In each program, a boom was fabricated and attached to the tractor such that an anemometer could be placed approximately 2-3 meters in front of the tractor at the approximate midpoint of the tractor's cross section.  A sample setup in the Michigan testing is shown in 2.1.  An ultrasonic anemometer was used in the Michigan testing, whereas a propeller-style anemometer was used in Lancaster.

      Figure 2.1 Photo of Boom and Anemometer Setup for Michigan Testing

First, we determined which runs were valid, based on instrument readings, weather, and other criteria.  We largely based this on data quality and SAE J2263 weather restrictions.

Using the onboard anemometer required a few corrections to the measured wind speed, which is, naturally, measured relative to the vehicle.  During the coastdown, air will "pile up" near the front of the tractor.  This causes our anemometer wind speed readings to be offset from the actual relative wind speed.  To correct for this, we calculated the ratio between the vehicle speed and measured wind speed at each data point.  For the initial Michigan program, this was calculated on the coastdown data themselves.  For the Lancaster tests, after gaining knowledge from our Michigan program, this was calculated on constant speed runs at 40 mph, 50 mph, and 60 mph, which were performed prior to the coastdowns.  We then averaged this ratio by run direction.  We then averaged each run direction's ratio for each test and applied this ratio back to the measured wind speed to estimate actual wind speed.  This calculation is described by Equation 1.
Equation 1

Vr = Relative wind speed
V = Vehicle speed
i = i[th] data record
n = number of records in each direction
dir = direction (to or from: i.e. north or south, SE or NW, etc.)

We also observed an offset to the anemometer's wind direction measurements.  For the Michigan testing, we corrected this by assuming that at high speeds, wind direction is head-on (zero degrees).  For each date, we averaged the first five seconds (25 measurements for 5-hz data) of wind direction for each run direction.  We then averaged the two directions' average.  We then subtracted the resulting value from all of the measured wind direction values to get our correct wind direction.
Equation 2

In general, the J2263 analysis method and equations were used as a foundation for this analysis:
Equation 3

We used a mixed model (through SAS(R) software) to describe our 5-hz data with the above equation.  A mixed model allows us to accurately predict the mean coefficients for each vehicle, while accounting for the scatter within each run and also the run-to-run variability when determining the standard error of the coefficient estimates.  This takes into account the fact that measurements are not independent within each run, but each run is independent from all other runs.
The equations below represent the versions of Equation 3 we modeled to determine means and significances of each of the variables.  As an initial simplification, a1, a3, and a4 were eliminated in all iterations since we determined that yaw angle did not vary enough during testing to warrant such a complex polynomial characterization.  We also set a0=1 so that the drag coefficient could be characterized by the D term.  Since our elevation change was negligible in the stretch of road on which we conducted coastdowns, the grade term was also eliminated for all runs.  The following mixed models were run:
Equation 4

Equation 5

, rewritten as
, where
MM1
Equation 6

MM2
Equation 7

MM3
Equation 8

MM4
Equation 9

MM5
Equation 10

MM6
Based on statistical significance of the various effects, one of the mixed models was chosen as the model to appropriately determine the road load coefficients.  For heavy-duty trucks, this was usually MM6.
Michigan results
In each mixed model (MM1-MM6), we found that the Bm, Cm, and E were not consistently significant from zero.  As examples, models MM4 and MM6 are described below.

In MM4, the results consistently show that Bm -  is not significant from zero.  Table 2.1 summarizes these results from the Michigan testing.  The inclusion of Bm often causes the estimates and uncertainties of the other terms to vary.

Table 2.1  -  Mixed Model MM4 Does Not Show a Significant Linear Effect on Road Load.
Date
Truck configuration (tractor_trailer_payload)
Am [lb]
% Std err
Sig from zero?
Bm [lb/mph]
Std err
Sig from zero?
D [lb/mph[2]]
% Std err
Sig from zero?
5-Aug-09
FL60_N/A_full
153.8
7.75%
Yes
0.165
497.00%
No
0.143
9.64%
Yes
6-Aug-09
FL60_N/A_full
137.7
5.24%
Yes
1.105
41.42%
Yes
0.127
5.86%
Yes
1-Sep-09
Int'l_flatbed_full
490.5
10.94%
Yes
-2.070
-177.70%
No
0.233
25.87%
Yes
2-Sep-09
Int'l_flatbed_full
483.3
7.69%
Yes
-2.065
-122.70%
No
0.237
17.99%
Yes
3-Sep-09
Int'l_flatbed_full
551.5
7.76%
Yes
-6.123
-47.40%
No
0.291
16.55%
Yes
18-Sep-09
Int'l_flatbed_half
372.2
9.72%
Yes
-1.979
-127.80%
No
0.244
17.38%
Yes
23-Sep-09
Int'l_flatbed_empty
226.3
9.38%
Yes
1.153
119.90%
No
0.174
12.27%
Yes
24-Sep-09
Int'l_box_full
521.5
6.51%
Yes
-3.480
-63.15%
No
0.248
14.11%
Yes
25-Sep-09
Int'l_box_full
495.7
8.47%
Yes
-1.149
-238.00%
No
0.208
21.04%
Yes

In MM6, the elimination of Bm shows confident and stable estimates of Am and D, with lower relative standard errors.  This indicates that the road load curve is best described by just Am and D.

Table 2.2  -  Mixed Model MM6 Shows the Most Confident Estimates of A and D.
Date
Truck configuration
(tractor_trailer_payload)
Am [N]
Am [lb]
% Std error
D [N/(m/s)[2]]
D [lb/mph[2]]
% Std error
5-Aug-09
FL60_N/A_full
693.9
156.0
3.81%
3.24
0.145
2.05%
6-Aug-09
FL60_N/A_full
676.8
152.2
2.63%
3.23
0.145
1.13%
1-Sep-09
Int'l_flatbed_full
2060.3
463.2
4.85%
4.45
0.200
6.08%
2-Sep-09
Int'l_flatbed_full
2030.6
456.5
3.71%
4.51
0.203
4.59%
3-Sep-09
Int'l_flatbed_full
2093.6
470.7
3.89%
4.25
0.191
5.55%
18-Sep-09
Int'l_flatbed_half
1539.8
346.2
3.92%
4.71
0.212
4.09%
23-Sep-09
Int'l_flatbed_empty
1076.2
242.0
4.53%
4.27
0.192
2.39%
24-Sep-09
Int'l_box_full
2119.1
476.4
3.87%
4.32
0.194
4.06%
25-Sep-09
Int'l_box_full
2136.5
480.3
4.12%
4.23
0.190
4.88%

Compared to the MM4, MM6 produces more confident mean coefficient values.  Also, for the same configurations, the MM6 shows better day-to-day variability, confirming that the coastdown procedure is repeatable from one day to the next.  Often, the MM6 model is used to simplify the road load versus speed curve through rolling resistance and aerodynamic drag coefficients.  The EPA MOVES heavy-duty inventory model and the CRC E-55/59 chassis dynamometer emissions test program are two examples of this.  In general, the equation implemented during a coastdown is:
Equation 11

Therefore,
Equation 12
                                     and
Equation 13
Equation 11 and Equation 12 assume that the rolling resistance coefficient  is wholly contained in the Am coefficient and the drag coefficient cd is wholly contained in the D coefficient.  The equations also imply that any values of Bm and Cm that would be used in the other mixed models are mechanical drag forces, other than rolling resistance, that are dependent on vehicle speed.  To check the reasonability of our results and feasibility of using our coefficients to accurately determine  and Cd, we can compare our results to other measurements of rolling resistance and drag coefficients.

Rolling Resistance Coefficient
For the International truck, we recorded the tire model and obtained different laboratory results of tire rolling resistance coefficients.  These values were determined through the SAE J1269 standard.  This standard does not contain a provision that lets a laboratory result be corrected against a reference laboratory result.  As a result, each laboratory has its own bias for any given tire.  When we weighed the truck, we recorded the weight measured over each axle: steer, drive, and trailer.  Since we had no more than one tire model on any one axle, we can weight-average the laboratory rolling resistance coefficients to estimate the truck's overall rolling resistance coefficient.
Equation 14

Figure 2.2 below compares our coastdown rolling resistance results with those from three different tire labs.  We are not naming the tire models or the laboratories to protect confidential business information.  The dimensionless rolling resistance coefficient is multiplied by 1000 for convenience (resulting "unit" is often referred to as kg/metric ton).

Figure 2.2 Coastdown-Determined and Independent Lab Rolling Resistance Coefficients Match Reasonably Well.

There are only three different labs, with four unique weightings (flatbed full, flatbed half, flatbed empty, and box full) for each lab.  Lab results were only available for the tires used on the International truck.  Our coastdown results show reliable day-to-day repeatability for the same truck configuration (Sep 1-3, Sep 24-25).  Also, when we reduced the weight on the flatbed trailer, we found that our coastdowns produced a higher theoretical tire rolling resistance.  This is most likely due to the fact that reducing weight from full payload increases the relative weight over the drive axle.  Since the tires on the drive axle have a higher rolling resistance coefficient (inverse relation with grip for a given tire material and surface), the overall rolling resistance coefficient increased.  This is confirmed by the lab tests, which showed higher rolling resistance coefficients for the drive and steer axles tire models.  Our coastdown results do, however, show a larger increase in coefficient due to complete payload removal compared to the lab results.
While investigation of rolling resistance coefficient from coastdowns was performed for the Michigan testing, coastdown testing will not be used to determine the tire rolling resistance.  The separate tire test procedures are discussed in RIA Section 3.3.

Drag Coefficient

We estimated frontal area of the International truck to be 99 ft[2] (9.2 m[2]) by measuring the various dimensions of the tractor cab and other equipment such as exterior mirrors and tires.  We used this value as a placeholder estimate for the FL60 vehicle also.  Using these frontal area estimates and Equation 13, Figure 2.3 shows our coastdown-estimated drag coefficients for each date and truck configuration.

Figure 2.3 Drag Coefficient Calculated from D from Mixed Model

Unlike rolling resistance, we do not expect our drag coefficient to change with payload removal because the physical configuration of the tractor-trailer is not significantly altered, which is reflected in Figure 2.3.  Also, while we are using a frontal area of 9.2 m[2] specific to the International tractor, a uniform frontal area, such as an average box trailer frontal area or typical tractor frontal area, may be used for all trucks of a certain class when determining drag coefficient as an input to the compliance model.
Lancaster results
     The Lancaster test program involved more trucks and more truck configurations.  Comparing drag from one vehicle configuration to the next was better done using a term called drag area, or CdA.

Equation 15

	Table 2.3 summarizes the results of our Lancaster testing using MM6.  We were able to clearly see coarse differences due to different configurations.  For example, running a box trailer with a low-roof tractor, which creates a bluff body from the top of the tractor roof to the top of the trailer, resulted in a higher drag area than high-roof with box trailer configurations.  Similarly, high-roof tractors tested with flatbed trailers generally had higher drag areas than their low-roof counterparts due to their higher frontal areas.  Standard errors of the drag areas range from 2 to 6 percent.
Table 2.3 Summary of Results from Lancaster Coastdown Testing Using MM6
Truck #
Date
Truck configuration
# of runs
Am [N]
Crr
CdA [m[2]]
HD-01
17-Mar-10
Intl-Prostar_sleeper-highroof-aero_flatbed_68k
18
2666
0.0087
5.26
HD-01
18-Mar-10
Intl-Prostar_sleeper-highroof-aero_box_68k
18
2595
0.0086
5.20
HD-01
19-Mar-10
Intl-Prostar_sleeper-highroof-aero_box_68k
16
2494
0.0082
5.45
HD-01
24-Mar-10
Intl-Prostar_sleeper-highroof-aero_twin_68k
16
2595
0.0084
5.35
HD-02
26-Feb-10
Intl-Prostar_day-lowroof-nonaero_flatbed_68k
18
2666
0.0091
4.64
HD-02
5-Mar-10
Intl-Prostar_day-lowroof-nonaero_box_68k
10
2445
0.0081
8.00
HD-02A
13-Aug-10
Intl-Prostar_day-highroof-aero_box_68k
18
2579
0.0085
5.81
HD-03
1-Mar-10
Intl-Prostar_day-highroof-nonaero_flatbed_68k
10
2460
0.0084
6.60
HD-03
19-Mar-10
Intl-Prostar_day-highroof-nonaero_box_68k
16
2673
0.0088
6.04
HD-06
1-Jul-10
Volvo-D16_sleeper-midroof-aero_emptytanker_33k
18
1099
0.0078
5.16
HD-07
1-Jul-10
Frliner-Century_sleeper-highroof-nonaero_box_68k
16
2991
0.0074
5.72
HD-08
6-Aug-10
Intl-Prostar_day7-lowroof-aero_flatbed_51k
18
1734
0.0063
4.41
HD-08
12-Aug-10
Intl-Prostar_day7-lowroof-aero_flatbed_51k
18
1729
0.0072
5.74
HH-09
6-Aug-10
Peter-389_sleeper-lowroof-nonaero_flatbed_68k
18
2319
0.0057
4.25
HD-10
24-Sep-10
Frliner-Col_sleeper-lowroof-aero_box_68k
18
1923
0.0063
5.58

      Upon further investigation, a general linear model (more commonly thought of as a regression) yields very similar results for the fixed effect (D coefficient) in MM6.  Therefore, given that the general linear model feature is available in nearly every statistical or spreadsheet software, we recommend using that as the model to estimate drag area.

      Also, the agency conducted an additional study of the airflow over the tractor with and without a tractor-mounted boom using CFD.  This study showed that the flow structure is altered by such a setup compared to not having the boom (i.e. normal operation).  We have described this study in RIA Chapter 3.  As a result, based on this and stakeholder feedback, we are recommending finalizing our coastdown procedure based on SAE J1263, which does not require onboard anemometry.

                  Coastdown Program 2 for Heavy-Duty Tractors

         ATDS- Lancaster Test Site Tractor-Trailer Configuration Table

       ATDS- Arizona Proving Grounds Tractor-Trailer Configuration Table

                      Complete Test Article Descriptions
                     ATDS at Arizona Proving Grounds Site
                               Wittmann, Arizona

                      ATDS at Lancaster, California Site

Coastdown Wind Analysis

Introduction

The Agency through a contract with Automotive Testing and Development Services, Inc. (ATDS) conducted extensive coastdown testing of Class 7/8 heavy-duty trucks at Lancaster, California and at the Arizona Proving Grounds (APG) in Wittmann, Arizona during the months of May to July 2011.

The ambient wind velocity and direction were collected using two anemometers located at track-side or road-side locations. One anemometer was positioned approximately at one-quarter distance from the start of the test track or road and the other anemometer was positioned approximately at three-quarter from the start of the test track or road. Each anemometer was mounted at a height of 81 inches +- 6 inches (about half of the test vehicles maximum height), and positioned > 127.5 inches (or >= 2.5 vehicle widths) away from the test vehicle's centerline while it was running along the test track or road.

Wind data was gathered when the vehicle was running from a maximum speed of 70 mph down to 9 mph. The average wind speed during each coastdown run must be <10 mph, the maximum wind speed must be <12.3 mph, and the average cross wind speed must be <5 mph to comply with the wind speed requirements of SAE J1263.

When the wind speed exceeded the requirements of SAE J1263, the SAE J2263 procedure for data collection and analysis was used. To comply with the wind speed requirements of SAE J2263 the average wind speed during each coastdown run must be <21.7 mph, the maximum wind speed must be <31.3 mph, and the average cross wind speed must be <9.3 mph. If the SAE J2263 procedure was required, an additional anemometer mounted to a boom about mid-point of vehicle and approximately 6.6 feet (2 meters) in front of the vehicle was used to measure the wind speed.

The testing in Lancaster was done in a recently paved public road that had less than 0.25% grade. During testing, the road was closed to traffic going in the same direction of travel as the test vehicle, but traffic on the opposite direction of travel was allowed.

The testing in APG was done at a straight line test track that had less than 0.02% grade. The test track is not long enough to allow for the vehicle decelerate from 70 mph down to 9 mph. Therefore, split runs were conducted in accordance to the guidelines of SAE J2263.

Lancaster Wind Speed Analysis

By the time of this report we had gathered data of fifteen tests in twelve days of testing. The average wind speed, maximum wind speed and average crosswind for each test are shown in Table 2.4. The test usually had about 10 paired runs; but when noted, calculations were done with at least a minimum of five paired runs. Tests within SAE J1263 conditions are shown in green. Test that are within the average wind speed requirements of SAE J1263 but failed the maximum wind speed of SAE J1263 are shown in yellow. Tests that fail the conditions on SAE J1263 but were within the conditions of SAE J2263 are shown in red.

Of the fifteen tests, eight tests (53%) were within the wind conditions of SAE J1263, two tests (14%) had the average wind speed and cross wind speed of SAE J1263 but failed the maximum wind speed. Five of the tests (33%) were outside of the SAE J1263 wind conditions but were within the SAE J2263 wind conditions. No test was conducted when the wind conditions exceeded the SAE J2263 requirements.

Table 2.4 Wind Speeds During Testing at Lancaster, California

                               ATDS Wind Speeds
                                 Average Wind
                                 Maximum Wind
                                Avg Cross Wind
                             Lancaster, California
                                     (MPH)
                                     (MPH)
                                     (MPH)
                                  C4XM71CTGTW
                                      2.5
                                     10.5
                                      1.6
                                 C3JM32KTGTW*
                                      2.7
                                     11.3
                                      1.7
                                 C4XM71CTRHR*
                                      2.7
                                     11.4
                                      1.7
                                  C3JM22HTXCR
                                      3.6
                                     10.9
                                      2.4
                                  C3JM22KTGTW
                                      3.6
                                     10.7
                                      2.5
                                 C3JM21FTXCR
                                      4.3
                                     11.6
                                      2.7
                                 C3JM21BQXCZ*
                                      5.4
                                     11.9
                                      3.4
                                 C3JM32KTRJR*
                                      5.5
                                     11.9
                                      3.4
                                  C3JM22HTXER
                                      7.6
                                     20.2
                                      4.9
                                  C3JM21BTXCR
                                      9.6
                                     26.1
                                      3.2
                                  C4XM71CTRHS
                                     10.2
                                     26.6
                                      6.5
                                  C3XM21AQXCZ
                                     10.9
                                     30.5
                                      3.7
                                  C3XE21DTXCR
                                     12.9
                                     28.2
                                      6.5
                                 C3XM21ATXCR*
                                     14.8
                                     29.1
                                      6.4
                                 C3JM21BTXBR*
                                     15.4
                                     28.9
                                      9.2

* Does not uses all the test's pair runs, but uses at least 5 pair runs.

The range of the average wind speed for tests that complied with SAE J1263 was 2.5 mph to 5.5 mph with an average of 3.8 mph. The range of the maximum wind speed for tests that complied with SAE J1263 was 10.5 mph to 11.9 mph with an average of 11.3 mph. The range of the average crosswind speed for tests that complied with SAE J1263 was 1.6 mph to 4.7 mph with an average of 2.7 mph.

APG Wind Speed Analysis

At APG we have data for sixteen tests in thirteen days of testing. The average wind speed and maximum wind speed for each test are shown in Table 2.5. At the time of this report, we had not received the summary of the crosswind on APG. The test usually had about 10 paired runs; but when noted, calculations were done with at least a minimum of five paired runs. Tests within SAE J1263 conditions are shown in green. Tests that fail the maximum wind speed of SAE J1263 are shown in yellow.

Of the sixteen tests, twelve tests (75%) were within the wind conditions of SAE J1263, four tests (25%) had the average wind speed and cross wind speed of SAE J1263 but fail the maximum wind speed.

Table 2.5: Wind Speeds during Testing at APG Wittmann, Arizona

                               ATDS Wind Speeds
                                 Average Wind
                                 Maximum Wind
                            APG Wittmann, Arizona
                                     (MPH)
                                     (MPH)
                                  B3JJ32KTRER
                                      2.9
                                      9.4
                                 B3JM22KTXER*
                                      3.7
                                      9.8
                                 B3JE71DTXBR*
                                      3.8
                                     12.0
                                 B3XM24MTBCR*
                                      3.8
                                     11.5
                                  B3JM32KTGTW
                                      3.9
                                      8.7
                                 B3XM21AQXCZ*
                                      4.0
                                     11.9
                                 B3JV22HTRER*
                                      4.0
                                     11.7
                                 B3JM71DTXBR*
                                      4.3
                                     11.9
                                 B3JM24NTXCR*
                                      4.3
                                     11.7
                                  B3JX32KTRER
                                      4.7
                                     11.1
                                 B3JM32KTRJR*
                                      5.2
                                     10.9
                                 B3JM21DTXBR*
                                      5.3
                                     12.1
                                  B3JM22HTXER
                                      6.0
                                     17.7
                                 B3JM21DTXCR*
                                      8.2
                                     17.4
                                  B3XM21ATXCR
                                      8.8
                                     25.5
                                  B3JM21DQXCZ
                                      9.8
                                     25.0

* Does not uses all the test's pair runs, but uses at least 5 pair runs.
The range of the average wind speed for tests that complied with SAE J1263 was 2.9 mph to 5.3 mph with an average of 4.2 mph. The range of the maximum wind speed for tests that complied with SAE J1263 was 8.7 mph to 12.1 mph with an average of 11.1 mph.

Observations

Average wind speeds of less than 2 mph during a complete set of testing were not obtained at either test site. But we were able to have average wind speeds of less than 6 mph during the complete set of testing for all the vehicle tests that complied with the wind speed conditions requirements of SAE J1263.

Maximum wind speeds of less than 8 mph during a complete set of testing were not obtained at either test site. No maximum wind speeds less than 10 mph during a complete set of testing were obtained at Lancaster. All the times that the wind speed conditions requirements of SAE J1263 failed it was due to the maximum wind speed being exceeded.

For this report, only information on average crosswind speed was obtained for the Lancaster test site. Average crosswind speeds of less than 2 mph during a complete set of testing were obtained on three out of eight tests (38%) at Lancaster that complied with the wind speed conditions requirements of SAE J1263. But it was only three out of all the fifteen tests (20%) conducted at Lancaster. Average crosswind speeds of less than 4 mph during a complete set of testing were obtained for all the vehicle tests that complied with the wind speed conditions requirements of SAE J1263 at Lancaster.

Regarding the average crosswind speed at APG, it is almost certain than the average cross wind stayed within the requirements of SAE J1263 of <5 mph because the maximum average wind speed of the tests that complied with the SAE J1263 conditions was 5.3 mph and the average crosswind speed is always less than the average wind speed.

Based on our observations on wind speeds at two test sites, the data does not support the recommendation proposed by the Engine Manufacturers Association of setting the average wind speed and average crosswind speed < 2 mph. Based on the data the Agency does feel confident that wind speed conditions that conform with requirements of SAE J1263 are achievable and are not overly stringent. The data do support recommending doing coastdown testing when the predicted average wind speed is lower than 6 mph because at that condition the maximum wind speed and average crosswind speed stayed within the SAE J1263 requirements.

Comparison of Coastdown Analysis

Introduction

As the agency reviewed use of on-board and stationary, road side anemometry, it became important to compare results from SAE J1263 and SAE J2263 analyses.

The SAE J2263 program was designed to use wind speed and direction information obtained from a boom mounted anemometer affixed to the front of the vehicle. To use the road side stationary anemometer wind speed and direction information obtained using the SAE J1263 procedure, the true wind speed and direction would have to be converted to the relative wind speed and direction that the anemometer would have recorded if attached to a boom in the front of the vehicle.

To convert from the true wind speed and direction to the relative wind speed and direction we use a simple vector analysis. Figure 2.4 shows a representation of the vector diagram used for this analysis.
W
 V
   R

        180-



Figure 2.4: Vector Diagram

The vehicle speed and direction is considered to be a vector in which the vehicle speed is the vector's magnitude (V), and the direction of travel of the vehicle is the vector's angle (). To simplify the mathematical calculations the vehicle's travel direction is considered to be along the axis so its angle will be zero ( =0).

Similarly, the true wind speed and direction is considered to be a vector in which the wind speed is the vector's magnitude (W), and the direction of travel of the vehicle is the vector's angle ().
Knowing the magnitude and direction of vehicle and the wind, we can add these two vectors to obtain the resultant vector for relative wind speed (R) and direction (), which corresponds to the wind speed and direction that would have being measured by a boom mounted anemometer to the front of the vehicle.

The equation for the resultant relative wind speed (R) and direction () are:

Cosine Law 	R = (W[2] + V[2] -2VW COS(180-[][][]

Sine Law	 = SIN[-1]((W/R) SIN(180-)

The SAE J2263 uses the vehicle speed (V) and the relative wind speed (R) and direction () to determine the A mechanical, B mechanical and C total values. The result is the road load force (F) as a function of vehicle velocity (V):

F = A mechanical + B mechanical V + C total V[2]

Analysis

The testing was conducted with class 7/8 heavy-duty trucks with aerodynamic treatments. Several different combinations were tested. The vehicles included high, mid or low roof trucks. The tractors were run bobtail, with a trailer box 53 feet in length or 28 feet in length, with a tank trailer, and with a flat bed.

The vehicles in this analysis were tested at Lancaster, California. The testing was conducted by Automotive Testing and Development Services, Inc. (ATDS) during the months of May to July 2011 through a contract awarded by the EPA.

The testing in Lancaster was done in a recently paved public road that had less than 0.25% grade. During testing, the road was closed to traffic going in the same direction of travel as the test vehicle, but traffic on the opposite direction of travel was allowed.

The ambient wind velocity and direction were collected using two anemometers located at track-side or road-side locations. One anemometer was positioned approximately at one-quarter distance from the start of the test track or road and the other anemometer was positioned approximately at three-quarter from the start of the test track or road. Each anemometer was mounted at a height of 81 +- 6 inches (205.74 +- 15.24cm) or about half of the test vehicles maximum height, and positioned > 127.5 inches (323.85cm) or >= 2.5 vehicle widths away from the test vehicle's centerline while it was running along the test track or road.
Wind data was gathered when the vehicle was running from a maximum speed of 70 mph down to 9 mph. But the analysis of the data was conducted using only data from 70 mph down to 15 mph. Since we were comparing results from tests using equations from SAE J1263 and SAE J2263, the data presented here is from testing that comply with the more stringent wind speed conditions, which are these of SAE J1263. The average wind speed during each coastdown run must be <10 mph, the maximum wind speed must be <12.3 mph, and the average cross wind speed must be <5 mph.

Table 2.6 shows the A mechanical, B mechanical and C total obtained using the equations on SAE J1263 and using the program provided by SAE using the SAE J2263 equations. The test usually had about 10 paired runs, but for some runs the wind conditions were outside the requirements of SAE J1263. When that was the case, the noncompliant run and its paired run were taken out of the analysis. The paired runs used in the calculation are noted in the table. Since testing was conducted using two separate anemometers, the results using the SAE J2263 program are shown for each anemometer. The road load force is a function of speed; for this analysis the force was calculated for a vehicle speed of 55mph. The difference () between the road load force obtained using the SAE J1263 equations and the SAE J2263 program is shown. The average wind speed during testing is also shown as a reference.

                        Table 2.6: Analysis of Results

Figures 2.5 to 2.12 show the road load force as function of speed obtained using the equations on SAE J1263 and the SAE J2263 program for each vehicle.

                 Figure 2.5 C3JM21FTXCR Force vs. Speed Curve

                 Figure 2.6 C3JM21BQXCZ Force vs. Speed Curve

                 Figure 2.7 C3JM22HTXCR Force vs. Speed Curve

                 Figure 2.8: C3JM22KTGTW Force vs. Speed Curve

                 Figure 2.9: C3JM32KTGTW Force vs. Speed Curve

                 Figure 2.10 C3JM32KTRJR Force vs. Speed Curve

                 Figure 2.11 C4XM71CTGTW Force vs. Speed Curve

                Figure 2.12  C4XM71CTRHR Force vs. Speed Curve

For the purpose of generating the coefficient of drag (Cd) for heavy-duty vehicles, the agencies are using the equations of SAE J1263. There remains some uncertainty regarding Cd values generated by the SAE J2263 program for heavy-duty vehicles and therefore the agencies are not using it at this time.

Observations

Table 2.6 shows good correlation between the road load force obtained using the SAE J2263 program and the road load force using the SAE1263 equations.

The difference () between the road load force using the SAE J1263 equations and the road load force using the SAE J2263 program for both anemometers varies between 0.2% to 7.9%, with an average difference of 4.6%. This difference is not excessive, and it is within what could be expected given that we are expanding the use of the SAE program beyond its original intent.

There was no correlation between average wind speed during testing and the difference () between the road load forces obtained using the SAE J2263 program and the SAE J1263 equations. The lower wind speeds tests do not have the lower difference in road load force; it was completely random.

The agencies previous testing was done following the SAE J2263 procedure and requirements and used the provided SAE J2263 program. The agencies were able to get comparable road load force curves using the SAE J2263 program with the calculated resultant relative wind speed and direction, to the road load force curves obtained with the SAE J1263 equations. The fact that we were able to have some correlation between the two different methods increases the agencies confidence that the SAE J1263 is a good method. Since the testing was done using the conditions specified in SAE J1263, the agencies are confident that the analysis of the data using SAE J1263 equations is valid and we recommend using the SAE J1263 approach.

Test Data Summary

           Table 2.7 Results for Configurations Not Included in RIA

Cab type
Roof height
Aero type
Trailer
Configuration ID
Weight [lb]
CdA [m2]
Std error
# of valid runs
Sleeper
Mid
Aero
28 ft-box
B-3JX3-2K-TRER
27778
6.79
1.5%
18
Sleeper
High
Aero
28 ft-box
B-3JM2-2K-TXER
27878
5.59
1.6%
18
Sleeper
High
Aero
28-ft box
C-3JM2-2H-TXER
27900
6.33
2.1%
10
Sleeper
Low
Non-Aero
28-ft box
B-3JE7-1D-TXBR
30284
7.40
1.4%
20
Sleeper
Mid
Aero
Tank
B-3JM3-2K-TRJR
33300
6.00
2.3%
14
Sleeper
Mid
Aero
Tank
C-3JM3-2K-TRJR
32220
6.48
1.8%
18
Sleeper
High
Aero
53-ft box
C-3JM2-1B-QXCZ
69820
6.79
3.5%
16
Day
(Class 7)
Low
Aero
Flatbed
C-4XM7-1C-TRHR
25260
5.18
2.3%
18

3.0 - Full Scale Wind Tunnel Testing

Introduction

For full-scale wind tunnel testing, we used the National Resources Council-Canada (NRC-C) wind-tunnel in Ottawa, Ontario.  The 9 meter x 9 meter Low Speed Wind Tunnel facility is located on the National Research Council (NRC) campus adjacent to the Ottawa International Airport and has been in operation since 1970.  The wind tunnel is a horizontal closed circuit atmospheric facility with a large test section (9.1 m wide x 9.1 m high x 22.9 m long (30 ft x 30 ft x 75 ft)). It is powered by an air-cooled 6.7 MW (9000 hp) DC motor that drives an 8-bladed fan.  Its speed may be varied and set at any value from 0 to 230 rpm and can be maintained within +-0.1 rpm. The maximum wind speed is about 55 m/s (180 ft/s).  The wind tunnel can accommodate a full-size tractor and a trailer of length up to 28 feet (see Figure 3.1 below).  As seen in the figure, the vehicle can be yawed up to positive or negative ten degrees via rotating turntable.  Models in the tunnel are supported directly by extensions to the balance turntable and rectangular air bearings with instrumented pressure taps to isolate and measure the full aerodynamic forces  on the model.  In addition, the floor is static for full size tractor testing but does possess a moving belt system for smaller scale testing (e.g., 1/2 scale models).

Source:  National Research Council-Canada

Figure 3.1 Full-scale, Fixed Floor Test in the NRC 9-meter Wind Tunnel (model tested for this program not shown)

For our test program, we recruited a commercially-available, Class 8, heavy-duty, on-highway, high roof, sleeper cab tractor with full aerodynamics package.  For our test runs, we used a base tractor-trailer gap of 45 inches as specified in this rulemaking.  Baseline testing was performed using the as-received configuration with full aerodynamics package components on the tractor.  The 28' trailer used for this testing was acquired from the tractor OEM and is the same trailer they use for testing in this facility.  Full yaw sweeps from positive to negative 10 degrees were conducted with equal increments of 2.5 degrees in between zero and +/- 10 degrees.  Redundant zeros were conducted before, between the positive-negative transitions, and at the end of the sweep.

Analysis

NRC provided the corrected results of the full yaw sweeps in the full scale wind tunnel.  We calculated the average of all the zero Cd values and normalized the data by dividing each result by the average to give us an idea of the spread for each individual point.  Figure 3.2 shows the results of the zero yaw Cd results as compared to the average of all of the zero yaw Cd results.

Figure 3.2 Delta between Individual Zero Yaw Cd Values and the Average of All Zero Yaw Cd Values for Full Scale Wind Tunnel Testing of Class 8, High Roof, Aero Tractor with a 28' Trailer in the NRC Wind Tunnel

Observations

The deltas for each individual result are well below 0.5%, approximately 0.2% of the zero yaw Cd result average with an overall standard deviation of -0.0009 for all zero yaw Cd results showing excellent agreement from test to test.

Summary/Conclusions

The data confirms that the full-scale wind tunnel test is highly repeatable and, once a manufactured has approval to use a certified facility, there is high confidence in the results from a single test on a tractor model with a 28 foot trailer.  Later, we will compare this data with the other aerodynamic methods.

4.0 - Reduced Scale Wind Tunnel Testing

Introduction

For reduced-scale wind tunnel testing, we used the Automotive Research Center (ARC) in Indianapolis Indiana.  The ARC wind tunnel is a closed single return tunnel with 3/4 open-jet working section and moving ground plane (2.3 m wide x 2.1 m high x 5.5 m long (7.5 ft x 6.8 ft x 18 ft)).  It is powered by an air-cooled 373 kW (274 hp) variable speed DC motor that drives a 9-bladed fan with carbon fiber blades.  Its speed may be varied and set at any value from 0 to 610 rpm. The maximum wind speed is about 50 m/s (164 ft/s). The wind tunnel can accommodate a model up to 50% scale (1/2 scale) for race car applications down to 12.5% scale (1/8th scale) for Class 8 tractor and trailer combinations.  The wind tunnel is equipped with a moving ground plane (i.e., rolling road), four-stage boundary layer suction system, and a top-mounting "Sting" system allowing for yawing of the model.  For model development, ARC has in-house model developers and can create highly detailed scale models using original computer aided design and engineering (CAD/CAE) drawings or using in-house scanning equipment to perform scanning and digitizing to create CAD/CAE drawings (see Figure 4.1 below).

                     Table 4.1 Scale Model Testing Summary

Figure 4.1 1/8th Scale Tractor-Trailer Model in ARC Reduced Scale Wind Tunnel

For our test program, we assumed a base tractor-trailer gap of 45 inches as specified in this rulemaking and the full aerodynamics package components that are sold on the full size version of the tractor.  We were fortunate to test 1/8[th] scale models from three out of the four North American manufacturers of Class 8, heavy-duty, on-highway, high roof, aero, sleeper cab tractors.  All test runs were performed with a full yaw sweep from positive to negative 9 degrees in equal increments of 3 degrees in between zero and +/- 9 degrees.  Redundant zeros were conducted before, between the positive-negative transitions, and at the end of the sweep.

Analysis

ARC provided the results of the full yaw sweeps in the reduced-scale wind tunnel for all three models.  Each truck was assigned a generic moniker:  Truck A, B and C.  We calculated the average of all the zero Cd values and normalized the data by dividing each result by the average to give us the spread for each individual point.  Below are graphs showing the results of the zero yaw Cd results as compared to the average of all of the zero yaw Cd results for Truck A, B and C (see Figures 4.2-4.4).

Figure 4.2 Delta between Individual Zero Yaw Cd Values and the Average of All Zero Yaw Cd Values for Truck A Reduced-Scale Wind Tunnel Testing

Figure 4.3 Delta between Individual Zero Yaw Cd Values and the Average of All Zero Yaw Cd Values for Truck B Reduced-Scale Wind Tunnel Testing

Figure 4.4 Delta between Individual Zero Yaw Cd Values and the Average of All Zero Yaw Cd Values for Truck C Reduced-Scale Wind Tunnel Testing

Observations

As with full scale wind tunnel testing, the reduced-scale wind tunnel results showed excellent agreement from test to test.  The standard deviations for reduced-scale wind tunnel results were very low from 0.0008 for Truck B up to 0.003 for Truck C, with Truck A in between the other two at 0.002.  In addition, the highest variation for an individual result when look across all of the trucks is 0.00565 for Truck C.

Summary/Conclusions

The data confirms that the full-scale wind tunnel test is highly repeatable and, once a manufactured has approval to use a certified facility, there is high confidence in the results from a single test on a tractor model with a 28 foot trailer.  Later, we will compare this data with the other aerodynamic methods.

5.0 - Computational Fluid Dynamics (CFD) Analysis

Introduction

Computational Fluid Dynamics, or CFD, capitalizes on today's computing power by modeling a full size vehicle and simulating the flows around this model to examine the fluid dynamic properties, in a virtual environment.  CFD tools are used to solve either the Navier-Stokes equations that relate the physical law of conservation of momentum to the flow relationship around a body in motion or a static body with fluid in motion around it, or the Boltzmann equation that examines fluid mechanics and determines the characteristics of discreet, individual particles within a fluid and relates this behavior to the overall dynamics and behavior of the fluid.  Therefore, there are predominantly two types of commercially-available software code either Navier-Stokes or Lattice  - Boltzmann based.  We will discuss the set up and results for each of these separately since their approaches and calculations are different.

                            Table 5.1 CFD Analysis

For this test program, we acquired a full scale, Class 8, high-roof, aero sleeper tractor-trailer and had a third-party, Southwest Research Institute, scan and digitize the tractor and trailer.  The vehicle was elevated and the surface and underbody details, as much as possible, was scanned to create a digital model of the tractor and trailer.  Below are some figures from the scanning and digitizing process (Photos courtesy of Southwest Research Institute).  More details on the scanning and digitizing process can be found in the docket in the report titled "EPA SwRI Truck Digitization Summary.pdf".

Figure 5.1 Photo of the Class 8, High-roof, Aero Sleeper Tractor Acquired for Scanning and Digitizing Purposes

Figure 5.2 Class 8, High-roof, Aero Sleeper Tractor Elevated for Scanning and Digitizing Purposes

Figure 5.3 Southwest Research Institute (SwRI) Personnel Collecting Reference Grid Points on the Tractor

Figure 5.4  Laser Scanning the Surface with the Portable Arm

Figure 5.5 Spatial Analyzer Screen Capture of Reference Grid Points for the Tractor

Figure 5.6 Partial View of Raw Scan Data from the Tractor

Figure 5.7 Front Perspective View of the Final 3D Model (SolidWorks 2011)

Figure 5.8 Rear Perspective View of the Final 3D model (SolidWorks 2011)

We supplied the digitized model information to three sources, two using Navier-Stokes and one using Lattice-Boltzmann based CFD software codes.  The results for one of the Navier-Stokes based CFD sources was not available at this time and will be added later to the docket for the rulemaking.  Therefore, we will discuss the analysis conditions and results for the two available sources.

Based on the digitized model provided, the sources were able to prepare the model for CFD analysis by ensuring closed-surfaces, accurate component connections, and representative, component spatial relationships.  Due to simplification, the digitized tractor model fidelity was less than 100% realistic as compared to the actual tractor model.  Therefore, the sources either used the digitized the model as provided, made some assumptions and modifications based on experience, or had enough experience with the OEM that they were able to add OEM-level of detail to the digitized model.  We will discuss the set up process for each software code separately below.

Navier-Stokes Based CFD Software  -  CD Adapco

CD-Adapco has been developing commercial CDF tools since 1987 beginning with their STAR-CD and continuing with the recent generation of their CFD tool, STAR-CCM+.  CD-Adapco used the simplified digitized model we provided to them with minimal changes (see Figure 5.9).

Figure 5.9 Bottom/Front Perspective View of 3D Model Prepared by CD-Adapco

The analysis process for the digitized model involves three main steps:  meshing, where the model and surrounding environment are divided up into discreet elements to form a grid; solving which involves calculations to solve the Navier-Stokes equations; and post-processing to quality assure/quality check (QA/QC) the run and the data.  If the run passes the QA/QC, the analysis results are output to a Powerpoint presentation for easier viewing (see Figure 5.10 below).

Figure 5.10 Overview of CFD Analysis Process Used by CD-Adapco

For setting up the mesh, CD-Adapco used the following parameters:

      High Reynolds Region
            :: Target Y+: 30-300
                   -  2 Layers, 4mm Wide
                   -  Near Wall ~ 1mm
            :: Trailer uses 20mm prism layer with 6 Layers to blend outward.

      Low Reynolds Region
            :: Target Y+: < 5
                   -  Minimum: 8 Layers
                   -  Near Wall ~0.05mm
            :: Applied to CAB and tires (not treads grooves)

The Y+ value is a calculated value using the equation:  (u* x y) / ν, where u* is the frictional velocity near the wall, y is the distance to the nearest wall, and ν is the fluid kinematic viscosity.  The y+ value determines where to put the first grid line in the mesh by identifying the first point where the frictional stresses acting between the fluid and the wall are significant enough to cause velocity differences in the fluid (i.e., the fluid adheres to the wall and the forces act on the fluid changing its velocity profile).  By lowering this Y+ value, the distance to the wall is shortened where the boundary lines are defined and, consequently, resulting in the mesh grid in Figure 5.11.  The darker areas represent higher cell concentrations in areas where resolution of the flow is critical, such as closer to the surface of the tractor-trailer or other obstructions in the flow.  Conversely, the lighter areas represent lower cell concentrations in areas where flow resolution is not that critical, such as areas further away from the surface of the tractor-trailer.  This helps to give an accurate analysis of the model aerodynamics while minimizing the computing time to resolve the flow relationship between cells.

Figure 5.11 Overview of Mesh Grid for Tractor-trailer Model Prepared by CD-Adapco

For the test conditions, the analysis assumed an open road with moving ground plan and rotating wheels with the grill open on the tractor.  Vehicle speed was assumed to be 24.585 meters per second (55 miles per hour) with an assumed air density of 1.185 kilograms per cubed meter (kg/m[3]).  Using these environmental conditions, they conducted analysis at a range of yaw angles:  0, +3, +6, +9, -3, -6, and -9.  The Navier-Stokes based CFD code results are discussed in the analysis section below.  More details on the analysis performed by CD-Adapco can be found in the docket under the document titled "CD Adapco Comments on EPA update 7.13.2011.pdf".

Lattice-Boltzmann Based CFD Software  -  Exa Corporation

Exa Corporation develops, markets, and supports simulation software for fluids engineering with a full suite of engineering consulting services. PowerFLOW, their flagship product, is a revolutionary CFD solution for simulating some of the most complex fluid flow problem and utilizes a unique methodology called the Lattice Boltzmann method.  Using existing knowledge and established relationships, Exa was able to prepare and analyze a highly detailed model, as shown in Figure 5.12, of the tractor-trailer including addition of detailed engine bay and suspension components.  Exa estimated that the process to create this model took 3 days for one person or 72 "man" hours.

Figure 5.12 Detailed Tractor-trailer Model Prepared by Exa Corporation

The analysis process for the digitized model involves the same three main steps above for Navier-Stokes based code but the meshing process is very different.  Exa uses a mesh grid process that defines regions and assigns a number to each region with varying cell size as shown in Table 5.2.

Table 5.2 Exa Mesh Grid Definition Using Regions and Cell Size to Define Critical Flow Areas

The larger-number regions are areas closest to the surface of the tractor trailer and use a smaller cell size and consequently, the cells in this area are more concentrated (i.e., smaller in size and are thus more densely packed or closer together).  As a result, the mesh grid is similar in concept as stated above for the Navier-Stokes based CFD software code.   The darker areas represent higher cell concentrations in where resolution of the flow is critical, such as closer to the surface of the tractor-trailer or other obstructions in the flow.  Conversely, the lighter areas represent lower cell concentrations in areas where flow resolution is not as critical, such as areas further away from the surface of the tractor-trailer (see Figures 5.13 and 5.14 below).

                             VR6: 24 mmVR5: 48 mm

Figure 5.13 Mesh Grid Preparation Showing Finer Levels of Cell Concentration in Critical Flow Areas/Regions Prepared by Exa Corporation

                              VR7: 12 mmVR8: 6 mm

Figure 5.14 Mesh Grid Preparation Closer to the Surface of the Tractor-trailer Model Prepared by Exa Corporation

For the test conditions, the analysis assumed an open road with moving ground plan and rotating wheels with the grill open on the tractor.  Vehicle speed was assumed to be 26.82 meters per second (60 miles per hour) with an assumed air density of 1.204 kilograms per cubed meter (kg/m^3).  Using these environmental conditions, they conducted analysis at a range of yaw angles:  0, +1, +3, +6, +9.  For minimum cell size, Exa used their best practices recommendation of 6mm.  They also explored a smaller case of 1.5mm, as close to the suggested 1mm case in our proposed rulemaking, and an interim cell size of 3mm.  In this case, model symmetry was assumed and the negative cases were not conducted to save costs.  The Lattice-Boltzmann based CFD code results are discussed in the analysis section below.  More details on the analysis performed by Exa Corporation can be found in the docket under the documents titled "20110526-Exa-Full-Results-Overview-for-EPA-final.pdf", "Exa-Mtg-with-EPA-070611-final.pdf" and "20110708-Exa-Additional-Results.pdf".

Analysis

For CFD, there is no issue regarding repeatability since the software will repeatedly give the same answer once the conditions are defined.  Therefore, a more useful comparison for the purposes of this memo is a cross-method and cross-source comparison.  The cross-method comparison is useful since manufacturers may uses either of the software codes to perform and submit their Cd values and we would like to know if they give wildly divergent results.  The cross-source comparison is important because different programmers and different conditions can impact the results and this would provide some quantification of that difference.

Accordingly, Table 5.3 shows the difference between the two results.  Since they conducted different yaw angles, we are only presenting data for overlapping yaw angles between the sources.

Table 5.3 Percent Difference for Cd Results from Exa and CD-Adapco CFD Analysis

                                   Yaw Angle
                   Delta (Exa Results  -  CD-Adapco Results
                    Exa and CD-Adapco Result Difference (%)
                                       0
                                     0.056
                                    11.75%
                                       3
                                     0.057
                                    11.14%
                                       6
                                     0.066
                                    11.33%
                                       9
                                     0.071
                                    10.76%

Observations

Despite the lack of consistent model details, base assumptions and software code differences, the 10.8 to 11.8 percent difference between the source results is in the realm of acceptability.  The data does show a consistent percentage difference indicating a structural bias either due to the assumptions by the modeler or the level of model detail.  Without further study, we are not able to isolate the source of this structural bias but it does highlight an area of concern.

Summary/Conclusions

To get consistent results from CFD analysis, regardless of the software code used, we took the following steps on CFD analysis.  First, for any CFD analysis the most accurate result will require original CAD/CAE files of the tractor to support the development of a model with sufficient detail and fidelity.  In addition, the environmental conditions from the coastdown test used to develop the aerodynamic correction factor so that the analysis will closely match the real conditions experienced by the vehicle.  Second, to ensure data consistency, a minimum set of characteristics and criteria must be included in this rulemaking for CFD analysis to ensure that the boundary and surface conditions are not too coarse and, thus, not representative of the real truck and environmental conditions.  The latter point also overlaps with the key issue of boundary/surface condition sensitivity and the secondary issue of trade-offs between model fidelity and cost/run-time.  As a result, we looked at cell size, one of the main input conditions, to assess the trade-offs between model fidelity and human resources and computing cost/run-time and tables below provide more information.

We originally proposed a mesh cell size of 1.0mm everywhere in the mesh.  We were informed that this is extremely rigorous and, instead, the smallest mesh cell size of 1.5 mm was used as a starting point.  We were also informed that this minimum cell size is used at the localized areas/regions where high flow/high pressure regions are typically expected or occur.  Therefore, as shown above, this was used in the VR8 region (shown in Figure 5.14) and the cell sizes increased from that point.

Table 5.4 Zero Yaw Angle Results from the CFD Analysis for Localized Cell Sizes of 1.5, 3.0 and 6.0 mm
                             Finest Cell Size (mm)
                   Cd Delta Change vs. cell size resolution
                                       6
                                      --
                                       3
                                    0.421%
                                      1.5
                                    2.360%

Table 5.5 Delta and Percent Difference for Cd Values at Positive 0, 1, 3 6, 9 Yaw Angles for the 1.5 mm and 6.0 mm Case
                                   Yaw Angle
                                     Delta
                                 % Difference
                                       0
                                    0.0136
                                     2.77%
                                       1
                                    0.0139
                                     2.80%
                                       3
                                    0.0062
                                     1.21%
                                       6
                                    -0.0065
                                    -1.14%
                                       9
                                    -0.0026
                                    -0.39%

Table 5.6 Case Size Estimates of Computational Cost and Computer Run-time in CPU Hours

As the tables show, there is little difference for Cd values between the 1.5, 3.0 and 6.0 mm cell size case.  Further, there is little difference for the Cd values between the 1.5 and 6.0 mm cell size but a very high cost in computing run time and, ultimately, cost.  We also looked at cell size beyond 6.0 mm as shown in Figure 5.15.  Beyond about 9 mm, the mesh becomes too coarse and the values begin to fall out of the acceptable error band.  Based on this, we used the smallest cell size, 6.0 mm, as the smallest allowable cell size for Lattice-Boltzmann based CFD analysis.  For Navier-Stokes based analysis, we established similar criteria using the Y+ value instead of actual cell size.

Figure 5.15 Cd Results for Cross Method Comparison Using Normalized, Nominal Frontal Area of 10.4 Meters Squared

6.0 - Summary Comparison for All Aerodynamic Assessment Methods

Introduction

As shown above, the full scale wind tunnel, reduced-scale wind tunnel, and CFD all have the ability to yield repeatable test results.  The other remaining question was how well do the coefficient of drag (Cd) results compare to each other across the methods on the same tractor model.  To explore this further, we compared the results for each of the methods above and to the coastdown test results.  Specifically, the same tractor-trailer model (i.e., Truck A) that we used for scanning/digitizing and CFD analysis was also coastdown tested and full scale wind tunnel tested.  Although the 1/8[th] scale tractor-trailer model tested in the reduced-scale wind tunnel was not created using our actual tractor-trailer model, the model type and aerodynamic components are identical. Therefore, the results from the reduced-scale wind tunnel are reasonably comparable to the other results.

In addition to Truck A, we also procured a "clone" or second tractor (i.e., Truck B) that matched the specifications of Truck A.  This model was not tested in a wind tunnel nor did receive a CFD analysis, but was coastdown tested.  This was performed to understand the influence that using different tractor models (i.e., truck-to-truck variability) has on Cd estimation.

In addition, we also coastdown tested Truck B in two different locations to understand the impact that test source on the same vehicles (i.e., source-to-source variability) has on Cd estimation.  Coastdown testing was performed by Automotive Testing & Development Services, Inc. (ATDS) in Ontario, California and at the Arizona Proving Grounds (APG) in Yucca, Arizona.  The three Cd results, one for Truck A at APG and two for Truck B at ATDS and APG, were compared to the wind tunnel and CFD Cd results.

Analysis

Prior to the comparison, we had to normalize the data for frontal areas.  NRC assumed a frontal area of 10.595 square meters (114.04 square feet) for full scale wind tunnel testing, ARC assumed a frontal area of 10.69 square meters (115.07 square feet) for the reduced-scale wind tunnel testing, Exa assumed a frontal area of 10.595 square meters (114.04 square feet) and CD-Adapco assumed a frontal area of 10.595 square meters (114.04 square feet) for CFD analysis.  In the rulemaking, we assume a frontal area of 10.4 square meters (111.94 square feet) in the rulemaking and we are using this as the nominal frontal area for all testing.  Therefore, we took all of the Cd values, multiplied by the assumed frontal areas and divided them by 10.4 square meters to get Cd values corrected for the rulemaking frontal area.

Finally, to make the comparisons more obvious, we normalized all the data to the Truck A coastdown result by dividing all the other Cd values by the Truck A coastdown Cd after correction for frontal area.  For multiple test results from the same source and test conditions, we took the average of the corrected, normalized Cd values and used this value to simplify the comparison.  Given the repeatability shown above for wind tunnel and CFD, this was not an issue.  Below is a graph showing the Cd results from all the aerodynamic methods considered in the rulemaking (see Figure 6.1).

Figure 6.1 Cd Results for Cross Method Comparison Using Normalized, Nominal Frontal Area of 10.4 Meters Squared.

Observations

Initially, we hoped that the results from each method would be exact but, once the coastdown test procedure was selected as the reference method, this became less of an issue.  Manufacturers would simply have to correlate their results from the other aerodynamic methods to the coastdown procedures and this would be sufficient, given the repeatability of the other aerodynamic methods.  Therefore, it came more important to understand how equivalent each method is to the coastdown to anticipate the range of necessary correction and overall trends when comparing the methods.

The graph shows some of that cross-methodology equivalence, with a couple of caveats for some of the methods.  First, the full scale wind tunnel's use of a shorter trailer (28 feet for the test vs. 53 feet in the field) and the lack of a moving ground plane create some divergence.  With additional research, it may be possible to improve this estimate by developing a static floor and a trailer correction factor.  For now though, the results are in the range of acceptability when comparing them to the coastdown test.

Second, for CFD analysis, the lack of matching environmental conditions and consistent model fidelity, in one case, also produced some divergent results.  Addressing these two areas should help reduce some of the divergence between the CFD analysis and coastdown.

Finally, the reduced-scale wind tunnel produced the most comparable results to the coastdown test.  Specifically, the wind-average coefficient of drag (WACd) nearly matches the coastdown results with a 95.5% level of agreement.  Since the WACd takes into account the full yaw sweep, this may indicate that, although the coastdown test is primarily concerned with zero yaw, it may be capturing some of the non-zero yaw wind affects.

Summary/Conclusions

Based on the results, we confirmed that although the results from all the methods were not exact, they were equivalent. Therefore, we believe that any of the aerodynamic methods discussed in this memorandum are acceptable for generating Cd values.  However, since the coastdown test is being used as the reference method, a correlation to the coastdown test is necessary if the other aerodynamic assessment methods, wind tunnels or CFD, is used.

Accordingly, there is a need for an aerodynamic method adjustment factor when aerodynamic methods other than the coastdown reference method are used and we developed the following equation to calculate the adjustment factor:

	Adjustment Factor  =  Cd result (coastdown) / Cd result (wind tunnel or CFD).

Once a manufacturer performs a correlation between the coastdown method and the other aerodynamic method, and receives agency approval for this other aerodynamic method, the manufacturer can use the other aerodynamic method to test all of their models.  Subsequently, the adjustment factor would be applied to all the test results from the other aerodynamic method and a manufacturer would be able to continue using this method for all testing.