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food_energy.pdf
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@ -34,7 +34,7 @@ Science and Social Policy classes are full of bespoke units and involve many dif
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\maketitle
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\section{Introduction}
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When the United States entered World War One one of the problems they faced was logistics. How much food do you need to ship overseas to Europe to feed a million soldiers? That early work in nutrition led to the 3000 Calorie diet many people remember from secondary Health Education class. A bit about ``Calorie'' (uppercase) vs ``calorie'' (lowercase) units you might remember: $1~Calorie = 1~kilocalorie~(kcal)$, and a dietitian might build a $3000 kcal$ diet for a 20 year old basketball player. A \textit{calorie} is the amount of energy it takes to heat a gram of water by a degree Celsius. There are about 4.2 Joules in a single calorie, and a Joule occurs all over introductory physics. If you need to buy a new home furnace, the sales brochure might advertise that it is capable of delivering 100,000 BTU's of heat each hour. What's a BTU? Heat a pound of water by $1^{\circ}F$. Of course Heat Pumps are far more efficient than simply burning methane or propane, but they consume kilo-watt-hours (kWh) of electricity, not BTU's. What's a kWh? Run a 1000 Watt toaster for an hour and you'll have pulled one kWh off the grid, it will cost you about \$0.13 in Minnesota. If you decide to put solar panels in your backyard, they will probably collect about $10\%$ of the 3.5kWh the the sun delivers to each square meter of your lawn (in Minnesota) each day.
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When the United States entered World War One one of the problems they faced was logistics. How much food do you need to ship overseas to Europe to feed a million soldiers? That early work in nutrition led to the $3000$ Calorie diet many people remember from secondary Health Education class. A bit about ``Calorie'' (uppercase) vs ``calorie'' (lowercase) units you might remember: $1~Calorie = 1~kilocalorie~(kcal)$, and a dietitian might build a $3000 kcal$ diet for a 20 year old basketball player. A \textit{calorie} is the amount of energy it takes to heat a gram of water by a degree Celsius. There are about $4.2$ Joules in a single calorie, and a Joule occurs all over introductory physics. If you need to buy a new home furnace, the sales brochure might advertise that it is capable of delivering $100,000$ BTU's of heat each hour. What's a BTU? Heat a pound of water by $1^{\circ}F$. Of course Heat Pumps are far more efficient than simply burning methane or propane, but they consume kilo-watt-hours (kWh) of electricity, not BTU's. What's a kWh? Run a $1000$ Watt toaster for an hour and you'll have pulled one kWh off the grid, it will cost you about $\$0.13$ in Minnesota. If you decide to put solar panels in your backyard, they will probably collect about $10\%$ of the $3.5kWh$ the the sun delivers to each square meter of your lawn (in Minnesota) each day.
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As the previous paragraph illustrates, there are a frustratingly large number of different units in an ``Energy'' class. At Winona State, this 3 credit class fulfills a ``Science and Social Policy'' general education requirement and is taken by students from across the university. Lots of college majors don't require a math class beyond algebra or introductory statistics and the population is largely math-averse. You could jokingly say that one of the main things students learn in the class is unit conversion, but it isn't far off. Nearly every field finds energy a useful representation, and every profession has their own set of units and terminology most well suited for quick calculation. Would a medical lab scientist talk about the fractional acre-foot of urine needed test kidney function? No, but someone in the central valley of California would certainly care about the acre-feet of water necessary to grow almonds! Does a gas station price their gasoline in dollars per kWh? Given the growing electrification of cars, they might soon.
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@ -56,8 +56,8 @@ A proto-college-student at Winona's China King Buffet, dreaming about visiting t
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\end{figure}
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\subsection{Converting food into body heat}
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Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am, eg figure \ref{buffet}. If he brings homework and stretches the meal out for a few hours he can get all $3000~kcals$ with only one meal bill. Food is fuel for the human body -- could too much fuel make his body feel sick? If his body burned all this food at once, how much warmer would he get?
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Useful information: the student has a mass of 80kg and is made mostly of water. A Calorie heats 1 kg of water $1^{\circ}C$.
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Planning to save money, one college student decides to go to an all-you-can-eat buffet each day at 11am, eg figure \ref{buffet}. If he brings homework and stretches the meal out for a few hours he can get all $3000kcals$ with only one meal bill. Food is fuel for the human body -- could too much fuel make his body feel sick? If his body burned all this food at once, how much warmer would he get?
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Useful information: the student has a mass of $80kg$ and is made mostly of water. A Calorie heats $1 kg$ of water $1^{\circ}C$.
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Here's a possible answer:
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equate food energy with calorimetric heating and assume human bodies have the same heat capacity as water, about $1\frac{kcal}{kg\cdot\degC}$. This allows us to calculate the body's temperature increase.
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@ -73,16 +73,17 @@ Again, assuming $3000kcal$ is burned over $24 hours$, with useful information: $
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\be
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\frac{3000kcal}{24hours}\cdot\frac{4200J}{1kcal}\cdot\frac{1hour}{3600sec}\approx145W
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\ee
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Most students still remember $75Watt$ lightbulbs, but given the spread of LED lighting, ``A person's body heat is two 75W light bulbs'' will probably only make sense for a few more years. Desert or cold-weather camping, alone versus with friends, and survival swimming are also examples for students to make sense of this answer. If you can take advantage of other people's waste body heat, you'll sleep more pleasantly and survive longer in cold water.
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Most students still remember $75Watt$ lightbulbs, but given the spread of LED lighting, ``A person's body heat is two $75W$ light bulbs'' will probably only make sense for a few more years. Desert or cold-weather camping, alone versus with friends, and survival swimming are also examples for students to make sense of this answer. If you can take advantage of other people's waste body heat, you'll sleep more pleasantly and survive longer in cold water.
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Another application to discuss is that of ``brown fat,'' a sort of biological space heater that humans and other mammals develop in response to cold weather. This tissue's mitochondria can burn lipids and carbohydrates in a useless proton pumping scheme, which produces metabolic heat \cite{brown_fat_1,brown_fat_2,brown_fat_3,brown_fat_4}. Most common in rodents and infants, this mechanism can be stimulated by extended exposure to cold temperatures -- the original work was done on lumberjacks in Finland \cite{finland_lumberjacks} . The idea of a biological space heater that takes a month to turn on and a month to turn off matches the lived experience of college students in Minnesota, who wear down jackets in $4\degC$ weather in November, and beachwear in the same $4\degC$ weather in March. Additionally, transplants to northern climates often take a few years to ``get used to'' the colder weather up north. It seems just as easy to say that transplants' bodies take a few years to develop the brown fat cells which allow them to be comfortable in cold weather.
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One other distinction to emphasize is the difference between power and energy. A graph of a human body's ``kcal content'' over the course of a day can be a useful illustration. When sedentary, this graph probably has the slope of $-150W\approx -125 \frac{kcals}{hour}$. If the $3000kcal$ meal at the buffet takes an hour, this period corresponds to an energy-time slope of $+3000\frac{kcal}{hour}\approx +3500W$.
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One other distinction to emphasize is the difference between power and energy. A graph of a human body's ``kcal content'' over the course of a day can be a useful illustration. When sedentary, this graph probably has the slope of $-150W\approx -125 \frac{kcals}{hour}$. If the $3000kcal$ meal at the buffet takes an hour, this period corresponds to an energy-time slope of
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$+3000\frac{kcal}{hour}\approx +3500W$.
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In medicine, these slopes are effectively equivalent to ``Metabolic Equivalent of Task'' (METS), a common measure in cardiology and exercise physiology. METS is power normalized by mass, $1METS=1\frac{kcal}{kg\cdot hour}$, and METS levels are available for many different physical activities. \cite{METS}
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\subsection{Burning off food energy}
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Imagine that after eating a $600~kcal$ bacon-maple long-john (donut), you decide to go for a hike to ``work off'' the Calories. Winona State is in a river valley bounded by $200m$ tall bluffs. How high up the bluff would you have to hike to burn off the donut?
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Imagine that after eating a $600kcal$ bacon-maple long-john (donut), you decide to go for a hike to ``work off'' the Calories. Winona State is in a river valley bounded by $200m$ tall bluffs. How high up the bluff would you have to hike to burn off the donut?
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Useful information: human muscle is about $1/3$ efficient, and on Earth's surface, gravitational energy has a slope of about $10~\frac{Joules}{kg\cdot m}$.
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\begin{figure}[h]
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@ -102,9 +103,9 @@ The other $2$ blocks of energy are transformed into heat and leave the hiker's b
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&=& 80kg\cdot10\frac{Joules}{kg\cdot m}\cdot height \label{eq:bar_chart}\\
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height &\approx& 1000 m
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\eea
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This estimate is again surprising to students. Five trips up the bluff to burn off $\$2$ of saturated fat, sugar, and flour! A nice followup calculation is to imagine a car that can burn a $100kcal$ piece of toast in the engine: from rest, what speed will the toast propel it to? If (again) the engine converts $1/3$ of the energy into motion (kinetic energy), a 1300kg Honda Civic will reach a speed of about $13\frac{m}{s}\approx33mph$!
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This estimate is again surprising to students. Five trips up the bluff to burn off $\$2$ of saturated fat, sugar, and flour! A nice followup calculation is to imagine a car that can burn a $100kcal$ piece of toast in the engine: from rest, what speed will the toast propel it to? If (again) the engine converts $1/3$ of the energy into motion (kinetic energy), a $1300kg$ Honda Civic will reach a speed of about $13\frac{m}{s}\approx33mph$!
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The point of these energy calculations is not to give students an eating disorder. Rather, the numbers show food's amazing power. A single slice of toast will bring a car up to the residential speed limit! A day's food, $3000kcal$, will power you up an $8000m$ mountain peak! The body-work food allows us to do is astonishing, and increases in food production have made modern comforts, unimaginable 150 years ago, possible to the point of being taken for granted.
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The point of these energy calculations is not to give students an eating disorder. Rather, the numbers show food's amazing power. A single slice of toast will bring a car up to the residential speed limit! A day's food, $3000kcal$, will power you up an $8000m$ mountain peak! The body-work food allows us to do is astonishing, and increases in food production have made modern comforts, unimaginable $150$ years ago, possible to the point of being taken for granted.
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\clearpage
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@ -150,27 +151,27 @@ A table from a USDA booklet giving 1917 yields for various farm products.
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\end{figure}
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So, another question using this data. If you want to feed your family of four people potatoes, how much land will you need to cultivate?
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Here's an estimate: a family of 4 requires 3000kcal/person each day\cite{calorie_age}. If we over-estimate and produce food for the entire year, the family will need about $4.4$ million kcals.
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Here's an estimate: a family of 4 requires $3000kcal/person$ each day\cite{calorie_age}. If we over-estimate and produce food for the entire year, the family will need about $4.4$ million kcals.
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\be
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4~people\cdot\frac{3000kcal}{person\cdot day}\cdot\frac{365~days}{year} \approx 4.4 M kcal
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\ee
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A brief aside for those bored by the simplistic unit conversion: when I ask students to solve problems like these, one undercurrent of conversation is ``Should I divide by 365 or multiply?'' Particularly with online homework systems, checking your answer for reasonability isn't typically graded. Asking the students to reason proportionally with units is a skill that can give meaning to numbers.
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From figure \ref{1917_yields} we can estimate 1.9 million kcals per acre of potato production. Again the students might ask, should I multiple 4.4 and 1.9 or should I divide them? It can be useful in a class discussion to have the students discuss and vote which of the following two forms will give the meaningful answer.
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From figure \ref{1917_yields} we can estimate $1.9~million~kcals$ per acre of potato production. Again the students might ask, should I multiple $4.4$ and $1.9$ or should I divide them? It can be useful in a class discussion to have the students discuss and vote which of the following two forms will give the meaningful answer.
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\bea
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\frac{4.4 M kcal}{family}\cdot\frac{1 acre}{1.9M kcal} & \textrm{~~or~~}&
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\frac{4.4 M kcal}{family}\cdot\frac{1.9M kcal}{1 acre}
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\eea
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The choice of operation is difficult to make without seeing the units present, which is again a learning opportunity for the students.
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What does the answer of $2.3$ acres mean? The university's $91m\times49m$ football field has an area of about $1.1$ acres, so you could say that a football field planted in potatoes will probably feed a family through the winter \cite{Deppe}. Can a person enjoy the benefits of urban living and grow all their own food? The population density of New Jersey is $1,263~people/mile^2 \approx1.97~people/acre$ and our 4 person family needs 2.3 acres for their potatoes.
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What does the answer of $2.3$ acres mean? The university's $91m\times49m$ football field has an area of about $1.1$ acres, so you could say that a football field planted in potatoes will probably feed a family through the winter \cite{Deppe}. Can a person enjoy the benefits of urban living and grow all their own food? The population density of New Jersey is $1,263~people/mile^2 \approx1.97~people/acre$ and our 4 person family needs $2.3$ acres for their potatoes.
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Unless the social model is one of a country Dacha or an endless suburb with no duplexes or apartment buildings, urban living and food self-sufficiency seem mutually exclusive.
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% This is interesting, but probably a weak argument because organic yields can be as high as ~ 140bu/acre BUT must be grown in a 3 or 4 year rotation vs corn's 2-year rotation.
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%
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% https://www.google.com/url?sa=t&rct=j&q=&esrc=s&source=web&cd=&ved=2ahUKEwjswtTZo8X8AhXkjokEHW-yD74QFnoECA8QAQ&url=http%3A%2F%2Fextension.agron.iastate.edu%2Forganicag%2Fresearchreports%2Fn-kltar98.pdf&usg=AOvVaw2mLZB25pv44LX_EBAR5kXU&cshid=1673638241316994
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%
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More emotionally charged conversations can be had about converting the United States to all organic agriculture, which, for corn, typically has a yield penalty of about $20-40bu/acre$ when compared to conventional production. The 1917 data isn't directly applicable, but it relates. At $180bu/acre$ conventional corn requires 22 million acres (half of Wisconsin, or all of Indiana) to feed the US population (350 million people) corn for a year. The remainder of the corn belt can be devoted to animal feed, ethanol, and export. If the corn belt was devoted to producing organic corn at lower yield \cite{organic_corn_yield}, we probably wouldn't starve, but cheap meat and ethanol vehicle fuel would likely disappear.
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More emotionally charged conversations can be had about converting the United States to all organic agriculture, which, for corn, typically has a yield penalty of about $20-40bu/acre$ when compared to conventional production. The 1917 data isn't directly applicable, but it relates. At $180bu/acre$ conventional corn requires $22~million~acres$ (half of Wisconsin, or all of Indiana) to feed the US population ($350$ million people) corn for a year. The remainder of the corn belt can be devoted to animal feed, ethanol, and export. If the corn belt was devoted to producing organic corn at lower yield \cite{organic_corn_yield}, we probably wouldn't starve, but cheap meat and ethanol vehicle fuel would likely disappear.
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%WI 42M acres
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%IN 23M acres
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%
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@ -183,17 +184,17 @@ More emotionally charged conversations can be had about converting the United St
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\clearpage
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\section{Example: How big could Tenochtitlan have been?}
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The questions described thus far have largely been centered within a physics context. The paper closes with two more examples that leverage this food energy picture to make historical claims. The first example relates to the pre-columbian capital of the Aztec Empire, Tenochtitlan, now known as Mexico City. Tenochtitlan was built on and around a endorheic lake, Texcoco. Crops were grown in shallow parts of the lake via chinampas \cite{national_geo}, floating patches of decaying vegetation and soil. Given the proximity to water and decaying vegetation, these fields were very fertile \cite{HortTech_2019,Chinampas_1964} and some continue to be used in the present day \cite{google_earth}.
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The questions described thus far have largely been centered within a physics context. The paper closes with two more examples that leverage this food energy picture to make historical claims. The first example relates to the pre-Columbian capital of the Aztec Empire, Tenochtitlan, now known as Mexico City. Tenochtitlan was built on and around a endorheic lake, Texcoco. Crops were grown in shallow parts of the lake via chinampas \cite{national_geo}, floating patches of decaying vegetation and soil. Given the proximity to water and decaying vegetation, these fields were very fertile \cite{HortTech_2019,Chinampas_1964} and some continue to be used in the present day \cite{google_earth}.
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Estimates of Tenochtitlan's population in 1500CE vary widely, from 40,000 \cite{40k} to more than 400,000 \cite{400k} inhabitants, comparable in size to Paris at that time. These estimates come from oral and written records and estimates of archaeological building density and land area. While cannibalism was part of Aztec religious ritual and practice \cite{Aztec_Cannibalism}, the staple Calorie sources for the Aztecs were corn and beans.
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Few if any Native American cultures made use of draft animals for food or power before the Columbian Exchange. This means that the food that fed Tenochtitlan must have been brought to the city center by foot or canoe. How much land must have been devoted to chinampas to feed the population, or conversely, how many people could be supported by the land within walking or paddling distance from the city center?
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A 1964 paper in Scientific American \cite{Chinampas_1964} gives a general outline of the chinampas in the area of Tenochtitlan in 1500CE. This map seems to be the basis for the similar figure in Wikipedia \cite{chinampas_wikipedia}. Descriptions of chinampas agriculture indicate that as many as 7 successive crops could be grown and harvested from the same plot of soil each year, two of which could be maize (corn). This is truly amazing productivity, given that in the midwestern United States corn is normally grown, at most, every other year because of it's extreme nutrient demands on the soil.
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A 1964 paper in Scientific American \cite{Chinampas_1964} gives a general outline of the chinampas in the area of Tenochtitlan in 1500CE. This map seems to be the basis for the similar figure in Wikipedia \cite{chinampas_wikipedia}. Descriptions of chinampas agriculture indicate that as many as $7$ successive crops could be grown and harvested from the same plot of soil each year, two of which could be maize (corn). This is truly amazing productivity, given that in the midwest United States corn is normally grown, at most, every other year because of it's extreme nutrient demands on the soil.
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There are many ways to approach this estimation problem. We could assume a Tenochtitlan population of $100,000$ people has a $3000kcal/day$ diet that comes completely from corn. Assuming that corn's density and nutritional content haven't changed in the 4 centuries preceding the 1917 data in figure \ref{1917_yields}, we could assume $1lbs$ of corn contains $\approx1594kcal$ of food energy.
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Looking at the map with ImageJ, it seems like the recorded area devoted to chinampas might be about
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There are many ways to approach this estimation problem. We could assume a Tenochtitlan population of $100,000$ people has a $3000kcal/day$ diet that comes completely from corn. Assuming that corn's density and nutritional content haven't changed in the $4$ centuries preceding the 1917 data in figure \ref{1917_yields}, we could assume $1lbs$ of corn contains $\approx1594kcal$ of food energy.
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Looking at the map with ImageJ \cite{imageJ}, it seems like the recorded area devoted to chinampas might be about
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$16,000~acres$ -- details are given in \ref{appx_imageJ}.
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With these assumptions, we could equate the corn energy production from chinampas with the population's yearly food need. Note, in this version of the story, the corn productivity, $P\frac{bu}{acre}$ is treated as an unknown variable.
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\bea
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@ -202,7 +203,7 @@ Population~requires &=& 100,000~people\cdot \frac{3000kcal}{person\cdot day}\cdo
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P \approx 38\frac{bu}{acre} &&
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\eea
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This crop productivity is in remarkable agreement with the 1917 USDA yields, $35bu/acre$, which seems to validate the assumed 100,000 person population of Tenochtitlan. Some references \cite{Chinampas_1964} describe an extensive tribute system that Aztec government required of it's subjects, which certainly would have been necessary to support populations on the upper end of historical estimates \cite{400k}.
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This crop productivity is in remarkable agreement with the 1917 USDA yields, $35bu/acre$, which seems to validate the assumed $100,000$ person population of Tenochtitlan. Some references \cite{Chinampas_1964} describe an extensive tribute system that Aztec government required of it's subjects, which certainly would have been necessary to support populations on the upper end of historical estimates \cite{400k}.
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@ -217,7 +218,7 @@ As the story goes, the two main commodity crops in Ireland were potatoes (for hu
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This inflammatory claim, which is certainly a simplified version of history, serves as a useful evaluation example for students. Specifically, in years that the potato crop failed because of weather or late blight, could the amount of oats produced (and exported) have fed the Irish population? More broadly, was the Great Famine due to weather and disease, natural causes ``we can't do anything about,'' or was the depth of the tragedy a result of political choices?
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Some estimates follow: Ireland's population in 1845 was about 8.5 million people. The island has an area of about $70,000km^2$ and you might estimate that $64\%$ of the land ($44,800km^2$) is arable for agriculture \cite{arable_percentage}.
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Some estimates follow: Ireland's population in 1845 was about $8.5$ million people. The island has an area of about $70,000km^2$ and you might estimate that $64\%$ of the land ($44,800km^2$) is arable for agriculture \cite{arable_percentage}.
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It seems reasonable to use the 1917 productivity, figure \ref{1917_yields}, to make calculations for Ireland in 1845. Reminder, in 1917, potatoes produced $1.908\times10^6 kcal/acre$ and oats $1.254\times10^6kcal/acre$.
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With students, evaluation of the claim could be approached as a series of questions:
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@ -241,7 +242,7 @@ How much land area, sown in oats, would produce this food?
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&\approx& 30,000 km^2 \nonumber
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\eea
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Added, $49,700km^2$, these two farmland areas devoted to oats and potatoes only slightly exceed the amount of arable land estimated above for Ireland, $44,800km^2$ \cite{arable_percentage}. What do the numbers mean? Did there have to be a famine? If all of the potato crop failed because of late blight, there would likely have been enough oats to feed the population a $2000kcal$ ration of oats with leftover to spare.
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Summed, $49,700km^2$, these two farmland areas devoted to oats and potatoes only slightly exceed the amount of arable land estimated above for Ireland, $44,800km^2$ \cite{arable_percentage}. What do the numbers mean? Did there have to be a famine? If all of the potato crop failed because of late blight, there would likely have been enough oats to feed the population a $2000kcal$ ration of oats with leftover to spare.
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Like the Holodomor or the Great Leap Forward, the numbers suggest that large-scale suffering wasn't a natural disaster, but rather a human disaster resulting from poor government policy insensitive to the value of human life.
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@ -257,7 +258,7 @@ The population of Ireland over time, file from Wikipedia \cite{pop_image}, data
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\section{Conclusion}
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A class about Energy and Social policy and the author hasn't mentioned climate change, coal, or solar panels even once! What is he thinking?
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A class about Energy and Social Policy and the author hasn't mentioned climate change, coal, or solar panels even once! What is he thinking?
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How many tons of carbon does your car release in a year? How many shiploads of iron oxide will we have to dump into the ocean for phytoplankton to eat up the equivalent about of carbon? Every question in a class like this is, to at least some extent, informed by numerical calculation and it's pretty arrogant to assume that ``those students'' don't need to (or can't) do the math. If you're going to have success talking about numerical calculations, you might as well start with examples that everyone can relate to, and everyone eats! Along the way you might find fascinating historical questions to investigate.
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%\begin{acknowledgments}
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%\ack
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%The work was influenced and improved by discussions with
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%Diane Dahle-Koch,
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%Larry Moore,
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%John Deming, Carl Ferkinhoff, and Sarah Taber.
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\ack
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The work was influenced and improved by discussions with
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Diane Dahle-Koch,
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Larry Moore,
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John Deming,
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Carl Ferkinhoff,
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and Sarah Taber.
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%\end{acknowledgments}
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%The command \appendix is used to signify the start of the appendices. Thereafter
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\appendix
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\section{Creating the historical kcal/acre figure from USDA data}
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\label{how_yield_plot_is_made}
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The United States Department of Agriculture (USDA) provides historical crop information via the National Agricultureal Statistics Service, \url{https://www.nass.usda.gov/Statistics_by_Subject/index.php?sector=CROPS}. Data was downloaded in spreadsheet csv format and then combined and plotted via a Python Jupyter notebook.
|
||||
The United States Department of Agriculture (USDA) provides historical crop information via the National Agricultureal Statistics Service
|
||||
\cite{USDA_NASS} .
|
||||
Data was downloaded in spreadsheet csv format and then combined and plotted via a Python Jupyter notebook.
|
||||
|
||||
Each crop has its own bespoke units, for example potatoes are sold by hundredweight (CWT) but sugar beets are measured by the ton.
|
||||
Every imaginable agricultural product seems to be tracked in the NASS site, for example Maple Syrup production is tracked and given in gallons of syrup per tap!
|
||||
Conversion factors used are summarized in Table \ref{conversions}.
|
||||
Calorie (kcal) density for each crop was taken from \url{https://fdc.nal.usda.gov/fdc-app.html}. Within this database, foods are identified by an FDC ID.
|
||||
Calorie (kcal) density for each crop was taken from the USDA's Food Data Central
|
||||
\cite{USDA_FDC}.
|
||||
Within this database, foods are identified by an FDC ID.
|
||||
|
||||
An example calculation (implemented in the Jupyter notebook) follows for Corn.
|
||||
In 2022 the USDA reported an average production of 172.3 bushels of corn per acre of farmland.
|
||||
In 2022 the USDA reported an average production of $172.3$ bushels of corn per acre of farmland.
|
||||
\be
|
||||
172.3\frac{bu}{acre}\cdot\frac{56lbs~corn}{bu}\cdot\frac{453.6~grams}{lbs}\cdot\frac{365~kcal}{100~grams} = 15,974,657 \frac{kcal}{acre}
|
||||
\label{example_calculation}
|
||||
|
|
@ -310,7 +317,7 @@ Obviously the result is only reasonable to two significant figures!
|
|||
A summary of units and conversions used to create figure \ref{ag_yields} from USDA NASS data. $1cwt$ is a hundred pounds of potatoes.
|
||||
A bushel, $1bu$, is a volume unit of about 35liters and corresponds to about 60lbs of grain. Calorie content per 100 gram (mass) of food is taken from the USDA's ``Food Data Central'' database.
|
||||
For context, typical serving sizes are included.
|
||||
It isn't clear from any of these resources if lb is pound-force (lbf) or pound-mass (lbm) and so I am ignorantly treating them as ``grocery store units'' where $1 lbs \approx 453.6 grams$.
|
||||
It isn't clear from any of these resources if lb is pound-force (lbf) or pound-mass (lbm) and so I am treating them as ``grocery store units'' where $1 lbs \approx 453.6 grams$.
|
||||
}
|
||||
\begin{indented}
|
||||
\item[]\begin{tabular}{@{}llllll}
|
||||
|
|
@ -407,10 +414,10 @@ Available from: \url{https://fdc.nal.usda.gov/fdc-app.html#/food-details/175154/
|
|||
Some sources claim that bear metabolism can vary between $4,000$ to $20,000$ kcals per day,
|
||||
North American Bear Center [Internet].
|
||||
Ely, MN, USA 2023.
|
||||
5 Stages of Activity and Hibernation
|
||||
5 Stages of Activity and Hibernation.
|
||||
[cited 2023 Jan 16]; [about 2 screens].
|
||||
Available from: \url{https://bear.org/5-stages-of-activity-and-hibernation/},
|
||||
and comically illustrated by the National Park Service at
|
||||
Available from: \url{https://bear.org/5-stages-of-activity-and-hibernation/}.
|
||||
This is comically illustrated by the National Park Service at
|
||||
National Park Service, Katmai National Park and Preserve Alaska [Internet].
|
||||
Fat Bear Week 2022.
|
||||
[updated 2022 Oct 11, cited 2023 Jan 16]; [about 5 screens].
|
||||
|
|
@ -559,7 +566,7 @@ Ebel R.
|
|||
Chinampas: An Urban Farming Model of the Aztecs and a Potential Solution for Modern Megalopolis.
|
||||
HortTechnology.
|
||||
%Roland Ebel
|
||||
Volume/Issue: Volume 30: Issue 1
|
||||
%Volume/Issue: Volume 30: Issue 1
|
||||
2019; 30(1): 13-19
|
||||
%DOI: https://doi.org/10.21273/HORTTECH04310-19
|
||||
|
||||
|
|
@ -595,7 +602,8 @@ Ortiz de Montellano BR.
|
|||
Aztec Cannibalism: An Ecological Necessity?
|
||||
%Bernard R. Ortiz de Montellano
|
||||
Science.
|
||||
May 12, 1978 May 12; 200(4342):611-7
|
||||
1978 May 12;
|
||||
200(4342):611-7.
|
||||
%American Association for the Advancement of Science
|
||||
%https://www.jstor.org/stable/1746929
|
||||
|
||||
|
|
@ -613,7 +621,8 @@ ImageJ is a free tool for measurement of photographic data.
|
|||
Schneider, C. A., Rasband, W. S., Eliceiri, K. W.
|
||||
NIH Image to ImageJ: 25 years of image analysis.
|
||||
Nature Methods.
|
||||
2012;9(7):671-5.
|
||||
2012;
|
||||
9(7):671-5.
|
||||
%doi:10.1038/nmeth.2089
|
||||
|
||||
\bibitem{potato}
|
||||
|
|
@ -654,5 +663,16 @@ Ask about Ireland [Internet].
|
|||
Land Use in Ireland; [cited 2023 Jan 16]; [about 2 screens].
|
||||
Available from: \url{https://www.askaboutireland.ie/enfo/sustainable-living/farming-in-ireland-overvi/land-use-in-ireland/}
|
||||
|
||||
\bibitem{USDA_NASS}
|
||||
United States Department of Agriculture National Agricultural Statistics Service [Internet].
|
||||
Statistics by Subject; [updated 2020 Oct 13; cited 2023 Jan 18]; [about 1 screen].
|
||||
Available from: \url{https://www.nass.usda.gov/Statistics_by_Subject/index.php?sector=CROPS}.
|
||||
|
||||
\bibitem{USDA_FDC}
|
||||
United States Department of Agriculture Agricultural Research Service [Internet].
|
||||
FoodData Central; [cited 2023 Jan 18]; [about 1 screen].
|
||||
Available from: \url{https://fdc.nal.usda.gov/fdc-app.html}.
|
||||
|
||||
|
||||
\end{thebibliography}
|
||||
\end{document}
|
||||
|
|
|
|||
Loading…
Reference in New Issue
Block a user