Tractive Effort Fundamentals and Resistance Explained

The term tractive effort is often qualified as starting tractive effortcontinuous 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 (x) between the driving wheels and supporting surface, and the weight applied to the driving wheels (m). The product of x and m is the factor of adhesion, which determines the maximum torque that can be applied before the onset of wheelspin or wheelslip.

Starting tractive effort: Starting tractive effort is the tractive force that can be generated at a standstill. This figure is important on railways because it limits the train weight that a locomotive can set into motion.

Maximum tractive effort: Maximum tractive effort is defined as the highest tractive force that can be generated under any condition that is not injurious to the vehicle or machine. In most cases, maximum tractive effort is developed at low speed and may be the same as the starting tractive effort.

Continuous tractive effort: Continuous tractive effort is the tractive force that can be maintained indefinitely, as distinct from the higher tractive effort that can be maintained for a limited period of time before the power transmission system overheats. Due to the relationship between power (P), velocity (v) and force (F), described as:

P = vF or P/v = F

tractive effort inversely varies with speed at any given level of available power. Continuous tractive effort is often shown in graph form at a range of speeds as part of a tractive effort curve.

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.



Fundamental Characteristics


Forces acting on a vehicle

Tractive effort and resistance are the two main forces that oppose one another and determine the performance of roadway vehicles. Tractive effort is the force exerted against the roadway surface to allow a vehicle to move forward. Resistance encompasses all forces that push back and impede motion. Both of these are in units of force. The general formula for this is outlined below:

  F_t  = ma + R_a  + R_{{ rl }}  + R_g  \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\,\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\!


F_t\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\,\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\! = Tractive Effort

m\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\,\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\! = Vehicle Mass

a\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\,\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\! = Acceleration

R_a\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\,\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\! = Aerodynamic Resistance

R_{{ rl }}\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\,\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\! = Rolling Resistance

R_g\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\,\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\! = Grade Resistance

These components are discussed in greater detail in the following sections.