Fuel Economy for Tractor-Trailer Trucks Design Project II EGR 365 Fluid Mechanics Grand Valley State University Padnos College of Engineering Instructor: Dr. Mohammadzadeh Author: Matt Brower 17 July 2006Introduction In the Greater Grand Rapids area, most trucks traveling an interstate either travel north south (on I-131) or east west (on I-96). Using actual meteorological data for wind speed and direction taken at the Gerald R. Ford International Airport, the fuel efficiency for a semi-truck was found. Each member of the spring-summer EGR 365 Fluid Dynamics class was given a slightly different scenario for determining fuel efficiency. For this report the given criteria were that of a Mack tractor-trailer, cab over engine, non-sleeper, traveling 55 mph west during the day in July. Using the given meteorological data the fuel efficiency was found considering not only wind drag, but also driveline efficiency, drag on the tires, and braking horsepower. Theory To determine the wind drag, the yaw angle had to be calculated for the resultant vector of the wind and truck direction. Since the truck was traveling 55 mph west (or 270 degrees of north) the velocity vector for the wind due to the truck was 55 mph east (or 90 degrees of north). Figure 1 below shows a schematic of the velocity and wind vectors and their resultant vector. The yaw angle is the angle between the direction the truck is heading and the resultant vector. The yaw angle was used to find the drag coefficient for the truck. The drag coefficient was used to find the force of the wind drag. Figure 1: Graphic depiction of resultant wind vector and yaw angle ψ Vr V Vw ΦTo find the yaw angle, the meteorological data of wind direction probability and average wind speed was used. The yaw angle was used to find the drag coefficient from the graph of drag coefficient vs. yaw angle provided in the project description. Next, the drag coefficient was used in Eq (1) below to find the aerodynamic drag on the truck for that specific yaw angle. DRACAVD221ρ= (1) Whereρ= density of air, A = cross-sectional area of the truck,RV= magnitude of the resultant wind velocity vector, andDC is the drag coefficient. This drag value was then multiplied by the probability that the wind would actually be blowing from that direction. The sum of all of these percent probabilities gave the final average aerodynamic drag on the truck. Table 1 shows the meteorological data and the resulting values from the procedure described above. Appendix A contains all the sample calculations. Table 1: Meteorological data and Resulting Aerodynamic Drag Compass Angle July '94-day Vx Vy yaw angle Drag Coefficient Drag Force Percent Drag 0 0.0242 -0.0007 -5.0000 5.19 0.871 772.77 18.70 30 0.0484 -2.5005 -4.3298 4.71 0.844 682.29 33.02 60 0.0484 -4.3304 -2.4995 2.82 0.738 555.74 26.90 90 0.0762 -5.0000 0.0005 0.00 0.678 497.15 37.88 120 0.0403 -4.3299 2.5003 2.83 0.738 555.75 22.40 150 0.0484 -2.4997 4.3303 4.72 0.844 682.31 33.02 180 0.1210 0.0002 5.0000 5.19 0.871 772.80 93.51 210 0.1694 2.5001 4.3300 4.31 0.811 786.46 133.23 240 0.2097 4.3302 2.4999 2.41 0.711 734.07 153.94 270 0.1129 5.0000 0.0000 0.00 0.678 715.90 80.82 300 0.0806 4.3302 -2.4999 2.41 0.711 734.07 59.17 330 0.0161 2.5001 -4.3300 4.31 0.811 786.46 12.66 Calm 0.0081 0.0000 0.0000 0.00 0.678 601.55 4.87 Avg. wind speed = 5.00 Avg. Drag = 710.12 The rolling drag was then determined using the following equation: WbVaDR)( += (2) Where a = 7.5 lbf/1000 lbf, and b = 0 are constants based on tire construction, V = velocity of the truck, and W is the weight. The total drag on the truck is the sum of Eqs. (1 and 2). The truck is assumed to be traveling on a flat road and with zero acceleration, otherwise these two factors wouldhave to be considered since the engine would have to work harder to accelerate or climb hills. Once the total drag force was found as described above, the gallons per mile (GPM) was found. This was found using the equation: )/()( VBSFCBHPGPMfγ= (3) Where fγis the density of diesel fuel, which was given as 6.952 lbm/gal. In Eq. (3), BHP stands for the braking horsepower and BSFC stands for Brake specific fuel consumption. BHP was calculated using Eq. (4) below. accDTPVDBHP +=η/ (4) Where Dη is the driveline efficiency andaccP is the power used by accessories on the truck, which were given as 0.85 and 0, respectively. BSFC was estimated from the graph given in the project description of BSFC vs. BHP for various engine RPM. The RPM of the engine for the truck in this description was found to be approximately 1800 RPM. Refer to Appendix A for the calculation of this and other values described above. Results The resultant wind speed due to the truck and the wind was found to be 59.38 mph. This value along with the wind direction probability yielded an aerodynamic drag force of 734.86 lbf. The rolling drag for a truck with slightly worn bias ply tires and a weight of 53,780 lbf was 403.35 lbf. This yielded a total drag of 1,113.47 lbf. The BHP was found to be 192 hp which, along with the estimated engine RPM of 1800, yielded a BSFC value of 0.392 lbm/BHP*hr. Using these values in Eq. (4) yielded 0.197 GPM for the truck under the given circumstances. Discussion The value of 0.197 GMP described above is equal to 5.1 MPG, which is how most people think of fuel consumption. While this value seems low compared to cars, it is not excessive when the payload that a semi-truck carries is considered. Also, since the truck was traveling west, and west-southwest is the highest probability wind direction for the Greater Grand Rapids area, the fuel economy should improve for a truck heading east. It should also be noted that acceleration and grade angle were neglected in this study. This means that the comparative values are relevant, but actual fuel consumption will likely be higher than what was calculated. Recommendations One of the useful aspects of the study performed by the class would be to compare the results for different truck speeds to determine if traveling faster, and thusmaking more deliveries in shorter time, would lead to an increase in profit when compared to the increased fuel consumption. Another useful aspect would