Getting to Mars--cheaply

Asteroid mining. Source

NASA estimates a cost of $100 billion for 5 astronauts to get to Mars and back. $20 billion per person!  It's no wonder the date mankind will reach Mars is always 15 years from today.  No government will fund that kind of expense.  But what if the cost could be dramatically, massively, cut?

If SpaceX manages to make the BFR and BFS reusable, even for just 10 times, the cost of getting to Mars will be 4 or 5 orders of magnitude less than NASA's mission.  (An order of magnitude is a 10 fold increase or decrease)

There are three parts to the Falcon 9: the first stage, or booster; the second stage; and the payload which is protected by a fairing.  Already the Falcon 9 first stage is being used twice, and with each successful launch and relaunch, the steps needed to reuse the first stage have been reduced and the speed with which SpaceX can reuse them rises. But the second stage and the fairings are discarded, and allowed to fall back to earth where they burn up in the atmosphere or crash into the sea.

We know from SpaceX that each launch of the Falcon 9 costs $62 million, and the launch of Falcon Heavy costs $90 million.  Musk has said that the fairings cost several million, but he has also said that the first stage is somewhat less than 75% of the total cost.   Reconciling these two statements is beyond my skills.  So let's assume that the second stage plus fairing costs 1/2 the first stage.  That gives us 3 equations, where A = the cost of stage 1, B=the cost of stage 2 plus fairing and C = profit margin.

(1) A+B+C=62
(2) 3A+B+C=90
(3) B=A/2

Three variables, three equations--hey, I can solve that!  And the solution is:

A (cost of stage 1)=$14 million
B (stage 2 + fairing)=$7 million
C (profit) = $41 million

The high profit margin (66%) explains why SpaceX is still going despite its heavy outlay on development, and despite frequent predictions that it was in imminent danger of bankruptcy.  (In that sense it's not really a profit margin, rather development cost recovery)

Undoubtedly I've got things wrong, but it gives us some reasonable guesses.

Let's use the number of engines as a proxy for the cost of the BFR vs the Falcon 9.  I know that's far from exact, but the engines are a big part of the cost and if they are all the same size, the number should be proportional to the size of the rocket, and therefore its cost.  The BFR (i.e., stage one of the Mars Transporter) will have 31 Raptor engines, compared with the Falcon 9's 9 Merlin engines, so a very rough calculation would put the cost of a BFR at 14/9*31=$48 million.

The BFS (the upper stage of the BFR, the proper "spaceship") will have 4 vacuum Raptor engines and three smaller atmospheric "sea-level" engines) The BFS will cost much more than stage 2 and fairing of the Falcon 9--it'll be much bigger and will have life support (though the tanker and cargo versions won't.)  To get some idea, let's again assume the rule of thumb we used with the BFR.  That suggests the BFS might cost 14/9*7=$11 million.

Now, profit/development costs.  Much of the development cost has already been spent, with the development of the Raptor engine and the composite-fibre fuel/lox tanks.  But this still has to be redeemed from future launches.  Let's assume that the profit/development costs are 5 times the profit on the F9, or roughly $200 million.  That gives a total cost of about $260 million. That's for ONE use: if the BFR/BFS combo can be reused just 10 times, the cost per launch drops to $26 million.

Musk thinks the BFR can be reused 1000 times, the BFS 20 times.   But BFS reuse assumption is low because it's being used for Mars journeys, which means 2 years between journeys because Mars is only in opposition to Earth every 26 months.  If it's used for journeys to the International Space Station, the moon, and to launch SpaceX's fleet of satellites for its world-wide internet system, its reuse will be greater.  On the other hand, maybe it's just impossible to actually reuse spacecraft several times because the rigours of launch and re-entry are too great.  I've seen estimates of 12 reuses of stage 1, followed by a major refurbishment.  Refurbishment will however be expensive.  So let's ride with 10 reuses.  Even that will be enough to make the BFR/BFS combo ridiculously cheap.  And 12 reuses will cut the cost another 20 percent, 20 reuses by  50% more.

The cost of fuel is (relatively speaking) negligible in this context: $200K for a F9, so perhaps $1 million for the BFR. So the cost of each launch (with 10 reuses) would be $27 million. For a Mars trip, the BFS will have to be refuelled in space 7 times.  That suggests the total cost of the first Mars trip of $432 million -- $216 million each for one manned ship and one cargo ship, with 7 refuelling flights for both. Subsequent launches will require less cargo, because machinery will be manufactured on Mars using 3-D printing and local resources, so costs will fall sharply.  Each manned ship will be able to carry 100 passengers, so cost per passenger will be under $500K for the first few trips, much less thereafter. (This compares with $5 billion per person with NASA's current plans.)  However, Musk reckons the total cost per launch will be lower than the Falcon 1, which was $7.3 million in 2015 dollars. This is way lower than my estimates, which means he is assuming more reuses than I am--at least 30 or so.  However for the point to point rocket flights on Earth, to get the cost down to the price of a business class air ticket, you'd need to get 100 reuses.  Hmmm.

The key is reusability. If SpaceX delivers that, especially if they get even 100 reuses, the whole solar system opens up to manned exploration. People have consistently dismissed Musk's plans, with both Tesla and SpaceX. And he's achieved all his goals, though admittedly it's usually taken longer than he said ("Elon time"). Perhaps most significantly, where NASA, ULA, Ariane, Uncle Tom Cobley and all seriously doubted or even rubbished his efforts to make rockets reusable, he succeeded. The first few landings failed, right enough. But there have been 20 perfect landings in succession to date.

Musk has clearly dismissed any hope of finance from NASA.  SpaceX generates a "profit" of $41 million per launch of the F9.  That's $6.1 billion over the next 5 years with 30 launches a year (SpaceX will have half the market this year), enough for 26 BFR/BFS sets, assuming $200 million "profit" per set.  But of course, SpaceX will be selling the services of BFR when it is built, getting revenue that way.  When the BFR/BFS becomes the workhorse rocket within the firm, launching satellites and servicing the ISS, SpaceX will be making $20 million per launch.  And given the probable elasticity of demand for space services at much lower prices (remember the BFR/BFS will carry 150 tonnes to LEO compared to F9's 22.8 tonnes,  at a cost of $180K per tonne vs $2.7 million per tonne), there will likely be thousands of launches per year, not 60.   Development costs will be spread across far more launches.  Up until SpaceX slashed the cost of space launches, it cost $22,000 per kilogram, or $22 million per tonne to get stuff into orbit.

Why does all this matter?  

Well, there is already one spin-off.  Cheap satellite launches will make SpaceX's world-wide high-speed internet feasible.  In the past, the biggest component of satellite costs has been the launch.  A truly world-wide high speed internet, available in the middle of the Pacific, the Amazon jungle, the Sahara desert, Africa, outback Australia, etc, not just in wealthy cities in the West, will transform the world.   SpaceX envisages that you will need no more than a book-sized receiver on your roof to access internet speeds 180 times faster than they are on average in the world today. 

Another possible spin-off: to extract CO2 from the Martian atmosphere, SpaceX will need to develop its own machinery or use machines created by others. Just as they have with everything else, they'll cut costs and improve efficiency.  What works on Mars will likely work on Earth too.  This will be tremendously useful on Earth.

Probably, all the things we'll need to do to maintain life in our domes on Mars, and later on its surface, will have useful applications for Earth too.  NASA is responsible for a long list of useful inventions which are spin-offs of the space program.  Solar panels were first developed for use in satellites.  Now they will save the world by replacing fossil fuels.

The asteroid belt beyond Mars and near-Earth asteroids closer to Earth are a treasure trove of minerals, containing a planet's worth broken up into bite-sized chunks.  The BFR will make getting to the asteroid belt cost effective, and shipping minerals back will be cheap because the asteroids have hardly any gravity--a small push will send them on their way to Earth or Mars.  Mars will be a way station for miners in the asteroid belt, because it's much closer than Earth.  So they will likely also mine the asteroids for water and ammonium (for the nitrogen) for Mars, as well as minerals for the Earth.

When the mobile phone and the internet were invented, no one could foresee how they would revolutionise society, or how disruptive they would be to established industries.  Cheap space travel will change the world for ever.  We will start a colony on Mars, we will mine the asteroids, and the spin-offs from rapid technological advancement in space will change our lives here on Earth in ways no one can foresee.   That's if we don't blow ourselves to bits with nuclear war before that.  Or cause global temperatures to rise by more than 1.5 degrees C, which will lead to huge adaptation costs in low-lying cities as well as massive numbers of refugees. Or do something else stupid.  I live in hope.

[Update 21/1/18:  I found a news report where Musk costs the fairings alone at 6 million.  If you recast the equations so that the cost of stage 2 without fairings is 75% of the total cost before profit, the cost breakdown comes to something like this:-

Stage 1--$14 million
Stage 2--$4.6 million
Fairings--$6 million
Profit/Development cost--37.4.

So profit margin 60% not 66%.  The cost of the BFR/BFS doesn't shift much.]