I wrote this piece for teachers committed to making education more relevant and experiential, but also to celebrate robust science as a tool for better understanding the world around us.
What does a forest produce? A shoestring is all you need to measure it...
The power of science
Overshoot assessments compare how much human demand from nature, and how much nature can regenerate. Demand on regeneration (or people’s “Footprint”) can be captured by tracking how much area is needed to replenish what is being taken. The counter piece, biocapacity is represented by how much is regenerated on a particular area. This makes this measurement approach simple and accessible, despite criticism about the approach, much of which is misplaced as discussed at length here.
Because of this simplicity, we call Ecological Footprint accounting “pedestrian science”. It is an intended pun: these accounts and their principles are based on very basic, totally accessible high school math and science. Because the science is so basic, results are also robust. That has been the intention all along: to be elementary and nonspeculative, descriptive rather than normative or hyperbolic, so the accounts produces powerful results that are robust even as they contradict mainstream policy advice.
Pedestrian is good, particularly as the world struggles to shed its fossil fuel dependence. In fact, the underlying science of Footprint accounting is so pedestrian that all you need is a shoestring to execute primary, empirical Footprint studies. This is what the following exercise demonstrates. This exercise might be a great way for a scouts club, a biology or math class, or just a nerdy bunch of friends to kill a beautiful afternoon in the forest.
Exploring the world with a shoestring: measuring Ecological Footprint and biocapacity
In its simplest manifestation, this exercise requires the following materials: One 4meter long string per group. If you do it with a group of students, divide them into groups of three, and equip them with one string each, plus some paper and pencils to record, and one pocket calculator per group, if mental arithmetic is too demanding for them.
Set up for Exercise: Find a nice forest close by in which you are allowed to walk around. Take your students there and divide them in groups of 3.
Task 1: Hand a string of 4 meters long to each of the groups. Prepare the strings with them to turn them into a measurement tool: fold them in half and make a knot (or use a pen) for the two meter mark, then fold again to identify the place for the one meter mark. Keep going with the same folding technique to get finer resolution, beyond 50 cm (1/2 meter) marks, all the way to 1/16th meter which is 6.25 cm. This gives you a tool that allows people to measure with at least 3 cm precision.
Task 2: Ask each group to measure and identify one hectare. First measure with the shoestring how long your average steps are. Calculate how many steps you need to take for 100 m. One person stays put, the other two persons from team move away 100 m, on trajectories that are perpendicular to each other. Each person marks the corner with a piece of cloth, a hat, a stick, or a bag. These flags represent three of the four corners of a onehectare large square (100 m times 100 m = 10,000 m^2).
[m^2 means square meter, this page does not support superscripts, sorry. m^3 is a cubic meter]
Task 3: Now ask the students to calculate the standing biomass.
You do it by taking a subsection of the hectare (since doing the entire hectare would be too time consuming). Once you have defined an area (and know how big it is) develop an inventory of the trees.
Let me give a specific example. In this case, the calculation for a plot of 20 m times 50 meters (= 1000 m^2 or 1/10th of a hectare) is as follows.
Develop an inventory (first three columns of the table). The height you can estimate by taking a twometer stick (or person) and have the stick held close to the tree. Take some distance, stretch out your arm and span thumb and index finger sufficiently to capture with your eye the entire 2m stick. Then walk with this visual finger gauge upwards to find out how many times the two meters can be put on top of each other until the gauge reaches the top of the tree.
The circumference is easy to measure with the shoestring measure. Just sling it around the tree.
Depending on the forest type, you may need more or fewer categories for the different tree sizes in the forest. The assessment could look like this  a hypothetical example to illustrate the exercise:
number of trees  height  circumference  cross section  standing volume in entire category 
#  m  m  m^2  m^3 
measured  measured  measured  calculated  calculated 





4  20  1.5  0.179  14.3 
9  20  0.9  0.064  11.6 
15  20  0.7  0.039  11.7 


 TOTAL  37.6 
Once the inventory is complete, calculate the results (4th and 5th column).
Now, here, a little bit of geometry comes handy. Who knew?
The circumference of a circle is c. c = 2 * π * r. The area A is calculated as A = π r^2.
Hence the cross section of the tree you calculate with the following formula:
A = π * (c / (2* π)^2).
This can be simplified to A = c^2 / (4* π) or A ~ 0.08 * c^2
Trees are skinnier further up, but they also have branches on the upper part above the trunk. To simplify, we assume that these two “complications” compensate each other. Therefore, we calculate the volume by analyzing the cylindrical volume over the cross section.
Therefore, the “standing volume in entire category” can be approximated as number of trees height cross section.
The result in the presented case is a standing volume of 37.6 m^3 on these 1000 m^2.
Hence the standing volume for this particular one hectare, assuming that the 1000 m^2 are representative, is 37.6/1,000 * 10,000 = 376 m^3/ha.
Task 4: Now you can figure out the forest’s productivity (per year and per hour). How much wood is being created, just as we are in this forest.
Find out how old the stand is (oldest tree is the indicator). Let’s assume it is 40 years old. You may want to ask the local forest service or just count the rings of a recently felled big tree.
This means the average bioproduction is 376 m^3/ha /40 year.
There are 365 * 24 hours in a year = 8760 h.
The bioproduction per hour of this forest is: 376/40 years / 8760 = 0.011 m^3 per hour.
In other words, averaged out, every hectare of this forest produces 0.011 m^3 or 11 liters of timber per hour.
Given seasons, not all hours are equally productive. If you are in a temperate forest and are there in a summer hour during the day, and also assume that forests don’t grow in the winter (1/4 of the year) and also rest at night (½ the time), then the growth happens only during ¾ times ½ = 3/8th of the time. This means during the time you were in the forest, growth was faster than average. It would be more like 8/3 * 11 liters or 29 liters in that particular daytime hour.
Task 5: finally find out how far a car could get with one hour of productivity of this hectare.
How much energy does this represent, and how far could one go with a conventional car.
One liter of gasoline contains 35 Mj of chemical energy.
One kg of wood contains 20 Mj of chemical energy.
One kg of wood corresponds to about 2 liters of wood (to find out how dense wood is watch how it swims. About half the wood is outside of the water. Since one kg of water is one liter of water, 2 liters of wood would be 1 kg of mass) – another way of saying this: the density of wood is about 500 kg per m^3 of wood (average)
This means that about 4 liters of wood correspond to the energy content of roughly 1 liter of gasoline.
An average car needs 12 liters of gasoline per 100 km. Hence the 0.029 m^3 produced in one hour on this particular on this one hectare would produce the equivalent amount of energy needed to drive one car 100/12* 29/4 = 25 km. (or 9 km on what's produced in an average hour, winter and nights included).
(Remember: energy production is roughly the equivalent of CO2 absorption).
Note for American readers: If you want to do the whole exercise in US standard, you can, but it is harder to convert sizes into volume (how many inches in a foot? how many cubic inches in a cubic foot or a gallon?). Converting liters into gallons and km/100 liters into miles per gallon is simple. Here I chose 20 miles per gallon as the US fuel efficiency average for conventional cars, which is the same as 11.8 l per 100 km.
Task 6: Interpret the results with them, ask for reflections on what they experienced and learned, and celebrate. Time for a picnic.
Epilogue
Reliable, meaningful measurements require science. Science is an endeavor, a deliberate method, to gain ever more robust understanding of how the world works. As a result, predictions become increasingly reliable. And we can make better decisions.
Good science can even be done with just a shoestring, and even on a shoestring. At the core, it requires asking good questions, turning them into testable, measurable ones, and then empirically testing them, as you did here. If you have questions or comments, please let me know.
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