Saturnian Cloud-Cities Pt. 6 :- Geothermal Cables Vs Stupendously Large Airships

Question

In my previous questions, I discussed the possibility of cloud cities on Saturn

Saturn is a large planet, and if we were to settle on its moons, such as Titan, it would be easily overpulated in just a few millenia

And there were a few technologies which could be useful for the colony. The cloud-cities in question are giant airships, based on tensegrity spheres (not mentioned in the diagram as I am bad at making shapes in Paint), which use wind-energy to generate electricity. The city's oxygen supplies come from algae-bioreactors (electrolysers-too much energy and constant ice supply from Saturn's clouds) and the food is derived from plants that are grown on the airship, and from livestock (mainly cows, goats and sheep). The population varies from city to city, from meagre scientific outposts of 500 people, to a bustling city of 5-10 million people, with about as much as 3 times the number of pets. In order to prevent the supersonic Saturnian winds (~1700km/h) from making sonic booms constantly, a thick glass dome is installed over the colony, meaning that the people won't have to lose sleep due to continuous wind noises.

However, there is a major problem with the airships.... and that is lift.

In Saturn's mostly hydrogen atmosphere, a hydrogen balloon would provide really little lift. The only gas that could provide sufficient lift is heated hydrogen. The advantage is that the airships are based on the Cloud Nine tensegrity sphere model, which means that just a increase of 1 degree can lift the airship. But.... there is a paucity of heat sources on Saturn.

Saturn is more than 1 billion miles away from the Sun, and solar energy is pathetically weak at these distances. Nuclear energy requires a constant supply of fissile materials from Earth, or noisy fusion reactors which would result in lack of sleep for the colonists and other health issues. There isn't a heat source on Saturn which would be enough to heat up the hydrogen.... unless you counted on geothermal Kronothermal heat.

Kronothermal Cables

Actually that's what my world uses as a heat source for making the hydrogen hot enough to provide sufficient lift. The concept revolves around the fact that Saturn's interior is really hot, and that heat can be utilized to heat up the hydrogen for lift.

Graphene cables, which are miles long and are about a quarter of a foot thick, are dangled from the cloud-city, deep into Saturn's atmosphere. The cables harvest this heat to heat the hydrogen to sufficient temperatures for proper lift. Sort of like this-

However, in the answers to my previous questions, many responded that this technology would not work properly due to the following reasons:

• Ammonia, a powerful phase-driven refrigerant would simply suck the heat out of the cables, meaning that there would be little heat to heat the hydrogen. Also the temperature gradient on Saturn is pathetically low.

• Dangling cables from the city to pull up heat is actually dangerous instead of beneficial as they provide a lot of weight to the tensegrity airship, raising dangers of sinking.

So, I came up with a alternate solution for the airship.

Stupendously Large Airships

No matter how light Saturn's atmosphere is, it would always be denser than hydrogen

In fact, Saturn's atmosphere at the 1-bar level is about 0.19 kg/m³, denser than Jupiter's 0.16 kg/³ at the 1-bar level. Really light, but still it's twice as dense as hydrogen which leads me to think of this possibility.

If you could get an airship to be large enough, you could possibly lift an entire city in Saturn's atmosphere. These airships are extremely Stupendously large, to make up for the buoyancy required to keep a city to float in the light atmosphere. The interior of these airships consist of pure hydrogen. And since there is no massive cable dangling down and providing too much weight, theoretically, our cloud-city should float on Saturn. I call them Stupendously Large Airships due to their tremendous size.

However, there seem to be a few disadvantages in this design. The airship would be extremely voluminous, meaning that there is more surface area for strong winds to tear it apart. And if rockets carrying tourists/passengers made a mistake, they could end up hitting the airship, and release the gas, and causing it to sink.

What should I choose for the Saturnian Cloud-City :- Geothermal Cables or Stupendously Large Airships?

Answer 1

I believe the "stupendously large airship" is the way to go.

Calculating a tensegrity aerostat

Let's first find out how much mass a tensegrity aerostat can lift in these conditions. Because hydrogen is very leaky (and building a miles-wide pressure vessel is very hard), my calculations will use Saturn's atmosphere as the lifting gas.

You state that the colony sits at the 1-bar altitude (what they call the "surface level" for gas giants), so atmospheric pressure, $P$ Pa, is given to us. Temperature, $T$ K, of Saturn's atmo. at that altitude is around -180 °C, or about 90 °K. That leaves density, $\rho$ kg/m^3, which can be estimated via:

$$\rho =\frac{P}{R_{s}T}$$

$R_{s}$ is the specific gas constant of Saturn's atmospheric mixture, which, from this table, is ~3890 J/kg/K. Running the math, I get $\rho = 0.30$ kg/m^3.

The tensegrity aerostat's lifting mass will be the difference in densities, internal and external, multiplied by its volume. Because the gas mixture is the same (because our balloon is not a pressure vessel), our density difference comes from a temperature difference, $T-T_{in}$.

$$m_{lift}=V_{aerostat}\frac{P}{R_{s}}\left(T^{-1}-T_{in}^{-1}\right)$$

You mention a 1-degree difference, but that likely isn't going to cut it (not if you want to lift anything serious). For a mile-wide sphere ($V_{aerostat}=1.72\cdot10^{10}$ m^3) with a 10 Kelvin difference ($T_{in}=100$ K), I find a lifting mass of ~500,000 metric tonnes. For a 30 Kelvin difference ($T_{in}=120$ K), I find ~1.2M metric tonnes. That's about 12.5 Lexington-class battlecruisers of mass. This mass represents our "budget". The tensegrity superstructure needs to weigh less than this to produce net lift.

Due to a previous worldbuilding project of mine, I have some experience estimating the mass of Cloud Nine tensegrity structures. For a mile-wide, 20V geodesic structure made of 20 cm diameter aluminum 6061 compression members (tension member mass is approximated by doubling compression member mass; a likely conservative estimate), enveloped in a 5 mm Kevlar membrane, I get a superstructure mass of ~370,000 metric tonnes.
Close to a quarter of our lifting mass budget, leaving ~800,000 metric tonnes (about 8 Lexington-class battlecruisers) of "free" lifting mass for really any number of people/cargo/additional structures.

However, straight-up Kevlar is not a great insulator, so this structure loses a lot of heat to the environment. We can calculate its wattage output, $W_{output}$, by calculating the thermal transmittance over its surface area, via:

$$W_{output}=A_{aerostat}\cdot U\cdot\left(T_{in}-T\right)$$

Where:

• $A_{aerostat}$ is the aerostat's surface area, m^2.
• $U$ is the transmittance U-factor, a value specific to the surface material, W/(m^2*K).

Kevlar has a U-factor of $\frac{0.04}{x}$ where $x$ is the thickness of the membrane m. Plugging in our 5 mm value for thickness, I get an output of ~7.7 gigawatts across the entire surface area of the sphere. So, yeah, . . . Kevlar's pretty lossy. That value represents how much energy must be inserted back into the tensegrity structure to maintain thermal equilibrium, or in other words, the output of our powerplant/power generation mechanism. However, if you could manage to bump the insulation of the membrane up to that of a well-insulated roof, with a U-factor of 0.15, then we get a loss of only ~144 megawatts. That ought to be manageable for a small nuclear power station.
I'll leave you to determine how strengthening the insulation could be done (foam layer, aerogel, etc.?)

This completely ignores the contribution of solar flux at Saturn, which would warm the structure and alleviate the strain somewhat (at least, during the day).

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Conclusions:

I've found that a mile-wide tensegrity structure comprised of a 5 mm Kevlar envelope and 20 cm diameter aluminum spars (with assumptions about tension member mass), comprising a 20V geodesic sphere, weighs ~370,000 metric tonnes. I've found that such a tensegrity structure heated 30 Kelvin above ambient generates a buoyancy adequate for lifting ~800,000 metric tonnes after subtracting structural mass (about 8 Lexington-class battlecruisers).

Such a tensegrity structure, if poorly insulated, could radiate as much as ~7.7 gigawatts of thermal energy; or, if well-insulated, as little as ~144 megawatts, easily replenished by a modest nuclear power station.

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Comments

There are still concerns about the OP's choice of setting, in an atmosphere with wind speeds as high as 1,700 km/h. Tensegrity derives its strength from the fact that the structure is loaded largely in tension. A little extra tensile strength could help alleviate any shear forces/torques.

It's my opinion that the aerostat would be fine as long as it navigates away from storm centers and remains inside bulk wind streams. The aerostat should not try to stay stationary in the atmosphere (and suffer the up to 1,700 km/h windspeeds) but instead travel with the bulk of the atmosphere.

Also, it should be noted that if the OP goes with a pressure vessel alongside a temperature differential for producing lift, that will increase the available lifting mass budget of the structure (at the expense of whatever engineering and materials are used to create the pressure vessel (for hydrogen no less) in the first place). But, lower pressure + higher temperature than ambient would contribute to lifting capacity, but it's my opinion that increasing temperature further is easier than creating a mile-wide pressure vessel.

Answer 2

Stupendously Large Airships sounds safer. You could add wind barriers and elevated landing platforms, so the pilots wouldn’t be able to puncture the city. More pressing problems than wind or incompetent pilots are the sheer drain on resources, and the fact that the infrastructure needed to keep the city from collapsing into the hydrogen chamber would reduce the buoyancy greatly.