Solar planes?

When the era of cheap air travel ends in a haze of kerosene fumes, we may have to once again view the world's faraway places only in our imaginations.

Yet even though aircraft cause around 5% of CO2 emissions, perhaps there's a way out. I recently read an article about the first viable electric airplane, a creature which was previously deemed unfeasible. For now, it's only small with limited range ... but it's possible.

Let's get serious, though. What about powering 400-person planes, say, with completely renewable fuel sources? What about the entire world's fleet?

Solar-power air travel might be a fix. Not directly -- we can't run a massive aircraft on solar -- but perhaps we can run it on hydrogen made from solar. If solar power continues to expand at its current rate, we might be able to develop a surplus store of hydrogen to supply the aviation industry.

Let's figure out how much hydrogen (H2) fuel we'd need to get from Sydney to Dallas on a 747. (The world's longest route, I think.) A 747's tank holds 240,000L, so let's assume that monster route uses the whole darn lot. 

A solar plant can make hydrogen via electrolysis -- that is, splitting water into its constituents of hydrogen and oxygen. According to Popular Mechanics, creating 150 million US tons of hydrogen (around 140 million metric tonnes) would take '113 million 40-kilowatt systems'. This works out at 4520 GW. 

Let's say we need four times as much hydrogen to fuel the plane as we would need kerosene -- near enough to 1,000,000L. (Hydrogen has less energy content than kerosene.) One litre of liquid hydrogen weighs only 70g. So, 1,000,000L of hydrogen -- the amount needed for our flight -- would weigh 70,000kg, or 70 tonnes.

Now, we have to figure out how many times 70 goes into 150 million. Answer: 2.14 million. 

So, 4520GW/2.14 million = 2.1MW. A 2MW solar plant like this one could theoretically produce enough hydrogen fuel for a single Sydney--Dallas flight every hour. Let's say this particular solar array could produce 5 flights' worth a day. 

There are around 15,000 commercial aircraft in the world--say, the equivalent of 5,000 747s. That means you'd need 1000 2MW solar arrays to produce enough hydrogen to supply the world's passenger aircraft fleet. 

I feel like there are many, many places I could have made a miscalculation. What are people's thoughts on my back-of-the-envelope calculations?