Assessing Road Load Coefficients of a Semi-Trailer Combination Using a Mechanical Simulation Software with Calibration Corrections.
Recent regulations on fuel economy and carbon dioxide emissions around the world in an effort to curb global warming have led to the development of vehicles with higher fuel efficiency. The National Highway Traffic Safety Administration (NHTSA) and Environmental Protection Agency (EPA) have proposed standards to improve fuel efficiency and cut carbon emission . Automakers are, in response, developing fuel-efficient vehicles. This has led to an interest in researchers studying ways to reduce external forces (road load) on vehicles, especially heavy-duty and medium trucks [2, 3, 4, 5]. Federal test procedures to achieve this mandate require in part coast-down tests and the use of chassis dynamometers for fuel economy and emissions testing.
Road load studies involving coastdown began in the 1950s. Beginning in the 1970s, the Society of Automotive Engineers (SAE) issued a standardized method of performing road load testing (SAE J1263) . Several follow-up studies in the 1980s and 1990s led to an enhanced testing standard, J2263, for small vehicles . Other standards for coastdown testing have been developed with slight variations such as the World Harmonized Light Vehicles Testing Cycle (WLTC), National Emission Ceiling Directive (NECD), and EPA title 40 coastdown testing. All the tests are typically based on the same method: accelerating a test vehicle, shifting the gear to neutral and letting the vehicle coast within a speed range on a flat road, measuring the deceleration duration during the coastdown, and computing the road load [8, 9, 10].
Coastdown testing has been applied to other studies where drag force analysis is required such as in the development of the grade severity rating systems [11,12]. Such studies required the average drag force to be calculated over different truck weights.
Coastdown testing in the field is challenging and has to overcome several environmental bias issues . Field testing requires stringent wind speed and direction conditions which are mostly not met [14, 15]. Standardizing these environmental differences to standard conditions is sometimes computationally intensive and may not completely account for variations in test conditions when average values are used. Other biases present in road load results from field tests are due to unaccounted factors such as pavement temperature during coastdown runs, test driver, test site, test vehicle, and test devices .
Recent advancement in computer technology has led to the development and use of several simulation softwares. The use of computer simulation for the determination of the aerodynamic characteristic of vehicles is admittedly a much easier approach compared to full-scale road and wind tunnel testing. Computational fluid dynamics (CFD) has offered a leap in the simulation of aerodynamic drag of different vehicle types and classes. The popularity of CFD software has resulted in a plethora of research on modeling aerodynamic drag of trucks, drag reduction accessories, and recommendations for drag-reducing designs [16, 17, 18, 19]. Despite the fact that CFD has found wide applications in aerodynamic analysis of vehicles, the approach is limited when it comes to the determination of full road load. Most current computer simulation programs based on CFD analysis are based solely on the aerodynamic drag of the road load.
There currently exist several other simulation software on the market which are predominantly used to analyze the impact of vehicle designs on fuel efficiency and greenhouse gas emissions. These software used for simulation rely on detailed models, accurate input data, and vehicle parameters to output reliable results . Greenhouse Gas Emissions Model (GEM) of the EPA and the Vehicle Energy Consumption Calculation Tool (VECTO) of the European Commission are two of such software that are used to model heavy-vehicle fuel efficiency [20, 21, 22].
Other classes of simulation software allow for coastdown analysis by providing velocity-time trace graphs and allowing users to input a variety of vehicle and ambient characteristics. One of such software, TruckSim used for this study, is purposely built for analyzing vehicle dynamics and calculating a truck's performance characteristics . The software enables the generation of different scenarios and test sequences from which coastdown analyses can be conducted. The software has a database for several test vehicle configurations. TruckSim can also develop a custom vehicle model based on specifications defined by the user.
The goal of this article is to assess the suitability of a vehicle dynamic software in deriving acceptable road load coefficients for a typical combination truck. Most coastdown and drag simulation software in the market used for fuel conservation analysis overwhelmingly focus on the aerodynamic drag coefficient, without a similar attention paid to the rolling resistance component. This study seeks to add to the growing body of literature on simulation of coastdown by proposing a simple method to estimate road load coefficients.
The report is organized follows. The theoretical basis of coastdown analysis was first presented. This involved an explanation of how the coastdown coefficients are derived from equations of motion. A description of the field experiments to obtain the road load coefficients was given. The test truck, test conditions, data acquisition method, actual coast-down procedure, and the use of the TruckSim software were also explained. Next, the results of the analysis, comparison of the coefficients of drag and rolling resistance to published data, and the derivation and use of the calibration curve were explained. Finally, the summary and conclusions of the study were presented and the potential use of the methodology and its limitations highlighted.
The coastdown analysis model is used to infer the road load acting on a vehicle when it is unpowered. The test vehicle is driven to a maximum speed of interest, shifted into neutral, and allowed to decelerate freely, while velocity and time of deceleration are measured. For a vehicle in free motion as described, the forces that resist forward motion are:
* Aerodynamic drag ([F.sub.aero])-resistance to motion due to air
* Rolling resistance ([F.sub.rr])-resistance to motion due to frictional force between the tires and road surface
* Grade drag ([F.sub.grade])-resistance to motion due to grade effects
Taking into account that drag forces always act in a direction opposite to vehicle speed and using Newton's second law for a vehicle traveling in a straight line gives:
-[M.sub.e] dv/dt = [F.sub.aero] + [F.sub.rr] [+ or -] [F.sub.grade] Eq.(1)
where [M.sub.e] is the effective mass of the vehicle (kg), V is the vehicle speed (m/s), and t is the deceleration time (s). The effective mass accounts for the rotational inertia of the wheels and other rotating components and is different from the static mass of the vehicle. For coastdown analysis, the effective mass of the drivetrain components may be ignored . The rotational inertia of the wheels is a property that inhibits changes to the speed of the wheels and acts in an equivalent manner as an extra mass to the vehicle that inhibits changes to the vehicle speed . The effective mass may be estimated as 3% of the total mass of the test vehicle . Thus:
[M.sub.e] = 1.03M Eq. (2)
where Mis the total mass of the test vehicle. The aerodynamic drag is written as:
[F.sub.aero] = 1/2.[rho].[v.sup.2].[C.sub.D].A Eq.(3)
where [rho] is the density of air (kg/[m.sup.3]), v is the speed of the vehicle (m/s), [C.sub.D] is the aerodynamic drag coefficient, and A is the reference cross-sectional area ([m.sup.2]). Air density is a function of ambient air pressure, temperature, and relative humidity. The dimensionless [C.sub.D] is a function of yaw angle and has been shown to change with wind speed.
The rolling resistance ([F.sub.rr]) according to the SAE J1263 procedure is assumed to be affected by only vertical load influences. The standard also assumes that all the tires of the vehicle act in the same manner such that a constant rolling resistance coefficient ([C.sub.rr]) can be assumed for the whole vehicle . The rolling resistance coefficient is expressed as:
[C.sub.rr] = [F.sub.rr]/Fz Eq.(4)
where [F.sub.z] is the vertical load on all the test vehicle s wheels.
For the low-grade levels specified for coastdown testing, the vertical load is assumed to be equal to the vehicle weight (W = mg) . The rolling resistance is thus modeled as:
[F.sub.rr] = [C.sub.rr]W Eq.(5)
The grade drag is affected by vehicle weight and the known grade of the track. The grade drag is defined as:
[F.sub.grade] = [+ or -]W dh/ds = [+ or -]W sin[theta] Eq.(6)
where dh/ds is the sine of the slope. Combining all the forces into the equation of motion gives:
-[M.sub.e] dv/dt = 1/2.[rho].[v.sup.2].[C.sub.D].A + [C.sub.rr]W[+ or -]Wdh/ds Eq. (7)
Road load is mostly analyzed using regression analysis where the road load force is defined as a three-term equation which is a function of speed :
F = A + BV + [Cv.sup.2] Eq. (8)
where A, B, and C are coefficients to be determined by regression. Yasin notes that coastdown data collected in the real world requires only a two-term equation if testing is restricted to periods of light wind . The approximation of the two-term equation becomes exact for describing road load under field conditions if the forces are averaged for back-to-back runs in opposite directions . This reduces the output of the coastdown to the form:
F = A + [Cv.sup.2] Eq. (9)
This is the form recommended by SAE J1263 and the J1263-modified EPA Phase 1 protocol. The intercept A is analogous to the rolling resistance, while C is the aerodynamic drag term.
The field coastdown tests to determine road load were carried out in accordance to the EPA Phase 1 modified SAE JI263 procedure . This is because the standardized coastdown testing protocols (SAE J1263 and SAE J2263) were established primarily for passenger vehicles and light-duty trucks .
The EPA procedure requires that coastdown data be gathered between a maximum speed of 31.34 m/s (113 km/h) and 6.67 m/s (24 km/h). Average wind speed at the test site during coastdown runs is not to exceed 4.44 m/s (16 km/h). Grade effects are to be considered in the analysis for tracks with grades greater than 0.02%. Wind and load corrections are applied to drag terms according to section 10.5 of SAE J1263.
A typical five-axle aerodynamic semi-trailer (class 8) truck was used for running the tests. The truck and its specifications are found in Figure 1 and Table 1, respectively.
The coastdown tests were conducted over a period of 2 days. The average wind speed on the test site were generally calm and did not exceed the wind limits specified by the modified SAE JI263 procedure. Pairs of runs in separate directions constituted a cycle. Wind conditions were monitored from a nearby weather station.
The tests were carried out under the following conditions:
1. Cycles 1, 2, and 3: prevailing wind 1.8 m/s, East South East, and 101.73 kPa atmospheric pressure
2. Cycle 4: prevailing wind 2.7 m/s, South East, and 101.35 kPa atmospheric pressure
3. Cycles 5 and 6: 2.9 m/s, West South West, and 101.456 kPa atmospheric pressure
Ambient air temperatures recorded during runs were 292.9 Kelvin (K), 292.3 K, and 291.8 K for cycles 1, 2, and 3, respectively. Air temperature for cycle 4 was 291.9 K, while they were found to be 288.7 K and 287.5 for cycles 5 and 6.
The test track selected for coastdown runs was on Wyoming highway 789 outside Worland, Wyoming. The track is straight and approximately 4000 m long with a gentle grade of 0.14% in the southbound direction. The test track is shown in Figure 2.
The coastdown test procedure requires measurement of vehicle position, vehicle speed, time, engine speed, ambient conditions (temperature and barometric pressure), and wind conditions. Vehicle location was measured by an onboard GPS system. The speed, time, engine rpm, and some other variables of interest were measured using a J1939 datalink. Communication with the truck's computer system to extract and log data was achieved by using a proprietary software. The air temperature was measured by a thermocouple temperature probe which was installed on a trailer axle of the vehicle. Data was logged every half second.
The test procedure was for the truck to approach the beginning of the test section at a speed of 33.3 m/s (120 km/h) which is slightly above the predetermined target speed of 31.4 m/s (113 km/h) and select the neutral gear and coast through the section. The truck was tested in loaded and unloaded conditions (36,287 kg and 18,144 kg). A loaded heavy-duty truck requires a long stretch of road to coast to the lower speed required for the test. The test track was not long enough to accommodate the entire coastdown run. SAE J1263 recommends that runs should be split in such situations. The runs were therefore divided into two portions: a highspeed range of 31.4 m/s (113 km/h) to 20.0 m/s (72 km/h) and a low-speed range of 20.0 m/s (72 km/h) to 6.7 m/s (24 km/h). It is recommended to limit data collection to speeds above 6.7 m/s (24 km/h) due to the effects of head and tail winds at low speeds . The tests were run in both directions and paired for analysis.
The difference between the coastdown simulation carried out in this study and other research is that the scenarios considered mimicked actual field coastdown runs and not just air stream analysis as is done in a wind tunnel or in CFD. In addition to the aerodynamic forces usually considered in such studies, rolling resistance was analyzed in the simulation runs. The simulation scenarios were developed and run on the TruckSim platform, a typically easy-to-use software.
The 2018 version of TruckSim was used for the simulation analysis. Multiple combinations of tractors and trailers exist in the TruckSim software from which the user can choose. The steering, powertrain, brakes, and number of axles among other parameters can be defined by the user for both the tractor and trailer. The current version of TruckSim does not allow users to define aerodynamic add-ons such as tail, skirts, vortex generators, and cab top deflectors among others. Other types of simulation analyses such as CFD would have to be performed to determine the effects of such aerodynamic add-ons. However, TruckSim has an extensive database of different tractor and trailer design and dimensions representing current truck configurations.
The software has a standard interface to MATLAB/Simulink and provides the ability to test different scenarios including numerous test vehicles and road and environmental conditions. To run an analysis in the software, the user first has to determine the truck type from the configurations available. The tires, powertrain, number of axles, and brake types among other parameters have to be determined. A screenshot for configuring a tractor is shown in Figure 3. The user then defines the attributes of the trailer. These would include trailer length and height, number of axles, load configuration and shape, center of gravity of the load, and height of the load. The third step would then involve specifying the track length, its geometry, and condition (wet or dry). The user also inputs the wind speed and direction.
On the simulation procedure page, the initial coastdown speed has to be defined. The track chosen for analysis is also selected. Finally, a start and stop time have to be specified for the analysis. The stop time should be chosen such that the required lowest speed chosen for the coastdown analysis is covered during the time. It is much more appropriate to select a time which ensures that a speed of 0 is attained during the coastdown run time. The user can also determine the types of plots and outputs to obtain from the software. An example of the user interface for the simulation procedure is as shown in Figure 4.
It is important to note that TruckSim does not calculate the road load coefficients. Rather, the coefficients are estimated from outputs of velocities and times of coastdown runs using standard regression techniques. The road load coefficients for this study were determined using the data analysis package in the Microsoft Excel software. Additional information and documentation for TruckSim can be found on the mechanical simulation website .
The coastdown data for each half run was combined with its corresponding half in the same direction. A total of 12 valid runs were used for the analysis. A comparison of the coastdown times between field and simulated runs is shown in Table 2. The table indicates that the field tests lasted longer on most occasions compared to the simulation runs. This difference was much more pronounced in the unladen southbound runs. The differences observed may be attributed to the inability of the simulation to completely capture all the conditions in the field.
Coastdown coefficients were derived for both field and simulated data as specified by the EPA Phase 1 procedure using regression analysis. The procedure neglects mechanical resistance effects and assumes that [C.sub.rr] is constant . The regression coefficients were then corrected for wind effects, temperature, weight, and air density in accordance with section 10.5 of SAE J1263. Details of the correction of the drag terms ([f.sub.0] and [f.sub.1]) will not be discussed in this article for purposes of brevity. Tables 3 and 4 list the regression coefficients obtained from the analyses. SAE J1263 recommends the coefficients of paired runs be averaged. These were referred to as cycles. The simulation runs and drag term corrections were carried out under the same wind, temperature, and air density conditions as the field runs. Average drag terms were obtained by first averaging laden and unladen cycles separately. The averages from the two loading conditions were then averaged again to derive a single road load equation. For comparison purposes, the coefficients of aerodynamic drag ([C.sub.D]) and rolling resistance ([C.sub.rr]) were calculated for both field and simulated data. A projected front area of 7.73 [m.sup.2] was used for the analysis.
The projected front area (A) was approximated according to Equation 10 specified by SAE J1100 :
A = 0.8 *(H)*(W) Eq. (10)
where H is the vehicle height measured vertically from the highest point on the vehicle body to the ground and W is the dimension between the widest points on the body, excluding mirrors, hardware, and applied moldings but including fenders when integral with the vehicle.
The analysis shows that weight has a significant effect on rolling resistance. As the weight increases, the rolling resistance drag also increases. This is expected and consistent with previous studies [14, 15]. Aerodynamic drag on the other hand is mainly affected by vehicle and wind speed. Previous studies have found the overall effect of load on aerodynamic drag and consequently on [C.sub.D] to be insignificant [11, 14].
However, the results seem to show some weight sensitivities on the aerodynamic term for the coastdown runs. It should however be noted in Table 3 that field coastdown runs for cycles 5 and 6 (unladen conditions) were conducted under higher wind speeds than for cycles 1 to 3. This accounts for the higher drag terms under cycles 5 and 6 in comparison to the other runs. Estimation of accurate drag terms, especially the aerodynamic drag which is dependent on wind effects, requires accurate measurement of prevailing wind parameters at test sites. This study did not account for small-scale fluctuations of wind over short periods which may add some inaccuracies into the measurements. Additionally, the EPA and other similar procedures assume wind speed can be accounted for as a constant vector over the length of the test track, an assumption which is rare in the field . The lack of onboard anemometry and explicitly accounting for the effects of wind in the current EPA procedure may limit accurate estimation of coastdown coefficients. Vehicles traveling along a road will experience constantly changing wind conditions which are not constant in either velocity or direction. As the EPA intensifies efforts to include onboard anemometry in its coastdown procedure, future studies will eliminate inaccuracies in coefficient estimation due to not incorporating accurate wind effects .
To compare the results of the field and simulated analyses, it is imperative to note that simulation is unable to account all the ambient field conditions as well as variations that may be encountered during testing. Factors unaccounted for using the simulation software include temperature of the test track, changing wind conditions, air density, variations in test track texture and grade, vehicle preparation, tire pressure, and operation of steering system by the driver among others.
Based on the analyses, the average rolling resistance term for the field test was found not to differ much from the simulation runs. The average rolling resistance term differed only by 11.99N (0.65%) for the field and simulated results. This is despite the inability to incorporate all the characteristics of the test tires and track surface into the simulation. On the other hand, the aerodynamic drag term was found to be higher for the simulated data in all the runs analyzed. The average aerodynamic drag term difference for the two conditions was about 15%. This implies that the wind and speed effects were more pronounced in the simulation than on the field tests. A reason for this difference is the inability to account for the variations in wind conditions in the simulations. The effect is that as the speed increases, the road load from simulation becomes higher than the road load from the field tests. For example, at a typical highway speed of 27 m/s (97 km/h), the difference between the simulated and field road load was found to be 391 N (using the overall drag coefficients).
For additional comparisons, [C.sub.D] and [C.sub.rr] values were calculated. Comparisons using these coefficients are ideal because they are standard metrics for comparing drag forces . These coefficients are shown in Table 5. Published [C.sub.D] values show it to be between 0.6 and 0.7 for commonly aerodynamically designed semi-trailer trucks but may be as high as 0.9 for some other truck designs [2, 31, 32, 33]. [C.sub.rr] on the other hand ranges between 0.007 and 0.009 for typical semi-trailer trucks [2, 3, 15, 33]. It can be seen from Table 5 that both [C.sub.D] and [C.sub.rr] change with different test cycles. These changes are attributable to changing wind speed and direction, air and track temperatures, air pressure, humidity, and friction coefficient . Additionally, the coefficients may differ due to random errors in the individual coefficient calculations but which are minimized by averaging runs in both directions of testing . Inspection of the figures in Table 5 shows that the average [C.sub.D] value for the field tests falls within the range of an aerodynamically designed semi-trailer while being much higher for simulation.
For [C.sub.rr] values, the results show them to be nearly similar, not deviating much from published data. This finding may be an indication that the simulation is unable to adequately model aerodynamic drag in the presence of wind effects even when corrections are applied. Therefore, a different simulation analysis was undertaken considering different loads but with no wind effects (simulations run under zero-wind). The results of this analysis under loading increments of 2268 kg (5000 lb) are displayed in Table 6.
The simulation under zero-wind condition resulted in an average [C.sub.D] value identical to when wind effects were considered. It can also be noted that drag coefficients exhibit a trend of increasing with increasing test vehicle mass. This finding does not conform to past literature which have observed that [C.sub.D] is independent of weight [H, 14]. The apparent sensitivity of [C.sub.D] values to weight is due to simulation under zero-wind effects. Under this idealistic scenario, the influence of momentary gusts of wind, slight turbulences, and other wind effects on [C.sub.D] is absent. Air around the vehicle moves as a single mass resulting in more resistance. This may explain the sensitivity of the simulation [C.sub.D] to weight. The use of this zero-wind condition, though not representative of the real-world condition, provided a base from which a calibration correction could be developed and applied. The findings from Table 6 also show that the average [C.sub.rr] is identical to what was found when wind effects were considered in the simulation. This finding is expected and confirms the a priori belief that rolling resistance is not influenced by wind. The consistency of the rolling resistance term and [C.sub.rr] implies that wind effects account for the main difference between the simulation and field results.
From the analysis of the simulation results above, the aerodynamic road load and consequently [C.sub.D] values are overestimated even when wind effects are not considered. The results indicate that the use of the terms derived from the zero-wind condition in calculating road loads as they are will lead to higher drag forces than expected. To correct this situation, a calibration curve was developed from the field and simulated data. The condition of zero-wind and grade from the simulation was chosen for the analysis because the coastdown procedure assumes very minimal to no wind conditions and a level track . The flowchart for deriving the calibration curve is shown in Figure 5.
Average drag terms for laden and unladen conditions (both field and simulation) were used in developing the calibration curve. The average drag terms from the laden and unladen coastdown runs were first calculated separately for the field tests. These were then averaged for the field drag terms to be used in the calibration analysis. The drag terms for the simulation were simply averaged for the loaded and unloaded conditions.
The next step in developing the calibration curve involved using regression analysis to derive an equation. The equation obtained was of the form:
[F.sub.corrected] = [[beta].sub.o] + [[beta].sub.1][F.sub.simulation] Eq. (11)
where [F.sub.corrected] is the corrected simulation drag force, [F.sub.simulation] is the drag force from simulation under zero-wind condition for a weight, and [[beta].sub.o], [[beta].sub.1] are regression coefficients. To assess the calibration curve, drag forces from different simulation loads under zero-wind conditions were corrected using the calibration equation. Drag terms were then obtained from the corrected forces and vehicle speed according to Equation 11. Subsequently, [C.sub.D] and [C.sub.rr] were computed from the terms derived from the corrected simulation drag force. The calibration curve from the analysis is as shown by Equation 12:
[F.sub.corrected] = 357.77 + 0.785[F.sub.simulation] Eq. (12)
Tables 7 and 8 display the results of the drag terms and coefficients obtained after applying the calibration correction to the simulated drag forces. For comparison purposes, the uncorrected terms and coefficients previously shown in Tables 5 and 6 are also displayed.
It should also be noted from Table 8 that the average corrected terms for the loaded and unloaded conditions yield the almost same average coefficients from the field analysis as was expected; (F= 1853.07 + [2.99v.sup.2]). The preceding analyses show that correcting the simulation drag forces using the calibration curve yields consistently lower aerodynamic drag terms. This in turn led to lower [C.sub.D] values as seen in Table 8. The [C.sub.D] values were found to be lower than the uncorrected coefficients and compare better with published data. However, it is still apparent that [C.sub.D] is sensitive to weight. The results also show that the rolling resistance drag term did not consistently decrease or increase after applying the calibration curve but stayed within a narrow range.
The use of TruckSim and other similar software is advantageous for a number of reasons. First, TruckSim is easy to use and does not require a deep understanding of fluid dynamics or any programing as is required some other simulation software. Second, the proposed approach using the software is much more economical compared to full-scale field tests. Full-scale field coastdown testing requires instrumentation and good weather conditions for reliable results to be achieved. Bad weather may lead to prolonged test times with reliable results not guaranteed. TruckSim can model a wider range of vehicle types and provides a controlled environment. Though TruckSim is not an exclusive coastdown simulation software, reliable estimates of both aerodynamic and rolling resistance terms can be obtained from its output. Predominantly, simulation software on the market focus on the aerodynamic aspects of road load analysis. TruckSim can be used to estimate road loads due to both aerodynamic drag and rolling resistance.
Summary and Conclusions
This study analyzed and compared drag forces and coefficients derived from field and simulated coastdown runs using a five-axle semi-trailer. Road load analysis of the field tests was done according to the Phase 1 EPA modified SAE J1263 procedure for heavy vehicles. The simulation was carried out using a simple mechanical simulation software known as TruckSim. The software was able to incorporate both the effects of aerodynamic and rolling resistance into the simulation process. The simulated coastdown coefficients under different wind and loading conditions were further compared to published values of the coefficients. A calibration curve was then developed to correct drag forces obtained from the simulation runs to better correlate the simulated drag coefficients with field and published data. The analysis showed that:
* Significant differences exist between coastdown drag terms for field and simulation tests. These differences are much more pronounced for the aerodynamic drag term than for the rolling resistance term. The differences remained when wind effects were corrected. Coefficients derived from the simulation analysis under calm, wind conditions indicated that [C.sub.D] was higher than values obtained from the field tests and published data.
* The [C.sub.rr] value did not show a lot of variation between field and simulation tests. The same observation was made for simulation results under wind and zero-wind conditions. This shows that the simulation software was able to adequately model rolling resistance forces.
* A calibration curve was developed using the field test and zero-wind condition results to correct the drag terms from the simulation. Drag coefficients derived from using the calibration curve indicated that the aerodynamic drag reduced in all instances. The average [C.sub.D] was found to fall within the range of published values expected for an aerodynamically designed truck. However, some of the loads still had [C.sub.D] values higher than what was found in published data. This effect was attributed to the modeling of zero-wind in which the air acted as a solid mass lacking any turbulence thereby increasing [C.sub.D].
* Based on the analysis, it is concluded that the use of available mechanical simulation software will yield higher than expected drag forces. These drag forces can be adequately corrected using a calibration curve. Simulation may be used to fill in for different test loads in situations when it will not be possible to conduct field tests which are expensive and require specific atmospheric conditions.
A number of studies have explored the effects of aerodynamic drag reduction devices on road loads using scale models of trucks in wind tunnels, simulation, and CFD analysis. Future work should take into account the effect of these devices on road load coefficients derived using the proposed methodology. Such devices include vortex generators, boat tails, and skirts, among others. Modeling software similar to TruckSim but with the capability of incorporating drag devices into the coastdown procedure may be used for the analysis.
The authors would like to acknowledge that this work is part of project #RS08216 funded by the Wyoming Department of Transportation (WYDOT). All figures, tables, and equations listed in this article will be included in a WYDOT final report.
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Milhan Moomen, Mahdi Rezapour, Amirarsalan Mehrara Molan, and Khaled Ksaibati, University of Wyoming, USA
Received: 07 Jun 2018
Revised: 23 Oct 2018
Accepted: 06 Nov 2018
e-Available: 07 Jan 2019
TABLE 1 Test truck specifications. Specification Description Cab style Sleeper Make/model Kenworth T680 Series (2016) Trailer model Hyundai (2007) Gross vehicle weight rating 36287 kg Trailer length 16.15 m Tires Bridgestone 295/75R22.5 Engine Cummins ISX-15 Engine Engine model year 2013 Transmission Eaton Fuller 13-Speed Manual TABLE 2 Field and simulation test times. Run no. Direction Loading condition Field test time (s) 1 Northbound Laden 259.88 2 Southbound Laden 214.04 3 Northbound Laden 248.52 4 Southbound Laden 218.10 5 Northbound Laden 255.42 6 Southbound Laden 217.34 7 Northbound Laden 256.51 8 Southbound Laden 213.70 9 Northbound Unladen 233.40 10 Southbound Unladen 181.50 11 Northbound Unladen 240.50 12 Southbound Unladen 186.52 Simulation test [DELTA]T (simulation test time - Run no. time (s) field test time) 1 244.00 -15.88 2 206.25 -7.79 3 244.00 -4.52 4 206.25 -11.85 5 244.00 -11.42 6 206.25 -11.09 7 248.03 -8.48 8 216.50 2.80 9 228.00 -5.40 10 157.77 -23.73 11 228.00 -12.50 12 157.77 -28.75 % error ([DELTA]T/field Run no. test time) 1 -6.1 2 -3.6 3 -1.8 4 -5.4 5 -4.5 6 -5.1 7 -3.3 8 1.3 9 -2.3 10 -13.1 11 -5.2 12 -15.4 TABLE 3 Drag terms from field coastdown analysis. Test mass Rolling resistance Direction/cycle (kg) term ([f.sub.o]) (N) NB1 2020.04 SB1 36287 3810.04 Cycle 1 2915.04 NB2 2164.9 SB2 36287 3542.25 Cycle 2 2853.58 NB3 1989.37 SB3 36287 3867.00 Cycle 3 2928.19 NB4 2035.15 SB4 36287 3901.31 Cycle 4 2968.23 NB5 18144 688.97 SB5 1524 Cycle 5 1106.49 NB6 792.96 SB6 18144 1398.8 Cycle 6 1095.88 Average drag terms Corrected rolling Aerodynamic term Direction/cycle resistance term ([f.sub.2]) ([f.sub.o]) (N) [N/[(m/s).sup.2]] NB1 1871.81 2.97 SB1 3657.82 2.97 Cycle 1 2764.82 2.97 NB2 2009.75 2.88 SB2 3374.83 2.92 Cycle 2 2692.29 2.90 NB3 1822.67 2.99 SB3 3695.3 2.62 Cycle 3 2758.98 2.81 NB4 1825.27 2.95 SB4 3690.8 2.59 Cycle 4 2758.04 2.77 NB5 541.95 4.54 SB5 1403.53 2.27 Cycle 5 972.74 3.41 NB6 642.27 4.26 SB6 1262.58 2.54 Cycle 6 952.42 3.40 Average drag terms 1853.06 Corrected aerodynamic term Direction/cycle ([f.sub.2]) [N/[(m/s).sup.2]] NB1 2.87 SB1 2.87 Cycle 1 2.87 NB2 2.77 SB2 2.81 Cycle 2 2.79 NB3 2.87 SB3 2.52 Cycle 3 2.70 NB4 2.84 SB4 2.49 Cycle 4 2.66 NB5 4.33 SB5 2.17 Cycle 5 3.25 NB6 4.05 SB6 2.41 Cycle 6 3.23 Average drag terms 3.00 TABLE 4 Drag terms from simulated coastdown analysis (wind effects considered). Test mass Rolling resistance Corrected rolling Direction/cycle (kg) term ([f.sub.o]) (N) resistance term ([f.sub.o]) (N) NB1 36287 1937.01 1927.61 SB1 3618.64 3605.49 Cycle 1 2695.52 2766.55 NB2 36287 1937.01 1733.44 SB2 3618.64 3392.61 Cycle 2 2695.52 2563.02 NB3 36287 1937.01 1726.08 SB3 3618.64 3378.2 Cycle 3 2695.52 2552.14 NB4 36287 1910.76 1655.91 SB4 3254.67 2937.88 Cycle 4 2546.3 2296.89 NB5 18144 880.46 768.78 SB5 1684.40 1518.37 Cycle 5 1240.36 1143.57 NB6 18144 880.46 760.59 SB6 1684.40 1502.21 Cycle 6 1240.36 1131.4 Average drag terms 1841.07 Aerodynamic term Corrected aerodynamic term Direction/cycle ([f.sub.2]) ([f.sub.2]) [N/[(m/s).sup.2]] [N/[(m/s).sup.2]] NB1 3.96 3.82 SB1 4.17 4.03 Cycle 1 4.07 3.92 NB2 3.96 3.81 SB2 4.17 4.01 Cycle 2 4.07 3.91 NB3 3.96 3.81 SB3 4.17 4.01 Cycle 3 4.07 3.91 NB4 3.83 3.68 SB4 4.74 4.56 Cycle 4 4.23 4.12 NB5 2.89 2.76 SB5 3.79 3.62 Cycle 5 3.27 3.19 NB6 2.89 2.74 SB6 3.79 3.60 Cycle 6 3.27 3.17 Average drag terms 3.57 TABLE 5 Field and simulated drag coefficients. Cycle Field Simulation 1 0.63 0.87 2 0.62 0.87 Drag 3 0.60 0.86 coefficient 4 0.59 0.91 ([C.sub.D]) 5 0.72 0.70 6 0.71 0.70 Average 0.65 0.83 1 0.0078 0.0078 2 0.0076 0.0072 Rolling 3 0.0078 0.0072 resistance coefficient 4 0.0078 0.0065 ([C.sub.rr]) 5 0.0062 0.0064 6 0.0062 0.0064 Average 0.0072 0.0069 TABLE 6 Drag terms from simulated coastdown analysis (zero-wind effects). Rolling Test Rolling Aerodynamic Drag resistance mass resistance term ([f.sub.2]) coefficient coefficient (kg) term ([f.sub.o]) [N/[(m/s).sup.2]] ([C.sub.D]) ([C.sub.rr]) (N) 36287 2554.24 4.28 0.95 0.0072 34019 2388.11 4.17 0.92 0.0072 31751 2222.57 4.06 0.90 0.0071 29484 1898.89 3.64 0.81 0.0066 27216 1891.73 3.82 0.86 0.0071 24948 1726.74 3.69 0.85 0.0063 22680 1562.21 3.56 0.79 0.0070 20412 1397.77 3.42 0.76 0.0070 18144 1253.84 3.35 0.74 0.0070 Average drag coefficients 0.84 0.0069 TABLE 7 Comparison of drag terms after calibration correction. Uncorrected simulation drag terms (no wind condition) Rolling resistance term Aerodynamic term ([f.sub.2]) Test mass (kg) ([f.sub.0]) (N) [N/[(m/s).sup.2]] 18144 1253.84 3.35 20412 1397.77 3.42 22679 1562.21 3.56 24948 1726.74 3.69 27216 1891.73 3.82 29484 1898.89 3.64 31751 2222.57 4.06 34019 2388.11 4.17 36287 2554.24 4.28 Corrected simulation drag terms derived from calibration curve Rolling resistance term Aerodynamic term ([f.sub.2]) Test mass (kg) ([f.sub.o]) (N) [N/[(m/s).sup.2]] 18144 1342.46 2.63 20412 1455.50 2.69 22679 1584.64 2.80 24948 1584.61 2.80 27216 1842.78 3.00 29484 1849.01 2.86 31751 2103.20 3.19 34019 2233.25 3.27 36287 2363.67 3.36 TABLE 8 Comparison of drag coefficients after calibration correction. Uncorrected Corrected coefficients coefficients (no derived from calibration wind condition) curve Test mass (kg) [C.sub.D] [C.sub.rr] [C.sub.D] [C.sub.rr] 18144 0.75 0.0070 0.58 0.0075 20412 0.77 0.0070 0.59 0.0073 22680 0.80 0.0070 0.62 0.0071 24948 0.83 0.0063 0.62 0.0065 27216 0.86 0.0071 0.66 0.0069 29484 0.82 0.0066 0.63 0.0076 31751 0.91 0.0071 0.70 0.0068 34019 0.94 0.0072 0.72 0.0066 36287 0.96 0.0072 0.74 0.0066 Average 0.85 0.0069 0.66 0.0070 coefficients
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|Author:||Moomen, Milhan; Rezapour, Mahdi; Molan, Amirarsalan Mehrara; Ksaibati, Khaled|
|Publication:||SAE International Journal of Commercial Vehicles|
|Date:||Mar 1, 2019|
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