is ridiculously expensive. Manufactured antimatter is going to be at least as energy-expensive as Unobtanium.

Quote:
 Originally Posted by Sempu Robert Forward did some calculations on antimatter production; I'm too lazy to look for them right now. But I'll bet he came up with some ways of producing more. I was at a talk he gave once on antimatter propelled spacecraft and he enumerated the world's current antimatter production (picograms/year I think), then said he wanted, I think it was about a ton of it. And worked out how. Don't remember the details. Might have been a sunlight pump on or in the orbit of Mercury. With the Sun converting 4 million tons of matter to energy per second IIRC there's a lot of energy available if you can harvest it.
Yeah, if you can do astro-engineering, (i.e. covering Mercury in solar panels, Dyson shell fragments) you can produce that quantity of antimatter in days or less, but there's no evidence to suggest that the RDA have access to those.

Quote:
 Originally Posted by Helicoradian Perhaps the RDA found a way to produce or harvest antimatter without expending a massive amount of energy? That would allow them to produce more of it given a set amount of energy available for production.
That's theoretically possible, but unlikely, since if there was some process producing antimatter in macroscopic quantity, we'd notice it very quickly.

Quote:
 But the first few trips to Pandora would have been a real challenge, because the early ISV's were so much more massive due to using low-temperature superconductors instead of Unobtanium. They would have had to carry much more fuel...
Every kilogram is so incredibly expensive, I don't see how that could possibly work.
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#15
08-19-2011, 01:31 PM
 Pamtseo Vitra Fkeu'itan hasn't been here in years. Join Date: Mar 2010 Location: Aberystwyth, Wales. Posts: 2,562

Quote:
 Originally Posted by Clarke It'd be nice if the artistic license didn't shoot itself in the foot.
Uhh... lol?

That's kind of the definition of artistic lisence?
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