UNITED STATES ENVIRONMENTAL PROTECTION AGENCY

NATIONAL VEHICLE AND FUEL EMISSIONS LABORATORY

2565 PLYMOUTH ROAD

ANN ARBOR, MI 48105-2498

 

OFFICE OF

 AIR 

AND RADIATION

May 13, 2015

MEMORANDUM

SUBJECT: Development of an Alternative, Nationally Representative, Activity Weighted Road 

Grade Profile for Use in EPA GHG Certification of Medium- and Heavy-Duty Vehicles

FROM: Rafal A. Sobotowski, Engineer, OTAQ/ASD

TO: Greenhouse Gas Emissions Standards and Fuel Efficiency Standards for Medium- and 

Heavy-Duty Engines and Vehicles - Phase 2 - Docket EPA-HQ-OAR-2014-0827

Introduction

This memorandum presents a road grade profile developed by the EPA and NHTSA (“the agencies”) as 

an alternative to the profiles designed by the National Renewable Energy Laboratory (NREL) and 

described in report NREL/TP-5400-63853 entitled “EPA GHG Certification of Medium- and HeavyDuty Vehicles: Development of Road Grade Profiles Representative of US Restricted Access 

Highways” also available in Docket EPA-HQ-OAR-2014-0827.

The EPA profile is based on the same national half hill database that was used by NREL, but relies on a 

different methodology of defining the parameters of half hills which constitute the profile. It is a goal of 

the agencies to present a range of options and select the most appropriate road grade profile(s) on the 

basis of being nationally representative as well as reasonably similar to real-world driving conditions.

EPA Road Grade Profile

The EPA profile relies on direct characterization of the complete activity weighted national half hill 

population, not on random sampling from that population. It consists of half hills representing unique, 

contiguous segments of that population. Any half hill in this profile is associated with a single segment

and vice versa. The activity assigned to any segment, defined as in the NREL report as vehicle miles 

travelled (VMT) by medium-duty and heavy-duty vehicles on restricted access highways, is calculated 

as the sum of activities of its constituent half hills. The parameters of each half hill in the profile

(length, average grade, maximum grade, grade distribution) are based on parameters of half hills 

constituting the particular segment. This provides a clear interpretation of why a particular half hill in 

the profile is associated with a particular length, grade distribution, average grade or maximum grade. 
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The complete national half hill population is split into segments in such a way that that the lengths of all 

half hills in this nationally representative profile are directly proportional to the share of activity their 

segments represent. This enables proper activity weighting of all profile parameters and characteristics. 

For half hill length the process, illustrated in Figure 1, starts with defining the length of the longest half 

hill, as this parameter defines the total length of the profile. In this particular example, the desired 

length of the profile was 11-12 miles. All half hills spanning the 55-75 mph range of truck speed limits 

in the NREL database were used. Their lengths ranged from 0.01 to 24.98 miles.

Figure 1. Segmentation of the half hill dataset

Based on prior experience with profile designs, it was estimated that the longest half hill in the profile 

should not exceed 3.0 miles if the above requirement was to be met. After some iteration, the agencies

settled on 2.78 miles. This half hill length is the arithmetic mean length of the 8,402 longest half hills in 

the database representing 25% of activity. This defined the bounds of Segment 20 (1.77 and 24.98 

miles) as shown in Figure 1. The ratio of half hill length to normalized activity identified for Segment 

20 (namely 2.87/0.25 = 11.48), was subsequently used as the main criterion in defining the lengths of all 

the remaining half hills of the profile. Specifically, starting with the lower bound of Segment 20 as the 

upper bound of Segment 19, the lower bound of Segment 19 was shifted left until the ratio of mean half 

hill length for this segment to normalized activity reached 11.48. This process was successfully 

0.0 0.5 1.0 1.5 2.0 2.5 3.0

Half Hill Length, mi

0.00

0.10

0.20

0.30

0.40

0.50

0.60

0.70

0.80 Activity

Mean length of half hill in segment Binned activity

Segment 20

Segment 19

18

17

16

15
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repeated until the whole half hill dataset was exhausted in Segment 1. Detailed results of this process 

are provided in Table 1.

Table 1. Segmentation of the half hill dataset

The activity weighted distribution of half hills identified in the segmentation process described above is 

compared in Figure 2 to the national activity weighted, cumulative distribution of half hill length. At 

first look, the two distributions do not match. For example, the first one attains the 100% of cumulative 

activity at 2.87 miles and the other at 24.98 miles. However, the half hills identified in the segmentation 

process represent ranges of half hill length associated with the respective segments of the national half 

hill population. The cumulative activity associated with any of those segments is therefore not 

represented by the mean half hill length but by the upper bounds of the respective segments. This is 

illustrated in Figure 2 using the example of Segment 19. More specifically, the horizontal line

representing cumulative activity associated with Segment 19 intersects the upper bound of this segment 

Activity

Activity 

(A)

Mean 

Half Hill 

Distance 

(D)

D/A

% - mi -

1 0.1 0.001 0.01 16.43

2 0.3 0.003 0.04 11.49

3 0.7 0.007 0.08 11.48

4 1.1 0.011 0.13 11.48

5 1.5 0.015 0.17 11.48

6 1.8 0.018 0.21 11.48

7 2.1 0.021 0.24 11.48

8 2.4 0.024 0.28 11.48

9 2.7 0.027 0.31 11.48

10 3.1 0.031 0.35 11.48

11 3.4 0.034 0.39 11.48

12 3.9 0.039 0.44 11.48

13 4.4 0.044 0.50 11.48

14 5.0 0.050 0.57 11.48

15 5.7 0.057 0.65 11.48

16 6.6 0.066 0.76 11.48

17 7.8 0.078 0.90 11.48

18 9.6 0.096 1.10 11.48

19 12.7 0.127 1.46 11.48

20 25.0 0.250 2.87 11.48

Segment
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at a point located on the line representing the national distribution of half hill length. The same is true of 

all remaining half hills constituting this profile.

Figure 2. Cumulative activity weighted distributions of half hill lengths in the NREL database and in 

the candidate profile 

Once the lengths of all half hills were defined, they were used to construct various versions of the 

profile. In the first approximation, the arithmetic means of average grade and maximum grade were 

used in the design. The signs of average road grade in consecutive half hills were alternated, though this 

is not a firm requirement, and the half hills were sequenced in such a way as to ensure that the profile 

starts and ends at the same elevation. Once that was achieved, the progression of grade along the length 

of each half hill was defined by applying methodology described in Section 4.1 of NREL report 

NREL/TP-5400-63853 entitled “EPA GHG Certification of Medium- and Heavy-Duty Vehicles: 

Development of Road Grade Profiles Representative of US Restricted Access Highways”. 

The resulting profile shown in Figure 3 is 11.48 miles (18.44 km) long, its longest half hill spans 2. 87 

miles (4.47 km) and its highest grade equals 2.5%. The net elevation change between its beginning and 

end equals 7 cm. Detailed numerical representation of this profile is provided in metric units in file 

EPA_SyntheticRoadGradeProfile.xlsx available in the docket.
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Figure 3. EPA road grade profile 

Work is continuing to further refine this profile. Alternate approaches to weighting half hill length, 

average grade and maximum grade are being evaluated and incorporation of half hill specific road grade 

distributions into each half hill of the profile is planned. In addition, separate 55 and 65 mph profiles, 

analogous to those described in NREL report NREL/TP-5400-63853, are being considered. The 

agencies have analyzed the effect of different road grade profiles on vehicle performance as simulated in 

GEM and describe these in a memorandum to the docket titled, “Possible Tractor, Trailer, and 

Vocational Vehicle Standards Derived from Alternative Road Grade Profiles”.