Airborne Hotels - Stabilizing and steering a Cloud Nine tensegrity sphere

Question

Following on from this question: Can Cloud Nine be built?

Let us assume we have constructed a Cloud Nine tensegrity sphere with a 2 kilometer diameter out of a durable material for use in Earth's atmosphere. We have mastered making it go up and down. Now we need to stabilize and steer it.

How do we stabilize it? In other words how do we stop it from rotating and tumbling end over end like a beach ball? If we put weight at the bottom would it still wobble in high wind? To be useful it would have to be very stable.

The economic value of a Cloud Nine sphere is much higher if it is mobile rather than tethered to the ground (bonus question: is this even possible?). So how do we steer it in any direction we want to go in a practical way? In other words it needs to move under its own power without changing altitude. It doesn't have to be able to move fast, but it does have to be able to move against the various atmospheric forces, wind and weather that are pushing it around. Can this be done feasibly with current technology? For example, could this be done with solar power and propellers, maybe giant sails? Could we get some power out of electrostatic charge, maybe lightning strikes? What else is there using today's technology?

Finally, a sphere is only useful if it has lots of heavy stuff in it. People, buildings, and so forth. For example, imagine a hotel/tourist complex built at the center. Also, the weight of the sphere's shell could be quite substantial depending on the materials used and the desired thickness of the shell (we don't want the sphere destroyed by nature or attack). Please keep these two points in mind when answering. Thanks! And don't forget to include calculations of forces involved if possible. This question is tagged "hard science" and is basically an engineering/math question. Once we understand the physics and engineering of what's involved, we can work out whether it's economically viable using today's technology.

To be even more explicit: I'm just not sure how much power will be needed to push/pull the sphere around given its size and shape and whether you could even do it with current technology at a 2km or greater diameter. From Wikipedia: "Hindenburg was powered by four reversible 890 kW (1,190 hp) Daimler-Benz diesel engines which gave the airship a maximum speed of 135 km/h (84 mph)." The Hindenburg was 245m long, our sphere is 2000m wide (it may have to be much wider to lift a hotel, I don't know). If the sphere could go that fast by strapping lots of engines and propellers to it and the whole thing didn't use too much fuel then that's more than fast enough to be economical as a cruise ship/hotel. At Hindenburg speed it could cross the USA in 36 hours! So that's blazing fast. I was thinking, you know, could it float from city to city without taking a month and using an unrealistic amount of power? Consider a cruise ship in the Mediterranean for comparison. Except it flies.

I should also point out I have no idea how wide the sphere would have to be to lift a small "hotel city" / cruise ship equivalent. I've said 2km as a starting point. Maybe the diameter needs to be much greater.

EDIT #1: Let me clarify: if most of the weight is at the bottom, e.g. a hotel complex or something, considering the size of this 2km diameter (or wider) structure, could Earth weather provide a force strong enough so that there would be a wobble? Say a gust or hurricance or something pushed more on the top of the structure than the bottom. It would wobble until it settled right? That's why I tagged this hard science. I don't know how to do the calculations without much more research.

EDIT #2: When I say "steer" I mean can we move the sphere toward any point on the compass at a reasonable speed, regardless of what the weather is doing? So basically, can we move against the wind, and if so, with today's technology, how fast could we go, using propellors, maybe giant sails, and so forth? Again, not sure how to do the calculations, and that's how you should approach this question: by calculating.

Answer 1

This is regarding the steering, navigation and anchoring parts of the question:

The easiest possible way of navigation would be to stay anchored to the ground, and only release the Cloud Nine when the wind is blowing in the exact right direction.

The problem is: Is it actually possible to anchor it?

When anchored, the anchor has to resist all the force that the sphere experience, and the cross section of the thing does really catch a lot of wind. Let us consider the drag equation: $$F_D=\frac{1}{2}\rho u^2C_DA$$ Let us say we must tolerate wind speeds, $u$, up to $30 m/s$,
the mass density, $\rho$, of air is around $1.2kg/m^3$,
the drag coefficient for a sphere is around $0.47$,
and using the OP's reference sphere with a diameter of $2km$, $A$ is equal to $3.14 \cdot10^{6}m^2$

That is a force of almost $800,000,000 N$!

But strong fibres can manage that. Aramid has a tensile strength of $3,620 MPa$, meaning a cable with a cross section of only $0.22 m^2$ is enough.

In conclusion, anchoring seems to be possible, and gives us a way to slowly and securely move the sphere wherever we want.

Answer 2

How do we stabilize it?

Put the city at the bottom of it. If you want to be cautions add earthquake stabilizers and inertial dampeners to your tall buildings.

If we put weight at the bottom would it still wobble in high wind?

Lighter than air crafts simply float with the wind.

So how do we steer it in a practical way?

It's a sphere. You can steer it by saying "ok let's think of that as the front now".

move the sphere toward any point

Same as any other lighter than air craft does. Like this:

During the flight, the pilot's only ability to steer the balloon is the ability to climb or descend into winds going different directions. Thus, it is important for the pilot to determine what direction the wind is blowing at altitudes other than the balloon's altitude. To do this, the pilot uses a variety of techniques. For example, to determine wind directions beneath the balloon a pilot might simply spit or release a squirt of shaving cream and watch this indicator as it falls to determine where possible turns are (and their speed). Pilots are also looking for other visual clues such as flags on flagpoles, smoke coming from chimneys, etc. To determine wind directions above the balloon, the pilot will obtain a weather forecast prior to the flight which includes upper level wind forecasts. The pilot will also send up a helium pilot balloon, known as a met-balloon in the UK and pibal in the USA, prior to launch to get information about what the wind is actually doing. Another way to determine actual wind directions is to watch other hot air balloons, which are the equivalent of a large met-balloon.

Wikipedia: Hot air ballooning

There's your science. You conduct experiments and make observations. Not everything needs a calculation.

It doesn't have to move fast, just faster than the various atmospheric forces that are pushing it around. Can this be done feasibly with current technology? For example, could this be done with solar power and propellers?

Faster? Just faster? Not 5 miles per hour faster? Ok fine. lean out the back and blow hard. Congrats, your going faster.

If you really insist on trying to out speed the wind you could just make an oversized blimp, complete with propellers. Sphere isn't the most aerodynamic shape.

• a sphere is only useful if it has lots of heavy stuff in it.
• the weight of the sphere's shell could be quite substantial depending on the materials used and the desired thickness of the shell

The square cube law ensures that we're going to get plenty of lift if we can simply keep these things warm enough. Thickness translates to insulation so that could help with maintaining heat.

Since the roof is held up by air the structure doesn't have to be substantial. Most of the forces on it are tension not compression. Thus it's really tensile strength that limits the size of these things.