Sunday, October 31, 2010

Powering Our Future

Concern over the environmental impact of energy production has been rightfully high in recent years. In deciding how we are going to provide energy in the future, we need to consider how much energy we are going to be able to provide and at what cost it is going to come, cost being both environmental and financial.

The Present Situation

As our population has continued to grow and we adopt wealthier standards of living over time worldwide energy consumption has continued to increase accordingly. As of 2008 worldwide energy production was 5.1*10^20 Joules (4.9*10^17 Btu). For those of you not familiar with these units, a typical 60 Watt light bulb uses 60 Joules of energy every second. This world total does not include only electrical energy, but also energy used to drive our cars, heat our homes or perform any number of other tasks. As of 2008 Oil accounted for 33.2% of our energy production, Coal 27.0%, and Natural Gas an additional 21.1%. The next largest source of energy production comes from the combustion of biomass (wood and other plant materials) and other wastes both municipal and industrial, accounting for 10.0% of energy production. Next we have Nuclear energy accounting for 5.8% of production and Hydroelectric energy accounting for another 2.2%. The remaining 0.7% of our production is the amount currently produced by all of the other methods we currently hear about; the sum total of all our efforts for renewable energy.

Check out the International Energy Agency's 2010 Key World Energy Statistics report for additional information on our present situation.

Future Challenges

Our three main energy sources at present are problematic for a number of reasons. Most obviously, they are all finite and at present use rates are each going to run out between a few decades and a few millennia from present. Extracting each of them will become increasingly difficult in the future as the more easily accessible sources of each become depleted.

More importantly perhaps, each of these make a huge contribution to anthropogenic global warming. Our atmosphere is transparent in the visible and near-visible parts of the electromagnetic spectrum. Our sun emits electromagnetic radiation including the light we see because it has a temperature. At it's surface temperature of roughly 5800K most of the light it emits is in the part of the spectrum where our atmosphere is transparent. The earth's surface temperature of roughly 300K emits virtually all of its energy as radiation in the infrared portion of the spectrum. Carbon dioxide and other greenhouse gasses are opaque in the infrared portion of the electromagnetic spectrum and thus absorb a great deal of radiated energy from the earth's surface once again. The burning of each of our three main fuel sources is the largest anthropogenic source of carbon dioxide.

Finally, the burning of coal in particular emits quite a large amount of particulate matter and a number of other pollutants into the atmosphere which can be detrimental to health in excess.

Replacing these means replacing the energy they provide. Not merely the electrical energy generated from these sources, but we need to be able to replace the energy used to drive our cars, heat our homes, fuel our stoves, build our products, and transport our goods as well, which largely comes from these three main sources.

There are a number of energy alternatives to these three main sources which have been proposed. A great deal of effort has been put into making many of these a reality, but they still have seen little success in replacing our present system of production. Some of them, such as cold fusion or perpetual motion are nothing other than magical thinking, but many others have actual potential for energy generation and have even been put into place to some extent. This post is going to attempt to look at the several most realistic of these sources in particular assessing both their potential costs and their potential for energy generation.


After biomass and nuclear energy, hydroelectric energy is the only remaining energy source with any significant implementation to date. Hydroelectric energy comes from the potential energy water (or any mass) has when in a gravitational well. This energy can be calculated by multiplying the mass by the force of gravity by the distance the mass is moving in the direction of the gravity force. If we wish to calculate this energy in Joules for a mass on earth we would use 9.8 (m/s/s) as the value for gravity and the distance in meters that the mass of water in kilograms is traveling up or down. Assuming that a typical area of land has 80cm of rain a year falling at a mean altitude of 100 meters, this would equal roughly 1.2*10^20 Joules of energy per year for the entire landmass of the earth, still only a fraction of the supply we need to replace. Additionally, it is obviously unrealistic to expect us to be able to capture every bit of potential energy from when a water drop lands anywhere on land until it reaches sea level. More realistically the best hydroelectric resources have already been utilized and there is only marginal room for growth potential in this area.


One of the positive aspects about hydroelectric energy was that when water is held behind dams, it can be released to generate electricity as there is demand for it. One problem that comes with adopting solar-heavy energy generation is that we are only able to generate energy as it comes in. This means we need to find ways to store sufficient energy during the day to supply our needs at night and sufficient energy during the summer to supply our needs during the winter as well.

At the earth's distance from the sun, solar radiation amounts to roughly 1367 Watts (Joules per second) for every square meter of surface perpendicular to the direction to the sun. This varies by about 50 Watts per square meter over the course of the year due to the earth's slightly eliptical orbit and by roughly half a Watt per square meter over the course of the 12 year solar cycle.

Not all of this light makes it through our atmosphere and earth, as a rotating sphere, doesn't have all of its surface perpendicular to the direction to the sun. A good area of desert at low latitude can expect somewhere around 300-350 Watts of energy to reach every square meter of surface. Solar power doesn't need to include only solar electrical generation, it is currently used in many areas for heating hot water as well as homes.

When it comes to generating electricity from heat we cannot achieve anywhere near full conversion. The finest solar cells we are able to assemble in labs are able to achieve slightly over 40% conversion efficiency at present. A typical multicrystalline silicon cell someone might install on their roof however would probably be able to achieve between 14% and 19% efficiency. Large solar power generating facilities often use parabolic reflectors to focus light on a single small area which is then usually able to achieve around 35% efficiency.

As of 2008 Solar energy accounted for less than 0.02% of the world's total energy production. This is likely due to the high costs of installing solar cells compared to other technologies and the accordingly higher costs for the electricity generated (usually a few times that of most other technologies Source. Solar energy, however, does at least have the potential to meet the world's present demand for energy if we were able to build the required infrastructure. Assuming we are using 18% efficient solar cells in an area receiving 300 Watts per square meter of energy from the sun, we would need to cover 3*10^11 square meters with these cells in order to meet the world's demand. This is almost exactly equal to the area of the US state of Arizona (and covering their entire state with solar cells sounds about as reasonable as the “birther” and illegal immigration legislation they've passed this year).


At present, wind power accounts for approximately 0.24% of worldwide energy generation. Wind power is even less reliable than solar, depending entirely on wind conditions to determine the energy it generates. Accordingly if we are going to adopt an electrical grid dependent upon wind power we need to be able to find ways to store energy for possible multiple week periods of calm winds.

A 2005 study from Stanford University attempted to estimate the world potential energy generation from wind power by attempting to measure wind speeds around the world at the height of a modern large wind turbine. Assuming all of the world's windy land or near-land areas were covered with massive 80 meter high, 77 meter diameter wind turbines, the authors estimate wind could provide 2.3*10^21 Joules or roughly 4.5 times the world's current energy needs.

Achieving this potential would require massive engineering well beyond anything ever completed before. Each of these 77 meter diameter wind turbines towers into the air roughly as high as a 38 story building. Most of this potential does not exist on land, but rather offshore where building challenges become much greater and costs also skyrocket.


Roughly 1.4*10^21 Joules of energy flows out through the earth's crust from the mantle each year. This represents roughly 2.7 times the planet's present energy demands. Of this, roughly 2/3 is replaced by radioactive decay. The difference between these two values is due to the huge amount of energy left over from the accretion of our planet.

Most of this energy can not be reasonably harnessed. Part of this is because most of the planet is underwater and also because most areas have very small amounts of geothermal energy coming up through the crust. The most optimistic estimates for how much energy we could ever expect to extract from geothermal power is roughly 8.0*10^19 Joules per year or roughly 17% of our worldwide demand. More sober estimates for the potential of geothermal are as low as 2.2% of present worldwide demand.


Waves are generated by winds blowing across large open bodies of water such as our oceans. The energy in wave power depends upon the square of the wave height and the frequency of the waves.

Estimates from the International Energy Agency for the total energy available in wave power vary widely from 3*10^19 Joules per year to 3*10^20 Joules per year. The World Energy Council estimates the wave resource as at least 6*10^19 Joules per year. Overall these estimates range from 6% to 60% of our present supply. Harnessing all of this resource would mean covering all of our coastline or an equivalent region of open sea entirely with wave collectors.


Tidal energy is, in my opinion, the most fascinating of our proposed energy sources. Tides are generated by the gravitational pull from the moon (and partially the sun as well). Water is held to the earth by the earth's gravity, but the slight impact the presence of these celestial bodies has on the gravitational force at the earth's surface creates two small tidal bulges of water following the moon around the sky. Since the earth rotates faster than the moon, the effect of friction from the earth's surface keeps these bulges slightly ahead of the moon's position. This has the effect of pulling the moon forward just slightly sending it into a higher orbit and robbing the earth of a small amount of its angular momentum.

The earth has a gravitational impact upon the moon as well, enough to slightly distort its distribution of mass as it rotates. This is the reason the moon has become “tidally locked” with the earth, always showing the same side to those on the earth's surface.

The earth has quite a bit of energy stored in its rotation, a total of roughly 2.1*10^29 Joules, or enough to supply the world's energy at today's rate of demand for a little over 400 million years. We cannot simply take this angular momentum from our planet at our will however, it depends entirely on the changes in water distribution caused by our moon.

The equation for energy in water works very similarly to our equation for hydroelectric power. If the tides raise the height of water by two meters over a square kilometer area (1,000,000 square meters) then this water with a density of 1000 kg per cubic meter will have a mass of 2*10^9 kg (2 million tonnes). Not all of this water will have two meters it is able to descend however. Only the water at the very top of our column will be able to return a full two meters down, the water in the middle will only be able to descend a single meter and the water at the bottom of the column will have remained at the original sea level. The average distance the water will be descending will be only a single meter. Thus, a 2 meter tide over a square kilometer region has 9.8 (gravity) *2*10^9 or 19.6 billion Joules of energy. There are roughly 700 tides per year so this would mean 1.4*10^13 Joules of energy per year in our hypothetical square kilometer.

Tides in the open ocean are fairly small and much harder to harness. The potential for harnessing tidal power exists mostly in bays and estuaries with large tides. No worldwide estimate exists for the total amount of tidal energy that can be reasonably harnessed; however, estimates have been made for bays and estuaries with at least one bank in England, which has a relatively large coastline and fairly high tides. England is estimated to have roughly 1.8*10^17 Joules per year of useable tidal energy. This represents less than 0.04% of the world's present energy supply. Even if we did scale this up to all of earth's useable bays and estuaries it would be difficult to imagine more than a couple percent of our demand being met by tidal power.


The United States department of energy has put together a report estimating the costs of most of the energy sources we discuss for the year 2016.

The overall cost is listed in the far right column, one megawatt-hour being equal to 3.6*10^9 Joules.

Most of the energy sources are able to compete fairly closely in terms of price with three exceptions: offshore wind, solar photovoltaics, and solar thermal. The main trouble is that offshore wind and solar were the two energy sources we investigated that actually had the potential to replace our current major energy sources, or even come reasonably close. The good news is that we have yet to look at the two energy sources we ignored at the beginning, biomass and nuclear energy. These two energy sources have the most potential to replace our current energy supply, but are also the most controversial for their perceived risk. Because of this, each of these energy sources will get the attention they deserve in their own future post.


Note: If you have trouble verifying any of the numbers in this post feel free to ask in the comments for additional clarification. Most of the calculations are simply changing units to maintain consistency, but occasionally some additional steps were done.


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