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@ -23,11 +23,12 @@
\title{How many acres of potatoes does a society need?} \title{How many acres of potatoes does a society need?}
\shorttitle{How Many Potatoes?} \shorttitle{How Many Potatoes?}
\leftheader{Moore} %\leftheader{Moore}
\leftheader{}
%IOP header %IOP header
\title{How many acres of potatoes does a society need? Using food and historical claims to introduce energy.} \title{How many acres of potatoes does a society need? Using food and historical claims to introduce energy.}
\author{Nathan T. Moore} %\author{Nathan T. Moore}
\affiliation{Department of Physics, Winona State University, Winona, MN 55987, USA} %\affiliation{Department of Physics, Winona State University, Winona, MN 55987, USA}
%\email{nmoore@winona.edu} %\email{nmoore@winona.edu}
\date{\today} \date{\today}
@ -42,7 +43,9 @@ Science and Social Policy classes are full of bespoke units and involve many dif
\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 remember: $1~Calorie = 1~kilocalorie=1 kcal$, and a dietitian might build a $3000 kcal$ diet for a 20 year old basketball player. $One~ calorie = 0.001kcal$, 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: $1~Calorie = 1~kilocalorie=1 kcal$, and a dietitian might build a $3000 kcal$ diet for a 20 year old basketball player. $One~ calorie = 0.001kcal$, 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 As the previous paragraph illustrates, there are a frustratingly large number of different units in an ``Energy'' class. At
XXXX
%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. 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, (Kraushaar et al., 2022; Muller, 2010), Everyone eats, maybe not $3000 kcals$ per day, but at least something every day. When I teach our energy class, (Kraushaar et al., 2022; Muller, 2010),
@ -56,7 +59,9 @@ To introduce Food Energy, I ask the students to work through a few questions:
\centering \centering
\includegraphics[width=\columnwidth]{at_the_buffet.jpg} \includegraphics[width=\columnwidth]{at_the_buffet.jpg}
\caption{ \caption{
A proto-college-student at Winona's A proto-college-student at
XXXX's
%Winona's
China King Buffet, dreaming about visiting the steam tables every day. China King Buffet, dreaming about visiting the steam tables every day.
} }
\label{buffet} \label{buffet}
@ -100,7 +105,9 @@ In medicine, these slopes known as ``Metabolic Equivalent of Task'' (METS), a co
\subsection{Burning off food energy} \subsection{Burning off food energy}
Imagine that after eating a $600kcal$ bacon-maple long-john (donut), you decide to go for a hike to ``work off'' the Calories. 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? %Winona
XXXX
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?
Useful information: human muscle is about $1/3$ efficient, and on Earth's surface, gravitational energy has a slope of about $10~\frac{Joules}{kg\cdot m}$. Useful information: human muscle is about $1/3$ efficient, and on Earth's surface, gravitational energy has a slope of about $10~\frac{Joules}{kg\cdot m}$.
\begin{figure}[h] \begin{figure}[h]
@ -140,7 +147,7 @@ As figures \ref{corn_and_potato_yields} and \ref{ag_yields} show, the epoch of `
\includegraphics[width=\columnwidth]{corn_potatoes_raw_production_per_acre.pdf} \includegraphics[width=\columnwidth]{corn_potatoes_raw_production_per_acre.pdf}
\caption{ \caption{
USDA per acre Corn and Potato production figures, plotted over time. Data is given in harvest units, $56lbs$ bushels per acre for field corn and hundred-weight (CWT) for potatoes. By mass, corn is about $4.5$ times more calorie dense than potato which results in a nearly equal $kcal/acre$ values for both crops in figure \ref{ag_yields}. USDA per acre Corn and Potato production figures, plotted over time. Data is given in harvest units, $56lbs$ bushels per acre for field corn and hundred-weight (CWT) for potatoes. By mass, corn is about $4.5$ times more calorie dense than potato which results in a nearly equal $kcal/acre$ values for both crops in figure \ref{ag_yields}.
Details on the data source and conversions are given in \ref{how_yield_plot_is_made}. %Details on the data source and conversions are given in \ref{how_yield_plot_is_made}.
} }
\label{corn_and_potato_yields} \label{corn_and_potato_yields}
\end{figure} \end{figure}
@ -178,14 +185,13 @@ If we over-estimate and produce food for the entire year, the family will need a
\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 proportionally 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.
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. %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} & \approx& 2.3 acre
\frac{4.4 M kcal}{family}\cdot\frac{1.9M kcal}{1 acre} .
\eea \eea
The choice of operation is difficult to make without seeing the units present, which is again a learning opportunity for the students. %The choice of operation is difficult to make without seeing the units present, which is again a learning opportunity for the students.
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. (Deppe, 2020) 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. 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. (Deppe, 2020) 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.
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. 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.
@ -256,7 +262,7 @@ Average USDA per acre yields for a number of commodity crops over time. This ``
\section{Example: How big could Tenochtitlan have been?} \section{Example: How big could Tenochtitlan have been?}
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-Colombian 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, (Borunda \& Rodriguez, 2022) floating patches of decaying vegetation and soil. Given the proximity to water and decaying vegetation, these fields were very fertile (Coe, 1964; Ebel, 2019) and some continue to be used in the present day.\footnote{ 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-Colombian 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, (Borunda \& Rodriguez, 2022) floating patches of decaying vegetation and soil. Given the proximity to water and decaying vegetation, these fields were very fertile (Coe, 1964; Ebel, 2019) and some continue to be used in the present day.\footnote{
Chinampas are still visible in sattelite imagery. See for example $latitude=19.268$, $longitude=-99.087$. Chinampas are still visible in satellite imagery. See for example $latitude=19.268$, $longitude=-99.087$.
} }