Pulling Power

Education - Part 5A2

Motive Power - Pulling Power

Pulling Power or Tractive Effort

Motive power amounts to the energy needed to move a train. This power may be called pulling power or (better) tractive effort. Tractive effort is the energy needed to overcome friction, which arises from several points. For one, there is the friction of the bearings that facilitate the turning of the axels of the rolling stock. While the object of the bearings is to minimize this friction, it cannot be reduced to zero. On a long train with many axels, bearing friction is significant.

Another source of friction is that of the wheels against the rails. Such friction is absolutely necessary if the train is to be moved or stopped. But it is also a cost in tractive effort necessary to overcome wheel/rail friction. A related source of friction is called truck hunting (bogie hunting) in which an oscillation occurs as the wheels of the truck "hunt" for lateral equilibrium. This oscillation manifests itself as swaying of rolling stock and as a cost in tractive effort.

Another source of friction is the air through which a train must pass. Aerodynamic friction is meaningless when the train is stationary, but it increases as the square of the velocity of the train in motion.

Finally, there is a friction due to gravity. On a grade of 0° the friction due to gravity is a constant that provides the adhesion (wheel/rail friction) necessary for a train to move. But if the grade is greater than 0° there will be a cost in tractive effort necessary to overcome the force of gravity. If the grade is less than 0°, then the force of gravity contributes to the tractive effort.

Measuring Tractive Effort

Tractive effort is determined by the equation

Fmax = coefficient of friction × weight on drive wheels

where the coefficient of friction for steel on steel typically ranges between about 0.35 to 0.5. Fmax will have the dimension Newtons (N) which is a measure of acceleration such that 1N = 1 kg⋅m/s/s. In words, one Newton is the acceleration of one kilogram of mass 1 meter/second per second. For motive power, consider a locomotive with mass 50 tons (45359 kg) operating under a coefficient of friction of 0.4. Weight on drive wheel will be 45359 kg x 0.4 = 18143 N or 18.143 kN.

For practical purposes, there are two types of tractive effort, starting tractive effort and continuous tractive effort. It takes more effort to start a train from stand-sill than it does to keep a train moving once started thanks to momentum. There is also a point at which, if acceleration continues, the train will eventually reach a velocity at which the available tractive force of the locomotive(s) will exactly offset the total drag (sum of friction components), causing acceleration to cease and the train will run at a constant velocity as long at the tractive effort remains constant.

The problem is, tractive effort decreases as velocity increases, as the following formula shows:

F = P/v

where F is the tractive force in Newtons, P is the power output of the locomotive in watts and v is the velocity in meters per second. Maximum F can be maintained up to about 10 mph (16 k/h) after which it must fall fairly rapidly because the power transmission from engine to axels will rapidly overheat at full power.

For modern motive power, a different approach to measurement of pulling power may be used because neither of the above formulas accurately yields tractive effort, because the first formula does not take into account velocity and the second does not take into account mass or coefficient of friction.

Railroads now use dynamometer cars to measure tractive force at speed (velocity) in actual road testing. This provides a more accurate and realistic measure of a locomotive's ability to move a train. Today, motive power can be expressed in kiloNewtons (kN), watts or horsepower (see table below). Tractive effort is measured in Newtons.

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