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That would of course make sense to use hydrogen peroxide, take the energy it gives off as it splits into water and oxygen gas and then use that pure oxygen gas to burn hydrogen gas with it.
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I thought this was what Niri meant in the first place, so I ran the calculation earlier. It comes out to something like 8MJ/kg, IIRC, producing lots of water in the process. (Which I guess you could then throw out the back? Anyone want to try to calculate the thrust for that?

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I can imagine that this really gives off a lot of energy, but the storability and energy density of hydrogen peroxide and hydrogen gas is still not close to fossil fuels, hence I think it would be hard to fuel an airplane with it because of all the weight it would have to carry.
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1kg of hydrogen weighs the same as 1kg of water, but to store those two in the same volume, the hydrogen has to be stored at 11,000 atmospheres. I can't really imagine how to store a substance at 11katm in such a way it'd be light enough for an aircraft.
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A blimp might work as it does not have to actively use energy to float the heavy weight, but its payload would be small compared to the size - smaller than in fossil fuel driven blimps.
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It being a blimp would mean a far greater air resistance, though, meaning it would consume more fuel moving. (It's top speed would also be very limited.) I think you run into lots of logistical problems if you try and use the blimp's ballast itself as fuel.
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If it is refueled by solar energy in some way during flight, it basically is just a temporary storage and could be much smaller.
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Solar panel input is proportional to the area you can devote to solar panelling, and even then, it is very limited compared to any sort of fuel. (e..g the absolute maximum power you can get is 1kW/m^2, and no real solar panel is anywhere near that. IIRC, modern ones are on the order of 300W/m^2 in perfect conditions.) I think you'd have to use it as a augmentation for a fuel source, not the vehicle's only source of power, at best.
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And indeed - the addiction of the "civilized" part of the human species is due to these properties of fossil fuels.
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As efficient and clean as using micro-nuclear reactors or nuclear batteries on board aircraft would be, I doubt it would catch on.