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% formatted for IOP % formatted for IOP
\documentclass[12pt]{iopart} \documentclass[12pt]{iopart}
%PLOS guidelines
%https://journals.plos.org/plosone/s/submission-guidelines
% possible editor, Luís A. Nunes Amaral
% ORCID Icon orcid.org/0000-0002-3762-789X
\pdfminorversion=4 \pdfminorversion=4
\usepackage{float} \usepackage{float}
@ -21,19 +26,21 @@ Department of Physics, Winona State University, Winona, MN 55987, USA}
\ead{nmoore@winona.edu} \ead{nmoore@winona.edu}
\date{\today} \date{\today}
\begin{abstract} \begin{abstract}
One of the main difficulties in a class on Sources of Energy and Social Policy is the wide variety of units used by different technologists (BTU's, Barrels of oil, Quads, kWh, etc). As every student eats, I think some of this confusion can be resolved by starting and grounding the class with a discussion of food and food production. A general outline for this introduction is provided and two interesting historical cultural examples, Tenichtitlan and the Irish Potato Famine, are provided. One of the main difficulties in a class on Sources of Energy and Social Policy is the wide variety of units used by different technologists (BTU's, Barrels of oil, Quads, kWh, etc). As every student eats, I think some of this confusion can be resolved by starting and grounding the class with a discussion of food and food production. A general outline for this introduction is provided and two interesting historical cultural examples, Tenochtitlan and the Irish Potato Famine, are provided.
Science and Social Policy classes are full of bespoke units and involve many different contexts. Starting the class with a discussion of food energy is a nice way for everyone to start with the same context. In addition, discussion of Food Energy can lead to interesting historical claims. Science and Social Policy classes are full of bespoke units and involve many different contexts. Starting the class with a discussion of food energy is a nice way for everyone to start with the same context. In addition, discussion of Food Energy can lead to interesting historical claims.
\end{abstract} \end{abstract}
\noindent{\it Keywords\/}: Energy, Social Policy, kcals, Tenochtitlan, Irish Potato Famine, History, self-reliance \noindent{\it Keywords\/}: Energy, Social Policy, kcals, Tenochtitlan, Irish Potato Famine, History, self-reliance
\submitto{\PED} %\submitto{\PED}
\maketitle \maketitle
\section{Introduction} \section{Introduction}
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 remeber: $1~Calorie = 1~kilocalorie~(kcal)$, and a dietician 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. 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.
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 fulfulls 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 converstion, 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 that's 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 certianly 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. 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.
Everyone eats, maybe not $3000 kcals$ per day, but at least something every day. When I teach our energy class, I spend a few weeks talking about food energy before all other types. While food production is not central to climate change and wars over oil, food is essential in a way that diesel and gasoline are not. Vehicle fuel makes modern life possible, but we could live, unpleasantly, without it. We can't live without fats and protein. Everyone eats, maybe not $3000 kcals$ per day, but at least something every day. When I teach our energy class,
\cite{Energy_textbook,PFFP},
I spend a few weeks talking about food energy before all other types. While food production is not central to climate change and wars over oil, food is essential in a way that diesel and gasoline are not. Vehicle fuel makes modern life possible, but we could live, unpleasantly, without it. We can't live without fats and protein.
\section{Food Energy} \section{Food Energy}
@ -58,7 +65,7 @@ equate food energy with calorimetric heating and assume human bodies have the sa
3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot \degC}\cdot\Delta T\\ 3000kcals &=& 80kg\cdot1 \frac{kcal}{kg\cdot \degC}\cdot\Delta T\\
\Delta T &\approx& +37.5\degC \Delta T &\approx& +37.5\degC
\eea \eea
Students are normally quite surprised at this number. Although wildly unrealistic, $\Delta T \approx +6\degC$ is typicaly fatal, there is a related phenomena of diet-induced thermogenesis\cite{meat_sweats} known informally as ``the meat sweats''. Some students connect this calculation to feeling quite hungry after a cold swim in the pool (a similar effect). On a larger scale, discussing what's wrong with this estimate is useful. The main storage mechanism for storing food energy is fat tissue, which the calculation completely ignores. Infants are generally born with little fat, and an infant sleeping through the night often coincides with the baby developing enough fat tissue to store sufficient kcals to make it though a night without waking up ravenously hungry. A related follow-up is that if a person is stranded in the wilderness, they should immediately start walking downstream (ie, towards civilization) as they likely won't be able to harvest an amount of kcals equivalent to what they already have stored on their hips and abdomen.\cite{trout} The contrast of bear hibernation \cite{fat_bear} and songbirds constantly eating through the winter are related connections to investigate. Students are normally quite surprised at this number. Although wildly unrealistic, $\Delta T \approx +6\degC$ is typically fatal, there is a related phenomena of diet-induced thermogenesis\cite{meat_sweats} known informally as ``the meat sweats''. Some students connect this calculation to feeling quite hungry after a cold swim in the pool (a similar effect). On a larger scale, discussing what's wrong with this estimate is useful. The main storage mechanism for storing food energy is fat tissue, which the calculation completely ignores. Infants are generally born with little fat, and an infant sleeping through the night often coincides with the baby developing enough fat tissue to store sufficient kcals to make it though a night without waking up ravenously hungry. A related follow-up is that if a person is stranded in the wilderness, they should immediately start walking downstream (ie, towards civilization) as they likely won't be able to harvest an amount of kcals equivalent to what they already have stored on their hips and abdomen.\cite{trout} The contrast of bear hibernation \cite{fat_bear} and songbirds constantly eating through the winter are related connections to investigate.
\subsection{Biophysical Power} \subsection{Biophysical Power}
A more realistic question to follow up with relates to the average \textit{power} given off by a person over a day. A more realistic question to follow up with relates to the average \textit{power} given off by a person over a day.
@ -72,7 +79,7 @@ Another application to discuss is that of ``brown fat,'' a sort of biological sp
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 $+3000\frac{kcal}{hour}\approx +3500W$. 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 $+3000\frac{kcal}{hour}\approx +3500W$.
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 physcial activities. \cite{METS} 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}
\subsection{Burning off food energy} \subsection{Burning off food energy}
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? 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?
@ -88,7 +95,7 @@ Useful information: human muscle is about $1/3$ efficient, and on Earth's surfac
One way to approach this problem is by using Energy Bar Charts \cite{energy_bar_charts} to illustrate how the energy held in food changes form as it is used. An approximation for this question is shown in figure \ref{bar_chart}. One way to approach this problem is by using Energy Bar Charts \cite{energy_bar_charts} to illustrate how the energy held in food changes form as it is used. An approximation for this question is shown in figure \ref{bar_chart}.
In this story, the ``system'' is taken to be the earth, food, and hiker. The hiker's body is assumed to be $1/3$ efficient, which means one of the food energy blocks of energy is transformed into gravitational energy (elevation) at the end of the hike. In this story, the ``system'' is taken to be the earth, food, and hiker. The hiker's body is assumed to be $1/3$ efficient, which means one of the food energy blocks of energy is transformed into gravitational energy (elevation) at the end of the hike.
The other $2$ blocks of energy are transformed into heat and leave the hiker's body, most likely by mechanisms of respiration and sweat evaporation. The purpose of a bar chart like this is to provide a pictoral and mathematical representation of the energy conservation equation given in \ref{eq:bar_chart}. The other $2$ blocks of energy are transformed into heat and leave the hiker's body, most likely by mechanisms of respiration and sweat evaporation. The purpose of a bar chart like this is to provide a pictorial and mathematical representation of the energy conservation equation given in \ref{eq:bar_chart}.
\bea \bea
\frac{1}{3}\cdot600kcal\cdot\frac{4200J}{1kcal} \frac{1}{3}\cdot600kcal\cdot\frac{4200J}{1kcal}
@ -102,7 +109,7 @@ The point of these energy calculations is not to give students an eating disorde
\subsection{Where does food energy come from?} \subsection{Where does food energy come from?}
One feature of the aught's ``homesteading'' culture \cite{homesteading} is the idea that a person should probably be able to move to the country, eat a lot of peaches, and grow all their own food. Learning that farming labor is \textit{skilled} labor can be brutal and disheartening. Eating $3000kcals$ each day means planting, weeding, harvesting, and storing more than a million kcals each year \cite{Haspel}. Where will those Calories come from? Is your backyard enough to homestead in the suburbs \cite{backyard_homestead}? One feature of the aught's ``homesteading'' culture \cite{homesteading} is the idea that a person should probably be able to move to the country, eat a lot of peaches, and grow all their own food. Learning that farming labor is \textit{skilled} labor can be brutal and disheartening. Eating $3000kcals$ each day means planting, weeding, harvesting, and storing more than a million kcals each year \cite{Haspel}. Where will those Calories come from? Is your backyard enough to homestead in the suburbs \cite{backyard_homestead}?
At some point bewteen 1920 and 1950, US chemical manufacturers realized that in the post-war period, they could repurpose processes developed for manufacturing munitions and chemical warfare agents, to produce chemicals that would kill insects and increase the nitrogen levels in the soil. At some point between 1920 and 1950, US chemical manufacturers realized that in the post-war period, they could repurpose processes developed for manufacturing munitions and chemical warfare agents, to produce chemicals that would kill insects and increase the nitrogen levels in the soil.
As figures \ref{corn_and_potato_yields} and \ref{ag_yields} show, the epoch of ``Better Living Through Chemistry'' produced a dramatic increase in per-acre yields across all comodity food crops, particularly corn and potatoes. As figures \ref{corn_and_potato_yields} and \ref{ag_yields} show, the epoch of ``Better Living Through Chemistry'' produced a dramatic increase in per-acre yields across all comodity food crops, particularly corn and potatoes.
\begin{figure}[ht!] \begin{figure}[ht!]
@ -128,7 +135,7 @@ It would be interesting to know if there are patterns of scaling among vegetable
\end{figure} \end{figure}
However, if you're discussing backyard Calorie production it isn't reasonable to use modern yield estimates for planning. ``Roundup Ready'' Corn, Soybean, and Sugar Beet seeds are not available to the public, nobody wants to put on a respirator to apply Atrazine ten feet from the back door, and the edge effects from deer and insects are much smaller on a $600$ acre field than they are in an community garden allotment. As mentioned in the introduction, in 1917 the USDA published a pamphlet \cite{USDA_1917_yields_pamphlet} giving detailed Calorie estimates a farmer might expect from a given acre of a crop. A table from this pamphlet is shown in Figure \ref{1917_yields}. However, if you're discussing backyard Calorie production it isn't reasonable to use modern yield estimates for planning. ``Roundup Ready'' Corn, Soybean, and Sugar Beet seeds are not available to the public, nobody wants to put on a respirator to apply Atrazine ten feet from the back door, and the edge effects from deer and insects are much smaller on a $600$ acre field than they are in an community garden allotment. As mentioned in the introduction, in 1917 the USDA published a pamphlet \cite{USDA_1917_yields_pamphlet} giving detailed Calorie estimates a farmer might expect from a given acre of a crop. A table from this pamphlet is shown in Figure \ref{1917_yields}.
The pamphlet data came from pre-war, pre-chemical agriculture, and the yields cited were produced with horses, manure, lime, and large families full of children. If you want to be self sufficient, these yield numbers are probably a good upper bound on what's realistically possible by a dedicated luddite. The pamphlet data came from pre-war, pre-chemical agriculture, and the yields cited were produced with horses, manure, lime, and large families full of children. If you want to be self sufficient, these yield numbers are probably a good upper bound on what's realistically possible by a dedicated Luddite.
\begin{figure}[ht!] \begin{figure}[ht!]
\centering \centering
@ -146,9 +153,9 @@ Here's an estimate: a family of 4 requires 3000kcal/person each day\cite{calorie
\be \be
4~people\cdot\frac{3000kcal}{person\cdot day}\cdot\frac{365~days}{year} \approx 4.4 M kcal 4~people\cdot\frac{3000kcal}{person\cdot day}\cdot\frac{365~days}{year} \approx 4.4 M kcal
\ee \ee
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 proportionaly with units is a skill that can give meaning to numbers. 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.
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. 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.
\bea \bea
\frac{4.4 M kcal}{family}\cdot\frac{1 acre}{1.9M kcal} & \textrm{~~or~~}& \frac{4.4 M kcal}{family}\cdot\frac{1 acre}{1.9M kcal} & \textrm{~~or~~}&
\frac{4.4 M kcal}{family}\cdot\frac{1.9M kcal}{1 acre} \frac{4.4 M kcal}{family}\cdot\frac{1.9M kcal}{1 acre}
@ -162,7 +169,7 @@ Unless the social model is one of a country Dacha or an endless suburb with no d
% %
% 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 % 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
% %
More emotionally charged conversations can be had about converting the United States to all organic agriculture, which typicaly 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. 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.
%WI 42M acres %WI 42M acres
%IN 23M acres %IN 23M acres
% %
@ -176,13 +183,13 @@ More emotionally charged conversations can be had about converting the United St
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 build 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}. 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 build 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}.
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 archeological building density and land area. While canibalism was part of Aztec religious ritual and practice \cite{Aztec_Cannibalism}, the staple Calorie sources for the Aztecs were corn and beans. 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.
Few if any Native American cultures made use of draft animals 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? 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?
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. 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.
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 nutrituional content haven't changed in the 5 centuries preceding the 1917 data in figure \ref{1917_yields}, we could assume $1lbs$ of corn contains $\approx1594kcal$ of food energy. 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.
Looking at the map with ImageJ, it seems like the recorded area devoted to chinampas might be about Looking at the map with ImageJ, it seems like the recorded area devoted to chinampas might be about
$16,000~acres$ -- details are given in \ref{appx_imageJ}. $16,000~acres$ -- details are given in \ref{appx_imageJ}.
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. 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.
@ -200,10 +207,10 @@ This crop productivity is in remarkable agreement with the 1917 USDA yields, $35
%\begin{acknowledgments} %\begin{acknowledgments}
\ack %\ack
The work was influenced and improved by discussions with %The work was influenced and improved by discussions with
Diane Dahle-Koch, %Diane Dahle-Koch,
John Deming, Carl Ferkinhoff, and Sarah Taber. %John Deming, Carl Ferkinhoff, and Sarah Taber.
%\end{acknowledgments} %\end{acknowledgments}
%The command \appendix is used to signify the start of the appendices. Thereafter %The command \appendix is used to signify the start of the appendices. Thereafter
@ -228,7 +235,7 @@ In 2022 the USDA reported an average production of 172.3 bushels of corn per acr
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} 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} \label{example_calculation}
\ee \ee
Obviously the result is only reasonable to two signifigant figures! Obviously the result is only reasonable to two significant figures!
%grams_per_lbs=453.592 %grams_per_lbs=453.592
%corn_lbs_per_bu=(56.0/1.0) %corn_lbs_per_bu=(56.0/1.0)
%corn_kcal_per_gram=(365/100) %corn_kcal_per_gram=(365/100)
@ -262,7 +269,7 @@ Raw data from the USDA NASS is plotted in figure \ref{raw_production_per_acre}.
\centering \centering
\includegraphics[width=\columnwidth]{raw_production_per_acre.pdf} \includegraphics[width=\columnwidth]{raw_production_per_acre.pdf}
\caption{ \caption{
USDA yields from pre-chemical US ag Average USDA per acre yields for a number of commodity crops over time. This ``raw'' data (in bespoke harvest units) was scaled to produce the data in figure \ref{ag_yields} earlier in the paper.
} }
\label{raw_production_per_acre} \label{raw_production_per_acre}
\end{figure} \end{figure}
@ -271,9 +278,9 @@ USDA yields from pre-chemical US ag
\section{Estimating land area devoted to chinampas with ImageJ} \section{Estimating land area devoted to chinampas with ImageJ}
\label{appx_imageJ} \label{appx_imageJ}
ImageJ is a free software program developed by the National Institue of Health for photo analysis, \cite{imageJ}. I used the program to measure a calibration scale in a map and I also used the program to measure the area of two polygons that I drew on the map. The length and both areas are shown in figure \ref{imageJ}. ImageJ is a free software program developed by the National Institutes of Health for photo analysis, \cite{imageJ}. I used the program to measure a calibration scale in a map and I also used the program to measure the area of two polygons that I drew on the map. The length and both areas are shown in figure \ref{imageJ}.
Specifically, to find the area of the two large chinampas areas near Tenoctitlan, I took a screenshot from the 1964 paper, \cite{Chinampas_1964}, and saved it in jpg format. Then, I opened the image in the Windows-Java edition of ImageJ \cite{imageJ}. The length of the 10 mile distance scale was 213 pixels. The long chinampas area at the south end of the lake was measured with a Polygon selection via the Mesure tool to have an area of $9940~pixel^2\approx21.9miles^2$. The smaller region near Chalco had an area of about $1439~pixel^2\approx3.2miles^2$. While there were undoubtably other regions devoted to chimanpas agriculture, the portion visible seems to be about $25.1miles^2$ or $16,000acres$. Specifically, to find the area of the two large chinampas areas near Tenochtitlan, I took a screenshot from the 1964 paper, \cite{Chinampas_1964}, and saved it in jpg format. Then, I opened the image in the Windows-Java edition of ImageJ \cite{imageJ}. The length of the 10 mile distance scale was 213 pixels. The long chinampas area at the south end of the lake was measured with a Polygon selection via the Mesure tool to have an area of $9940~pixel^2\approx21.9miles^2$. The smaller region near Chalco had an area of about $1439~pixel^2\approx3.2miles^2$. While there were certainly other regions devoted to chimanpas agriculture, the portion visible near the Aztec capital seems to be about $25.1miles^2$ or $16,000acres$.
\begin{figure}[ht!] \begin{figure}[ht!]
\centering \centering
@ -295,6 +302,16 @@ Three screen captures showing chinampa areas and the calibration stick used to c
\section*{References} \section*{References}
\begin{thebibliography}{99} \begin{thebibliography}{99}
\bibitem{Energy_textbook}
Energy and the Environment
Jack J. Kraushaar , Robert A. Ristinen , Jeffrey T. Brack
Wiley; 4th edition 2022
\bibitem{PFFP}
Physics and Technology for Future Presidents: An Introduction to the Essential Physics Every World Leader Needs to Know
Richard A. Muller
Princeton University Press 2010
\bibitem{meat_sweats} \bibitem{meat_sweats}
https://www.bonappetit.com/story/meat-sweats https://www.bonappetit.com/story/meat-sweats
P. Trayhurn, P. Trayhurn,