Calculations and Formulas

The train weight is simply the gross weight of the train at any moment in time.  This includes the weight of all of the railcars in the string plus the weight of the locomotive/s or railcar mover.  The train weight will change as railcars are loaded or unloaded, as fuel is used, etc.

The machine weight is the gross weight of the locomotive or railcar mover.  Effective machine weight applies to railcar movers that use weight transfer. In this case they lift up on the railcar coupler to transfer part of the railcar's weight onto the railcar mover.  This can be up to 46,000 lbs.  AAR rules limit this to 50,000 lbs. but most machines are limited to 46,000 lbs. to allow room for error without exceeding the 50,000 lb. limit.

When referring to locomotives and railcar movers the adhesion factor is the average coefficient of friction that the wheels develop with the steel rail without wheel slippage.   For standard DC locomotives without high adhesion traction control systems the adhesion factor is normally assumed to be about 25%.  High adhesion DC locomotives can have an adhesion factor of up to 34%.  High adhesion AC locomotives have reported adhesion factors of 35% to 38%.

The maximum tractive effort that a machine can produce is simply the effective machine weight multiplied by the adhesion factor.  This is the force that is available to move the machine plus the drawbar required to move the remainder of the train without slipping the machine's wheels.  

Maximum TE = Effective Machine Weight in lbs. x Adhesion Factor  

In practice the instantaneous tractive effort produced is equal to the force necessary to move the train, which includes the locomotive/s or railcar mover plus all of the railcars, at a given speed.  The formula 

Track Speed in mph  = (375 x Traction HP x Mechanical Efficiency)/TE in lbs.

shows that speed and tractive effort are inversely proportional at a fixed horse power.  However the TE in lbs. at any speed is still limited to the maximum TE as calculated from the machine weight and adhesion factor.  The tractive effort is always changing in a moving train as the pull of the train on the locomotive/s or railcar mover changes under varying grades, curves, speed changes, etc.

The maximum tractive effort is normally only a factor when starting off from a dead stop or when climbing steep grades.  Running tractive effort is the average instantaneous tractive effort required to move the train from point "A" to point "B".  the maximum running tractive effort available is limited to the maximum tractive effort above.  In order to run at higher track speeds it is necessary to increase horsepower.  

The instantaneous drawbar pull that a locomotive or railcar mover produces is always equal to the instantaneous tractive effort minus the force required to move the weight of the locomotive/s or railcar mover.

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