Push Me Pull You

Let's start with a train of 100 cars with a gross weight of 100 tons each on straight and level track, with a set of locomotives on the front. The force required to keep the train moving at a given speed is equal to the forces of friction, aerodynamic drag and so forth. (I'll just say friction from now on to indicate all these forces.) For this example we'll take an oversimplification and say the friction is 1% of the car's weight. So we need 100 tons force to keep the train at speed, and a bit more to actually get the train moving to begin with. Now the tension on the coupler between the locos and first car is also equal to this force, so we have 100 tons total tension between the first rail car and the loco.

Now let's add a grade, say 1%. Now we need not only enough force to overcome the friction, but also need enough to overcome gravity. On a 1% grade this is, conveniently enough, also 1% of the car's weight. So we now need 2 tons per car or 200 tons to keep the train moving. And this is also the tension on the coupler between the loco and first car. A 2% grade will be 2 tons of gravity plus 1 ton of friction per car or 300 tons force required and 300 tons of tension on the first car's coupler.

Obviously we need to double the loco's to handle a 1% grade, and triple the locos for a 2% grade. But if we put them on the front we also need to increase the strength of the coupler and the car's frame. Adding loco's is easy, modifying freight cars not so much. If we add locos to the back we can get the full increase of force to keep moving up the grade and we reduce the amount of tension on the lead car's coupler. It is common on the BNSF over the Tehachapis to have 4 engines up front and two on the rear. So approximately the first two thirds of the train is being pulled and the last one third is being pushed.

Since no single MU'd set of locomotives is actually strong enough to move all the cars in the train there is very little chance of buckling the train or over stressing the couplers.

This is why the SP put Cab-forwards every thirty cars or so on trains heading over Donner Pass. Also, both BNSF and UP will put a set of locos in the middle of heavier trains heading over the Tehachapis.

Oh and one other thing - it's a lot easier to cut off the helper engines at the top of the grade if they are on the rear. But that is a secondary consideration.

Eric,

They aren't just running them that way as helpers over the passes, they are just running them that way period. They come out of the Powder River Basin and stay that way all the way to where-ever they are going and back. Through Montana all the helpers are MRL over the southern line (old NP). I see them over Bozeman pass, and they are cutting the MRL helpers in mid-train. Watched one the other day with 2 BNSF engines on each end and 4 MRL sd70ACe's mid-train. Some trains seem to have 2 on front, 1 on rear and some have 2 and 2, but as you said, all the coal trains seem to be running that way.