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.


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


years of experience.

very limited experience in our country.

systems, experience being acquired on 25-kV ac systems.



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


Steam locomotive

Diesel locomotive

Electric locomotive


Only low speeds are possible; on gradients, speed gets reduced further.

Higher speeds can be achieved; even on gradients, better speeds possible.

Very high speeds; can negotiate steep grades because of high are overload capacity.

Rate of acceleration

Very low



Flexibility in haulage

Can haul only a limited number of coaches to ensure the economic utilization of power.

Can haul a greater number of coaches.

Can haul a large number of coaches.

Condition of track

The track gets damaged due to hammer blow action.

No such damage is caused.

Movement is smooth and there is no damage.

Shed arrangement and time

Shed should have arrangement

Shed is simpler than for a steam

Shed is simple like the diesel ones.

required for service

for turning. General service and boiler maintenance require about 70 hours per month.

locomotive. Maintenance requires about 20 hours a month.

Maintenance required is about 4 hours a month.

Transport of fuel

Carries its own fuel supply of water and coal, this consumes a lot of power.

The quantity of oil required is about one-eighth that of coal; cost of transport of fuel is much lower.

Does not require fuel. Overhead electric lines are required for power transmission.

Fuelling points

Intermediate fuelling points required for replenishing the supply of coal and water.

Intermediate fuelling points required for filling diesel oil.

No intermediate fuelling points are required.

Repairs and renewals


Comparatively less.



> Wherever traffic density is not heavy.

> For heavy traffic.

> For heavy loads and on gradients. For underground railways.


Steam locomotive

Diesel locomotive

Electric locomotive

> Wherever coal is available at cheap rates.

> As an intermediate stage between steam operation and electric traction.

> For high speed.

> Wherever water is available.

> As intermediate traction.

> For suburban traffic and for quick acceleration/deceleration.

Future prospects

> Steam locomotives have

> Bright prospects; more

> Best prospects. An increasing

been phased out on IR.

diesel locomotives are being procured.

number of electric locomotives are being procured.

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