Could the Sun supply all our electricity?

How feasible would it be to derive the world’s electricity entirely from the sun?

I recently read an intriguing interview in The Guardian given by Professor Sir David King, the UK government’s former Chief Scientific Advisor. Amongst other things, he has posited the notion that only a relatively small area of the Earth’s surface might be needed to collect sufficient solar energy to meet the entire planet’s energy needs. By “energy” I assume he means “electricity”.

Now I am most definitely an advocate of renewables as opposed to other “alternatives”, such as nuclear power; so I was, to say the least, curious to get some idea of just how feasible this might actually be. Of course it’s not easy to do more than a rough-and-ready calculation, but I enjoy messing about with figures, so here goes:

OK - according to Wikipedia, the world’s annual electricity demand from 2005 onwards has amounted to about 6 x 10¹⁹J.

The same reference gives a figure of 1.5 x 10²²J for the daily solar radiation falling on the Earth. I’m not sure whether this is the total energy flux striking the outer atmosphere, or the net energy reaching the surface. Let’s be conservative, and assume it is the former. So suppose, finger-in-the-air, that about one third of this amount is actually useful (ie could be collected by PV panels, say). Thus, we have about 5 x 10²¹J available daily.

We now need to find the power density corresponding to this figure – that is, the energy arriving per second per unit area. This should be something like:

5 x 10²¹/(A x 24 x 3600) Wm^-2

where A is the area (in m²) presented by the Earth’s disk to the incoming light. I do realise the light will be obliquely incident on the surface to varying degrees depending on latitude and (for a given time of day) longitude; but this is, after all, a guesstimate. In any case, it is partly for this reason that A is regarded as the area of a disk and not the area of a hemi-sphere.

The mean radius of the Earth (it isn’t quite a sphere) is roughly 6370km. Therefore:

A = Pi x (6370)² x 10⁶m² = 1.27 x 10¹⁴m²

This gives a surface solar power density of about 456Wm^-2. (I should point out, here, that there are other estimates of the “solar constant”, and thus plenty of room for error in this figure.)

The next thing to do is to convert the annual world electricity demand into an average power requirement. This will be approximately:

6 x 10¹⁹/(365 x 24 x 3600) W = 1.9 x 10¹²W

That is, 1900 gigawatts. (Does that sound about right?)

Then, we ask, what area of solar-collector could supply this? At this stage let’s conveniently neglect the inefficiency of solar panels!

The answer is about 1.9x10¹²/456 = 4.17 x 10⁹m² or about 4000km².

Now on the face of it this seems like quite a huge area. However, suppose it were divided up into 100 separate installations, strategically placed worldwide. (After all, one of the problems that would need to be solved is that of power distribution). Each power-plant would thus need to have a collecting area of 40km². This could be accomplished as a square array measuring about 6km by 6km - not all that vast, in the grand scheme of things.

If the scale still seems out of reach, think of this: suppose an average house or public building has an available roof area of 50m² (eg 10m x 5m). How many such buildings would be needed to do the job for us? The answer, on the above data, would be 4.17 x 10⁹/50

= 9.4 x 10⁷.

In other words: 94 million buildings. The population of the UK is only around 60 million, but then the UK is tiny by world standards. Spread across the globe, maybe it’s not so far-fetched.

So, is it conceivable that we could avoid non-renewables altogether, for electricity-production? In my view certainly; especially given that direct solar power is – and would increasingly be - supplemented by other forms of renewable – wind, tidal, wave, hydro-, etc.

Of course there are many associated problems, and we did neglect the inherent inefficiency of PV panels. Still, even allowing for these drawbacks, perhaps it could be a practical proposition given sufficient political and commercial will.

And incidentally, my own very modest solar electricity supply is working brilliantly (pardon the pun); at latitude some 53^oN, on 2^nd February. If it can work here, now, it can work practically anywhere!

I can always hope, anyway.

Cheers,

Mike

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