13. Making the Numbers Speak As a rule, large numbers are not easily grasped. They just seem vaguely large until they can be related to something we can comprehend. Furthermore, writing for newspapers, magazines and blogs does not permit the use of exponents because the general public is not familiar with powers of ten and most readers will only have a fuzzy idea of what the prefixes “mega” and “giga” stand for. There is therefore a need to express large numbers as small multiples of large yard sticks. The larger the number, the bigger the yard stick. For example, if 1 million gallons of fuel have been saved, the corresponding distance by the average US automobile (consuming 33.5 miles per gallon [1]) is 33.5 million miles, which is better expressed as 70 round trips to the moon. 13.1. Distances Across the United States Driving distance along the US West Coast from Canadian border to Mexican border 1,380 miles = 2,221 kilometers Driving distance from New York to Los Angeles 2,790 miles = 4,490 kilometers Driving distance from the northern tip of Maine to the southern tip of Florida 3,188 miles = 5,131 kilometers Elsewhere on the planet Length of the Trans‐Canadian Highway 4,860 miles = 5,821 kilometers Length of the Trans‐Siberian Railway (from Moscow to Vladivostok) 5,772 miles = 9,289 kilometers Length of Australia’s Highway 1 (around the entire island, longest highway in the world) 9,010 miles = 14,500 kilometers Earth’s diameter (at the equator) 7,926 miles = 12,756 kilometers Earth’s equatorial circumference 24,902 miles = 40,075 kilometers Extra‐planetary distances Earth to moon (center to center) 238,857 miles = 384,403 kilometers or approximately 30 earth diameters Earth to sun (average over the course of the year) 92.96 million miles = 149.6 million kilometers or 389 times the earth‐moon distance 115
13.2. Volumes In discussions of solid waste and water effluents, one often needs to express volumes in a meaningful way. A popular choice of unit for sizes too large to be expressed in liters or gallons is the Olympic‐size swimming pool (50m long, 25m wide and 2m deep), which holds 2,500 m3 = 88,300 ft3 = 660,400 US gallons [2]. Alternatively, a volume can be expressed as a layer thickness covering an American football field, the dimensions of which are 360 ft x 160 ft = 57,600 ft² = 5,351 m2. The international soccer field has dimensions of 105 m x 68 m = 7,140 m² = 76,854 ft2 [3]. Should the volume of the Olympic swimming pool or the area of a football filed happen to be too small, a better choice is the volume of the Empire State Building in New York, which can be calculated from the total floor area (2,768,591 ft2) multiplied by the average height of one floor (1,250 ft / 103 floors = 12.14 ft) and found to be 3.35994 x 107 ft3 = 951,429 m3 [4]. Still larger units may be taken as a certain thickness covering the United States (with area equal to 3,794,100 square miles = 9,826,675 km2; or 3,201,265 square miles = 8,291,238 km2 without including Alaska and Hawaii) or Africa (11,668,598 square miles = 30,221,532 km2). Yet larger volumes are those of the largest lakes on the planet: Lake (location) Lake Baikal (Asia) Lake Tanganyika (Africa) Lake Superior (North America)
Lake Malawi (Africa) Lake Michigan (North America)
Lake Huron (North America) Lake Victoria (Africa) Sources: [5], [6] Volume
23,600 km3
18,900 km3
12,100 km3
7,725 km3
4,920 km3
3,540 km3
2,700 km3
Surface area 30,500 km2 32,900 km2 82,100 km2 30,044 km2 57,800 km2 59,600 km2 68,800 km2 Incidentally, the volumetric flow rate through Niagara Falls is 2,800 m3/sec (= 6 million ft3/min) during peak daytime tourist hours [7]. 13.3. Energy and carbon emissions We often hear that certain energy conservation measures are equivalent to keeping so many cars off the road, or that new types of energy generation will be able to power a 116
certain number of homes. This can be done if we know the average energy consumption of cars and homes. In the United States, the average fuel efficiency of passenger cars was 23.1 miles per gallon (10.2 L per 100 km) and the average distance driven annually is 10,614 miles in 2011 [8]. Thus, the annual fuel consumption of a typical car is 460 gallons per year. At 117 MJ per gallon of gasoline, this is equivalent to 53,820 MJ per car per year (= 14,950 kWh per car per year). In terms of carbon dioxide, this amounts to xxx kg of CO2 emitted per car per year. In 2011, the average electricity consumption in a U.S. residence was 11,280 kWh/year = 940 kWh/month, with Louisiana having the highest annual consumption at 16,176 kWh and Maine the lowest at 6,252 kWh [9]. Translated into carbon emission, the numbers are xxx kg of CO2 per year for the average home (xxx and xxx kg CO2/year for Louisiana and Maine, respectively). One million metric tons of carbon dioxide‐equivalent emission equals: ‐ The combustion of 530,000 short tons (= 480,800 metric tons) of coal; ‐ The coal input of 1 coal plant (200 MW capacity) in about 1 year; ‐ The combustion of 18 billion cubic feet (= m3) of natural gas; ‐ The combustion of 119 million gallons (= liters) of gasoline, which is the combustion of gasoline for 7 hours in the USA, equivalent to 700,000 passenger cars each making a round trip from New York to Los Angeles; ‐ The combustion of 192 million gallons (= liters) of LPG; ‐ The combustion of 107 million gallons (= liters) of kerosene; ‐ The combustion of 102 million gallons (= liters) of distillate fuel; ‐ The combustion of 87 million gallons (= liters) of residual fuel; ‐ 17 minutes of world energy emissions; ‐ 90 minutes of U.S. energy emissions; ‐ 3.9 hours of U.S. buildings energy emissions; ‐ 7 hours of U.S. residential buildings energy emissions; ‐ 8 hours of U.S. commercial buildings energy emissions; ‐ 1.2 days of lighting in U.S. buildings; ‐ Average annual per capita emissions of 53,000 people in the USA. Source: U.S. Dept. of Energy – Energy Efficiency & Renewable Energy – Buildings Energy Data Book – 1.5: Generic Fuel Quad and Comparison – 1.5.3 Carbon Emissions Comparisons <buildingsdatabook.eren.doe.gov/TableView.aspx?table=1.5.3> 13.4. Trees How many times have we heard that recycling so much paper has prevented the cutting of so many trees? While there is not a single paper‐tree conversion factor because 117
different tree species and different manufacturing methods produce different amounts of paper, we can use the following numbers: http://www.epa.gov/osw/conserve/materials/paper/basics/ http://climatechangepw.blogspot.com/2011/02/how‐many‐trees‐are‐needed‐to‐make‐
given.html Production of 1 metric ton of paper requires 17 trees 12,770 MJ of energy 25 m3 of water 680 gallons (2.57 m3) of oil and generates 6.93 tons of CO2. (numbers to be verified, here as well as in Paper section in Materials) Sources [1] U.S. Department of Transportation, National Highway Traffic Safety Administration (NHTSA) "Summary of Fuel Economy Performance" 25 April 2013 <www.nhtsa.gov/fuel‐economy> [2] Wikipedia, Olympic‐size swimming pool <en.wikipedia.org/wiki/Olympic‐size_swimming_pool> [3] Wikipedia, Football Field <en.wikipedia.org/wiki/Football_field> [4] Wikipedia, Empire State Building <en.wikipedia.org/wiki/Empire_State_Building> [5] The Largest Lakes in the World <geography.about.com/od/lists/a/largestlakes.htm> [6] U.S. Environmental Protection Agency, Great Lakes fact Sheet <www.epa.gov/greatlakes/factsheet.html> [7] Niagara Parks, Niagara Falls Geology Facts & Features <www.niagaraparks.com/media/geology‐facts‐figures.html> [8] U.S. Energy Information Administration, Motor Vehicle Mileage, Fuel Consumption, and Fuel Economy <www.eia.gov/totalenergy/data/monthly/pdf/sec1_17.pdf> [9] U.S. Energy Information Administration – Frequently Asked Questions <www.eia.gov/tools/faqs/faq.cfm?id=97&t=3> [10] 118