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Transporting things in space

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December 21st, 2015. The SpaceX Falcon 9 rocket hurls 11 ORBCOMM satellites into orbit. It is a cornerstone moment of space transportation history, because it is the first time an orbital booster lands back. It opens a way towards a future where we are not disposing rockets after using them, and where they become a mean of transportation like any other. It is this launch that made me realize we lived at an important moment for humanity – the moment where we gain access to new continents beyond our atmosphere. It is this moment that decided me to change career to work in the space industry, after 3 years of software development in another sector. This long exposure photo shows the take-off flame track (left) and the landing (right). Without exagerating, even if the benefits of reusable rockets are still to prove today, because we have not yet tamed the complex engineering to routinely craft them, future generations in a thousand years living everywhere in the solar system will wonder why we waited so long to improve our knowledge of making them. Since this event, other companies looked into reusing their rockets, like Rocket Lab (US/NZ) or Linkspace (China), to cite only 2. Organizations around the world accelerated their research program on this subject. In France, for instance, there is a plan to develop reusable launchers with the Callisto -> Themis -> Ariane Next programs, where the CNES, DLR, JAXA, ESA, and Ariane Group are collaborating. Skeptics are still around, but the revolution has started.

Space is very different from what we experience daily, so a bit of introduction is probably needed. If you already studied aerospace, this post will contain stuff you already know. But it will allow everyone to catch up, and we’ll have a reference to link when talking about space transportation concepts on this blog.

Cars move by rotating their wheels: that creates friction against the ground, and that makes them go forward. Boats and planes with propellers work a bit similarly, except they don’t push against the ground but against the surrounding fluid (water, air). Planes with reaction engines and rocket engines work differently: they throw something backward (hot gas), and that makes them go forward. The more mass and the faster we eject reaction mass, the more the spacecraft accelerates.

Specific impulse

To measure how fast mass is ejected we use the “specific impulse” (Isp) metric. It gives you how efficient an engine is, like “liters per 100km” for cars. The bigger the specific impulse, the more you can accelerate with a given amount of fuel. Without going into equations, keep in mind that a higher Isp is often better, because we want to minimize the mass of the propellant (because it also has a mass we have to move with us).

Delta-V

There are two kind of distances in space. Sort of… At least, that’s how I like to think of it.

The first kind distance is obvious: it is how much physical space separates two things. For instance, the Moon is at 384,000km from the Earth. This physical distance is important because it gives you a clue about how much time it will take to reach something. Space is big so even if we go really fast, the distances are so large that it can take months (years!) to reach a desired target.

But there is another kind of “distance”, and it is the most relevant when transporting things in space. The ISS’s orbit is 400km above our heads, yet it is much more difficult to go there than to go from Toulouse to Paris (a 600km trip). This is because the ISS is moving very fast: more than 7500m/s (22 times the speed of sound)! The difference of velocity (Delta-V, DV) measures how much one needs to accelerate to go as fast as the target. Once you go as fast as your target (and in the same direction), your relative motion is 0, so you see your target fixed, and you can interact with it. Like when you are chatting with your friend during a jog session: you are both moving, but in the same direction, so you can talk even though you are moving.

There is a chart I love that maps the Delta-V between bodies of the solar system:

Solar system Delta-V map (open in large).

For our purposes on this blog, that will be mostly about the Earth, Moon, Mars, and Near-Earth Asteroids, this chart provides more details:

Delta-V map in cislunar space and Mars.

There are more exotic ways to move around, but we’ll see that in due time!

Dry mass

Conceptually, a rocket is made of 3 parts:

  1. The payload: that’s the useful thing you want to transport (satellites, humans in a pressurized module, …).
  2. The propellant: that is the thing you want to throw backwards in order to accelerate.
  3. The dry mass
Be prepared, I’m an expert graphic designer.

What we call dry mass is the rocket’s parts that are not useful and that we can’t throw backwards. Dry mass is bad but it is needed: the rocket structure, the propellant tanks, the engine and nozzle, the on-board computers, …

Certain fuel combinations have a high specific impulse, like LOX/LH2 (liquid oxygen & hydrogen), but require big tanks and insulation because they need to be stored very cold (hydrogen evaporates at -253°C). There is no magic formula for designing a rocket: some have better Isp but higher dry mass, others have lower dry mass but need to carry more fuel because their fuel has a lower Isp, like LOX/CH4 (liquid oxygen & methane – methane evaporates at -161°C).

By the way, notice we must carry the oxygen to burn the fuel, because there is no oxygen in space, unlike planes that burn kerosene with ambient air. If you’re wondering how we can keep propellant so cold for so long, consider this: there are boats carrying liquid natural gas (that is essentially methane) sailing for multiple weeks!

It even has it written on it: “Liquid Natural Gas”.

Useful mass (payload)

Let’s say you have a rocket. You know where you want to go (the Delta-V), how efficient your engine is (the Isp), and the dry mass of your rocket. How much payload can you take with you? This is what the rocket equation is about. It relates the initial mass (payload + dry mass + propellant mass) to the final mass (payload + dry mass, no more propellant), using the Delta-V and Isp.

“ve” – exhaust velocity – is specific impulse times a constant, so I didn’t lie to you. We already see a logarithm, that will be the most complicated math tool we’ll need to use here.

Imagine you have a rocket of 100 tons. The rocket equation is exponential, so if you want to accelerate 1000m/s, maybe you can carry 70 tons of payload. But if you want to accelerate 7000m/s, you can only carry 6 tons of payload.

The payload mass fraction when launching from Earth to LEO (Low Earth Orbit) is around 1/30th (it changes for every rocket). That means, to put 100 tons in LEO, you need a 3000t rocket on the ground.

This is why rockets are so big (it’s hard to realize when only watching videos). A French high-speed train locomotive weights around 400 tons. Can you imagine how much mass needs to be thrown backwards in order to move?

This Saturn V rocket exhausts a gas mass equivalent to multiple elephants per second.

This notion of payload mass fraction is important to study the space economy: depending on where a resource is produced and where it is demanded, there can be big differences in price. Most of the cost of something is due to its transportation.

Aerobraking

Such a sophisticated word, I love it.

Having 100% of payload mass fraction is theoretically impossible, but we can get close. It would mean that the payload is alone, that there is no rocket attached to it. Concepts like “catapults” have been proposed, where a rail or sling system launches the payload towards its destination, where it is catched. We’ll have to talk about this futuristic possibility in a dedicated blog post, because that would change a lot of things.

Two examples of aerobraking, more or less intense.

For trajectories arriving at Earth or Mars (or anywhere with an atmosphere – not the Moon), we can use aerobraking to lose some speed. That reduces the Delta-V performed with engines, so it improves the payload mass fraction (it goes up). The spacecraft hits the thin upper atmosphere, which creates friction, like a parachute, but less intense.

This process converts some kinetic energy (speed) into thermal energy (heat): the spacecraft slows down but heats up. The more extreme example of aerobraking is for Earth-return capsules: they are not equipped with rocket engines and are only based on thermal protection shielding and parachutes to slow down. It’s obviously a trick that can only work one-way. In practice it requires a bit of additional mass for structure & thermal handling. It also takes a lot of time, because we want only a bit of friction on every orbit to not stress the spacecraft too much.

As an example, ESA’s TGO mission aerobraking saved around 1km/s of Delta-V and took about a year.

4 replies on “Transporting things in space”

Thanks for the good summary. It was easy to read and understand with smooth chronology.

Maybe topic for the next post could be wider explanation of rocket equation? I would like to read your take.

In the rocket equation comment section, it says, exhaust speed is Isp times “constant”. This constant is g0 for Earth(according to wiki).

Lets consider, that we have engine w. vacuum optimized nozzle.
In Low Earth Orbit we should be fine with g0.

However, I struggle with:
1) Does that mean that the rocket equation will deliver different values for Low Lunar Orbit with different g?

2) How about the deep space? Is there even space with literally zero gravity? I assume very small g is everywhere, but still it will destroy the exhaust speed to multiply with very small number.

Can you help me to understand this relationship better?

Thanks

PS: Another topic, probably more into astrophysics. Description of gravity, how far can it reach, how strong, how to calculate and think about it, etc.

Hi Lex,

Thanks for the suggestions, I’m planning on writing articles related to the Moon right now, but since this post was pretty popular, I may do another one, and your ideas are welcome 😊

1) It’s pretty confusing to use a specific impulse in “seconds”, honestly it got me a bit of time to wrap my head around that…

The exhaust velocity of your engine does not change, wherever you are (low gravity, high gravity…). It’s the pressure of the combustion chamber and the shape of the nozzle that determine it.

Here is how I picture the specific impulse expressed in seconds: if you have 1 ton of propellant, how long can you keep burning it to hold a 1 ton rocket above the ground (neither going up, neither falling), with Earth’s gravity (g0) ? In this case, your rocket would have 1 ton of thrust (when we talk about *weight unit* thrust, it’s also assuming standard gravity). The faster your exhaust it, the less you need to use per second, so the more time you will be able to levitate (= higher isp). When you are doing this, you are accelerating 1 ton upwards with your engine by 9.81 m/s², but the Earth’s gravity accelerates you downwards by 9.81 m/s² too, so you’re stationary. The specific impulse is how much time you will be able to levitate, here on Earth under standard gravity.

If you were in a lower gravity, like on the Moon, your 1 ton thrust engine would work the same way, accelerating upwards by 9,81 m/s² but the gravity pull would only be 1.62 m/s². You would go up. The engine would be the same, with the same exhaust velocity. It’s just that we conventionally chose to represent the “seconds of levitation capability” as relative to Earth’s gravity.

2) There is indeed gravity everywhere, in fact you’re feeling my gravitational pull right now lol, it’s just very small. Gravity is a product of the mass of 2 bodies divided by the distance squared, so the further you go from massive bodies, the less you feel gravity, but it’s everywhere. It’s not so much of an issue in space except when you take off, because your acceleration vector is often perpendicular to the biggest gravitational pull, so the “cosine loss” is zero. In orbit, for most maneuvers you’re either pushing forward or backward of your speed vector (prograde or retrograde). It’s pretty counterintuitive and would make an interesting blog post !

Hope this helps…

Thanks, it cleared some misconceptions of mine.

I will gladly digest through that next blogpost too, in time.

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