 In the last class, we were looking at subjective evaluation. We will continue this topic. This is probably one of the most important topics, especially for people who design vehicles. They want to understand how to satisfy the driver. In other words, that is what we call as subjective evaluation. Usually, there is a jury of drivers, 6-7 people who conduct a number of maneuvers and then answer questions in terms of ratings. For example, there can be a 1 to 7 rating for a question, 1 being bad and 7 being the best and so on. Now that is what we call as subjective rating. Objective is, as I told you before, it is the characteristics of the vehicle. For example, 4 of the objective metrics which we called as memorometric. It was already introduced to you and the most important thing for a designer is to correlate between the subjective evaluation of the drivers with the objective metrics. It is not a very easy task, very difficult task. Number of papers are available on this particular issue. As I told you in the last class, I am going to take some of the references which give clarity to this subject. Yes, there are others which have appeared recently. So, we will concentrate on these references. Though we have done some work on this and because of some appropriateness, we are not able to project all the results. So, we will concentrate on published literature in order to understand this topic. Just to summarize what we did, understand that we were essentially subjective evaluation, in subjective evaluation we are concentrating on how steering is given and how vehicle is going to behave to that steering input. Now that is the most important thing. Now the steering also involves, the steering input also involves how the steering is going to get a feedback from the vehicle due to certain maneuvers which we are going to do. Already we have seen this. We said that straight ability as the vehicle goes straight on a road. What are the things that we should look for in a vehicle? We were looking at the steerability in the sense that how does the vehicle behave when you want to steer a vehicle. So, in terms of agility, in other words, how much of steering angle you have to give in order that vehicle is going to listen to you, precision or able to follow a path with precision with the steering angles which you feel should be given. In other words, what is the feedback that you get from the vehicle and comfort? It is a steering torque that you apply is very high or very low and so on. So, these are the three things that are very important as far as the steerability is concerned. We had already seen on center field. We had seen steering response. We had talked about, you remember that we talked about the time delay and so on and then we had talked about steering linearity. How much linear or non-linear is the input as the path changes? We were looking at what we called as steering precision. Steering precision is actually a subjective evaluation of the path that is followed. How much of steering input I have to give or how precisely is the path that is followed as I give the steering input? So, that is again a subjective evaluation of the path to be followed. Then we have the steering angle. This again is a subjective evaluation of input versus output. Say, for example, you can draw. So, you give a graph between time and the steering angle. For example, the steering angle, of course you are going to take some time to give the steering angle. Let us say that is the steering angle you give. So, you steer the vehicle to go at a particular path. Now, if that is the case, you can draw another graph between steering gain versus time. In other words, how much, since we are talking right now about steering angle, how much the vehicle is turning because of the steering angle with respect to time that you have given. Say, there can be two graphs. Let us say that one graph is like this. The other graph is like this. Please note that when the steering gain is low, you have to give more steering. So, this may be due to two tires, say tire A and tire B, two different tires. Now, this is where subjective evaluation comes into picture. If you look at tire B, for example, it responds quickly to the gain. In other words, to the steering input that you give. It realizes the steering input and quickly gets that gain that is required. Or the, what we call as hand wheel to road wheel. The road wheel quickly realizes, raises and then the input is realized. But the gain stops. In other words, the gain is a constant which means that you have to give, please note, gain is a ratio and so you have to give more steering in order to achieve what you want, the path you want. So, race time is high, but lot more steering has to be given. But on the other hand, tire B, the race time is low, but the amount of steering you have to give is less. So, this is what is realized or this is what we call as subjective evaluation. How does the driver feel or when does the driver feel comfortable with tire A or tire B? This is what we feel or what we say as subjective evaluation. Yeah, then we have what is called as the steering effort. In steering effort, you talk about the steering torque that you have to give, the amount of torque that you have to give is steering effort. Returnability, we saw that when I, when I leave the steering, how fast time versus the steering angle. So, how fast the steering comes back to where I left, right? So, that is the returnability. So, it returns to its original position. One of the most important things, so just go back. So, here we are talking, all these things we are talking about is the steering and its effect on the vehicle. So, that is what we call as steerability, ability to steer. That is what we call as steerability, term used by Jim. Then we have what is called controllability. Am I going to, am I able to control the vehicle and controllability comes especially at limit driving. It does not come on a very ordinary driving at 30 kilometers or 40 kilometers per hour in the city roads. So, when we talk about controllability, we are talking about the limit driving at limit. So, with the grip we are going to lose the grip what is going to happen, okay. This is what we are looking at. So, in controllability, one of the first things that people today look at is what is called as balance FARA, balance between the front axle grip and rear axle grip. Actually when they talk about, this is a common terminology that is used. When they talk about balance between the front axle grip and rear axle grip, actually what they mean is the slip angle that is developed between the front axle and the rear axle. Though this term grip is loosely used, it is actually the force generated or in other words it is the slip angle that is created between the front and the rear. That is what we call as balance FARA. It depends upon of course on the characteristics of the front tire and the rear. So, this to a great extent is a tire characteristics which you can see that this in many of the websites of the tire manufacturers where they will talk about balance FARA and usually it is talked in a scale, okay or termed in terms of a scale, right. So, in other words, balance FARA is a measure of a transient oversteer or a transient understeer. We already talked about transient oversteer and transient understeer. Remember that when I am going to take a turn, okay, I am going to take a turn, I am in a transient situation and we had talked about usually whatever analysis we had done with respect to K was in steady state. So, transient oversteer and transient understeer is when I enter a turn, when I power on or power off, okay or accelerate. In other words, I accelerate or break and so on. Please understand that this again a confusion in the literature on braking, acceleration, power on, power off, okay. These are rather power off and power on. In other words, we are looking at the vehicle's behavior in deceleration. It does not matter whether you are applying a brake in order to decelerate a vehicle or taking a pedal of the accelerometer, sorry accelerator, okay. Taking the pedal of the accelerator is as much a braking as you apply brakes, right or in other words power you do not give power off is also braking. So, usually I would say that they are synonymous that you take the, take your pedal, I mean leg off the accelerator pedal is braking, okay. So, both of them it is very important how the vehicle behaves in both of both these conditions. Why? As we had said before whenever there is a load transfer there is going to be a load transfer be a change in the what? Slip angles. We saw that whenever the vehicle rolls there is a change in the slip angle. In the same fashion whenever there is a roll, sorry whenever there is a pitch or in other words whenever there is a transfer of load between the front and the rear again I am going to have a difference in alpha f and alpha r. So, whenever there is a transfer like that alpha f, alpha r gets affected and hence I get into a variation in the steer over steer or under steer characteristics of the vehicle, okay. So, this is what is tested. This is what is tested when what happens when I power on and power off in a turn whether the vehicle is going to become how much it is going to become under steer or over steer because of this transfer of power, clear? I agree because yes I agree with you. We are I fully agree with you that brake system characteristics become important and the rate at which it is braking is important, no doubt about it okay. It is a good question, good observation but from a vehicle dynamics point of view, okay I am looking at deceleration. So, when I take my you know leg of this pedal, automatically the vehicle speed comes down that means in other words it is decelerating, right? This is what I meant. Of course deceleration or power off okay is no substitute for braking there are other issues because the intensity of deceleration also is different but I just wanted to tell you that the behavior is similar. In other words you can look at the behavior from both this perspective, right, okay. So, usually when we say controllability we are looking at the limit of the grips, you know I am going to go a bit fast in this. In other words we are looking at the stability of the vehicle at the limits, at the limits. I am going to lose the grip, okay or I have almost lost the grip or I have lost the grip how does my vehicle behave? This is the condition you know at the limit conditions. The first thing under these conditions that you look at is what is called as your stability. So look at the slide you know what are the things that we are looking at. So the first thing that we are looking at is your stability. What is meant by your stability? So the vehicle at the, at this limiting conditions would actually your, okay. This is because I mean there are number of design reasons maybe this is because of the lateral compliance differences and so on, okay. So the vehicle would your, the vehicle would be like this then would be like this then would be like this and so on, okay. So the yaw, the vehicle yaw as the vehicle yaws what also becomes important is your damping, okay. How much are you, is it going to go? It is going to be difficult to control the vehicle as it yaws, okay. Does it yaw? How much it yaws and how difficult it is to control the vehicle? How does the yaw damping bring it back, bring back the oscillation to a steady condition and so on is what we mean by your stability, okay. So that is the oscillation around yaw, right. The other thing is what we call as rear axle stability which means that it is the, if this is the vehicle, okay. So how much, so the, actually it goes, you know the slips up and down like that. So it is a straight line where the rear backs the tail, okay. So that is rear axle stability. Again it is a question of oscillation, okay about the rear axle. Steering stability, sorry, roll stability. How much as I take a turn, okay, the vehicle rolls, right and this is slightly different from roll over stability where we are looking at the propensity of the vehicle to roll over, okay. This is a very severe test usually done with steering robot. There are standards for this and so on. So roll stability is what does the driver perceive as the roll and roll over is that the vehicle just rolls over. Then we are talking about braking stability. That means that you go straight, break the vehicle, okay. How much of attitude of the vehicle I lose? Is it breaking straight and standing there as I go or does it move and so on. Then bumps here, the change in the tow as you go over a bump, okay. This you, all of you who drive would have felt it in your vehicle. As you go over a bump, the actually the steering steers and you have to hold the steering and so what is the steering that input that is given without your effort due to bump. You know this is bump steer. So these are some of the things that you have to look at. So in a nutshell, when you test a vehicle, you look at how the vehicle behaves in a straight line, when you go straight, how when you give a steering input or what is the effect of the steering and how the vehicle can be controlled. These are the three things that you need. Sir, you said you control, look at how my control of the vehicle is when it is at the end of say, you also. No, no. At the limit means I am talking about the grip, okay. At very high speeds when you take a turn and so on, okay. We are not looking at, see this goes with the limit of handling of the vehicle, okay. We are not talking about these things at very low speeds. That is what I mean, okay. Under normal 40 kilometers per hour conditions of operation, okay. That is what I said that controllability at the limit. So what are the things that you do in the subjective test? Yeah. Sir, we talked about your stability. There are cases when the driver only able to steer the vehicle. Yeah, of course. That is what is subjective rating. So how much that driver is, in one case, there may be a yaw of the vehicle and the vehicle may come back, okay. In another case, it may go out of control. He may feel very uncomfortable. So these are the feeling. You know, that is what we call as subjective rating. No, sir. They like to evaluate. Yes. See, again, see, that is true. That is what we are calling as the subjective evaluation. When we say about subjective evaluation at the limit, it is not that the driver has lost complete control, it is all gone and what happens? No, okay. What we call at this point, when I reach a limit, that additional input that is given, how does it behave? So the additional steering effort at the limit is what we are looking at. It is not that I have lost control, okay. For example, if you look at grip, okay, grip is again a loosely used term. It is just for a force that grip is used. For example, you know that alpha versus Fy force, right. If you know that it is going to reach a limit and it can come down or it will come down, okay. So this is what we call as unstable region. But a tire may not have a very sharp unstable region. It can be quite flat, okay. In which case, the controllability of this tire or at the limit or the grip as we call it, okay, is better than this, okay. So what are we trying to do when there is a change, this is exactly next half another sort we are going to see. When there is a change in the characteristics of the vehicle, okay, how does the driver perceive, okay. Just wait for some time and we will look at all these things. So in other words, quickly summarizing this, we are looking, going to look at straight ahead, okay, free steering, free steering. I am not giving an input. Fixed steering, I am going to hold. I am going to look at the torque of the field in my hand. Power on and off, okay, and braking. We have introduced braking because a friend here said that, yes, often braking are different, okay. So we have introduced braking. Steering, on-centre steering we already saw, on-centre steering, off-centre steering when the steering is not at the center, how does it behave. Progressive steering, this we called as linearity as a increase. Limit grip steering is what we have been talking about and flick steering. When I just flick the steering, what is the returnability? That is what is given by flick steering. So we give a number of steering input when the steering is straight or when the steering is off-center, away from the center. This is what we are looking at. We are also going to look at the vehicle during lane changing, that is single lane change. So in other words, the vehicle goes straight and then does a single lane change or what is called as double lane change. So you go straight. Due to some reason, you have to take a sudden severe double lane change because of some obstacle here, you have to do a double lane change. So this is what we call as lane changing. Cornering, circuit driving. Circuit driving is very important. There is a circuit and how do you travel in that circuit. Next time when you watch this Formula 1 car racing, you look at how actually drivers drive their vehicle. Very, very important. For example, if you, let us say that there is a sharp corner like this. There are a number of things the driver has to do in order to efficiently, I say efficiently, it means the least time with least risk and so on. They have to take a turn. What is that they have to do? They have to actually start braking. They have to start braking. At what distance are you going to brake? How are they going to hold the pressure of the brake? Then where do they take the turn? What do they do is, what usually it is called as apex hitting. So they would not go like that. So they would go like this. So they would hit the apex and go. In other words, as far as possible, these drivers will not take a large or a small curvature of this or small, large curvature or small radius. They would not take it. As long as far as possible, they would go like this and you would always see that in any of these Formula cars, racing cars, they would go out and come down. You would see, next time when you see, you see that. That is because they want to hit the apex, brake, hit the apex and then power on. As they come out of the corner, there will be power on. So there will be a power off, power on and then get into the straight lane. So it is very important that one understands. This is what we meant by cornering. So what happens when I power on or power off in a turn and what happens if I brake in a turn and I hope there is no rollover propensity. We will talk about rollover in the next class but this is very important. We are not going to talk about ride now. Ride is what is called as a primary, sorry not drive ride, primary ride, mistake this ride and secondary ride and impact ride. These are the three things. That depends upon the frequencies. We will talk about that later. So with this subjective rating, Krohler and his group, they did, the University of Leeds, they did a number of tests. The whole idea is to understand what are the questions that you have to ask the driver. What are the, in other words, what are these or what are the questions which are related to certain metrics of the car and what should be the optimum range of this metrics. So this is sort of an objective of this whole study. So what is more important, what is very important is what are the type of questions that you have to ask. So in order to do that, what they did was a very interesting, very elaborate study done with the help of Meira. So you would see that they changed eight vehicle parameters. They changed front tires, rear tires, front damping, rear damping, front roll stiffness, rear roll stiffness, yaw inertia and bump steer, all these things they changed in the vehicle. So they get different, 16 configurations, eight vehicle parameters they changed it and they got 16 configurations. In other words, they had 16 vehicles with various parameters which are, these are the parameters that they changed. Then they did a test, what is called a step steer test. They, it is a J turn test. They give a steering, hold the steering. Then they did an impulse test and then a steering pad. They went around and so on. So ultimately they wanted to know whether it is possible to relate the subjective question. For example, if there is a question like, ease with which line is held in smooth road cornering, if this is a question. They wanted to know whether this can be related to metrics like lateral acceleration gain at 0.4 hertz, yaw rate gain at 0.4 hertz and yaw rate phase, sorry this spelling mistake again at 0.4 hertz. So in other words, they wanted to relate the metric which is a vehicle characteristics with a question answer. Is that clear? Any questions? Now the first thing you may ask is, what happened? We have left that memory model in the air. What is the subjective, objective evaluation of memory model? You know, where do we stand? Very important question. This is the first question that was answered. Why is memory model important? Because there are only 4 parameters. You see that in this study the parameters increase. 4 parameters are easy to study. So what happens? Is that subjective evaluation correlate well with this 4 metrics? That is the first question. We will look at... Yes, there is a whole set of statistical techniques that they had used. What is called as regression analysis and so on. We are not going into the details of it. I have given you the reference. Look at the reference very nicely written. They call this as ridge regression. So you can look at the reference, how they came up with. Ultimately, did they come up with this and what is the driver? See, one of the major problems here is that they had a number of drivers. Remember, right, 7 drivers. So the drivers had to agree. There was a substantial difference between the drivers, their inputs, because it is subjective rating. The drivers, you know, that is why we have 7 drivers and if the group is not well behaved then there will be a difference between drivers themselves. One guy would say that, ease with which line is held in a road cornering. This is again in a scale of say 1 to 7. He may give a rating of 3. Another can give a rating of 5 and the average may be 4, but the range may be very large and so on. So there has to be a number of statistical measures that has to be introduced given in the thesis. In the objective evaluation, we are doing away with all that. We are replacing them with proper parameters. Yeah, exactly. That is what I am going to see now. But does it have, see, subjective evaluation is, as I said, is the ultimate because whatever be the objective numbers, okay, you should feel that the car is good. That is what we call subjective evaluation. So in objective evaluation, we had 4 nice metrics. Do they really correlate with the rating by a driver, okay. That is what we are looking at. For example, we said that the memorial rhombus is bigger, better. Is it really better? Can I get some cars and drive it with various memorial metrics, various memorial rhombus and say what you are doing, that is what is done here. So I have now 16 cars. What memorial, for example, did was to take 20 Japanese cars and showed that these 20 Japanese cars had really a good correlation. The handling of these 20 cars had a good correlation with those 4 metrics. This is what he said. But this study here again wants to confirm whether that really works, right. So that is a very interesting. That is the interesting part of the study. Do you understand? Any questions? Yes. Exactly. So is that true? That is what I am telling. Just wait for some time, okay. Then I will take the questions. So you have a steering pad in which you give a constant steering and go in a circle. Circle, okay. Just go like that. There is a steering pad where there is a circular path which you follow. So these are the things we had already seen that steady state turning, power on, power off, sudden braking, transient cornering. These are the subjective questions were based on these things. We have seen this list already. Now comes the interesting part. The first thing he did was to check whether this Mimuro model, which is Mimuro rhombus is good to give us a clue about driving. So remember that there were cars tested by Mimuro and that is there in that red, you know, the red line indicates the range. In other words, between the two red, you know, blocks or red lines. Say for example, all the Japanese cars which was tested by Mimuro were between those two lines. You know, this is the least and that is the biggest, okay. So all these Japanese cars were between those two red boundaries, right. And when Chen who is, who did his PhD in this group and Ash, when they got these cars tested for the Mimuro rhombus, their Mimuro rhombus which is depicted in that blue were between this boundary and this boundary. The very first thing that you see here is that the Japanese car had more understeer characteristics. So when I go to the right, that side, more understeer characteristics when compared to what was tested by the Leeds group which had more oversteer characteristics. See the complete difference, okay. Then the next question you would ask is, see these cars were, you know, an experimental car. These guys were doing their PhD. So they had experimental cars, okay. So their experimental cars were oversteer, okay. The Japanese cars you say are understeered cars, okay. What about European cars for example, okay? How much are they understeer or oversteer? Where do the actual European cars fall in this Mimuro model, okay. In other words practically where do they stand. Interesting, they did that. So this is where, okay, the two cars fall between what is being done by Chen in the European cars and before that we will let us compare that. So this is where, this is what is the difference between the European cars and the Japanese cars, okay. The range of the European cars were much less, okay, what has been tested than the Japanese cars. In other words what it simply means is that what the experiment that they did, the Chen and as their experimental car, even when compared to the European cars had much more oversteer characteristics. No, no, no, no. See this is between the Japanese car and their car, okay. They had oversteer and Japanese cars had understeer characteristics. The European cars do not have that kind of understeer characteristics like the Japanese cars which were tested, okay. But they still do not have, sort of it is more towards the, towards the neutral state. They do not have as much oversteer characteristics as was tested by this group, okay. So clearly oversteer characteristics of the cars tested were much more, much more for this study, okay. Now, so they ask these questions, what are the questions, which, for which there was a correlation, okay. Do you understand these graphs? Any questions? That is how they, I mean, that is the design, I, this is not a question of country. There is no generally tested, you know, Japanese cars have that kind of understeer characteristics, okay. That is a philosophy, right. The more, more important question is, which we are going to ask is, what makes them like this? What is, what are the characteristics of the car which makes them, makes them more or ombus like that? Do you understand? So this is what has been observed, observed when we take, I think about 6, 7, the European cars and then they test it, they take 20 Japanese cars and test it, okay. What is the difference between the two? It is this. But that would have been put into them by the manufacturers, right? They should have been some logic. Yes, they are, this is put by the manufacturer. That is why one car is different from the other. So maybe you can say that the understeer characteristics of Japanese car is more, which means that much safer, you know, especially when you drive fast and so on, right. So it is, it is a question of philosophy of, of the car designers, okay. So that is why we are not, what we are going to do, we are going to answer your question by looking at an optimized car, okay. Let me not go that side. Let me not go this side. Please understand that we are still, we are, this is theory. This is objective, okay. The more important question you should be asking is, do people like Japanese cars or do people like European cars, okay? We are live. So still, you know, I do not want to answer that question, okay. But which car is better from a subjective evaluation? That is the, that is a more important question, right. So this is an objective evaluation. But I am not going to answer that question. I am not going to talk for one car or the other, okay. That is not my, my intention. I am saying that ultimately that is, that is what you should be asking, okay. No, that is, that is exactly the point, okay. That is why we have expert drivers for subjective evaluation. It is not a question of who is driving, okay. If you are driving, that when we talk about subjective evaluation, that is why we, I repeatedly said that we are not driving at 40 kilometers per hour in our Chennai roads. You know, this is not, that is not the issue, okay. We are talking about driving at the limits we are talking about. That is why we, I gave all those conditions here. So it is not a question of who is driving, okay. So when we say, when we talk about subjective evaluation, we are talking about expert drivers. We are not talking about novice drivers, okay. Drivers who understand cars who have been doing this for a long time. Absolutely. But it is usually felt that if there is an expert driver who feels that it is good, so that is why you choose an expert driver, okay. Such a fashion that you test a car and he tests a car, it is the same, feel is the same. Of course, you are free to choose whatever car you want. I am not advocating for you to buy this car or that car. You know, you go to showroom, get a car and that is why you have cars for test drive and you buy a car, you know. That is your will and your pleasure and your money. It does not matter, okay. We are talking about a subjective evaluation by an expert driver. Yeah, let us go ahead. Exactly. That is what I am going to come to. So can you wait till I finish? You know, then you ask questions, you know. I understand. I understand there are a lot of questions. You just wait. I am going to answer all your questions, okay. These guys have answered all your questions. So wait, right. So the first thing is whether the drivers felt that this murmur or rhombus as it expands, okay, the car becomes better. There was a small, I would say, error in what they had said. Mimuro in his paper, in fact, very clearly said, I have this, I think I have the paper here, very clearly states that the face angle, phi, right is better, okay. So in fact, you would see that I am just reading the statement, the right axis, phi denotes following controllability. The smaller, that in other words, to the right is better. Smaller is not by magnitude. It is not minus 80 is small than 0. That is fine. But he has very clearly said, the smaller, that means to the right is better, okay. But there is a small confusion in what Chen and Asha said and what has been said in this paper by Mimuro, okay. So first thing is that whether the car is tested and the driver's input, how did it correlate with expanding the murmur or rhombus? That is the first question, right. That is very interesting, okay. Now this is what happened. The red ones are by Mimuro. As you move away like that from the center, okay, they agreed. The blue ones, the blue ones were by the Chen's group, okay. In other words, there was a small difference. There is a difference between what has been said by Chen. One second, just, I will just give you the, I hope you have given you the reference. If you want, you know, you can also look at this reference. Subjective, objective assessment of vehicle handling and performance by Krohla et al. in Seoul, 2000, Fisitta World Automotive Congress. I mean, where also you can see what I am talking to you about, okay. That is the reference, okay. Now you can look at that, you know, this is, so there is a difference. Now why is there difference? In other words, is Mimuro wrong in saying this? That is the question. Is it that when he said that I want steady state gain to increase in order that the car should behave better, was contracted by saying that these, by these group, that it has to be less. Is there a, is there a controversy or is there a difference? No. The most interesting fact that comes out is that the, that is why I had presented sometime back. The type of characteristics of the car tested by this group is more oversteer, okay. But the car tested by these guys I repeatedly said by Japanese is understeer. In other words, in other words, the sentence is that it is not that there is a monotonic increase of these parameters. It simply means that there is a range, okay, an optimum range which would give you the best performance, okay. So, if you want to design a car, it should be an optimist. It is not that I keep on increasing the Mimuro rhombus from this study that is what you, you get, okay. It would become better. It was better for Mimuro basically because that the cars he was testing had that characteristics. So, slightly better it became better. But when you test a car with a completely different characteristics, okay, then these, these, these statements may not make a meaning. So, in other words, there is always a range, a range in which the driver is going to feel good, okay. Or in other words, his subjective evaluation is going to increase, okay. This is a range and maybe it is a range or maybe it is a value where after a certain, certain value, he is going to say it is better, okay, right. So, what this group did was to expand this. Four, they wanted to make it 8 and so on, expanded, okay. So, there were a number of questions. I am not going to go through this now but there are a number of questions which actually correlated with Mimuro metrics, okay. Look at the, look at the paper. We will come back to this but we will. So, what he, what, what these people did was to expand, expand the metrics, okay. Instead of four, they started using, in my opinion, four is very good, the correlation has been good. But if you want a more, a closer, you know, interaction with the subjective rating, then you can expand that metric. So, for example, natural frequency we are steady state gain of your velocity, phase delay at 1 hertz is fine. Then they introduced also your rate gain at 0.7 hertz. Road wheel steer gain, road wheel is steering wheel to road wheel, okay. The road wheel steer gain at 1 hertz. Lateral acceleration gain at 1 hertz. The road wheel steer, steering of the road wheel, okay, the phase of this road wheel steer at 0.4 hertz, here at 0.4 hertz, okay. So, these are the further metrics that was added as far as the frequency response is concerned. So, they expanded the metrics. No more four, four guys who are going to form a rhombus, okay. So, numbers are increasing. They said these are the vehicle parameters which correlate with subjective rating, okay. In other words, when the vehicle is driven straight or when it takes a turn, when you brake during cornering, all those things are affected by these parameters, okay. Apart from that, you know, other further metrics are, we will talk about TB characteristics at 0.2 G, TB characteristics at 0.6 G, peak steer velocity torque at 0.2 G. What is the velocity torque peak steer? TB is what is called as the, you know, defined as a product of the response time of the yaw velocity. It is quite involved, okay. Just read this. Defined as the product of the response time of the yaw velocity to the first peak, to the first peak and the steady state slip angle. It is a product and the steady state slip angle, okay, achieved from the J turn test, okay. Things are becoming complex, right. So, the numbers are increasing, right, okay. So, TB which is a product of these two things, time and the slip angle at 0.2 G. When you take a turn or when you take a J turn, okay and when the acceleration is 0.2 G, what is TB characteristics? Then 0.6 G, which means that you increase the velocity and take a turn so that the lateral acceleration that you achieved is 0.6 G. Peak steering wheel torque, okay, peak yaw rate at 0.2 G, peak roll rate response at 0.2 G, understeer parameter K, understeer gradient, steering torque at 0.3 G, then D slip by D lateral acceleration at 0.4 G, okay. The next question is, oh God, this is becoming, okay, losing track. The next question is, it has not been answered, is why are we looking at these things, okay. Who told you or what is the logic of suddenly coming and telling me that TB characteristics at 0.2 G or yaw, peak yaw rate at 0.2 G has a correlation with vehicle performance? We are saying that these things are important for vehicle performance, okay. Why is this at 0.2 G? Why is it that steering torque at 0.3 G is important? Why is it that you are looking suddenly at road wheel steer gain at 1 hertz, okay? And why is it that we are looking at other things like D slip angle by D, that is the slope of the slip angle to lateral acceleration at 0.4 G, taken at 0.4 G. Why are they important? Not clear. Sir, but the basis for choosing these was from the statistical study, right, they said. Correct. That is all. That is all. It is a question of curve fitting. If, when I have these parameters, when drivers answer a question, okay, number of questions and when they agree, when they, when I look at these two things, okay, looks like these are the parameters which are affecting, okay. This is an open research yet. Why should it be at 0.6 G? May be different, okay. So, this is actually an open, yes, it has, it has a science because you look at some frequency response at these positions and so on. But I would say that still there, it is a, it is an open, open thing. It may be, I mean, there is still a lot of scope to understand this. That is why, that is what makes one car different from the other, okay. So, the interesting point is this. We close this. Ultimately, we come up today's class with this. So, ultimately, we come up with a range of objective metrics for good subjective rating. So, in other words, if you want to design a car and if you want this to be approved by expert drivers, hopefully, the customers will follow the expert drivers, then how do you design the car? That is the question, right. So, I will design a car with a natural frequency of your velocity between 1.7 to 2.1 hertz, okay. Looks like if this is the range, people are happy, right. This is the range. That is what I said. This is a range. But the damping ratio, I mean, damping ratio of your velocity is some, I do not have that figure, but I will get that. So, steady state gain of your velocity point 1 to, is between point 1 to point 2 degrees per second per degree. Face delay of lateral acceleration at 1 hertz is less than minus 75 degrees. Your rate gain at 0.7 hertz is between 0.2 to 0.25 degrees per second per degree. So, you have, I will just leave this. Maybe next class we will again go through this. You see that each one of them has a range greater than or approximate values, okay. So, that is the important of the study that it gave a sort of numbers for designers. What should be your aim? Where should you stand if you want to get a good car whose handling characteristics are good, okay. So, that is the important of the study. We will continue this in the next class. We will look at questions and these things in the next class.