SpaceX and NASA did something awesome over the weekend. They successfully launched two astronauts, Bob and Doug — cue Canadian humor clip — to the ISS on the SpaceX Crew Dragon from American soil. This is the first time since July 8th, 2011, when the last Shuttle launch occurred.
This led me to dust off some old calculations I’d done around powering the Shuttle entirely with renewable energy. At the time, I figured that we could turn water into rocket fuel sufficient for a Shuttle launch using a month’s wind power from a small wind farm at a cost of about $285,000, a bit more than market prices but a drop in the bucket compared to the $450 million to $1.5 billion per Space Shuttle launch.
How does that work out? Let’s start with what most rocket propellant is.
“LOX and liquid hydrogen, used in the Space Shuttle orbiter, the Centaur upper stage of the Atlas V, Saturn V upper stages, the newer Delta IV rocket, the H-IIA rocket, and most stages of the European Ariane 5 rocket.”
LOX is not something you eat with bagels and cream cheese, but liquid oxygen.
So, basically one form of rocket fuel is oxygen and hydrogen. And one of the most common chemical compounds around is H2O, or two hydrogen and one oxygen bound together to form water, which is about as non-combustible as things get. It’s so non-combustible that it’s the most common mechanism used for putting out fires.
Okay, so far, so good. We have water which contains only the two things we need to make rocket fuel. But what about getting at it? Could we do that with renewable energy?
Absolutely, it turns out. Turning water into hydrogen and oxygen gases is done by a process called electrolysis, which unsurprisingly uses electricity. And it’s easy and cheap to make lots of electricity with wind and solar energy, that’s why they are the fastest growing sources of energy globally, with China, for example, having put in almost as much solar energy in the first three months of 2015 [guess when I wrote this Quora answer originally] as exists in the US, and China’s wind power at 115 GW now has more nameplate capacity than all of the US’ nuclear plants and is expected to reach 200 GW by 2020. Then more electricity is required to supercool the hydrogen and oxygen into liquids.
So we can get sufficient electricity and we can use it to turn water into rocket fuel. And hey, when we burn them shoving rockets into space we get water back. That sounds pretty good!
So what’s the kicker? Well, rockets use a lot of fuel. For this, I’ll just turn to the space expert and NASA engineer, Robert Frost, and his detailed assessment of the number of pounds of rocket fuel necessary to propel a pound of mass in Earth’s orbit from sea level.
“So, if our imaginary rocket with a final mass of 1 kg started off at 10.39 kg, then 90.3% of the mass of the rocket was propellant. Our rule of thumb was pretty darn close.”
Even that is a bit of an understatement, because a lot of stuff you throw into orbit is just there to contain the actually useful payload, whether that’s a military stealth satellite that can catch people cheating on their taxes or an astronaut who does a rocking version of Bowie’s Space Oddity.
Let’s look at the Space Shuttle for a nostalgic and mildly sad example.
“The Space Shuttle weighed 165,000 pounds empty. Its external tank weighed 78,100 pounds empty and its two solid rocket boosters weighed 185,000 pounds empty each. Each solid rocket booster held 1.1 million pounds of fuel. The external tank held 143,000 gallons of liquid oxygen (1,359,000 pounds) and 383,000 gallons of liquid hydrogen (226,000 pounds). The fuel weighed almost 20 times more than the Shuttle. At launch, the Shuttle, external tank, solid rocket boosters and all the fuel combined had a total weight of 4.4 million pounds. The Shuttle could also carry a 65,000 [sic] payload.”
That’s about 24 pounds of fuel for each pound of payload. That’s not quite the 90% that the rule of thumb talks about, but good enough.
So how much electricity would it take to put a loaded shuttle into orbit? Let’s start with how much hydrogen and oxygen a kWh of electricity could create from water:
“1 kilowatt hour of electricity can split about 270 grams of water and produce about 350 liters of hydrogen and 175 liters of oxygen.”
Making LOX and liquid hydrogen doesn’t change the mass of the elements, so 270 grams of water could be divided into the total mass of fuel and you’d get an approximation, but it wouldn’t be accurate. Let’s look at the mass of hydrogen and hydrogen separately:
“1 litre of water weighs 1 kilo and when electrolysed will produce hydrogen and oxygen as described by the following equation:
2 H2O(l) → 2 H2(g) + O2(g)
in atomic weight terms 36.0012kg of water with give 4.0032kg of hydrogen and 31.998kg of oxygen
So a single kilo you will get 4.0032/36.0012 or 111.19gm of hydrogen and 31.998/36.0012 or 888.81gm of oxygen”
So we need 617,727 kilos of LOX and 102,727 kilos of liquid hydrogen. The mass doesn’t change when you change state, it just gets a lot denser. That means that we would need about 925,471 liters of water to get the necessary hydrogen, and only 695,639 liters for the oxygen. As such, we can limit ourselves to the amount needed for hydrogen and we’ll have some left over oxygen to get high on.
Because we know a kWh can electrolyze 270 grams of water, we can do some simple math and voila, we can see that we need 3.427 GWh of electricity to produce sufficient LOX and hydrogen.
Is that a feasible amount of electricity to produce with renewables? Absolutely. It would only take about a month for a 13.6 MW renewable source with a capacity factor of 35% to generate that much electricity. That’s a wind farm of maybe 8 turbines.
But that’s to produce these gases at room temperature. We need the gases turned into liquids, which means spending even more electricity to cool and compress them. Oddly, that information isn’t easy to find, mostly because it’s a complex calculation which is process dependent — different combinations of compression and cooling in different environments will have significantly different results –, but we can make some approximations. Let’s start with liquid oxygen.
“Liquid oxygen has a density of 1.141 g/cm3 (1.141 kg/L or 1141 kg/m3) and is cryogenic with a freezing point of 54.36 K (−361.82 °F, −218.79 °C) and a boiling point of 90.19 K (−297.33 °F, −182.96 °C) at 101.325 kPa (760 mmHg).”
Then let’s look at liquid hydrogen.
“To exist as a liquid, H2 must be cooled below hydrogen’s critical point of 33 K. However, for hydrogen to be in a full liquid state without boiling at atmospheric pressure, it needs to be cooled to 20.28 K (−423.17 °F/−252.87°C).”
So we have to cool 617,727 kilos of oxygen to 90.19 K from about 295 K, and 102,727 kilos of hydrogen to 33 K from about 295 K. Specific heat is the energy required to raise one kilogram of a material one degree Kelvin. It changes depending on the degree of compression and the temperature, but we can make an approximation by picking a point partway down. For oxygen we’ll use a specific heat of 0.910 kJ/kg.K at 175 K. For hydrogen we’ll use a specific heat of 13.12 kJ/kg.K at 175 K. Note that it takes 14 times more energy to cool (or heat) hydrogen than oxygen. That means it will take in the range of 115,000,000 kJ to liquify the oxygen and 350,000,000 kJ to liquify the hydrogen.
Of course, as everyone with access to Google knows, a kiloJoule is equivalent to 0.000277778 of a KWH, so it will take about another 130 MWH to liquify the gases.
So is it economical? Well, 3.567 GWH of electricity at 8 cents per KWH is about $285,000 worth of electricity. That doesn’t seem out of line, especially given the average cost of launching the shuttle was $450 million and if you actually amortized development the cost was about $1.5 billion per launch. And according to one source, buying the LOX and liquid hydrogen at market prices would cost around $200,000, which is in the ballpark.
This of course ignores the solid fuel rockets also used in Shuttle launches. Of course, the wind farm electricity is only useful for launches from ground to space, as there is no moving atmosphere to speak of in space. Replace the wind energy with solar energy and the river or lake water with comets or Martian/Lunar polar ice, and the result is a lot of rocket propellant ready to be made in the solar system.