# Tractive Effort of a Locomotive

The tractive effort of a locomotive is the force that the locomotive can generate for hauling the load. The tractive effort of a locomotive should be enough for it to haul a train at the maximum permissible speed. There are various tractive effort curves available for different locomotives for different speeds, which enable the computation of the value of tractive effort. Tractive effort is generally equal to or a little greater than the hauling capacity of the locomotive. If the tractive effort is much greater than what is required to haul the train, the wheels of the locomotive may slip.

A rough assessment of the tractive effort of different types of locomotives is provided in the following sections.

442 Railway Engineering

## Steam Locomotive

The tractive effort of a steam locomotive can be calculated by equating the total power generated by the steam engine to the work done by the driving wheels.

Assume P to be the difference in steam pressure between the two sides of the cylinder, A is the area of the piston of the engine, d is the diameter of the piston of the engine, L is the length of the stroke of the engine, D is the diameter of the wheel of the locomotive, and Te is the mean tractive effort of the locomotive. Work done by a two-cylinder steam engine

= 2 x difference in steam pressure x area of the piston x 2 x length of the stroke = 2P x A x 2L

= 2P x pp x 2L = pPd2 L (25.12)

Work done in one revolution of the driving wheel of the locomotive:

= tractive effort x circumference of the wheel

= Te xpD (25.13)

on equating Eqns (25.12) and (25.13),

pPd2 L = Te x pD Pd2 L

or Te = (25.14)

It is clear from Eqn (25.14) that tractive effort increases with an increase in steam pressure difference and the diameter and length of the piston, but decreases with an increase in the diameter of the driving wheel of the locomotive.

## Diesel Locomotive

Tractive effort of a diesel-elective locomotive can be assessed by the following empirical formula.

^ 308 x RHP _ .

Te =-v-(25.15)

where Te is the tractive effort of a diesel-electric locomotive, RHP is the rated horsepower of the engine, and V is the velocity in km/h.

## Electric Locomotive

The tractive effort of an electric locomotive varies inversely with the power of speed. The empirical formulae for calculating the approximate value of tractive effort are as follows.

For an dc electric locomotive: Te = a/V (25.16)

For an ac electric locomotive: Te = a/V5 (25.17)

where a is a constant depending upon the various characteristics of the locomotive.

The important characteristics of three types of tractions are compared in Table 25.2.

 Characteristics Steam locomotive Diesel locomotive Electric locomotive Design characteristics Source of energy and basic Coal or oil is burnt to generate Diesel oil is used for the Electric energy is supplied from a design characteristics steam; a steam engine converts the heat energy of the steam into the rotary energy of the moving wheels. generation of power with the help of a diesel engine, the generated power is transmitted by means of a mechanical, hydraulic, or electrical transmission system for propelling the wheels. stationary prime mover, which is converted into mechanical energy for propelling the wheels. Simplicity of design The design of the engine is simple. The engine itself is heavy and bulky. The design is not as simple and compact, the engine weighs less. The design is complicated but the weight is comparatively low. Tractive effort Tractive effort is low because torque is not uniform. Tractive effort is higher because torque is uniform. An even higher tractive effort is obtainable. Adhesion (ratio of tractive 0.20-0.25 because torque 0.25 for electric transmission, 0.25 dc effort to weight on wheels, is not uniform. 0.33 for hydraulic transmission. 0.33 ac beyond which slipping occurs) Ratio of horse power and weight 75 kg per horsepower 45 kg per horsepower 25 kg per horsepower Overload capacity 10%-25% overload capacity. Only 6%-10% overload capacity, which is the overload capacity of the diesel engine. Over 50% overload capacity, as energy is drawn from an outside source. Thermal efficiency About 7% About 25% About 90% Technical experience on Indian Simple machinery, over hundred More complicated machinery, Some experience on 1500-V dc Railways years of experience. very limited experience in our country. systems, experience being acquired on 25-kV ac systems. (contd)
 Characteristics Steam locomotive Diesel locomotive Electric locomotive Cost of locomotive About Rs 5 million About Rs 15 million About Rs 18 million Reversing arrangement A steam locomotive requires a turntable for reversing its direction. Reversing of engine is not required. Only the driver and guard have to change their positions. Reversing of locomotive is not required. Life of locomotive About 40 years About 30 years Over 30 years Utilization of power Operational characteristics Fuel is consumed from the moment it is lighted, whether the locomotive is in use or not. There is no wastage of power when idle if the engine has been switched off. There is no wastage of power when idle. Requirement of staff for operation One driver and two firemen One driver One driver Smoke and fire Both fire and smoke present. No fire and little smoke. No smoke and no fire. Promptness of service Takes time for igniting coal and raising enough steam for the engine to start. Service is readily available. Ready service without any wastage of time. Importance of driving skill Driving skill is important because the driver is required to control each regulating factor separately. There is not much variance in the regulating factor and so the driver's skill is not important. Driving is simpler and normal driving skills are sufficient. Normal working hours About 12 hours a day About 21 hours a day About 21 hours a day Monthly kilometrage 3500 km/month 9000 km/month 10,000 km/month