I'm wondering if its possible to make a helium blimp large enough to hold up an island (big enough to lift the island of Nauru) at an altitude of about 4500 feet above sea level. how much helium would this take? what are some problems that might occur on this scale? assume the island wont fall apart and has some sort of effectively indestructible bottom.
Yes and no.
Yes its possible by using balloons. Balloons and airships are one of the few things that benefit from the square cube law. You could for example take the Hindenburg without its passenger compartments. Then fasten it to another Hindenburg, and place another above it, and one besides it etc. The Hindenburgs can carry their own weight, and with some engineering you can protect against the large forces between the Hindenburgs as wind pushes them unevenly. You can make this as large as you want, as long as it fits within the atmosphere. Naturally you dont want to use the actual Hindenburg, but a custom made balloon. As Ash's answer shows that is going to be big, but rather than a sphere I would make it more elliptical so you have more space above to keep it flying (besides that lifting power goes down the higher up you go).
No because the bigger problem is carrying the island. You cant lift it from the top, so you have to build a plate below the island that can carry it, adding an aweful lot of weight to an already massive project. One advantage is that the plate can be bigger than the island, offering more surface area to attach the balloon(s) to.
You could then also think of other things, like placing balloons beneath the carrying plate to help lift it and alleviate some of the stress that it puts on the plate.
Yes - but you need to import helium to Earth from elsewhere in the solar system to accomplish it.
There isn't enough helium on Earth to do this by 2 order of magnitude actually. So your plan involves basically sticking a straw into Jupiter and shrinking it by a few cm, and then trucking trillions of litres of helium back to Earth - which is actually more interesting sci-fi premise than taking Australia's Shame up to a height of about 1.2km. (Honestly Scotty from marketing - what will you think of next?)
But first, numbers from casual googling and writing down the first answer:
- Nauru is 21 square km.
- The highest point is 65 meters.
- Modelling this as a square based pyramid, we get a volume of 4.39e8 cubic meters.
- Naru is mostly phosphate-rock according to wikipedia.
- Which is 1762kg per cubic meter
- Gives a total weight of 773,518,000,000kg
So there's the best online calculator I've ever seen. How many helium balloons would you need to lift something.
Summarising the results:
- You'd need 75 trillion standard helium balloons, filled with 864 trillion litres of helium
- Or you'd need 107 billion 98inch weather balloons. 864 trillion litres of helium
- Or one balloon 14.1km in diameter.
How much helium is on planet Earth? 1.5 trillion litres. Hence - you need to import 862 trillion litres from jupiter.
How high will the balloons go? 15.7km. How big is the cluster of balloons? A sphere 14.1km in diameter. That's 1.6km remaining. 5249.34 feet. You've just made it.
Note that You can't use weather balloons or anything smaller! Using smaller balloons in a cluster will fail. Packing spheres in a sphere shape is only 74% space efficient, or put another way, using smaller balloons will make the cluster ~30% bigger than one large balloon, meaning the top balloons will hit 15.7km and burst while the lower balloons are still on the ground. Nauru is only so big so there's only so far an area you have to spread your balloons out over.
I also did an estimate on the calculations for whether it's bursting would asphyxiate anyone on the ground or give them silly voices - I think we're all safe for the moment, but there'd be a massive ozone hole created over the following years.
There's enough Hydrogen on Earth to do this, but you couldn't afford it:
Switch to Hydrogen? 681 trillion litres of hydrogen. We'd need to electrolyse a lot of water. At 70c/kg you're looking at 476 trillion dollars to pay for it. The GDP of Earth is 87 trillion.
A balloon cannot lift an island
Instead of looking at Hokkaido, let's start with a smaller island.
Behold Rockall, one of the smallest islands in the world. Let's say you only have to lift the part of the island that's above sea level and that the island is 6 meters on each side. That would work out to a weight of more than half a million kilos. This calculator suggests that you'd need 48,797,824 party balloons filled with helium to lift it. For perspective, the CargoLifter (below) claims a lift capacity of 160,000 kilos.
So if you had a team of several balloons of that scale, they might by able to pick up one of the world's smallest islands. And remember that this island is one solid piece of rock, so you don't need to worry about structural stability. Hokkaido is so much larger that it's just not possible to lift it.
Without doing any mathematics, we can observe that the balloon part of a blimp is always an order of magnitude bigger in volume that the load they can carry. Your blimp would have to be at least ten times the volume of Hokkaido that you want to lift.
That is not the problem though. An island of that size would simply break apart if not supported at every point from underneath. You cannot attach sufficient numbers of ropes between the blimp and the island to provide this sort of support. You would have to drill holes everywhere. There would be no island left.
Firstly: What is an island?
Your Island of Nauru is the extreme tip of a column of rock that extends 6300kilometers down into the Earth.
NO it is not just the bit that sticks out above water level. An island is the tip of a mountain in the ocean, and that mountain goes down as far as "down" is defined.
But, let's CHEAT
Lets only consider the bit that sticks out of the ocean. Never mind that if we lift just that bit, then it would crumble in our hands.
Surface area = 21 square kilometer. Material = 2.7 tons per cubic meter (sorry @Ash, no phosphate rock/fossilized guano left. that's all been sold off. All that remains is the original limestone island) Average height = 40m Can be considered as a cylinder of this height, as the entire interior of the island is a plateau. Mass = 21 * 1e6 * 40 * 2.7 * 1000 = 2.268e12 kg
Can we lift this, using air buoyancy? Nevermind the lifting gas, etc.. Assuming we make the balloon extend from sealevel up to infinity, and make the balloon weigh zero, it will lift exactly as much as the current sealevel air pressure.(handy shortcut, this!)
So each 1 square meter of perfect balloon can lift:
At sealevel Pressure = 101325 pa on 1 m2 = 101325 Newton force = 101325/gravity kg = 10328.746 kg
Unfortunately, OP want this lifted to 4500feet.
That reduces the amount of air that can be substituted by lifting devices.
Using the elementary formula of p = 101325* (1 - 2.25577e-5 h)^5.25588
,with h being altitude in m, gives us air pressure at 4500ft of 85.9kPa
Which gives us lifting force of 8756kg per m2
To lift our mass of 2.268e12 kg, we will need a lifting force that exactly matches this.
So using a balloon that extends from the base of the floating island up to space, with the balloon weighing nothing at all, using zero-mass cables and canopy, will require:
surface = 2.268e12/8756 = 2.59e8 square meter of balloon-to-space
This is a circle of Radius of 9079.77m.
259 square kilometers.
Now all you have to figure out is how to attach (using zero mass!!) your 18-kilometer wide balloon to the 5-kilometer wide island.
There. I have converted your impossible balloon problem into a much simpler (but still impossible) suspension bridge problem.
Effectively, you need to build a zero-mass bridge, capable of supporting 2.268e12 kg (2.268 billion metric tons) over a single span of 4 kilometers.
Frame challenge of sorts:
Sure. Sort of.
You didn't actually specify that the balloon/blimp has to be above the island. So, all you need is a really sturdy material out of which to make the lifting bag, and a way to get it under the island (how to accomplish this is left as an exercise for the reader). You may want a sort of doughnut-shaped bag, possibly with a bunch of closed cells to help it keep its shape and to keep the island from sliding off the side. The part of the lifting bag beneath the island will be... about 4500 feet tall. (Maybe taller if it's floating on water, to compensate for its water displacement.) Since the bottom isn't actually floating (or is floating on water, not air), you don't need it to be large enough to displace its weight in air, and you can also fill it with straight up air; no helium needed.
How to propel this monstrosity is also left as an exercise for the reader.