# Order of Magnitude Morality

I wrote this page in 2005. It's now superceded by my book, Sustainable Energy - without the hot air.

## I: Energy

##### Summary

`The earth receives more energy from the sun in just one hour than the world uses in a whole year'. So, does that mean that we can convert to solar and everything is going to be fine?

No: I show that the current rate of power consumption of the `developed' world is unsustainable. The `developed' world must cut its consumption by at least a factor of 10, and must put all possible resources into developing solar energy technology, which, along with hydroelectricity, is the only* significant source of sustainable power.

* - Some conditions may apply! See below for details

 Global energy consumption Expressed as a plain power And as a power per human 1998 total energy consumption rate 380 QUAD BTU per year 111 x 1012 kWh per year 12 x 109 kW i.e. 2 kW per person, if shared equally among 6x109 1998 USA energy consumption rate 94 QUAD BTU per year 27 x 1012 kWh per year 3 x 109 kW i.e. 13 kW per American. total worldwide hydroelectric energy production 26.6 QUAD BTU per year 8 x 1012 kWh per year 0.8x109kW 1998 Other Renewable energy consumption (biomass, geothermal, solar, and wind) 196x109 kWh/year 0.02x109kW total worldwide wind energy production 2000 4x106 kW (4000 MW) Typical power station 500-3000 MW.

Let's think about energy consumption, and express it in ordinary human-scale units, instead of exajoules. In these calculations, I ignore all economic considerations, and think simply about the maximum available power.

Assume the earth's human population remains steady at N = 1010 (10 billion) for the next few millenia. What is a fair rate of energy consumption for a typical individual? Well, it's impossible for everyone to consume more than PSmax/N, where PSmax is the maximum sustainable power that can be harvested on the whole planet.

So, what is PSmax? Let's start by finding upper bounds, and see if those are sufficient to make us pause and think about our lifestyle.

Almost all the sustainable power comes from the sun. (Tide and geothermal are the others.) `The earth receives more energy from the sun in just one hour than the world uses in a whole year', says the Solar advertising industry. Let's check, using the ground-level flux in the absence of clouds.

PSolar = Area * Flux = π (6x106m)^2 * 1kW/m^2 = 113x1012 kW

Bzzzp! Non-human quantity alert! Let's re-express this in human units. If we divide by the number of humans, N the per-person total solar power is

PSolar/N = 113x1012 kW / 1010 = 11,000 kW per person.

(The perpendicular area per person is 11,000m^2.)

So, if all the earth's surface is converted to perfectly efficient solar cells, then it will be morally defensible for a human to use 10 MW. That's about 1000 times more than the average American, and 5,000 times more than the `average' human.

OK, so can we just stop using fossil fuels (which is obviously immoral), switch over to solar, and feel moral when consuming 13kW?

##### Can we live on solar?

Let's take into account oceans and a few other constraints. The earth is about 1/4 land -- 150,000,000 km2, or 15,000m2 per person. What fraction of that area is habitable and/or solar-power-friendly? We should knock off a factor of 10 either in area or in flux. Take your pick: You can have your 15,000m2 in Greenland (low flux) or just 1,500m2 per person in Africa. So now, if we have perfect solar cells, covering the whole habitable land area, each human can use 1MW. That is still plenty of power by modern standards.

 Solar Insolation | (Source: Earth Observatory, NASA) (obtained from worldenergy.org)

But what if we allow for the need for a bit of land for other uses -- walking, cycling, sport, farming? According to the internet, `11 percent of the earth's surface is used to grow food'; and half of the world's area that could be used for plant-growing is already in use by farmers. Realistically, I find it hard to imagine more than 7% of the habitable surface being filled with solar panels! Moreover, real solar cells have an efficiency of 15% or so (and Hopfield and Gollub have shown that the best theoretical efficiency that a solar cell could ever have is 45%). Whoops, there goes a factor of 100! So suddenly we are down to the following fact: consuming more than 10kW of power is not sustainable; even if 7% of the world were paved with solar cells, there wouldn't be enough power for everyone to use above 10kW.

OK, we've established 10kW as a bound, but only by assuming that we will be happy to turn over to solar panels all possible land that is not already used for farming. If we want to preserve Nature, wildlife, and beauty, it follows that we must constrain our energy consumption still further, if we are to live sustainably. What fraction of natural space are we willing to turn over to solar power? In Britain, many people find factory-like forests for the production of trees unbearably ugly. What fraction can we imagine giving to solar? Will Grand Canyon be set aside? The Grand Tetons? Will we leave the Giza plateau? Every space that we decide cannot be impinged upon reduces the total power we will be able to harvest sustainably, and thus reduces the power that it is moral for one person to consume.

This fraction is hard to estimate. I would put it at about 0.01, which could be achieved by adding solar panels at the edge of every piece of farmland. If we accept this figure, we find that the sustainable power permissible for one human is 0.1kW (roughly the same as the power of the food that we eat). If we push the fraction to 0.1, we find the permissible power per human is 1kW.

Conclusion: we have to enhance solar power technology, urgently; and we have to cut the power consumption of the `developed' world.

There is no point in developing secondary and tertiary sustainable sources such as wind power and wave power in place of solar. Our sustainable energy needs are going to be so enormous, the primary source must be tapped. (My reasoning is: wind energy comes, very inefficiently, from solar energy; so if we tried to get all our power from wind instead of solar, the maximum possible power per person would be thousands times less than the 10kW bound we found above. Wave power offers even less. However, I return to wind and waves below; I may have been wrong to estimate that wind is useless.)

### Yes, I think the people of the `developed' world are living immorally

To put it another way, if you want to use 13kW of power (which is what the gas-guzzlers of the world do), you should install roughly 520m2 of solar panels in a very sunny spot. (The factor of 40=4x10 is to allow for 10% efficiency of photovoltaics, and the fact that your panels will be in sunlight only one quarter of the time.) Plus I guess you will need another 300m2 or so to provide the power to create, service, maintain, and replace all your panels. Whoops! That is over 800m2 of panels. [There isn't enough space on the planet for everyone to have that much area!] I guess a typical house might have 40m2 of roof area per person, so if you want to live sustainably, you'd better buy a big garden to put all your panels in, like this American millionaire: his array has a size of about 300m2 and generates an average of about 5kW. His website is highly recommended.

A huge crisis is upon us, unless we change our lifestyle.

#### What I included and left out

My calculations above neglect the possibility of using solar power more directly than through photovoltaics. It's obviously a good idea, and more efficient, to use direct thermal solar systems for water heating, for example. But water heating is only a small fraction of the power that the `developed' guzzle.

Another idea I should have considered is the possibility of putting solar generators off-shore.

I didn't mention `solar biomass' either - that is, growing plants for energy and for materials; ; I like to classify plants as `solar panels' :-). From the point of view of a physicist, photovoltaic panels and plants do much the same thing: capture photon energy in electrons! Perhaps the solar panels of the future will incorporate technology borrowed from plants or from bacteria. I particularly like the idea of evolving photosynthetic bacteria to generate electricity rather than carbohydrates.

While we wait for bacteriolectric research to get research funding, we should estimate whether biomass could provide our needs, sustainably[]. Biomass certainly has advantages: compatibility with coal power station technology, miniaturizability. If we focus on electricity production, our calculation has two steps: from photon to chemical energy, then from chemical energy to electricity. This order-of-magnitude calculation says that the photon-to-chemical-energy efficiency of plants is in the range 0.5% (pine forest) to 1.5% (corn in Summer). Typical coal power stations have an efficiency of about 35%; the very best, 55%. Multiplying these two efficiencies, and including a factor of (1/4) for loss of daylight, let's use 0.15% as a ballpark figure for the efficiency of biomass solar (to be compared with the 15% figure used for photovoltaic). The area per human required for biomass to give a sustainable 1kW is then 2400m^2. (The figure for a willow-burning biomass plant in England is indeed 2500m^2 per kW of electricity.) This area is huge, though not as big as the area per person currently devoted to farming worldwide. But for a place like England, where the population density is 377 per square kilometre, i.e., the area per person is 2650m^2, biomass is, sadly, not a sustainable power solution, if everyone is to have 1kW. For further criticism of biomass, see George Monbiot's article.

I have also neglected hydroelectric power, which is a secondary way of benefitting from solar power. Hydro supplies 7% of current power consumption, so it clearly will play a big role in saving our bacon. If the `developed' world can cut its power consumption by a factor of 10, then maybe hydro and solar together can provide a sustainable solution. Hydro has the excellent advantage that it can be switched on and off in response to demand.

What about fusion? Well, maybe it'll work, but the precautionary principle says we should make plans for the worst case.

##### Conclusion

`Even at 10% efficiency, 1 thousandth of the Earth's surface should be able to provide sufficient power for current consumption'.

But 1 thousandth of the Earth's surface is a hell of a big area! It's about 10m2 per person. We need to get to work, researching solar, making economical solar panels and putting them up! I can see no alternative.

PS: Why do I say it's urgent to get to work on solar panels now? `Fossil fuels might last another 200 years!', an anti-solar `stop-fussing' person might argue; `Just let our great-grandchildren clean up our mess'.

But reasons for acting urgently are (a) the IPCC is unanimous that CO2 emissions are causing catastrophic climate change. We should therefore cease all fossil fuel consumption as soon as possible; (b) even if you don't believe in the risk of global warming, it's plausible that an oil crisis is coming within just a few decades, or perhaps even sooner; this oil crisis is beyond politicians' short-sighted 5-year radar, but science and technology need longer than 5 years to create solutions.

My friend Matthew Bramley suggests the best way to fund the research would be this: mandate the electricity producers to produce small but steadily increasing percentages of solar power - with the possibility of selling the excess in the form of tradeable solar certificates it they exceed their targets. They would then have a powerful incentive (if the electricity market is competitive, and they can't just pass on costs to consumers) to do their own research to cut the costs. This is likely to be more efficient than having the government commission the research.

Conversion Factors: (from usgs.gov)
Volume/weight/mass
1,000 ft3 = 28.3 m3
Cubic feet X 0.02831685 = cubic meters
1 cubic meter = 1,000 liters = 35.31 cubic feet
1 gallon = 3.785 liters
1 barrel = 42 gallons = 159.0 liters
Barrels X 0.1589873 = cubic meters
1 kilogram = 2.205 pounds
1 pound = 0.4536 kilograms
1 short ton = 0.9072 metric tonne
1 metric ton = 2205 pounds

Energy
1 Btu = 252.0 calories = 1055 joules
1000 joules = 0.9479 Btu
1 joule = 0.2388 calories
1 calorie = 4.187 joules
1 kilowatthour = 3.600 x 106 joules = 3,412 Btu
1 quad = 1015 Btu = 2.931 x 1011 kilowatthours
1 therm = 100,000 Btu

Power
1 watt = 1 joule/sec = 3.412 Btu/hr
1 Btu/hr = 0.2931 watts
1 kilowatt = 0.9478 Btu/sec = 1.341 horsepower
1 Btu/sec = 1.055 kilowatts
1 horsepower = 0.7068 Btu/sec = 0.7457 kilowatts

Pressure
1 psi = 6.9 kilopascals

Other:
1 bbl oil = 1700 kw hr = 6120 X 106 joules
1000 ft3 gas = 300 kw hr = 1080 X 106 joules
1 metric ton peat = 5370 kw hr = 19,332 X 106 joules
1 short ton coal = 0.9078 metric ton = 6600 kw hr = 23,760 X 106 joules
1 metric ton of oil = 7.64 barrels for oil with API gravity of 40°

1 acre = 4 046.85642 meter^2

In preparation...
 Power per person Area that must be devoted to solar panels of efficiency 15% (assuming no cloud cover) How that compares with the 10^10 acres (4x10^13 m^2) currently used for farming: farming is 8000m^2 per person. 1kW 80m2 Actual area used for a willow-burning biomass plant in England: 2500 hectares for 10 MW (electricity) 2500m^2 per kW.

## Other options

The sustainable powers we are arriving at from solar power are so small, we should really consider all sorts of other power sources. For example, humans! If the rules of sustainable power say I can only have 0.1kW from solar, then, occasionally, I would be happy to hop on the electric bicycle generator, and pedal up an extra 0.1 kWh for myself. (Of course, I would need to be fed; so this is another biomass system, and hasn't really fixed the problem.)

## Vegetarianism

Becoming vegetarian will free a load of land area that could be used for biomass or photovoltaic.

## Population shrinkage

A ten-fold reduction in world population would make matters easier.

## Tide

Why dismiss tide? Tide would have the nice property, for Britain, that power could be generated continuously, because there is at all times a low tide location somewhere on the perimeter of Britain. Let's check how much power tide offers. Rather than estimate the total power available, let's go directly for the power per unit area that a tidal plant could generate.

The power of a unit area is

ptide = 1/2 ρ g h^2 / T
where h is the tidal range (1m in oceans, bigger in a few places like Britain); ρ is the density of water, 1000kg/m^3; g = 10m/s^2; and T=12 hours = 4x10^5 seconds is the time between flushings.
ptide = 0.1W.
Gosh, that's small! So, to generate one kW, we require 10,000m^2. (Also known as 1 hectare or 2.5 acres.) To generate 100million kW for the population of Great Britain, how wide a tidal generator strip would we need around the coastline, length l = 11072 miles (18000km)?
w = 100million kW / ( ptide 18x10^6 m ) = 1.2km.
Wow. One kilometer. So tide is no solution, if everyone needs a kilowatt. The only tidal solution worth considering is to use naturally occurring tidal basins, such as the North sea. Underwater tidemills could be used in the english channel.

## Wind

A 4-metre windmill makes 6kW. One big windmill = 2 MW (that's peak?). Let's use 0.5MW as an average figure, allowing for a factor of 4 loss relative to peak production in perfect conditions. So the required windmill density for a country like Britain, if everyone gets 1kW, is one windmill per 1.3 km^2.
That's a very high density, but it is not out of the question. So maybe wind power is better than solar power as a way of supplying all our energy sustainably. The down-side of having one windmill per 1.3 km^2 is, I imagine, that that would be the end of bird-life.
What if all the windmills are put off-shore? We need 120,000 big windmills, to deliver 1kW each for 60 million people. If we devote 1000km of coast to windmills, that would be 120 windmills per kilometre (assuming they do not interfere with each other). I find this hard to imagine.
A website criticising wind power. Another website with OOM calculations indicating that to replace one ordinary GigaWatt power station, a wind farm of 300 square miles would be needed. This excellent Danish site has an explanation of Betz's law, which shows that windmills can be at most `59% efficient'. And graphs of actual efficiency of Danish turbines. More tables. Vestas provide data on how long it takes for a windmill to pay back the energy for its own production and destruction (9 months). And graphs of impact in milli-person equivalents.

## Waves

According to a guy called Thorpe, `If the technologies being developed today become widely used, wave energy could amount to nearly 16 percent of the world's current total electricity output'. Wave power prototypes have been made. (pictures) The 'Osprey', which was meant to produce 2MW, broke the same day it was launched. Let's check the numbers. The power of ocean waves is said to be 40 kW per metre of coastline. [We could estimate that by

pwaves ρ g h^2 v,
where v is the typical wave velocity (10m/s?), and h is the amplitude (0.5m).
pwaves ρ g h^2 v = 25kW/m.]
So the total power that Britain could be obtained from waves with shore-line facilities (assuming a coastline of length 10^6m, since the wiggly coastline is not appropriate here) is 40kW/m*10^6m = 40 GW; or, about 0.66kW per person. Blimey! Even though waves are a tertiary form of solar energy, a perfect energy-extractor would deliver quite a lot of energy. [Question: The Osprey size was only `the size of a small house'. How could it produce 2MW? Surely, at 50% efficiency, it would have to be at least 100 metres wide? From the picture it looks only 20m.] wave info

## Geothermal

The flux of geothermal energy is not enough for us to live sustainably on it. (The average flux is clearly much less than that of sunlight.) But another option would be the unsustainable harvesting of heat from the magma reservoirs of the earth (at a rate faster than the heat is generated by tide and nuclear decay). It's not sustainable, but if the heat would last tens of thousands of years, maybe we should do back-of-envelope calculations.

# II: Carbon

coal-fired electricity produces about 1 kg CO2 per kWh.
More links: Peak Oil | Oil crash | warming-induced switchoff of Gulf Stream |
Jeffrey S. Dukes. Burning buried sunshine: Human consumption of ancient solar energy. Climatic Change, 61:31-44, 2003 has the biomass-energy conversion calcs: it took over 23 tonnes of plants to produce each and every litre of petrol you pump into your tank.
Thanks to Michael Cates, Matthew Bramley.
David MacKay