Monday, January 24, 2011

Our Energy Allowance

In order to shift our society from fossil fuel to renewable energy, we need to know how much renewable energy is available, how much daily solar allowance can we count on? One study shows that there is more energy reaching the Earth from the Sun in one hour, than the entire world uses in one year. It seems there is plenty.

The following model tries to determine how much solar energy can be harvested on a global scale, it doesn't look at what we actually use today for transportation, food, or other things. This is how much we get, whatever we do with it.
The model uses the area presented by the Earth to the Sun at any time, 24/7. For that, I used the area of the disk presented by the Earth, instead of the surface area of the Earth itself, which, because it is a sphere, would receive variable amounts of energy depending on latitude and time of day. Using the surface area of the Earth would require going through multiple use cases, while using the disk that the Earth presents to the sun at any time, allows to determine the global energy received from the sun, regardless of latitude, day-night, equivalent sun-hours or other fancy formulas. This is what we get on a global scale.
The model doesn't tell how we will harvest that energy. Again, this is another problem. Before we decide how we will harvest it, we need to know how much we get.

So here we go...

Solar irradiance = 1400 W/m2 at the top of the atmosphere. This is the amount of solar power on a one square meter area. The atmosphere will absorb and reflect a part, so it is estimated that the average amount of solar power reaching the Earth surface is ~ 1000 Watt / m2.

[ Solar Irradiance Reference ]

Now we can calculate how much square meters the Earth presents to the sun.
Diameter of Earth = 12,000 km = 12*10^6 meters
Radius = 6*10^6 meters.
Surface presented to the Sun = PI * (6*10^6)^2 = 113*10^12 m2.

The total amount of energy reaching the Earth surface is:

113*10^12 m2 * 1000 Watts/m2 = 113*10^15 Watts.

About 70% of the Earth surface is covered by water, so 30% remains. Of those 30% land area, we can assume that covering 1% of the land area with solar panels would be a maximum practical ratio, so 0.3% of the total energy may be harvested.

113*10^15 * .3% = 34*10^13 Watts
This is the amount of electrical power we receive from the Sun over 1% of the land area.

We are 6 billion people, so we need to share this power.

34*10^13 / 6*10(9) = 56 KWatts per person

Energy is power multiplied by time.

56*10^3 Watts * 24 hours ~ 1.3 MWh / day / person.

This is the solar allowance each of us can use before we start depleting resources.
Now this is before conversion into useful energy. The average conversion efficiency is about 20% for electricity (best case).

[ Photovoltaic Efficiency ]

Converting all of our solar energy allowance to electricity, we would have:
1.3 MWh * 0.2 = 271 KWh / day / person

Now lets see where we are today in the United States, as far as energy usage per capita.

Total energy usage of USA in 2005 = 29*10(15) Wh
US population = 300 Millions = 300*10(6)
Energy usage per capita in 2005 in the US = 100 MWh/year = 280 KWh / day / person.

[ US Energy Usage Reference ]

We can fulfill our electrical needs if we cover 1% of the land surface of the Earth with solar panels.


  1. Andre,

    Have you compared your calculations with those of anyone else? And have you taken any other approaches? For example, how much land do you need to grow food in this climate and collect energy? How much energy is collectable? Is that enough.

    Also you haven't included transportation, etc. uses of energy.

    Let's keep refining this.

  2. Hi Dean,

    This is a calculation of the global average solar energy allowance. Whether we use it for transportation or something else doesn't really matter. It is the only truly renewable energy we have, regardless of what we do with it.

    I used numbers from different websites, making sure I was getting several references (for the 1400W/m2 for example). I haven't found any similar calculation as far as the global average daily allowance per person.

    Food is another matter. A similar calculation could be made, maybe based on calory produced by solar energy units, but I don't have the knowledge in this area.

    However, separating the different energy uses would vastly complicating the estimation. This is the global allowance, all uses included.

  3. Hi Andre,

    Thanks for showing this calculation! this is very informative for me, especially that i'm sharing this type of information to my clients.

    I'm curious of the next phases of this calculation if in the event this will be refined as it goes along. What will the next steps be?

  4. Hi Joshua,

    you are welcome. I hope my calculations are accurate, it took a few corrections to get the current results, and I hope there aren't any inaccuracies.
    If you think something looks not right, don't hesitate to tell me.

    The conclusion is a little misleading. When I say 1% of the land area, it is actually 1% of the surface presented to the Sun that is emerged, that is quite different. The next step could be to clarify that difference.

    I may also add graphics to represent the equations in a more understandable way.