1. BIRLA INSTITUTE OF TECHNOLOGY
ASSIGNMENT
ON
AUTOMOBILE ENGINEERING
Title : –Braking of vehicle on curved path.
Submitted By
Nitesh Prasad (BE/1183/08)
Mechanical Engineering
8th Semester

2. Acknowledgement
Braking of vehicle is an important concept of automobile
and is also related to my area of interest. I would like to
thank our Automobile Engg. teacherProf. S K Sinhasir,
for giving me such topic as assignment. Without his
guidelines, support, direction and time to time help I
could not bring this project in its present form.
I am also thankful to BIT library,lan facility and
foremostmy friends who helped me a lot and provide
dme resources for building up the project.
Once again thanks to all.
Submitted By:-
Nitesh Prasad (BE/1183/08)
Mechanical Engineering
8th Semester

3. Motion of a vehicle in a bend curve path:-
Motion along a curved path can be analyzed in terms of circular motion.
We all experience motion along a curved path in our daily life. The motion is not exactly a circular
motion. However, we can think of curved path as a sequence of circular motions of different radii.
As such, motion of vehicles like that of car, truck etc, on a curved road can be analyzed in terms of
the dynamics of circular motion. Clearly, analysis is done for the circular segment with the smallest
radius as it represents the maximum curvature. It must be noted that "curvature" and "radius of
curvature" are inverse to each other.
Motion along a curved path
Figure 1
One common experience, in this respect, is the experience of a car drive, which is negotiating a sharp
turn. If a person is sitting in the middle of the back seat, she/he holds on the _xed prop to keep the
posture steady and move along with the motion of the car. If the person is close to the farther side
(from the centre of motion) of the car, then she/he leans to the side of the car to become part of the
motion of the car.
In either of the two situations, the requirement of centripetal force for circular motion is fulfilled.
The bottom of the body is in contact with the car and moves with it, whereas the upper part of the
body is not.
When she/he leans on the side of the car away from the center of motion, the side of the car applies
normal force, which meets the requirement of centripetal force. Finally, once the requirement of
centripetal force is met, the complete body is in motion with the car.
Motion along a curved path
Figure 2: The person presses by side of the car.
The direction in which the body responds to curved motion is easy to find by just thinking what
would be the natural direction of motion of the free part of the body. In the example discussed above,
the body seeksto move straight, but the lower part in contact with car moves along curved path
having side way componentof motion (towards centre). The result is that the upper part is away from

4. the centre of curvature of the curved path. In order to keep the body upright an external force in the
radial direction is required to be applied on the body.
Braking of vehicle moving on 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 ofcentrifugal 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.
Referring to Fig.
Let W = weight of the vehicle, N
C = radius of curved path, m
Figure 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 brakingforceFf 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 centreof 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.
Referring Fig. 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

5. 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.
Stability Criteria of vehicle on curved path
According to the robust stability criterion, it results that the vehicle is stable as it is shown in the fig.
bellow
Fig.The stability limit of the vehicle on a curved path.
The curve from the fig. above represents the stability limit of the studied vehicle, that means if the
vehicle has a small velocity and a brakeage angle of the wheel such that the point corresponding to
the respective coordinates is under the curve, then the motion on the specified trajectory is stable and
if the point is above the curve then the motion is unstable.
From the performed analysis, it results that the vehicle is stable until a 110 km/h velocity when the
brakeage angle reaches the value of 10o, at the value of 15° of the brakeage angle the stability is at
its limit for the same velocity, and when the wheels have more than 15o the instability tendency
grows more, until the value 25o of the brakeage angle when the stability is lost at velocities less than
90 km/h.
The original mathematical model with six freedom degrees is without Approximations this
contributing to the exactness of the results obtained. The stability criterion applied is also an original
approach regarding this type of application due to the higher degree of difficulty of the Liapunov
function finding. It is important to notice that this criterion shows the tendency of loosing the
stability, this means that it indicates exactly the conditions when the vehicle starts loosing adherence
or contact with soil for at least one of the wheels.

6. How to apply brake on curved path
Braking is a lost skill. With so many cars with anti-lockbrakes (ABS), people just slam on the brakes
in any situation. This can be a good option, but it is not always the best. Braking (even with ABS)
can cause reduced handling capabilities and actually place you in more danger. It's better to learn
how to brake properly if you want utmost safety and control
Avoid braking and turning at the same time. Turning while on the brakes can cause the vehicle to not
turn as well or not slow down as much. Race car drivers, who are always on the edge with their
vehicles, have learned the needed skill of separating braking from turning. In 90% of corners, many
racers use their brakes before they get to the corner, make the corner, then use the accelerator. Each
section of the corner (or the straights before and after the corner) has its own purpose and separation
of brakes and turning gives the best traction for the vehicle to make a desired corner. However, it is
possible to brake and turn, in one of the following cases:
Apply the brakes smoothly: Depress your brake pedal with rapidly, but not instantly. This is essential
to maximize the braking potential of your vehicle. The goal is to bring the vehicle's tires just shy of
breaking traction. It is important, though, to avoid "squeezing" down on the brakes. The reason for
this is that at the beginning of the braking procedure, when the car's speed is still very fast, it actually
takes more, not less, brake pressure, to slow it down effectively, as the car's inertia is greater. The
key is to apply the brakes quickly and deeply, while applying pressure with the left foot against the
footrest to stabilize the body. As the car's speed is being scrubbed off, you can progressively and
gently ease off of the brakes to keep them at the point of maximal efficiency.
Practice stopping in an empty parking lot. Start by intentionally over-applying the brakes (skidding),
then reduce your braking force until you have a good sense for your maximum braking potential.
Roll down your windows and start at one end of the lot. Accelerate to a safe speed (30-40 MPH
should be good) and apply your brakes as hard as you can. You should hear a good deal of squealing
(if you do not, you may have ABS, or your brakes may need service). Go back and forth until you
are able to apply your brakes while only hearing a whisper of squealing (this is called the optimal
squeeze point — OSP). This is the point where your tires' rubber is being twisted and contorted to a
degree that only parts of your tires are actually skidding; this is the absolute limit of your tires'
traction, and the quickest way to stop.
Use ABS brakes, in almost all cases, by depressing your brake pedal smoothly (albeit quickly) to the
floor. You will likely feel the pedal either vibrate (dependent ABS) or feel like it gives out altogether
(independent ABS). Either way it is a sign of the ABS working--don't panic and don't take your foot
off the brake! Of course, if the pedal feels like it gave out, and you aren't stopping, your brakes
probably gave out, in which case you should try shifting into neutral (N) in an automatic
transmission vehicle or a lower gear than your current in a manual transmission vehicle (or read the
wikiHow article, How to Stop a Car with No Brakes). Do not however shift your vehicle into reverse
or park, these will not slow you down, but simply cost you an expensive trip to the transmission
shop.
Avoid using your transmission for quick stops. The transmission is design to accelerate the vehicle
not slow it down. The design of the load points on the transmission gears are not designed for this. It
is not a component of the braking system. If you operate a tractor trailer, it is a different story. They
are equipped with air brakes and engine brake for a reason that is irrelevant for cars. However, it is a
good practice to use engine braking (i.e., a lower than usual transmission gear) for maintaining or
decreasing speed on long downhill stretches. The heat generated is absorbed by the engine and

7. removed efficiently by its coolant, radiator, and fan, which prevents the brakes from overheating so
they will be most effective when needed for maximum braking.
Focus on where you want to go, not what you want to avoid. It's very difficult to steeraway from
something that you're looking at directly, and many people have a tendency to focus on what they are
worried about colliding with. Instead, concentrate on where you want the car to go (to the side of the
object) and pay attention to how the car feels—whether you're at OSP or locking up
Use of Front Brake :-
Maximum braking occurs when the front brake is applied so hard that the rear wheel is just about to
lift off. At that point, the slightest amount of rear brake will cause the rear wheel to skid.
If you ride a conventional bike, the best way to master the use of your front brake is to practice in a
parking lot or other safe space, applying both brakes at once, but putting most of the effort into the
front brake. Keep pedaling as you brake, so that your legs will tell you immediately when the rear
wheel starts to skid. Squeeze, don't grab, the brake levers, so you can sense when this happens.
Practice harder and harder stops, so that you will learn the feel of stopping fast, on the edge of rear-
wheel liftoff.
Test the brakes in this way whenever you are about to ride an unfamiliar bike. Some brakes are more
sensitive than others, and you need to know the "feel" of the brakes.
Once you are comfortable with the front brake, also practice releasing the brakes to recover control,
until this is an automatic, reflex action. At a very low speed, apply the brakes hard enough that the
rear wheel skids, or just begins to lift. When it does, immediately release the brakes. Wear your
helmet.
Some cyclists like to ride a fixed-gear bicycle, that is, a bicycle that does not permit coasting. When
you brake hard with the front brake on a fixed gear, the drivetrain gives you excellent feedback about
the traction at the rear wheel. (This is one of the reasons that fixed gears are favored for winter
riding.)
If you ride a fixed gear with only a front brake, your legs will tell you exactly when you are at the
maximum brake capacity of the front brake. Once your fixed gear has taught you this, you will be
able to stop any bicycle better, using the front brake alone.
If you find the fixed-gear concept intriguing, I have a major article on Fixed Gears for Road Use on
this site, and also a page of Fixed-Gear Testimonials from happy converts.
Use of Rear Brake
Skilled cyclists use the front brake alone probably 95% of the time, but there are instances when the
rear brake is preferred:
Slippery surfaces. On good, dry pavement, unless leaning in a turn, it is impossible to skid
the front wheel by braking. On slippery surfaces, however, it is possible. A front wheel skid

8. almost always leads to a fall, so if there is a high risk of skidding, you're better off
controlling your speed with the rear brake.
Bumpy surfaces. On rough surfaces, your wheels may actually bounce up into the air. If
there is a chance of this, don't use the front brake. If you ride into a bump while applying
the front brake, the bicycle will have a harder time mounting the bump. If you apply the
front brake while the wheel is airborne, it will stop, and coming down on a stopped front
wheel is a Very Bad Thing.
Front flat. If you have tire blowout or a sudden flat on the front wheel, you should use the
rear brake alone to bring yourself to a safe stop. Braking a wheel that has a deflated tire can
cause the tire to come off the rim, and is likely to cause a crash.
Broken cable...or other failure of the front brake.
When to Use Both Brakes Together
Generally I advise against using both brakes at the same time. There are exceptions, however:
If the front brake is not sufficiently powerful to lift the rear wheel, the rear brake can help,
but the best thing to do is to repair the front brake.
Typical rim brakes lose a great deal of their effectiveness when the rims are wet, so using
them both together can reduce stopping distances.
If the front brake grabs or chatters so you can not modulate it smoothly, you must only use it
lightly. Again, repair is in order.
On long, straight mountain descents, your front brake hand may get tired, or you may be at
risk of overheating a tire and blowing it out, so it is best to spread the work between both
brakes. Pumping the brakes, alternating between one and the other, will briefly heat the
surface of each rim more and dissipate more heat before it spreads inwards to the tires.
When sharp deceleration is needed, the front brake is more effective, as usual.
When leaning in a turn, traction is shared between braking and turning. Using both brakes
together reduces the likelihood that one wheel or the other will skid and dump you. The
steeper you lean, the less you can brake, so moderate your speed before a curve. When you
are leaning deeply, you need to release the brakes entirely.
Long or low bicycles, such as tandems and long-wheelbase recumbents, have their front
braking limited by the possibility of skidding the front wheel, since their geometry prevents
lifting the rear wheel. Such bikes can stop shortest when both brakes are applied.
Tandem caution: when riding a tandem solo (no stoker on board) the rear brake becomes
virtually useless due to lack of traction. The risk of fishtailing is particularly high if a solo
tandem rider uses both brakes at once. This also applies to a lesser extent if the stoker is a
small child.
Which Brake Which Side?
There is considerable disagreement as to which brake should be connected to which lever:
 Some cyclists say it is best to have the stronger right hand (presuming a right-handed
cyclist) operate the rear brake.

9.  Motorcycles always have the right hand control the front brake, so cyclists who are also
motorcyclists often prefer this setup. A moment of confusion in an emergency situation
can be deadly. The left lever on a motorcycle operates the clutch, which will not stop you.
 In countries where vehicles drive on the right, it is common to set the brakes up so that the
front brake is operated by the left lever. In countries where vehicles drive on the left, it is
common to set the brakes up so that the front brake is operated by the right lever. The
European Union has adopted this as a standard, even though only the United Kingdom
and Ireland are left-side driving countries.
The theory that seems most probable to me is that the national standards arose from a concern that
the cyclist be able to make hand signals, and still be able to reach the primary brake. This logical
idea is, unfortunately, accompanied by the incorrect premise that the rear brake is the primary brake.
For this reason, I set my own bikes up so that the right hand controls the front brake, which is not the
norm in the U.S.
I also do this because I'm right-handed, and wish to have my more skillful hand operate the more
critical brake.
On the other hand, if you have already developed a preference, it is usually best to stick with it -- or
at least, choose a few weeks of riding under undemanding conditions to retrain your reflexes. In an
emergency, you must act faster than you can think. If you switch between a Mac and a Windows PC,
where the same keys don't make the same characters, or between a clarinet and a saxophone where
they don't make the same musical notes, you know how reflexes can trip you up. If you are used to
skidding the rear wheel with the rear brake, switching the brake cables can result a flight over the
handlebars. If you mostly use the front brake, switching the cables can result in rear-wheel skidding
and increased stopping distance. These problems are most likely when first riding an unfamiliar bike,
so, again, always test the brakes with a light brake application when you first start out.
Leaning in Turns
To turn a bicycle, you must lean inward toward the direction of the turn. The faster you are going,
and the sharper the turn, the more you must lean. You have no choice about this, for a given speed
and turn radius, the center of gravity of the bike/rider must be moved sideways a particular amount
or the bicycle will not balance.
What you do have control over is whether you lean the bicycle more than, less than, or the same
amount that you lean your body, to get the overall center of gravity to the place that it has to go.
Leaning the bicycle sharply while keeping your upper body more upright.This approach is
popular with beginners who are scared to lean over sideways, and who feel less disoriented by
keeping their bodies more upright. -- though actually, they don't. The cyclist is much heavier
than the bicycle, which leans over farther, instead.Captaining a tandem with a stoker who
doesn't know about leaning in turns can be a very unsettling experience, because you must lean
farther to compensate.Keeping the upper body more upright is recommended by some racers
and coaches as offering the possibility of recovering from a skid, but I don't believe it.I think
there might be something to this. If you start to skid out, you might be able to yank the bicycle
up and momentarily press the wheels harder into the road surface to gain more traction --
though the side force also might potato-chip a wheel, or roll atubular off the rim.Racers also

10. sometimes drop the knee that is to the inside of the turn. Yanking the knee inward may also
help ro recover from a skid.
Leaning the upper body sharply while keeping the bicycle more upright.This approach is
popular with riders who are afraid of striking a pedal on the road. This is a particular concern
for riders of fixed-gear bicycles, since they cannot coast through corners.This technique is also
recommended by some racers. Leaning the upper body and the bicycle together, keeping them
in line as when riding straight.This technique has the advantage of keeping the steering axis,
tire contact patches and center of gravity all in the same plane. This preserves the proper
handling characteristics of the bicycle, and makes a skid less likely.
Importance of banking of road
Definition :-The phenomenon of raising outer edge of the curved road above the inner edge is to
provide necessary centripetal force to the vehicles to take a safer turn and the curved road is
called Banking of Roads.
In the above discussion, we see that the maximum permissible velocity with which a vehicle can go
round a level curved road depends on μ, the coefficient of friction between tyres and road. The value
of μ decreases when road is wet or extra smooth or tyres of the vehicle are worn out. Thus force of
friction is not a reliable source for providing the required centripetal force to the vehicle. Especially
in hilly areas where the vehicle has to move constantly along the curved track, the maximum speed at
which it can run will be very low. If any attempt is made to run it at a greater speed, the vehicle is
likely to skid and go out of track. In order that the vehicle can go round the curved track at a
reasonable speed without skidding, the sufficient centripetal force is managed for it by raising the
outer edge of the track a little above the inner edge. It is called banking of the circular track
or Banking of Roads.
Fig.Vehicle moving on Banked Road
Roads are generally banked for the average speed of vehicles passing over them. However, if the
speed of a vehicle is somewhat less or more than this, the self adjusting state friction will operate
between tyre and road and vehicle will not skid.

11. Extra caution while applying brakeon curves and
winding road
According to the U.S. Federal Highway Administration nearly 30% of fatal vehicle collisions each
year happen on curves. About 83% of these crashes on winding roads are roadway departures from
sliding, skidding or rolling over. Another 2005 study in the U.S. found that "run-off-road" collisions
were30% of all fatal crashes, but only accounted for 16% of all crashes.
Considering the above statistics, it is easy to see why extra caution needs to be taken when driving
on a curvy, winding road. Consider also most roads with lots of bends are rural. If you were in a
serious collision on a rural back road and couldn't call for help yourself, there's a good chance you
would wait a while before someone would notice you since these roads often have very little traffic.
Precautions
1. Do remember braking while in a curve or turn puts more stress on the brakes because of the pressure
when turning the wheel.
2. Remember there are two things you have less of on winding roads, visibility and control. This is why
it is necessary to take a bend in the road at a slower speed than a straight road.
3. All the causes mentioned above for running off the road, sliding, skidding and rollover are themselves
caused by taking the bend at too high a speed. Speeding is the number one cause of these kinds of
collisions.
4. Watch for the warning signs that tell you what the safe speed for the bend is.
5. Notice the steep decline on the edge in the top left picture. Because this road is wider and on more
level ground, it can be driven at a faster speed even with a steep drop-off to the right.
6. The bottom pictures is a road going downhill, slightly narrower than the road above, with a curb easy
to hit on either side. Bends with a downward grade greatly increase the potential for loss of car control
while driving.
7. Slow BEFORE entering a bend. Just as in a turn, you should slow down before you enter a curve. This
will probably mean braking on level ground or going downhill. It will mean lighter on the gas pedal
going uphill.
8. Coast until you reach the apex of the turn. Once you are into the bend, you should be off the brake
unless it is a steep downhill.
9. You shouldn't need the accelerator through the apex of a turn unless you are going uphill.
10. Hug the center line especially on narrow roads
11. Check your rear view Mirrors on the straight part of a winding road BEFORE you enter the bend.It's
especially important to be looking well ahead to see what direction the road goes and how wide or
narrow the bend is.

12. BIBLIOGRAPHY
1. Automobile Mechanics
:- B N Giri
2. Automobile Engg
:- Kirpal Singh
3. PDF titled “Vehicle dynamics modeling during moving along a
curved path”
:- Oana-carmenniculescu-faida.
4. PDF titled “ROBUST STABILITY”
:- Adrian niculescu-faida.
5. www.wikihow.com
6. www.drivingtips.org
7. www.ehowcar.com
8. en.wikipedia.org
9. www.answer.com