It’s a matter of weight and area. Let’s do the math on this:
Vital stats on the [Hindenburg](https://en.wikipedia.org/wiki/LZ_129_Hindenburg):
* Length: 245 meters l(4 times longer than an [A-380](https://en.wikipedia.org/wiki/Airbus_A380)
* 40 m wide (about half as wide as an A380))
* Engine power: four 890 kilowatt engines, total of 3.6 megawatts.
* Top speed: 135 km/h (85 mph)
* Carried 50 passengers, 40 crew, and their food baggage and furniture plus 12 tonnes of cargo, so ballpark estimate 30 tonness total carrying weight.
[Typical commercial solar panels](https://www.goosolarpower.com/2023/06/solar-panel-weigh-size.html) generate 150 watts per square meter under absolutely ideal conditions, closer to 50 W/m^2 on average. To produce an average 3.6 megawatts you’d need 72,000 square meters of them. Given its length and width, the surface area of the top of the Hindenburg is about 5000 m^2 — so it’s about **14 times too small** to carry the solar panels needed to power it — and that’s assuming perfectly efficient electric motors.
Residential solar panels weigh about [9 kg/m^2](https://www.goosolarpower.com/2023/06/solar-panel-weigh-size.html), so 5000 square meters worth would weigh about 45 tonnes. Residential panels don’t have to be particularly lightweight, though, so it’s possible we could bring the weight down to the 30-tonne cargo capacity of the Hindenburg. But we wouldn’t have any weight left to carry batteries. Or cargo.
So the problem is the largest aircraft in the world ever built (by surface area) is way too small to carry our solar panels. But making an airship even bigger than the Hindenburg doesn’t help: the solar power goes up in proportion to the surface area of the airship, but so does the air drag.
One thing that might help is to **make the airship go slower**. Power needed to overcome air drag goes like the [cube of airspeed](https://en.wikipedia.org/wiki/Drag_(physics)#Power), so if the airship went 2.5 times slower than the Hindenburg, it would need 15 times less engine power and we could fit the required solar panels on the airship. But that would put its top speed at 50 km/h (35 mph), only a little faster than a [cargo ship](https://www.marineinsight.com/guidelines/speed-of-a-ship-at-sea/). But going this slow would make it completely **unable to fly into the wind** if the upper-air windspeed was faster than this — which it almost always is — and completely **unable to land safely** if the ground-level winds were faster than this — which they often are.
This isn’t unique to airships. As a general rule, **none** of the combustion-powered vehicles we’ve come to rely on can run on solar panels on their roofs. Not airships or planes or cars or ships, they all are too small to carry enough solar panels to power them continuously, usually by a factor of 10 or more.
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