Teaching Notes

Grade Level

Mathematics are designed for upper level high school or college student (multiplying and unit conversion), although younger students should also be capable of the general concepts if the spreadsheet for calculations is more fully prepared for them.

Learning Goals

After completing this unit, users will be able to:

  • Create equations in a spreadsheet and manipulate data to calculate greenhouse gas emissions.
  • Compare and analyze options to select a mode of travel that minimizes GHG emissions.
  • Understand the consequence of long-distance travel and the differences among modes of travel on greenhouse gas emissions.
  • Gain familiarity with the lexicon of greenhouse gas inventory vocabulary.

Rationale

The combustion of fossil fuels for transportation purposes is a major contributor to our National and global greenhouse gas emissions.  In the United States, greenhouse gas (GHG) emissions from the transportation sector are approximately one-third of the nation’s total and represent the fastest-growing major source of greenhouse gases. Transportation emissions are related to the amount of carbon in the fuel and how much fuel is used. Between 1990 and 2003 greenhouse gas emissions from passenger vehicles increased by 19 percent due to the increased sales of light-duty vehicles (SUVs, minivans, etc.) and a 34% increase in the number of miles Americans travel every year.

Key Concepts and Vocabulary

Global warming potential (GWP) is a relative measure of how much heat a greenhouse gas traps in the atmosphere relative to the amount of heat trapped by a similar mass of carbon dioxide.  More formally, the GWP of a greenhouse gas is defined as the ratio of the time-integrated radiative forcing from the instantaneous release of 1 kilogram (kg) of a trace substance relative to that of 1 kg of a reference gas (Intergovernmental Panel on Climate Change (IPCC) 2001). A GWP is calculated over a specific time interval, commonly 20, 100 or 500 years and is expressed as a factor of carbon dioxide (whose GWP is standardized to 1).  The GWP is determined from its lifetime in the atmosphere and the intensity of its radiative forcing at specific wavelengths.

For a given mixture and amount of greenhouse gases, the carbon dioxide equivalencydescribes the amount of CO2 (parts per million by volume, ppmv) that would have the same global warming potential (GWP) over a specified timescale (e.g., 100 years). The carbon dioxide equivalency for a gas (kg CO2 eq./y) is obtained by multiplying the mass of the greenhouse gas emitted (for example, kg CH4/y) by its GWP
(24 kg CO2 eq./kg CH4).

Greenhouse gas inventory is an accounting of all of the sources and sinks of greenhouse gases over a specified system boundary and time period (typically one year).  A GHG inventory can be determined for a country, an industry, a school district or an individual household.  In 1992, the United States signed and ratified the United Nations Framework Convention on Climate Change (UNFCCC), which included a commitment to conduct an annual greenhouse gas inventory.  The U.S. EPA published the inventory for the country on an annual basis. Carbon footprint calculators are an example of tools to help a household or school district to conduct their own greenhouse gas inventory.

An emission factor is the average emission rate of a given pollutant from a given source or activity; for example grams of carbon dioxide released per megajoule of energy produced. Emission factors for many different types of pollutants are reported by federal agencies and the IPCC.  Some examples of the activities for which emission factors are available include fuel combustion, animal husbandry, industrial production, and travel.

Fuel economy is a measure of the efficiency of automobile travel in terms of miles driven per gallon (MPG) of gasoline consumed.  The U.S. tracks the total average fuel economy of vehicles operated and sold in the U.S.  In 2008, the average fuel economy of passenger cars was 22.6 miles per gallon. Standards are set to define the corporate average fuel economy (CAFE), which is an average of all of the vehicles sold by an individual manufacturer. The 2011 CAFÉ standard for passenger cars is 27.5 MPG.

Concepts:

  • An inventory of greenhouse gas emissions requires an understanding of human activities and the amount of greenhouse gases produced from each of these various activities.
  • A GHG inventory can be used to identify specific human activities that are better or worse in terms of their impact on global warming and other changes in the climate.
  • A GHG inventory for transportation modes requires that the miles driven, fuel consumption per mile, and GHG emissions associated with the fuel consumption be quantified.
  • A significant amount of GHGs are emitted during long-distance air travel.

Background Information

The key calculations the students require are:

  • For each type of travel and each GHG:

Emission = activity X emission factor

where the “activity” is defined as gallons of gasoline consumed for passenger vehicles and passenger miles travelled for all other transport modes. The emission factors are included in Table 1 (see also details on the MS Excel Spreadsheet).

  • For passenger vehicles – the fuel required is calculated as:

Gasoline consumed = vehicle miles travelled / fuel economy of the vehicle

The fuel economy used can be the current U.S. average (22.6 MPG for passenger cars) or a known fuel economy for a particular vehicle (http://www.fueleconomy.gov/ )

  • To determine the total greenhouse gas emission, the totals for each leg of the travel are summed for each greenhouse gas and then the greenhouse gases are aggregated using their global warming potentials (Table 2):

Total GHG emissions = CO2 Emissions + CH4 Emissions X GWPCH4 + N2O Emissions X GWPN2O

The units of the total GHG emissions will be kg CO2 equivalents for the trip.

Table 1: Greenhouse gas emission factors for travel

Passenger Vehicle 

CO2 Emission Factor

(kg CO2/
gallon gasoline combusted)

CH4 Emission Factor

(g CH4/
gallon gasoline combusted)

N2O Emission Factor

(g N2O/
gallon gasoline combusted)

Car or Light-duty Truck

8.81

0.75

0.77

Rail/Bus System 

CO2 Emission Factor   (kg CO2/passenger -mile)

CH4 Emission Factor  (g CH4/passenger -mile)

N2O Emission Factor  (g N2O/passenger -mile)

Intercity Rail  (e.g., Amtrak)

0.185

0.002

0.001

Commuter Rail

0.172

0.002

0.001

Transit Rail (e.g., Trams and Subways)

 

0.163

 

0.004

 

0.002

Bus

0.107

0.0006

0.0005

Airline Travel  Distance

CO2 Emission Factor   (kg CO2/passenger -mile)

CH4 Emission Factor  (g CH4/passenger -mile)

N2O Emission Factor  (g N2O/passenger -mile)

Long Haul (_> 700 miles)

0.185

0.0104

0.0085

Medium Haul (_> 300 and < 700 miles)

 

0.229

 

0.0104

 

0.0085

Short Haul (< 300 miles)

0.277

0.0104

0.0085

Distance Not Known

0.271

0.0104

0.0085

Table 2: Global Warming Potentials for primary greenhouse gases emitted during transportation

Species

Units

Global Warming Potential
(Time Horizon)

20 years

100 years

Carbon dioxide

kg CO2 eq./ kg CO2

1

1

Methane

kg CO2 eq./ kg CH4

56

21

Nitrous oxide

kg CO2 eq./ kg N2O

280

310

Other Resources

Global warming potential: http://en.wikipedia.org/wiki/Global-warming_potential ; http://www.ipcc.ch/publications_and_data/ar4/wg1/en/ch2s2-10.html

Values for global warming potentials http://unfccc.int/ghg_data/items/3825.php

U.S. Greenhouse Gas Inventory: http://www.epa.gov/climatechange/emissions/usinventoryreport.html

Global GHG inventories: http://cait.wri.org (registration required)

U.S. EPA Personal Household Carbon Emissions Calculator: http://www.epa.gov/climatechange/emissions/ind_calculator.html

Fuel economy of automobiles http://www.fueleconomy.gov/

Corporate Average Fuel Economy - http://www.nhtsa.gov/fuel-economy

Emission factors for travel - http://www.epa.gov/climateleaders/documents/resources/commute_travel_product.pdf

Instructional Strategies

General Approach

Prior to the calculation and evaluation aspects of this activity, students should have had an introduction to greenhouse gas inventories, including the concept and use of global warming potentials and emission factors. 

This activity is best done with computer access, one or two students per computer.  The students should have ready access to internet resources to estimate the miles travelled to their destination and MS Excel to estimate their total GHG emissions. 

The students should follow the instructions and questions in the MS Excel spreadsheet to document their findings and explore how changes in their travel plans (mode of travel or destination) will impact the total greenhouse gas emissions.

Students can each add tags to a Google Earth file to show their mode of transport and GHG emissions to their destination.  This is most illustrative if all tags get added to the same file for comparison purposes.

Optional approaches:

  • You may want assign different types of travel (regional, national, international) to different sets of students to help to ensure that a wide range of results are obtained for comparison and evaluation.
  • The calculation and conceptual complexity can be reduced if only CO2 emissions are calculated.  The global warming potentials and CO2 equivalency concepts can then be ignored and the activity focus more on miles and choices of transportation modes.
  • The Google Earth component can be deleted with only the loss of some geography concepts.

Implementation

Anticipatory Set Ask students about their travels – either actual or ideas of where to go and how to get there.  List all of the steps in a trip that would result in GHG emissions. Pose the questions – “Have you ever thought about making travel plans in a way to reduce GHG emissions?”  “What do you think you could do when planning a vacation to reduce GHG emissions?”

Procedure The use of the MS Excel spreadsheet should be modeled with a short example with a common local trip.  Project spreadsheet image and show students how to enter data and review the calculations required to determine the total GHG emissions. Students can then complete the activity. (Note – the teacher can choose to pre-populate the calculation cells with equations in the case where the interpretation from this exercise is more valuable than building MS Excel skills. A tutorial is available with basic MS Excel functions and equations).

Closure The activity should be closed with a comparison of student findings in terms of where they travelled, how they travelled, and the resulting GHG emissions.  The following general conclusions should be apparent by the end of this group discussion and comparison of their findings:

  • Long distance travel, especially by airplane, can add substantially to an individual’s average annual greenhouse gas emissions.
  • For moderate distances, fewer GHGs are emitted from passenger cars than airplanes, especially if several travelers (e.g., a family) participate.

Learning Contexts

This investigation could be done in combination with a social studies unit if students are studying geography or history.  “Vacation destinations” could also be related to business travel.

There are several concepts that can be integrated with a mathematics classroom: unit conversions, using units to help develop logic of calculations and determine which operations needed, and percentage change calculations.

Standards

National Science Education Standards Grade 9-12 (http://pals.sri.com/pals/standards/nses9-12text.html)

Science as Inquiry (12ASI)

12ASI1.3 Use technology and mathematics to improve investigations and communications. A variety of technologies, such as hand tools, measuring instruments, and calculators, should be an integral component of scientific investigations. The use of computers for the collection, analysis, and display of data is also a part of this standard. Mathematics plays an essential role in all aspects of an inquiry. For example, measurement is used for posing questions, formulas are used for developing explanations, and charts and graphs are used for communicating results.

12ASI2.4 Mathematics is essential in scientific inquiry. Mathematical tools and models guide and improve the posing of questions, gathering data, constructing explanations and communicating results

Science and Technology (12EST)

12EST1.1 Identify a problem or design an opportunity. Students should be able to identify new problems or needs and to change and improve current technological designs.

12EST1.2 Propose designs and choose between alternative solutions. Students should demonstrate thoughtful planning for a piece of technology or technique. Students should be introduced to the roles of models and simulations in these processes.

12EST1.4 Evaluate the solution and its consequences. Students should test any solution against the needs and criteria it was designed to meet. At this stage, new criteria not originally considered may be reviewed.

12EST1.5 Communicate the problem, process, and solution. Students should present their results to students, teachers, and others in a variety of ways, such as orally, in writing, and in other forms - including models, diagrams, and demonstrations.

Science in Personal and Social Perspectives (12FSPSP)

12FSPSP3.1 Human populations use resources in the environment in order to maintain and improve their existence. Natural resources have been and will continue to be used to maintain human populations.

12FSPSP4.2 Materials from human societies affect both physical and chemical cycles of the earth.

12FSPSP4.3 Many factors influence environmental quality. Factors that students might investigate include population growth, resource use, population distribution, overconsumption, the capacity of technology to solve problems, poverty, the role of economic, political, and religious views, and different ways humans view the earth.

12FSPSP6.1 Science and technology are essential social enterprises, but alone they can only indicate what can happen, not what should happen. The latter involves human decisions about the use of knowledge.

Mathematics Standards (9-12) (http://www.nctm.org/standards/content.aspx?id=4294967312 )

Number and Operations - Compute fluently and make reasonable estimates:

  • develop fluency in operations with real numbers, vectors, and matrices, using mental computation or paper-and-pencil calculations for simple cases and technology for more-complicated cases.
  • judge the reasonableness of numerical computations and their results.

Algebra - Use mathematical models to represent and understand quantitative relationships 

  • identify essential quantitative relationships in a situation and determine the class or classes of functions that might model the relationships;
  • draw reasonable conclusions about a situation being modeled

Measurements - Understand measurable attributes of objects and the units, systems, and processes of measurement 

  • understand relationships among units and convert from one unit to another within the same system (6-8);
  • make decisions about units and scales that are appropriate for problem situations involving measurement
  • use unit analysis to check measurement computations.

Process Standards

  • Solve problems that arise in mathematics and in other contexts
  • Apply and adapt a variety of appropriate strategies to solve problems
  • Communicate their mathematical thinking coherently and clearly to peers, teachers, and others
  • Recognize and use connections among mathematical ideas
  • Recognize and apply mathematics in contexts outside of mathematics
  • Create and use representations to organize, record, and communicate mathematical ideas
  • Select, apply, and translate among mathematical representations to solve problems
  • Use representations to model and interpret physical, social, and mathematical phenomena

National Geography Standards
(http://www.nationalgeographic.com/xpeditions/standards/matrix.html )

  • How to Use Maps and Other Geographic Representations, Tools, and Technologies to Acquire, Process, and Report Information from a Spatial Perspective.
  • How to Analyze the Spatial Organization of People, Places, and Environments on Earth’s Surface
  • The Physical and Human Characteristics of Places
  • The Characteristics and Spatial Distribution of Ecosystems on Earth’s Surface

Assessment

Completed worksheets with discussion questions should be submitted by each student to be graded.

Other Resources

MS Excel Workbook

MS Excel worksheet used for itinerary and calculations: vacation-GHGs.xlsx

Travel information sources

Fuel economy of automobiles: http://www.fueleconomy.gov/

Flying distances:  www.webflyer.com/travel/mileage_calculator/  

Driving distances:  www.mapquest.com

Case Study

Case Study: How many GHGs are emitted to travel to Hawaii?

Imagine a family vacation in Hawaii as we leave the cold northern New York winter for some sun, palm trees, black sand beaches and tours of active volcanoes.  But for a family of four, that is a lot of air miles that result in the combustion of jet fuel and the release of GHGs into the atmosphere.  How “bad” would such a trip be for a family that otherwise is quite efficient in our energy and material use?

A greenhouse gas calculator for an adult in a conservative household in Potsdam, NY, with no air travel, shows an annual greenhouse gas footprint of 6.4 metric tons CO2equivalents per year, which is substantially less than the ~20 metric tons for the average U.S. resident.

The itinerary for a dream trip to Hawaii requires the following travel:

  1. Drive from Potsdam, NY to Montreal, Canada
  2. Fly to Honolulu, HI (assume that even with one stop, each leg of the trip is >700 miles)
  3. Drive around the island of Oahu
  4. Fly to Hilo, HI
  5. Drive around the island of Hawaii
  6. Fly to Oahu
  7. Fly to Montreal, Canada
  8. Drive to Potsdam, NY

The distances traveled were determined with internet resources and are included in the MS Excel worksheet.

Wow!  Travel attributed to each of the four members of the family was 2.03 metric tons (mt) CO2 eq.  This is almost a third more than the personal annual GHG emissions associated with daily life and standard travel.  Over 90% of the total is associated with the long distance flight (4,900 miles) from Montreal to Honolulu.  Personal travel really can make a big (and negative) impact on a personal greenhouse gas footprint.

Because the air travel was the most significant impact, consider going to another location that has similar attributes, but not as far away.  How about Freeport (Grand Bahama Island), which is only 1,330 miles from Montreal? The island is smaller, so we can also anticipate less driving on the island.  The new total is 0.53 mt CO2 eq. per person.  This is now only about 25% of the per person contribution for the trip to Hawaii, yet the destination offers a lot of the same attributes as a trip to Hawaii would.  Table 1 summarizes the results of the analysis.  It is clear that the long distance travel is still the most important component of the GHG emissions for transportation for both trips (95% for the trip to the Grand Bahama Island).  In all cases, the CO2 emissions predominated, with minimal extra contributions from the methane or nitrous oxides.

As you consider your own trip, think about where you want to go and how you might get there.  Changes either in your destination or mode of travel can have a profound impact on your GHG emissions.

Table 1: GHG emissions for components of the dream trip. 

Step-By-Step

Part 1— Define your dream trip

Part 2— Determine the total greenhouse gases emitted for your trip

Part 3— Evaluate ways to reduce your GHG emissions

Part 4— Analyze the impact of your trip on your total GHG emissions and report your results

Part 5— Integrate your results into a Google Earth file to illustrate your results (optional per teacher instructions)

Part 1—Define your Dream Trip

  • Select a Starting point, Destination, Number people who travel
  • Define your itinerary (stops on your trip, modes of transportation for each leg of your trip)
  • Open the MS Excel Spreadsheet to begin entering information for your travels (columns A and B)
  • Estimate miles travelled for each leg of your trip and add to the spreadsheet (Column C) (this can also be done directly through Google Earth, but with less accuracy)

Part 2— Determine the total greenhouse gases emitted for your trip

  • Determine the gallons of fuel required for the legs of your trip that you drive:
    • Estimate the fuel economy of the automobile you will be driving from http://www.fueleconomy.gov/ (or use the current national average for passenger cars – 22.6 MPG)
    • Create an equation in your spreadsheet to calculate the gallons of fuel required (orange cells, column E)

Gasoline consumed (gal) = vehicle miles travelled (miles) / fuel economy of the vehicle (miles/gal)

  • Enter emission factors for the specific transportation methods into the spreadsheet (yellow cells, Columns J, N, P)
  • Calculate the emissions for each leg of your trip
    • Create an equation in the spreadsheet to estimate the emissions for each of the three greenhouse gases (orange cells in columns K, N, Q)

Emission = activity X emission factor

  •  The “activities” are passenger miles (bus, plane, rail) or gallons of fuel consumed (passenger car).
  • Add an equation to your spreadsheet (column S) to convert all GHG emissions into carbon dioxide equivalents (Note – the GWPs are included in row 16):

Total GHG emissions = CO2 Emissions
+ CH4Emissions
 X GWPCH4
+ N2O Emissions
 X GWPN2O

  • Calculate both the total emissions for all of your travelers and the per person average emissions. Note that “passenger miles” should be added for each individual.  The vehicle miles are already the total for all of the passengers in the vehicle.
  • Evaluate your results and answer the following questions within the text box of the spreadsheet:
    •  Which GHG contributes most to your total CO2 equivalents? (CO2, CH4 or N2O)  Is this what you expected?
    • Which leg of your trip contributes most to the greenhouse gas emissions?
    • How do your emissions for this trip compare to your annual total greenhouse gas emissions?  (you can use results of a personal GHG calculator (e.g., http://www.carbonfootprint.com/calculator.aspx ) or compare to the U.S. average ~19 metric tons CO2 eq./person/year; Global average ~4 mt CO2 eq./person/year; or a global goal  ~2 mt CO2 eq./person/year )

Part 3— Evaluate ways to reduce your GHG emissions

  • Use the analysis of the primary contributions to your total emissions to identify changes in your dream vacation plans.  This could include changes in your destination or mode of travel.
  • Copy your completed spreadsheet and create a new version of the spreadsheet within your workbook. (Select entire spreadsheet (Ctrl-A); click on “Sheet 2” click on cell “A1” and paste your selection (Ctrl-V))
    (Note – second sheet for your second itinerary has already been created.  However, you will have to recreate your equations if you use this sheet rather than copying and pasting your already completed sheet.)
  • Repeat part 2 above – although calculation cells now created, you only have to edit the appropriate cells in your new worksheet to change miles for your destination of GHGs from a different mode of travel.
  • Answer questions as posed above in Part 2.  Evaluate the benefits of changing your destination or mode of travel.
  • Write a short report (at least three paragraphs) to summarize what you did (introduction of your trip and desire to calculate GHG emissions, general methods, and findings). Include tables of final results to help explain your findings and comparison.

Part 4— Analyze the impact of your trip on your total GHG emissions and report your results

  • Answer questions as posed above in Part 2.  Evaluate the benefits of changing your destination or mode of travel.
  • Write a short report (at least three paragraphs) to summarize what you did (introduction of your trip and desire to calculate GHG emissions, general methods, and findings). Include tables of final results to help explain your findings and comparison.

Part 5— Integrate your results into a Google Earth file

  • Open Google earth
  • Create a new folder under your “My Places” section of Google Earth for this project.
  • Follow tutorial directions for adding pushpins to the major destinations of your trip and make a path to connect your destinations.
  • Add details to the pushpin information balloons that describe your destination, distance and mode of travel and the GHG emissions that result from the traveling.  If you consider a second destination, add pushpins, information balloons and a path for your alternative trip too and save to your My Places folder.

Tools

Tool – Microsoft Excel

Microsoft Excel: A spreadsheet application is needed to analyze the data. Microsoft Excel is used in this activity and is available as part of Microsoft Office.

Tool Builder

Microsoft Corporation - www.microsoft.com

Tool Cost

Excel is part of the suite of Microsoft Office software. Students and educators may be able to purchase this software at a reduced cost. The Student and Home Edition is sufficient for use in this activity.

Tool - Google Earth

Google Earth lets you fly anywhere to view satellite imagery, maps, terrain, 3D buildings, galaxies in outer space, and the depths of the ocean. Students can add “pushpins” with information to document their findings for different destinations. Google Earth desktop is available free of charge http://www.google.com/earth/explore/products/desktop.html

References

http://www.epa.gov/climatechange/emissions/ind_road.html

http://www.bts.gov/publications/national_transportation_statistics/html/table_04_23.html

http://www.epa.gov/otaq/climate/420f05004.htm#key

http://www.epa.gov/climateleaders/documents/resources/commute_travel_product.pdf

http://unfccc.int/ghg_data/items/3825.php