Solar Energy, My Colleague's Response

Today's Toronto Star:


A bright energy future without coal or nuclear

This week, our dirty coal-fired power plants were back in the news with electoral candidates arguing the ifs and whens of their necessary shutdown. Shutting down coal plants, our guiltiest climate-change-causing beasts, seems like a no-brainer, but heels keep dragging.

For Ontario, a decision to invest billions of dollars in nuclear megaprojects or coal scrubbers is a decision not to invest in clean renewable technology. Every dollar sunk into huge transmission systems to support centralized megaprojects is a dollar not invested in "smart grids" that accommodate local production of renewable energy.

A bright energy future without the need for coal or nuclear is doable. With renewable energy, energy efficiency and co-generation, we can cut our greenhouse gas emissions by half of what's called for in the OPA plan. Ontarians could actually be saving money on their electricity bill rather than deepening our nuclear debt with at least another 40 years of expensive and unreliable power, not to mention generating more long-lived, unsolvable radioactive waste.

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My Colleague's Musings:

Some back-of-the-envelope calculations on the short-term prospects of solar energy

Starting from Stefan/Boltzman’s radiation law where one uses the Sun’s temperature (6000K) and that of the Earth(300K) and the solid angle of the Earth as seen from the Sun (6o), we calculate an available energy flux of approximately 1.4 kW/m2. Being close to the per capita average usage (calculated based on the total world energy consumption divided by total population), this is a very promising number.

Thus, if we were to capture all the energy arriving from the Sun (and, in the long run, this is the source of ALL our energy) we would each need only 1 m2. Not bad!. Yes but .... we have to make several small corrections ....

The formula calculates the energy flux on a plane perpendicular to the direction of the flux i.e. the cross-section of a sphere. For our Earth, we would have to multiply with the ratio between the surface of the sphere (4ðr2) and that of the cross-section (ðr2), i.e. 4. Therefore, we each need 4m2.

Well, that’s still not bad. Let’s cover the Earth with solar collectors. Oh, but the dry portion is only about one quarter; our planet is covered by oceans for the rest. The answer is easy, we’ll take 4 times more of the dry land, i.e. 16m2 each. In communist Russia the calculation of the built living area allowed just 10m2 per person .... we’re already exceeding their "standard". Unfortunately, we still have some small adjustments to make ....

I forgot about yield. Nothing operates at 100%; this applies to the conversion of solar energy to electricity too. The best solar panels have reached nowadays 5% (or less). Let us hope that science will bring us to the yield close to that of the plants, i.e. 25% - the conclusion is that we have to .... multiply again by 4. We need now at least 64 m2 each!

Oh, but I forgot a small detail. All these calculations referred only to our average use of electric energy; we use many other forms: the gas in the tank of the car, the steam in industrial boilers, the propane in the BBQ tank, that in lighters, etc. . . . Well, we can ignore the lighters for this exercise but since electric energy is only approximately one quarter of the total energy consumption of the "average person" .... we multiply by 4, again. We need thus at least 256 m2 each!

If we remember that man needs food to live, and for this rough calculation we decide to ignore the needs and aspirations of the animals and plants - after all, there are many that we do not eat but who would also have a "natural" right to exist - and, if we decide that we should share equally these energy resources with all the other lining species, i.e. 50:50, we conclude that the per capita area needed (to be covered with solar collectors) doubles yet again; 512 m2 per person!

All the above were calculated for averages. Generating capacity is calculated for peak consumption. A factor of 2 may not be unreasonable at the scale of the planet. Therefore, we each need at least 1024 m2!

My conclusions from all this back-of -the -envelope calculation are:

1 - There is too many of us;

2 - For now, solar energy alone is not yet "the answer"; conversion yields are too low; we have to consume some of the reserves while developing a more permanent answer because it is quite evident that we cannot, in the long run, consume more than what we get from the Sun.

3 - All the numbers we used appear to increase in the pattern quite similar with the one observed in our need of computer memory; especially since the arrival of Windows. It appears obvious to me that Bill Gates is the one that controls the energy of our world! Many of us had this suspicion!