## Train Resistance:-

Definition :-The resistance acting at the points of contact of the wheels of the vehicle with the surface of level roadway which opposes the rolling if the wheels over it and thus the movement of the vehicle.

The tractive force developed by the locomotive should be sufficient:

1. to overcome the train resistance.

2. to haul the train along the track at the desired

speed.

Types of Resisting Forces:-

- Train resistance.
- Resistances due to track profile.
- Resistances due to starting and acceleration.
- Wind resistance

1) Resistance Independent of Speed

2) Resistance Dependent On Speed

3) Atmospheric Resistance

## Resistance Independent of Speed:

This resistance is due to following reasons:

1. Rolling Resistance:

This is due to friction between the metal surface of rails and the wheels. It consists of following:

(a) Journal Friction:

It is the friction of the locomotive, wagons and compartment itself. Its amount will depend upon the type of bearing, the lubricant used and the temperature of atmosphere.

(b) Frictional Resistance:

It is the resistance offered to the movement of steel wheels on steel rails. It is maximum at starting and is reduced as motion is caused and it increases as the speed increases.

(c) Track Resistance:

This is caused due to the wave action of rails

(d)Resistance Due To Internal Parts:

Its a resistance of the moving parts and locomotive.

Rt1= 0.0016w

where,

w= weight in tonnes

## Resistance dependent on speed:

(a) Track Irregularities:

If the track is not properly maintained, the additional resistance has to overcome.

(b)Due To Vertical Movement Of Wheels On Rails:

Due to improper joints and poor maintenance of track.

(c) Due To Flange Friction, Oscillations, Swaying:

This resistance is directly proportional to the square of the speed of train and inversely proportional to the length of rigid wheel base.

Rt2= 0.00008* w*v

Where,

v= speed in kmph

w= weight in tonnes

## Atmospheric Resistance:-

This is the resistance which is developed on the ends and sides of the train when wind velocity is considered to be zero.

Rt3 = 0.0000006 w*v^2

where,

w= weight in tons

v= speed in km

Resistance Due to Track Profile Can be categorised as follows:

## 1) Resistance Due To Gradients

## 2)Resistance Due to Curves

This resistance comes into consideration when the train moves on the curvilinear path.

## 3) Resistance Due to Starting and accelerating:-

These resistances are experienced by the train at the station while starting, accelerating and decelerating. This resistance can be expressed by:

1. Resistance due to starting(Rs):

Rs= 0.15w1+0.005w2

where,

w1= weight of locomotive

w2= weight of vehicle in tonnes

2. Resistance due to acceleration(Ra):

Ra= 0.028w*((v1-v2)/t)

## 4)Wind Resistance:-

Wind resistance can be divided into 2 components:

1. which helps in the forward movement of train.

2. which opposes the motion of train.

It depends on the angle at which the wind impinges the train.

Wind resistance(Rw)= 0.000017aV^2

where,

a= exposed area of the train in m^2

V= speed of wind in kmph

Finally the total resistance to traction i.e.

Rt=Rt1+Rt2+Rsa+Rw

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