This document provides an introduction to vehicle dynamics and its key concepts. It discusses topics such as ride and handling, suspension systems, forces acting on vehicles, vehicle motion including pitch, roll and yaw, and power characteristics. Vehicle dynamics is the study of how vehicles react to driver inputs based on mechanics. Key aspects covered include body flex, weight transfer during braking, types of steering like understeer and oversteer, suspension design impacts on ride quality, and engine power outputs. The document provides a high-level overview of fundamental vehicle dynamics principles.

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1. INTRODUCTION
Vehicle dynamics is the study of how the vehicle will react to driver inputs on a given
road. Vehicle dynamics is a part of engineering primarily based on classical mechanics.
Vehicles
 Wheels
 Motion
 Self-powered
 Dynamics
Greek “DYNAMIS”
 power
 Vehicle Ride and Handling
 Ride is associated with comfort and grip
 Handling is associated with path following
 Driving task has two components: Command and control
Acceleration forces, braking forces and steering forces acting on the vehicle are dynamic forces
that depend upon the tyre-to-road friction. The amount of friction depends on the type and surface
condition of tyre and road as well as the weight on the tyre. Control is lost on any wheel if the dynamic
load exceeds the friction between tyre and road, because the tyre slips or skids.
Ideally, the tyre should contact the ground squarely and should roll without my sidewise force or thrust.
This is not practically possible with a moving automobile encountering road irregularities, wind gust,
required directional control, changes in weight, acceleration and braking, and in addition the presence
of movable suspension systems to absorb shock. Tyres encounter both large and small bumps as they
roll over the road surface. Deflections due to small bumps are absorbed by the tyre, but the vertical
deflections from the larger bumps are carried through the wheels, drums and bearings to the vehicle
suspension system. Suspension, if designed for large deflection, absorbs these bumps and allows the
body to run smooth. Suspension with limited deflection bounces the vehicle body. The suspension
system, therefore, must not only absorb shock and support the automobile weight, but it keeps the tyre
in contact with the road to ensure vehicle control. The suspension system, therefore, must not only
absorb shock and support the automobile weight, but it keeps the tyre in contact with the road to ensure
vehicle control. Its proper design produces minimum wear on the tyre and other parts of the suspension
system.

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2. ASPECTS OF VEHICLE DYNAMICS
Some attributes or aspects of vehicle dynamics are purely dynamic. These include:
1. Body flex
2. Body roll
3. Bump Steer
4. Bundorf analysis
5. Directional stability
6. Understeer, oversteer
7. Pitch
8. Roll
9. Yaw
10. Noise, vibration, and harshness
11. Ride quality
12. Speed wobble
13. Weight transfer and load transfer
2.1. BODY FLEX
Body flex is a lack of rigidity in a motor vehicle's chassis. It is often something to be avoided
by car manufacturers as higher levels of body flex is a sign of structural weakness, and means that the
vehicle's suspension cannot work as efficiently - the body takes up some of the 'slack', rather than the
parts of the car which were specifically designed for this purpose. A chassis that flexes may be prone to
fatigue and further "softening" with use will eventually result in failure.
2.2. BODY ROLL
Body roll is the load transfer of a vehicle towards the outside of a turn. When a vehicle is fitted
with a suspension package, it works to keep the wheels or tracks in contact with the road, providing grip
for the driver of the vehicle to control its direction. This suspension is compliant to some degree,
allowing the vehicle body, which sits upon the suspension, to lean in the direction of the
perceived centrifugal force acting upon the car.
2.3. BUMP STEER
Bump steer or roll steer is the term for the tendency of the wheel of a car to steer itself as it moves
through the suspension stroke. It is typically measured in degrees of steer per metre of upwards

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motion or degrees per foot.
2.4. BUNDORF ANALYSIS
A Bundorf analysis is a measure of the characteristics of a vehicle that govern
its understeer balance. The understeer is measured in units of degrees of additional yaw per g of lateral
acceleration.
2.5. DIRECTIONAL STABILITY
Directional stability is stability of a moving body or vehicle about an axis which is perpendicular
to its direction of motion. Stability of a vehicle concerns itself with the tendency of a vehicle to return
to its original direction in relation to the oncoming medium (water, air, road surface, etc.) when disturbed
(rotated) away from that original direction. If a vehicle is directionally stable, a restoring moment is
produced which is in a direction opposite to the rotational disturbance. This "pushes" the vehicle (in
rotation) so as to return it to the original orientation, thus tending to keep the vehicle oriented in the
original direction.
2.6. UNDERSTEER AND OVERSTEER
Understeer and oversteer are vehicle dynamics terms used to describe the sensitivity of a vehicle
to steering. Oversteer is what occurs when a car turns (steers) by more than the amount commanded by
the driver. Conversely, understeer is what occurs when a car steers less than the amount commanded by
the driver.
Figure 1. Oversteer

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Figure 2. Understeer
2.7. PITCH
Pitch is the front-and-rear motion of a car about an axis that extends from the left to right of a
vehicle and trough the center of gravity, or transverse (side-to-side) Y - axis. Pitch is typically taken to
be positive (+) for upward movement of the vehicle nose and negative (-) for downward movement of
the vehicle nose. The effects of pitch will increase as a function of vehicle altitude. Pitch is happening
in response to acceleration and deceleration forces, and is hard to flight.
Figure 3. Pitching, Rolling, Yawing

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2.8. ROLL
The rolling moment acts about the longitudinal axis and is produced by that side wind forces it
has only minor influence on the vehicle stability depending on the suspension system.
2.9. YAW
Angular oscillation of the vehicle about the vertical axis is called yawing. It is the vertical
movement of the complete vehicle body so the complete body rises up and down and known as
Bouncing.
2.10. NOISE, VIBRATION, AND HARSHNESS
Noise, vibration, and harshness (NVH), also known as noise and vibration (N&V), is the study
and modification of the noise and vibration characteristics of vehicles, particularly cars and trucks. While
noise and vibration can be readily measured, harshness is a subjective quality, and is measured either
via "jury" evaluations, or with analytical tools that can provide results reflecting human subjective
impressions. These latter tools belong to the field known as "psychoacoustics."
2.11. RIDE QUALITY
Ride quality refers to a vehicle's effectiveness in insulating the occupants from undulations in
the road surface (e.g., bumps or corrugations). A vehicle with good ride quality provides a comfort for
the driver and passengers.
2.12. SPEED WOBBLE
Wobble, shimmy, tank-slapper, speed wobble, and even death wobble are all words and phrases
used to describe a quick (4–10 Hz) oscillation of primarily just the steerable wheel(s) of a vehicle.
2.13. WEIGHT TRANSFER
Mechanism Of weight transfer
The mechanism (cause) of fractional weight transfer may be understood by the free body diagram
showing forces and moments acting on a vehicle at the time of braking. From mechanics it is known
that when a body is accelerated in a straight path, the inertia force IF acts on its centre of gravity (C.G.)
and whose magnitude is given by :
IF = m × f(=
W
G
× f)

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where m is mass of the vehicle and f is its acceleration. The braking force FR acts on the road surface in
the opposite direction to IF.
When brakes are applied, the forces IF and FR form an anticlockwise couple whose tendency is to cause
overturning effect on the vehicle. The magnitude of this overturning couple is given by
C =
W
g
× f × h
However, the vehicle is not going to overturn due to a righting couple produced on the
establishment of forces Q between the wheels and the ground .The directions of Q on front and rear
wheels are such so as to cause clockwise moment of righting couple whose magnitude is
Cright = Q × L
Where L is the wheelbase of the vehicle. Its consequence is to increase the perpendicular reaction
between front wheels and the ground by an amount equal to Q, and to decrease it between the rear wheels
and the ground by the same amount. Initially the weight of the vehicle is shared equally by each wheel.
In a 4-wheeler, it is W/4 which now becomes,
W/4+Q on front wheels, and W/4-Q on rear wheels.
It is thus seen that a fraction of vehicle weight is transferred to the front from the rear wheels.
Figure 4. Forces and moments to explain as to why a part of weight is transferred on braking

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3. POWER AND TORQUE CHARACTERISTICS OF AUTOMOBILE
Figure 5. Variation of IP, BP, FP and torque as a function of engine speed in rpm.
4. ENGINE POWER OUTPUT
The charge (fresh fuel-air mixture) on ignition converts into gas, and impinges upon the piston
inside the cylinder. This causes movement of the piston, and thus the work is done on it. The rate at
which this work is done, is called power and is measured in terms of power (in kW) or horsepower (hp).
An engine that can deliver 75 kgf-m of work in 1 second is known to be a 1 hp engine. Following types
of powers are being quoted with reference/to engines.
1. Indicated power (IP)
2. Brake power (BP)
3. Frictional power (FP)
4. Taxable horsepower (THP)
5. Drawbar power (DHP)
4.1. INDICATED POWER
The power developed inside the cylinder by combustion of gases is called indicated horsepower.
An indicating device an oscilloscope is used to determine IP. This device measures the pressure in the
cylinder by Electronic means during all the four piston stroke.
IP =
pLANk
1000
kW

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4.2. BRAKE POWER
The power available at the crankshaft (for onward transmission to drive the vehicle) is called the
brake power. Rating of automotive engines is done m terms of BP. Brake power can be measured by
dynamometer. The brake horsepower of an engine is calculated by the following formula :
BHP =
2πNT
4500
where N is in rpm and T in kgf-m.
If N is in rps and T in Nm, then 4500 will be replaced by 1000 and power will be kW. Then it will be
calculated by,
BP =
2πNT
1000
4.3. FRICTION POWER
Loss of power due to friction occurs at many places inside the engine despite proper lubrication.
One of the major causes of this loss is friction between piston-rings and the cylinder. It normally
accounts for about 75% of all frictional losses in the engine. Other sources of friction losses are crankpin
and connecting rod big end joint, crankshaft and main bearings etc. Friction losses in an engine are
expressed in terms of friction power (FP). This loss is less at low speed of an engine, and increases
rapidly at higher speeds. Variation of frictional horsepower (a loss) as a function of engine speed is
shown in Figure. It is related to indicated power and brake power by
FP = IP - BP
4.4. TAXABLE HORSEPOWER
The taxable horsepower (THP) rating of engines is used to assess engines for taxation purposes.
It is also used to categorize engines on a uniform basis. To illustrate, we consider a race event of auto
vehicles in which all types of vehicles ranging from mopeds, scooters, motorcycles, cars etc. are the
participants. Question arises whether all these vehicles should run together, or they be grouped in
different categories.
It is expressed by
THP =
D2
N
2.5

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A logical answer is, of course, the latter alternative i.e. the participating vehicles should be
grouped in different categories. This is similar to weightlifting or boxing games in which the players are
grouped on the basis of their weights. Grouping of vehicles is done on the basis of their THP. Thus a 2-
wheeler and a car will run in the same group if their engines are of the same THP rating .
4.5. DRAWBAR HORSEPOWER
A larger proportion of brake horsepower goes waste in overcoming various resistances in a
moving vehicle. Rest of the Power is utilized to propel the vehicle. This power which is utilized to propel
the vehicle is known as drawbar horsepower (DHP). Thus
DHP = BHP - RESISTANCES
5. AUTOMOTIVE RESISTANCES AND PROPULSIVE POWER
The brake horsepower available at the crankshaft of an automotive engine is not fully utilized to
Speed up the vehicle much of it goes waste to overcome various resistances which are given as under.
1. Road resistances:
(a) Rolling resistance
(b) Frictional resistances
2. Road gradient resistance
3. Air (or wind) resistance
4. Accelerating resistance
5.1. (a) Rolling Resistance
It mainly occurs due to the deformation of road and tyre, and dissipation of energy through impact.
The toning resistance depends upon,
 Mass of the vehicle
 Material of the road surface such as; asphalt, macadam, gravel, clay, wood or sand.
 Nature (quality) of the road surface such as poor, good, dry or wet.
 Material of the tyres
 Inflation of the tyres
It is greater on soft muddy and sandy road than the hard, dry or wooden paving. Also it is less with
pneumatic tyres than the solid tyres. It is directly proportional to the gross vehicle weight.

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The rolling resistance R, can be expressed by,
Rr = Cr mg
where Cr is rolling resistance constant and m is mass of the vehicle. The value of Cr, depends upon the
condition of tyre and road surfaces in contact. A reasonable value of 0.015 may be taken for it when Rr,
is expressed in newton and m in kilogram.
The rolling resistance may also be determined empirically by the following formula which includes the
effect of velocity V of the auto vehicle.
Rr = (0.0112 + 0.00006V) mg
Here Rr is in newton, m in kg and V in kmph. This formula has been suggested by General Motors
Company of USA, and is valid for steady speed on level paved road. A comparison equations shows
that the rolling resistance constant is related with the vehicle’s velocity as
Cr = 0.0112 + 0.00006V
Rolling resistance for different road surfaces and tyres can be approximated from the values given in
Table for speeds between 20 to 50 kmph.
Table 1. Road resistances for different road surfaces
5.1. (b) Frictional resistances
Another kind of road resistance is frictional resistance that includes resistance due to
transmission losses also. Such losses are owing to
 Lower gear efficiencies in first, second, and top gears.
 Churning of oil in gearbox and the rear axle system.
 Adhesion of tyre which is about 65% of the total losses in chassis. The frictional resistance R
can be approximated by
Rf =132.5 + 50.5 m

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The frictional resistance also depends upon the driving conditions driving habits and maintenance of the
vehicle. Those losses are comparatively low in privately owned vehicles single hand driven vehicles and
periodically maintained vehicles.
5.2. Road gradient resistance
Slope (Gradient) of the road has considerable effect on the resistance to motion of the vehicle. The
gradient resistance depends upon
 mass of the vehicle
 slope of the Road on which vehicle is moving
The road gradient resistance Rg is expressed by
Rg = mg sin θ
where m is the mass of the vehicle and ϴ is slope of the road gradient resistance is higher on a steeper
road than on the road with mild slope it is zero on the level road since ϴ is equal to zero for such roads.
Figure 6. Gradeability of vehicle
5.3. Air (or wind) resistance
The air resistance faced by an automobile depends upon
 Speed of the vehicle
 Size and shape of the vehicle
 Speed of moving air
 Direction of wind with respect to direction of the vehicles motion
The effect of speed on the air resistance is illustrated in figure the air resistance varies such as the
square of speed it means that if the speed is doubled the resistance increases by four times. For slow
speed vehicles such as trucks and Lorries, the air resistance is small but for higher speed vehicles it is
considerable.

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For racing cars, it is of paramount importance the air resistance Ra is expressed by :-
Ra = Ca A V2
Figure 7. Effect of speed on Air resistance
where Ca is coefficient of air resistance A is projected frontal area of the vehicle and V is speed of the
vehicle if Ra is expressed in a Newton, A in square metre and V in kmph then value of Ca for different
categories of auto vehicles as given below in the chart.
Table 2. Value of Ca for different categories of auto vehicles
6. TRACTIVE RESISTANCE AND PROPELLING POWER
The sum of the resistances discussed earlier is known as the tractive resistance RT and is
considered at the axle of the vehicle. Thus
Rt = Rr + Rf + Rg + Ra + Racc

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here Racc is the accelerating resistance expressed as a mf and is required when and the vehicle is to be
accelerated now the power required to propel the vehicle can be determined as follows by finding the
work required to be done at the axle.
Thus,
WR = RT × V (N-km/hr)
=
RT × V × 1000
60 × 60
watt
therefore required power is obtained as :
HP =
RT × V × 1000
60 × 60
watt
if the efficiency of transmission between the engine crankshaft and the driving axle is η
HP =
RT × V
60 × 60 × η
The transmission efficiency is generally taken as 85 %.
7. MEASUREMENT OF THE TEST VEHICLES
Many of the following tests are correlated against results from instrumented test vehicles.
7.1. BENCH TESTS
7.1.1. LOCATION OF CENTRE OF GRAVITY
The location of centre of gravity of the test vehicle is determined in a longitudinal, lateral and
vertical direction. Below, the longitudinal direction is called the x coordinate, the lateral direction y
coordinate and the vertical direction z coordinate. The location of centre of gravity in the x and y
directions is determined by measuring the four wheel loads by means of wheel-load scales, onto which
the vehicle is placed. Alongside the overall weight of the vehicle determined in this way, the position of
the centre of gravity in an x and y direction can be calculated with the known wheel base and track width
variables by production of torque equilibria. The height of the centre of gravity is determined by weight
displacement when lifting an axle. In this process, the brakes are released and the transmission is in
neutral, through which the wheels can be freely turned. The efficiency lines of the axle loads pass
through the wheel centre lines. To detect the axle load of the axle which has not been lifted, two wheel-
load scales are used.

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Figure 8. Measurement of the vehicle’s centre-of-gravity height hcog
As a function of the inclination of the vehicle, the axle loads on the front and rear axle change.
The height h of the centre of gravity above the level passing through the front and rear wheel centre line
can be calculated via the torque equilibrium around the rear wheel centre line from the difference of the
axle loads and the angle of inclination of the vehicle in question:
The dynamic wheel radius is measured with the vehicle at a standstill.
7.1.2. MOMENT OF INERTIA
The moment of inertia, otherwise known as the angular mass or rotational inertia, of a rigid
body is a quantity that determines the torque needed for a desired angular acceleration about a rotational
axis; similar to how mass determines the force needed for a desired acceleration. It depends on the
body's mass distribution and the axis chosen, with larger moments requiring more torque to change the
body's rotation rate. It is an extensive (additive) property: for a point mass the moment of inertia is just
the mass times the square of the perpendicular distance to the rotation axis. The moment of inertia of a
rigid composite system is the sum of the moments of inertia of its component subsystems (all taken
about the same axis). Its simplest definition is the second moment of mass with respect to distance from
an axis.

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Now that the location of centre of gravity is known, the moments of inertia (MOI) around the
longitudinal, lateral and vertical axes can be measured. This is done by the vehicle oscillating around
the corresponding axes at the centre of gravity of the vehicle against springs of a known stiffness. By
measurement of the oscillation time T, the moments of inertia can be calculated with known spring
stiffness.
To determine the moments of inertia around the lateral axis of the vehicle, the vehicle is placed
on a cutting line transverse to the direction of travel. The cutting line is aligned in such a way that the
centre of gravity of the vehicle in a horizontal position of the vehicle is vertically above the cutting line.
In the longitudinal direction of the vehicle, springs on which the vehicle supports itself via the auxiliary
frame are clamped in at identical distances.
Figure 9. Measurement of the MOI around the transversal vehicle axis
Euler's theorem is used to calculate the moment of inertia of the vehicle/frame unit around the cutting
line axis from the frequency of the oscillations of this system:
This approach for the calculation of the moment of inertia holds for the entire vehicle/frame unit
around the cutting line axis. In order to obtain the MOI for the vehicle around its lateral axis passing
through the centre of gravity alone, two items obtained up to now must be subtracted:

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On the one hand, an item is contained corresponding to the MOI of the frame. To remove it from
the result up to now, the measurement with the auxiliary frame alone is repeated and the moment of
inertia of the frame around the cutting line axis ϴy,Frame is calculated. By subtracting Θy,Frame from
the overall moment of inertia around the cutting line Θy, total, the moment of inertia of the vehicle alone
around the cutting line axis.
Θ y,Veh = Θ y,total – Θ y,Frame
The second item having an influence on the moment of inertia around the lateral axis is the so-called
“Steiner ratio” of the vehicle. The Steiner ratio results from the distance between the rotary axis of the
cutting line and the required reference axis, the axis through the centre of gravity of the vehicle. By
subtracting the Steiner ratio in , the moment of inertia in a lateral direction of the vehicle through the
centre of gravity is determined.
Θy,CoG = Θy,Veh -mVeh ∆h2
y,Veh
Figure 10. Test-bench structure for the MOI measurement around the transversal axis
7.2. BRAKE FORCE DISTRIBUTION
In the course of this study, the connection between brake pressure applied by the hydraulic unit
of the brake and the resulting brake power on the wheel must be determined. During the driving tests
held at a later point in time, there can be a deduction of the brake power actually existing on the wheels
with the help of this ratio.

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These measurements are done on the “ABS test bench” of the ika. The ABS test bench has four
sets of rollers driven independently of one another onto which the vehicle is placed. Thanks to a movable
frame for the rollers for the rear axle, the test bench can be adjusted to various wheel bases. All four
wheels are driven evenly via the rollers with a speed corresponding to a traction of 6.5 kph. The reaction
torque and thus the effective brake power up to a maximum of 5 kN are measured by a force transmitter
interposed between the drive unit support and the frame. A detection roller measures the actual wheel
speed in order to switch the test bench off automatically in the event of excessive slip between the rollers
and the wheel. A principal diagram of the ABS test bench is shown in Figure.
Figure 11. ABS test-bench
While the test is being held, the ABS test bench drives all four wheels evenly to start with. Thanks
to a continuous operation of the brake pedal, the brake power on all the wheels is increased until the
blocking of one axle results, by which the vehicle is lifted out of the contact rollers. During this process,
the four wheel brake powers and the brake pressures are recorded, the two brake powers of one axle
being identical.
7.3. DRIVING TESTS
In order to be able to hold the driving tests to examine the test vehicles and specifically the
vehicle dynamics controller, the vehicles are equipped with extensive measurement technique. All the
measurement devices used and the measurement variables recorded by them are listed in below table.

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.
Table 3. Driving test instruments
8. CONCLUSION
1. Enhance vehicle steerability and stability
 Steerability is enhanced in normal driving condition.
 Braking is involved only when the vehicle tends to instability
2. Precise steering control requires understanding of interaction between tyre and road.
 Treated as disturbance to be cancelled out.
3. Vehicle state estimation uses interaction between tire and road as source of information.
 Seen by observer as force that govern vehicle’s motion.
4. Vehicle dynamics are important to enable a good overall design of such a complex product as a vehicle
intended for mass production at affordable cost for the customers.

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9. REFRENCES
1. K.M. Gupta, “Automobile Engineering” by Umesh Publications, Third Edition, Page no. 78-84, 87-
90,.
2. R.S. Khurmi, J.K. Gupta, “ Theory Of Machines” by S. Chand Publications, Third Edition Page no.
253-255.
3. K.M. Moeed, “Automobile Engineering” by Katson Publications, Revised Edition 2016, Page no. 63-
64.
4. J. J. Uicker; G. R. Pennock; J. E. Shigley (2003). Theory of Machines and Mechanisms (3rd ed.).
New York: Oxford University Press. ISBN 9780195155983.
5. Marion, JB; Thornton, ST (1995). Classical dynamics of particles & systems (4th ed.).
Thomson. ISBN 0-03-097302-3.