I N T E R D I S C I P L I N A R Y L I V E L Y A P P L I C A T I O N S P R O J E C T

AUTHORS:Lei Yu(Transportation Studies)yu_lx@tsu.edu

Texas Southern University3100 Cleburne AvenueHouston, TX 77004

Don Small(Mathematics)

U.S. Military AcademyWest Point, NY 10996

Lafayette CollegeEaston, PA 18042

CONTENTS1. Introduction2. Remote Emission-Sensing

Technique3. Emission Data Collection4. Data Conversion5. Regression Analysis6. Emission-Based Speed

Optimization7. Real-World ApplicationsReferencesSample SolutionNotes for the InstructorAbout the Authors

The UMAP Journal 24 (4) 451-472. © Copyright 2003 by COMAP, Inc. All rightsreserved. Permission to make digital or hard copies of part or all of this work for per-sonal or classroom use is granted without fee provided that copies are not made ordistributed for profit or commercial advantage and that copies bear this notice.Abstracting with credit is permitted, but copyrights for components of this workowned by others than COMAP must be honored. To copy otherwise, to republish, topost on servers, or to redistribute to lists requires prior permission from COMAP.

Vehicle Emissions 451

Vehicle EmissionsMATHEMATICS CLASSIFICATIONS:

Algebra

DISCIPLINARY CLASSIFICATIONS: Traffic Engineering

PREREQUISITE SKILLS:1. Elementary algebra2. Regression techniques3. Elementary optimization

PHYSICAL CONCEPTS EXAMINED: 1. Concept of a mobile source for vehicle emissions2. Optimal driving speeds to minimize emissions3. Total vehicle emissions for a given speed profile

COMPUTING REQUIREMENT: 1. Spreadsheet and ability to use it2. Calculator and ability to use it

452 24.4 (2003)

Contents1. Introduction2. Remote Emission-Sensing Technique3. Emission Data Collection4. Data Conversion5. Regression Analysis6. Emission-Based Speed Optimization7. Real-World ApplicationsReferencesSample SolutionNotes for the InstructorAbout the Authors

1. IntroductionCars, trucks, motorcycles, and buses emit significant quantities of carbon

monoxide (CO), hydrocarbons (HC), nitrogen oxides (NOx), and fine particles(PM). These chemical compounds play dominant roles in air pollution prob-lems. In the densely populated Northeast, where the air pollution problem isespecially severe, the Environmental Protection Agency (EPA) has projectedthat highway vehicles will account for approximately 38% of the total NOx in-ventory and 22% of the total HC inventory in 2005, in spite of the tighter motorvehicle standards in the 1990 Clean Air Act Amendment (CAAA) (Figure 1).

Figure 1. Traffic.

Vehicle emissions, especially CO, NOx, and HC, are harmful to the healthof humans. CO is a tasteless, odorless, and colorless gas produced throughthe incomplete combustion of carbon-based fuels. CO enters the bloodstreamthrough the lungs and reduces the delivery of oxygen to the body’s organsand tissues. The health threat from exposure to CO is most serious for those

Vehicle Emissions 453

who suffer from cardiovascular disease, particularly those with angina or pe-ripheral vascular disease. Exposure to elevated CO levels is associated withimpairment of visual perception, work capacity, manual dexterity, learningability and performance of complex tasks. NOx emissions also produce a widevariety of health and welfare effects. Nitrogen dioxide can irritate the lungs andlower resistance to respiratory infection (such as influenza). NOx emissions areimportant in acid rain, affecting both terrestrial and aquatic ecosystems. At-mospheric deposition of nitrogen leads to excess nutrient enrichment problems(“eutrophication”). Finally, HC, in combination with NOx in the presence ofheat and sunlight, will form ozone. Ozone forms readily in the atmosphere,usually during hot summer weather. Ground-level ozone is the prime ingre-dient of smog, the pollution that blankets many areas during the summer.Short-term exposures (1–3 hours) to high ambient ozone concentrations havebeen linked to increased hospital admissions and emergency room visits forrespiratory problems.

With the rapid increase of the number of motor vehicles along with world-wide economic development, the vehicle emission problem has worsened.Many governments have started to implement certain vehicle emission-controlstrategies. Steady progress in reducing certain air pollution problems is occur-ring in the US, Europe and Japan. Globally, the use of advanced pollution-control technology, especially catalysts has been spreading, as has the use ofunleaded gasoline. However, the continued economic growth in the world re-quires the use of strategies that do not impose negative effect on the economicdevelopment, in other words, do not restrict vehicle ownership. Examplesof such strategies that have already been implemented in many cities in theworld include advanced traffic-control techniques, integrated transportationplanning process, and Intelligent Transportation Systems (ITS) technologies.

Past research has shown that driving patterns greatly influence the amountof vehicle emissions. Frequent acceleration and deceleration tend to generatemore emissions than smoother driving. An effective traffic signal timing plancan smooth traffic flow in a manner that reduces the emissions. In addition, wellplanned transportation projects or activities can change the driving patterns ofvehicles in the city at a more macroscopic level.

2. Remote Emission-Sensing TechniqueThe key to success in developing an emission-control strategy is obtaining

accurate quantification of vehicle emissions under various traffic and envi-ronmental scenarios. The remote emission-sensing device that is used in thisproject is called SMOG DOG. It performs environmental monitoring to measureautomotive emissions. The SMOG DOG can simultaneously measure emissionconcentrations of CO, HC, NOx, and CO2 in the dispersing exhaust cloud ofvehicles. A special feature of the SMOG DOG is its capability in detecting avehicle’s instantaneous speed and acceleration rate.

454 24.4 (2003)

Figure 2. SMOG DOG in action.

3. Emission Data CollectionSMOG DOG was used to collect vehicle emission data from a freeway on-

ramp in Houston, TX (Figure 2). The operation of SMOG DOG requires thatthe vehicle be in motion. Hence, the emission data for the idling mode arenot collected. Instead, vehicle idling emissions will be calculated based on theregression models that are developed. Table 1 illustrates the emission data onCO and HC concentrations that were collected.

Problem: Develop models relating vehicle speed and vehicle exhaust emissionsof CO and HC. Formulate speed recommendations based on your model andthe given data. Use of spreadsheet technology is strongly recommended. Inputthe data in Table 1 into a spreadsheet (4 columns). You will add four morecolumns in Requirement 2 and two more in Requirement 4.

Requirement 1Use the data in Table 1 to

• plot the CO concentration (%) vs. speed data, and

• plot the HC concentration (%) vs. speed data.

Vehicle Emissions 455

Table 1.

CO and HC concentration data collected by SMOG DOG in Houston.

Data # Speed (mph) CO% HC% Data # Speed (mph) CO% HC%

1 9.98 0.27 0.000027 31 43.22 0.32 0.0000322 10.97 0.22 0.000022 32 44.20 0.29 0.0000293 15.40 0.30 0.00003 33 45.05 0.39 0.0000394 15.69 0.03 0.000003 34 46.59 0.79 0.0000795 16.44 0.21 0.000021 35 47.06 0.73 0.0000736 17.11 0.89 0.000089 36 47.51 0.54 0.0000547 18.66 0.19 0.000019 37 47.86 0.07 0.0000078 19.04 0.79 0.000079 38 48.92 0.33 0.0000339 20.95 0.08 0.000008 39 49.78 0.43 0.000043

10 21.52 0.07 0.000007 40 49.81 0.55 0.00005511 23.41 1.61 0.000161 41 50.50 0.72 0.00007212 24.82 0.77 0.000077 42 50.52 0.21 0.00002113 25.15 0.76 0.000076 43 51.48 0.18 0.00001814 26.35 1.91 0.000191 44 52.18 0.61 0.00006115 27.02 0.40 0.00004 45 52.87 0.92 0.00009216 27.62 0.06 0.000006 46 53.25 0.19 0.00001917 29.90 0.36 0.000036 47 53.62 0.44 0.00004418 30.04 0.18 0.000018 48 54.32 0.22 0.00002219 30.67 0.58 0.000058 49 55.19 0.34 0.00003420 31.99 0.12 0.000012 50 56.07 0.49 0.00004921 34.97 1.02 0.000102 51 56.33 0.15 0.00001522 35.10 0.53 0.000053 52 56.56 0.76 0.00007623 35.94 1.11 0.000111 53 58.29 0.12 0.00001224 36.98 0.29 0.000029 54 58.75 0.12 0.00001225 37.69 1.67 0.000167 55 59.44 0.35 0.00003526 37.90 0.62 0.000062 56 61.40 0.83 0.00008327 38.74 0.27 0.000027 57 62.00 0.21 0.00002128 40.58 0.09 0.000009 58 63.65 0.35 0.00003529 41.63 0.30 0.00003 59 67.11 0.35 0.00003530 42.12 0.54 0.000054 60 76.68 0.47 0.000047

4. Data ConversionTo develop models relating vehicle speed to emission quantities, we intro-

duce two emission quantities: emission factor (g/mi) and emission rate (g/s).

The emission factor is the number of grams emitted when the vehicletravels one mile.

The emission rate is the total emission in grams that a vehicle emitsper second.

We define the following variables:

• CO%: CO emission concentration (%);

• HC%: HC emission concentration (%);

• COs: CO emission rate in grams per second (g/s);

456 24.4 (2003)

• HCs: HC emission rate in grams per second (g/s);

• COm: CO emission factor in grams per mile (g/mi);

• HCm: HC emission factor in grams per mile (g/mi);

• u: a vehicle’s instantaneous speed in miles per hour (mph);

• uoptimal: optimal speed (mph) that minimizes emissions;

• b0, b1, c0, c1: constant values (regression model coefficients).

Conversion of emission concentrations to emission rates is problematic.Many scientists and engineers use the following linear correlation relationships,developed for the emission concentrations and emissions factors by the SouthCoast Air Quality Management District (SCAQMD).

Conversion from emission concentrations to emission factors:

COm (g/mi) = 11.1 × CO% + 21.3, (1)

HCm (g/mi) = 63.3 × HC% + 1.7. (2)

Conversion from emission concentrations to emission rates:

COs (g/s) =COm (g/mi) × u mph

3600, (3)

HCs (g/s) =HCm (g/mi) × u mph

3600. (4)

Requirement 2Use (1)–(4) to convert the CO/HC concentrations in Table 1 to CO/HC

emission factors and CO/HC emission rates. Expand your spreadsheet tableto include the 8 columns: Data #, Speed, CO%, HC%, COm, HCm, COs, andHCs.

Requirement 3Draw four graphs to show the relationships between speed and CO/HC

emission factors as well as CO/HC emission rates using the data prepared inRequirement 2. Based on your visual analysis of these graphs, which rela-tionships display a better regularity of shapes and trends; emission factors oremission rates?

Vehicle Emissions 457

5. Regression AnalysisIn many engineering and scientific applications, relationships between vari-

ables are established by first collecting data from experimental studies in eitherthe laboratory or the field. This data is then plotted and relationship discerned.In this project, the two variables in the relationship represent the speed andthe CO/HC emission rates. Because of potential errors in measurement, thedata shown in the graphs drawn in Requirement 3 may not fall precisely on asmooth curve. For this reason, the task of the analysis becomes threefold:

• to hypothesize the mathematical form of the relationship between the twovariables (model postulation);

• to estimate the parameters of the model based on the collected field data(model calibration); and

• to determine how well the calibrated relationship explains the observed data(goodness of fit).

This analysis process is called regression.Scientific research on vehicle emissions has shown that the best mathemat-

ical function to model the relationship between the speed and the CO or HCemission rate is the natural logarithm, expressed in the following forms:

ln(COs) = b0 + b1u, (5)

ln(HCs) = c0 + c1u. (6)

The speed u is the independent or explanatory variable. The emission rates, COsor HCs, are called the dependent or explained variables. The constant coefficientsc0 and c1 are the model parameters. Data from Requirement 2 can be used toplot ln(COs) vs. speed and ln(HCs) vs. speed. Calibrating the model meansdetermining the unknown values of the parameters in (5) or (6) to obtain thebest fit to these plots. The goodness of fit is measured by the coefficient ofcorrelation, r. Its value can range from −1 to +1. If r is near +1, there exists ahigh positive correlation; if it is near−1, there exists a high negative correlation;and if it is around zero, there exists no correlation between the independentand the dependent variables.

Requirement 4Use the regression technique and the data prepared in Requirement 2 to

calibrate (5) and (6). The data for COs and HCs prepared in Requirement 2need to be transformed by the natural logarithm (ln) before a simple linearregression can be carried out. Hint: Add columns for ln(C0s) and ln(HCs) toyour spreadsheet table constructed in Requirement 2. Then plot the ln(C0s)vs. speed and form the linear regression. Repeat for ln(HCs) vs. speed.

458 24.4 (2003)

Requirement 5Calculate the coefficient correlations for the regressions in Requirement 4.

Are the models acceptable? Why? Draw the line plot for each of the regressionequations generated.

6. Emission-Based Speed OptimizationEmission rates (g/s) can be transformed into emission factors (g/mi) by

solving (3) for COm and (4) for HCm. The new equations are:

COm (g/mi) =COs (g/s) × 3600 (s/h)

u (mi/h), (7)

HCm (g/mi) =HCs (g/s) × 3600 (s/h)

u (mi/h). (8)

Equations (3) and (4) for the emission rates are in the form y = mx, where theslopes are COm/3600 and HCm/3600. Because these slopes are positive, theemission rates are monotonically increasing functions of speed; hence, thereare no minimum values for a moving vehicle. The situation is less clear for theemission factors described by (7) and (8). These equations can be transformedinto explicit functions of speed by solving for COs and HCs in the results ofRequirement 4 and then substituting these results into (7) and (8). Doing thisyields

COs (g/s) =3600eb0+b1u

u, (9)

HCm (g/s) =3600ec0+c1u

u. (10)

A graphical analysis can now be made to determine what speeds will min-imize the emission factors. Knowledge of these speeds is critical informationfor developing an advanced traffic management scheme to reduce emissionamounts.

Requirement 6Draw a graph with two curves, one for the relationship between the speed

and the CO emission rate, and the other for the relationship between the speedand the CO emission factor. Draw a second graph with two curves, one for therelationship between the speed and the HC emission rate, and the other for therelationship between the speed and the HC emission factor. Let the speed bemeasured starting from 0 to 70 mph in increments of 5 mph. Then calculatethe emission rates by solving for COs and HCs in the equations generated inRequirement 4, and the emission factors using (9) and (10). Based on the visualanalysis of the graphs, is there a speed that can minimize the emission factor?

Vehicle Emissions 459

Requirement 7Approximate the speeds corresponding to the minimum points on the emis-

sion factor plots. What speed do you recommend for minimizing both the COand HC emission factors? Hint: On a graphing calculator, use the trace featureto trace a point along the curve to the minimum position or use the table featureto determine the coordinates of the minimum point. For a spreadsheet, iteratethe function values to determine the minimum.

7. Real-World ApplicationsIf all drivers traveled at the optimal speed, the total CO or HC emissions

would be the minimum. On the other hand, if vehicles are driven at varyingspeeds, the resulting emissions will be higher. To analyze such a pattern, we as-sume two different speed profiles experienced by two different vehicles. Bothvehicles are driven for 30 s, but the first vehicle travels at a constant speed of35 mph while the speed of the second vehicle varies between 29 and 42 mph (seeTable 2). After 30 s, both vehicles have driven the same distance, 1540 ft. Al-though both vehicles have been driven the same distance during the same timeperiod, it is expected that the resulting vehicle emissions would be different.Table 2 illustrates the details of these two different speed profiles.

Requirement 8Based on Table 2, plot two graphs, one for the constant speed profile, and

one for the varying speed profile. For each speed profile, there should betwo curves, one for the relationship between time and speed, and one for therelationship between time and the distance. Use different y-axes for speed anddistance.

Requirement 9Use the regression equations derived from Requirement 4 to calculate the

CO and HC emissions at each second for the two different speed profiles inTable 2. Make your calculation in a table. Then, calculate the total CO and HCemissions for the entire travel of the two speed profiles. What can you concludefrom your calculations?

Requirement 10Assume that an accident happened on a location of a freeway segment. A

police officer came to the scene to process the necessary paperwork for thisaccident and towing vehicles came to remove all vehicles involved. It took a

Time (Sec) Speed (mph) Distance (ft) Time (Sec) Speed (mph) Distance (ft)1 35 51 1 42 622 35 103 2 41 1223 35 154 3 40 1804 35 205 4 39 2385 35 257 5 38 2936 35 308 6 38 3497 35 359 7 37 4038 35 411 8 36 4569 35 462 9 35 507

10 35 513 10 34 55711 35 565 11 33 60612 35 616 12 32 65313 35 667 13 31 69814 35 719 14 30 74215 35 770 15 30 78616 35 821 16 30 83017 35 873 17 29 87318 35 924 18 29 91519 35 975 19 30 95920 35 1027 20 31 100521 35 1078 21 32 105222 35 1129 22 33 110023 35 1181 23 34 115024 35 1232 24 35 120125 35 1283 25 36 125426 35 1335 26 37 130827 35 1386 27 38 136428 35 1437 28 39 142129 35 1489 29 40 148030 35 1540 30 41 1540

Constant Speed Profile Varying Speed Profile

460 24.4 (2003)

Table 2.

Speed profiles driven by two vehicles.

total of 40 min from the start of the accident to the time when the accident sceneis completely cleared. During this period, a total of 200 vehicles have to stop.Assume the average wait is 30 min per vehicle. Calculate the total additionalCO and HC emissions that were generated by these 200 vehicles due to thetraffic accident. What can you conclude from your calculation? Hint: Derivethe idling emissions rates by setting the speed equal to zero in the results ofRequirement 4.

ReferencesEuropean Conference of Ministers of Transport (ECMT). 291. Vehicle Emission

Reductions. Paris, France: OECD Publications Services (2, rue Andre Pascal,75775 Paris Cedex 16, France).

Sorbe, N. 1995. Hughes Employee Vehicle Exhaust Remote Sensing and Emis-sions Evaluation Project. Report prepared for the Mobile Source Air Pollu-tion Reduction Review Committee (MSRC) under the AB2766 Program. ElSegundo, CA: Hughes Environmental Systems, Inc.

Vehicle Emissions 461

Yu, L. 1998a. Collection and Evaluation of Modal Traffic Data for Determinationof Vehicle Emission Rates under Certain Driving Conditions. ResearchReports 1485-1, 1485-2, and 1485-3F for TxDOT Project No. 0-1485, Centerfor Transportation Training and Research. Houston, TX: Texas SouthernUniversity.

. 1998b. Remote vehicle exhaust emission-sensing for traffic simu-lation and optimization models. Journal of Transportation Research Part D:Transport and Environment 3: 337–347.

CO% Versus Speed

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Speed (mph)

CO

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nce

ntr

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%)

462 24.4 (2003)

Title: Vehicle Emissions

Sample SolutionRequirement 1: The graphs between the speed and CO and HC concentrationsare shown in Figures S1 and S2.

Figure S1. CO concentration vs. speed.

Based on visual analysis of these graphs, clearly the speed is not correlatedwith the CO or HC concentrations. The data are scattered and do not show anyregularity of shapes or trends.

Requirement 2: The generated table is shown in Table S1.

Requirement 3: See Figures S3–S6. A visual analysis of the graphs suggeststhat the CO/HC emission rates have greater regularity of shape and trend withthe speed than do the CO/HC emission factors.

Requirement 4: The resulting regression equations are:

ln(COs) = −2.46215 + 0.028383u, or COs = e−2.46215+0.028383u,

ln(HCs) = −4.91624 + 0.030929u, or COs = e−4.91624+0.030929u.

HC% Versus Speed

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0.005

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0.015

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0.035

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Speed (mph)

HC

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nce

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n (

%)

CO (g/mi) Versus Speed

0.0000

5.0000

10.0000

15.0000

20.0000

25.0000

30.0000

35.0000

40.0000

45.0000

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Vehicle Emissions 463

Figure S2. HC concentration vs. speed.

Figure S3. CO emission factor vs. speed.

Data # Speed CO% HC% COm(g/mi) HCm(g/mi) COs(g/sec) HCs(g/sec)

1 9.98 0.27 0.0096 24.2970 2.3077 0.0674 0.00642 10.97 0.22 0.0058 23.7420 2.0671 0.0723 0.00633 15.40 0.30 0.0038 24.6300 1.9405 0.1054 0.00834 15.69 0.03 0.0031 21.6330 1.8962 0.0943 0.00835 16.44 0.21 0.0161 23.6310 2.7191 0.1079 0.01246 17.11 0.89 0.0031 31.1790 1.8962 0.1482 0.00907 18.66 0.19 0.0055 23.4090 2.0482 0.1213 0.01068 19.04 0.79 0.0241 30.0690 3.2255 0.1590 0.01719 20.95 0.08 0.0065 22.1880 2.1115 0.1291 0.0123

10 21.52 0.07 0.0007 22.0770 1.7443 0.1319 0.010411 23.41 1.61 0.0063 39.1710 2.0988 0.2547 0.013612 24.82 0.77 0.0187 29.8470 2.8837 0.2057 0.019913 25.15 0.76 0.0257 29.7360 3.3268 0.2077 0.023214 26.35 1.91 0.0370 42.5010 4.0421 0.3110 0.029615 27.02 0.40 0.0206 25.7400 3.0040 0.1932 0.022516 27.62 0.06 0.0050 21.9660 2.0165 0.1685 0.015517 29.90 0.36 0.0256 25.2960 3.3205 0.2101 0.027618 30.04 0.18 0.0041 23.2980 1.9595 0.1944 0.016319 30.67 0.58 0.0036 27.7380 1.9279 0.2363 0.016420 31.99 0.12 0.0161 22.6320 2.7191 0.2011 0.024221 34.97 1.02 0.0013 32.6220 1.7823 0.3169 0.017322 35.10 0.53 0.0084 27.1830 2.2317 0.2650 0.021823 35.94 1.11 0.0122 33.6210 2.4723 0.3356 0.024724 36.98 0.29 0.0061 24.5190 2.0861 0.2518 0.021425 37.69 1.67 0.0350 39.8370 3.9155 0.4171 0.041026 37.90 0.62 0.0206 28.1820 3.0040 0.2967 0.031627 38.74 0.27 0.0152 24.2970 2.6622 0.2615 0.028628 40.58 0.09 0.0037 22.2990 1.9342 0.2514 0.021829 41.63 0.30 0.0063 24.6300 2.0988 0.2848 0.024330 42.12 0.54 0.0133 27.2940 2.5419 0.3193 0.029731 43.22 0.32 0.0147 24.8520 2.6305 0.2983 0.031632 44.20 0.29 0.0141 24.5190 2.5925 0.3010 0.031833 45.05 0.39 0.0247 25.6290 3.2635 0.3207 0.040834 46.59 0.79 0.0239 30.0690 3.2129 0.3891 0.041635 47.06 0.73 0.0079 29.4030 2.2001 0.3844 0.028836 47.51 0.54 0.0171 27.2940 2.7824 0.3602 0.036737 47.86 0.07 0.0071 22.0770 2.1494 0.2935 0.028638 48.92 0.33 0.0248 24.9630 3.2698 0.3392 0.044439 49.78 0.43 0.0345 26.0730 3.8839 0.3605 0.053740 49.81 0.55 0.0150 27.4050 2.6495 0.3791 0.036741 50.50 0.72 0.0138 29.2920 2.5735 0.4109 0.036142 50.52 0.21 0.0173 23.6310 2.7951 0.3316 0.039243 51.48 0.18 0.0056 23.2980 2.0545 0.3332 0.029444 52.18 0.61 0.0352 28.0710 3.9282 0.4068 0.056945 52.87 0.92 0.0186 31.5120 2.8774 0.4627 0.042346 53.25 0.19 0.0282 23.4090 3.4851 0.3462 0.051547 53.62 0.44 0.0013 26.1840 1.7823 0.3900 0.026548 54.32 0.22 0.0329 23.7420 3.7826 0.3582 0.057149 55.19 0.34 0.0211 25.0740 3.0356 0.3844 0.046550 56.07 0.49 0.0054 26.7390 2.0418 0.4165 0.031851 56.33 0.15 0.0039 22.9650 1.9469 0.3593 0.030552 56.56 0.76 0.0351 29.7360 3.9218 0.4671 0.061653 58.29 0.12 0.0169 22.6320 2.7698 0.3664 0.044854 58.75 0.12 0.0103 22.6320 2.3520 0.3693 0.038455 59.44 0.35 0.0038 25.1850 1.9405 0.4158 0.032056 61.40 0.83 0.0068 30.5130 2.1304 0.5204 0.036357 62.00 0.21 0.0084 23.6310 2.2317 0.4070 0.038458 63.65 0.35 0.0068 25.1850 2.1304 0.4452 0.037759 67.11 0.35 0.0089 25.1850 2.2634 0.4695 0.042260 76.68 0.47 0.0073 26.5170 2.1621 0.5648 0.0460

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Table S1.

Speed profiles driven by two vehicles.

HC (g/mi) Versus Speed

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CO (g/sec) Versus Speed

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Vehicle Emissions 465

Figure S4. HC emission factor vs. speed.

Figure S5. CO emission rate vs. speed.

HC (g/sec) Versus Speed

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Speed Line Plot

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ln(C

O)

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Predicted LN(CO)

466 24.4 (2003)

Figure S6. HC emission rate vs. speed.

Requirement 5: r(COs) = 0.9089, r(HCs) = 0.8644.Both correlation coefficients are close to one, so both regression equations

have acceptable goodness of fit. Since r(COs) is slightly higher than r(HCs),the regression equation for COs is better than the one for HCs.

Figure S7. Line plot for the speed and the CO emission factor.

Requirement 6: From Figures S9–S10, there clearly exists a speed value thatminimizes either the CO emission factor or the HC emission factor. On theother hand, the emission rates are monotonically increasing functions of thespeed.

Requirement 7: uoptimal for CO = 35 mph; uoptimal for HC = 32 mph.

Speed Line Plot

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ln(H

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Predicted LN(HC)

CO Emissions Versus Speed

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HC Emissions Versus Speed

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HC

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/mi)

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HC (g/sec)

Vehicle Emissions 467

Figure S8. Line plot for the speed and the HC emission factor.

Figure S9. Relationships between the CO emission rates/factors and the speed.

Figure S10. Relationships between the HC emission rates/factors and the speed.

Speed Profile 1 - Constant Speed

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468 24.4 (2003)

Requirement 8: See Figures S11–S12.

Figure S11. Illustration of constant speed profile.

Figure S12. Illustration of varying speed profile.

Vehicle Emissions 469

Requirement 9: See Table S2.

Table S2.

Second-by-second calculations.

Constant Speed Profile Varying Speed ProfileTime Speed 1 CO 1 HC 1 Speed 2 CO 2 HC 2

1 35 0.2302 0.02163 42 0.2808 0.026862 35 0.2302 0.02163 41 0.2730 0.026043 35 0.2302 0.02163 40 0.2653 0.025254 35 0.2302 0.02163 39 0.2579 0.024485 35 0.2302 0.02163 38 0.2507 0.023736 35 0.2302 0.02163 38 0.2507 0.023737 35 0.2302 0.02163 37 0.2437 0.023018 35 0.2302 0.02163 37 0.2437 0.023019 35 0.2302 0.02163 37 0.2437 0.02301

10 35 0.2302 0.02163 36 0.2368 0.0223111 35 0.2302 0.02163 35 0.2302 0.0216312 35 0.2302 0.02163 34 0.2238 0.0209713 35 0.2302 0.02163 33 0.2175 0.0203314 35 0.2302 0.02163 32 0.2114 0.0197115 35 0.2302 0.02163 31 0.2055 0.0191116 35 0.2302 0.02163 30 0.1998 0.0185317 35 0.2302 0.02163 29 0.1942 0.0179718 35 0.2302 0.02163 29 0.1942 0.0179719 35 0.2302 0.02163 30 0.1998 0.0185320 35 0.2302 0.02163 31 0.2055 0.0191121 35 0.2302 0.02163 32 0.2114 0.0197122 35 0.2302 0.02163 33 0.2175 0.0203323 35 0.2302 0.02163 34 0.2238 0.0209724 35 0.2302 0.02163 35 0.2302 0.0216325 35 0.2302 0.02163 36 0.2368 0.0223126 35 0.2302 0.02163 37 0.2437 0.0230127 35 0.2302 0.02163 38 0.2507 0.0237328 35 0.2302 0.02163 39 0.2579 0.0244829 35 0.2302 0.02163 40 0.2653 0.0252530 35 0.2302 0.02163 41 0.2730 0.02604

TOTAL EMISSIONS 6.9064 0.6489 7.0382 0.66273

For the CO emissions, the varying speed profile generates a total of 7.04 gcomparing with the 6.91 g for the constant speed profile (2% higher). Similarlyfor the HC emissions, the varying speed profile generates a total of 0.663 g com-paring with the 0.649 g of emissions for the constant speed profile (2% higher).Since the optimal speed is 35 mph for CO and 32 mph for HC, the constantspeed profile in this requirement should result in the minimum CO emissionsand close to minimum HC emissions. Although the 2% higher emissions doesnot seem like a significant amount, this is just for 30 s for a single vehicle. Youcan imagine how much additional emissions would be generated if all vehiclesin the city drive at varying speeds of a significant level. On the other hand, thetraffic managers should try to implement traffic management strategies thatwould encourage or force drivers to drive at desired and constant speeds.

470 24.4 (2003)

Requirement 10: Set speed to 0 in the regression equations in Requirement 4to derive the idling emission rate in units of grams per second:

COs when idling = e−2.46215+0.028383u= 0.08525 g/s,

HCs when idling = e−4.91624+0.030929u= 0.00733 g/s.

Therefore, during the 30 min delay, a vehicle will emit the following total COand HC emissions:

CO idling emissions for one vehicle for 30 min = 0.08525 × 30 × 60=153.45 g,

HC idling emissions for one vehicle for 30 min = 0.00733 × 30 × 60= 13.194 g.

Therefore, the total CO emissions for 200 vehicles = 153.45 × 200 = 30,690 g andthe total HC emissions for 200 vehicles = 13.194 × 200 = 2,639 g.

From the above calculation, we can see that one traffic accident can resultin considerable additional CO and HC emissions. Considerably more emis-sions will be produced if many traffic accidents happen in the city. Therefore,reducing the number of traffic accidents can reduce the vehicle emissions.

Vehicle Emissions 471

Title: Vehicle Emissions

Notes for the InstructorThis project is designed for students to practice algebraic calculations, data

analysis, and optimization using real-world vehicle emission data. The vehicleemission issue is becoming more and more important because of the stricterregulations imposed by the U.S. Environmental Protection Agency (EPA). Ve-hicle emissions are a big source of air pollution and are related to many of ourhealth problems.

The key to the successful completion of this project is a clear understandingof the sequence of the data, the definitions of the variables, the relationshipsbetween variables, as well as the algebraic, data analysis, and optimizationconcepts. Any additional information related to vehicle emission-control canbe introduced in the class. The instructor can introduce various emission datacollection techniques. The instructor can also introduce more complicated mod-eling and data analysis techniques.

The simplest regression equation is used in this project, which althoughnonlinear, includes only one variable. The instructor can encourage studentsto test various regression formulas and different combinations of variables. Forinstance, other regression models to consider include

COs = b0 + b1u + b2u2,

HCs = c0 + c1u + c2u2.

Requirements 4–9 can be repeated with these other regression formulas.The instructor can also encourage students to search literature on other

existing vehicle emission models. Students can compare the calculation resultsbetween the models developed in this project and other models.

472 24.4 (2003)

About the Authors

Lei Yu is Professor and Chairperson of the Trans-portation Studies Department at Texas Southern Uni-versity. He is also a Changjiang Scholar of Beijing Jiao-tong University. He received a bachelor’s degree inTransportation Engineering from Northern Jiaotong Uni-versity, Beijing, China and a master’s degree in Pro-duction and Systems Engineering from Nagoya Insti-tute of Technology, Nagoya, Japan. His Ph.D. degreein Civil Engineering was awarded by Queen’s Univer-sity in Kingston, Ontario, Canada. His research inter-ests involve highway traffic operations and modeling,

urban transportation planning, the ITS-related technologies and applications,and vehicle exhaust emission modeling. Since 1994, Yu has been the Princi-pal Investigator (PI) of more than 25 research projects that were sponsored byTexas Department of Transportation (TxDOT), Federal Highway Administra-tion (FHWA), Federal Transit Administration (FTA), Southwest Region Univer-sity Transportation Center (SWUTC) program, National Institute of Standardsand Technology (NIST), and Houston Advanced Research Center (HARC); thetotal funding amount is over $2 million. Dr. Yu has published more than 50research papers in the Journal of Transportation Research, Transportation ResearchRecords, and the Journal of Transportation Engineering, as well as in various peer-reviewed conference proceedings. Dr. Yu is an active member of the Institute ofTransportation Engineers (ITE), the American Society of Civil Engineers (ASCE)and the Transportation Research Board (TRB). He is a registered engineer inthe State of Texas. He also belongs to numerous committees, councils, and taskforces in regional, state, national, and international organizations.

Don Small graduated from Middlebury College andreceived his Ph.D. degree in mathematics from the Uni-versity of Connecticut. He taught mathematics at ColbyCollege for 23 years before joining the Mathematics Depart-ment at the U.S. Military Academy in 1991. He is activein the calculus and college algebra reform movements—developing curricula, authoring texts, and leading facultydevelopment workshops. Active in the Mathematical As-

sociation of America (MAA), Don served a term as Chairman and two termsas Governor of the Northeast Section and has been a long-term member ofthe MAA’s CRAFTY committee. His interests are in developing curriculumthat focuses on student growth while meeting the needs of partner disciplines,society, and the workplace. He is also a member of AMATYC and AMS.