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I want to design an airship using modern-day technology. I have read around the stack exchange and while there are many questions on airships they do not completely answer my questions.

My main idea is based on a short galleon ship 105ft in length that weighs around 350 to 400 tonnes. Using a custom hot air balloon that is heated through a closed heating system (to remove water loss) composed of a form of modern-day steam or sterling engine. The fuel source is hydrogen as I can perform electrolysis on harvested water from clouds using an onboard battery in emergencies.

I would like answers to a few points:

  1. What size would the balloon need to be to carry the said ship?
  2. How much fuel do I need to sustain at least a 6 to 12 hour flight time?
  3. Would my heating element be viable or is there a more efficient way of heating up my balloon?

Any information would be appreciated and the answer that covers my questions to the most satisfying extent will be picked as the final answer.

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    $\begingroup$ The hot gas in your balloon is air? Since this is a fiction why not use steam? H2O is a light little molecule. $\endgroup$ – Willk May 31 '20 at 22:52
  • $\begingroup$ How hot is your hot air? That's the basic variable in calculating the volume of the balloon. And anyway, expect an answer on the order of a million cubic meters (35 million cubic feet). (No, it is neither a joke nor an exaggeration.) (For comparison, the galleon has an interior volume of a few hundred cubic meters, say 500 cubic meters. The ballon needs to be on the order of 2,000 times bigger than the ship.) $\endgroup$ – AlexP May 31 '20 at 23:09
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Lifting Bag Size

Average hot air balloon needs 64 ft^3 to lift 1 pound with an internal temp of 100 degrees F.

400 tonnes = 881,000 lbs -> 881,000 lbs * 64 ft^3/lb = 56,384,000 ft^3

Assuming your lifting bag is 3x the length of your hull...

3 * 105 ft = 315 ft length

... and assuming a cylindrical lifting bag (sharp edges, unrealistic), cross sectional area of lifting bag is...

56.384 * 10^6 ft^3 / 315 ft = 179,000 ft^2

... diameter of lifting bag is therefore...

2 * ( 179,000 ft^2 / 3.146 ) ^ 0.5 = 477 ft diameter

... which is a wide load, might want to make it longer.

Fuel use *This is going to be quick and dirty on the heat transfer, in reality heat loss would not scale linearly and fuel consumption would be lower.

Average hot air balloon (77,000 ft^3) consumes thirty gallons of liquid propane an hour.

56,384,000 ft^3 / 77,000 ft^3 = 732 average hot air balloons

732 * 30 gal = 22,000 gal/hr

... with propane you get 91,330 Btu/gal...

... with hydrogen you get 51,585 Btu/lb...

91 Btu/gal / 51 Btu/lb * 22,000 gal/hr = 39,254 lb/hr or ~18 metric tons an hour of hydrogen burned to heat your bag.

18 tons/hr * 16 hr = 288 tons of hydrogen for sixteen hours of flight time

Your aircraft is only 72% fuel by mass, good enough for government work.

Heating Element Viability

... 72% mass taken up by fuel is unfortunately likely not good enough, even for government work. Your heating element is viable--heat is generally pretty easy to obtain from an energy source, especially when heating a large volume like a hot air balloon--but your understanding of using a battery to recover hydrogen from clouds, then using that hydrogen as a heat source needs work. Implemented as is will lead the crew of your airship to a fatal end. All the energy in the system you've described will need to either be A. contained within your hydrogen storage or B. contained within your battery at the beginning of your flight. It would be a better idea to just carry more hydrogen instead of the battery weight and associated machinery for performing electrolysis.

As a further suggestion, I would strongly advise you to investigate replacing hot air as a lifting gas with something that doesn't require constant fuel input. Helium will do, so will hydrogen-- 64,000 ft^3 of helium will lift 4454 lbs., while the same volume of hydrogen will lift 4808 lbs., both nearly four times as much with no fuel consumption to boot. That reality is why (unheated) hydrogen and helium are the lifting gases used in real world airships; I have not seen a hot air balloon of similar size, though I have read about theoretical floating cities in geodesic domes held aloft by a slightly higher internal air temperatures (which are neat). I also agree that airships are awesome; read some thermodynamics textbooks, learn like you'll live forever, and fly safe.

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    $\begingroup$ Note that you can use Mathjax of WB SE for writing e.g. $ft^3$ and of course numbers and mathematical expressions. $\endgroup$ – StephenG Jun 1 '20 at 2:35
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    $\begingroup$ @StephenG: Note that $ft^3$ means something notated $f$ times something notated $t$ (time?) cubed. Cubic feet are ft³ (or, if you want to use MathJax, $\text{ft}^3$). (That is, symbols for units of measurements are set in upright type.) $\endgroup$ – AlexP Jun 1 '20 at 4:58
  • $\begingroup$ How much does the bag weigh? And do you have enough lift to carry the fuel as well? $\endgroup$ – David Hambling Jun 1 '20 at 11:23
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    $\begingroup$ You should be able to get a better heat loss estimate by considering bag surface area rather than volume. This is a great answer though. Welcome to Worldbuilding! $\endgroup$ – Ryan_L Jun 1 '20 at 15:59
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    $\begingroup$ Geodesic airships (Buckmaster Fuller's "Cloud 9") become viable when the sphere is something like half a mile in diameter. As a thought experiment it is interesting, but for the people living aboard issues like resource consumption and economics likely "ground" the idea. $\endgroup$ – Thucydides Jun 1 '20 at 18:51
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Electrolysis is an endothermic process, you have to put energy in to do it. You can't get more energy out of the hydrogen than it took to make that hydrogen from water. Which begs the question, why not cut out the middle man and just use whatever power source powers the electrolysis to heat the balloon itself?

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  • $\begingroup$ Sorry I forgot to include that I would have an on board battery for the electrolysis in a state of emergency. $\endgroup$ – The Last Remnant May 31 '20 at 22:54
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    $\begingroup$ @TheLastRemnant the point still stands splitting water just makes the system drastically less efficient for no good reason. $\endgroup$ – John May 31 '20 at 23:40
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If you already have hydrogen that would be much, much efficient for lift than hot air, assuming you can contain it.

Hot air balloons of this size have not proven viable.

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