Could you float a boat on a gas giant?

Let's look at some key Jovian atmospheric characteristics:

• Density at $P=1\text{ bar}$ (i.e. the surface): $\rho_J=0.16\text{ kg m}^{-3}$
• Temperature at $P=1\text{ bar}$: $T=165\text{ K}$
• Mean molecular weight: $\mu=2.22$
• Primary atmospheric constituents: H (89.8%), He (10.2%)

In other words, if you want to float close to the surface, you're in a cold, gaseous region with a low density. This isn't great; according to Archimedes' principle, any lifting gas you use must be less dense than the medium surrounding it. The atmosphere outside is already not too dense, which is problematic.

1. Float low

High in Jupiter's atmosphere, there's a smooth transition to the interplanetary medium, where you see a lot more hydrogen. Lower, near (and below) $P=1\text{ bar}$, $\mu$ is higher and $\rho$ is also higher. This means that your lifting gas doesn't have to be as lightweight as if you were trying to float near the top of the atmosphere.

As kingledion's chart shows, temperature is roughly constant from $P=10^{3}\text{ bars}$ to $P=10^0\text{ bars}$ - i.e. right below the "surface" of Jupiter. However, at the surface, it rapidly increases, as density and pressure rapidly decrease. I would aim for this region - at the surface or a bit below it. You'll probably be stuck in the same temperature range, $150\text{ K}$ to $200\text{ K}$, and pressure is the main difference.

2. Don't go for a vacuum airship.

We already know that that sort of thing is hard on Earth. In the regions we're considering, the outside pressure is going to be even stronger. Sure, you can maybe mitigate that with whatever tech you've developed by the time humans can get to Jupiter, but you can only handwave away so much. It just won't work at this part of Jupiter.

Instead, use something like heated hydrogen! This is why I like the low-temperature region of the planet. The surrounding gas will have a higher density and a lower temperature, and so any particular lifting gas at a certain temperature will be more effective. Obviously, hydrogen is flammable, but hey, it's cheaper than helium, and if you're safe, maybe things won't go so poorly.

Let's say the ship is designed like a Zeppelin, with a chamber of gas of volume $V_g$ and a cabin of volume $V_c$. The mass of the gas is $m_g$ and the mass of the cabin is $m_c$. We then need, for the ship to float at equilibrium, $$F_{\text{buoyant}}=(m_g+m_c)g=\rho_J(V_g+V_c)g=F_{\text{gravity}}$$ where $\rho_J$ is again the atmospheric density of Jupiter at $P=1\text{ bar}$, and $g$ is Jupiter's surface gravity. Now, $m_g=\rho_gV_g$, where $\rho_g$ is the density of the gas. Therefore, $$(\rho_gV_g+m_c)g=\rho_J(V_g+V_c)g$$ Rearranging, cancelling and solving for $\rho_g$, we find $$\rho_g=\rho_J\left(1+\frac{V_c}{V_g}\right)-\frac{m_c}{V_g}$$ Given that $V_c\ll V_g$, we can appxoximate this as $$\rho_g\approx\rho_J-\frac{m_c}{V_g}$$ Choose your cabin mas wisely, and adjust the other two parameters as you desire. For the Hindenburg, for instance, $V_g\approx200,000\text{ m}^3$. This actually allows us to have a comfortable cabin mass, if we're willing to raise the temperature enough inside. You'd be able to look for something in the vicinity of a couple tens of tons. Not a lot, but enough.

Let's use the ideal gas law for the inside of the gas sac. Assume $p=1\text{ bar}$ (roughly) and $\rho_g\approx0.10\text{ kg m}^{-3}$. Then we have $$P=\rho_g \frac{k_b}{\mu_gm_u}T_g$$ where $k_B$ is the Boltzmann constant, $\mu_g\approx1$ is the mean molecular weight of the gas, and $m_u$ is one atomic mass unit. I find that $T_g\approx121\text{ K}$. We can afford to have a higher $\rho_g$, too, so the hydrogen gas can be a bit hotter. Now, this means we must have a smaller cabin mass, but still.

3. Insulate well

It's all very well and good having a warm bubble in a cold atmosphere, but if there's heat transfer, your ship will soon freeze. I've continued to do reading on possible materials without much luck (although I daresay that someone else probably knows enough to find something good), but then again, I'm not great at materials science.

I do think that you'll want to have some sort of composite skin on your airship. You need it to be able to survive pressures both a bit higher and lower than on Earth - while still keeping the hydrogen gas inside - as well as withstanding some pretty cold conditions. Neither of these are overly problematic; there are plenty of materials that can do this.

The problem is, quite simple, one of weight. Anything that flies - and this ship will fly, in a sense - needs to take weight into account. I've already done this when considering the mass of the crew cabin. However, I'm a lot more concerned about covering the envelope with something that's strong, lightweight, and a good thermal insulator.

posted almost 7 years ago

HDE 226868‭

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