# Tractive Effort

## Tractive Effort

Tractive effort” (TE) is the force applied by a locomotive for moving itself and a train.  Tractive effort or tractive force is measured in kilo-Newtons (kN) or pounds force (lbf) where 1 kN = 228.4 lbf.

As with “power” there are different methods of measuring tractive effort:

• Drawbar tractive effort – the force applied by a locomotive to the connection to its train.  If the locomotive is running light (with no train) then its drawbar TE = 0.
• Wheel-rim tractive effort – the force applied by a locomotive to the rails through its driving wheels.  The difference between Wheel-rim TE and Drawbar TE is the force required to move the locomotive in overcoming internal (mechanical), rolling and wind resistances.
• Indicated or Cylinder tractive effort – a hypothetical force estimated by adding to the Wheel-rim TE the force required to overcome the frictional resistance of piston against cylinder, piston-rod against gland, crosshead against slidebar and the rotational resistance of big and small-end bearings.  In the case of the 5AT (FDC 1.1 lines 46 and 47), the Wheel-rim TE is estimated to be 93% of Cylinder TE at starting and 96% when running.
• Starting tractive effort – the pulling force exerted by a locomotive when starting from rest.

The commonly used formula for calculating a locomotive’s starting Tractive Effort is

The formula takes no account of piston rod diameter, which reduces the effective area of (and therefore the force applied to) the rear side of the piston.  In the case of the 5AT (and a few other locomotive types) the presence of a tail-rod reduces the effective area of both sides of the piston.

A locomotive’s starting tractive effort provides only an indication of the size of train that it can start.  It does not measure the ability of the locomotive to pull a train at speed.  This is because tractive effort reduces as speed increases.  A locomotive that can maintain a high tractive effort at speed is a more “powerful” locomotive than one that cannot since Power = Tractive Force x Speed.

The relationship between TE and Speed for a variety of locomotives is illustrated in the diagram below (copied from page 499 of Wardale’s book “Red Devil and Other Tales from the Age of Steam“) in which it can be seen that the TE of the “Super Class 5 4-6-0 (5AT) remains higher than even the most powerful British Pacifics once their speed exceeds 70 km/h.  The 5AT’s ability to maintain high TE at speed is a measure of its ability to deliver and make use of steam that is supplied to the cylinders  i.e. “good breathing”.  (The diagram can be compared to the Power – Speed diagram copied from the same page, which is shown on the Drawbar Power page of this section of the website.)

A locomotive’s tractive effort (at all speeds) is limited by its adhesive weight and the available coefficient of adhesion between wheel and rail, as discussed on the Adhesion page of this website.

The maximum speed that a locomotive can attain with any given train occurs when the locomotive’s drawbar tractive effort exactly equals the rolling resistance of the train (see the Rolling Resistance page of this website).

The acceleration that a locomotive can achieve with any given train can be calculated by applying Newton’s Second Law of Motion – i.e. by subtracting the rolling resistance of the locomotive and train from the locomotive’s wheelrim tractive effort, and dividing the difference by the total mass of the locomotive and train.