# Rockets, Planes, and Space

Rockets. There are not many things more awesome than watching a rocket engine ignite and propel an object to ludicrous speed.

Today’s xkcd What If? about putting stuff in space is very interesting:

But getting to space is easy. The problem is staying there.

Gravity in low Earth orbit is almost as strong as gravity on the surface. The Space Station hasn’t escaped Earth’s gravity at all; it’s experiencing about 90% the pull that we feel on the surface.

To avoid falling back into the atmosphere, you have to go sideways really, really fast.

The speed you need to stay in orbit is about 8 kilometers per second.

Inspired, I started wondering: What would take to put my Raspberry Pi and its camera in low earth orbit?

What I found was pretty cool.

## Getting to Orbit

Getting a Raspberry Pi to the edge of space takes little more than a nicely sized weather balloon (and a parachute, assuming you ever want to see it again). But getting to that magic 8 km/s is a game played on a completely different field.

Most terrestrial rocket systems use some kind of “rocket fuel” made from refined petroleum. Petroleum fuels generally have a specific energy of around 45 megajoules (MJ) / kilogram (kg) — that means we get 45 MJ of energy from burning 1 kg of gasoline.

Of course, not all that energy is converted into propulsion: some of it is lost as heat, some of it goes into propelling the exhaust backwards.

A good rocket engine converts about 70% of the fuel’s energy into usable thrust. From burning 1 kilogram of rocket fuel, we end up with about 31.5 MJ of usable energy.

Above the atmosphere, we need to carry our own Oxygen to burn fuel. RP-1, the rocket fuel used in the early Saturn V rockets (and also more recently in SpaceX’s Falcon 9), needs 2.56 kg of Oxygen per kg of fuel, so our 1kg of “rocket fuel” is really just 0.28 kg of RP-1 and 0.72 kg of Oxygen.

That leaves us with just 8.8 MJ of usable energy.

A 1 kg mass traveling at 8 km/s has 32 MJ of energy. (Yes, this means that 1 kg of our “rocket fuel” has less useful energy in it than is necessary to get a 1 kg mass to orbital speed. No, this isn’t a deal-breaker.)

Some of that energy is wasted on the exhaust particles, but we can use the conservation of momentum and energy in our “rocket + exhaust” system to figure out how much speed our payload gets from the burnt fuel.

We can use basic physics to get a sense for the minimum amount of fuel we’d need to burn:

Eexhaust = 1/2 vexhaust2 · mexhaust
Erocket = 1/2 vrocket2 · mrocket
Eexhaust + Erocket = 8.8 MJ/kg · mexhaust

pexhaust = vexhaust · mexhaust
procket = vrocket · mrocket
pexhaust + procket = 0

${v}_{\mathrm{rocket}}=\sqrt{\frac{8.8\mathrm{MJ/kg}·{m}_{\mathrm{exhaust}}}{\frac{1}{2}·{m}_{\mathrm{rocket}}·\left(1+\frac{{m}_{\mathrm{rocket}}}{{m}_{\mathrm{exhaust}}}\right)}}$

mexhaust = mrocket = 1kg   ➝   vrocket = 3 km/s.

The reality is much more complicated, of course, but even in the ideal scenario assumed above, 1 kg of rocket fuel gets us less than half the speed we need.

The solution is not as simple as tripling the fuel — the first kilgram of fuel burned doesn’t just accelerate the payload, it also accelerates the remaining fuel! Our rocket needs to carry at least 4.5 kg of rocket fuel to get a 1 kg payload to orbital speed. No wonder rockets look like they’re 80% fuel tanks.

## Flying

I won’t be launching a Raspberry Pi into orbit anytime soon, but it turns out flying a plane with one is much easier.

Instead of rocket fuel, today’s RC planes and drones are often powered by Lithium Polymer batteries. Those have a specific energy of 0.72 MJ/kg — less than 2% as much energy per kilogram as rocket fuel. (At least they’re rechargable.)

And unlike rockets, planes don’t require more fuel than cargo; flying a plane through the air requires much, much less energy than putting something in orbit. 100 grams’ worth of battery can power a 500 gram plane in regular controlled flight for nearly 30 minutes.

Crazy to think that only 54 years passed between the first powered flight (the Wright Flyer, 1903) and the first successful launch of a man-made satellite into orbit (Sputnik, 1957).