The thrust known as tractive effort provided by the engine at the driving wheels varies at different engine speeds and gear positions. A moving vehicle is opposed by the various forces known as resistances. In order to keep the vehicle moving, tractive effort equal to the sum of all the opposite forces has to be applied to it. If the tractive effort exceeds the sum of all the resistances, the excess tractive effort will accelerate the vehicle, but if the tractive effort is less than the sum of all the resistances, it will decelerate the vehicle. Following are the main forces, which opposes the motion of the vehicles:

### 1. Rolling resistance

The rolling resistance is mainly due to the friction between the wheel tyre and the road surface. It mainly depends upon the load on each road wheel, type of tyre tread, wheel inflation pressure and type of road surface. Mathematically, rolling resistance,

Rr = KW

where

K = Constant of the rolling resistance, and

W = Weight of the vehicle in newtons.

The value of K for best roads and loose sandy roads is generally taken as 0.0095 and 0.18 respectively.

### 2. Wind or air resistance

The wind or air resistance depends upon the shape and size of vehicle body, air velocity and speed of the vehicle. It increases as the square of vehicle speed owing to which much importance is given to streamlining and frontal area of modern automobiles. When calculating air resistance, air velocity is usually neglected. Mathematically, air resistance,

Generally, for calculating air resistance, it is easy to take the value of vehicle speed (V) in km / h. Thus, air resistance,

It may be noted that since the air resistance increases with the square of speed, thus at twice the speed, the air resistance is 4 times. For best streamlined cars, coefficient of air resistance (Ka) is 0.023, for average cars, Ka = 0.031 and for buses and trucks, Ka = 0.045.

### 3. Gradient resistance

The gradient resistance is due to the steepness of road gradient. It depends upon the vehicle weight and the road gradient. Mathematically, gradient resistance,

It may be noted that when the vehicle is moving along a level road, it has to face rolling and air resistance. When the vehicle moves up the gradient, it has to encounter the gradient resistance in addition to the rolling and air resistances.

The power required to propel a vehicle is proportional to the total resistance to its motion and speed. Mathematically, power required (in watts) to propel a vehicle is given by

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