 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 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, Gillespie Fundaments of Vehicle Dynamics, a very well-known textbook in this field. Yazar, Raza, Yazar, Vehicle Dynamics, Theory and Applications, Springer book, Hans Perseka, Thayer and Vehicle Dynamics, slightly advanced in compared to the first two books and then Bern Heising, Chessy 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. Let us now start with the formal introduction. I am not going to use, you know, this is going to be chalk and talk. I may use or I will use the PowerPoint presentations, especially when the figures and the drawings are difficult. I may use that, 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. We will have the class on Mondays, Tuesdays, tomorrow 8 o'clock and Wednesday at 12 o'clock. As I told you, vehicle dynamics is the dynamics of 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 you come to your mind is 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 in what we are going to study now. So, if you look at the vehicles, per se, you can broadly classify them into the power module 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. 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 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 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. Now, you can also, if you want, you can also in this category include also the axles. It does not matter we are only categorizing them. 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 which you can include here, tires and wheels which you can include here or you can include in the axle system. Of course, you have the body which makes you comfortable to sit in the vehicle or carry goods and so on. So, broadly in other words, I am not, 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 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 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 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. 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 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. That is not our interest. So, for example, when we say safety, what does that we mean? For example, when a vehicle takes a turn, how does it behave? When you break, how does it behave and so on. So, when we say safety, we are not looking at situations like crash. So, we are looking at safety from a dynamics point of view. Comfort, we are going to look at how the comfort, your comfort as you travel in the vehicle is affected. How do you characterize comfort? What are the subsystems of the vehicle which are going to have an effect on comfort? 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, 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 a separate course 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 the result of the vehicle properly listening to the driver. Hence, that is 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 at that as well. 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 the two? We are going to look at that kind of very exciting things in this course. 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 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 break the vehicle and so on. So, he interacts with the vehicle by means of things which are around him. Because of that, there is a response of the vehicle. The vehicle responds, vehicle decelerates, the vehicle takes a turn and so on. So, there is a response to the input and the response may make him modify or not 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. In other words, there is a very close interaction between the driver, vehicle and the response. The response has another effect. The response has an effect on the occupants of the vehicle. In other words, the effect on occupants is also important. 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 under normal circumstances, what is the effect on the occupants. 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 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 5 minutes back to have subsystems consisting of a number of them can be also looked at from a very different perspective as a set of differential equations. So, this forms a very important part of this course or the core of this course, the mathematical model of the vehicle. So, what are the things that participate in this mathematical model? We will come to that in a minute. So, this mathematical model will have an input 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. 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. So, what is this mathematical model and what is it based on? Very simple, all of us know it. When we talk about dynamics, we have to talk about Newton. We have to talk about Euler. Of course, we have to talk about Euler, Newton Euler equations and so on. So, these equations 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 I x x, I y y and I z z or z z and so on. We will see that, we will use three moment of inertia as not I x 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 compliances, just opposite of the 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. 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. 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. 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 behaviour in the longitudinal direction, the lateral direction which is perpendicular to the vehicle and in the vertical direction 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 three directions. Now, you may ask a question, what is this input, say steering behaviour, what do you mean by steering behaviour, 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, in a traffic then I give all sorts of inputs. It can be a sudden braking or I can do a manoeuvre, very fast manoeuvre, I can do lane change and so on. There are so many, 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 behaviour. It is 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 we do. There are a set of standard tests 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 behaviour. So, we have ISO standard for understanding the vehicle behaviour. These are called by different names and there are number of them. 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. 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 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 and then you go back. So, you do what is called as double lane change, double lane change. So, there is a test called double lane change or you can just do a single lane change. 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 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, a 40 degree change in less than a second. So, I just change it and then bring it back. 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. 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 or to bring out certain scenarios. There is other tests like constant radius cornering or constant radius test and there are tests which say for example, there is a test called j hook test and so on which bring out extremity conditions. 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. So, these conditions or there are number of tests. These tests are given as an input to this mathematical model which is based on good old Newton, Newton Euler techniques and so on. Now, what are the outputs that we are going to look at? 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 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 break a vehicle. Suddenly, I see some obstacle. I want to break the vehicle. So, I said that I want safety during braking. Actually, what does it mean or how does this output look like? If I have 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. If the braking distances are large, then obviously I am not going to satisfy this condition of safety. I may go on crash with that obstacle. In other words, we are going to look at as outputs, quantities which are related to what I said before. This at least is simple, braking distance. We are going to look at that kind of output distance. There are other outputs that typically what I said is that we are going to go back to Newton. What are the things when you look at Newton's equations, what are the things that comes to your mind? Yeah. So, what comes to your mind is accelerations, what comes to your mind is velocity and so on. So, the outputs will now be in terms of these quantities, distances, distance, velocities and so on. There will be other things. We will see that later, but all of them are to do with the dynamics. Now, who is this related to say for example, comfort? You may ask a question. You get acceleration. How do I deduce 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 is not happening as the driver wishes it to be, maybe he can jam or press the brakes hard. Fine. That I understand from braking distance. If he wants to reduce the velocity or increase the velocity, he either presses the brake pedal or that I can understand. But you are talking about effect of the occupants. What is that? So, for example, I want to be comfortable sitting in the back seat and 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 your comfort levels inside the vehicle. In other words, we will map certain of the outputs like for example, vertical or acceleration, 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 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? In order to understand the mathematical model itself, we will introduce to you or I will introduce to you certain technical information to write down these 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. 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 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 need a braking force and a traction force. You can tell me that the braking force emanates when I press the brake pedal. It is of course, it 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 say 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 vehicle or grip of the tire 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 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, when I say book at that time I will give you a reference. So, we will follow that also in this course and there will be short introduction on aerodynamics, the effect of the body on the aerodynamic forces. So, in other words yes there is I would say an environmental interaction between you know 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. So, this is we are talking about the equation part of it. So, the point I do not want you to get confused is that force is force an input or an output. So, you may look at it like that yes force can be an input breaking force can be an input, but in the equation that is formed the force naturally comes and that is why I wrote this along with that equation. So, this is what 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 because of this mathematical model and how does the vehicle behave or how is it that I convert a vehicle into a mathematical model. So, that is the perspective that we are going to look at in this course. 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 call it technical terms the course is not complete unless you understand these terms. So, you cannot converse or express your ideas if you do not understand the corresponding language of a course. So, from that perspective there will be lot of new jargons or definitions or terms that we will introduce in this course. How does this jargons look like? Let us look at it from a different perspective. So, let us now 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 three different angles. The first angle is what I call as driving dynamics and same thing but termed in a different way. Another what I would call right comfort and the third one is safety. So, what are the things what when I say jargons 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 driving dynamics the first thing that comes is straight line tracking where we are studying we want to study the vehicle's 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 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. But we are going to talk about this what is called a slip angle how a slip angle developed and so on. We are also going to study driving dynamics since it is dynamics and this is a dynamical system or a system which is controlled by equations from dynamics immediately you would say that there 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 a 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 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 manoeuvrability changing gives like two 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 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 A okay and has a force opposing its motion so A becomes a deceleration and we will call that yes A we will not call acceleration deceleration every time you just call that as A depending upon positive or negative you can come to your own conclusion. So you can look at a simple mathematical model f is equal to m A 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 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 have to 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 breaking 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 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 complexities increase 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 we look at 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 blah blah blah with a of the 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 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 behaviour 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 analyse in driving dynamics okay. In other words whether it is a longitudinal dynamics or vertical dynamics or you can say lateral dynamics okay the vehicle can it should be able to capture the vehicle. It is a usual practice to start with to delink the behaviour 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 behaviour you are not going to say that. So in other words I will have another model. So the models can also can also bring out the behaviour in a particular direction or a particular dynamics clear okay. We will go into some details on the technicalities that are 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 much more complex than this okay to study longitudinal dynamics. So the intellectual property right of this whole thing belongs to Newton, 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.