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Jan. 25, 2011 How much sunshine goes into a loaf of bread? Making a reasonable rough estimate to answer this question is very thorny, primarily because of the many units of measure involved in the calculations: seconds, hours, days, Joules, calories, kilocalories, Watts, kilowatt-hours, square centimeters, square meters, acres, square miles, bushels, pounds, tons, Langleys. But let me try. The first thing to note is that a “calorie”, as understood in relation to food, is in reality a “kilocalorie” in the parlance of physicists. So, a one-pound loaf of white bread, which is said to contain 1000 calories, actually contains 1000 kilocalories, or 1,000,000 calories. The next question is how much bread is grown in a square mile of land. According to the US Department of Agriculture, the average yield of wheat lands in the US is 42 bushels per acre. A bushel of wheat weighs 60 pounds, there are 640 acres in a square mile, and 2000 pounds in a ton. So we can figure that 42 bushels an acre amounts to a little more than 800 tons per square mile. This is the gross yield. But 20% comes off the top for seed for the next season and for losses and waste. So the net yield is about 640 tons per square mile. Only 42 pounds of flour can be milled from 60 pounds of wheat. So it looks as if an average square mile can produce around 450 tons of flour. If we assume a one-to-one relationship between bread and flour, our average square mile gives us 900,000 pounds of bread, which contains 9E11 or 900,000,000,000 (900 billion) physicists' calories of energy. Wikipedia's article on insolation (sic), the amount of incoming sunshine, has a map of the US, which can be seen at this link: http://en.wikipedia.org/wiki/File:Us_pv_annual_may2004.jpg Judging from the map, we can see that North Dakota, a good solid wheat state, receives insolation of from 4.5 to 5 kilowatt-hours per square meter per day. Another unit of insolation is the Langley, which is 10,000 physicists' calories per square meter. A calorie is 4.184 Joules. So a Langley is also 41,840 Joules per square meter. A kilowatt-hour is the product of 1000 Watts and 3600 seconds (one hour), which equals 3,600,000 Joules. So a kilowatt-hour per square meter is equal to about 86 Langleys, and North Dakota's insolation might also be expressed, if Wikipedia's map is right, as 387 to 430 Langleys per day. I mention Langleys only because I am more familiar with them than with kilowatt-hours per square meter. This seems high to me for an anuual average in North Dakota, but accepting it, and assuming insolation peaks in summer, we can surmise that North Dakota gets about 475 Langleys in the wheat-growing season. This would be about 5.5 kilowatt-hours per square meter per day. There are about 1609 meters in a mile, and about 2,600,000 square meters in a square mile. This means that North Dakota may get something like 14,300,000 kilowatt-hours per square mile per day. If we figure the wheat growing season at 150 days, we can estimate that North Dakota's square mile gets 2.145E9 or 2,145,000,000 kilowatt-hours of energy per season. Multiplying this by 3,600,000 Joules per kilowatt-hour, we get 7.722E15 or 7722 trillion Joules per square mile per season. Dividing this by 4.184 Joules per calorie, we find that perhaps 1.846E15 physicists' calories fall on the select square mile, which produces 9E11 physicists' calories of bread. So it may take as much as 2,000 calories of sunshine to make one calorie of bread. I've chosen the most conservative estimates, so it could be less. In an article I wrote years ago, I came up with 500 to 2000. The present article was calculated anew without my referring to the earlier one till I had the answer. So for every calorie of bread we eat, up to 2000 calories of sunshine hits the dirt. Another question is how much of the sunshine reaching the stratosphere actually hits the dirt. In places where the sun's rays are vertical, solar energy flux density is around 1400 Watts per square meter. However, North Dakota, centered about latitude 45 north, receives rays oblique from 22 to 45 degrees from the vertical in the wheat season. Cosine 22 is about .93. Cosine 45 is about .71. These average to .82. Multiplying this by 1400, we find North Dakota gets more like 1150 Watts per square meter. This is at high noon. In the 14 hours of light in the summer, I estimate that average insolation is about .6 of high-noon insolation, say 700 Watts per square meter. Multiplying this by the supposed 14 hours, we find that stratospheric insolation above North Dakota is about 9.8 kilowatt-hours per square meter per day, compared with 5.5 kilowatt-hours per square meter per day that hits the dirt. So stratospheric insolation is perhaps 1.8 times as great as insolation on the ground. The rest of the energy is blown around the atmosphere. So it may take up to 3600 calories of sunshine reaching the stratosphere to make 1 calorie of bread. Summary: 3600 calories at the stratosphere = 2000 calories on the ground = 1 calorie of bread. If you disagree, don't hesitate to e-mail me. ------------ About the author Thomas Keyes: I have written five books: ELEMENTS OF GRAMMAR and A SOJOURN IN ASIA (non-fiction); A TALE OF UNG, THE ENNUNMENT and GVAGMA (fiction). I have studied languages for years and traveled extensively on five continents. Visit my website here. Email: udikeyes@yahoo.com
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