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J_Coll_Sci_Teach_submission/food_energy.tex
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@ -23,11 +23,12 @@
\title{How many acres of potatoes does a society need?}
\shorttitle{How Many Potatoes?}
\leftheader{Moore}
%\leftheader{Moore}
\leftheader{}
%IOP header
\title{How many acres of potatoes does a society need? Using food and historical claims to introduce energy.}
\author{Nathan T. Moore}
\affiliation{Department of Physics, Winona State University, Winona, MN 55987, USA}
%\author{Nathan T. Moore}
%\affiliation{Department of Physics, Winona State University, Winona, MN 55987, USA}
%\email{nmoore@winona.edu}
\date{\today}
@ -42,7 +43,9 @@ Science and Social Policy classes are full of bespoke units and involve many dif
\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.
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.
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
\includegraphics[width=\columnwidth]{at_the_buffet.jpg}
\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.
}
\label{buffet}
@ -100,7 +105,9 @@ In medicine, these slopes known as ``Metabolic Equivalent of Task'' (METS), a co
\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.
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 $10~\frac{Joules}{kg\cdot m}$.
\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}
\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}.
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}
\end{figure}
@ -178,14 +185,13 @@ If we over-estimate and produce food for the entire year, the family will need a
\be
4~people\cdot\frac{3000kcal}{person\cdot day}\cdot\frac{365~days}{year} \approx 4.4 M kcal .
\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.
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.
%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.
\bea
\frac{4.4 M kcal}{family}\cdot\frac{1 acre}{1.9M kcal} & \textrm{~~or~~}&
\frac{4.4 M kcal}{family}\cdot\frac{1.9M kcal}{1 acre} .
\frac{4.4 M kcal}{family}\cdot\frac{1 acre}{1.9M kcal} & \approx& 2.3 acre
\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.
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?}
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 $latitude=19.268$, $longitude=-99.087$.
}