Optimizing the Aerodynamic Efficiency of Intermodal Freight Trains

Yung-Cheng LaiChris BarkanHayri Önal

University of Illinois at Urbana - Champaign

November 13, 2005

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As of 2004, fuel costs had increased by more than 88% since 1998

Average Cost Per Gallon(Cents)

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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

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Loads should be assigned not only based on “slot utilization” but also “slot efficiency”

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

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

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Gap Length (ft)

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Frequency diagram is used to evaluate the aerodynamic efficiency of IM trains

How can we further assist railroads in fuel savings?

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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

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We present an IP model and a heuristic approach that incorporate IM train aerodynamics

Intermodal train aerodynamics

Models for optimal loading:1. Integer programming (IP)2. Heuristic method

Comparison of IP and heuristic results

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“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)

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Larger gaps resulting in a higher aerodynamic coefficient and greater resistance

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Unit (k) Drag area (CDA) Adjusted factor

# (ft2)1 (locomotive) 31.618 1.5449

2 28.801 1.40733 26.700 1.30464 25.133 1.22805 23.963 1.17096 23.091 1.12837 22.440 1.09648 21.954 1.07279 21.591 1.0550

10 21.320 1.0418100 20.466 1.0000

The front of the train experiences the greatest aerodynamic resistance

Objective:

Minimize the total “adjusted” gap length within the train(adjusted gap length = adjusted factor x gap length )

Placing loads with shorter gaps in the frontal position generates less aerodynamic resistance

base value

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We present an IP model and a heuristic approach that incorporate IM train aerodynamics

Intermodal train aerodynamics

Models for optimal loading:1. Integer programming (IP)2. Heuristic method

Comparison of IP and heuristic results

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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 TypeP = 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

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Loading assignment must follow loading capability of each unit as well as length & weight constraints

Subject to:

Where: Ripk = Loading Capabilitywij = Weight of jth Load in i TypeCk = Weight Limit of kth UnitQkp = Length limit of position p in kth Unitδk = 1 for well-car unit; 0 otherwiseФ = an arbitrarily specified large numberxk = 1 if the top slot of kth Unit can be used; 0 otherwise

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loading capabilities

double-stack rules

weight constraint

length constraint

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Load the train sequentially by selecting the best load in the pool for the current unloaded slot

Length of actual load100%

Length of ideal loadScore =

The position-in-train effect is automatically accounted for because the train is loaded sequentially from front to back

Trailers Score53' 100%48' 91%40' 75%28' 53%

none 0%

53-foot-slot spine car

Start Last slot?

Stop

Determine best-fit load

Best-fitin pool?

Assign best-fit load to current

slot

Yes

No

No

Yes

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We present an IP model and a heuristic approach that incorporate IM train aerodynamics

Intermodal train aerodynamics

Models for optimal loading:1. Integer programming (IP)2. Heuristic method

Comparison of IP and heuristic results

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Loads: fifty , fifty , fifty

Train: ten 5-unit 53-foot-slot spine cars followed byten 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

Applying both methods to a train w/o well cars result in the same optimal loading pattern

53’48’40’ 150 loads

100 slots

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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)

Applying both methods to a train with well cars result in different loading patterns

myopic decision

53’48’40’

53’48’

53’

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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

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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?