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In the late 21st century C.E. total human population on the Martian soil reaches 5 millions with the majority inbred. They are scattered across the red planet living in football field sized domes and the plan to terraform Mars is put on hold due to budget constraints so the air are still as toxic as ever!

Despite most of the surfaces are dry and road are laid to connect between facilities most of the terrain are still inaccessible by land transport.

With only solar power and minimum liquid fuel due to the lack of fossil fuel or natural biofuel, what kind of engine would be the most economical and reliable option to ferry hundreds of people and their luggage (Max. 100 tons) across 26.219 miles on a daily basis?

Making multiple trips is acceptable but that would require more pilots and transportation. No nuclear tech yet, no FTL and no magic!

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  • $\begingroup$ Can I ask why your facilities are almost exactly marathon lengths apart? $\endgroup$ – Ross Oct 13 '16 at 14:48
  • $\begingroup$ @RossC: No, cannot. $\endgroup$ – user6760 Oct 13 '16 at 15:45
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The answer is clearly zeppelins. First off, there would be no Hindenbergs, since hydrogen can't burn in a mostly carbon dioxide sky. So if you fill the airships with hydrogen you get a solid 3 tons of lift per Hindenberg of enclosing volume.

King, you might say, 3 tons seems awfully little for an airship that was 245 meters long. Problem? Of course not! You can get 100 tons of lift from a ship that is a mere 776m long! Tell you what, make it an even 1 km long, and you get 207 tons of lift, half for the craft and another half for all the passengers you can carry!

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    $\begingroup$ And where do you expect to find your buoyancy in an atmosphere that has 6 / 1000 the pressure of that on Earth? $\endgroup$ – MichaelK Oct 14 '16 at 6:32
  • $\begingroup$ @MichaelKarnerfors Thats all ideal gas law hard math, bruh. 3032 kg worth of lift from displacing 200,000 m^3 of 0.0155 km/m^3 CO2 atmosphere at 600 Pa with 0.0003369 kg/m^3 H2 at 600Pa. $\endgroup$ – kingledion Oct 14 '16 at 11:47
  • $\begingroup$ 200 000 cubic meters is the volume of the Hindenburg. That ship had lift for 232 ton, of which 10 ton was useful lift. That same volume on Mars provides lift for - as you just calculated - 3 ton. And here is the really annoying part: the lower gravity of Mars does not help you, even though you have a lower weight to lift, because according to Archimedes's principle, buoyancy also comes from the weight you displace. So... where are you going to get the remaining 229 ton of buoyancy from? $\endgroup$ – MichaelK Oct 14 '16 at 12:18
  • $\begingroup$ And how do you make this magic ultralight airship? We barely break even on Earth, where we have a very dense atmosphere compared to Mars. I hope you realize that you need to lower the specific mass (mass per unit of volume) of your airship by a factor of almost 80(!) compared to the Hindenburg... that if your airship had the same volume as the Hindenburg — 200 000 cubic meters — it would weigh less than 3 tonnes. How(!) do you propose to achieve that and still have any kind of sturdiness? $\endgroup$ – MichaelK Oct 14 '16 at 12:34
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    $\begingroup$ Well that leaves us with a problem: you just said that your answer is not actually valid because your proposed solution cannot work. Yet you got the "accepted" mark on it. So what do you intend to do with your answer? Just let it stand even though you by your own admission just said the solution — literally — cannot fly? $\endgroup$ – MichaelK Oct 14 '16 at 13:50
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Rail

...also: your premise is slightly flawed.

The air on Mars is not "toxic", it is practically non-existent.

The air pressure on Mars is a mere 6 / 1000 what we have on Earth.

This works in your favour because with this rail becomes incredibly economic. The main advantage of rail on Earth is that you lower the rolling friction to near nothingness. The only thing holding a train back is wind resistance. So on Mars, with air pressure being so incredibly low, Elon Musk('s descendants) could build the Hyperloop without with the bother of building a vacuum tunnel around it.

Powering the rail is easy: you use electricity.

And why "no nukes"? You do realize that putting up a nuclear reactor is stupidly easy, right? If you are saying that the setting is "late 21st century", chances are great that fusion reactors have become commonplace. If Polywell turns out to work, then Mars will most definitely have fusion reactors. But even without that, having fission reactors will not be a big thing. If mankind have gotten to Mars and colonized it to the point you describe, then they will have solved the issue of energy.

Also: why would they be spread out so much, necessitating travelling back and forth all the time?! That is a completely illogical thing to do.

But no matter what justification you may or may not find for this premise... with too little air-pressure, that therefore cannot support aircraft of any sort; with no roads, no air, no fossil fuels and with scarce energy you cannot have personal transports (to any great degree); with no water you cannot have sea travel; and with the immense distances you need to travel, you need something that can attain great speed while using very little energy per passenger-kilometer.

Hence: rail is the way to go.

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Aqueducts

Assuming you are commuting between 2 domes every day, why not build two inclines, one for each way? You can supplement the vehicle with some solar power and put it on some rails; since there is little air resistance and less gravity (=less frction) you may be able to do this witouth too crazy of a slope. You just have to lift the vehicle vertically again to put it on the return slope when you want to go back (so you may want to design your vehicle as mostly cargo container-like objects that you can more easily pick up)

Instead of making the slope a straight line, you can make it in the shape of a skewed parabola so that the vehicle slows down on its own

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Use the spaceships that transported the five million colonists to the planet Mars. Because if: "In the late 21st century C.E. total human population on the Martian soil reaches 5 millions with the majority inbred." It follows that space travel has become ludicrously cheap and energy efficient. Otherwise it would be impossible to move five million people across interplanetary space at sometime in the next eighty or so years unless spaceships have become super-cheap and super-low-energy compared to the spacecraft of 2016.

Also the spacecraft would have to carry large numbers of passengers and crew. Therefore, if you need "to ferry hundreds of people and their luggage (Max. 100 tons) across 26.219 miles on a daily basis", then this is a mere hop and a skip for an Earth-Mars spaceship. It just has to load up the people and their luggage, lift off and land them in a thrice at the next dome. The space-drive engines will barely get warm with these short-range flights.

Of course, anyone will any sense will install an optical cable between domes. People now don't need to commute or travel between domes, they can communicate via videophone or immersive virtual reality. Also, it's much safer and there's less wear and tear. No time wasted being ferried between domes too.

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