# Mod-01 Lec-01 Introduction to Vehicle Dynamics

welcome to this course on vehicle dynamics

we are going to spend the next 35 hours on understanding the dynamics of vehicle as the

name indicates vehicle dynamics simply means that we are going to study vehicles in motion

so we are going to look at how vehicles are going to behave before we go into a formal

introduction of this course let us first look at what are the books that i am going to follow we will follow that with the syllabus and

then brief introduction this will be the first class this class will be towards motivating

you to look at vehicle dynamics so these are the text books that i am going

to follow the text books are you know gillespie fundamentals of vehicle dynamics a very well-known

textbook in this field reza jazar vehicle dynamics theory and applications springer

book hans pacejka tire and vehicle dynamics slightly advanced when compared to the first

2 books and then bernd heibing chassis handbook where we will take some data in order to illustrate

the practicality of what we are going to see in this course so i suggest that you periodically look at

these books in order to understand what is being done in this course okay let us now

start with the formal introduction this is going to be chalk and talk i may use or i

will use the power point presentations especially when the figures and the drawings are bit

difficult i may use that if it is difficult to draw in the board or else it will only

be with the chalk that i am going to talk the reason is that i want to give you time

to assimilate things especially there will be lot of derivations in this course and it

is important that you have the time to assimilate as i write down these equations hence the

course will completely be based on this method okay we will have the class on mondays tuesdays

tomorrow at 8 o’ clock and wednesday at 12 o’ clock okay it has been 3 hours okay as i told you vehicle dynamics is a dynamics

or the vehicle in motion and we are going to study what happens in motion of course

when you talk about vehicle a number of things come to your mind the first thing that come

to your mind is the part of the vehicle so if you study this as a course what constitutes

a vehicle just briefly let us review quickly what are the components of vehicle that will

be involved in what we are going to study now so if you look at the vehicle per se you can

broadly classify them into the power module okay which involves engine and so on the chassis

module and if you want to add you can further divide

this and say that you can involve this what i call as a body module say anything and everything

of the vehicle can be brought into these 3 categories for example if you look at the

power train or the power which gives the power to the vehicle you can include the engine which is of course

the most important thing for power as well as other subsidiary equipments or the components

which actually take the power to the wheel so if you look at the power that is given

to the vehicle it is given by the engine and the power that is developed by the engine

goes to the wheel so you can include all those transmission systems that go to the wheel

which you can say gearbox etc okay now if you want you can also in this category

include also the axles it does not matter we are only categorizing them okay if you

are looking at the chassis then you are looking at a number of subsystems which is say for

example the suspension systems you are looking at the steering system and you are looking at tires and wheels which

you can include here or you can include in the axle system okay of course you are the body okay which makes

you comfortable to sit in the vehicle or carry goods and so on so broadly in other words

this is not complete but i know that you know all these things you know the mechanisms of

many of these things so i am not going to cover that broadly vehicle consists of a number

of subsystems all these subsystems are going to act in order that you carry from one place

to the other and so what is the fundamental requirement

of a vehicle or what does these subsystems do when you go in a vehicle? or in other words

what are the requirements of the vehicle? of course it has to carry people do not tell

me that it has to carry people yes of course it has to carry people but they have 3 important

requirements when it carries people obviously safety it has to carry people safely it has

to carry people comfortably and of course economically

okay so these are the 3 fundamental requirements if you look at vehicle as it moves the second category i am not saying it is

not important as important as the first one is the driver interaction with the vehicle

so in other words the vehicle has to listen to the driver it has to do what he wants him to do and it

has to do that again in a prompt and effective way so in this course this is what essentially

we are going to study what are the factors which affects safety? now when i say safety we are not looking at

things like crash that is not our interest okay that is not our interest so for example

when we say safety what is that we mean? for example when a vehicle takes a turn okay how

does it behave? okay when you brake how does it behave and so on? so when we say safety

we are not looking at situations like crash okay so we are looking at safety for our dynamics

point of view comfort we are going to look at how your comfort as you travel in the vehicle

is affected? how do you characterize comfort? what are the subsystems of the vehicle which

you are going to have an effect on comfort? okay how does the road profiles interact with

the vehicle and affect your comfort? and more importantly what defines comfort? so these are the things that we are going

to look at in terms of comfort we are not going to spend lot of time on economical part

of your travel but we are going to concentrate here and there the economics of vehicle operations

in this course we are not going to cover for example engines that is the separate course

okay but we will talk about certain other subsystems like tires how that affects the

economics of vehicle motion? so essentially we will be concentrating on

these 3 aspects safety is linked with the second part of this categorization safety

is the result of the vehicle properly listening to the driver hence that is why i have put

that as a second category and that the vehicle has to listen listen in such a fashion that

it is safe for the people inside so we are going to look that as well okay so for example we are going to pick up the

difference between a formula 1 car and for example the cars you drive what is the difference

between that 2? we are going to look at that kind of very exciting things in this course

right so these are the things that we are going to look at it the same thing can be

looked at in different perspective in other words there are various perspectives to look

at these 3 aspects and that is what we are going to cover in the next 30 minutes in other words a broad picture emerges when

we talk about this in terms of a driver this is simple maybe you very easily understand

this and already know it but this gives us a picture of what we are going to do a driver

a vehicle a response and then effect so the most important thing is that triangle the

driver interacts with the vehicle because of his interaction say for example what is

meant by interaction? he may give a steering input he may accelerate

the vehicle he may brake the vehicle and so on so he interacts with the vehicle okay by

means of things which are around him okay because of that there is a response of the

vehicle the vehicle responds the vehicle decelerates the vehicle takes a turn and so on so this

is the response to the input okay and the response may make him modify or not you know

depending upon what is the response so there is a lot of feel depending upon what

is the response the driver may modify his input okay so in other words there is a very

close interaction between the driver vehicle and the response okay the response has another

effect the response has an effect on the occupants of the vehicle so in other words the effect

on occupants okay is also important right now this is what we are going to look at we will not be going into details of what

is the effect of the occupants and so on but we will definitely point out under normal

circumstances what is the effect on the occupants? okay so we are going to look at these 3 things

very carefully so the driver of course as i said accelerates and brakes now how are

we going to study this? we are going to study this using mathematical models now what do i mean by mathematical model?

so i have a vehicle is represented by means of a set of differential equations so vehicle

which was introduced 5 minutes back to have subsystems consisting of a number of them

okay can be also looked at from a very different perspective okay as a set of differential

equations okay so this forms a very important part of this course or the core of this course

a mathematical model of the vehicle so what are the things that participate in

this mathematical model will come to that in a minute so this mathematical model will

have an input okay which will be from the driver so we are going to deal with this input

and you will get a set of output so in other words the vehicle will be reduced to a system

with an input and an output of course you can add a feedback you can modify this like

in what you did in control systems and so on we will do that we will use a lot of control

system concepts in this course okay we will of course revise some of them as we go along

but the perspective now of a vehicle is that of a mathematical model okay so what is this

mathematical model and what is it based on? very simple all of us know it okay when you

talk about dynamics we have to talk about newton we have to talk about euler of course

we have to talk about newton-euler equations and so on so these equations okay will form the basis

of our development of mathematical model so that being the basis the language of defining

the vehicle is going to be different it is not in terms of the subsystems which we had

defined it will be in terms of mass of the vehicle we will talk in terms of moment of

inertias of the vehicle moment of inertia and say i xx i yy and i zz and

so on okay we will see that we will use 3 moment of inertias

and not i xy and so on we will talk about stiffness or in other words we will include

in this stiffnesses we will talk about the stiffness of the springs which form a part

of the suspension system we will talk about damping so damping stiffness these are the

things that enters into the mathematical model the other things which enter into the model

are compliances just opposite of stiffnesses and there are going to be very special terms

which may also be used here and we will introduce that as we go along so in other words the

mathematical model looks at the vehicle from a very different perspective or in terms of

very different quantities whose definition most of it at least you already know clear

okay so i hope you remember all the dynamics that you did in your previous classes which

will be used and which will be applied in this course clear from another perspective the vehicle dynamics

study can be broadly classified into what is called as longitudinal dynamics lateral dynamics

and vertical dynamics in other words a mathematical model covers the vehicle behavior in the longitudinal

direction the lateral direction which is perpendicular to the vehicle and in the vertical direction

okay as it goes over a bump or as it goes in a rough road and so on so basically the mathematical models are the

ones which are written in such a fashion that we understand what happens in these 3 directions

clear okay now you may ask a question what is this input? say steering behavior what

do you mean by steering behavior? what is deceleration acceleration and so on? because

the question that may come to your mind is when i drive my vehicle in a crowded road

okay in the traffic then i give all sorts of inputs okay it can be a sudden braking or i can do a maneuver

which is very fast maneuver i can do lane change and so on in other words there are

so many things that i do when i drive the vehicle and what do you mean by this input

and what are the types of input that you are going to give or in other words are you going

to create every scenario that happens outside on the road here in order to understand the

vehicle behavior very important to understand that first that

we are not going to build scenarios in this course and that is not what when you develop

a vehicle v2 there are a set of standard tests okay which are available in order to understand

the vehicle in other words there is an iso standard which tells you what are the inputs

that are required in order to understand the vehicle behavior so we have iso standard for understanding

the vehicle behavior these are called by different names and there are number of them okay so

i am going to list a few of them not going to complete list here but we will see that

later in the course so when we come to the input part we are going to talk about say

for example you want to overtake a vehicle in the actual scenario okay suppose you are driving in a highway and you

want to overtake a vehicle of course i want to understand how my vehicle is going to behave

if i want to overtake a vehicle okay and so what do you do? suppose the vehicle is going

like this and there is a vehicle before you so in order to overtake the vehicle you go

okay and then you go back right so you do what is called as double lane change so there is a test called double lane change

okay or you can just do a single lane change right in other words which to a great extent

mimics what happens in reality but there are other tests which may not exactly mimic but

is used in order to understand the dynamics of the vehicle they are much more technical

for example there will be a test which we will talk about a lot in this course which

is called as the pulse test or pulse steer in this test i am going to give a steering

input okay 40 degree change in less than a second okay so i just change it and then bring

it back right this is called a pulse test you may ask me are you using this anywhere?

may not or will not be using it in your day to day driving but it brings out the dynamics

of the vehicle okay so this is one of the tests that we will be doing or which will

be given as an input to this in other words input has been very carefully

defined by this iso standard in order to understand the dynamics of the vehicle okay or to bring

out certain scenarios there is other tests like constant radius cornering or constant

radius tests and there are tests okay which say for example there is a test called j-hook

test and so on which bring out extremity conditions so in other words what is that we are going

to do or what is usually done? there are tests the tests involve either an

input through steering or through brake and acceleration we will mostly be using braking

conditions okay so these conditions there are number of tests these tests are given

as an input to this mathematical model which is based on a good old newton-euler techniques

and so on now what are the outputs that we are going to look at? okay ultimately as i said i want to look at

comfort level i want to look at safety this is what i said the whole ideal of studying

vehicle dynamics is to study the safety economics and so on let us take the condition of braking

let us say that i want to brake a vehicle okay suddenly i see some obstacle and i want

to brake the vehicle okay so i said that i want safety during braking actually what does

it mean or how does this output look like? if i want to be safe then i have to look at

braking distance for example i cannot have a vehicle whose braking distances are large

we will see what typically they are later is large right if the braking distances are

large then obviously i am not going to satisfy this condition of safety and i may go and

crash with that obstacle so in other words we are going to look at as outputs okay quantities

which are related to what i said before this at least is simple braking distance okay

so we are going to look at that kind of output distance and there are other outputs that

typically what i said is that we are going to go back to newton “professor – student

conversation starts” so what are the things when you look at newton’s equation? what

are the things that comes to your mind? lateral and longitudinal dynamics “professor – student

conversation ends” yeah so what comes to your mind is accelerations

what comes to your mind is velocity and so on right so the outputs will now be in terms

of these quantities distances accelerations velocities and so on there will be other things

we will see that later but all of them are to do with the dynamics clear now how is this

related to say for example comfort? i may ask you a question okay you get acceleration how do i deduce my comfort

levels or in other words what is the effect? so this is the output response is the output

yes i can understand that if the braking is not happening as the driver wishes it to be

maybe he can jam or press the brakes hard fine that i understand okay from braking distance

if you want to reduce the velocity or increase the velocity he either presses the brake pedal

all that i can understand okay but you are talking about effect of the occupants

what is that? you know say for example i want to be comfortable sitting in the back seat

and you know enjoying my ride so how does this give me or how does this outputs give

me that feeling of goodness? so whole lot of research has been done as to how say for

example the acceleration levels affect your comfort levels inside the vehicle or in other words we will map certain of the

outputs like for example vertical acceleration okay lateral acceleration and so on we will

map them into your comfort level by lot of research has been done on this topic map them

into your comfort level okay and tell you what is the effect of the occupation so it

is a large topic we are going to give a glimpse of this towards the end of the course as to

the effect the cause and the effect on the occupants

clear so in a nutshell this is what we are going to look at in this course we are going

to look at first the mathematical model input output and so on clear okay in order to understand

the mathematical model itself okay we will introduce to you or i will introduce to you

a certain technical information to write down these equations if you remember newton’s equations on one

side we have quantities or newton-euler equations if you want to call it you have these quantities

on the left hand side or right hand side however you write on the other side of the equation

you have forces moments and so on so we have to understand those as well so i should add

to these lists the right hand side of the equation which i would call as generalized

force moment and so on okay so we also have to understand the source of

these forces how does this force originate? how does it act on the vehicle? how is it

transferred to the vehicle? so this is one of things also when we come to the mathematical

model becomes important just to give you an example if i have to brake the vehicle or

accelerate the vehicle then i need a braking force and a traction force alright yeah you can tell me that the braking force

emanates when i press the brake pedal yes of course that is the braking system but we

are not going to look at you know the braking system per se in this course but ultimately

as a vehicle when it brakes the forces emanate from that interface between the tire and the

ground so we are going to look at actually how the vehicle talks to the road how actually the traction is developed? how

actually the force is developed? so when you take a turn also you should look at what generally

called as the grips in all these conditions i have to talk about

the grip of the vehicle or grip of the tire okay with the road so in that process of understanding

the mathematical model we will go into the details of tire mechanics and tire behavior

because that forms the basis for one of the quantities on the right hand side there are

other quantities as well the other quantity or other force which is

important in that mathematical model is aerodynamic forces so we have to look at the aerodynamic forces

how do they act on the vehicle? and what are the design parameters of the vehicle which

affects aerodynamics? we will follow let say a book at that time i will give you a reference

so we will follow that also in this course okay and there will be a short introduction on

aerodynamics the effect of the body okay on the aerodynamic forces okay so in other words

yes there is i would say an environmental interaction with the vehicle and this is due

to various components body of the vehicle and so on so we are going to look at that

because that forms a basis for the vehicle model right okay this is we are talking about the equation

part of it okay so the point of view i do not want you to get confused is at force is

force and input or an output so you may look at it like that yes okay braking force can

be an input but in the equation that is formed okay the force naturally comes and that is

why i wrote this along with that equation clear any questions? so the view that we are

going to take is that we have a mathematical model we have an input and we have an output

okay because of this mathematical model and how does the vehicle behave or how is

that i convert a vehicle into a mathematical model? so that is the perspective that we

are going to look at in this course clear okay we are going to introduce of course a

number of terminologies no course is complete if you do not understand the words call it

jargons or call a technical terms okay the course is not complete unless you understand

these terms so you cannot converse okay or express your

ideas if you do not understand the corresponding language of a course so from that perspective

there will be a lot of new jargons or definitions or terms that we will introduce in this course

okay how does this jargons look like? okay let us look at it from a different perspective

so we now know what we are expecting from this course? what is that we are going to

do? the other way of looking at it also the another

perspective is look at the course or look at what we are going to study from 3 different

angles the first angle is what i call as driving dynamics same thing but termed in a different

way another what i would call ride comfort and the third one is safety okay so when i

say jargon what are the type of things that we are going to introduce? so of course when i say driving dynamics i

am going to look at the vehicle in driving dynamics the first thing that comes is straight-line

tracking where we are studying we want to study the vehicles interaction with the external

atmosphere we are going to see simple things first we are looking at maneuverability then we are going to introduce some other

jargons we are going to introduce things like self-steer behavior watch out that from the

terms which you understand from pure english we are going to terms which you are not going

to make out that easily unless you know the definitions so self-steer behavior if i am

going to define now you would not understand anything but we are going to do that later is the difference

in the slip angle between the front and the rear tires does not make sense right now to

you okay but we are going to talk about this okay what is called a slip angle? how is slip

angle developed and so on? we are also going to study driving dynamics okay since it is

dynamics okay and this is a dynamical system or system which is controlled by equations

from dynamics immediately you would say that that can be

what are called as oscillatory behaviors and does the vehicle also have this oscillatory

behavior? if so how does that affect the vehicle? there are lot of very interesting things happen

when you give or when you maneuver a vehicle things like what is called as load shift you

would have realized that when you take a turn in a vehicle you would have realized that okay you are

pushed to one side and then you can easily realize that there is going to be load shift

okay in other words certain of this driving dynamics gives rise to certain effects like

for example load shifts so maneuverability changing gives rise to load shifts

okay now one of the things that i want why i am

writing one of the things i want you to realize is that your mathematical model should be

able to capture all that driving dynamics okay which i am going to put forth here so

when i say there is a load shift okay the first thing you have to ask is is this going

to captured by my mathematical model? you will see that mathematical model is a general

term there are simple models the simplest model

you can think of is just vehicle consisting of mass m okay one mass the vehicle as an

acceleration a okay and has a force opposing its motion so a becomes deceleration will

call that s a we will not call acceleration deceleration every time we just call that

depending about positive or negative you can come to your own conclusion so you can look at simple mathematical model

f=ma right this does not talk about various driving dynamics so that is the reason why

i have put this on the other hand this also does not talk about what happens when the

vehicle goes over a bump goes over a rough road and all these things right so mathematical

model is a very general term okay and that you have to understand many of these

things in order to understand the limitations or what can be achieved using the mathematical

model so if i just give you a braking force and if i say mass is this one tell me the

deceleration okay simple calculation back of the envelop you can tell me what is this

from this equation okay now when i say that the vehicle is taking a turn i want to know

what is the role of the vehicle and so on this would not work so in other words what is also required is

a proper understanding of the physics okay which would be the result of your input and

whether your mathematical model will capture that physics okay so from that sense mathematical model can

be very simple like what we had seen or it can be complex and the complexity is increased

as we increase what is called as the degrees of freedom as we increase the degrees of freedom

so that is the reason why we look at driving dynamics suppose i want to look at oscillatory

motion of the vehicle as it goes over a bump okay you would immediately reject this and you

would go back to your vibration class and say oh this we had studied okay that is the

vehicle let me replace all your suspension by a spring okay let me replace the damping

bla bla bla of the suspension system by a damper okay so let me say that the tire is

just another spring and that the tire goes over a rough road and so on so what did i

do? the same vehicle okay a different mathematical

model or a different view of the vehicle’s behavior i have given and the type of degrees

of freedom here what i have chosen is different from what i have given here and so on so the

mathematical model in simple terms should capture what you want to analyze in driving

dynamics okay in other words whether it is a longitudinal dynamics or vertical dynamics

or you can say lateral dynamics because it should be able to capture the vehicle it is usual practice to start with to d-link

the behavior of the vehicle in the longitudinal direction okay in the vertical direction and

in the lateral direction i can d-link them okay and study them with simple models as

if nothing happens in the other directions so this model quite good maybe you would have

done problems in vibration class with this kind of models for the vehicle but if i ask you what happens during a cornering

behavior you know i am going to say that so in other words i will have another model so

the models can also bring out the behavior in a particular direction or a particular

dynamics clear okay we will go into some details on the technicalities that have involved before

we jump into what is going to be the longitudinal dynamics? in other words we are going to have models

which are like this but much more complex than this okay to study longitudinal dynamics

so the intellectual property right of this whole thing belongs to newton-euler and we

have to salute him for whatever he has done to us with that we will stop this class and

we will continue in the next class