Last time, we talked about Delta-V, the “distance” to go from one place to another in space. We also talked about the rocket equation, used to compute payload mass fraction, and specific impulse… Let’s try to play with these concepts to have a better understanding of them, and unserstand why in-space refueling is useful.

But first, what is in-space refueling? It’s like refueling a car, but with the cryogenic propellant of a rocket (the thing we throw backwards to accelerate).

It can be done in 3 ways :

1) With an orbital fuel depot : a space station that stores propellant, and wait for our rocket to fill it. Obviously, the depot needs to be along our trajectory, otherwise it is pointless 😅

2) With direct transfer from vehicle to vehicle, as proposed by SpaceX for the Starship. To achieve this, one needs to launch multiple vehicles in a short interval. A pretty big challenge!

3) Simply with a “gas station” on the surface of a celestial body, like the Moon or Mars… or Earth. Yep 😛 on Earth, near the launch pads, there is a big gas station to fill the rocket a few minutes before it departs.

Now that we know what refueling is, and where it can be done: why is it useful ?

The rocket equation tells us that the further we want to go* (Delta-V increases), the more initial mass is needed for the same final mass… growing exponentially! 😟

** it is a difference in terms of energy (acceleration), not an actual distance.*

Intuitively, we can understand the exponential shape: the fuel we use at the end also needs to be itself accelerated, because we carry it with us from the beginning. Therefore, we need more fuel, to push not only the payload, but also the fuel that we’ll use at the end. It’s a snowball effect.

Because it is not very convenient to build giant rockets, this relationship between initial and final mass limits either the Delta-V we can perform, or the mass of the payload we can carry.

It is also the reason why rockets sometimes have multiple stages (actually, each stage is a rocket that is the payload of the rocket below it): instead of transporting all the dry mass of the rocket all the way, after the fuel in the first stage is expended, we discard the first stage to decrease the dry mass.

Obviously, what is of our interest is the payload mass that we can carry to a given destination. So we should look at the equation in reverse. A rocket, once designed and built, has a given dry mass (its structure), and can contain a given maximum amount of propellant (its tanks). For a given rocket, the initial mass is therefore fixed. The further we go, the smaller the final mass – including payload – decreases.

For a rocket of 1500 tonnes (let’s dream big), a specific impulse of 380 seconds, a ratio between dry mass & propellant mass of 12.5% (1 tonne of structure for 8 tonnes of propellant), and a nominal mission Delta-V of 6000 m/s (enough for a one-way trip from LEO to Mars or the Moon)…

It gives us 1200 tonnes of propellant, 150 tonnes of structure, and 150 tonnes of payload. Weird of how it matches the first numbers SpaceX gave for its Starship. 😉

The chart looks like it:

How to read it ?

➡️ If we want to go to the Moon (6000 m/s), we can bring 150 tonnes of payload (vertical axis is marked every 100 tonnes).

➡️ With a propellant reserve full (1200 tonnes), if we want to do only 4000 m/s, we can bring 400 tonnes of payload.

Actually, the fairing volume probably won’t fit 400 tonnes (unless we assemble the payload in orbit, without fairing…), so it means we don’t need to fully fill the 1200 tonnes of propellant if we “only” bring 150 tonnes of payload (the maximum we could fit).

To know how much propellant is needed to transport 150 tonnes at 2000 m/s, we simply use the rocket equation:

- m0/mf = 1/exp(-
**DeltaV**/(9,81 ***ISP**)) = 1,71 - mf =
**150 (payload)**+**150 (dry mass)**= 300 tonnes - m0 = 1,71 * 300 = 513 tonnes
- m0 – mf =
**propellant mass**= 213 tonnes

*m0 = initial mass, mf = final mass, DeltaV = 2000, ISP = 380* 🤓

Let’s employ the same color scheme as last time. Here is how **dry mass** (constant, since it’s a 1 stage rocket), **payload** (max. 150 tons), and **propellant mass** (max. 1200 tonnes), changes vs. **Delta-V**.

After 6000 m/s of **Delta-V**, the rocket can’t hold enough **propellant **to continue sending 150 tonnes of **payload** all the way to destination. If we want to go further, we need to bring less **payload**. Beyond 8200 m/s, the **payload** is negative : these missions can’t be performed with this rocket. We would need to use multiple stages, or optimize the **dry mass**.

On this chart, the light-green part of **propellant mass** represents the part of the propellant that is used to accelerate the **payload**, while the dark-green part represents the **propellant mass** used to accelerate the vehicle’s **dry mass**.

What has this all to do with refueling? Well, looking at these graphs, we understand something: if we could cut the 6000 m/s trajectory into 3 pieces of 2000 m/s, refueling 213 tonnes each time, we would only need 213 * 3 = 639 tonnes of fuel total to bring our 150 tonnes of payload to destination (instead of 1,200 tonnes). We could also make a smaller rocket, because it would not need large tanks capable of holding 1,200 tonnes. It would be lighter (less dry mass), and that would be all the more payload that we could carry each time!

For missions to the surface of the Moon, 6000 m/s of Delta-V from low Earth orbit (LEO), there is a great place to stop on the way: the Lagrange point n°1 of the Earth-Moon system (EML1).

There is a point halfway between the Earth and the Moon where their gravities balance out. This region of equilibrium allows one to orbit around a point in space where there is nothing. 🤯

From this place, it is easy to go either to the Moon or to the Earth. The Delta-V to get there is pretty much like the Earth’s geostationary orbit (GEO), for which there are many launchers available. Existing launchers could therefore send payloads to EML1 with modest modifications.

If our spacecraft could refuel in EML1 on the way to the Moon, that would cut the 6000 m/s trajectory into two sections of 3800 m/s and 2500 m/s. The total is a bit larger (6300 m/s instead of 6000 m/s) because there are additional maneuvers compared to a direct path, but this has the advantage of “resetting the exponential” of the rocket equation. 👍

A total of 531 + 287 = **818 tonnes of propellant **are required to make the trip and bring **150 tonnes of payload** to destination, instead of 1200 tonnes.

This is why it is interesting to transfer fuel from vehicle to vehicle, or to build fuel depots in LEO, in lunar orbit, or elsewhere like in EML1.

Planetary bases producing fuel from local resources on the Moon and on Mars follow the same logic, because they allow to “reset the exponential” between the outward trip and the return trip.

The Starship’s mission architecture makes it “too big” for many uses, its fuel tanks will not be filled to the max all the time. Its transport capacity of over 100 tonnes makes it a vehicle for colonization and massive transport. It is both a reusable “second stage” and a lander. SpaceX relies on its assembly line production methods and on reuse to achieve (very) low transport costs, and be able to fly their vehicle without using it to the maximum without profit losses. It will be oversized for a lot of uses, but if it’s cheaper, does it matter?

It has nothing to do with the way we design rockets today, because we optimize everything to the maximum. However, this is not the case with planes or cars, which often travel partially empty.

In any case, the Starship is a vehicle that is made for Mars, sized to return from Mars without needing a first stage there. So that leaves room for competitors who would make vehicles optimized for other segments, for example LEO-Moon trips, or LEO-EML1, or EML1-Moon, … etc!

To end this article, one last important point.

You may have already understood it, but the earlier you refuel a rocket in its trajectory, and the more often you refuel, the better.

Low Earth orbit (LEO) is already 9500 m/s away from sea level… And it’s impossible to stop before without falling! That’s why it’s the best place to make a fuel depot or refuel from vehicle to vehicle. If we can do other depots further, that’s better, but having one in LEO would change everything already.

Most of the mass we send into orbit is fuel. If we had a LEO fuel depot, rockets could carry more payload, further.

A fuel depot would make launch mass to LEO fungible. This means that we could more easily exchange one tonne to LEO for another. We could launch the payload on one flight, and the fuel to propel it further on another. There could be missions without payload, only intended to refuel the depot, and missions with a large payload, without fuel but which plan to refuel at the depot. It would promote wholesale prices and big launchers (big rockets are more mass efficient). Competition would further reduce the costs of access to space. Fuel is fuel, no matter who launches it, so that would also facilitate international cooperation.

But most importantly: we could do ambitious missions with middle class launchers. No need for mega-rockets. This means that countries of modest size could do it too, and not just the superpowers.

Ariane 6 has a second stage (ULPM) much larger than Ariane 5 (ESC-A): it can contain 31 tonnes of fuel, compared to 14 tonnes for that of Ariane 5. It is particularly synergistic with a LEO depot, because if we could refuel the 31 tonnes of fuel in the upper stage of Ariane 6, we could send around **27 tonnes in TLI** (intersection trajectory with the Moon), instead of 8.5 tonnes planned today.

It’s as much as the SLS block 1 mega-rocket with which the Americans are launching their Artemis program. We don’t have launchers like that in Europe, because we don’t have 15 billion € to invest in them. With refueling, you don’t need to invest that much!

It is also an additional step towards reuse, another vector for reducing costs. If you can refuel a rocket, why throw it away every time? Once empty, we refuel, and off we go for another mission! Once this technology is developed, I think we’ll see a lot more reusable second stages using technologies like IVF from ULA , and even second stages converted to landers like the XEUS .

Refueling will have a gigantic impact on the way we design and use spacecrafts, so even if today it is a technology that is still in development, when we consider sustainable development of space capabilities, it is with this paradigm that we must think. Planning today for systems that can adapt to this change, such as the Ariane 6 rocket and its large second stage, is the way to go!