Issues in Earth Science
“Eww, There’s Some Geology in my Fiction!”
Issue 7, July 2017
Suggestions for Activities and Discussions to accompany a Reading of
Nuugyaa by L. L. Hill
Nuugyaa, our story for issue 7, includes a number of elements of interest in earth science, including a tsunami, a slump, and a landslide. However, the main science element embedded in the story is the idea of mass and energy balance. Mass balance and energy balance are the ideas that matter and energy are neither created nor destroyed and that we can keep track of the amount of mass and energy as they move from place to place. Understanding mass and energy balance is important not only for understanding the science of the origin of the tsunami, but understanding the mitigation system put in place to save the coast of Canada from the tsunami.
Mass and energy balance are, in fact, the key ideas in all of earth system science. Understanding global climate and climate change, earth carbon balance, pollutant migration, global precipitation patterns, etc., are all problems in mass and energy balance. To some extent, engineering involves applying science ideas—like mass and energy balance—to solving problems. Many problems—like the problem of mitigating the tsunami in the story—require thinking in these terms.
Thus, Nuugyaa provides a great opportunity to both engage students in thinking about mass and energy balance and engage them in applying that science thinking to a real problem—a perfect opportunity to include STEM* in the classroom. Most of the exercises below are math and engineering puzzles. The final problem—problem 6—also allows from some mapping and spatial reasoning exercises— skills needed in fields that use GIS technology (Geographic Information Systems).
From an Engineering perspective, there are at least three types of constraints on the Nuugyaa tsunami mitigation system.
· Energy balance. Does the amount of energy delivered by a collapsing mountain justify the size of the wave? Is the energy available to the protagonists sufficient to counteract the energy of the wave?
· Mass balance: Is the infrastructure put in place to stop the wave adequate to move the volume of water implied by the height of the wave?
· Logistical constraints: Is there some realistic method for moving water such that the energy of the wave might be dissipated? Is there realistic reaction time for the protagonists to actually take any meaningful action?
Let’s consider some of these constraints in an effort to understand how systems work, both in nature and in engineering problems.
Problem 1—Energy of the original landslide
Having students try to figure out how to calculate the energy of the landslide is probably a better starting point than simply giving them an equation and telling them to plug in numbers—after all, learning how to pushing buttons on a computer or calculator is not really a very valuable goal of the science classroom. However, as mentor and fellow practitioner of science, the teacher shouldn’t be simply sitting back and waiting for students to figure it all out. A few questions and prompts can go a long ways. Ideally, you, the teacher, are also trying to figure it out with them and can showcase your own interest in and approach to the problem! (Check out the essay on teachers as practitioners of science for seed thesis for our 8th issue in Topics for Debate).
Clearly, how much prompting you do, and how much initial guidance you offer, depends on the age and experience of your students. 8th graders, for example, will have the experience to do calculations and understand what they mean, but may not yet have encountered the physics equations and so won’t be able to identify correct equations without guidance.
Prompts might include any of the following ideas:
How do we determine potential energy or kinetic energy of a suspended or falling object? A bit of physics might be needed here. Kinetic energy = ½ times mass times velocity squared. From this relationship, we can get the potential energy (equal to the energy that an object would have if it fell a given distance in Earth’s gravity field) by calculating how fast the object will be travelling after falling that given distance (velocity = square root of (2 times height times the acceleration of gravity). Or, we might start with the equation for potential energy = mass times height times the acceleration of gravity. Acceleration of gravity on Earth is about 9.8 meters per second squared.
That the potential energy at the start of the landslide must equal the total energy dispersed by the landslide is one idea of energy balance.
How can you estimate the mass of the rock of the landslide?
The story indicates that the volume of rock is ‘the equivalent of a million transport trucks.’ Trucks come in quite a few different sizes, so we can’t get an exact number from this. However, an online search on “volume of transport truck” yields a mid value of around 30000 liters for large tanker trucks. For comparison, a typical gravel dump truck holds a little over 10000 liters. Anyway, 30000 liters gives us a ball-park number.
But our equation for energy requires us to use mass, not volume. How do we estimate the mass of 30000 x 1 million liters of rock?
An internet search on ‘density of rock’ gives us a typical range from 2 to 2.9 grams per cubic centimeter. There are 1000 cubic centimeters in each liter.
So, can your students figure out how to put the values together to get mass? What gets multiplied or divided?
(30000 x 1 million) liters x 1000 cubic centimeters per liter x 2.6grams per cubic centimeter = 7.8 x 1013 grams = 7.8 x 1010 kilograms
This might be a good opportunity to have students think about units and unit analysis. If a calculation is done correctly, the units have to cancel out to yield the correct final units.
How far does the rock of the landslide fall? From the story, it falls about a kilometer, or 1000 meters.
Can students figure out how to calculate the energy?
7.8 x 1010 kilograms x 1000 meters x 9.8 meters per second squared = 7.6 x 1014 Kilogram-meter squared per second squared (kgm2/s2) = 7.6 x 1014 Joules. (1 joule = 1 kg-m2/s2 = the standard SI unit of energy).
It might be interesting to compare the energy of the landslide to other types of energy to get a feel for what this number means. For example, how much energy does burning a gallon of gasoline release? An online search shows that a gallon of gasoline has about 120 megajoules of energy. So we can calculate that the landslide releases the equivalent of
7.6 x 1014 Joules/ 120 x 106joules per gallon = 6.3 million gallons of gasoline
Problem 2—Does the energy of the landslide account for the size of the tsunami?
Calculating energy of the tsunami wave is less straightforward than the landslide energy calculation because the speed, height, length of the wave crest and wavelength of the wave are complex functions of the water depth and surrounding landscape. However, engineering often involves making ‘best estimate’ of values and so an exercise like this can be a valuable experience in how engineering problem-solving proceeds. This exercise would be appropriate only for older students given multiple days to tackle this fairly involved engineering and math project.
An online search yields a paper that gives an equation for wave power (although in deep water, so it may only approximate the energy of the shallow water tsunami of the story). From the reference--Amir Vosough (2011) Wave Energy, International Journal of Multidisciplinary Sciences and Engineering V 2.--we can get the following:
Power = 0.5 (kilowatts/m3-s) x length of wave crest x height of wave squared x period of wave
(Period of the wave is the time for one wavelength to pass)
The story gives us an estimate of the wave height, since it went more than 500 meters up the side of Mount Bartholomew. Making some guesstimates for our imaginary tsunami of the story—suppose the wavelength of the wave is about 500 meters, comparable to the wave height, and the length of the wave crest is about a kilometer (1000 meters) and that the wave travels about 160 kilometers per hour (this is comparable to the speed of the real-world tsunami at Lituya Bay in Alaska in 1958).
We get power of 0.5 kW/m3-s) x 1000m x 250000m2 x 11.25 seconds = 1.4x109 kWatts
Or converting to energy (power x time) = 1.4x109 kWatts x duration of wave (11.25 seconds) = 4.4 x 106 kilowatt-hours.
Using a handy internet converter gives us 1.6 x 1013 Joules.
Can the energy of the falling rock account for this? What percentage of the total energy of the landslide is accounted for by the energy in the tsunami? Is it the same, or more or less? Compare the two, remember we calculated the energy in the landslide to be 7.6 x 1014 joules. This is an order of magnitude more energy than the 1.6 x 1013 joules in the tsunami.
Problem 3— Where does all the other energy go (an energy-balance consideration)?
The wave energy is only about 2.7% of the energy from the landslide (1.6 x 1013 joules/7.6 x 1014 joules). One order of magnitude is a BIG deal: Remembering our idea of energy balance, where did the rest of the energy go?
Can you hear the landslide? Might energy be going into making sound waves?
Can you feel the vibrations of the landslide through the ground? Might energy be going into making seismic waves?
What might happen to the rest of the energy? Throwing rocks around? Creating a gust of wind? Friction, within the landslide, between tsunami and ocean floor, or within the water column, converting the energy to heat?
Problem 4: Could a system like the Nuugyaa mitigation system really dissipate this much energy?
If the tsunami has 1.6 x 1013 Joules (4.4 x 106 kilowatt-hours) energy, it will take at least that much energy to dissipate it. According to the story, the power is supplied by wind turbines. How many wind turbines would it take to supply that much energy, say over a period of 3.4 minutes—the time it takes the tsunami to travel about 9 kilometers (that’s the length of the Nuugyaa network as reported by the story)?
Power production depends on wind speed and height of the turbine as well as its capacity, however, an online search indicates that typical wind turbines today generate about 500 kilowatts power on average over a year. Remember that energy = power x time. For power used over the 3.4 minutes it takes the wave to move through the Nuugyaa system, that would correspond to an energy of about 500 kwatts x 0.057 hours = 29 kilowatt-hours energy or 1.04 x 108 joules. Thus, we can calculate that the Nuugyaa system would require about .6 x 1013 Joules/1.04 x 108 joules = 580,000 such turbines on an average day (hopefully the tsunami wouldn’t happen during a lull in the wind!).
Problem 5: How much water does the Nuugyaa system have to move in the 3.4 minutes of the wave’s passage (a mass-balance problem)
A simplified way of approximating the volume of water in the wave is to consider the wave to be triangular shaped in cross-section (ok, so that isn’t such a great approximation—if you want to use a sine wave function, go for it!) With the triangular assumption, the volume of water will be the cross-sectional area of the triangle times the length of the wave. With a wave height of 500 meters, a wavelength of 500 meters, and a length of crest of 1000 meters (same numbers as used above), we get a wave water volume of
0.5 x 500m x 500m x 1000m = 125000,000 cubic meters of water = 125 billion liters
That’s a lot of water to move in 3.4 minutes. The story features a network of 2-meter-diameter pipes in sections of which the mid-section has 30 pipes.
What is the total rate of water movement required to move 125 billion liters of water in 3.4 minutes (discharge can be thought of as volume per unit time, or liters per second for example)?
= 125 billion / 204 seconds
Those pipes have to move water at a rate of 613 million liters per second.
How many pipes would that reasonably take?
With a pipe diameter of 2 meters (as reported in the story) and a reasonable rate of flow (say a maximum of 5 meters per second extrapolated from an internet search on maximum flow rate in pipe by size).
discharge = cross-sectional area of pipe x velocity
Cross sectional area = pi r2
Yielding discharge = pi x 1m2 x 5m/s = 15.7m3/s maximum
This corresponds to 3200 m3 for the entire 3.4 minutes per pipe.
(15.7 m3/sec x 204 seconds)
To transport 125 million cubic meters of water in 3.4 minutes would take a minimum of
125,000,000 m3 /3200 m3/pipe = 39000 pipes of the size described in the story.
Problem 6: How far from the landslide must the Nuugyaa system of pipes and pumps be to allow the protagonists in the story time to do what they do? Is that distance reasonable for the cited location of the story, in Desolation Sound?
At 160 km per hour (approximate velocity of the real-life tsunami in a similar setting in Alaska in 1958), you can figure it out. How much time passes in the story? How far would the wave travel in that time? Use Google Maps, and its ability to measure distances (click on the little ruler icon) to figure out distances in Desolation Sound. Where do you think that the Nuugyaa system might be located in the bay, given the setting of the story?
Educational Benefits in addition to STEM thinking:
There is a tendency of students to have a type of magic thinking concerning how technology can solve our problems, perhaps because so much of our modern technology does come to us seemingly like magic. Hopefully this exercise can give students an understanding not only of how to approach an engineering problem like a scientist or engineer, but give a sense of why protecting ourselves from natural disasters is so difficult (building 580,000 wind turbines and a system of nearly 40000 nine-kilometer long pipes and pumps to protect from a one-time event that we don’t know for sure when will happen—Wow!).
Application to the Next Generation Science Standards (NGSS) 2013: Ideas of mass and energy balance are central to several NGSS earth science cross-cutting concepts, disciplinary core ideas (DCI), and performance expectations, including
Energy and Matter: Flows, Cycles and Conservation – Tracking energy and matter flows into, out of, and within systems helps one understand the system’s behavior. Crosscutting concept #5
“All earth processes are the result of energy flowing and matter cycling within and among the planet’s systems.” ESS2.A—End point grade 8.
"Use a computational representation to illustrate the relationships among Earth systems and how those relationships are being modified due to human activity. HS-ESS3-6
The scope and scale of these NGSS ideas and goals are much too large for any classroom (they’re even too large for any particular scientific study). Breaking the concepts of mass and energy balance into smaller pieces, like that in Nuugyaa, and then thinking about how this is just one piece of a bigger puzzle, is a better approach to addressing the NGSS goals than having students memorize diagrams with lots of arrows and labels showing movement of mass and energy on a global scale.
*STEM is acronym for Science, Technology, Engineering and Mathematics, and reflects a current effort in US schools to integrate more technology, engineering, and math into science classes rather than treat these disciplines as separate or unrelated ideas.
The Teacher Resources for Nuugyaa are written by Russ and Mary Colson.
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