yeah 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'll follow that with with the syllabus and then a brief introduction this will be the first class this class will be towards motivating you to look at vehicle dynamics so these are the textbooks that I am going to follow the textbooks are you know JAL SP fundaments of eglee dynamics a very well-known textbook in this field yowser yowser yowser vehicle dynamics theory and applications Springer book hands pass a car tire and vehicle dynamics slightly advanced compared to the first two books and then burn Ising chassis handbook where we take some data in order to illustrate the practicality of what we are going to see in this course so I 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 I am NOT going to use you know this is going to be chalk and talk and I may use or I will use the PowerPoint presentations especially when the figures and the drawings are bit difficult I may use that if it is difficult to draw on the board or else it will only be you know 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'll have the class on Mondays Tuesdays tomorrow at 8 o'clock and wetness stay at 2 o'clock okay the three eyes as I told you vehicle dynamics is the dynamics of or the vehicle in motion and we got 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 you come to your mind the part of the vehicles of the vehicle so you have studied this you have studied this as a course what constitutes a vehicle just briefly let us review quickly what are the components of vehicle that will be involved and what we are going to study now so if you look at a vehicle per se you can broadly classify them into the power module okay which involves engine and so on the chassis module 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 so anything and everything of the vehicle can be brought into these three categories for example if you look at the powertrain or the power which will 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 which are the components which actually take the power to the to the wheel so the power if you look at the power that is given to the vehicle it is given by the engine and the power that is developed to the 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 acceptor okay now you can also if you want you can also in this category include also the axles 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're looking at tires which you can include here 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 it comfortable to sit in the vehicle or carry Goods and so on so broadly in other words I'm not I just 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 are carried 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 way or what are in other words what are the requirements of the week 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 they have three important requirements when it carries people people obviously safety it has to carry people safely it has to carry people comfortably and of course economically okay so these are the three fundamental requirements if you look at the 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 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 affect 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 from a dynamics point of view comfort we are going to look at how the comfort you are comfort us you travel in a vehicle is effective how do you characterize comfort what are the subsystems of the vehicle which 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 economics economics is part of the of your travel but we are going to concentrate here and there the economics of vehicle operations this course we are not going to cover for example engines that is a 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 three aspects safety is linked with the second part of this categorization safety is is the result of the vehicle properly listening to the driver hence that's why I had 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 at that as well okay so for example we are going to pick up the difference between a Formula One car and for example the cars you drive what is the difference between the two 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 there are various the same thing can be looked at in different perspective in other words there are various perspectives to look at these three 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 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 response and an 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 break 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 make Latisse elevates the vehicle takes a turn and so on so there is a response to the 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 week 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 what is the not under normal circumstances what is the effect on the occupants okay so we are going to look at these three things very carefully so the driver of course as I said accelerates and breaks now how are we going to study this we are going to study this using mathematical models now what is what is what do I mean by mathematical model so I have a vehicle is represented by means of a set of equations set of differential equations so vehicle which was introduced five minutes back to have to be to have subsystems consisting of a number of them okay can we 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 the mathematical model of the wake so what are the things that participate in this mathematical model we'll come to that in a minute so this mathematical model will have an input we'll 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 you have to talk about Euler Newton Euler equations and so on so these equations okay we will form the basis of our development of the 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 inertia of the vehicle moment of inertia and say ixx iyy and i zi c or is e and so on okay we will see that we will use three moment of inertia as not IX Y 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 complaints just opposite of these differences 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 very different perspective or in terms of very different quantities whose definition so most of it at least you already know clear okay so I hope you remember all the dynamics that you did your previous classes which will be used and which will be applied in this course clear from another perspective the vehicle dynamic study can be broadly classified into what is called as longitudinal dynamics lateral dynamics and vertical dynamics in other words the mathematical model covers the vehicle behavior in the longitudinal direction the lateral direction which is perpendicular to the vehicle and in the vertical direction acid 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 are written in such a fashion that we understand what happens in these three directions clear okay now you may ask a question what is this input say steering behavior what what do you mean by steering behavior what is a deceleration acceleration and so on because a question that may come to your mind this when I Drive my vehicle in a crowded Road okay and that to you know traffic then I give all sorts of inputs okay it can be a sudden braking or I can do a maneuver very fast maneuver I can do lane change and so on there are so many in other words there's 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 week 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 you are driving in a highway and you want to overtake a week 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 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 double lane change so there is a test called double lane change okay or you can just do a single lane change right now in other words there are tests which to a great extent mimics what happens in reality but there are other tests which may not exactly mimic what 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 pulsed here in this test I am going to give a steering input okay a 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 how 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 week 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 like 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 are there are number tests these tests are given as an input to this mathematical model which is based on the good old Newton 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 idea of studying weakly dynamics is to study the safety economics and so on let us take the condition of of braking let us say that I want to break awake okay suddenly there is a I see some obstacle I want to break the weak okay so I I said that I want safety during braking actually what does it mean or how does this output look like I want to look at if I ought 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 it is large right if the baking braking distances are large then obviously I am not going to satisfy this condition of safety I may want classroom 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 breaking distance okay so we are going to look at that kind of output distance and there are other outputs that typically what what I said is that we are going to go and go back to neutral so what are the things when you when you look at Newton's equations what are the things that comes to our mind 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 are to do with the dynamics clear now who's this related to say for example comfort you mask your question okay you get acceleration how do I reduce my comfort levels in other words what is the effect so this is the output response is the output yes I can understand that if the braking 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 or that I can understand okay but you are talking about effect of the occupants what is that you know so for example I want to be comfortable sitting in the backseat and you know enjoying my ride so how does this give me 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 you our comfort levels inside the vehicle in other words we will map certain of the outputs like for example particular acceleration okay lateral acceleration and so on we will map them into your comfort level by lot of research has been done on 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 here okay in order to understand the mathematical model itself okay we will introduce to you or I will introduce to you certain technical information to write down this equations if you remember Newton's equations on one side we have quantities or newton euler equation 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 equations or to this list the right-hand side of the equation which I would call as generalized force force moment and so on okay so we also have to understand the source of this forces how does this force originate how does it act on the vehicle how is it transferred to the vehicle so this this is one of the things also when we come to the mathematical model becomes important just to give you an example if I have to break the vehicle or accelerate the vehicle then I have I need a braking force and a traction force right yeah you can tell me that brakes braking force emanates when I press the brake pedal is of course is a braking system yes of course there is a 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 breaks 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 grip so in all these conditions I have to talk about the grip of the week 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 entire 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 the 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 Ness 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 between and 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 so this is we are talking about the equation part of it okay so the point you I do not want you to get confused is that force is force an input or an output so you may you may look at it like that yes okay force can be an input 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 question so this is what so the 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 it that I convert a vehicle into a mathematical model and so that is the perspective that we are going to look at in this course clear we're 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 it 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 lot of new jargons or definitions or terms that we will introduce in this course okay how does this uh this this jargons look like okay let us look at it from from a different perspective so let us let us now so we now know know what we are expecting from this course what does that be able 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 three different angles the first angle is what I call as driving dynamics the same thing but termed in a different way another what what I would call right comfort and the third one is safety okay so what are the things whatever when I say jog and what are the type of things that are going to introduce so of course when I say driving dynamics I am going to look at the vehicle driving dynamics the first thing that comes is straight length tracking where we are studying we want to study the vehicles interaction with the external atmosphere we are going to first 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 terms which you understand from from pure English we are going to terms which you are not going to make out okay that easily unless you know the definitions so self steer behavior if I am going to define now you won't understand anything but you're going to do that later is the difference in the slip angle between the front and the rear tires doesn't make sense right now to you okay but we are going to talk about this okay what is called a slip angle how the 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 just the way could also have this oscillatory behavior if so how does that affect the weight there are a lot of very interesting things happen when you give or when you men over awake things like what is called as load shift you would have realized that when you 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 a load shift okay in other words in other words certain of this driving dynamics gives raise to certain effects like for example load shifts so maneuverability changing gives like to load shifts okay now one of the things that I want why am I writing this one of the things I want you to realize is that your mathematical model should be able to capture 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 be 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 has an acceleration ay okay and has a force opposing its motion so a becomes a deceleration I will call that Y a we will not call acceleration deceleration every time you just call the Tajik you see depending upon positive or negative you can come to your own conclusion so you can look at the simple mathematical model F is equal to Ma right this does not talk about various driving dynamics so that's the reason why I have put this on the other hand this also does not talk about what happens when a 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 would understand many of these things in order to understand the limitations or what it can 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 envelope you can tell me what is this you know 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 won't 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 increase as we increase what is called as the degrees of freedom so we increase the degrees of freedom so that is the reason why we we look at driving dynamics we look at suppose I want to look at oscillatory motion of the vehicle as it goes over a bump okay you would immediately recheck this and you would go back to your vibration class and say oh this we had study okay that is the vehicle let me replace all your suspension by a spring okay let me replace the damping bla-bla-bla with the of the turb of the suspension system by a damper okay so let me say that that is the tire is just another spring and that the tire goes over or off-road and so on so what did I do the same vehicle okay a different mathematical model or a different view of the vehicles 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 okay the the vehicle can it should be able to capture the weak it is usual practice to start with to d-link the behavior of the vehicle in the longitudinal direction okay in the vertical direction in the lateral direction I can delink them okay and study them with simple models as if nothing happens in the other directions so this model quite quite good maybe you would have done problems in vibration class with this kind of models for the vehicle but if you ask if I ask you what happens during a cornering behavior you're not going to say that so in other words I will have another model so models can also can also bring out the behavior in a particular direction or a particular dynamics clear we will go into some details on on the technicalities that have involved Before we jump into what is going to be the launch tool dynamics in other words we are going to have models which are like this much more complex than this okay to study longitudinal dynamics so the intellectual property right off of this whole thing belongs to Newton Newton Euler and we have to salute him for whatever he has done to us with that will stop this class and will continue in the next class you