100 g to LEO

[cicatrix]

Imagine I want to launch a 100 g payload to LEO from my backyard.

Provided I only use commercially available parts and materials, how big (or how small) my rocket should be?

[Streetwind]

To my knowledge, no hobby rocket, even with zero payload, has ever reached orbit. A cursory Google search reveals a current amateur rocketry altitude record of 116km for a ~7 meter tall solid fuel rocket. That is above the Karman line, making it officially "in space", but unfortunately being "in space" is not in any way, shape or form comparable to being "in orbit". The latter is orders of magnitude more difficult to do; you need to accelerate to Mach freaking 25.

[cicatrix]

I know nobody made it to orbit. I just want to estimate the minimum size/mass needed for that.

[Frozen_Heart]

To my knowledge, no hobby rocket, even with zero payload, has ever reached orbit. A cursory Google search reveals a current amateur rocketry altitude record of 116km for a ~7 meter tall solid fuel rocket. That is above the Karman line, making it officially "in space", but unfortunately being "in space" is not in any way, shape or form comparable to being "in orbit". The latter is orders of magnitude more difficult to do; you need to accelerate to Mach freaking 25.

Did it have a second stage? As that could have helped.

[Streetwind]

I know nobody made it to orbit. I just want to estimate the minimum size/mass needed for that.

I have no idea where to begin estimating such a thing... but it depends strongly on your choice of materials and fuel. And you're going to need at least two stages, better three. You can't do single stage to orbit with the low quality fuels available to amateurs, even if you carry no payload.

Maybe ask having this thread moved over into the science subforum, where more people better qualified than I are posting.

Edited March 11, 2015 by Streetwind

[RainDreamer]

Wiki says achieving low earth orbit require about 9.4km/s of delta-V and more.

So can anyone more familiar with hobby rocket figure what fuel and engines we will need, and how much mass it would be in the end?

[GoSlash27]

I'll do a crude back of the envelope estimate later today.

Best,

-Slashy

[Streetwind]

Well, you can use the rocket equation to get a basic idea of what kind of fuel mass fractions it takes to achieve certain dV figures.

Amount of fuel per 1 kg of stage dry mass at various Isp values for ca. 10 km/s dV (single stage to orbit):

- 164 kg at 200s

- 129 kg at 210s

- 105 kg at 220s

- 84 kg at 230s

- 69 kg at 240s

- 59 kg at 250s

To understand what those numbers mean, you look at fuel tanks. A given fuel tank can carry x kg of fuel per 1 kg of its own mass. This represents the upper limit of what a rocket can theoretically achieve; practically, the limit lies even lower because you have to add mass from things that are not fuel tanks, such as engines.

I don't know real life tankage fuel/mass fraction numbers, but I know them for KSP. Ingame, most tanks let you bring 8 kg fuel for every 1 kg of tank mass. Now, this is actually quite a bit worse than real life tanks, especially for liquids, but still. Look at this number, and now look at the table above, understand that hobby rocketry fuel is closer to the 200s end of the scale than the 250s end, and despair. This is why you don't do SSTO.

Amount of fuel per 1 kg of stage dry mass at various Isp values for ca. 5 km/s dV (two stage to orbit):

- 11.9 kg at 200s

- 10.4 kg at 210s

- 9.2 kg at 220s

- 8.2 kg at 230s

- 7.4 kg at 240s

- 6.7 kg at 250s

Now we're getting somewhere that appears in the realm of the possible. The solid first stage of ESA's Vega rocket carries 12 kg of fuel per 1kg of dry mass. If you had a solid fuel of 200s specific impulse, it would not be possible in two stages (there's additional dry mass in the form of decouplers, interstages, flight control systems, fairings and the like that aren't factored in here for a first stage). On the other hand, if you could do 230s, you might have a realistic chance. With 250s, it would definitely possible. Still, I'm not sure an amateur can get their hands on something that good.

Let's say you're filling your stages with an even 9 kg fuel per 1 kg of dry mass (slightly better than 220s Isp). Let's further assume that the second stage has a dry mass of 20kg, including the 100g payload, the staging equipment, the electronics and everything (I have no idea if that figure is utter BS or not ). Then your second stage weighs 200 kg, of which 180 kg is fuel. Your first stage then has these 200 kg as its payload. You need 1800 kg of fuel to lift that. But assuming that your tankage's best fuel/mass ratio is 12 kg per 1kg tank mass, those 1800kg are going to add another 150 kg dry mass to the first stage. To lift those, you need another 1350kg of fuel. Which is going to add more dry mass. And so on.

Ultimately you're going to have to add another 600 kg of dry mass and the 5400 kg of fuel to lift it to the first stage, on top of the 1800 kg already budgeted. Total mass of the first stage is now 8 metric tons, of which 800 kg is tank dry mass plus the entire second stage.

Yay lunchbreak napkin math

EDIT: After some thinking, I have concluded that a 20kg dry mass second stage is indeed total BS. it would need to be heavier. But the second stage would also get a higher specific impulse than calculated with here, so let's call it a wash.

Edited March 11, 2015 by Streetwind

[cicatrix]

Yup, I forgot that to fly this rocket I'd need some extra equipment like servomechanisms, control equipment, guidance unit, etc. I doubt 100 g is enough for that.

Still, it appears, a rocket roughly about 10-15 ton can do it. And I was never suggesting SSTO. I was considering 2 or maybe even 3 stages.

Now I wonder when anyone actually tries to build that

[RainDreamer]

I think whoever spend that much effort is probably already a start up space business instead of being an amateur doing it as a hobby.

[Streetwind]

Those who do generally realize it's so expensive that it's pointless to bother unless they can find someone to pay them to carry a payload...

...and then they figure that they might as well found a company around it...

EDIT: Damn you RainNinja.

[cicatrix]

I think whoever spend that much effort is probably already a start up space business instead of being an amateur doing it as a hobby.

I was considering someone like Tony Stark

[Yukon0009]

Well, SpaceX technically is Elon Musk's hobby, so yeah.....

[GoSlash27]

I tried dabbling around with hobby motors. Wasn't able to come up with anything that could achieve that DV.

Going with a 3 stage kerosene/ LOX rocket, it worked out to roughly 22 tonnes by my math.

No guarantee that it would actually work, either...

Best,

-Slashy