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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 related to ``Metabolic Equivalent of Task'' (METS) and are commonly discussed in cariology 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 physcial activities. \cite{METS} \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? -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] \centering @@ -77,36 +77,42 @@ Useful information: human muscle is about $1/3$ efficient and on Earth's surface \label{bar_chart} \end{figure} -One way to approach this problem is by using Energy Bar Charts \cite{energy_bar_charts} to illustrate how the food energy changes form as it is absorbed and 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. The other $2$ blocks of energy are transformed into heat and are removed from the hiker's body via body heat, 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}. +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. +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}. \bea \frac{1}{3}\cdot600kcal\cdot\frac{4200J}{1kcal} &=& 80kg\cdot10\frac{Joules}{kg\cdot m}\cdot height \label{eq:bar_chart}\\ height &\approx& 1000 m \eea -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 -- 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 $13\frac{m}{s}\approx33mph$! +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 $13\frac{m}{s}\approx33mph$! -The point of these energy conversion 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 $8000m$ 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. +The point of these energy conversion 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. \subsection{Where does food energy come from?} -One modern feature of the aught's ``homesteading'' culture is the idea that a person can probably move to the country and grow all their own food. Learning that farming labor is \textit{skilled} labor can be a brutal and disheartening realization. $3000kcals$ each day is about is one million kcals each year. Where will those Calories come from? Is your backyard enough to homestead in the suburbs? +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 a brutal and disheartening realization. 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 chemical processes developed for chemical warfare and munitions to produce chemicals that would kill insects and increase the Nitrogen levels in the soil. As figure \ref{ag_yields} shows, a dramatic increase in per-acre yields has ocurred across all comodity food crops. +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. +As figure \ref{ag_yields} shows, the epoch of ``Better Living Through Chemistry'' produced a dramatic increase in per-acre yields across all comodity food crops. -\begin{figure}[h] +\begin{figure}[ht!] \centering -\includegraphics[width=\columnwidth]{bar_chart.png} +\includegraphics[width=\columnwidth]{yield_over_time.png} \caption{ -USDA yields +USDA yields over time +The data plotted comes from the USDA +\url{https://www.nass.usda.gov/Statistics_by_Subject/index.php} +The idea for this plot came from an online blog, \cite{math_encounters} } \label{ag_yields} \end{figure} -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 seets are not available to the public, and the edge effects from deer and insects are much smaller on a 600acre field than they are in an community garden allotment. As mentioned in the introduction, in 1917 the USDA published a pamphlet, shown in \ref{1917_yields} about yields a farmer might expect. Their 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. +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, 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, shown in \ref{1917_yields} about yields a farmer might expect. Their 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. -\begin{figure}[h] +\begin{figure}[ht!] \centering -\includegraphics[width=\columnwidth]{bar_chart.png} +\includegraphics[width=\columnwidth]{USDA_1917_cropped.pdf} \caption{ USDA yields from pre-chemical US ag } @@ -201,6 +207,26 @@ Eric Brewe PHYSICAL REVIEW SPECIAL TOPICS - PHYSICS EDUCATION RESEARCH 7, 020106 (2011) https://journals.aps.org/prper/abstract/10.1103/PhysRevSTPER.7.020106 +\bibitem{Haspel} +In defense of corn, the world’s most important food crop +The Washington Post +Tamar Haspel +July 12 2015 + + +\bibitem{homesteading} +See for example, the Discover television show, ``Alaska the Last Frontier,'' any issue of ``Mother Earth News,'' or Backyard Chicken feeds on Instagram. + +\bibitem{backyard_homestead} +The Backyard Homestead: Produce all the food you need on just a quarter acre! +Carleen Madigan +Storey Publishing, LLC; 14th Printing edition (February 11, 2009) + +\bibitem{math_encounters} +https://www.mathscinotes.com/2017/01/calorie-per-acre-improvements-in-staple-crops-over-time/ +Mark Biegert +Math Encounters +2017 \bibitem{Aztec_Cannibalism} for crop productivity diff --git a/references/Calorie Per Acre Improvements in Staple Crops Over Time _ Math Encounters Blog.pdf b/references/Calorie Per Acre Improvements in Staple Crops Over Time _ Math Encounters Blog.pdf new file mode 100644 index 0000000..1339148 Binary files /dev/null and b/references/Calorie Per Acre Improvements in Staple Crops Over Time _ Math Encounters Blog.pdf differ diff --git a/references/Carol Deppe The Nearly All Potato Winter.pdf b/references/Carol Deppe The Nearly All Potato Winter.pdf new file mode 100644 index 0000000..00867cf Binary files /dev/null and b/references/Carol Deppe The Nearly All Potato Winter.pdf differ diff --git a/references/In defense of corn, the world’s most important food crop - The Washington Post.pdf b/references/In defense of corn, the world’s most important food crop - The Washington Post.pdf new file mode 100644 index 0000000..ad9b3d1 Binary files /dev/null and b/references/In defense of corn, the world’s most important food crop - The Washington Post.pdf differ diff --git a/references/Science_1978_Aztec_ag_and_cannibalism_1746929.pdf b/references/Science_1978_Aztec_ag_and_cannibalism_1746929.pdf new file mode 100644 index 0000000..c620d61 Binary files /dev/null and b/references/Science_1978_Aztec_ag_and_cannibalism_1746929.pdf differ diff --git a/references/USDA_1917_ORC00000242.pdf b/references/USDA_1917_ORC00000242.pdf new file mode 100644 index 0000000..d052bef Binary files /dev/null and b/references/USDA_1917_ORC00000242.pdf differ diff --git a/references/USDA_1917_cropped.pdf b/references/USDA_1917_cropped.pdf new file mode 100644 index 0000000..db5f883 Binary files /dev/null and b/references/USDA_1917_cropped.pdf differ diff --git a/references/little ice age - Irish Potato Famines.pdf b/references/little ice age - Irish Potato Famines.pdf new file mode 100644 index 0000000..5123e4c Binary files /dev/null and b/references/little ice age - Irish Potato Famines.pdf differ diff --git a/yield_over_time.png b/yield_over_time.png new file mode 100644 index 0000000..f2af1d6 Binary files /dev/null and b/yield_over_time.png differ