Optimizing the Aerodynamic Efficiency of Intermodal Freight Trains

1. Optimizing the Aerodynamic Efficiency of Intermodal Freight Trains Yung-Cheng Lai Chris Barkan Hayri Önal University of Illinois at Urbana - Champaign November 13, 2005

3. As of 2004, fuel costs had increased by more than 88% since 1998 ~ Average Cost Per Gallon (Cents) ?

4. Intermodal (IM) trains incur greater aerodynamic penalties and fuel consumption than general trains IM trains suffer from their equipment design and loading pattern IM trains are the fastest freight trains operatedin North America Investigation of options to improve IM train fuel efficiency have the potential to reduce fuel costs

5. Loads should be assigned not only based on “slot utilization” but also “slot efficiency” 53 53 53 53 53 Maximizing slot utilization improves train efficiency since it eliminates empty slots and the consequent large gaps However, two trains may have identical slot utilization, but different loading patterns and aerodynamic resistance Loads should be assigned not only based on slot utilization but also better matching of loads with cars (slot efficiency) Train resistance could be lowered by as much as 27% and fuel savings by as much as 1 gallon/mile/train 40 40 40 40 40

6. A machine vision system has been developed to monitor the slot efficiency of intermodal trains

7. Frequency diagram is used to evaluate the aerodynamic efficiency of IM trains How can we further assist railroads in fuel savings?

8. A model to automatically assign loads to the train ensuring minimum fuel consumption is needed Loading assignment at intermodal terminals is still a largely manual process Containers or trailers are assigned to available well, spine or flat cars following weight and length constraints We treat the train make-up as given because cars in an IM train generally are not switched

9. We present an IP model and a heuristic approach that incorporate IM train aerodynamics Intermodal train aerodynamics • Models for optimal loading: • Integer programming (IP) • Heuristic method Comparison of IP and heuristic results

10. “Gap Length” and “Position in Train” are the two most important factors to IM train aerodynamics • Based on the wind tunnel testing of rail equipment, three important factors to IM train aerodynamics were identified: • 1. Gap Length between the IM loads • 2. Position in Train • 3. Yaw Angle: wind direction (canceled out over the whole route)

11. Larger gaps resulting in a higher aerodynamic coefficient and greater resistance

12. base value The front of the train experiences the greatest aerodynamic resistance Placing loads with shorter gaps in the frontal position generates less aerodynamic resistance Objective: Minimize the total “adjusted” gap length within the train(adjusted gap length = adjusted factor x gap length )

13. We present an IP model and a heuristic approach that incorporate IM train aerodynamics Intermodal train aerodynamics • Models for optimal loading: • Integer programming (IP) • Heuristic method Comparison of IP and heuristic results

14. U1 U2 Minimize the total “adjusted” gap length within the train Where: i = Type of the Load (40’, 48’, 53’ etc.) j = Load Number within the Specific Type P = Position in the Unit (P1 or P2) k = Unit Number (1,2,…,N) Ak = Adjusted Factor of kth Gap Uk = Length of kth Unit Li = Length of ith Type Load (ft) yijkl = 1 if jth Load in i Type was Assigned to kth Unit Lth Position; 0 otherwise

15. loading capabilities double-stack rules weight constraint length constraint Loading assignment must follow loading capability of each unit as well as length & weight constraints Subject to: Where: Ripk = Loading Capability wij = Weight of jthLoad in i Type Ck = Weight Limit of kth UnitQkp = Length limit of position p in kth Unit δk = 1 for well-car unit; 0 otherwise Ф = an arbitrarily specified large number xk = 1 if the top slot of kth Unit can be used; 0 otherwise

16. Load the train sequentially by selecting the best load in the pool for the current unloaded slot The position-in-train effect is automatically accounted for because the train is loaded sequentially from front to back

17. We present an IP model and a heuristic approach that incorporate IM train aerodynamics Intermodal train aerodynamics • Models for optimal loading: • Integer programming (IP) • Heuristic method Comparison of IP and heuristic results

18. 53’ 48’ 40’ Applying both methods to a train w/o well cars result in the same optimal loading pattern 150 loads Loads: fifty , fifty , fifty Train: ten 5-unit 53-foot-slot spine cars followed by ten 5-unit 48-foot-slot spine cars Optimum based on IP & heuristics = 514 (ft) Worst case by manual assignment = 1170 (ft) Fuel savings is 0.95 gallons/mile/train 100 slots

19. 48’ 53’ 53’ 40’ 53’ 48’ myopic decision Applying both methods to a train with well cars result in different loading patterns Loads: fifty , fifty , fifty containers Train: ten 5-unit 48-foot-slot well cars and ten 5-unit 53-foot-slot spine cars IP result = 637 (ft) Heuristic result = 1096 (ft)

20. In summary, both IP & heuristics methods are better than the current manual assignment IP approach guarantees the best fuel efficiency, whereas the heuristics produces good but often sub-optimum There is a 20.6% difference in adjusted gap length between IP & heuristics based on 100 simulation runs Compared to the worst case by manual assignment, the potential fuel savings can be 0.95 gal/mile/train Extrapolating the savings over BNSF transcon would be at least 1,500 gal/train

21. The IP model can be extended to optimize the aerodynamic efficiency at the system level In this study, we focus on optimization of the aerodynamic efficiency of one outgoing train for a given set of loads Optimizing the daily/weekly loading plan would be beneficial for further increasing the fuel efficiency of the operation The complete model is intended to be incorporated into the terminal operation software in the future Questions?