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 2006 Introduction 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 nonsleeper 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 Vw V Vr Figure 1 Graphic depiction of resultant wind vector and yaw angle To 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 D A 1 2 AVR2 C D 1 density of air A cross sectional area of the truck VR magnitude of the resultant wind velocity vector and C D is the drag coefficient Where 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 0 30 60 90 120 150 180 210 240 270 300 330 Calm 0 0242 0 0484 0 0484 0 0762 0 0403 0 0484 0 1210 0 1694 0 2097 0 1129 0 0806 0 0161 0 0081 Vx Vy 0 0007 2 5005 4 3304 5 0000 4 3299 2 4997 0 0002 2 5001 4 3302 5 0000 4 3302 2 5001 0 0000 5 0000 4 3298 2 4995 0 0005 2 5003 4 3303 5 0000 4 3300 2 4999 0 0000 2 4999 4 3300 0 0000 yaw angle 5 19 4 71 2 82 0 00 2 83 4 72 5 19 4 31 2 41 0 00 2 41 4 31 0 00 Drag Coefficient 0 871 0 844 0 738 0 678 0 738 0 844 0 871 0 811 0 711 0 678 0 711 0 811 0 678 Avg wind speed 5 00 Drag Force 772 77 682 29 555 74 497 15 555 75 682 31 772 80 786 46 734 07 715 90 734 07 786 46 601 55 Percent Drag 18 70 33 02 26 90 37 88 22 40 33 02 93 51 133 23 153 94 80 82 59 17 12 66 4 87 Avg Drag 710 12 The rolling drag was then determined using the following equation DR a bV W 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 would have 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 GPM BHP BSFC f V Where 3 f is 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 BHP DT V D Pacc 4 Where D is the driveline efficiency and Pacc 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 thus making more deliveries in shorter time would lead to an increase in profit when compared to the increased fuel consumption Another useful aspect would be to see the effect of heading and wind speed …