A blog post that claims a 200×200 miles square collects enough solar energy to power all of humanity did create quite a lot of buzz on Twitter recently. I decided to check whether this is indeed true.

I started with finding out how much energy we really get from our nearest star – the Sun. It turns out there is a number known as the solar constant which describes exactly this and it was measured to be 1368 watts per square meter (W/m²).

200×200 miles is 40,000 square miles, or 103,684 square kilometeres, about 5 times the size of Wales. If we compute the potential power using the solar constant mentioned above we get 141.8 TW (tera watts) from this area. The total energy consumption of the world is estimated to be 15 TW (tera watts) – so far so good.

However, the solar constant is the energy we get from the Sun as measured in the orbit above the atmosphere. As long as we don’t consider energy collecting satellites we have to compute further. At ground level not only absorption and reflection by the atmosphere has to be taken into account, but also the fact that due to Earth’s rotation any given point on its surface is in the dark (not getting any energy) roughly half of the time.

The number we get when we factor all of this in is 342 watts per square meter. With this our 200×200 miles square produces 35.46 TW (tera watts). But this still doesn’t take into account the weather and the variation of solar irradiation related to latitude. Most of the current “developed world” is in the areas north and south of tropics, getting less sunlight. Because of this we can’t assume it will make sense to put all solar panels at the equator. And even there cloudy days happen.

I therefore assume solar generation would occur mostly in the southern regions of the “developed world” and base calculations on this. Different values are published re. irradiation on the ground in those regions. I decided to assume optimistically that what really reaches the ground is on average 275 watts per square meter. (source, source)

But this is just a potential energy – next problem is how effectively we can convert it into something that is useful for us, like electricity. Part of this is that the numbers above describe total energy of radiation coming from the sun, which is distributed along the spectrum (see how), not all of which can be changed into electricity. The other part is the technology we have at our disposal and its limitations. Right now generally available photovoltaic cells operate at 30% efficiency, some experimental systems exist that can get up to almost 40%.

If we now take also this into account a 200×200 square covered with generally available cells would produce 8.554 TW, if we could get Fraunhofer’s cells working at 40% in quantity we would get 11.41 TW.

That means we would need just a bit more than a 200×200 miles square covered (1.31464 more to be exact) with Frauhofer’s high yield cells to satisfy world’s demand at 15 TW. In other words the area needed would be 52 586 square miles – or 229×229 miles square: about twice the size of lake Victoria.

Now, I wanted to check my computations to see if they really add up (this is where I discovered an error in my original post). I looked at solar panels available on the market and computed how much power would the give if they were used to cover a 200×200 miles square.

Let’s take BP Solar‘s BP 3125, to which I was able to get the technical spec sheet [PDF]. According to it this panel produces 125 W of power from 0.876 square meters of cells (36 square cells). That means it generates 109.51 W / m2. If we were to cover our 200×200 miles square with those panels we would get 11.355 TW.

Of course this panel generates this amount of power only if exposed directly to sunlight, which means in reality such an array would produce less power due to Earth’s rotation (it would spend some of the time in the dark) and weather fluctuations. However, amazingly the computations above confirm we would need just a tiny part of the Earth’s surface to produce all the energy we need without any kind of emissions (except those made when making the panels and soldering them together).

The interesting question is then: why are we not doing it?

One frequently mentioned problem is the price of the panels. The cost per installed watt is estimated between $7.5 and $9.5 (source). Let’s assume it at $8 – that would mean 120 US$ trillion to replace 15 TW of power we need. This is almost 15 times the current official US national debt. Even at the current levels of US$ loss of value it is still a huge price tag.

However, no one would expect US to pay for all of it (even though US has been consuming most of oil and is consuming most of the energy). If we spread it amongst all industrialized nations of the globe it should be doable.

Another problem could be availability of raw materials and energy needed to produce required quantities of those cells in the first place. But this a question for a separate different article.

This article existed here for a couple of days in a completely different version based on computations which were based on an error. Interestingly, no one noticed until I started to check them again by computing backwards – that is by taking a real, available solar panel and computing how many watts of energy from square meter it can deliver. Sorry for any confusion caused.