For anyone wondering what kind of numbers we're talking about in practice -- the Toyota Mirai holds about 5kg of Hydrogen.

In a pair of tanks that weigh 87.5 kg.

That's not that bad right? 15 gallons of gas could be 43 kg, and the gasoline fuel tank has some weight too.

Although, after google search, I see that the Mirai weight is 4075 lb, and the Prius weighs around 3100 lb.

That ratio looks depressing, but what would equivalent batteries weigh? 500 kg? 1,000 kg?

A Tesla battery pack of comparable range is about 500kg.

Note that the mirai also needs the fuel cells, which adds another 70 kg, so the difference isn't as stark

Once we start that game, we can also add the weight of the Mirai's 1.6kWh NiMH battery and other esoterica.

The proof is in the pudding: the curb weight of a Mirai is more than that of the larger and more capable Model 3.

How important is weight in their designs though? They're cars, so they don't have to hold themselves up, and they probably both have regenerative braking

You are right, weight isn't extremely important, especially with regenerative braking. It is only interesting in the comparison with battery electric cars - if the hydrogen car is even heavier, then there is basically no advantage left for the hydrogen car.

What is the energy came free, from renewables? What would the cost structure for hydrogen be in that case?

You'd still have to compare it to the equivalent usage of the same energy into a LiOn battery, and in many cases it wouldn't fare well.

Maybe there's a future world in which we can do it all in orbit -- harvest comets, produce hydrogen in space using solar power or nuclear, and efficiently drop it down to earth in some safe way. That would definitely alter the equation. But by the time we figure that out, it'll probably be too late.

If we're talking about space mining is Lithium abundant too? It's number 3 so should be everywhere in the universe?

Cost structure: ~$5/kg now; forecasted to drop to $2/kg by 2030 and $1/kg by 2050.

https://about.bnef.com/blog/hydrogen-economy-offers-promisin...

There is no free energy from renewables. Renewables are cheap, but not free. And we are very far from even having a 100% renewable grid.

When the spot price for energy can go negative due to renewable over production it's fair to say that energy can be free or even better.

Yes this is because there isn't enough grid storage yet. Massive amounts of stationary storage need to be produced whether that be pumped hydro or lithium ion battery or some other means of energy storage.

I recently worked out that the UK's installed capacity of pumped hydro is around 28GWh. This is around the worldwide total production of lithium batteries per year circa 2016 (realistically it may have doubled since then).

Personally I don't going into competition with laptops, mobile phones and car battery manufacturers as a viable long term strategy for grid scale storage.

I think your numbers are outdated, that's about the production numbers of Tesla alone, not counting the other manufacturers. And Tesla just announced their plans to move towards 3 TWh/year production rate towards 2030.

Any electric car plugged in is a great buffer for surplus electricity production.

In theory yes, in practice, which electric car charger has a built in 3kw inverter for backfeeding? Have you seen how large a 3kw inverter is? They are also not cheap. Secondly, most homes aren't metered in both directions. What is the ROI of one car plugged into the grid in this system? How much does it depend on how long the vehicle is actually plugged in and whether it is plugged in at useful times.

Taking the number above for installed capacity of pumped hydro. You are looking at nearly half a million cars and homes to match the capacity (assuming 50kwh per vehicle), before considering the plugged in factor.

At say a nice round £1000 to upgrade each home you are already looking at a cool half a billion. Already around the cost of the Dinorwig pumped hydro station before you figure out how to compensate electric car owners for the extra wear on their batteries or the fact that when they leave for work their car is flat because it has been powering your neighbors electric showers.

Yes, in those rather short time periods, energy prices are free. But for those periods, batteries are the better storage solution, as the total amount of "free" energy is rather small. Electrolysis plants would have to run basically 24/7 to be viable. More battery electric cars on the roads also mean a lot of storage for excess electricity. Just use the top 10 to 20 percent of the capacity to absorb production peaks.