# Tractive force

As used in mechanical engineering, the term tractive force can either refer to the total traction a vehicle exerts on a surface, or the amount of the total traction that is parallel to the direction of motion.[1]

In railway engineering, the term tractive effort is often used synonymously with tractive force to describe the pulling or pushing capability of a locomotive. In automotive engineering, the terms are distinctive: tractive effort is generally higher than tractive force by the amount of rolling resistance present, and both terms are higher than the amount of drawbar pull by the total resistance present (including air resistance and grade). The published tractive force value for any vehicle may be theoretical—that is, calculated from known or implied mechanical properties—or obtained via testing under controlled conditions. The discussion herein covers the term's usage in mechanical applications in which the final stage of the power transmission system is one or more wheels in frictional contact with a roadway or railroad track.

The term tractive effort is often qualified as starting tractive effort, continuous tractive effort and maximum tractive effort. These terms apply to different operating conditions, but are related by common mechanical factors: input torque to the driving wheels, the wheel diameter, coefficient of friction (μ) between the driving wheels and supporting surface, and the weight applied to the driving wheels (m). The product of μ and m is the factor of adhesion, which determines the maximum torque that can be applied before the onset of wheelspin or wheelslip.

Vehicles having a hydrodynamic coupling, hydrodynamic torque multiplier or electric motor as part of the power transmission system may also have a maximum continuous tractive effort rating, which is the highest tractive force that can be produced for a short period of time without causing component harm. The period of time for which the maximum continuous tractive effort may be safely generated is usually limited by thermal considerations. such as temperature rise in a traction motor.

Specifications of locomotives often include tractive effort curves,[3][4][5][6] showing the relationship between tractive effort and velocity.

The shape of the graph is shown at right. The line AB shows operation at the maximum tractive effort, the line BC shows continuous tractive effort that is inversely proportional to speed (constant power).[7]

Tractive effort curves often have graphs of rolling resistance superimposed on them—the intersection of the rolling resistance graph[note 1] and tractive effort graph gives the maximum velocity (when net tractive effort is zero).

In order to start a train and accelerate it to a given speed, the locomotive(s) must develop sufficient tractive force to overcome the train's drag (resistance to motion), which is a combination of inertia, axle bearing friction, the friction of the wheels on the rails (which is substantially greater on curved track than on tangent track), and the force of gravity if on a grade. Once in motion, the train will develop additional drag as it accelerates due to aerodynamic forces, which increase with the square of the speed. Drag may also be produced at speed due to truck (bogie) hunting, which will increase the rolling friction between wheels and rails. If acceleration continues, the train will eventually attain a speed at which the available tractive force of the locomotive(s) will exactly offset the total drag, causing acceleration to cease. This top speed will be increased on a downgrade due to gravity assisting the motive power, and will be decreased on an upgrade due to gravity opposing the motive power.