Living on Mars -- III

Mars with and without a dust storm

I talked here about the problems of living on Mars (temperature, air pressure, UV radiation, cosmic rays, toxic "soil") and about a solution to some of those problems (silicon aerogel, to raise temperatures and reduce UV radiation).  Now we come to the next big issue: energy.

With an glass/silicon aerogel/perspex dome cover, domes on Mars (at least between latitudes 40 N and S)  would be passively heated.  But it is very likely that heating will be required in winter, especially in the southern winter, when Mars is at its furthest from the sun (Mars has a more eccentric orbit than Earth).

That won't be the only need for energy by the first settlers, though.  A big need will be to manufacture fuel for return trips to Earth.   This will involve splitting water mined on Mars into hydrogen and oxygen, then harvesting CO₂ from the atmosphere.  A mixture of the CO₂ and H₂ is then passed at pressure and high temperature over a catalyst and this process (called the Sabatier process or reaction) produces methane.  More competent mathematicians than I have calculated that this will need 17MWh of electricity per tonne of fuel.  [But see below for an update—Robert Zubrin, the scientist who originally suggested propellant manufacture on Mars, has calculated it at 12 MWh/tonne.  About 70% my original information] Let's say each Starship requires 1100 tonnes or so of fuel (the Mars Colonial Transporter, the bigger first version of Starship, needed that), and there are 600 days between landing and relaunch.  That will require 31 MWh [22 on Zubrin's figures] of electricity per day, just to refuel a single Starship.

Average electricity demand in the US is around 12,000 kWh/person/year.  Assuming usage on Mars will be the same, for a colony of 100, that would mean 3.3 MWh of electricity per day.  Only, usage is likely to be higher on Mars than Earth.  If we use the higher consumption data for cold places on Earth (50,000 kWh/person/year for Iceland, 35,000 for Lichtenstein, 24,000 for Norway, 15,000 for Canada and Finland) then we're talking perhaps 10 MWh/day for the whole colony.   We will need electricity to heat domes, to control the air inside the domes (removing CO2 for example), to run rovers, to grow food, to light domes, etc.  So we'll need total output of 44 MWh [32 on Zubrin's calcs] per day—three-quarters of that for fuel production.

So where is this electricity going to come from?

Let's start with nuclear.   It's out of the question to build a large-scale nuclear reactor on Mars.  But NASA has been working on a smaller, simpler, safer reactor, designed specifically for use on spacecraft and on Mars and the Moon.  It's called KRUSTY (Kilopower Reactor Using Stirling Technology), and here's a video which gives a brief explanation of it.  A reactor 10 times larger is planned.  This will produce 10kW of electricity,  will weigh 1500 kg and will contain 44 kg of  U-235.  So each day, one of these reactors would produce 245 kWh of output.  We'd need 180 [130 on Zubrin's data] of the 10 kW kilopower reactors to produce enough electricity for the colony as well as refuelling one Starship.  They'd weigh 270 tonnes [195 tonnes Zubrin].  Just delivering them to Mars would require 3 Starships [2, Zubrin], assuming on current plans 100 tonnes of cargo per ship.

OK, what about wind?  You'd think that with the air pressure on Mars, just 0.6% of Earth's, wind turbines would be useless.  This informative video from Scott Manley shows how wind turbines on Mars could actually work quite well, despite the low atmospheric pressure.  For a start, don't confuse air pressure with air density.  Now on Earth, these two are related.  However, the air on Mars is denser than on Earth at the same pressure because it's 95% CO₂ and because it's much much colder.  This boosts the impact of air density on the output of a wind turbine by about 100% relative to Earth.

Also, average wind speeds on Mars at the Viking 2 lander site were 15 mph (just under 7 metres/second).  In the US, average wind speeds are between 6 and 12 mph, but of course, wind turbines tend to be sited where winds are stronger.  So, back-of the-envelope, 50% of Earth's wind capacity.   Small wind turbines will weigh something like 300kg, but more productive wind turbines are proportionately less heavy, because the power produced is proportional to the square of the blade radius. Let's assume one with a 10 m rotor diameter, twice the size of the rotors discussed in the link.  This will increase the electricity output four fold, but will weigh, say, 600 kgs.   Such a wind  turbine would produce half (on average) of a 10 kW Kilopower reactor at 1/3rd the weight, so we'd need two Starships to provide all the wind turbines you'd need for your  colony on Mars plus fuel production for the return home.  But—and this is key—it will be easy to manufacture small wind turbines on Mars, unlike (at least for the first decade) nuclear and solar generators.

Just as on Earth, the wind won't blow all the time, so you'll need complementary power source—solar.  Thin-film solar is less efficient than conventional solar cells, but they're 100 times lighter, and can be rolled up for transport.  Because Mars is further from the sun than Earth, solar panels there will be 40% less productive than on Earth.  At the equator on Earth (Singapore) 10 kW of solar panels will produce 12,600 kWh per year, or 34.5 kWh/day.  Reduce that by 60% at the Martian equator, and output of 10 kW of conventional solar panels would be 14 kWh/day per 10 kW of panels.  You'd need 32000 kW [23000, Zubrin] of panels.  One kW of solar panels would cover 2.75 metres.  So you'd need 12,000 square metres of panels on Mars to power the colony.  And if you use thin-film solar, some 25% more.  15,000 square metres.  Imagine a metre-wide strip of thin-film panel.  You'd need 15,000 metres in rolls.  15 kms!  It might be much the lightest generation source, but it will surely take up a lot of space inside a  Starship.  Solar output would be almost completely reduced to zero during Mars's periodic dust storms.  The good news is that wind speeds treble during the dust storms, so just as on Earth, wind is highly complementary to solar.

A couple of conclusions:

• It would make sense for all three generation sources to be used.  The nuclear would provide "baseload", i.e., for all the demand for electricity excluding fuel manufacture.  The first priority is maintaining life.   So the first colony would need 60 10 kW Kilopower reactors, enough to heat, grow food, light, air and water purification, rovers, etc.
• 120 10-metre diameter wind turbines, which would on average provide about the same power.  Any surplus energy would be used to make methane and oxygen.
• 15,000 kw of thin-film solar panels.  Again, the electricity they generate will go towards making methane.
• The cargo demands for all these generators, space and weight suggest to me that more than the planned 4 cargo ships will be needed to start colonisation.  Just for electricity generators, five Starships will be needed, one for nuclear, two each for wind and solar.  [Possibly just 3 using Zubrin's estimate]  It won't be a problem once the Mars-Earth trade route is established, because the cost of sending cargoes to Mars will fall precipitously.  As I guess here, the cost of delivering 1 tonne from Earth to Mars will prolly fall to $20K  by the third or fourth expedition, since re-usability is key.  It's only a serious problem for the first expedition. At each subsequent expedition, more wind turbines/solar panels/kilopower reactors will be brought.
• Reducing the number of people doesn't make much difference, since three-quarters of the electricity is needed for propellant manufacture.   The only way to cut the energy needs is to remove the option to return after 2 years, and stretch it out to 4 or 6 years.  Hmmm.  Or, more plausibly, we send ten Starships on the first crewed expedition, two crewed and eight cargo.  But only one will return to Earth (based on my calculations above), so re-usability is in effect reduced, raising costs.  It'll be different after the second expedition, because then there'll be enough electricity generation capacity to make fuel to send two Starships back, and the number will increase with each expedition to Mars.  
• On these numbers, it will take 10 expeditions of 10 Starships at a time for enough fuel to be available to send them all home.   That's 20 years.  
• Even if some of the Starships are in effect not re-usable (because there isn't enough propellant to fly them back to Earth), the cost will still be far below NASA's estimate of $150 billion for a crew of 5.  At $100 million per Starship**, 10 Starships to get the colony started would cost $1 billion, even if they were never used again—and they'd provide shelter to the first colonists while ground-based shelter was built.  Thus the cost will be $1 billion initially, then $500 million per year (Mars is in opposition to Earth only every 2 years)
• If Starship works, NASA will surely ditch SLS and use the $1.5-$2 billion per launch, never mind the $10 billion plus development cost, to send 200 people every 2 years for a permanent Mars base.

As usual, anyone who knows more about this than me, or who spots flaws in my calculations or analyses, is invited to comment below.

See also:

Living on Mars -- I

Living on Mars -- II

Update:

Robert Zubrin (the guy who first suggested we manufacture methane on Mars to reduce the crippling fuel burden involved in bringing it from the Earth) has estimated the energy cost of producing methane in this tweet:

In other words, my calculations are too pessimistic.  Reduce them by 30% to get a more accurate measure.  Just so y'all know.

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**  [Update 27/04/2020] Musk has stated that he's aiming for a total capital cost per Starship of under $5 million, and a cost per launch below $2 million (including the cost of Super Heavy), with a payload of 150 tonnes.  Each launch will use $800 K of fuel.   To get Starship from LEO  to Mars will mean it has to be refuelled in orbit, and that will require 6 launches per flight to Mars, costing say $16 million per Starship to Mars, or $21 million if we add in the capital cost, since the first ships won't be returning.  That means the initial expedition of 10 ships will cost $210 million.  64 cents per inhabitant of the USA.  And a berth on a flight could cost as little as  $210K per ticket.  One tonne to Mars would cost $140 K.  Subsequent flights will be cheaper, because Starship will rapidly get more efficient as SpaceX learns while doing, just as Falcon 9 got better, and because some Starships will return.  Costs per passenger or per tonne are likely to halve over the first 10 years.   SLS, meanwhile, will cost $1.5-$2.5 BILLION per launch.