NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

EPA GHG Certification of 

Medium- and Heavy-Duty 

Vehicles: Development of Road 

Grade Profiles Representative of 

US Controlled Access Highways

Eric Wood, Adam Duran, Evan Burton, 

Jeffrey Gonder, and Kenneth Kelly

Produced under direction of the U.S. Environmental Protection Agency (EPA) 

by the National Renewable Energy Laboratory (NREL) under Interagency 

Agreement IAG-14-1954 and Task No WFGY.1000.

Strategic Partnership Project Report

NREL/TP-5400-63853

May 2015
NREL is a national laboratory of the U.S. Department of Energy

Office of Energy Efficiency & Renewable Energy

Operated by the Alliance for Sustainable Energy, LLC

This report is available at no cost from the National Renewable Energy

Laboratory (NREL) at www.nrel.gov/publications.

Contract No. DE-AC36-08GO28308

National Renewable Energy Laboratory

15013 Denver West Parkway

Golden, CO 80401

303-275-3000 • www.nrel.gov

EPA GHG Certification of 

Medium- and Heavy-Duty 

Vehicles: Development of 

Road Grade Profiles 

Representative of US 

Controlled Access Highways

Eric Wood, Adam Duran, Evan Burton, 

Jeffrey Gonder, and Kenneth Kelly

Prepared under Task No. WGFY.1000

Strategic Partnership Project Report

NREL/TP-5400-63853

May 2015
NOTICE

This manuscript has been authored by employees of the Alliance for Sustainable Energy, LLC (“Alliance”) under 

Contract No. DE-AC36-08GO28308 with the U.S. Department of Energy (“DOE”).

This report was prepared as an account of work sponsored by an agency of the United States government. 

Neither the United States government nor any agency thereof, nor any of their employees, makes any warranty, 

express or implied, or assumes any legal liability or responsibility for the accuracy, completeness, or usefulness of 

any information, apparatus, product, or process disclosed, or represents that its use would not infringe privately 

owned rights. Reference herein to any specific commercial product, process, or service by trade name, 

trademark, manufacturer, or otherwise does not necessarily constitute or imply its endorsement, recommendation, 

or favoring by the United States government or any agency thereof. The views and opinions of authors 

expressed herein do not necessarily state or reflect those of the United States government or any agency thereof.

Cover Photos by Dennis Schroeder: (left to right) NREL 26173, NREL 18302, NREL 19758, NREL 29642, NREL 19795.

NREL prints on paper that contains recycled content.
iii

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List of Acronyms

ADA Advanced Driving Attributes 

DEM Digital Elevation Model 

DOE U.S. Department of Energy 

DRIVE Drive Cycle Rapid Investigation, Visualization, and 

Evaluation tool

EPA U.S. Environmental Protection Agency 

GHG greenhouse gas 

GPS global positioning system 

HD heavy duty

HH half hill

Hz hertz

I Interstate Highway

KS Kolmogorov-Smirnov 

MARTI Mobile Autonomous Robotics Technology Initiative 

MD medium duty 

MOVES Motor Vehicle Emission Simulator

mph miles per hour 

NED National Elevation Dataset 

NHTSA U.S. National Highway Traffic Safety 

Administration 

NREL National Renewable Energy Laboratory 

RMSE root mean square error 

SR State Route

SwRI Southwest Research Institute 

U.S. United States

USGS United States Geological Survey 

VMT vehicle miles traveled
iv

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Table of Contents

List of Acronyms........................................................................................................................................ iii

List of Figures ............................................................................................................................................. v

List of Tables .............................................................................................................................................. ix

Executive Summary.................................................................................................................................... x

1 Introduction and Background ............................................................................................................. 1

2 Grade Comparison ............................................................................................................................... 2

2.1 Road Grade Datasets..................................................................................................................... 2

2.1.1 SwRI’s MARTI Dataset................................................................................................... 2

2.1.2 USGS DEM NED ............................................................................................................ 4

2.1.3 TomTom’s ADA Road Grade Data Layer ....................................................................... 4

2.2 Local Level Comparison ............................................................................................................... 5

2.2.1 Filtered USGS versus SwRI............................................................................................. 6

2.2.2 TomTom versus SwRI ..................................................................................................... 8

2.2.3 Local Level Comparison Summary................................................................................ 10

2.3 National Level Comparison ........................................................................................................ 12

3 National Statistics .............................................................................................................................. 13

3.1 Road Grade by Distance Analysis............................................................................................... 15

3.2 Half Hill Analysis........................................................................................................................ 17

3.2.1 Analytical Approaches................................................................................................... 18

3.2.2 Half Hill Trends with Respect to Speed Limits ............................................................. 20

3.3 Activity-Weighted Values........................................................................................................... 22

4 Nationally Representative Sample Grade Profiles.......................................................................... 27

4.1 Synthetic Routes.......................................................................................................................... 27

4.1.1 55-mph Test Group ........................................................................................................ 29

4.1.2 65-mph Test Group ........................................................................................................ 34

4.2 Local Routes................................................................................................................................ 38

4.2.1 55-mph Test Group ........................................................................................................ 39

4.2.2 65-mph Test Group ........................................................................................................ 47

5 Known Limitations and Potential for Future Work.......................................................................... 53

6 References .......................................................................................................................................... 54

Appendix A: Supporting Documentation ............................................................................................... 57

Appendix B: Supplementary Distributions from Half Hill Analysis ..................................................... 64
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List of Figures

Figure 1. Three-hundred-mile loop near San Antonio, Texas, selected for SwRI on-road testing of Class 8 

combination truck. The loop was also used for data collection by SwRI MARTI vehicle...... 3

Figure 2. United States elevation map utilizing USGS 1/3 arc-second DEM............................................... 4

Figure 3. U.S. controlled access highways by TomTom ADA road grade................................................... 5

Figure 4. USGS elevation map near San Antonio, Texas, overlaid with GPS trace of MARTI vehicle 

driving from Junction, Texas, to San Antonio, Texas, on I-10................................................ 6

Figure 5. SwRI/USGS comparison over the 115-mile stretch of I-10 northwest of San Antonio, Texas. 

Top: SwRI integrated grade plotted against filtered USGS elevation. Bottom: SwRI grade 

plotted against filtered, differentiated USGS elevation. .......................................................... 7

Figure 6. SwRI/USGS comparison over a subset of the 115-mile stretch of I-10 northwest of San Antonio, 

Texas. Top: SwRI integrated grade plotted against filtered USGS elevation. Bottom: SwRI 

grade plotted against filtered, differentiated USGS elevation.................................................. 7

Figure 7. Filtered USGS grade scattered against SwRI grade from the 115-mile stretch of I-10 northwest 

of San Antonio, Texas.............................................................................................................. 8

Figure 8. SwRI/TomTom comparison over the 115-mile stretch of I-10 northwest of San Antonio, Texas. 

Top: SwRI integrated grade plotted against integrated TomTom grade. Bottom: SwRI grade 

plotted against TomTom grade. ............................................................................................... 9

Figure 9. SwRI/TomTom comparison over a subset of the 115-mile stretch of I-10 northwest of San 

Antonio, Texas. Top: SwRI integrated grade plotted against integrated TomTom grade. 

Bottom: SwRI grade plotted against TomTom grade. ............................................................. 9

Figure 10. TomTom grade scattered against SwRI grade from the 115-mile stretch of I-10 northwest of 

San Antonio, Texas................................................................................................................ 10

Figure 11. Visual description of the two sampling frequencies used in the comparative analysis: 1) based 

on available data, and 2) based on linear interpolation at uniform intervals of 10 feet (0.1 

mile interval is used for illustrative purposes) ....................................................................... 11

Figure 12. National distributions of road grade from filtered USGS and TomTom databases on the basis 

of absolute values................................................................................................................... 12

Figure 13. TomTom MultiNet map of U.S. controlled access highways.................................................... 13

Figure 14. U.S. controlled access highway map colored by state-defined truck speed limits per TomTom 

Trucking Logistics speed restrictions data layer.................................................................... 14

Figure 15. Mileage breakdown of U.S. controlled access highways by truck speed limit and U.S. Census 

urban area designation ........................................................................................................... 15

Figure 16. Cumulative distributions of road grade by distance for 1,728 U.S. counties............................ 16

Figure 17. Raw distance-based cumulative distribution of absolute road grade by truck speed limit........ 17

Figure 18. Example section of controlled access highway broken into 16 half hills (eight climbs and eight 

descents)................................................................................................................................. 18

Figure 19. All half hill (HH) distances plotted as frequency-based and distance-based cumulative 

distributions............................................................................................................................ 19

Figure 20. Raw distance-based cumulative distributions of half hill distance by truck speed limit........... 20

Figure 21. Maximum (or minimum) versus average road grade for all measured half hills....................... 21

Figure 22. EPA MOVES VMT database plotted by vehicle type and roadway classification ................... 22

Figure 23. EPA MOVES VMT database for MD/HD vehicles on controlled access roads only............... 22

Figure 24. EPA MOVES VMT database mapped by county for MD/HD trucks operating on controlled 

access roads............................................................................................................................ 23

Figure 25. Activity-weighted, distance-based cumulative distributions of absolute road grade by truck 

speed limit.............................................................................................................................. 24

Figure 26. Activity-weighted, distance-based cumulative distributions of half hill distance by truck speed 

limit........................................................................................................................................ 24
vi

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Figure 27. Combined activity-weighted, distance-based cumulative distributions of absolute road grade by 

target test speed...................................................................................................................... 25

Figure 28. Combined activity-weighted, distance-based cumulative distributions of half hill distance by 

target test speed...................................................................................................................... 26

Figure 29. Synthetic grade profile template................................................................................................ 28

Figure 30. KS statistics for absolute road grade match in the 55-mph test group with respect to target 

profile distance and maximum iteration count....................................................................... 29

Figure 31. KS statistics for half hill distance match in the 55-mph test group with respect to target profile 

distance and maximum iteration count .................................................................................. 30

Figure 32. Elevation and road grade profile from sample “150508 55mph 12mi 201210of1e6iter” ......... 31

Figure 33. Comparison of distance-based cumulative distributions between national activity-weighted 

dataset and sample profile “150508 55mph 12mi 201210of1e6iter” in terms of absolute road 

grade (left) and half hill distance (right) ................................................................................ 32

Figure 34. Elevation and road grade profile from sample “150508 55mph 12mi 727695of1e6iter” ......... 32

Figure 35. Comparison of distance-based cumulative distributions between a national activity-weighted 

dataset and sample profile “150508 55mph 12mi 727695of1e6iter” in terms of absolute road 

grade (left) and half hill distance (right) ................................................................................ 33

Figure 36. KS statistics for absolute road grade match in the 65-mph test group with respect to target 

profile distance and maximum iteration count....................................................................... 34

Figure 37. KS statistics for half hill distance match in the 65-mph test group with respect to target profile 

distance and maximum iteration count .................................................................................. 35

Figure 38. Elevation and road grade profile from sample “150508 65mph 15mi 467684of1e6iter” ......... 36

Figure 39. Comparison of distance-based, cumulative distributions between national activity-weighted 

dataset and sample profile “150508 65mph 15mi 467684of1e6iter” in terms of absolute road 

grade (left) and half hill distance (right) ................................................................................ 37

Figure 40. Elevation and road grade profile from sample “150508 65mph 15mi 883894of1e6iter” ......... 37

Figure 41. Comparison of distance-based cumulative distributions between national activity-weighted 

dataset and sample profile “150508 65mph 15mi 883894of1e6iter” in terms of absolute road 

grade (left) and half hill distance (right) ................................................................................ 38

Figure 42. Example 13-mile stretch of roadway segmented into 16 half hills and grouped into seven 

continuous stretches of 10 miles or less................................................................................. 39

Figure 43. Local route KS statistics for the distribution of absolute road grade versus round-trip profile 

distance for the 55-mph test group......................................................................................... 40

Figure 44. Local route KS statistics for the distribution of half hill distance versus round-trip profile 

distance for the 55-mph test group......................................................................................... 40

Figure 45. Local route from I-20 east of Abilene, Texas, statistically similar to national activity-weighted 

distributions for the 55-mph test group.................................................................................. 41

Figure 46. Local route from I-70 east of Glenwood Springs, Colorado, statistically similar to national 

activity-weighted distributions for the 55-mph test group..................................................... 42

Figure 47. Local route from Kentucky SR-9001 south of Louisville, Kentucky, statistically similar to 

national activity-weighted distributions for the 55-mph test group ....................................... 42

Figure 48. Local route from I-20 east of Abilene, Texas, statistically similar to national activity-weighted 

distributions for the 55-mph test group.................................................................................. 43

Figure 49. Local route from I-70 east of Glenwood Springs, Colorado, statistically similar to national 

activity-weighted distributions for the 55-mph test group..................................................... 43

Figure 50. Local route from Kentucky SR-9001 south of Louisville, Kentucky, statistically similar to 

national activity-weighted distributions for the 55-mph test group ....................................... 44

Figure 51. Comparison of distance-based cumulative distributions between national activity-weighted 

dataset and local profile from I-20 east of Abilene, Texas, in terms of absolute road grade 

(left) and half hill distance (right).......................................................................................... 44
vii

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Figure 52. Comparison of distance-based cumulative distributions between national activity-weighted 

dataset and local profile from I-70 east of Glenwood Springs, Colorado, in terms of absolute 

road grade (left) and half hill distance (right)........................................................................ 45

Figure 53. Comparison of distance-based cumulative distributions between national activity-weighted 

dataset and local profile from Kentucky SR-9001 south of Louisville, Kentucky, in terms of 

absolute road grade (left) and half hill distance (right).......................................................... 45

Figure 54. Local route KS statistics for the distribution of absolute road grade versus round-trip profile 

distance for the 65-mph test group......................................................................................... 47

Figure 55. Local route KS statistics for the distribution of half hill distance versus round-trip profile 

distance for the 65-mph test group......................................................................................... 48

Figure 56. Local route from I-10 west of San Antonio, Texas, statistically similar to national activityweighted distributions for the 65-mph test group .................................................................. 49

Figure 57. Local route from I-40 west of Gallup, New Mexico, statistically similar to national activityweighted distributions for the 65-mph test group .................................................................. 49

Figure 58. Local route from I-10 west of San Antonio, Texas, statistically similar to national activityweighted distributions for the 65-mph test group .................................................................. 50

Figure 59. Local route from I-40 west of Gallup, New Mexico, statistically similar to national activityweighted distributions for the 65-mph test group .................................................................. 50

Figure 60. Comparison of distance-based cumulative distributions between national activity-weighted 

dataset and local profile from I-10 west of San Antonio, Texas, in terms of absolute road 

grade (left) and half hill distance (right) ................................................................................ 51

Figure 61. Comparison of distance-based cumulative distributions between national activity-weighted 

dataset and local profile from I-40 west of Gallup, New Mexico, in terms of absolute road 

grade (left) and half hill distance (right) ................................................................................ 51

Figure 62. Vehicle fueling rate, road grade, vehicle speed, and vehicle to engine speed ratio for a 10-

minute section of SwRI on-road testing of a class 8 combination truck................................ 53

Figure A1. Three generalized categories of elevation profiles................................................................... 57

Figure A2. Elevation profile, grade profile, and grade histogram for example 2.8-mile stretch of road.... 58

Figure A3. Elevation profile, grade profile, and grade histogram for round trip on example 2.8-mile 

stretch of road......................................................................................................................... 58

Figure A4. Elevation profile, absolute grade profile, and absolute grade histogram for example 2.8-mile 

stretch of road......................................................................................................................... 59

Figure A5. Supremum measurement example for national and synthetic cumulative distributions of 

absolute road grade ................................................................................................................ 60

Figure A6. Scatter of activity-based versus distance-based county weights for the sample of 1,728 U.S. 

counties with controlled access highways.............................................................................. 61

Figure A7. Scatter of average absolute road grade versus the difference between activity- and distancebased weights for the sample of 1,728 U.S. counties with controlled access highways........ 62

Figure A8. Raw distance-based cumulative distributions of grade by distance and average half hill grade 

for the 55-mph test group....................................................................................................... 63

Figure B1. Raw frequency-based cumulative distributions of half hill distance by truck speed limit........ 64

Figure B2. Raw frequency-based cumulative distributions of half hill average grade by truck speed limit65

Figure B3. Raw distance-based cumulative distributions of half hill average grade by truck speed limit . 65

Figure B4. Activity-weighted distance-based cumulative distributions of half hill average grade by truck 

speed limit.............................................................................................................................. 66

Figure B5. Raw frequency-based cumulative distributions of half hill average grade by half hill distance66

Figure B6. Raw frequency-based cumulative distributions of half hill grade ratio (maximum to average 

half hill grade) by truck speed limit ....................................................................................... 67

Figure B7. Raw distance-based cumulative distributions of half hill grade ratio (maximum to average half 

hill grade) by truck speed limit .............................................................................................. 67
viii

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Figure B8. Activity-weighted distance-based cumulative distributions of half hill grade ratio (maximum

to average half hill grade) by truck speed limit...................................................................... 68

Figure B9. Raw frequency-based cumulative distributions of half hill grade ratio (maximum to average 

half hill grade) by half hill distance ....................................................................................... 68
ix

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List of Tables

Table 1. Numerical comparison of national datasets (USGS, TomTom) relative to SwRI data from 115-

mile stretch of I-10 outside San Antonio, Texas.................................................................... 11

Table 2. Summary of three local routes statistically similar to national activity-weighted distributions for 

the 55-mph test group ............................................................................................................ 46

Table 3. Summary of two local routes statistically similar to national activity-weighted distributions for 

the 65-mph test group ............................................................................................................ 52
x

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Executive Summary

In collaboration with the U.S. Environmental Protection Agency and the U.S. Department of 

Energy, the National Renewable Energy Laboratory has conducted a national analysis of road 

grade characteristics experienced by U.S. medium- and heavy-duty trucks on controlled access

highways. These characteristics have been developed using TomTom’s commercially available 

street map and road grade database.

This report includes a detailed comparison of the TomTom national road grade database relative 

to a local road grade dataset generated by Southwest Research Institute and a national elevation 

dataset publically available from the U.S. Geological Survey. This analysis concluded that the 

TomTom national road grade database was a suitable source of road grade data for purposes of 

this study.

Using the TomTom national road grade database, national statistics on road grade and hill 

distances were generated for the U.S. network of controlled access highways. These statistical 

distributions were then weighted using data provided by the U.S. Environmental Protection 

Agency on activity of medium- and heavy-duty trucks on controlled access highways.

The national activity-weighted road grade and hill distance distributions were then used as 

targets for development of a handful of sample grade profiles potentially to be used in the U.S. 

Environmental Protection Agency’s Greenhouse Gas Emissions Model certification tool as well 

as in dynamometer testing of medium- and heavy duty vehicles and their powertrains.

Future work in this area may include the development of a highway drive cycle with transient 

speeds aligned to reflect real-world operation of medium- and heavy-duty vehicles on controlled 

access highways. Such a drive cycle would consider the correlation between vehicle speed and 

road grade as observed in on-road data.
1

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1 Introduction and Background

In August of 2011, the U.S. Environmental Protection Agency (EPA) and the National Highway 

Traffic Safety Administration (NHTSA) adopted a national program to reduce greenhouse gas 

(GHG) emissions and improve fuel efficiency of medium-duty (MD) and heavy-duty (HD)

trucks [1–4]. In February of 2014, President Obama announced efforts to update MD/HD vehicle

regulations in Phase 2 of EPA’s national GHG program [5–6].

As part of the EPA’s proposed Phase 2 rulemaking, the U.S. Department of Energy (DOE) and 

EPA are partnering to support a targeted project to refine and evaluate appropriate duty cycles 

for tractor-trailers and vocational vehicles to be used as part of MD/HD vehicle certification 

procedures for GHG emission standards. The National Renewable Energy Laboratory (NREL) 

will provide technical leadership for this work utilizing DOE-supported data, tools, and 

expertise.

NREL’s experience with large transportation database projects, including the Transportation 

Secure Data Center [7] and Fleet DNA [8], demonstrates the prerequisite capabilities for tackling 

data-intense problems. Additionally, development of data analysis tools including the Drive 

Cycle Rapid Investigation, Visualization, and Evaluation tool (DRIVE) [9] showcases NREL’s 

ability to distill large volumes of information into statistically representative subsets suitable for 

testing and evaluation purposes. These skillsets combined with NREL’s long-standing efforts in 

evaluating the on-road performance of conventional and advanced technology MD/HD vehicles 

for large commercial fleets make it an ideal organization for national analysis of the U.S. 

controlled access highway network.

In particular, this report documents work done to characterize nationally representative road 

grade profiles for certification testing and simulation on highway drive cycles. Current EPA 

highway cruise drive cycles are performed at constant speeds of 55 and 65 miles per hour (mph)

with zero road grade. The goal of this project was to develop and identify road grade profiles that 

are representative of U.S. controlled access highways.

This analysis will:

• Evaluate the accuracy and coverage of multiple road grade datasets

• Generate activity-weighted distributions of road grade and hill length at the national level

• Propose several potential grade profiles for testing and simulation at highway speeds.

Additionally, limitations of this work and the potential for continued development of highway 

drive cycles for EPA certification are discussed.
2

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2 Grade Comparison

Road grade is known to have a significant impact on the fuel efficiency and emissions of lightduty vehicles [10–13]. These impacts are amplified for MD/HD vehicles operating at generally 

heavier weights than typical light-duty passenger vehicles [14–17]. Until recently, the ability to 

quantify these impacts has been limited by the lack of a comprehensive national database of 

high-accuracy road grades.

Three road grade datasets are compared:

• Southwest Research Institute (SwRI) Mobile Autonomous Robotics Technology

Initiative (MARTI) measurements near San Antonio, Texas

• United States Geological Survey (USGS) Digital Elevation Model (DEM) of the National 

Elevation Dataset (NED) (Release: 2009)

• TomTom Advanced Driving Attributes (ADA) road grade data layer (Release: 2014 3Q).

First, each dataset is described. Second, a detailed comparison is made over a 115-mile stretch of 

Interstate Highway 10 (I-10) northwest of San Antonio, Texas (coincident with data available 

from SwRI). Last, an aggregate comparison between USGS and TomTom data is conducted.

2.1 Road Grade Datasets

2.1.1 SwRI’s MARTI Dataset

During 2013, EPA contracted with SwRI to study the impact of road grade on HD vehicles. As 

part of this effort, SwRI conducted on-road and dynamometer testing of a Class 8 combination 

truck. On-road testing consisted of multiple passes over a 300-mile highway loop in Texas 

between San Antonio, Uvalde, and Junction (highways US-90, US-83, and I-10) as shown in 

Figure 1.
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Figure 1. Three-hundred-mile loop near San Antonio, Texas, selected for SwRI on-road testing of 

Class 8 combination truck. The loop was also used for data collection by SwRI MARTI vehicle.

(Bing Maps credit: © 2015 Bing, Map Data)

Additionally, SwRI collected on-road data from the same 300-mile loop using its MARTI 

vehicle (part of SwRI’s MARTI Program [18]). The SwRI MARTI vehicle is a light-duty sport 

utility vehicle equipped with multiple sensing devices, including a high-resolution global 

positioning system (GPS) and inertial navigation system (three-axis inertial measurement unit 

with multiple accelerometers and gyroscopes).

Using measurements from the MARTI vehicle, SwRI estimated road grades along the 300-mile 

highway route. The road grades were spatially aligned with the time series fueling measurements 

from the Class 8 combination truck on-road data. As expected, a strong correlation between 

fueling rates and road grade was found. Details of this analysis can be found in SwRI’s 

presentation at the Technical Workshop supporting the need for including the effects of grade in 

EPA and NHTSA Phase 2 Standards for MD/HD GHG and Fuel Efficiency [4].

This analysis utilizes the MARTI-derived grade estimates from the 115-mile stretch of I-10 in 

Texas between San Antonio and Junction (the controlled access portion of the original 300-mile 

route) sampled at a nominal frequency of 100 hertz (Hz).
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2.1.2 USGS DEM NED

The USGS makes DEMs publically available as part the NED [19–20]. For this analysis, NREL

utilized a 1/3 arc-second DEM, which forms an approximate 10-meter × 10-meter grid across the 

United States. The 1/3 arc-second DEM is the finest resolution map with complete national 

coverage currently available from the USGS. Figure 2 shows a graphical representation of the 

national map. This DEM is a composite of several regional data sources digitally stitched 

together to form a seamless elevation map of the United States. Regional elevation datasets are 

generated using a variety of methods, including electronic image correlation, manual profiling, 

laser illuminated detection and ranging (lidar) digital camera correlation, and other remote 

sensing techniques. The USGS is continually updating its DEMs and is in the process of 

populating a NED with complete national coverage at 1-meter resolution as part of the 3D 

Elevation Program [21].

Figure 2. United States elevation map utilizing USGS 1/3 arc-second DEM

As part of NREL’s standard routine for processing vehicle GPS data for light-duty and MD/HD 

vehicle drive cycle databases [7–8], elevations from the USGS DEM are matched to each 

recorded point in a GPS trace. The raw elevation data are filtered, smoothed, and differentiated 

to calculate an estimate of road grades corresponding to second-by-second vehicle speed and fuel 

use data. This process was calibrated in 2014 to a commercially available road-grade database 

with a root mean square error (RMSE) of 1.48% road grade. For additional details on this 

process and calibration of the filtering routine, please refer to [22].

2.1.3 TomTom’s ADA Road Grade Data Layer

TomTom’s MultiNet road network and ADA road grade data layers [23–24] are used as a 

reference point for national road grade data. TomTom populates its road grade database using a 

combination of advanced mobile terrestrial sensing and aggregated mobile terrestrial sensing 

data [25].

Collection of advanced mobile terrestrial sensing data requires TomTom to drive U.S. roads in a 

vehicle instrumented with highly accurate remote sensing devices, including GPS, differential 

GPS, inertial measurement unit, gyroscopes, and accelerometers. The data are filtered and 
5

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synthesized using TomTom’s proprietary methodology to produce road grade estimates, which 

are linked to a digital road network. The majority of grade data from major U.S. highways is 

produced using this method.

For roads where TomTom has yet to achieve coverage with advanced mobile terrestrial sensing, 

aggregated mobile terrestrial sensing data are employed. Road grade estimates of this type are 

generated by spatially aligning GPS elevation readings from a high number of TomTom 

consumer devices. Using multiple passes over a single stretch of road, GPS recorded elevations 

are averaged, filtered, and differentiated using TomTom’s proprietary methodology to produce 

road grade estimates, which are linked to the digital road network.

The TomTom ADA product contains approximately 74 million points across the United States 

with a nominal advertised accuracy on road grade of ±0.3%. This dataset includes 100% 

coverage on U.S. controlled access highway routes consisting of approximately 2.6 million 

points over 127 thousand miles of roadway (resulting in an average distance between grade 

points of 258 feet). Grade points are provided as instantaneous grade measurements; road grade 

in between published points is interpreted using linear interpolation with respect to distance. By 

non-uniformly spacing grade points, TomTom is able to provide a complete road grade profile 

while minimizing database size and query time. Figure 3 shows TomTom’s national ADA road 

grade coverage on controlled access routes.

Figure 3. U.S. controlled access highways by TomTom ADA road grade

2.2 Local Level Comparison

Filtered USGS and TomTom data were evaluated against grade measurements from SwRI on the 

115-mile east-bound stretch of I-10 in Texas from Junction to San Antonio. Figure 4 shows a full 

USGS elevation map of the region with the I-10 highway trace overlaid in black.
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Figure 4. USGS elevation map near San Antonio, Texas, overlaid with GPS trace of MARTI vehicle 

driving from Junction, Texas, to San Antonio, Texas, on I-10

2.2.1 Filtered USGS versus SwRI

Figures 5, 6, and 7 graphically compare filtered USGS elevation and grade relative to SwRI data 

(plotted against distance, running west to east). Relative elevation from the SwRI data is 

calculated by integrating measured grade versus distance and adding an offset such that the SwRI 

elevation matches USGS data at mile zero. Raw USGS elevations are filtered and smoothed 

using NREL’s standard processing routine and plotted as USGS filtered elevations. This filtering 

routine has a relatively small impact on elevation values and is implemented primarily to 

produce a clean derivative. USGS road grade is calculated by differentiating the filtered USGS 

elevations with respect to distance.

Figure 5 graphically compares SwRI and filtered USGS elevation and grade values. This plot 

shows that elevation values agree well for the majority of the 115-mile stretch in question. This 

provides confidence that the SwRI grade data are free of bias that would cause the integrated 

grade signal to drift over the 115-mile route.
7

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Figure 5. SwRI/USGS comparison over the 115-mile stretch of I-10 northwest of San Antonio, 

Texas. Top: SwRI integrated grade plotted against filtered USGS elevation. Bottom: SwRI grade 

plotted against filtered, differentiated USGS elevation.

Figure 6 is a zoom of the SwRI/USGS comparison from miles 97 to 104. At this magnification, 

we can now see that the filtered, differentiated USGS elevation agrees generally well with the 

SwRI grade measurements.

Figure 6. SwRI/USGS comparison over a subset of the 115-mile stretch of I-10 northwest of San 

Antonio, Texas. Top: SwRI integrated grade plotted against filtered USGS elevation. Bottom: SwRI 

grade plotted against filtered, differentiated USGS elevation.
8

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In Figure 7, all grade measurements from the SwRI and filtered USGS datasets are scattered 

against one another. (The density of this scatter prompted applying a level of visual transparency 

to each marker to get a better sense of density.) All grade values would fall exactly on the red 

dashed diagonal line if the datasets matched exactly. Visual inspection reveals that the filtered 

USGS data generally result in grades of greater magnitude relative to the SwRI data with a 

calculated RMSE of 1.9%. This suggests that the 2014 version of NREL’s processing routine is 

potentially under-filtering raw USGS elevations in this region of the country.

Figure 7. Filtered USGS grade scattered against SwRI grade from the 115-mile stretch of I-10 

northwest of San Antonio, Texas

Dashed diagonal line provided as reference for exact agreement

2.2.2 TomTom versus SwRI

Figures 8, 9, and 10 graphically compare TomTom grade data relative to SwRI data (plotted 

against distance, running west to east). Because the TomTom database reports only road grade 

values, the TomTom grade data are integrated to calculate a relative elevation and offset to 

match SwRI’s integrated grade at mile zero.

Figure 8 provides a graphical comparison of SwRI and TomTom elevation/grade values. This 

plot shows that TomTom integrated grade values generally agree well with SwRI integrated 

grade. Just before mile 80, the integrated TomTom grade exhibits a slight offset, which holds for 

the remainder of the 115-mile stretch. This indicates that SwRI and TomTom grade values only 

disagree significantly for a relatively small segment of this 115-mile stretch.

Figure 9 is a zoom of the SwRI/TomTom comparison from mile 86 to mile 93. At this 

magnification, we can see that TomTom grades are nearly identical to SwRI data over this short 

stretch of road. Additionally, we find that TomTom grade points are reported at a frequency such 
9

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that linear interpolation of the TomTom data also agrees well with SwRI measurements (i.e., not 

only do TomTom markers match SwRI data, but linear segments connecting available TomTom 

grades overlay well with SwRI data).

Figure 8. SwRI/TomTom comparison over the 115-mile stretch of I-10 northwest of San Antonio, 

Texas. Top: SwRI integrated grade plotted against integrated TomTom grade. Bottom: SwRI grade 

plotted against TomTom grade.

Figure 9. SwRI/TomTom comparison over a subset of the 115-mile stretch of I-10 northwest of San 

Antonio, Texas. Top: SwRI integrated grade plotted against integrated TomTom grade. Bottom: 

SwRI grade plotted against TomTom grade.
10

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In Figure 10, all grade measurements from the SwRI and TomTom datasets are scattered against 

one another. The majority of the points along the 115-mile route fall very close to the red dashed 

line, indicating a strong agreement between these SwRI and TomTom data. RMSE for the 

TomTom dataset was calculated as 0.3%.

Figure 10. TomTom grade scattered against SwRI grade from the 115-mile stretch of I-10 

northwest of San Antonio, Texas

Dashed diagonal line provided as reference for exact agreement

2.2.3 Local Level Comparison Summary

Filtered USGS and TomTom descriptions of elevation and grade along this 115-mile stretch of 

I-10 were compared side-by-side relative to SwRI MARTI data. Numerical evaluations of road 

grade accuracy are conducted at two frequencies: 1) the frequency of available data, and 2) at 

uniform 10-foot intervals with linear interpolation of available data. Recall that the SwRI 

MARTI data were collected at 100 Hz, a higher spatial resolution than both the USGS and 

TomTom datasets; at a vehicle speed of 70 mph, this translates to grade readings approximately 

every 1 foot. Because the national databases feature larger, non-uniform measurement intervals, 

comparisons based on available data could potentially bias results. A visual representation of the 

two sampling frequencies is shown in Figure 11.

Table 1 summarizes the numerical comparison of the national datasets based on available and 

interpolated data. Based on available data, the SwRI measurements feature by far the highest 

sampling frequency per mile (nominally 100 Hz at highway speeds). There is an apparent 

tradeoff between sampling frequency and accuracy (quantified as RMSE relative to SwRI data)

in the national datasets. The filtered USGS data are available at the highest spatial frequency, but 

also exhibit the highest RMSE; conversely, the TomTom data have the lowest RMSE, but also 

exhibit the lowest spatial frequency.
11

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Figure 11. Visual description of the two sampling frequencies used in the comparative analysis:

1) based on available data, and 2) based on linear interpolation at uniform intervals of 10 feet

(0.1 mile interval is used for illustrative purposes)

Table 1. Numerical comparison of national datasets (USGS, TomTom) relative to SwRI data from 

115-mile stretch of I-10 outside San Antonio, Texas 

SwRI USGS TomTom

Based on 

available data

Distance, miles 115.65 115.65 115.65

Points per mile 5,636.3 160.9 15.6

Avg grade 0.0% 0.0% -0.2%

Avg abs grade 1.6% 2.5% 1.6%

Grade RMSE – 1.9% 0.3%

Grade maximum absolute error – 8.7% 3.7%

Based on 

interpolated data

Points per mile 528 528 528

Avg grade -0.2% -0.3% -0.2%

Avg abs grade 1.6% 2.5% 1.6%

Grade RMSE – 2.0% 0.4%

Grade maximum absolute error – 8.7% 3.7%

Comparison evaluated at two frequencies: 1) based on available data, and 2) based on linear interpolation 

at uniform intervals of 10 feet.

To normalize for bias associated with sampling frequency, the datasets are resampled using 

linear interpolation at uniform, identical 10-foot intervals such that all datasets provide 528 grade 

readings per mile over the 115-mile section of I-10 outside San Antonio, Texas. Based on 

uniform sampling, the TomTom data clearly result in the lowest RMSE and maximum error at 

0.4% and 3.7%, respectively.
12

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These numerical findings are consistent with visual inspections that also suggested the TomTom 

data as the best match to SwRI measurements.

2.3 National Level Comparison

In addition to a rigorous local investigation on I-10 near San Antonio, Texas, the filtered USGS 

and TomTom datasets were evaluated at the national level. For this analysis, a national 

distribution of road grade was generated from the filtered USGS and TomTom databases based 

on available data from controlled access routes. These distributions are shown in Figure 12 as 

percent of highway miles at a given absolute road grade. While road grade is necessarily 

represented as a signed value in testing procedures and in modeling exercises, at the national 

level the distribution of road grade by distance using signed values is symmetrical about zero 

percent road grade. As such, national road grade distributions can be fully described through the 

use of absolute values for ease of interpretation. For additional discussion on representing road 

grade distributions in terms of cumulative distributions of absolute values, please refer to 

Appendix Section A.1.

Figure 12. National distributions of road grade from filtered USGS and TomTom databases on the 

basis of absolute values

For the national analysis, we elected not to declare either dataset as “ground-truth” as was done 

with the SwRI data during inspection of the local route. Instead, the agreement between the 

national datasets is quantified at various levels of road grade. Visually, both national datasets 

follow the intuitive trend of having the majority of highway distance at relatively low grades 

(i.e., 57%–59% of distance is at less than 1% grade) and a small amount of highway distance at 

relatively high grades (i.e., 1%–2% of distance is at greater than 5% grade).

Based on the superior accuracy of the TomTom data (relative to filtered USGS data) when 

compared with SwRI measurements over the 115-mile stretch of I-10 near San Antonio, Texas, 

and the similarity of roadway distance at grade between the national databases, the TomTom 

database was selected as the preferred road grade database for the remainder of this analysis.
13

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3 National Statistics

Using the TomTom national road grade database as the source data for this analysis, a suite of 

statistical distributions was developed to describe grades experienced by MD/HD trucks on 

controlled access highways across the United States. This suite of descriptive statistics is 

developed using two analytical procedures: 1) quantifying the percent of national roadway 

distance at grade, and 2) evaluating national highway topography by segmenting roadways into a 

series of “half hills” (described in section 3.2) and recording statistics such as distance, average 

grade, and maximum grade for each segment. Finally, activity weighting is applied to account 

for the national distribution of MD/HD vehicle highway traffic.

As this analysis is intended to support the highway testing procedure, the U.S. highways to be 

examined are presented first. Figure 13 shows a map of the United States overlaid with 

controlled access roads per the TomTom MultiNet street network. This road network includes 

the U.S. interstate system (shown in red) in addition to a number of locally controlled access

highways (shown in blue).

Figure 13. TomTom MultiNet map of U.S. controlled access highways

Interstate highway system shown in red; locally controlled access highways shown in blue.
14

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Additionally, we would like to understand if road grade distributions feature significant variation 

when segmented by truck speed limits so as to align data generated in this report with EPA’s 

existing 55- and 65-mph constant-speed drive cycles. Figure 14 shows the same U.S. controlled 

access highway map colored by state-defined truck speed limits per TomTom’s Logistics data 

layer [26]. While truck classifications can vary by state, vehicles subject to truck speed limits 

generally fall in weights classes 7–8, feature gross vehicle weight ratings of over 26,000 pounds, 

and have three or more axles.

Figure 14. U.S. controlled access highway map colored by state-defined truck speed limits per 

TomTom Trucking Logistics speed restrictions data layer

Colored bubbles indicate truck speed limits in units of miles per hour.
15

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Figure 15 offers a breakdown of U.S. controlled access highway miles by truck speed limit and 

by U.S. Census Urban Area boundaries. From this plot, we see that the majority of U.S. 

controlled access highway miles come from routes with truck speed limits from 55- to 75-mph. 

Roadways with truck speed limits less than 55-mph are discarded on the basis that vehicle 

operation on such roads would likely be occurring in congested urban areas and would not be 

constant speed. Roadways with truck speed limits greater than 75-mph are discarded on the 

basis that these only occur in a very small area of the country, do not appear to be representative 

of national roadways, and their omission would not have a meaningful effect on the results. 

Therefore, the remainder of this analysis will focus on roadways in these five truck speed limit 

bins.

Figure 15. Mileage breakdown of U.S. controlled access highways by truck speed limit and U.S. 

Census urban area designation

3.1 Road Grade by Distance Analysis

The TomTom ADA road grade database was queried for all U.S. controlled access roads at 

uniform 52.8-foot intervals (100 points per mile) using linear interpolation. This procedure 

quantifies the percent of national highway distance at grade (distance in this analysis is defined 

as the horizontal component of roadway distance as described in Appendix Section A.2). Given 

that there are approximately 127 thousand miles of U.S. controlled access highway, these 

calculations result in generation of approximately 12-million road grade measurements. The data 

are aggregated by five truck speed limits and 1,728 U.S. counties with controlled access 

highways to produce 8,640 distributions of grade by distance.
16

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Figure 16 plots the data as cumulative distributions for all 1,728 U.S. counties in question (grade 

by truck speed limit is summed by county for this plot). While the density of data on this plot 

provided little in the form of analytical value, it is informative to understand the dramatic 

variability in road grade experienced by trucks in different regions of the country.

Figure 16. Cumulative distributions of road grade by distance for 1,728 U.S. counties
17

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In Figure 17, the 8,640 distributions are summed by truck speed limit with all data points having 

equal value within each truck speed limit segment (effectively resulting in distance weighting). A 

trend emerges from this plot that roadways with high truck speed limits generally have lower 

concentrations of road grade relative to roadways with low truck speed limits. For example, 

approximately 78% of distances on highways with truck speed limits of 55-mph exhibit less than 

2% absolute road grade. That figure jumps to approximately 87% for highways with truck speed 

limits of 75-mph.

Figure 17. Raw distance-based cumulative distribution of absolute road grade by truck speed limit

3.2 Half Hill Analysis

While querying the national road grade database by distance is informative, additional 

information can be gleaned. Our second round of analysis consisted of evaluating national 

highway topography by segmenting roadways into a series of “half hills” and recording statistics 

for each segment.

A half hill in this analysis was defined as a continuous stretch of roadway where grade does not 

change sign (i.e., sections of exclusive climb or descent). Figure 18 shows this half hill 

segmenting where a 13-mile stretch of controlled access highway is subdivided into 16 unique 

half hills (eight climbs and eight descents). A number of statistics are recorded for each 

identified half hill, including distance, average grade, and maximum grade (minimum grade for 

segments of descent). This processing routine is applied to the entire U.S. controlled access

highway system and results in generation of statistics for approximately 220 thousand half hills 

nationwide.
18

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Figure 18. Example section of controlled access highway broken into 16 half hills (eight climbs 

and eight descents)

3.2.1 Analytical Approaches

During internal reviews of half hill data, we discovered the potential for misinterpretation of 

results when not explicitly stating the method by which our distributions were compiled. Two 

methods for aggregating half hill data were used: 1) frequency-based distributions, and 2) 

distance-based distributions. In the previous analysis of grade by distance in Section 3.1, 

frequency-based and distance-based interpretations carried the same meaning because the 

distance between data points was assigned a uniform distance of 52.8 feet. Due to the nonuniform nature of half hill distances, frequency-based and distance-based distributions of half 

hill data result in dramatically different statistics. For example, Figure 19 presents frequencybased and distance-based distributions of distances from the entire half hill dataset.
19

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Figure 19. All half hill (HH) distances plotted as frequency-based and distance-based cumulative 

distributions

The frequency-based and distance-based cumulative distributions, P, of half hill distance, d, are 

generated by evaluating Equations 1 and 2, respectively, over the entire range of half hill 

distances.

(1)

(2)

In this set of equations, di represents the distance of half hill, i, and n represents the total half hill 

count. Using the same source data, we are able to create two types of distributions, each of which

provides a unique perspective. For example, examination of the frequency-based distribution in 

Figure 19 shows that approximately 40% of half hills inspected have a distance of 0.25 mile or 

less. Conversely, the distance-based distribution shows that only 10% of inspected highway 

distance falls on half hills of distance 0.25 mile or less. By assigning all half hills equal weight, 

the frequency distribution overstates the amount of distance driven on short half hills and 

understates the amount of distance driven on long half hills.

While both methods for aggregating the half hill source data are believed to be valid, we adopted 

the distance-based distribution as the default method for the majority of this analysis.

Pdddd(d) = ���

d < d d

eeee 0

n

=1

� �d

n

=1

�

Pffff(d) = 1

n��

d < d 1

eeee 0

n

=1
20

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3.2.2 Half Hill Trends with Respect to Speed Limits

Figure 20 plots raw distance-based cumulative distributions of half hill distance by truck speed 

limit. Similar trends in half hill distances are apparent for roads with truck speed limits between 

55- and 70-mph. However, half hill distances are noticeably longer on roads with truck speed 

limits of 75-mph. For example, approximately 70% of roadway distances on routes with 75-mph 

truck speed limits occur on half hills of 2 miles or less. That figure jumps to a range of 82%–

87% for routes with truck speed limits of 55- to 70-mph.

Figure 20. Raw distance-based cumulative distributions of half hill distance by truck speed limit
21

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Figure 21 shows national half hill data plotted by scattering maximum grade (minimum grade for 

segments of descent) against average grade for each half hill. The red dashed diagonal line 

indicates half hills where maximum and average grade are nearly equal. Overall, we find an 

average grade ratio (maximum over average half hill grade) of 1.76.

Figure 21. Maximum (or minimum) versus average road grade for all measured half hills

Red dashed diagonal line shows where maximum and average grade are nearly equal.
22

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3.3 Activity-Weighted Values

Activity data for MD/HD trucks are sourced from EPA’s Motor Vehicle Emission Simulator 

(MOVES) database of vehicle miles traveled (VMT) by county. The MOVES VMT database is 

summarized in Figure 22. EPA’s estimates for national, annual VMT by vehicle class and road 

type are also included. Light-duty vehicles, including motorcycles, passenger cars, passenger 

trucks, and light commercial trucks, comprise the majority of activity in this database.

Figure 22. EPA MOVES VMT database plotted by vehicle type and roadway classification

After removing light-duty vehicle activity and VMT from uncontrolled access roads, the 

remaining activity data from MD/HD vehicles on controlled access roads are plotted in Figure 

23. In this subset of the MOVES VMT database, the majority of activity is generated from shortand long-haul combination trucks. These are vehicles likely to fall into weight classes 7–8 and 

thus are subject to the truck speed limits discussed above.

Figure 23. EPA MOVES VMT database for MD/HD vehicles on controlled access roads only
23

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MOVES VMT data for the subset of MD/HD vehicles on controlled access roads are spatially 

plotted by county in Figure 24 to better understand regional variability with respect to MD/HD 

truck traffic. This map reveals concentrations of activity in urban centers and on select interstate 

highway systems primarily oriented in the eastern third of the United States.

Figure 24. EPA MOVES VMT database mapped by county for MD/HD trucks operating on 

controlled access roads

Because VMT from the MOVES database only allows resolution at the county level, VMT must 

be subdivided within each county prior to applying activity weighting. For the analysis of road 

grade by distance, county MD/HD controlled access VMT are uniformly distributed over queried 

grade points in a county (points uniformly spaced at 100 points per mile on all controlled access

roads within each county). For half hill statistics, weights are generated for every half hill 

according to Equation 3.

(3)

where wi is the individual weight of each half hill, VMTcounty,i is the MOVES VMT from the 

county containing half hill i, di is the distance of half hill i, and hhcounty,i is the total count of all 

half hills from the county in question. These weights are then used to generate activity-weight 

distributions of half hill distance as shown in Equation 4.

(4)

P(d) = ���

d < d w

eeee 0

n

=1

� �w

n

=1

�

w = VVVccc c, ∗ � d

∑ d hhcccccc,i

=1

�
24

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 25 provides activity-weighted distributions of grade by distance for the five truck speed 

limits in question.

Figure 25. Activity-weighted, distance-based cumulative distributions of absolute road grade by

truck speed limit

Similarly, activity weights are applied to the distance-based distributions of half hill distance by 

truck speed limit in Figure 26.

Figure 26. Activity-weighted, distance-based cumulative distributions of half hill distance by truck 

speed limit
25

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

To align with existing EPA highway test cycle speeds at 55- and 65-mph, the TomTom data 

from roads with truck speed limits of 55- and 60-mph are grouped into a shared distribution to 

inform testing at 55-mph. The remaining truck speed limit data for of 65-, 70-, and 75-mph are 

grouped into a shared distribution to inform testing at 65-mph. Further future on-road data 

analysis may help evaluate how closely the fixed 55- and 65-mph test cycle speeds align with 

actual on-road speeds for each of these road speed limit categories.

With the data now in two groups for EPA test cycles at 55- and 65-mph, the raw and activityweighted distributions of road grade by distance for both 55- and 65-mph test groups are plotted 

in Figure 27. Activity-weighted distributions for both test groups closely match the raw data.

Figure 27. Combined activity-weighted, distance-based cumulative distributions of absolute road 

grade by target test speed

In order to demonstrate the statistical difference between activity-weighted 55-mph and 65-mph 

test groups, Kolmogorov-Smirnov (KS) hypothesis testing (as described in Appendix Section 

A.3) was conducted at a 95% confidence level. Hypothesis testing revealed a KS statistic of 

0.046 and a P-value of 0.000, indicating that the two distributions were determined to be 

statistically unique (i.e., the null hypothesis that the distributions are equivalent was rejected).
26

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Activity-weighted data are also generated for the distance-based distributions of half hill 

distances, shown in Figure 28. The application of activity weights shifts both the 55- and 65-mph 

distributions toward shorter half hill distances.

Figure 28. Combined activity-weighted, distance-based cumulative distributions of half hill 

distance by target test speed

In order to demonstrate the statistical difference between activity-weighted 55-mph and 65-mph 

test groups, KS hypothesis testing (as described in Appendix Section A.3) was conducted at a 

95% confidence level. Hypothesis testing revealed a KS statistic of 0.111 and a P-value of 0.000 

indicating that the two distributions were determined to be statistically unique (i.e., the null 

hypothesis that the distributions are equivalent was rejected).

The combined activity-weighted, distance-based cumulative distributions of road grade and half 

hill distance shown in Figures 27 and 28 will serve as the basis in Section 4 for evaluating the 

representativeness of sample road grade profiles from synthetic generation and identification of 

local routes.

Figures 27 and 28 show that application of activity weights has relatively little impact on the 

underlying raw distributions. An explanation of this outcome is provided in Appendix Section 

A.4. Please refer to Appendix Section A.5 for a discussion on why grade by distance 

distributions are used as the national target in this analysis (as opposed to average half hill grade 

distributions). Supplementary data distributions from the half hill analysis not used for 

determining representativeness of local grade profiles are included in Appendix B.
27

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4 Nationally Representative Sample Grade Profiles

Two procedures for generating road grade profiles representative of the previously presented 

national statistics for testing and simulation purposes are implemented. The first method utilizes 

random number generation in a Monte Carlo process to synthesize a large number of profiles 

from which the most representative single profile is selected. The second involves data mining 

the TomTom national road grade database for a continuous section of actual highway that has 

statistics matching the national distributions within a predefined tolerance.

The statistical representativeness of sample grade profiles will be evaluated against the national, 

distance-based, activity-weighted, cumulative distributions of absolute road grade and half hill 

distance for both the 55-mph and 65-mph test groups using KS hypothesis testing (as described 

in Appendix Section A.3). KS hypothesis testing will be conducted at a 95% confidence level 

and we will target sample profiles with KS statistics of no greater than 0.05 and 0.10 for absolute 

road grade and half hill distance, respectively.

The sample grade profiles developed in this section of the report are intended to be paired with 

constant speed drive cycles at 55- and 65-mph and potentially used in the EPA’s Greenhouse 

Gas Emissions Model certification tool as well as in dynamometer testing of medium- and heavy 

duty vehicles and their powertrains.

4.1 Synthetic Routes

As part of this project, NREL developed an extension of its DRIVE tool [9] to synthesize 

representative road grade profiles from statistical distributions of the activity-weighted national 

road network. This extension builds on DRIVE’s core capability of generating representative 

drive cycles from large on-road datasets of real-world driving (see [27] for an example of 

compressing a large, real-world, drive cycle dataset into a single, statistically representative 

cycle).

Experience with DRIVE was leveraged to construct a method for synthesizing statistically 

representative road grade profiles. This procedure employs a Monte Carlo method in which 

grade profiles are synthesized one half hill at a time. Characteristics for the first half hill are 

determined by randomly sampling national frequency-based distributions of half hill distance, 

average grade, and maximum to average grade ratio (plots of frequency-based distribution are 

included in Appendix Section B). Once distance, di, average grade, gi, and grade ratio, ri, 

characteristics have been determined, the shape of the first half hill is constructed using the 

template shown in Figure 29.
28

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Figure 29. Synthetic grade profile template

This template assumes half hill road grades in the shape of a trapezoid (reduces to an isosceles 

triangle in the case ri ≥ 2) vertically symmetrical about di/2. The vertical coordinates for this 

template are readily determined by evaluating maximum grade as the product of the grade ratio 

and average grade. Horizontal coordinates are determined geometrically as a function of half hill 

distance and grade ratio.

This process is repeated with half hill grade sign calculated such that the profile descends when 

above starting elevation and ascends when below starting elevation. Half hills are appended to 

the synthetic profile until a target distance is reached, at which point one additional half hill is 

appended with average grade calculated to ensure net zero elevation change over the entire 

sample profile. After the synthetic grade profile is complete, relative elevation is calculated by 

integrating grade with respect to distance.

This Monte Carlo approach for generating synthetic road grade profiles is computationally 

efficient, which enables the generation of millions of potential sample profiles. A full design of 

experiments was conducted with this method for both the 55-mph and 65-mph test groups. For 

each test group, sample profiles were generated at target profile distances from 3 to 30 miles in 

3-mile increments. For each combination of test group and target profile distance, a fixed number 

of sample profiles were generated. The most representative profile from each combination was 

saved for further analysis. The degree to which sample profiles are representative of national 

distributions was quantified by calculating the weighted average of KS statistics for absolute 

grade and half hill distance with the KS statistic for absolute grade weighted 2:1, respectively 

(reflecting a greater emphasis on matching the distribution of absolute road grade). The fixed 

number of sample profiles was swept from 1,000 to 1,000,000 sample profiles in logarithmic 

intervals of base ten.
29

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4.1.1 55-mph Test Group

The results of this design of experiments for the 55-mph test group in terms of the KS statistic 

for road grade match are shown in Figure 30. The fixed black line at a KS statistic of 0.05 

represents the previously stated goal (KS statistics close to zero indicate better matches to the 

national dataset). The first trend observed from this plot is the tendency for synthetic profiles of 

greater distance to exhibit lower KS statistics. This result is intuitive from the standpoint that 

longer target profile distances allow for sample distributions of road grade to be more evenly 

distributed (i.e., there is not enough opportunity in the 3-mile sample profiles to capture all of the 

grade variation observed in the national dataset).

Figure 30. KS statistics for absolute road grade match in the 55-mph test group with respect to 

target profile distance and maximum iteration count

Secondly, KS statistics are (in general) improved by allowing a larger number of fixed iterations 

from which to draw. This finding is consistent with other Monte Carlo tools that (in general) 

experience improved performance given larger sample sizes. One exception to this trend is 

observed at the 12-mile test distance where the top scoring profile from the pool of 10,000 

samples had a lower KS statistic than the top scoring profiles from the pools of 100,000 and 

1,000,000 samples. This exception demonstrates the uncertainty in convergence time associated 

with random number sampling.
30

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In addition to sample profiles matching the national dataset in terms of absolute road grades, we 

would like to identify profiles with strong matches in terms of half hill distances. Design of 

experiment results for the 55-mph test group in terms of KS statistic for half hill distance match 

are shown in Figure 31. The fixed black line at a KS statistic of 0.10 represents the previously 

stated goal. As with the plot of KS statistics for road grade match, there are similar trends with 

respect to test profile distance and number of iterations.

Figure 31. KS statistics for half hill distance match in the 55-mph test group with respect to target 

profile distance and maximum iteration count

Having mapped the performance of the synthetic profile generator, we are now interested in 

identifying a small number of sample profiles for closer examination. The sample profiles of 

greatest interest are those most closely matching the national dataset (low weighted KS statistic) 

and those of shortest distance. The objective to identify sample profiles of short distance is 

driven by the desire to minimize the significant time and cost requirements associated with 

dynamometer testing of vehicles and powertrains. As such, we will now present two sample 

profiles from the 12-mile profile distance target where the KS statistics for both road grade and 

half hill distance are below the stated goals of 0.05 and 0.10, respectively.
31

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The first proposed road grade profile for 55-mph testing is shown in Figure 32 and named

“150508 55mph 12mi 201210of1e6iter” (name denotes date of generation, target test speed, 

target distance, and iteration count). The red dashed line in the elevation subplot shows that the 

profile is net zero elevation.

Figure 32. Elevation and road grade profile from sample “150508 55mph 12mi 201210of1e6iter”

Red dashed line on elevation subplot shows net zero elevation change.

Distance-based cumulative distributions of absolute road grade and half hill distance for sample 

profile “150508 55mph 12mi 201210of1e6iter” are shown in Figure 33. National activityweighted, cumulative distributions of the same parameters are provided as reference for the 

degree of match to the national dataset. Recalling that the KS statistic is a measure of similarity 

between two distributions and that a KS statistic of <0.05 was targeted for the distribution of 

absolute road grade, this sample achieved a KS statistic of 0.049 and a P-value of 0.316 and 

failed to reject the null hypothesis that the distributions are equivalent at a 95% confidence level. 

Recalling that a KS statistic of <0.10 was targeted for the distribution of half hill distance, this 

sample achieved a KS statistic of 0.095 and a P-value of 0.603 and failed to reject the null 

hypothesis that the distributions are equivalent at a 95% confidence level.
32

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 33. Comparison of distance-based cumulative distributions between national activityweighted dataset and sample profile “150508 55mph 12mi 201210of1e6iter” in terms of absolute 

road grade (left) and half hill distance (right)

The second proposed road grade profile for 55-mph testing is named “150508 55mph 12mi 

727695of1e6iter” (name denotes date of generation, target test speed, target distance, and 

iteration count) and is shown in Figure 34. The red dashed line in the elevation subplot shows 

that the profile is net zero elevation.

Figure 34. Elevation and road grade profile from sample “150508 55mph 12mi 727695of1e6iter”

Red dashed line on the elevation subplot is provided to show net zero elevation change.
33

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Distance-based, cumulative distributions of absolute road grade and half hill distance for sample 

profile “150508 55mph 12mi 727695of1e6iter” are shown in Figure 35. National activityweighted, cumulative distributions of the same parameters are provided as reference for the 

degree of match to the national dataset. Recalling that the KS statistic is a measure of similarity 

between two distributions and that a KS statistic of <0.05 was targeted for the distribution of 

absolute road grade, this sample achieved a KS statistic of 0.047 and a P-value of 0.346 and 

failed to reject the null hypothesis that the distributions are equivalent at a 95% confidence level. 

Recalling that a KS statistic of <0.10 was targeted for the distribution of half hill distance, this 

sample achieved a KS statistic of 0.095 and a P-value of 0.561 and failed to reject the null 

hypothesis that the distributions are equivalent at a 95% confidence level.

Figure 35. Comparison of distance-based cumulative distributions between a national activityweighted dataset and sample profile “150508 55mph 12mi 727695of1e6iter” in terms of absolute 

road grade (left) and half hill distance (right)
34

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

4.1.2 65-mph Test Group

The results of the design of experiments for the 65-mph test group in terms of the KS statistic for 

road grade match are shown in Figure 36. A fixed black line at a KS statistic of 0.05 represents 

our previously stated goal (recall that KS statistics close to zero indicate better matches to the 

national dataset). As with the plots of KS statistics for the 55-mph group synthetic profiles, the 

trends are similar with respect to test profile distance and number of iterations.

Figure 36. KS statistics for absolute road grade match in the 65-mph test group with respect to 

target profile distance and maximum iteration count
35

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Design-of-experiment results for the 65-mph test group in terms of the KS statistic for half hill 

distance match are shown in Figure 37. A fixed black line represents the goal of a KS statistic of 

0.10. As with the plot of KS statistics for road grade match, we see similar trends with respect to 

the test profile distance and number of iterations.

Figure 37. KS statistics for half hill distance match in the 65-mph test group with respect to target 

profile distance and maximum iteration count

Having mapped the performance of the synthetic profile generator, we are now interested in 

identifying a small number of sample profiles for closer examination. Sample profiles of greatest 

interest are those most closely matching the national dataset (low weighted KS statistic) and 

those of shortest distance. The objective to identify sample profiles of short distance is driven by 

the desire to minimize the significant time and cost requirements associated with dynamometer 

testing of vehicles and powertrains. Two sample profiles are presented for the 15-mile profile 

distance target where KS statistics for both road grade and half hill distance are below the goals 

of 0.05 and 0.10, respectively.
36

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

The first proposed road grade profile for 65-mph testing, named “150508 65mph 15mi 

467684of1e6iter” (name denotes date of generation, target test speed, target distance, and 

iteration count), is shown in Figure 38. The red dashed line in the elevation subplot shows that 

the profile is net zero elevation.

Figure 38. Elevation and road grade profile from sample “150508 65mph 15mi 467684of1e6iter”

Red dashed line on elevation subplot shows there is net zero elevation change.

Distance-based cumulative distributions of absolute road grade and half hill distance for sample 

profile “150508 65mph 15mi 467684of1e6iter” are shown in Figure 39. National activityweighted cumulative distributions of the same parameters are provided as reference for the 

degree of match to the national dataset. Recalling that the KS statistic is a measure of similarity 

between two distributions and that a KS statistic of <0.05 was targeted for the distribution of 

absolute road grade, this sample achieved a KS statistic of 0.041 and a P-value of 0.365 and 

failed to reject the null hypothesis that the distributions are equivalent at a 95% confidence level. 

Recalling that a KS statistic of <0.10 was targeted for the distribution of half hill distance, this 

sample achieved a KS statistic of 0.098 and a P-value of 0.631 and failed to reject the null 

hypothesis that the distributions are equivalent at a 95% confidence level.
37

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 39. Comparison of distance-based, cumulative distributions between national activityweighted dataset and sample profile “150508 65mph 15mi 467684of1e6iter” in terms of absolute 

road grade (left) and half hill distance (right)

The second proposed road grade profile, named “150508 65mph 15mi 883894of1e6iter” (name 

denotes date of generation, target test speed, target distance, and iteration count), for 65-mph 

testing is shown in Figure 40. The red dashed line in the elevation subplot shows that the profile 

is net zero elevation.

Figure 40. Elevation and road grade profile from sample “150508 65mph 15mi 883894of1e6iter”

Red dashed line on elevation subplot shows net zero elevation change.
38

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Distance-based cumulative distributions of absolute road grade and half hill distance for sample 

profile “150508 65mph 15mi 883894of1e6iter” are shown in Figure 41. National activityweighted cumulative distributions of the same parameters are provided as reference for the 

degree of match to the national dataset. Recalling that the KS statistic is a measure of similarity 

between two distributions and that a KS statistic of <0.05 was targeted for the distribution of 

absolute road grade, this sample achieved a KS statistic of 0.047 and a P-value of 0.266 and 

failed to reject the null hypothesis that the distributions are equivalent at a 95% confidence level. 

Recalling that a KS statistic of <0.10 was targeted for the distribution of half hill distance, this 

sample achieved a KS statistic of 0.094 and a P-value of 0.621 and failed to reject the null 

hypothesis that the distributions are equivalent at a 95% confidence level.

Figure 41. Comparison of distance-based cumulative distributions between national activityweighted dataset and sample profile “150508 65mph 15mi 883894of1e6iter” in terms of absolute 

road grade (left) and half hill distance (right)

4.2 Local Routes

As an alternative to generating synthetic grade profiles, the potential for extracting real-world 

grade profiles from continuous sections of highway using the TomTom national road grade 

database was explored. To this end, a procedure was established for processing the national 

network of controlled access highways and identifying stretches with statistics representative of 

the previously developed national activity-weighted distributions.

An example of this processing routine can be seen in Figure 42. For this example 13-mile stretch 

of highway, seven unique stretches of 10 miles or less are identified by starting at the beginning 

of the first half hill and expanding the search window as far as possible without exceeding the 

10-mile limit. The 10-mile limit in this example is an input variable for the processing routine. 

This process is repeated from the beginning of the next sequential half hill until the end of the 

highway has been reached. For each unique stretch of highway, local distributions of grade by 

distance and half hill length are compared to the national activity-weighted distributions. A KS 

statistic is calculated for both the grade and distance distributions, and segments where both KS

statistics are less than a predefined tolerance are recorded for further inspection.
39

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 42. Example 13-mile stretch of roadway segmented into 16 half hills and grouped into 

seven continuous stretches of 10 miles or less

For this exercise, input segment distance was swept from 5 to 20 miles in 1-mile increments, 

resulting in inspection of approximately 3-million unique segments, and segments where 

absolute road grade and half hill distance KS statistics were below 0.10 and 0.15, respectively, 

were recorded. In order to satisfy the requirement that example grade profiles feature net zero 

elevation, local routes in this section would necessarily be mirrored to reflect round-trip travel 

over a stretch of road (effectively doubling the distance of the example profile).

Additionally, a handful of criteria were imposed during the identification of local routes to 

facilitate potential on-road testing, including:

• Routes must feature identical grade profile in both directions of travel (to ensure net zero 

elevation change during on-road testing in support of the assumption that one-way 

profiles can be mirrored to create round-trip profiles)

• Prefer routes in areas designated by the U.S. Census as rural (decrease potential for traffic 

to interfere with on-road testing)

• Prefer routes south of the 40th parallel north [Kansas/Nebraska border] (decrease potential 

for winter weather to interfere with on-road testing).

4.2.1 55-mph Test Group

For the 55-mph test group, 8,826 local routes were identified with KS statistics less than 0.10 

and 0.15 for distributions of absolute road grade and half hill distance, respectively. Local route 

KS statistics for distributions of absolute road grade and half hill distance are plotted in Figures 

43 and 44 versus round-trip profile distance (color bands represent the sweep of input distance 

limit). As with the generation of synthetic grade profiles, we see a general trend towards lower 

KS statistics (implying better matches to the national activity-weighted distributions) as route 

distance is increased.
40

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 43. Local route KS statistics for the distribution of absolute road grade versus round-trip

profile distance for the 55-mph test group

Figure 44. Local route KS statistics for the distribution of half hill distance versus round-trip

profile distance for the 55-mph test group
41

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Only one local route was able to simultaneously achieve KS statistics of less than 0.05 and 0.10 

for distributions of absolute road grade and half hill distance, respectively (minimum criteria 

established for selection of synthetic routes in Section 4.1). Consequently, the performance 

criteria were adjusted for local routes such that candidate profiles must feature KS statistics of 

less than 0.05 and 0.15 for distributions of absolute road grade and half hill distance, 

respectively. This decision reflects the perceived priority for example grade profiles to match 

national activity-weighted distributions of absolute road grade with a greater level of accuracy 

relative to distributions of half hill distance.

Three local routes satisfying the new statistical criteria and conditions facilitating on-road testing 

have been identified:

• I-20 east of Abilene, Texas

• I-70 east of Glenwood Springs, Colorado

• Kentucky State Route (SR) 9001 (Western Kentucky Parkway) south of Louisville, 

Kentucky

Figures 45 through 47 present the three local routes that are similar to the national activityweighted distributions for the 55-mph test group (segments of interest highlighted in magenta).

Figure 45. Local route from I-20 east of Abilene, Texas, statistically similar to national activityweighted distributions for the 55-mph test group

(Google Maps credit: © 2015 Google, Map Data © 2015 Tele Atlas)
42

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 46. Local route from I-70 east of Glenwood Springs, Colorado, statistically similar to 

national activity-weighted distributions for the 55-mph test group

(Google Maps credit: © 2015 Google, Map Data © 2015 Tele Atlas)

Figure 47. Local route from Kentucky SR-9001 south of Louisville, Kentucky, statistically similar to

national activity-weighted distributions for the 55-mph test group

(Google Maps credit: © 2015 Google, Map Data © 2015 Tele Atlas)

One-way relative elevation and grade profiles for the three local routes similar to the national 

activity-weighted distributions for the 55-mph test group are shown in Figures 48 through 50.
43

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 48. Local route from I-20 east of Abilene, Texas, statistically similar to national activityweighted distributions for the 55-mph test group

Figure 49. Local route from I-70 east of Glenwood Springs, Colorado, statistically similar to 

national activity-weighted distributions for the 55-mph test group
44

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 50. Local route from Kentucky SR-9001 south of Louisville, Kentucky, statistically similar to

national activity-weighted distributions for the 55-mph test group

Graphical representations of the cumulative distributions of absolute road grade and half hill 

distance from the three local routes similar to the national activity-weighted distributions for the 

55-mph test group can be found in Figures 51 through 53.

Figure 51. Comparison of distance-based cumulative distributions between national activityweighted dataset and local profile from I-20 east of Abilene, Texas, in terms of absolute road 

grade (left) and half hill distance (right)
45

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 52. Comparison of distance-based cumulative distributions between national activityweighted dataset and local profile from I-70 east of Glenwood Springs, Colorado, in terms of 

absolute road grade (left) and half hill distance (right)

Figure 53. Comparison of distance-based cumulative distributions between national activityweighted dataset and local profile from Kentucky SR-9001 south of Louisville, Kentucky, in terms 

of absolute road grade (left) and half hill distance (right)
46

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Summary statistics for the three local routes identified for the 55-mph test group are provided in 

Table 2, including: one-way and round-trip distances, segment start and end coordinates, and KS 

hypothesis test results. All three local routes passed KS hypothesis testing at a 95% confidence 

level for similarity to the national activity-weighted distributions of absolute road grade and half 

hill distance (i.e., failed to reject the null hypothesis that the local and national distributions are 

equivalent).

Table 2. Summary of three local routes statistically similar to national activity-weighted

distributions for the 55-mph test group

I-20 east of 

Abilene, TX

I-70 east of 

Glenwood 

Springs, CO

Kentucky SR9001 south of 

Louisville, KY

One-way distance, mi 18.8 14.0 14.0

Round-trip distance, mi 37.5 28.0 28.0

Segment start latitude 32.3756 39.5586 37.3885

Segment start longitude -99.0450 -107.3395 -86.6981

Segment end latitude 32.3957 39.6166 37.3444

Segment end longitude -99.3620 -107.1319 -86.9353

KS statistic (grade) 0.048 0.046 0.049

P-value (grade) 0.027 0.052 0.054

Hypo Test Result (grade) Fail to reject Fail to reject Fail to reject

KS statistic (HH dist) 0.098 0.128 0.140

P-value (HH dist) 0.464 0.328 0.390

Hypo test result (HH dist) Fail to reject Fail to reject Fail to reject
47

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

4.2.2 65-mph Test Group

For the 65-mph test group, 7,424 local routes were identified with KS statistics less than 0.10 

and 0.15 for distributions of absolute road grade and half hill distance, respectively. Local route 

KS statistics for distributions of absolute road grade and half hill distance are plotted in Figures 

54 and 55 versus round-trip profile distance (color bands represent the sweep of input distance 

limit). As with the generation of synthetic grade profiles, we see a general trend towards lower 

KS statistics (implying better matches to the national activity-weighted distributions) as route 

distance is increased.

Figure 54. Local route KS statistics for the distribution of absolute road grade versus round-trip

profile distance for the 65-mph test group
48

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 55. Local route KS statistics for the distribution of half hill distance versus round-trip

profile distance for the 65-mph test group

Only one local route was able to simultaneously achieve KS statistics of less than 0.05 and 0.10 

for distributions of absolute road grade and half hill distance, respectively (minimum criteria 

established for selection of synthetic routes in Section 4.1). Consequently, the performance 

criteria were adjusted for local routes such that candidate profiles must feature KS statistics of 

less than 0.05 and 0.15 for distributions of absolute road grade and half hill distance, 

respectively. This decision reflects the perceived priority for example grade profiles to match 

national activity-weighted distributions of absolute road grade with a greater level of accuracy 

relative to distributions of half hill distance.

Two local routes satisfying the statistical criteria and conditions facilitating on-road testing have 

been identified:

• I-10 west of San Antonio, Texas

• I-40 west of Gallup, New Mexico

Maps of the two local routes similar to the national activity-weighted distributions for the 65-

mph test group are shown in Figures 56 and 57 (segment of interest highlighted in magenta).
49

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 56. Local route from I-10 west of San Antonio, Texas, statistically similar to national

activity-weighted distributions for the 65-mph test group

(Google Maps credit: © 2015 Google, Map Data © 2015 Tele Atlas)

Figure 57. Local route from I-40 west of Gallup, New Mexico, statistically similar to national

activity-weighted distributions for the 65-mph test group

(Google Maps credit: © 2015 Google, Map Data © 2015 Tele Atlas)

One-way relative elevation and grade profiles for the two local routes similar to the national 

activity-weighted distributions for the 65-mph test group are shown in Figures 58 and 59.
50

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Figure 58. Local route from I-10 west of San Antonio, Texas, statistically similar to national 

activity-weighted distributions for the 65-mph test group

Figure 59. Local route from I-40 west of Gallup, New Mexico, statistically similar to national

activity-weighted distributions for the 65-mph test group
51

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Graphical representations of the cumulative distributions of absolute road grade and half hill 

distance from the two local routes similar to the national activity-weighted distributions for the 

65-mph test group are shown in Figures 60 and 61.

Figure 60. Comparison of distance-based cumulative distributions between national activityweighted dataset and local profile from I-10 west of San Antonio, Texas, in terms of absolute road 

grade (left) and half hill distance (right)

Figure 61. Comparison of distance-based cumulative distributions between national activityweighted dataset and local profile from I-40 west of Gallup, New Mexico, in terms of absolute road 

grade (left) and half hill distance (right)
52

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

Summary statistics for the two local routes identified for the 65-mph test group are provided in 

Table 3 including: one-way and round-trip distances, segment start and end coordinates, and KS

hypothesis test results. Both local routes passed KS hypothesis testing at a 95% confidence level 

for similarity to the national activity-weighted distributions of absolute road grade and half hill 

distance (i.e., failed to reject the null hypothesis that the local and national distributions are 

equivalent).

Table 3. Summary of two local routes statistically similar to national activity-weighted

distributions for the 65-mph test group

I-10 west of San 

Antonio, Texas

I-40 west of Gallup, 

New Mexico

One-way Distance, mi 15.9 13.0

Round-trip Distance, mi 31.9 25.9

Segment Start Latitude 30.5226 35.2994

Segment Start Longitude -99.8762 -109.1330

Segment End Latitude 30.4654 35.2204

Segment End Longitude -100.1276 -109.3259

KS Statistic (grade) 0.046 0.041

P-Value (grade) 0.031 0.274

Hypo Test Result (grade) Fail to reject Fail to reject

KS Statistic (hh dist) 0.094 0.147

P-Value (hh dist) 0.599 0.370

Hypo Test Result (hh dist) Fail to reject Fail to reject
53

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

5 Known Limitations and Potential for Future Work

Development of sample grade profiles in this analysis has been intended to be directly coupled to 

constant-speed drive cycles at 55- and 65-mph for EPA certification testing and simulation 

activities. This type of duty cycle (constant speeds on positive and negative grades) is known to 

misrepresent real-world operation of MD/HD trucks.

Whether due to driving style or vehicle power limitations, on-road data suggest there is a 

correlation between road grade and transient highway speeds for MD/HD trucks. This 

observation is consistent with the SwRI on-road testing of a class 8 combination truck near San 

Antonio, Texas (described in Section 2.1.1). Figure 62 provides a 10-minute snapshot of this 

testing at highway speeds and over a number of steep hills. The correlation between vehicle 

speed and road grade is highlighted for the six instances where the measured road grade 

exceeded +4%. Vehicle speed consistently drops on these sections of climb (from approximately 

75 to 55 mph in the last instance), and on three occasions this drop in vehicle speed coincides 

with a transmission down-shifting event.

Figure 62. Vehicle fueling rate, road grade, vehicle speed, and vehicle to engine speed ratio for a 

10-minute section of SwRI on-road testing of a class 8 combination truck

Given the apparent mismatch between dynamometer testing at constant highway speeds over 

varying road grade and observed real-world operation, NREL and the EPA have identified the 

need to refine existing vehicle test speeds for highway cycles at grade. Development of a fully 

integrated speed and grade duty cycle for highway testing and simulation is the focus of an ongoing project between NREL and EPA.
54

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6 References

[1] U.S. Environmental Protection Agency. (2011). “EPA and NHTSA Adopt First-Ever 

Program to Reduce Greenhouse Gas Emissions and Improve Fuel Efficiency of 

Medium- and Heavy-Duty Vehicles.” EPA-420-F-11-031. Office of Transportation 

and Air Quality. Accessed February 16, 2015. 

http://www.epa.gov/otaq/climate/documents/420f11031.pdf

[2] U.S. Environmental Protection Agency. (2011). “Final Rulemaking to Establish 

Greenhouse Gas Emission Standards and Fuel Efficiency Standards to Medium- and 

Heavy-Duty Engines and Vehicles: Regulatory Impact Analysis.” EPA-420-R-11-

901. Office of Transportation and Air Quality and National Highway Traffic Safety 

Administration. Accessed February 16, 2015. 

http://www.epa.gov/otaq/climate/documents/420r11901.pdf

[3] Federal Register. (2011). “Greenhouse Gas Emissions Standards and Fuel Efficiency 

Standards for Medium- and Heavy-Duty Engines and Vehicles: Final Rule.” 

Environmental Protection Agency and Department of Transportation. (76:179); 

Accessed February 16, 2015. http://www.gpo.gov/fdsys/pkg/FR-2011-09-

15/pdf/2011-20740.pdf

[4] U.S. Environmental Protection Agency. (February 10, 2015). “Transportation and 

Climate: Regulations & Standards: Heavy-Duty.” Office of Transportation and Air 

Quality. Accessed February 16, 2015. http://www.epa.gov/otaq/climate/regs-heavyduty.htm

[5] The White House, Office of the Press Secretary. (February 18, 2014). “Remarks by 

the President on Fuel Efficiency Standards of Medium and Heavy-Duty Vehicles.” 

Accessed February 16, 2015. http://www.whitehouse.gov/the-pressoffice/2014/02/18/remarks-president-fuel-efficiency-standards-medium-and-heavyduty-vehicl

[6] The White House, Office of the Press Secretary. (February 18, 2014). “FACT 

SHEET: Opportunity for All: Improving the Fuel Efficiency of American Trucks –

Bolstering Energy Security, Cutting Carbon Pollution, Saving Money and Supporting 

Manufacturing Innovation.” Accessed February 16, 2015. 

http://www.whitehouse.gov/the-press-office/2014/02/18/fact-sheet-opportunity-allimproving-fuel-efficiency-american-trucks-bol

[7] “Transportation Secure Data Center.” (2014). National Renewable Energy 

Laboratory. Accessed October 31, 2014: www.nrel.gov/tsdc

[8] Walkowicz, K.; Kelly, K.; Duran, A.; Burton, E. (2014). Fleet DNA Project Data. 

National Renewable Energy Laboratory. http://www.nrel.gov/fleetdna
55

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

[9] National Renewable Energy Laboratory. (2013). “DRIVE Analysis Tool Generates 

Custom Vehicle Drive Cycles Based on Real-World Data.” NREL/FS-5400-54507. 

Golden, CO: National Renewable Energy Laboratory. Accessed February 16, 2015. 

http://www.nrel.gov/docs/fy13osti/54507.pdf

[10] Boriboonsomsin, K. and Barth, M. “Impacts of Road Grade on Fuel Consumption and 

Carbon Dioxide Emissions Evidenced by Use of Advanced Navigation Systems” 

Transportation Research Record: Journal of the Transportation Research Board, No. 

2139, Transportation Research Board of the National Academies, Washington, D.C., 

2009, pp. 21–30. DOI: 10.3141/2139-03 

http://trb.metapress.com/content/g77x60gv21123376/?genre=article&id=doi%3a10.3

141%2f2139-03

[11] Boroujeni, B.Y. and Frey, H.C. “Road grade quantification based on global 

positioning system data obtained from real-world vehicle fuel use and emissions 

measurements” Atmospheric Environment 85 (2014) 179-186, 

http://www.sciencedirect.com/science/article/pii/S1352231013009709#

[12] Wyatt, D.W., Li, H., and Tate, J.E. “The impact of road grade on carbon dioxide 

(CO2) emission of a passenger vehicle in real-world driving” Transportation Research 

Part D 32 (2014) 160–170, 

http://www.sciencedirect.com/science/article/pii/S136192091400100X

[13] Wood, E., Burton, E., Duran, A., and Gonder, J. “Contribution of road grade to the 

energy use of modern automobiles across large datasets of real-world drive cycles” 

SAE World Congress, April 2014, 2014-01-1789, 

http://www.nrel.gov/docs/fy14osti/61108.pdf

[14] Scora, G.A. “Heavy Duty Diesel Particulate Matter and Fuel Consumption Modeling 

for Transportation Analysis” Doctor of Philosophy Dissertation, University of 

California Riverside, March 2012, http://escholarship.org/uc/item/4sj7914b

[15] Franzese, O. “Effect of Weight and Roadway Grade on the Fuel Economy of Class-8 

Freight Trucks” Oak Ridge National Laboratory Technical Report, ORNL/TM2011/471, October 2011, 

http://cta.ornl.gov/cta/Publications/Reports/ORNL_TM_2011_471.pdf

[16] Delorme, A., Karbowski, D., Vijayagopal, R., and Sharer, P. “Evaluation of Fuel 

Consumption Potential of Medium and Heavy Duty Vehicles through Modeling and 

Simulation” Argonne National Laboratory Technical Report to National Academy of 

Sciences, October 2009, DEPS-BEES-001, http://www.autonomie.net/docs/6%20-

%20Papers/nas_mediumheavyduty_2009.pdf

[17] Ates, M., and Matthews, R., "Coastdown Coefficient Analysis of Heavy-Duty 

Vehicles and Application to the Examination of the Effects of Grade and Other 

Parameters on Fuel Consumption," SAE Technical Paper 2012-01-2051, 2012, 

doi:10.4271/2012-01-2051. http://papers.sae.org/2012-01-2051/
56

This report is available at no cost from the National Renewable Energy Laboratory (NREL) at www.nrel.gov/publications.

[18] Southwest Research Institute. (July 10, 2014). “Mobile Autonomous Robotics 

Technology Initiative Program.” Accessed February 16, 2015. www.marti.swri.org/

[19] United States Geological Survey. “The National Map.” Accessed April 21, 2014. 

http://nationalmap.gov/viewer.html

[20] United States Geological Survey. “National Elevation Dataset.” Accessed April 21, 

2014. http://ned.usgs.gov/

[21] United States Geological Survey. “3D Elevation Program (3DEP).” Accessed March 

2, 2015. http://nationalmap.gov/3DEP/

[22] Wood, E.; Burton, E.; Duran, A.; Gonder, J. (2014). Appending High-Resolution 

Elevation Data to GPS Speed Traces for Vehicle Energy Modeling and Simulation.

NREL/TP-5400-61109. Golden, CO: National Renewable Energy Laboratory. 

http://www.nrel.gov/docs/fy14osti/61109.pdf

[23] “TomTom MultiNet.” (2015). TomTom International. Accessed February 16, 2015. 

https://www.tomtom.com/en_gb/licensing/products/maps/multinet/

[24] “TomTom Advanced Driving Attributes: Road Grade.” (2015). TomTom 

International. Accessed February 16, 2015. http://automotive.tomtom.com/en/realtime-maps/adas-advanced-driver-assistance-systems

[25] TomTom International. (2013). MultiNet Advanced Driving Attributes 1.1: Data and 

Format Specifications. Document Version 1.0.0.

[26] “TomTom Logistics” TomTom International. Accessed March 17, 2015. 

http://www.tomtom.com/en_gb/licensing/products/enhanced-content/guide/logistics/

[27] Neubauer, J.; Wood, E. “Accounting for the Variation of Driver Aggression in the 

Simulation of Conventional and Advanced Vehicles.” Preprint. NREL/CP-5400-

57503. Presented at SAE World Congress, April 16–18, 2013. Golden, CO: National 

Renewable Energy Laboratory. 10 pp. http://www.nrel.gov/docs/fy13osti/57503.pdf

[28] Massachusetts Institute of Technology. “Chapter 5: Nonparametric Statistics and 

Model Selection.” In 6.S085 Statistics for Research Projects: IAP 2015. Accessed 

February 16, 2015. http://www.mit.edu/~6.s085/notes/lecture5.pdf

[29] Massachusetts Institute of Technology, Open Courseware, Statistics for Applications. 

“Section 13: Kolmogorov-Smirnov Test.” pp 83-90. Accessed February 16, 2015. 

http://ocw.mit.edu/courses/mathematics/18-443-statistics-for-applications-fall2006/lecture-notes/lecture14.pdf

[30] Mathworks, MATLAB Documentation. (2015). “kstest2: Two sample KolmogorovSmirnov test.” Accessed February 16, 2015. 

http://www.mathworks.com/help/stats/kstest2.html?refresh=true
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Appendix A: Supporting Documentation

A.1 Generating Distributions of Road Grade on Basis of Absolute 

Values

The impact of road grade on MD/HD truck fuel economy and emissions can generally be 

categorized into three elevation profiles:

A. Net elevation deltas (change in potential energy between start and end of a given trip)

B. Cumulative elevation deltas (multiple offsetting elevation changes in a trip with no 

net elevation delta)

C. A combination of types A and B.

These general elevation profiles are shown graphically in Figure A1.

Figure A1. Three generalized categories of elevation profiles

Over the course of a vehicle’s lifetime (potentially hundreds of thousands of miles), the impact 

of net elevation deltas (types A and C) is believed to be essentially negligible. For an extreme 

example, consider a HD truck with a relatively short service life of one hundred thousand miles 

that begins its life at sea level (approximate elevation: 0 ft.) and ends its life in the Rocky 

Mountains near the Continental Divide (approximate elevation: 12,000 ft.). This truck would 

experience a lifetime distance-averaged grade of less than 0.003%.

With this in mind, it becomes clear that a certification test cycle with road grade must contain a 

net zero elevation delta. Any other cycle would imply perpetual descent or climb (an obviously 

non-existent attribute of U.S. driving).

Additionally, road grades on such a test cycle can be fully described by their distribution of 

absolute grades. For example, consider the 2.8-mile stretch of road shown in Figure A2. In 

addition to exhibiting a net positive change in elevation, inspection of the grade histogram 

reveals the majority of distance presenting at positive grades.
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Figure A2. Elevation profile, grade profile, and grade histogram for example 2.8-mile stretch of 

road

Now consider a round-trip on the same 2.8-mile section of road as shown in Figure A3. 

Traveling in both directions over the same stretch of road, the elevation profile is net-zero and a 

grade histogram is symmetrical about 0% grade.

Figure A3. Elevation profile, grade profile, and grade histogram for round trip on example 2.8-mile 

stretch of road

When considering that round-trip travel on any section of road results in a grade histogram that is 

symmetric about 0% grade, it becomes evident that the grade content of any road can be fully 

described by the histogram of absolute road grade in one direction as shown in Figure A4 for our 

example roadway.
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Figure A4. Elevation profile, absolute grade profile, and absolute grade histogram for example 2.8-

mile stretch of road

A.2 Horizontal versus Projected Roadway Distance

All distances in this analysis are calculated as the horizontal component of the actual roadway 

distance. These distance calculations do not take the height or slope of the roadway into account. 

This methodology is consistent with the road network distances provided in the TomTom 

MultiNet database and with geographic information system analysis of this type in general.

While road grades on the order of 1%–2% have significant impact on MD/HD vehicle fuel 

economy and emissions, the impact on driven distance is nearly negligible. For example, 

calculation of horizontal distance on a 6% grade underreports driven distance by less than 0.2%. 

Given the national distribution of road grades presented in this analysis, it is estimated that 

roadway distance at the national level is underreported by less than 0.02% as a result of 

neglecting the vertical component of roadway distance.

A.3 Kolmogorov-Smirnov Hypothesis Testing

The degree to which sample grade profiles are statistically representative of national data was 

quantified using Kolmogorov-Smirnov (KS) hypothesis testing. KS testing is a widely used 

procedure for evaluating the statistical similarity of two cumulative distributions [28–30]. The 

primary input to KS hypothesis testing is the supremum of the two distributions over the region 

of interest and is referred to as the KS statistic. The supremum of two distributions is evaluated 

via Equation A1.

ss = mmmx( a (d1( ) − d2( ))) (A1)

Where d1(x) is the national cumulative distribution we are targeting to match, d2(x) is the sample 

cumulative distribution (generated via synthetic or data mining methods), and maxx is maximum 

of a one-dimensional array with respect to input variable x (e.g., absolute road grade or half hill 

distance). 

Figure A5 provides an example supremum calculation using the national distance-based, 

activity-weighted, cumulative distribution of absolute road grade from the 55-mph test group and 

a synthetically generated sample test profile. The synthetic generation process is described in 
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Section 4.1. From this example, we observe that the most significant discrepancy between the 

national and sample distributions occurs at an absolute road grade of approximately 2.5%. 

Approximately 85% of distances from the national data occur at or below 2.5% absolute grade, 

while 95% of the sample profile distance occurs at or below 2.5% grade. Calculating the 

supremum of these two distributions results in a KS statistic of approximately 0.10 (or 10%).

Figure A5. Supremum measurement example for national and synthetic cumulative distributions 

of absolute road grade

The KS statistic is incorporated with the sample size of each distribution in KS hypothesis 

testing to determine if the two distributions can be considered statistically equivalent at a given 

confidence level. A confidence level of 95% was used as the default for this analysis.

With a null hypothesis that the two distributions are statistically equivalent, KS hypothesis 

testing will either reject the null hypothesis (implying that the two datasets have been

demonstrated to be statistically different) or fail to reject the null hypothesis (implying that the 

two datasets have not been demonstrated to be statistically different).
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A.4 Impact of Activity Weighting

Application of activity weights to the raw national distributions was observed to have relatively 

low impact on cumulative distributions of absolute road grade and half hill distances as observed 

in Figures 27 and 28. This result prompted a search for the underlying cause of activityweighting having minimal impacts.

The first theory explored was that distance- and activity-based weights at the county level could 

be quite similar. To test this theory, distance- and activity-based county weights scatter against 

one another in Figure A6. A least squares linear fit to the data resulted in an R2 value of 0.6876. 

While this shows that there was indeed some correlation between the two sets of weighting 

terms, we wanted to know more about the counties with large discrepancies between distanceand activity-based weights.

Figure A6. Scatter of activity-based versus distance-based county weights for the sample of 1,728 

U.S. counties with controlled access highways

Our next step was to scatter average absolute grade versus the difference between activity- and 

distance-based weights (as shown in Figure A7). Two solid lines are provided for reference on 

this plot: 1) the vertical green line indicates counties with identical activity- and distance-based 

weights, and 2) the horizontal red line indicates the average absolute grade across all counties.
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Figure A7. Scatter of average absolute road grade versus the difference between activity- and 

distance-based weights for the sample of 1,728 U.S. counties with controlled access highways

In order for application of activity weights to significantly impact our national raw distributions, 

a large number of counties would have need to have significant discrepancies between activityand distance-based weights AND those counties would also have to exhibited statistics deviating 

from the average county. This analysis shows that while a number of data points met one of these 

criteria, very few met both. Consequently, the conclusion that application of activity-weighting 

to our raw distributions had relatively little impact is considered defensible.

A.5 Distributions of Grade by Distance versus Distributions of 

Average Half Hill Grade

National road grade distributions were developed by two methods in this analysis:

• Section 3.1, Grade by Distance: Query all U.S. controlled access roads at uniform 52.8-

foot intervals (100 points per mile) using linear interpolation

• Section 3.2, Average Half Hill Grade: Segment U.S. controlled access highway 

network into half hill sections and measure distance-averaged grade from each section.

National distributions of road grade by distance introduced in Section 3.1 were selected as the 

primary road grade metric in this analysis. Activity-weighting was applied to grade by distance 

distributions in Section 3.3 and used as the target for sample synthetic and local profiles 

presented in Section 4. By selecting grade by distance distribution as national target metric, this 

analysis seeks to develop sample grade profiles with proportions of driven distance at each grade 

bin that are comparable to national estimates for MD/HD trucks.

Aggregation of road grade data into half hill averages results in the loss of information regarding 

the distribution of grade within each half hill. Even when correcting for half hill distance, half 

hill aggregations feature a lower degree of grade variability relative to grade by distance 

distributions. Figure A8 illustrates this point by plotting the national raw distance-based 

cumulative distributions of grade by distance and average half hill grade for the composite 55-
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mph test group (a plot of the 65-mph test group features similar trends). This plot confirms the 

expected lack of variability exhibited by the distribution of average half hill grade. The national 

distribution of grade by distance can be seen to exhibit significantly higher percentages of data 

below 0.5% grade and above 2.5% grade.

Figure A8. Raw distance-based cumulative distributions of grade by distance and average half hill 

grade for the 55-mph test group
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Appendix B: Supplementary Distributions from Half 

Hill Analysis

Half hill analyses (discussed in Section 3.2) resulted in the generation of multiple data 

distributions with regard to distance, average grade, and grade ratio (maximum to average). 

These distributions were segmented by truck speed limit and half hill distance, plotted as 

frequency- and distance-based distributions, and generated with and without activity weighting. 

While many of these distributions were not incorporated into the body of the analysis, 

supplementary distributions are provided in Figures B1 through B9 as points of reference.

Figure B1. Raw frequency-based cumulative distributions of half hill distance by truck speed limit
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Figure B2. Raw frequency-based cumulative distributions of half hill average grade by truck speed 

limit

Figure B3. Raw distance-based cumulative distributions of half hill average grade by truck speed 

limit
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Figure B4. Activity-weighted distance-based cumulative distributions of half hill average grade by 

truck speed limit

Figure B5. Raw frequency-based cumulative distributions of half hill average grade by half hill 

distance
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Figure B6. Raw frequency-based cumulative distributions of half hill grade ratio (maximum to 

average half hill grade) by truck speed limit

Figure B7. Raw distance-based cumulative distributions of half hill grade ratio (maximum to 

average half hill grade) by truck speed limit
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Figure B8. Activity-weighted distance-based cumulative distributions of half hill grade ratio 

(maximum to average half hill grade) by truck speed limit

Figure B9. Raw frequency-based cumulative distributions of half hill grade ratio (maximum to 

average half hill grade) by half hill distance