Routine ISVs en route to Pandora

[Sothis]

I've been encountering different interpretations for how many ISVs are still en route to Pandora and at what rate they are arriving. Today, I finally got out a pen and paper (and Pandorapedia) to work it out. I thought I would share my results here to serve as a reference for others. If you disagree with any assumptions, calculations, or results, please share your thoughts here so that we can arrive at a consensus.

This is the page I used as my main reference. (I find Pandorapedia to be much more self-consistent and reasonable than the wiki):
ISV Venture Star | Pandorapedia: The Official Guide to Pandora | Own AVATAR on Blu-ray & DVD Now!

From the first paragraph, we know that the ISV Venture Star is part of a twelve-vehicle fleet that forms an "endlessly looping supply chain," meaning that at any moment in time, some ISVs are in transit to Pandora and some are in transit to Earth.

The ISVs currently en route to Pandora are just part of this "routine" supply loop; however, they cannot simply "turn around" when they receive word that circumstances at Hell's Gate have changed. They carry just enough fuel to allow them to decelerate from 0.7c when approaching Pandora. While in orbit, they must refuel in order to accelerate back up to 0.7c in the opposite direction. ("Power source" section.)

In order to calculate the rate at which ISVs are arriving, we must know the duration of the "endless supply loop" cycle. In the "Mission profile" and "mission duration" sections, we see that each leg of the round-trip is 6.75 earth-years long (in an inertial reference frame) and that there is also a 1-year loiter in orbit around Pandora.

In addition, I have chosen to assume that there would be a 1-year loiter in orbit around Earth as well. This is my own assumption; I can't find any references to how long ISVs remain in Earth's orbit. My reasoning is that the same considerations that necessitate a 1-year loiter around Pandora would also necessitate a similar loiter around Earth (getting people in and out of cryosleep, loading and unloading cargo, checking the vehicle and systems for damage, extra time to allow for a safety margin, etc). However, there's no reason that the Earth-loiter has to be exactly the same length as the Pandora-loiter.

**EDIT: The assumptions concerning the duration of the Earth-loiter have been revised. Please see post #22 for updated conclusions.**

Based on the chosen assumptions, however, the total duration of a complete cycle is 6.75 + 1 + 6.75 + 1 = 15.5 years.

If we further assume that the twelve ISVs are spaced equally throughout this cycle, each ship is ahead of the one behind it by (15.5 years) / (12 ships) = 1.29167 years (or 1 year, 3.5 months).

If you draw a diagram of the different phases of the cycle and how the ships are spaced throughout it, you'll see that at any given moment there is either 5 ships en route and 1 orbiting, or 6 ships en route and 0 orbiting (with the same being true for Earth, by symmetry). The first scenario is true 77% of the time; the second scenario is true 23% of the time.



I am going to make the assumption that the ISV Venture Star was a little over 3 months into its expected 1-year orbit when the big battle took place. Due to the forced evacuation, it probably leaves orbit ahead of schedule, unless it needs the entire year to refuel, or it's necessary to maintain some minimum distance from the ISV ahead of it. Regardless, the next ISV would be arriving about 1 year after the big battle. After that, four more ISVs will arrive at intervals of 1.29167 years (1 year, 3.5 months). The last “routine” ISV will arrive a little over 6 years after the battle.

Note that it's not logistically necessary for these ISVs to have any rendezvous with Pandora's surface at all. They can simply refuel and turn around, and refueling is accomplished using repurposed, unmanned Valkyries that act as automated gas harvesters, collecting hydrogen and deuterium from Polyphemus' upper atmosphere. Whether or not the personnel would try to shuttle down anyway is another question for a separate topic.

In summary, here are the assumptions I made in my calculations. (Asterisks indicate assumptions not found in Pandorapedia):

1) There are 12 ISVs total, including the ISV Venture Star that brings Jake and Norm to Pandora.
2) The journey between Earth and Pandora takes 6.75 earth years (in an inertial reference frame).
3) Each ISV spends 1 year in orbit around Pandora during each round-trip.
4) Each ISV spends 1 year in orbit around Earth during each round-trip.*
5) The ISVs are spaced at equal time-intervals throughout the "endless supply loop." *
6) The ISV Venture Star is a little over 3 months into its expected 1-year loiter when the battle occurs.*

And here are my conclusions:

1) There are five ISVs en route to Pandora during the events of the movie (not including the Venture Star).
2) Each ISV is 1 year, 3.5 months ahead of the one behind it.
3) The first ISV would arrive about a year after the battle.
4) The fifth ISV would arrive about 6 years after the battle.

Comments and criticisms are welcome!

[Patrice Maire]

Fascinating! whoa!
The only thing that I'd like to mention is Norm's comment to Jake about doing the videolog.
'It'll help keep you sane for the next six years.'
so.. if that's an indication then the next ship won't arrive for 6 years?
I think you're on target with your calculations, but given that quote, maybe every other one only bring supplies but the 6 year one is when people ship out if need be.
But then again... Quaritch told Jake he was getting his legs back and 'out on a shuttle tonight'.
So...he's been there less than a year... which means he would be shipped out on the Venture Star on it's trip back.

Not trying to shoot you down, just trying to piece together the continuity with your math..which is very cool and very worked out. Great stuff!

[SnowRider]

That's some interesting math and some interesting assumptions behind the math.

I think you did a pretty good job working out the practical logistics of the ISV supply/return chain that connects Earth and Pandora.

Basically, what you're saying is you figured out that at any one time, there should be one ISV around Earth, one around Pandora, five coming from Earth to Pandora, and five returning to Earth from Pandora.

That sounds about right, all of which means that about a year after the events at the end of the movie, Jake and the Na'vi should expect to see an ISV showing up in the sky of Pandora.

Now, the only real question is what do they do at that point?

We'll find out, I am sure.

(however, I think the last "routine" ship to leave Earth would still be able to stop and turn around if they got enough advance warning that the situation has changed on Pandora)

[Ashen Key]

No concrit just yet - too post work - but, SOTHIS I HEART YOU. This is utterly BRILLIANT, thank you for working this out!

Patrice Maire, I always saw that comment as being when Norm and Jake would LEAVE - and that it had nothing to do when other people get there. Particularly with the other ships constantly to and fro, to me it makes sense that people cycle on and cycle off at different times.

[Helicoradian]

There would need to be some interaction between the arriving ISV's and Hells Gate in order to restock on consumables for the crew. But given the circumstances, it should pose no problem to the humans and na'vi occupying Hells Gate.

I'd be worried about those in cryo. Jake describes it as an ass kicking, and that's just for a one way trip which would imply even though you don't age as fast, it's still hard on the body. Could a person withstand being in that state for such a long period of time?

But great job on figuring out the scheduling. The logistics of getting to Pandora are quite fascinating

[Sothis]

Thanks for the feedback, everyone!

Originally Posted by Patrice Maire

The only thing that I'd like to mention is Norm's comment to Jake about doing the videolog.
'It'll help keep you sane for the next six years.'
so.. if that's an indication then the next ship won't arrive for 6 years?

Originally Posted by Ashen Key

Patrice Maire, I always saw that comment as being when Norm and Jake would LEAVE - and that it had nothing to do when other people get there. Particularly with the other ships constantly to and fro, to me it makes sense that people cycle on and cycle off at different times.

Ash pretty much gave the answer I was going to give. Jake and Norm wouldn’t be leaving on the next ship. They would’ve left on the 5th ship to arrive after the Venture Star. I imagine the contracts are staggered, so different people are constantly arriving and leaving on each ISV.

Originally Posted by Patrice Maire

But then again... Quaritch told Jake he was getting his legs back and 'out on a shuttle tonight'.
So...he's been there less than a year... which means he would be shipped out on the Venture Star on it's trip back.

Exactly. The ISV is still in orbit, so they could’ve easily gotten Jake into cryosleep before its return trip.

Originally Posted by SnowRider

Now, the only real question is what do they do at that point?

We'll find out, I am sure.

(however, I think the last "routine" ship to leave Earth would still be able to stop and turn around if they got enough advance warning that the situation has changed on Pandora)

Indeed, I’m sure we will find out. In the meantime, that’s what fanfiction is for. :-p

Actually, I don’t think the last ship would be able to turn around any more than the ones that are further along in their journey to Pandora. Even if they’re able to receive immediate, superluminal communication that the situation has changed, they’d already be at least 6 or 7 months into their journey. This means that the 5.5-month acceleration phase has already passed and they are travelling at 0.7c. It takes a lot of energy to decelerate from relativistic speeds, and twice that to accelerate back up in the opposite direction. Unless they can stop at some kind of fueling station en route, they’d be dead in the water if they stopped.

Originally Posted by Ashen Key

No concrit just yet - too post work - but, SOTHIS I HEART YOU. This is utterly BRILLIANT, thank you for working this out!

Hehehe, no problem. :-p It had been bothering me. Of course, now that I’ve worked it out, it’s going to feel like a glaring flaw whenever I encounter fanfiction with “mistakes” in their timelines.

Originally Posted by Helicoradian

There would need to be some interaction between the arriving ISV's and Hells Gate in order to restock on consumables for the crew. But given the circumstances, it should pose no problem to the humans and na'vi occupying Hells Gate.

VERY good point; thank you for pointing this out. And yes, I’d imagine that the ISV crews would have orders not to create trouble, in exchange for Jake and co agreeing to keep the base operational and supply them with the necessary consumables. Not to mention it would make no sense for the “routine” ISVs to try anything.

Originally Posted by Helicoradian

I'd be worried about those in cryo. Jake describes it as an ass kicking, and that's just for a one way trip which would imply even though you don't age as fast, it's still hard on the body. Could a person withstand being in that state for such a long period of time?

I’d imagine that the “ass-kicking” has more to do with being completely frozen and then thawed out, and less to do with the duration of the cryosleep. I always imagined that once you have been successfully frozen, you can remain that way almost indefinitely until it’s time to thaw out. But I’m just conjecturing, so it’s a potential concern.

[Ashen Key]

Originally Posted by Sothis

Hehehe, no problem. :-p It had been bothering me. Of course, now that I’ve worked it out, it’s going to feel like a glaring flaw whenever I encounter fanfiction with “mistakes” in their timelines.

*g* Yeah, me too. I'll just. Be good and roll with it if they just mention 'a year'. Yes.

Originally Posted by Sothis

I’d imagine that the “ass-kicking” has more to do with being completely frozen and then thawed out, and less to do with the duration of the cryosleep. I always imagined that once you have been successfully frozen, you can remain that way almost indefinitely until it’s time to thaw out. But I’m just conjecturing, so it’s a potential concern.

Oh, yes, that's a good point - I was wondering on the potential damage caused to the sleepers if they were all turned back.

[txen]

Since the ships are accelerated and decelerated by lasers on the earth side, that constrains the time at earth some. If I remember correctly the ships accelerate at 1.5 g so that will take just under half a year to reach the 0.7c crusing speed. Guessing that there is just one earth side laser system it can either be speeding up or slowing down one ship. That means one ship incoming and one leaving per year. Each needs almost six months of laser time. So a ship comes back and as soon as it arrives another is sent to Pandora. The incoming ship has one year for refitment and can be sent after the next incoming ship arrives.

[Sothis]

Originally Posted by txen

Since the ships are accelerated and decelerated by lasers on the earth side, that constrains the time at earth some. If I remember correctly the ships accelerate at 1.5 g so that will take just under half a year to reach the 0.7c crusing speed. Guessing that there is just one earth side laser system it can either be speeding up or slowing down one ship. That means one ship incoming and one leaving per year. Each needs almost six months of laser time. So a ship comes back and as soon as it arrives another is sent to Pandora. The incoming ship has one year for refitment and can be sent after the next incoming ship arrives.

...THANK YOU for pointing this out. I totally knew about the laser / photon-sail system on the Earth end, but somehow forgot to check to make sure my version satisfies the constraint that only one ship can be accelerated or decelerated at a time. (I agree with your guess that there's only one laser system). As a matter of fact, this changes things. If you look at the diagram I drew, the ship labeled "t = 0" is about to leave earth... except it actually CAN'T, because the ship labeled "t = 14.21083" still has 3.5 months of deceleration left to go. So something has to be different... that incoming ship has to be either more than 5.5 months away when t=0 leaves, or it has to be already in orbit.

So far, I see 3 possible alternatives that would satisfy the laser acceleration constraints while still satisfying the canon (non-asterisk) assumptions:

1) The loiter around Earth is less than a year, short enough that a ship can arrive at Earth and leave again before the next one comes in range (Ship A arrives, Ship A leaves; Ship B arrives, Ship B leaves; Ship C arrives, Ship C leaves; etc).

2) The scenario txen described - i.e. There is a loiter of about a year around Earth, and a ship leaves shortly after the one behind it arrives (Ship A arrives, loiters for a year; Ship B arrives, Ship A leaves; Ship C arrives, Ship B leaves; etc) In this scenario, each ship would be about 1 year ahead of the one behind it instead of 1.29 years. However, because the total cycle would still be 15.5 years and there are 12 ships, there would be a long stretch at some point where ship #12 leaves Earth and then ship #1 doesn't arrive for 4.5 years. This would be discarding my previous assumption that the ISVs are spaced equally throughout the 15.5-year cycle.

3) We preserve the assumption that ISVs are spaced equally throughout the cycle, but make it a longer cycle such that the timing of arrivals and departures work out. This would mean that the loiter around Earth is longer than a year, with more than one ISV in orbit at a time.

I'm going to have to play around with the numbers and brainstorm logistics to figure out which scenario seems most reasonable, and what the revised parameters would be. Hopefully, I'll figure something out and post a revised version that satisfies all constraints.

[SnowRider]

Then another question occurs to me on the Pandora side of the question. Perhaps this has already been answered somewhere else, but I wonder about it.

If there needs to be a laser to accelerate and decelerate the ships leaving and returning to Earth, then there has to be a similar setup at Pandora. Otherwise the ISVs would never be able to get up enough speed just with their ion/plasma/whatever engines.

If so, then there has to be a pretty good size store of energy on Pandora (i.e., a LOT of deuterium and/or antimatter available to power the lasers) for the purpose of powering the laser at Pandora.

That isn't as much of a problem on Earth, because (in theory, at least) the Earth laser can tap into the whole worldwide energy grid to power up, but on Pandora, by necessity there must be a much, much smaller infrastructure to supply power to the laser.

So, they must have a way of very quickly refueling their power supply on Pandora (i.e., the used shuttles to get deuterium from Polyphemous) and they'd probably need a LOT of fuel every time they accelerate a ship that's leaving or decelerate one that is arriving.

If they have a fast turnaround time (and they'd need one if one ship is leaving and another one is arriving right on its heels) that can mean only one of two things.

Either a) they are very, very efficient with their use of energy or b) they can get a LOT of fuel in a very short amount of time.

(or perhaps there is Option C, they can do a little of both)

In any case, it must mean that keeping the laser supplied with enough fuel and Hell's Gate running at the same time must be a very, very complicated balancing act!

[Sothis]

Snowrider -

The acceleration / deceleration on the Pandora end works by a completely different system than on the Earth end. The Earth end is powered by a laser that strikes the ship's photon sail. The Pandora end is powered by an onboard matter / antimatter reaction fueled by hydrogen and deuterium, which are harvested by automated gas skimmers in Polyphemus' upper atmosphere. Thus, on the Pandora end, it is perfectly allowable to have one ship decelerating in while another accelerates out if that's how it happens to work out. Also, we know for sure from Pandorapedia that the loiter around Pandora is 1 year, while we don't have information on the length of the equivalent loiter around Earth (or at least not that I've found).

Sorry to render your musings moot; it would've indeed been a very interesting balancing act if the Pandora end was also powered by lasers. :-p All the above can be found on the Pandorapedia page, btw.

[txen]

As for the loiter time at earth, I don't think that it the correct term. When the ship returns from Pandora it's been in service for 13 years. I have a feeling that the time back at earth is spent rebuilding the thing. I would say that each time a ship left for Pandora it would have received a complete overhaul. That might take more than a year.

[Sothis]

Yeah, 14.5 years if you count the 1-year orbit at Pandora. I'm currently leaning toward scenarios 2 or 3, though I guess scenario 1 *might* be feasible if significant work can be done on the ISVs during their 1-year orbit around Pandora. Kind of a stretch but... maybe. In scenario 2, the "gap" of 4.5 years bothers me a little, although I guess it's possible that they're still in the process of building more ISVs. The Venture Star was the 9th of its class, and the voyage it makes in the movie is only its 2nd round-trip.

[Human No More]

Wow, this is well thought out

The ISV does not take a year to refuel, that is just how long for it to stay in orbit to load with unobtainium and people returning to Earth, then at Earth, to unload and load with equipment and new staff to bring to Pandora. I'd guess that would take maybe a month at most, or significantly less if it was just being refuelled and turned around without unloading and loading cargo.

Well, Jake's encounter with the Na'vi most likely happened on the third day (first using his avatar on the second), so he is told on the 4th that he has 3 months, so the timeframe seems about right. One of the deleted scenes actually shows the ISV leaving at the end of the film.

As for attempting to land, the ISVs contain relatively few marines (only as many as were intended to replace ones who would be leaving plus maybe a couple of extras to cover for casualties), the only safe place to land is Hell's Gate, and that has a lot of anti-air defences.

Originally Posted by Patrice Maire

Fascinating! whoa!
The only thing that I'd like to mention is Norm's comment to Jake about doing the videolog.
'It'll help keep you sane for the next six years.'
so.. if that's an indication then the next ship won't arrive for 6 years?
I think you're on target with your calculations, but given that quote, maybe every other one only bring supplies but the 6 year one is when people ship out if need be.
But then again... Quaritch told Jake he was getting his legs back and 'out on a shuttle tonight'.
So...he's been there less than a year... which means he would be shipped out on the Venture Star on it's trip back.

Not trying to shoot you down, just trying to piece together the continuity with your math..which is very cool and very worked out. Great stuff!

All ISVs carry passengers, 6 years is probably the length of a single contract for work on Pandora.

As for the laser system, I'd say having two would make more sense as it allows accelerating one away while decelerating another as it approaches.

Originally Posted by SnowRider

Then another question occurs to me on the Pandora side of the question. Perhaps this has already been answered somewhere else, but I wonder about it.

If there needs to be a laser to accelerate and decelerate the ships leaving and returning to Earth, then there has to be a similar setup at Pandora. Otherwise the ISVs would never be able to get up enough speed just with their ion/plasma/whatever engines.

The ISV engines use antimatter. Antimatter is produced on Pandora using fusion, with deuterium collected from Polyphemus by retired shuttles which are converted into automated vehicles for collecting it (the ISV leaves its shuttles behind on Pandora, then new ones are sent up from Earth when it arrives there).

If they have a fast turnaround time (and they'd need one if one ship is leaving and another one is arriving right on its heels) that can mean only one of two things.

Either a) they are very, very efficient with their use of energy or b) they can get a LOT of fuel in a very short amount of time.

(or perhaps there is Option C, they can do a little of both)

In any case, it must mean that keeping the laser supplied with enough fuel and Hell's Gate running at the same time must be a very, very complicated balancing act!

This is true, although it wouldn't be too close because fusion is an excellent source of power and the existing infrastructure would be more than enough to power Hell's Gate and the antimatter production.

The loiter time at Earth partly including a refit/servicing makes a lot of sense - while stress on the ship is actually relatively low when travelling through space, systems such as life support and the engines in particular would still need maintenance.

[SnowRider]

The thought also occurs to me that the ISVs returning to Earth probably have more mass (i.e., are carrying more) because their primary cargo (aside from returning humans to Earth) is getting the refined Unobtainium to Earth, where it can be put to use.

I suspect that an ISV with a full load of refined ore and people weighs a lot more than one coming to Pandora, just loaded with people and various pieces of equipment.