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I checked your numbers, and you are right.

The Hindenburg had a total mass of about 240 tons. In its last voyage it burned 42 tons of fuel over 77 hours. It was an unusually long voyage due to high winds, but presumably the engineers who built it took these type of conditions into account, so the takeoff fuel was probably 50 tons or so.

A modern airplane of the same size (mass) is A-330. It has a (fully loaded takoff) mass of 240 tons, and a takeoff fuel mass of about 110 tons, so more than double the Hindenburg's.

Hindenburg's speed was about 125 km/h, while A-330's speed is about 1000 km/h, so about 8 times faster. Indeed, a Frankfurt-New York flight takes about 8-9 hours in an Airbus, it used to take about 60 to 70 hours in a Hindenburg.

Of course, if it takes you 2 days to cross the Atlantic, you need a bed. So, Hindenburg was able to accommodate only about 70 passengers, while an A-330 can easily fly 250.

Finally, regarding solar power. Hindenburg's area as seen from above was about 10000 m2. Current solar panels can produce up to 220 w/m2, so if we cover a Hindenburg with such panels we'd get 2.2 MW peak power, or about 3000 horse-power. Hindenburg's engines were producing about 3300 HP in cruise mode. Today, with better propellers and CFD modeling, you may not need more than 3000 HP to get the same thrust, so at peak solar radiance (noon), you would not need to burn any gas at all. Of course, during the night, the solar panels' output will be zero, but the modern engines may be more efficient, so all in all it's likely that instead of 50 tons you may only need 25 tons.



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