Braking of Vehicle

Braking of Vehicle

Figure 28.2 shows the vehicle moving down a gradient inclined at an angle, G, to the horizontal. Retardation takes place when brakes are applied. To bring the whole system in equilibrium the inertia force, which is also known as reverse effective force, is included with the system of forces actually existing.

Fig. 28.2. Forces acting on a vehicle during braking while moving down on an inclined path.

 

Brakes may be applied (a) to the rear wheels only, (6) to the front wheels, and (c) to all the four wheels. All the three cases are discussed separately.

(a) Brakes Applied to the Rear Wheels.

Referring Fig. 28.2 let Fr be the braking force produced at the rear wheels. The limiting value of Fr is \lRr. The whole system is in equilibrium under the influence of coplanar forces. Therefore,

6) Brakes Applied to the Front Wheels.

The Fig. 28.2 can be referred, but in this case Fr is replaced by Ff acting at the front wheels. The limiting value of Ff is n Rf- Therefore as before,

(c) Brakes Applied to all the Four Wheels.

In this case both Fr and Ff act at the rear and front wheels respectively giving maximum possible braking force as

Example 28.5. A motor car has a wheel base of 2.64 m, the height of its C. G. above the ground is 0.61 m and it is 1.12 m in front of the rear axle. If the car is travelling at 40 kmlhr on a level track, determine the minimum distance in which the car may be stopped, when

(a) the rear wheels are braked,

(b) the front wheels are braked,

(c) all wheels are braked.

The coefficient of friction between tyre and road may be taken as 0.6. Prove any formula if assumed.

Example 28.6. A motorcar weights 13341.5 N and has a wheelbase of 2.65 m. The C.G. is 1.27 m behind the front axle and 0.76 m above the ground lever. Maximum braking on all four wheels on level ground will bring the vehicle uniformly to rest from a speed of 64 km Ihr in a distance of 25.9 m. Calculate the value of an adhesion between the tyre and the road.

Under the same road condition, the vehicle descends a hill of gradient 1 in 20 and is braked on the front wheels only. Determine the load distribution between the front and rear wheels and the distance required to bring the car to rest.

Braking of Vehicle Moving in a Curved Path

While moving along a curved path a vehicle comes under the influence of centrifugal force, which tries to move it outward. This action of centrifugal force is made futile by side forces acting at the tyres in the direction reverse to that of centrifugal force. When the vehicle is braked while moving along a curved path, the frictional forces between the tyres and the road become more complex (Fig. 28.3).

Referring to Fig. 28.3A,

Let W = weight of the vehicle, N

C = radius of curved path, m

Fig. 28.3. Forces acting on a vehicle during braking while moving on a curved path (plan view).

As the radius of the curved path is very large compared to the dimensions of the vehicle, P and Q are assumed to be parallel. Similarly braking force Ff and Fr are also parallel.

For simplification, it is assumed that the forces at the vehicle wheels are compressed into a single force on a single plane passing through the centre of gravity neglecting the rolling effect on the wheel reactions due to centrifugal action and turning tendency during braking caused by unequal forces at inner and outer wheels. Hence Fig. 28.3A is replaced by Fig. 28.3B.

Referring Fig. 28.3C let R is the vertical load on the wheel and \i is the coefficient of adhesion. A part of the frictional force ui? resists the side-slip and the rest is utilized for braking as shown in the figure. It is quite clear from this that the braking capacity of a vehicle is reduced while moving along a curved path. Finally it can be concluded from this figure that if the value of n is very high then vehicle moving above a certain speed may overturn before it slides sideways.

Example 28.7 (MKS Unit). A motor cycle has wheel base 1.44 mapart. The centre of gravity of the cycle and rider is 0.76 m above ground level and 0.61 m in front of the rear axle. The coefficient of friction between the tyres and the road is 0.75. If the rear wheel is braked, find the greatest deceleration that can be obtained.

(a) if the cycle is moving in a straight path.

(b) if it is going round a curve of 45.7 m radius at 48 kmlhr.

Assume a level road and neglect air resistance. Neglect rotational inertia and obliquity when turning.

Solution.

(a) Refer section 28.1.7. If rear wheels of the motor cycle are braked, then