Two Day Seminar On The Mathematics Of Earth's Energy Sources
Agenda
Day 1: Motivation for Alternatives, and Solar Experiments
 9:00 — 9:15:
 welcome
 who'swho
 expectations
 objectives
 Participants will see how mathematical training can be accomplished while studying important issues surrounding energy.
 Participants will gain knowledge about the current state of energy use in America.
 Participants will gain an appreciation for the state of their own energy consumption.
 Pathways for carbon will become more apparent to the participants.
 Students will gain an intuitive understanding for the relationship between pitch of a solar panel and the energy produced.
 Students will understand the relationship between blade angle and power of a wind/water turbine.
 Math:
 Gaining Skills Through EnvironmentBased Learning, from Closing the Achievement Gap, Lieberman and Hoody (1998)
 EIC (Environment as an Integrating Concept) students outperformed their peers from traditional programs at all five schools that conducted these analyses.
 Results:
 Improved understanding of mathematical concepts and content (73%)
 Better mastery of math skills (92%)
 More enthusiasm for studying math (89%)
 Math comprehension improved in objective scores:
 16 percentile points for low achievers
 13 percentile points for middle achievers
 7 percentile points for high achievers
 Learning in the context of the environment helps students recognize the practical value of math for quantifying and understanding the world around them. As their perception of math changes, students become more committed to its study.
 Mathematical Notions to focus on:
 Estimation
 Order of Magnitude
 Units and Unit Conversion
 Mathematical Modeling
 Gaining Skills Through EnvironmentBased Learning, from Closing the Achievement Gap, Lieberman and Hoody (1998)
 9:15 — 9:30:
 "Why Alternative energy?" Discussion: why are BP and so many other energy companies touting "Wind, Solar", etc.?
 Recent Human and Environmental Disasters:
 29 miners dead in Big Branch mine disaster, Massey/Blankenship
 BP's Gulf oil spill:
 Government survey of the situation: http://www.restorethegulf.gov/
 Estimation exercise:
 BP promises to make good on all claims, but "You can't put a price tag on nature."
 How many gallons per day can flow out of a 6inch pipe?
 I heard a fellow exclaim over some of the higherend estimates, saying "it's impossible to get 20,000 barrels of oil a day through a 6inch pipe!?" What do you think?
 Martin County coal slurry disaster  see also..., also the MSHA review of its own performance (bad). "…30 times larger than the Exxon Valdez oil spill…."
 Tennessee river coal slurry disaster (…101 times larger than the 1989 Exxon Valdez oil spill….)
 Mountaintop Removal
 Nonrenewable
 Conserve oil or coal for other uses (e.g. plastics, or coke for steel production)
 We're held hostage to foreign countries and their resources.
 Global Warming
 Recent Human and Environmental Disasters:
 "Why Alternative energy?" Discussion: why are BP and so many other energy companies touting "Wind, Solar", etc.?
 9:30 — 10:15
 Global Warming Begins at Home
 Example activity, illustrating several of our mathematical foci:
 Transportation Tally:
 Spend 15 minutes studying this example, looking at how the mathematical notions (estimation, units, order of magnitude, modeling) play a role in this lesson.
 Discussion (note: there are at least three errors! checked in TransTally.lsp)
 This is Population Connection Worksheet Activity #14, from Multiplying People, Dividing Resources © 2009, Population Connection
 Transportation Tally:
 Example two: Keeling Curve — NASA Space Math activity (local copy)
 My version of the Keeling Data (the original data doesn't have the model added, or the predictions)
 Keeling Data and Yearly Cycle
 Others:
 Maths Matters: Carbon Dioxide: using mathematics to understand the greenhouse effect
 Issue 18  Greenhouse Gases Global CO2 Emissions And Global Warming, pp. 195205, Environmental Issues
 Population Connection Worksheet Activity #13: Global Warming Begins at Home USA
 Chemical balance equation
 Unit conversions
 Note that airlines now partner with organizations doing carbon offsets for the trip you take (Continental gave me the option of offsetting my carbon from my flight to Belize in August…  I did!;)
 Example activity, illustrating several of our mathematical foci:
 Global Warming Begins at Home
 10:15 — 10:30: break
 10:30 — 12:00
 Solar is the ultimate power source (precursor to all fossil fuels, of course)
 Example from Maths Matters
 Solar Activities: there's more than one way to collect solar energy:
 Parabolic (quadratic function) collectors/reflectors: Flashlights and the sun
 Demo by Dolph Himmelbauer <moc.rewopralosnocihploD#moc.rewopralosnocihploD>
 modeling solar response to angle of inclination
 What mathematical features do we want our model to possess?
 How can we make this relevant to your grade level?
Day 2: Other alternative options
 9:00 — 9:30: Reducing our use of Fossil Fuels
 Review of yesterday
 Resources I failed to mention yesterday
 The value of models:
 Predicting 140km/h CO2 emissions (271.8 g/km)
 Keeling Data example
 Conservation
 Does anyone remember Jimmy Carter?
 Home Energy Audit
 Compact Fluorescent light bulbs (CFLs)
 Wrapping your water heater
 Insulating your attic
 Caulk!
 Monitoring your energy usage: Use the "detailed" version of your bill, if possible
 Encouraging Alternatives with Surcharges:
 Cap and Trade
 Better dynamics:
 FeenDividend  an alternative to CapnTrade, promoted by Jim Hansen
 Tax rebates for energy star appliances
 Tax incentives for going geothermal, solar, etc.
 Review of yesterday
 9:30 — 10:15:
 Is the Answer Blowing in the Wind? (Issue 16, pp. 175, Environmental Issues)
 Blade diameter versus Power generated
 Exponential growth in math modeling (doubling time, etc.)
 The estimated U.S. energy use in 2008 equaled 99.2 quadrillion BTUs (“quads”), down from 101.5 quadrillion BTUs in 2007.
 Is wind power a viable alternative to conventional electric power generation? (Denmark and wind power — from Environmental ProblemSolving, Isobel W. Heathcote, 1997)
 The state of wind power
 Currently:
 Huge Wind Farms across the country — e.g. Indianapolis. "wind energy is available over a much larger geographical range than hydropower—about onethird of the U.S. (an area stretching from Minnesota to Texas to Wyoming) has enough wind almost everywhere to generate electricity economically, and there are many hills and passes in other states that are windy enough as well. Altogether, 46 of the 50 states have some wind resources that could be developed."
 From http://www.awea.org/faq/wwt_basics.html:
 "An average U.S. household uses about 10,655 kilowatthours (kWh) of electricity each year. One megawatt of wind energy can generate from 2.4 to more than 3 million kWh annually. Therefore, a megawatt of wind generates about as much electricity as 225 to 300 households use."
 "a 50MW wind farm can be completed in 18 months to two years."
 "Wind speed is a crucial element in projecting turbine performance, and a site's wind speed is measured through wind resource assessment prior to a wind system's construction. Generally, an annual average wind speed greater than four meters per second (m/s) (9 mph) is required for small wind electric turbines (less wind is required for waterpumping operations). Utilityscale wind power plants require minimum average wind speeds of 6 m/s (13 mph)."
 "The power available in the wind is proportional to the cube of its speed, which means that doubling the wind speed increases the available power by a factor of eight."
 How it works (NGM)
 "Doubling the blade, or rotor, diameter can result in four times more power." (this is a quadratic increase)
 vertical shaft wind power generation
 Transmission troubles, and smarter grids: National Geographics 21st Century Grid (7/2010) Graphic
 Liquid wind? Hydrogen

 The Hindenberg….
 Splitting water
 Solar and Wind Hydrogen
 Other possibilities

 Currently:
 Is the Answer Blowing in the Wind? (Issue 16, pp. 175, Environmental Issues)
 10:15 — 10:30: break
 10:30 — 11:30: Activity: Twisty turbines: angle and performance
 Students will use wind turbines to investigate the effect of blade angle
 11:30 — 11:50
 Meeting in groups to talk about how to make this relevant to your grade level
 Report of discussions by group
Handouts
 Gaining Skills Through EnvironmentBased Learning, from Closing the Achievement Gap, Lieberman and Hoody
 Transportation Tally
 NASA Space Math Keeling CO2 Activity
 Is the Answer Blowing in the Wind? (Issue 16, pp. 175, Environmental Issues)
 Is wind power a viable alternative to conventional electric power generation? (Denmark and wind power)
 Optional:
Links
 Here is an outline of what was proposed.
 TwoDay Math and Energy Seminar Original Proposal
 NOVA program on the world's rapidly melting ice
 Physics Energy Definitions
 Energy: Energy is measured in units of mass times velocity squared, and the MKS and cgs units of energy are the Joule and erg, respectively. Other common units of energy include the Btu, calorie, and kilowatt hour, and Newtonmeter (the units of work).
 Power is defined as energy E (or work W emitted or expended over a given time interval.
 Kilowatthour: A unit of energy equal to 3.6x10^{6} J.
Units
page revision: 171, last edited: 03 Apr 2011 05:58