Humans like to reason by analogy. It’s a powerful problem solving technique because so much of our experience generalizes, while first-principles thinking is computationally costly. In space, however, thinking by analogy is almost always wrong, because our terrestrial experience shares so little with the realities of space travel.
One concrete example of this is our intuition around fuel. Humans need to eat to stay alive, and similarly we charge our devices and fuel our cars. All of them can perform their essential duties with a well-contained, discrete battery or fuel tank.
Rockets, on the other hand, are little BUT fuel tank, and it’s important to understand why. Going to orbit involves more than flying beyond the atmosphere, which while difficult is comparatively easy. Going to orbit involves going fast! Roughly 7.8 km/s, or 17,000 mph. These numbers are so huge it’s difficult to imagine how to go that fast.
Rockets work by throwing mass out the back, as fast as possible. A really good rocket engine can eject hypersonic exhaust gas at more than 10 times the speed of sound, which seems fast enough for anything. On the other hand, orbital velocity is more like 25 times the speed of sound. This means that a rocket entering orbit is throwing exhaust products behind it literally as fast as chemistry and physics allows, and yet that gas is still travelling forwards faster than its ejection speed.
The exhaust results from burning fuel, and the fuel that’s ejected has to also be accelerated to these great speeds. This is similar to the effect that fuel mass has on the efficiency of long haul jets, but much much worse. In a jet, the aircraft has to carry passengers, cargo, and the fuel it needs to land for the whole journey. In a rocket, the vehicle also has to carry the oxidizer and the speeds involved are much, much greater.
As a result, the final velocity of the rocket increases only logarithmically with the ratio of fuel mass to everything else, a brain-melting problem often called the “Tyranny of the rocket equation.”
Δv = v_e log(Mi/Mf),
where Δv is the change in velocity, v_e is the exhaust velocity, Mi is the initial mass, and Mf is the final mass. Astronaut Don Pettit has a nice summary of these issues.
In space travel, Δv is everything, and it determines how much fuel is needed to go from place to place, as summarized in this handy chart:
In addition to the absurd 9.3km/s necessary to reach Earth orbit, most other destinations are a reasonable fraction of any achievable exhaust velocity. As a result, mission design is primarily about figuring out how big the fuel tank is and where to put it.
This horrible state of affairs means that it’s basically impossible to get to orbit, let alone deep space, using conventional engineering. In other words, all rocket scientists need to employ at least one crazy idea if they want to get there. The problem with crazy ideas is that it’s hard to tell which ones are almost practical.
As an example, many rocket scientists will reach for hydrogen and oxygen as a high performance fuel, even though hydrogen’s low density and hard cryo temperature mean that the mass fraction of the rocket takes significant penalties. The Space Shuttle is another example of where following wild ideas can lead. SpaceX instead employed lithium/aluminium alloys, materials that are extremely light and almost impossible to weld. There are no easy options – all options involve a great deal of difficulty, and many turn out to be impossible.
At the end of all this, a really good rocket is able to deliver about 4% of its launch mass to orbit. Everything else is structure, engines, and fuel. This is why rockets are really nothing like cars and bicycles and planes.
So it is that, faced with the impossibility of the problem, creative scientists and engineers will face temptation to veer off into wild hypotheticals. Many of the subjects of this blog series deal with the relative impracticality of some of these ideas.
The subject of this blog, after a this fairly sizable preamble, is refueling depots.
The idea behind refueling depots can begin with an analogy to gas stations. Most launch vehicles arrive in LEO with both cargo, such as a satellite, and an empty upper stage. If that stage could be refueled like a car, it would have enough Δv to go almost anywhere in the solar system.
Yes, you read that right. A close examination of the chart above shows that while getting from the surface of the Earth to LEO requires about 9.3km/s of Δv, LEO to the Moon, Mars, or Jupiter requires only about another 3-5km/s of Δv. Since the upper stage of most rockets delivers just over half of the orbital Δv, if refueled they would be able to send missions all over the place.
This fact has been appreciated for a very long time. Indeed, the science fiction author Robert Heinlein said it best when he said “If you can get your ship into orbit, you’re halfway to anywhere.”
Under the status quo, these perfectly good rocket stages are discarded, wasted, and either left to rot in orbit or burned up in Earth’s atmosphere. If a refueling capability existed, existing rockets could also launch larger payloads, or existing deep space payloads could be launched on smaller rockets.
As it happens, I believe that miniaturization and modularity are not sustainable ways to save money on large-scale space projects, a concept embodied in SpaceX’s outsized Starship vehicle. But it turns out that there are bigger weaknesses with the fuel depot concept.
The fundamental problem with refueling from a depot is that, in space, the cost of fuel is not determined by volume or weight, but by location. It’s not possible to economize on fuel by making a hybrid Prius rocket and driving it more slowly, at least not in any conventional sense. Fuel needs to be in the right tank at the right time in the right quantity, and never for very long before it’s used.
The obvious place for a fuel depot is in LEO. Fuel depots further out, such as near or on the moon, have much less benefit. Launch to LEO is the hardest leg, so it makes sense to refuel at each end.
In more detail, when we think of space we think of the night sky overhead, with satellites zooming around. What this disguises, and was ignored in the film Gravity, is that even a set of orbits as restricted as LEO is not one place. In practice, getting from one orbit to another can require more fuel than launching from Earth to that orbit in the first place.
Most orbital vehicles, such as Soyuz, Dragon, or the Shuttle, have 200-500m/s of Δv for orbital maneuvering. Typically, this fuel is used to correct imperfections of the launch, approach and dock with the space station, and then de-orbit.
As players of Kerbal Space Program will know, 500m/s is plenty of Δv to tweak the relative orbital phase, eccentricity, and semi-major axis. It is, however, vastly inadequate to change the inclination or the longitude of the ascending node, which are two other Keplerian orbital elements. Indeed, if we break up all LEO orbits into inaccessible adjacent slots accessible within a 500m/s window, there are about 200 distinct inclinations, and 200 distinct longitudes of ascending node, for about 40,000 discrete orbits.
If orbital refueling was standard practice for every launch, then we’d need to build (and keep supplied) on order 40,000 separate depots. This is obviously impractical, since the cost of building and operating even one is probably more expensive than continuing to manage without them.
In practice, we have to select just a handful of these orbits, just as the ISS needed a discrete orbit. Various considerations can be employed to select these orbits. For example, the ISS, which can be thought of as an orbital depot of people and fatigued aluminium rather than fuel, was placed in an orbit that was accessible for the launch sites and vehicles of the contributing countries.
An ISS-like orbit is a natural choice for a fuel depot, but it would only be useful for a subset of deep space launches. If the depot’s orbital plane doesn’t align with the destination during the relevant launch window, that’s just tough. For the moon, this would mean being able to launch only two or three days per month. For Mars, a dedicated depot would be required for each launch window. There are orbits whose orbital plane precesses in as little as two months, enabling alignment during any launch window, but for only a few days in that time. It is also possible to reduce fuel requirements by changing planes during an extended series of departure burns, but even this strategy requires around 1km/s of Δv.
Additionally, a high inclination orbit like the ISS is designed to be accessible for launches from Baikonur,. This increases the inefficiency of launches from any other launch site, which inflates the operational cost of keeping it fueled.
Some proponents believe that the depot could be topped up by salvaging the dregs of conventional launches. All rockets carry slightly more fuel than they need to to ensure margin for orbital insertion. What little is left over, if it happened to be in the same orbit, could be transferred to a depot for storage and later dispensing. Although such fuel would be “free” as salvage, it’s unclear how enough fuel could be salvaged from a huge variety of launch orbits to meet any kind of demand. If fuel margin on launch is 2%, then the depot would need at least 50 successful salvage operations in close succession to be able to refuel even one additional stage.
Operationally, depot management is complicated by a boom-bust cycle of use. For regular gas stations, usage is relatively steady and predictable, while the cost of unsold fuel lurking in an underground tank for a week or two is relatively negligible. Deep space launches occur infrequently and have differing quantities of use and even propellants. In a future where human flight to LEO or the Moon is ramping up, a depot would have to constantly grow to meet demand, which is a nontrivial requirement. Storing cryogenic fuels for long periods in space is difficult because they heat up and boil off, not least because the Earth is radiating significant heat into the LEO space region.
In practice, an impending deep space launch that required depot refueling would require the depot to be refueled “just in time” by a series of accessory launches, all of which would involve a partly-empty upper stage docking and transferring fuel, only to transfer that fuel back to the probe-carrying upper stage. Given the inefficiencies and losses of doing so, it is much easier to dock the fuel-carrying upper stage(s) with the payload, and perform the requisite injection burn directly. Same outcome, reduced complexity, greatly reduced overhead.
There is a broad exception to the above considerations; a case in which propellant transfer in LEO does make sense. In the SpaceX Starship concept, a fully reusable Starship is refilled by a series of launches while in LEO, before continuing its journey. This is a different model to an orbital fuel depot, though conceivably a Starship could be permanently parked in some orbit as a depot if there was a good enough reason. Orbital refilling is more like the in-flight refueling of a fighter jet than the establishment of a chain of gas stations.
The Starship concept reflects a different line of reasoning. Rather than compensate for a vehicle with a small Δv with a series of gas stations, build a vehicle with a huge Δv and, by refilling in LEO, enable it to fly enormous distances with no further support. Indeed, unlike conventional three stage Lunar lander schemes capable of transporting at most a couple of tonnes of cargo, the Starship is able to refuel in LEO, deliver hundreds of tonnes of cargo to the Moon, and fly all the way back to Earth in a single stage, reusable format. This is more like cargo flights to remote bases and islands that do not refuel after landing.
This graph shows the cargo capacity of Starship to deliver or return cargo from the Moon, depending on where it’s refilled and how low the dry mass ends up being. It can fly similar quantities of cargo to Mars, but must be refueled there by a local propellant factory.
In summary, reasoning by analogy in space almost never works. Be wary of glib assertions that future cis-Lunar industry will employ orbital fuel depots filled by Lunar water and staffed by self-replicating robots. The natural place to fuel rockets is at their launch pad!