Complexity of train formation

Single freight cars do not arrive at the point of train formation in order of size and air resistance. Therefore imposing a specific waggon order would put another constraint on the train formation process and make it more time consuming unless a high degree of additional planning is applied. In any case, additional freight car ordering would increase train formation costs.

The air resistance of a freight train can be calculated in the following manner (according to Vollmer 1989):

1. For every car added to the train the air drag is increased by a certain specific value corresponding to the car type.
2. In case the previous car is lower than the car added there is an additional term accounting for the effect of the car front.
3. In case the previous car is of same height or higher, no additional term is needed since the added car runs in the lee of the previous car.
4. The first car of the formation is treated in a different manner since it is more exposed to the front wind.

The term described in 2. is the one, which an optimisation of car order intends to eliminate. If all cars are strictly ordered according to height beginning with the highest one, this additional term is zero between all cars.

The following example gives an idea of the optimisation potential:

Take a freight train consisting of 30 container cars, 15 empty cars and 15 cars loaded with 3 containers and compare the following two extreme types of car order:

A) worst case: one full car - one empty car - one full car - one empty car - etc.

B) best case: 15 full cars followed by 15 empty cars

Using the detailed empirical data from Vollmer 1989 one can calculate the air resistance for both configurations and find that B shows 26 % less air drag than A.

Considering the extreme height difference between the above freight cars and the fact that A is a worst case and that any more random order will be better aerodynamically, it is realistic to assume that the potential for improvement can be anything from 0 % (identical freight cars) to 25 % (in extreme cases).

Since air resistance usually accounts for about 50 % of the total energy demand of a freight train, reordering of freight trains has an energy saving potential ranging from 0 to 12 %.