Automobile

1. what-when-how
In Depth Tutorials and Information
Braking System (Automobile)
Braking System
The function of the braking system is to retard the speed of the moving vehicle or bring it to rest in a shortest
possible distance whenever required. The vehicle can be held on an inclined surface against the pull of gravity
by the application of brake. Brakes are mechanical devices for increasing the frictional resistance that retards
the turning motion of the vehicle wheels. It absorbs either kinetic energy or potential energy or both while
remaining in action and this absorbed energy appears in the form of heat. While moving down a steep gradient
the vehicle is controlled by the application of brakes. In this case brakes remain in action for a longer period
making it imperative to dissipate the braking heat to atmosphere as rapidly as possible.
Automobiles are fitted with two brakes; the service or foot brake and the emergency or hand brake. The foot
brake is used to control the speed of the vehicle and to stop it, when and where desired, by the application of
force on the brake pedal. The hand brake, applied by a lever, is used to keep the vehicle from moving when
parked. Hand brakes are called emergency brakes because they are applied when the service brake fails.
Virtually all vehicles are now equipment with 4-wheel brakes. The front brakes must operate without interfering
with the steering action.
The brakes must be capable of decelerating a vehicle at a faster rate than the engine is able to accelerate it.
Normally brakes have to absorb three times the amount of engine horsepower energy in its equivalent form.
28.1.
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2. Braking Fundamentals
Energy of Motion.
Kinetic energy is the force that keeps the vehicle moving. This energy is provided by the engine in order to
accelerate the vehicle from a standstill to desired speed. Kinetic energy is dissipated as heat by the brakes
during application of breaks (Fig. 28.1). The kinetic energy of a vehicle during braking is given by
Thus, the kinetic energy doubles as the weight doubles, but it increases four times as speed doubles.
Fig. 28.1. Illustration of braking.
Coefficient of Friction.
Frictional force opposes the motion of the vehicle. Consequently it consumes power and produces heat.
Frictional force occurs between the sliding tire and the road surface when wheel rotation is locked by brakes.
The ability of a vehicle to stop depends on the coefficient of friction between the contacting surfaces. Maximum
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3. useable coefficient of friction occurs between the tyre and road surface. Passenger car brakes have coefficient of
friction 0.3 to 0.5.
The amount of energy that can be absorbed by the brakes depends upon the coefficient of friction of the brake
materials, brake diameter, brake surface area, shoe geometry, and the pressure used to actuate the brake.
Stopping a car suddenly means very high friction, resulting in high brake temperature.
28.1.1.
Brake Balance
The braking of a vehicle occurs at ground level, so affective braking force acts on the ground. Vehicle weight
and kinetic energy of the vehicle act through center of gravity, which are above ground level. This causes the
vehicle to pitch forward as the brakes are applied. As a result of this action some of the vehicle weight is
effectively transferred from the rear wheels to the front wheels. Consequently, the front brakes must absorb
more kinetic energy than the rear brakes. The maximum transfer of weight amounts to
This weight is added to the static weight on the front wheels and subtracted from the static weight on the rear
wheels. The front wheel static weight is normally 55% of the vehicle weight. Front brakes are designed to
absorb this extra brake effort by selecting shoe-drum or shoe-disc
combination type, brake size, lining coefficient of friction, wheel cylinder size and differential hydraulic
actuating pressures. With full braking it is desirable to have the front brakes lock up slightly ahead of the rear
brakes. This causes the car to go straight ahead and to not spin out.
Example 28.1. A vehicle has its wheel base equal to 3 times the height of its CG above the ground. If the
vehicle is braked on all four wheels over a road whose adhesion factor is 0.6, determine the weight transferred
from the rear to front wheels.
28.1.2.
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4. Stopping Distance
Stopping distance is extremely important for emergency braking. The stopping distance is 1 based on the
deceleration rate. Also, it is affected by the tyre deflection, air resistance, braking efforts and the inertia of the
driveline. Distance travelled by the vehicle during application of brake can be obtained from the following
equations of motion assuming the brake efficiency as 100%.
If the vehicle comes to stand still due to application of brake, the final velocity, V = 0 in the above equations,
then stopping distance, S is given by the relations, S = U /2f.
The stopping distance remains same with the same tyre and road conditions, when the wheels are locked and
skidding, regardless of the weight, number of wheels or vehicle load. Maximum braking force occurs when the
wheels are braked just before the locking point or point of impending skid. Non-skid brake systems are
designed to operate at or below this point. Any changes in load on a wheel changes the point of impending skid.
Example 28.2. Calculate the minimum stopping distances for a vehicle travelling at 60 kmlhr with a
deceleration equal to the acceleration due to gravity.
28.1.3.
Brake Fade
Since brake lining material is a poor conductor of heat, most of the heat goes into the brake drum or disc during
braking. Under severe use, brake drums may reach 590 K temperatures. The coefficient of friction between the
drum and lining is much lower at these high temperatures so that additional pedal pressure is required. After a
number of severe stops or after holding the brakes on a long down hill grade, a point is eventually reached when
the coefficient of friction drops so low that little braking effect is available. This condition is called brake fade.
In drum brakes, the lining covers a large portion of the internal drum surface so that a little cooling space is
available. Therefore, drum brakes are more susceptible to fade than disc brakes. As the vehicle moves, cooling
air is directed around the drum and disc to remove brake heat. The maximum brake torque that can be absorbed
by the lining or pad depends on the size and type of brake, gross vehicle weight, axle loading, the front to rear
braking ratio and maximum attainable speed.
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5. The drum and disc expansion due to brake temperature is another factor for brake fade. The diameter of the
drum increases as it gets hot. The shoe no longer matches the drum and hence lining-to-drum contact surface
becomes smaller. The same stopping force requires higher pedal pressure and this is turn increases the
temperature on the smaller contact surface. Continued braking increases the problem until the braking becomes
ineffective, regardless of the pedal force. On the other hand, expansion of disc has little effect on braking
because the pads apply braking force on the side of the disc and hence braking surface area remains constant.
Leading shoes are more susceptible to fade than trailing shoes.
Fade-resistant drum brakes must limit brake shoe arc to 110 degrees and power absorption
to 28370 kW/m* of lining. The power absorbed by the brakes during a stop can be calculated as,
Brake Torque.
The braking torque is the twisting action caused by the drum or disc on the shoes or caliper anchors during the
application of brakes. The amount of torque is determined by the effective axle height and stopping force
between the tyre and road surface.
Brake torque on the front wheels is absorbed by the knuckle and suspension control arm. In rear, it is absorbed
by the axle housing and the leaf spring or control arm. Braking torque during an emergency stop is much higher
than accelerating torque at full throttle. Brake supporting and anchoring members must, therefore, have
sufficient strength to withstand these high braking loads.
Brake Safety.
All automobiles are equipped with an emergency brake that would operate independently from the service
brakes. Safety standard require the emergency brake to hold the automobile on a 30% slope indefinitely after
the brake has been applied until the operator releases it.
28.1.4.
Work Done in Braking
The kinetic energy possessed by a moving vehicle depends on the weight and speed of the vehicle. This energy
must be partially or totally dissipated when the vehicle is slowed down or brought to a standstill. The brake
converts the kinetic energy possessed by the vehicle at any one time into heat energy by means of friction.
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6. Example 28.3. A car of mass 800 kg is travelling at 36 kmph. Determine (a) the kinetic energy it possesses, and
(6) the average braking force to bring it to rest in 20 meters.
28.1.5.
Braking Efficiency
The force applied during braking of a vehicle opposes the motion of the wheels, as a result reduces the vehicle
speed or brings it to a standstill. Therefore the braking force is the force of resistance applied to stop a vehicle
or reduce its speed. The braking efficiency of a vehicle is defined as the braking force produced as a percentage
of the total weight of the vehicle. Thus,
The braking efficiency is generally less than 100% because of insufficient road adhesion, the vehicle is on a
down gradient or ineffective brake system. The brake efficiency is similar to the coefficient of friction, which is
the ratio of the frictional force to the normal load between the rubbing surfaces.
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7. Example 28.4. Determine the braking efficiency of a vehicle if the brakes bring the vehicle to rest from 60
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8. kmph in a distance of 15 meters.
28.1.6.
Tyre Adhesion
The amount of the force applied on a shoe against a drum controls the resistance to rotation of a road wheel.
Simultaneously the road surface has to drive the wheel around. This driving force attains its limit when the
resistance offered by the brake equals the maximum frictional force generated between the tyre and road which
is known as the adhesive force. This force can be determined from the expression :
Adhesive force = Load on wheel x Coefficient of friction
When the limit is reached, the wheel starts to skid, and any extra force on the brake shoe does not increase in
the rate of slowing down the vehicle, no matter how good is the braking system. This means that the adhesion
between the tyre and road is the governing factor for the minimum stopping distance.
Road adhesion depends on :
• Type of road surface.
• Conditions of surface e.g. wet, dry, icy, greasy, etc.
• Designs of tire tread, composition of tread material and depth of tread.
The stopping distance of a wheel is greatly affected by the interaction of the rotating tyre tread and the road
surface. The relationship between the decelerating force and the vertical load on a wheel is known as the
adhesion factor, ia. This factor is very similar to the coefficient of friction, i, that occurs when one surface
slides over the other. In the ideal situation of braking, the wheel should always rotate right up to the point of
stopping to obtain the greatest retarding resistance. Typical adhesion factors for various road surfaces are
presented in Table 28.1.
Table 28.1. Adhesion factors for various road surfaces.
No. Road Surface Adhesion Factor
i—» Concrete, coarse asphalt dry 0.8
2 Tarmac, gritted bitumen dry 0.6
3 Concrete, coarse asphalt wet 0.5
4 Tarmac wet 0.4
5 Gritted bitumen tarmac wet 0.3
6 Gritted bitumen tarmac greasy 0.25
7 Gritted bitumen, snow compressed dry 0.2
8 Gritted bitumen, snow compressed wet 0.15
9 Ice wet 0.1
It is a common thinking that the shortest stopping distance is achieved when the wheel is locked to produce a
skid. This idea is incorrect because experiments have confirmed that the force required to ‘unstick’ a tyre is
greater than the force required to skid it over the surface. A wheel held on the verge of skidding not only
provides the shortest distance, but also allows the driver to maintain directional control of the vehicle.
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9. 28.1.7.
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,
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10. (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
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11. 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.
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12. 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.
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13. 28.1.8.
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
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14. 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
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