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 a n 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

- 201 4

- 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 repo r t 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” 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, bu t 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 re presentative 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 po pulation. Any half hill in this profile is associated with a single segment

and vice versa

. The activity assigned to a ny segment , defined as in the N REL 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 h alf hill in the profile ( length, average grade, maximum grad e , grade distribution ) are based on parameters of half hill s 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.2

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 en ables p roper activity weighting of all profile parameters and characteristics

. For half hill length t he process, illustrated in Figure 1, starts with defining the length of the longest half hill, as thi s 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 length s ranged fr om 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 w as to be met

. After some iteration, the agencies

settled on 2.78 miles . This half hill length i s 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 16 153

repeated until th e 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 d o not match . Fo r example, t he first one attains the 10 0% 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 cu mulative 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 segment4

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 we re used to construct v arious versions of t he 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 r equirement, and the half hills we re sequenced in such a way as to ensure that the profile

starts and ends at the same elevation. Once that wa s achieved , the progression of grade alon g the length

of each half hill was defined by applying methodology described in Section 4.1 of NREL re po rt
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 l ongest 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 uni ts in file EPA_SyntheticRoadGradeProfile .xls x available in the docket.5

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 speci fic road grade

distributions into each half hill of the profile is planned. In addition , separate 55 and 65 mph pro files, analogous to those described in NREL re port 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”.