Limits To Growth/conversions

Constants, Conversions, and Equivalence Factors

Calculating limits to growth requires many conversions between equivalent, or near equivalent quantities of land area, energy, emissions, and other quantities. This page assembles various quantities useful in these conversions. These have been gathered from a variety of sources (cited and listed at the bottom of this page.) Where reliable sources provide a range of values, this is often presented, and the preferred value, used for calculations in the course, is indicated. This course favors the International System of Units (SI).

Land Area

The following area equivalences are helpful in converting various area measures. These can be easily obtained from Wolfram|Alpha.

Square Mile	Square Kilometer	Hectare	Acre
1	2.59	259	640
.3861	1	100	247.1
.003861	.01	1	2.471
.001563	.004047	.4047	1

Time

1 year	31,536,000 seconds	525,600 minutes
1 month	2,628,000 seconds	43,800 minutes
1 week	604,800 seconds	10,080 minutes
1 day	86,400 seconds	1,440 minutes
1 hour	3,600 seconds	60 minutes
1 minute	60 seconds	1 minute

Mass

Unit Name	Equals	Alternate Units
Kilogram	2.205	Pounds (weight on earth)
Metric Ton (Tonne)	1,000	Kilograms

Volume

Unit Name	Equals	Alternate Units
US Gallon	3.785	liters
Oil Barrel	42	US Gallons
Oil Barrel	159	liters
Bushel	35.24	liters
Acre foot	1,233	cubic meters
Acre foot	325,851	gallons

Power and Energy

Energy is the ability to do work. Rolling a boulder up a hill represents a particular amount of energy. Power is the rate energy is applied. It takes more power to roll the boulder faster than slower, but the energy is the same if the boulder is moved the same distance, regardless of the speed. The equivalency between various units of power and energy are shown in this table. These can be readily verified at WolframAlpha or Google.

Unit Name	Type	Equals	Alternate Units
Watt	Power	1	Joule Per second
Watt Hour	Energy	3,600	Joule
Kilowatt-hour	Energy	3,600,000	Joule
Megawatt-hour	Energy	1,000,000	Watt Hour
Kilowatt-hour / Day	Power	41.67	Watts
BTU	Energy	1055	Joule
BTU	Energy	.2931	Watt Hours
Therm	Energy	100,000	BTU
Therm	Energy	105,500,000	Joule
Therm	Energy	29.3	Kilowatt-hour
Therm	Energy	3.3454	Watt Years
Calorie	Energy	4.184	Joule
Kcal (food)	Energy	4184	Joule
toe (ton of oil equivalent)	Energy	41.868	GJ
toe (ton of oil equivalent)	Energy	11 630	Kilowatt-hour
toe (ton of oil equivalent)	Energy	10 million	Kilo-calories
toe (ton of oil equivalent)	Energy	39.68 million	BTU
Horsepower	Power	745.7	Watts
Foot-pounds	Energy	1.356	Joule
Foot-pounds per second	Power	1.356	Watts

Food and Nutrition

The United Nations Food and Agricultural Organization (FAO) uses the Minimum Dietary Energy Requirement, measured in kcal/person/day, to estimate the prevalence of undernourishment. Dietary energy requirements differ by gender and age, and for different levels of physical activity. Accordingly, minimum dietary energy requirements, the amount of energy needed for light activity and minimum acceptable weight for attained-height, vary by country, and from year to year depending on the gender and age structure of the population.

A listing of MDER by country is available as a spreadsheet from the FAO Food Security Statistics Division.

These have the following statistical characteristics for the years 2004-2006:

Statistic	kcal/person/day
Maximum	1990
Minimum	1680
Median	1820
Mean	1825

Because the MDER is expressed as a single aggregate number of kcal / person / day it does not directly account for variations in the distribution of food to individuals, nor the various requirements for fat, protein, and specific nutrients. Therefore the FAO follows a carefully developed statistical Methodology For The Measurement Of Food Deprivation when estimating the number of undernourished people.

Water for Food

Growing food requires significant quantities of fresh water. The amount of water required to grow each food type—"drops per crop"—varies significantly. The following table shows the average amount of water needed to produce 1 kilogram of food (2004 figures) along with the calorie equivalent of each.

Food Type	Liters / kg	Dietary calories / kilogram	Liters / Calorie	Calories / 1,000 Liters
beef	15,500	2,356	6.58	152
cheese	5,000	2,923	1.71	585
millet	5,000	1,190	4.20	238
goat	4,043	1,430	2.83	354
poultry	3,918	2,113	1.85	539
rice (husked)	2,975	1,274	2.34	428
sorghum	2,853	3,390	0.84	1,188
wheat	1,300	3,112	0.42	2,394
potato	625	1,265	0.49	2,024

If a person requires 2,000 calories / day to meet their minimum nutritional requirements, then the food they consume each day requires 840 liters of water to grow if they eat only wheat and 13,160 liters if they eat only beef.

Carbon Emissions

Burning fossil fuels emits carbon into the atmosphere in the form of carbon dioxide (CO₂). This contributes to the overall concentration of Carbon dioxide in Earth's atmosphere. One gram of carbon is contained in 3.67 (44/12) grams of CO₂.

Gasoline

Gasoline emits CO₂ when it is burned, often as automobile fuel. The amount of carbon dioxide emitted per gallon of motor gasoline burned is 8.92×10^-3 metric tons. This is equivalent to 8.92 Kg / Gallon. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html

An automobile getting 20 miles per gallon (mpg) emits 8.93/20 = .4465 Kg CO₂ / mile

In 2007, the weighted average combined fuel economy of cars and light trucks combined was 20.4 miles per gallon for the United States. The average vehicle miles traveled in 2007 was 11,720 miles per year.

Natural Gas

Natural Gas emits 0.005 metric tons CO₂ / therm when burned. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html

This is equivalent to:

• 5 Kg / therm and
• 170 g / Kwh

Note that emissions of unburned natural gas released to the atmosphere is 21 times higher.

Fuel Oil

Homes are often heated by burning heating fuel oil. According to the EPA Fuel oil emits 429.61 kg CO₂ / barrel which is equivalent to 10.23 kg CO₂ / Gallon or 2.70 kg CO₂ / liter.

Crude Oil

Crude oil is the basis for petroleum products. When consumed, typically by burning, it emits 0.43 metric tons CO₂ / barrel. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html

This is equivalent to 2.7 kg CO₂ / liter

Electric power

Electric power is generated in many ways, but primarily by burning fossil fuels. The quantity of CO₂ emitted as electricity is generated is listed below. The amount depends on the fuel used and the efficiency of the generating equipment. Because different regions include various types of electric power generation systems, the emissions factors vary by region.

• 6.91 x 10^-4 metric tons CO₂ / kWh as an overall average for the US. See: http://www.epa.gov/cleanenergy/energy-resources/refs.html
  • Equivalent to: .691 kg CO₂ / kWh
  • Equivalent to: 1.52 pounds CO₂ / kWh
  • Equivalent to: 1,520 pounds CO₂ / MWh
• From Coal fired power plants: .96 kg CO₂ / kWh See: http://www.wolframalpha.com/input/?i=carbon+footprint
• From Natural Gas fired power plants: .6 kg CO₂ / kWh See: http://www.wolframalpha.com/input/?i=carbon+footprint
• From petroleum fired power plants: .9 kg CO₂ / kWh See: http://www.wolframalpha.com/input/?i=carbon+footprint

These factors vary by location.

• See, for example: http://www.epa.gov/cleanenergy/documents/egridzips/eGRID2010V1_0_year07_SummaryTables.pdf
• and: http://www.inference.phy.cam.ac.uk/withouthotair/cI/page_335.shtml
• and: http://tonto.eia.doe.gov/FTPROOT/environment/e-supdoc-u.pdf

The book Our Choice, provides these somewhat different figures for the carbon footprints of electricity sources in Grams of CO₂ per Kilowatt-Hour:

Electricity Source	Grams CO2 Per Kilowatt-Hour
Solar Thermal	13
Wind	15
Geothermal	38
Photovoltaic Solar	39
Nuclear	66
Natural Gas	469
Coal	974

Various Petroleum Products

From: http://www.defra.gov.uk/environment/business/reporting/pdf/101006-guidelines-ghg-conversion-factors.xls

Fuel Type	kg CO2 per kWh (HHV)	kg CO2 per kWh (LHV)
Aviation Spirit	0.23762	0.25012
Aviation Turbine Fuel	0.24555	0.25847
Burning Oil	0.24564	0.25857
CNG	0.18485	0.20515
Coal (industrial)	0.31659	0.33325
Coal (electricity generation)	0.31907	0.33587
Coal (domestic)	0.29582	0.31139
Coking Coal	0.32979	0.34715
Diesel	0.25011	0.26607
Fuel Oil	0.26475	0.28164
Gas Oil	0.25214	0.26823
LNG	0.18485	0.20515
LPG	0.21419	0.22999
Lubricants	0.26190	0.27862
Naphtha	0.23654	0.24899
Natural Gas	0.18485	0.20515
Other Petroleum Gas	0.20568	0.22357
Petrol	0.23965	0.25227
Petroleum Coke	0.32152	0.33845
Refinery Miscellaneous	0.24512	0.25802

Gross Calorific Value or higher heating value (HHV) is the Calorific Value under laboratory conditions. Net Calorific Value or lower heating value (LHV) is the useful calorific value in typical real world conditions (e.g. boiler plant). The difference is essentially the latent heat of the water vapor produced (which can be recovered in laboratory conditions).

Converting Kwh / Day to Tonne CO₂ / Year

Many ecological footprint-oriented calculations are expressed in Tonnes CO₂ / year. How can we convert from Kilowatt-hour / Day to this measure?

First consider Electric power generation, which is high in emissions per Kilowatt-hour.

0.691 kg CO₂ / Kilowatt-hour × 365 days / year = 252.215 kg CO₂ / Year = 0.252 Tonne CO₂ / year

Then consider Natural Gas heating, which is relatively low in emissions per Kilowatt-hour.

0.17 kg CO₂ / Kilowatt-hour × 365 days / year = 62.05 kg CO₂ / Year = 0.062 Tonne CO₂ / year

Blending these two calculations to represent a mix of usage gives the very approximate equivalence of 10 Kilowatt-hour / day ≈ 1 Tonne CO₂ / year. Equivalently, 400 watts ≈ 1 Tonne CO₂ / year.

Carbon Capture

Carbon can be removed from the atmosphere and stored by various biological systems. These are characterized below:

Forests and Crop Lands

The average carbon density of U.S. forests in 2008 was estimated by the EPA at 73 metric tons per hectare, or 29.55 metric tons per acre. This is equivalent to 108.35 metric tons CO₂ per acre, or 267.73 metric tons CO₂ per hectare.

The carbon content of cropland is calculated by the EPA to be 5.0 metric tons of carbon per hectare, or 2.02 metric tons per acre. This is equivalent to 7.40 metric tons CO₂ per acre or 18.28 metric tons CO₂ per hectare.

Reforesting by converting cropland to forest increases carbon capture capacity by (29.55 – 2.02) 27.53 metric tons per acre. This is 100.94 Metric Tons CO₂ / acre, or 249.42 metric tons CO₂ per hectare.

Deforestation, converting forest to cropland decreases carbon capture by (29.55 – 2.02) 27.53 metric tons per acre. This is 100.94 Metric Tons CO₂ / acre, or 249.42 metric tons CO₂ per hectare.

Deforestation, converting forest to unplanted land decreases carbon capture by 29.55 metric tons per acre. This is 108.35 Metric Tons CO₂ / acre, or 249.42 metric tons CO₂ per hectare.

Resources

• The US Government Environmental Protection Agency, Clean Energy Calculations and References
• Sustainable Energy - without the hot air Quick reference
• The quick-reference list of conversion factors used by the Bioenergy Feedstock Development Programs at Oak Ridge National Laboratory.
• U.S. energy Information Administration, Energy Kids Energy Calculators.
• NIST Guide to the SI, Factors for units listed by kind of quantity or field of science
• Höhne, Niklas; Dian Phylipsen; Sara Moltmann (2007). Factors underpinning future action, 2007 update. http://fiacc.net/data/fufa2.pdf.