 The last class, we were talking about subjective, objective evaluation with run it a bit fast because we wanted to get an overall picture. We did not go into details of some of the things which may be of interest. You may be wondering for example, what are the type of questions that are asked to expert driver and what is he supposed to know and answer? How does he answer? All these things the details we just skipped it. We said that you can refer to the paper and the thesis but let me just take you through a few at least a few of the questions which is which was posed to these drivers. We said that there were you know seven drivers who are asked and one of the key things in this is also the correlation of the answers to the drivers. There are two things in this. One is the correlation of the answers to the drivers and the correlation of the questions itself. You know the questions require similar you know response from the driver and whether these questions were I mean similarly responded. So this is also important. We also said that the experimental car which Chen and Ash used at the Leeds University, they had eight vehicle parameters and then these eight vehicle parameters were changed and 16 configurations were arrived at or 16 different cars were the ones which were tested. Of course Adam's model has been used as well in order to get the objective rating and experiments were conducted in order to obtain these ratings as well. So let us now look at what are the type of questions and I am going to just read it out so that you understand. So the type of experiments are two things. One is a number of experiments were done. For example steady state turning or steady state cornering is an experiment that was done in a smooth road as well as in a rough road. So you have that steady state turning which were run in a rough road and in a smooth road. So there were a set of questions that were asked and in order to determine the cornering behavior. So for example the question is something like this over smooth roads progressive behavior with increasing lateral acceleration. How does this vehicle behave when you increase the lateral acceleration? Obviously when you say increasing the lateral acceleration you mean that the speed okay the two speeds which were chosen and as the speed increases how does this progressive behavior with lateral acceleration how does that driver feel on that? The other thing is that over smooth roads is with which this line is held. You know does he is it very easy for him to take this turn hold the line in other words hold the path or is it that he had to make constant changes in his you know the way he drives and so on. Then other thing is that what is the amount of body roll or degrees of body roll okay which the driver feels third one. Fourth question is that progressive behavior with decreasing lateral acceleration okay. So the progressive behavior of increasing as well as decreasing lateral acceleration okay and an indication of the feel of available grip okay and so on. In other words these are the type of questions that were asked and that these were rated as I said before in a one to seven scale of rating okay. If you go and look at this paper you see the spread of answers. In other words it is not that every driver is going to agree okay on that marks okay there are spreads and it was found that a few of them okay it is the spread of the answers or in other words the if you take an average as well as the spread of this you would see for some of them it was small and some of them it was large and so on. In other words it was not very easy for drivers to agree you know exactly on every question on these things okay. So that is why a very detailed statistical analysis was done. In fact in order to extract information things like neural network was done and so on. So the first thing is the steady state turning and the other as I had said is I mean this involved totally about 14 questions. So this involved about 14 questions. Then we had this power change as I said on or off we had already said that power change is going to look at the understeer and the oversteer characteristics of the car and figure out it is an exercise when there is a power on would there be more understeer characteristics or power off would it be less or vice versa. I leave it to you to think about it basically because this involves what? Low transfer okay and when low transfer happens what really whether it is going to be understeer or oversteer I would like you to think about this okay. So this power change involves I think 14, 15 to 20 that is so six questions then sudden braking in a turn okay. So what happens to for example during this case what happens to your response what is the roll stability what is the wheel lift and so on. So these were the questions which were asked when sudden braking in a turn okay transient cornering okay again there were a number of questions on transient cornering. So the the the third one sudden braking in a turn it went from sudden braking in a turn went from 21 to 24 okay. So then transient cornering straight line direction stability and so on. In other words a total number of questions that were asked was 49 was 49. So very large number of questions were asked. Now it was not that all these questions were relevant okay when compared to handling and when compared to subjective objective evaluation that's why later out of this 49 questions a few of them became I mean important. So the first thing is questionnaire was set these things this we had already seen okay. So out of these questions a few of the yes There are two purposes to this one is to quantify how good your vehicle is from a pure technical view point and the other is how what exactly the user wants. But in that case why can't it just subject the user to conditions they would normally face why do you want to put them through test like this. I don't know the the user band may be so high. No but it makes no sense to test them in the scenarios in which they would normally be operating and you could even use a steering robot or whatever to quantify how the performance. Okay okay two things one is that if the vehicle performance at the limit is good because most accidents if you see it is at the limits if it's limit is good then handling characteristics of the vehicle is supposed to be good okay. More importantly steering robot okay is today used for getting input for the objective metrics okay. Now here what are we trying to do ultimate all one of the important key things which in my experience we have done lot of work. We have seen that when it comes to handling when it comes to handling the drivers are very sensitive okay very sensitive to changes that take place. Alright that is the reason why for example when you have that pressure of driving as you for example accelerate in a corner okay and the vehicle feels that acceleration in a corner okay gives you a sort of a good feeling of the car. So in other words the feeling as you drive the car is brought out by this subjective evaluation right. Now the why are we okay let's put it like this. I have objective ratings okay objective parameters okay. First of all I do not know suppose you remove the the drive a subjective drivers. First of all I do not know what can be this this list what can or what should be this list look at the list you know there is so many things which we had seen yesterday. So what can be this list in order that I would satisfy a good behavior of the vehicle okay I don't even know it. So that is why I want a subjective to objective correlation okay and the the car is tested at its limit because I do not know you know how it will be used right I mean we are not talking about cars being used only at say in our roads where you can't go beyond 40 or in any city road where you can't go beyond 40 kilometers per hour. We are not testing cars just like that okay they are tested for different purposes. For example there is a city cycle the city cycle is used in order to to find out what is the fuel consumption okay. For example our roads we test the cars for very sharp transient manoeuvrabilities okay. So which is also reflected here. So in other words the city cycle it has its own use to evaluate the car especially from a fuel consumption point of view. But when you want to look at the performance of the car say suppose you take this in a in a highway okay and we know in our highway suddenly there is an obstacle that comes okay and you you do a double lane change under very severe conditions. So we are travelling at 120 kilometers I don't know whether you have driven this highways in Indian highways today people drive at 140 kilometers to 160 kilometers per hour. We know that some of the buses for example we have done lot of survey on entire lives we know that buses average 105 kilometers per hour okay. Those speeds are extremely high extremely high. So at those speeds at those speeds okay we do not know how the vehicle is going to behave. There have been issues when the vehicle touches 110 kilometers per hour okay. There are countries in which there are restrictions on speeds for example United States okay. In our country we do not have most instances we do not have restrictions on the speeds okay. In many countries like Germany you do not have restrictions on speeds. So you do not know what speeds people are going to drive. So that is why all these things are tested. Simple fact is that the drivers also do not want surprises okay. When you change when you do a transient understeer or transient oversteer the drivers also do not want surprises. So that is why we do such a subjectivity. So once I do a subjective and I do a subjective objective correlation also my design becomes simple. Now if I tell you that my yaw rate gain at 0.7 hertz is important then my next goal which you will do in the next course on our vehicle dynamics lab as to what are the design parameters which are going to have an effect. We have seen this with a simple bicycle model right. But there are other parameters which may have an effect. In a very detailed models there are other parameters which may have an effect. So it becomes easy for me once I have that kind of range which we defined okay that kind of range which we defined then it becomes easy for me to also design a vehicle. Clear? That is why. So what are the important things? How do you design a questionnaire is important okay. What are the type of questions or relevant questions are you asking okay. That is why the questions where objective metrics are found to model majority of the driver ratings are given here okay. Go back and look at the thesis batch you can do more I mean more about these questions. So from these 49 questions a few of them become important okay and tomorrow you want to test a car it is good to have or to model this or to have a questionnaire, design a questionnaire based on these questions okay. So it is a big topic I do not have time to go into each one of these questions and how it is related and so on that is why I have given you a reference I would like to move to the next topic okay but just want to spend a few minutes on what this subjective rating questions tell you right. Of course ultimately when you want to buy a car you are going to drive it that is a different thing but this is useful for the designers okay. At least now with the vehicle dynamics course you will also know how to test a car right. So that is yes okay you can do a test drive okay. Post that you are going to buy a car go and do a test drive and say that I will take I will tell you a decision after couple of days. Do not give your cell number to him because he will keep calling you right do not do that go and do this test okay fine. Anyway we are going to do some few tests in the next course on vehicle dynamics lab we will know more about these things right. So we will move away from this subjective objective correlations we will move to a last topic in lateral dynamics which is roll over yes. No no no I told you right I mean memorable plot is the easiest because I have only four parameters okay that seems to correlate well to a great extent in my opinion we have a great I have also done some tests it correlates well okay except that when the vehicle has a lot more oversteer characteristics then there is an anomaly. In other words what we said is that within a limited range the sentence that as the area of the rhombus increases gives a better drive or a right I mean handling is valid. But then this work further work after memory after all it was in 90s early 90s so there were lot more parameters which were included okay. Now those are the parameters which we had put down sometime back right and the difficulty as you add parameters is that I want to now be within that range then it becomes difficult whether I can have all those parameters within a range within that range. That is exactly see that is why this subjective how will you predict the range there are two things one is predicting the range the other is getting the value in a design. The predicting the range is that subjective objective correlation that is what I have been talking you know subjective objective correlation gives you that range okay clear. So in other words that is why drivers are asked to drive look at their answers then what are what are those cars which they have said very good what are those ranges and so on you know. That is why you did or people did in the Leeds University did a factorial experiment okay. So this range is obtained from that correlation there are number of ways in which they have obtained this correlation okay. So range is different from design then you have to go and design a car whose for example natural frequency at yaw is between these two 1.7 and 2.1 okay. So this is applicable to a range of say a sedan okay up to SUV right but may not be applicable for say trucks type of thing okay. So this range is for the vehicles tested which is which is sort of sedan SUV type of vehicles this range is valid your question is well taken. That is why if you are working in a car company you would like to have your own these numbers okay so that you can fine tune it. So this will be very useful for you to fine tune your vehicle. You can predict the range see this you can if you when you design a car you will get the values for these things. You will get the values the range is predicted as I keep telling between subjective objective correlation. It is just it is like how the car is when you don't face like that. So there what we did was we asked to rate it as 1 to 7 okay. In fact that is why this paper I don't know much time 980226 SAE there is a table say figure 4 rather okay. Figure 4 you get effect of objective metrics on subjective ratings is completely given there okay. Go and have a look at it for example effect on subjective ratings is in the y axis and you see that very many number of objective metrics are given in the x axis okay. So when you change this parameter say for example natural frequency of yaw at 0.7 yaw or yaw gain at 0.7 what is the effect on subjective rating is obtained okay. And he had also defined whether there is a uniform agreement or the drivers have unequivocally said that this particular parameter is important and so on right. So that is how this is arrived at change it for example I mean in simple words I change the configuration. So let us take one thing I change the natural frequency okay let's forget about the rest of it just as an example okay. Very good statistics is involved but let's forget it for a minute just to make you understand I know that students you'd be wondering why we are doing these things. So let us forget about everything I will say natural frequency I am going to take say 3 cars or 4 cars okay whose natural frequency at yaw varies from 1.6 okay 1.8, 2 and 2.4. Let's say that I take this cars and I give it to the drivers okay and ask a number of questions which I had listed okay. How does it behave in a turn whether you are going to hold that hold it you know is there are you losing a grip or and so on and so forth. And I am going to ask them a number of questions. Now then if I consistently get that drivers say that your car which is 1.6 okay is not good or his ratings for the questions are low for 1.6 and becomes high for 1.8 and 2 and again low for 2.4 okay right. Then I would say that look this range consistently if they say it and there is a statistical significance there are number of statistical significance test go through this thesis. Then you would see that with 95% confidence you know there are R what is called as R squared values in statistics and so on. Forget about all that jargons just say that these two values okay consistently people say it is good. Then I would say that look if the natural frequency at yaw is between these two people say that it's a good car and so you should keep it like that okay. Now we can't change okay let's say that I change similarly damping and so on I keep changing one by one and I want to find out each factor that's one way. But I can't do that because there are so many factors I can't do so we do a factorial experiment to understand okay the interactions and between the drivers feel and this and arrive at a set of values clear. So once you arrive at it you go and start working in your design okay. Now so natural frequency of yaw how is this going to be related the first thing I'll do is to go to a bicycle model you already know the formula for it okay. So you look at your vehicle where do I stand what is my natural frequency at yaw okay simple first cut okay maybe 2 degree of freedom or 3 degree of freedom where do I stand yes looks like it's fine okay. Like that whatever is possible for me to get okay yaw velocity gain or lateral acceleration gain okay phase and so on all these things I have simple formula and first I'll check okay what are the parameters. Maybe the mass of the vehicle will have an effect CG location may have an effect moment of inertia may have an effect lateral compliance may have an effect so many things may have an effect on these things. Okay then my job as designer is to optimize this and see that my vehicle lies in those ranges that's a challenge it's a good optimization problem which will do that in the next semester. I assure you that we are going to do a complete sensitivity parametric analysis okay. We will take a car we will change various parameters we will list down okay various parameters and then we are going to change them and see how these parameters are getting affected. So you can come to a very optimized car okay so in other words if you produce this car then and give it to this ratings of the drivers who are very important okay then you will get good ratings from them that's the fundamental basis yes. At some point I took someone to identify what these parameters are that is probably the toughest job because even now you are not sure of whatever. Absolutely that is that that's the that's a too good PhD that's why I took that in this course too good PhDs we were done a lot of work okay in my opinion that's an exhaustive work that's done right that is the you know the two good PhDs from Leeds and that's what. They had done but the problem is it is not one to one correspondence it is not that for that one question there is one objective parameter it's not like that it is that is why the statistical base I keep on telling that that becomes important. Yeah correct if you are not if you are in that I would say range okay this will be valid that's why I said that mostly if it is a sedan okay or SUV this would be valid okay so yes the validity has to be checked we are not questioning that but generally because of the range that was done okay this likely to be valid. Okay this is not something as a design rule we are saying that's why we are giving a range around this value looks correct looks value. Yeah correct so that is where again I want you to go through the thesis we will do that you know next semester in another course okay we will go into details. See we are only scratching the surface in this whole course we are only scratching the surface vehicle dynamics is a huge topic okay the questions which are still not answered is I said that with there been some answers and I am not convinced that every metric has been answered from very I would say use again the word in a very objective fashion. In other words some of them you may know that the response of the vehicle is in that frequency range and so the phase becomes important and so on but for some of them you don't even know. Say for example why is it at 0.4, 0.6 if you go back and look at it the list of for example metrics which they have studied okay which is given in their table 2 in this paper so you would see that the metric is studied at say for example 2 and 4 meters per second plus or minus 2 and 4 meters per second and that the peak lateral acceleration response time is taken at 2 and 6 meters per second squared lateral acceleration and so on okay. So in fact the authors themselves agree that this kind of you know why is it I wrote down a formula. Why is it that it is 1.1 multiplied by something minus 0.5 multiplied by something plus you know that is still not clear right. So that is why it is purely 2 data sets connected by statistics okay this is just a parameter identification okay some have meaning some do not have meaning okay I do not know why it is 1.1. Say for if you look at say I mean just like that I have given a formula I do not know why it is minus 1.1 into your rate gain at 0.4 hertz I do not know you know that is what the statistics throws out at you. The regression analysis throws out okay and that is the value if you ask me why 0.7 just a statistical output that is all I know I do not know more than that why minus 0.7 into this I do not know more than that okay. So in other words subjective objective evaluation is still in the realm of statistics okay it is still in the realm of statistics you are correlating it through statistical means clear okay. It is a challenge to produce a good car and you learn okay that is why many of these car companies have a huge data back okay. So let us shift to the next topic I know this is an interesting topic because it actually impacts design of the vehicle itself as I said vehicle dynamics we are scratching the surface. It is a huge topic extremely interesting I know that so much of interest the students it is an extremely interesting topic we cannot complete all the things maybe you need a couple of more courses on advanced vehicle dynamics. In fact I am guilty of not covering many things connected with vehicle dynamics for example the lot more vibration aspects and we are not covering the effect of suspension steering and so on. There is no time because of the limited about 35 hours of lecture we let us at least get a view of because it is an introductory course get a view of what happens okay. So let us get to the next topic which is rollover before we follow or we go to vertical dynamics where there is still a lot more to cover on vehicle dynamics as far as the vertical dynamics is concerned and so we will go to rollover. Rollover is a very important topic starting from SUV onwards you would have seen lot of accidents in SUVs sports utility vehicles where the vehicle would have rolled over the sides one and you would have seen huge trucks tractor trailers are some of them. Okay there rollovers you would have seen it a number of times you will be surprised to know that recent statistics shows that in United States 15,000 vehicles rollover a year okay so there is a lot of them. Okay in our in our country we have had cases where there are number of rollovers in fact we had looked at some of the cases where there are rollovers of huge trucks which take cars okay which are manufactured say around Chennai. They are huge vehicles which take over which take the cars right and usually the loss is upward of 5 million rupees okay the because of the cars that are involved unfortunately in this country we still do not have a law on how this kind of tractor trailers are designed. In fact how what is the height and what simple ratio which we will we will see in a minute you know these ratios are not followed and so on. Okay so there is a lot of scope to work on on rollover and in recent times control strategies have been used for rollover prevention. As I said again we would not have time to go into the control strategies for rollover prevention but let us let us quickly understand what we mean by by rollover. The simplest analysis is what I would call as a steady state analysis where we considered the vehicle to be rigid okay and sitting say for example very approximate diagram and let us say that that is the centre of gravity location sorry. Let us say that that is the centre of gravity location. Let us say that these are the centrifugal forces that are required okay in order that the vehicle takes a turn right and that is the corresponding D'Alembert's force okay or the centrifugal force okay which is MV squared by R or I would call that as M into Ay. Okay now of course there are reactions at the front and the rear okay and that we call that as the track width let us say that that is the track width which I would call as TW okay and of course the weight WX. Obviously you see the roll you know as the vehicle takes a turn let us say that this is the outer tyre that is the inner tyre just call that as outer tyre and inner tyre and the FZ that is acting here is FZ outer and FZ inner. Let us define I am defining it let us define that vehicle rolls over or we say that vehicle has rolled over once this FZ inner how is it going to roll over I am going to take now what am I doing I am going to take a turn to the right okay where will it turn over which side to the left right. So I assume that the roll over condition is achieved when I lose contact of the inner tyre with the roll okay this is the condition which I am assuming right. So let us let us just calculate what should be the critical Ay in order that this is you know this lift of the inner tyre takes place let me call that distance as H okay. Now take moments about this outer tyre okay and tell me what should be this Ay M into Ay into H minus W which is M into G into TW by 2 is equal to 0. We talk about steady state we are not introducing the time derivatives okay the no this FZ inner that is what I told you know so this is not there is nothing here there okay. So Ay is equal to G into TW by 2H very famous ratio T by 2H ratio as it is called or Ay by G usually expressed as the simplest formula okay is equal to T by 2H. The first thing that our commercial vehicle guys who carry those lovely cars have to do is to check what is their T by 2H ratios. We would be surprised we have done this calculation we would be surprised to know that this is 0.22, 0.23G in other words T by 2H is about 0.22, 0.23 very very low. So that is the level at which okay lateral acceleration levels at which this will roll over the typical car would be about 0.7, 0.8 and if you look at a formula one cars it will be more than 1.5 very high okay. So the very first thing first equation that you look at is what is called as the T by 2H ratio there are two things that we left here. There are a number of factors the number of factors which would now change T and H what is the assumption that we have made we have assumed that this whole thing is rigid not true. Actually the vehicle the body what is called as the sprung mass is actually going to roll right there is a roll center we have seen that and the vehicle is going to roll. So as it rolls say in other words as it rolls okay about the roll center the center of gravity location is going to change is going to change. So one is that H is going to be affected by the roll and hence due to the suspension and so on okay. The other factor and the roll is also this is one of them the roll is also due to the stiffness of the tire the tire stiffness is also going to have an effect okay. In other words you can imagine that FZ in this in the inner is going to go to 0 okay the whole of F the FZ that is the normal force will be transferred to the this tire. Yes sir I am coming down we will do one by one okay. So let us both of them are going to be affected okay there are number of factors which are which are going to affect both right agreed wait wait I know I am very happy that you are so involved but we have to go step by step right okay. Yes so that is also the roll also is affected there are two two rolls here. One is the roll of the unsprung mass which is basically due to the tire stiffness because of which there will be say let us say that let us look at the suspension system or this axle system okay which is a rigid axle system which is there in most of the commercial vehicles. So because of this this is going to be affected and the second one is that because on top of it is going to sit this our sprung mass okay and that sprung mass is now affected by the roll stiffness. So in other words there are factors which affect this there are factors which affect T okay there are factors which affect T. T is affected by the by the kinematics and compliance of the suspension system. For example it is affected straight away even without going into the details of kinematic and compliance system is affected by the tire lateral stiffness okay straight away tire lateral stiffness. It is affected by the camber it is affected by the camber change okay how does this camber change and so on. It is even affected by the torque that is produced due to the gyroscopic effects. So a number of factors affect this and this which we will we will list down in the next class okay and so usually if you design a vehicle it is if this factor is T by 2h is equal to say 0.8. This factor usually is the actual factor is less by about 25% okay number of these things are going to have an effect it is going to be less by about 25%. So there are at least 4 factors which have an effect. The major effect or maybe even 25-30% you know and so on the major effect is because of this role because of this role. So my first job here right now is to find out what is this role and how that affects this this H. So let me consider two of this role in role simply means that it is going to be an angle okay two of them one I would call as alpha 1. We are going to follow for this derivation the reference is that road vehicle dynamics by George Rill by George Rill road vehicle dynamics is very simple derivation which takes into account this. And if you want slightly more detailed and I will give you one more reference again due to okay which I will maybe next class I will give you that reference I do not have it right now. So there are these are the couple of references which talks about this but one of the things which we have not done here is that we have not considered actually the dynamic effects. You know in other words I have to write down a differential equation based on phi double dot i phi double dot and so on that we have not done you know that is the next step. The more interesting part is okay let us just finish this I will come to this okay one is this alpha 1 the role of the unsprung mass and alpha 2 which is the role due to the sprung mass. Okay we will do this to we will do the detail derivation next class and finish this topic. I just want to tell you that what we are doing is actually not dynamics even when I include these two we are not doing dynamics okay. So we have to do dynamics in other words we have to understand the dynamic behavior and role and that becomes very important in order to design okay. Control systems for preventing role okay. There have been number of papers and thesis on how to write down these equations. In fact goes back to the 50s write down these equations and then the recent attempt has been to rewrite the equations in state space and use a number of standard controls strategies okay. So we will talk about alpha 1 alpha 2 and its effect on on this parameter in the next class right okay. So any questions we will stop and we will continue in the next class.