 Now, let us quickly review what we were doing in the last class, put them the whole thing in proper perspective and then we will go to the next topic on subjective and objective evaluation. Essentially what we did was initially to look at understeer gradient from the point of view of the tires. That is the first thing. In fact, the whole language of understeer gradient was talked in terms of alpha f alpha r and so on and so forth. It is the first thing that we started here. When we expanded the concept of understeer gradient, remember that we were concentrating on the steering input and the corresponding behavior of the tire. In other words, whether I have to give more steering input or less steering input, this is what it came to. We realized that there are number of other factors which are going to play a role when it comes to the steering input. In other words, other factors may make us give more steering input or give less steering input. In other words, there are other factors which are going to cause what we called as understeer or oversteer. The first thing, remember we talked about the load distribution, redistribution during roll. We found that the nonlinearity with respect to FZ of the tire is going to cause a change in the alpha, in other words, the slip angle front and rear and so that roll would essentially cause a change in the understeer, oversteer characteristics of the car. This is the first thing we saw. We saw that with the derivation. The next we saw is with respect to the camber thrust. Remember that we defined camber thrust as the lateral force produced because of the presence of camber of the tire, in other words, the wheel. We saw that the slope of that curve which we curve, the camber force versus camber angle which we called as camber thrust, the slope of that curve that becomes important and that is what we call, if you remember, C gamma F. Camber thrust is basically a force. I should not say that this is the thing, but anyway that is the slope of this curve between the force and the camber. This we saw that that also has an effect. The result that I am very interested to find out what is the camber change due to the mechanism, the suspension mechanism and that is what you are going to do as a big exercise in the next course on vehicle dynamics, laboratory when we use packages like Adams. Then we come to what we called as a roll steer. We said that there is a change as the, again as there is a roll, then there is a change in the angle of this tires and that would again cause a behavior where I may have to give more steering input in order to compensate for that change of this tire angle and that is what we called as roll steer. Remember, we also defined when it is positive and negative and so on. So, essentially what we are looking at is how does the tire take the force, change the delta and correspondingly whether it becomes under steer or roll steer. Then we looked at what is called as the lateral compliance steer and again because the forces do not act exactly the center and may cause a yaw because they may be off center and depending upon whether the yaw center is the front or the rear, the vehicle will turn to the right and the left and so on, all those things we did. Lateral compliance steer is a very important concept from that point of view and it has a, this we distinguish between a front lateral compliance steer and the rear lateral compliance steer and the difference between them would cause the vehicle to under steer or over steer. So, that is one of the things that we introduced. Obviously, we made a comment at the end of the class, we will come back to the comment. Obviously, aligning torque will have an effect. After all, aligning torque is what makes the vehicle go straight and it is going to align the wheel. So, aligning torque, anything which has an effect on the wheel also will have an effect. So, aligning torque has an effect of course on the under steer gradient and so the aligning torque value is given by this where P is a pneumatic trail, L is the wheel base and so on. So, in other words, you have to give more delta. That is why it goes as an under steer because of the aligning torque as it becomes straight. So, I have to give more delta and I have to compensate for it and so that is the value for the aligning torque. Note that both P as well as C alpha f, both of them participate in this particular derivation. Before we close this, one more thing is the steering. There are lot of things that we talk about steering. Unfortunately, again, this course is so cramped that we will not be able to look at steering design and so on. Let us see that. We will do that in the component automotive structure and component analysis. Right now, I just want to state that steering also participates. Obviously, steering participates in under steer characteristics of the tyre. So, in the words, that being the input, steering has its own role to play. So, the K steering or the under steer gradient due to steering has an important component which is the, which we call as, of course, WF is known, which we call as KSS. So, this KSS, in fact, it is called as, let me check, yeah, this is called as KSS, where we look at the stiffness or the complaints of the steering as well as we look at the radius, wheel radius, we look at the castor angle and the pneumatic trail. So, all these things also participate in what is called as the role of steering on the under steer gradient. So, we will, we are going to talk a lot more about steering in a few minutes and its role on the whole of handling itself. And lastly, the two things which we have left out. One is, there is a load transfer to the front because of acceleration, deceleration and so on. We mentioned that. We have not taken that into account like what we had done for the rear, sorry, rear and front due to roll. Here, this is due to pitch. Unfortunately, the model which we have would not be able to take that into account. So, you have to go to a much more detailed model if you have to look at how load transfer is going to have an effect on this. But when you do testing, this becomes an important quantity. The way a transfer takes place, when you break or decelerate, the transfer takes place and due to which what would be the difference in the force that is developed in the front and rear is going to have an effect. We are not considering this as a formula here, but we will consider that when we look at the subjective and objective rating. And lastly, the tractive force, you know, the other one is the tractive force. Tractive force has an effect. I leave this derivation for you to look at in Gillespie. Whole of these things as I told in the last class, the reference is Gillespie. So, here you would see a very interesting thing. The FXF and front and the rear FXR are the forces that act in the front and the rear. So, if this is the rear tire and this is the, say for example, this is the front tire, then those are the FXF and FXR that act. Say for example, if there is a, if it is a traction and if it is a front wheel drive, then FXF is what you will get and you will, if it is just a front wheel drive, you would not get FXR whenever you are accelerating. Now, look at this. What happens? So, even for you know, a neutral steer with the rest of it or not there, in other words, the first geometric term is affected by the traction. The very first term is affected by the traction. So, what happens? Higher the term, higher this is, lower is delta and hence there is a tendency to austere or understeer. Yes, because you have to give me, give more delta to it. So, you will, you will understand here in every term here. For example, if you look at this term, there will be a more delta is minus, so it will become an oversteer quantity. So, that will, so delta is less, which means that it is oversteer. So, delta is less here because there is a minus term here, the car tends to oversteer. So, in other words, the front wheel drive has a tendency because of traction to be oversteered, but due to other factors like A and B, the distance between the, between the front axle and the center of gravity location, that being small has a tendency to understeer. So, that is one of the contributions or this is, this term is a contribution for the understeer gradient. So, in other words, what essentially we have done is, we have extended the understeer gradient to include eight different parameters. So, if you look at the understeer gradient of the car, you have to consider all these things. Now, we will move further than this. You can, you can look at the, I do not want to interpret this. You can do that interpretation in each one of these cases. It is quite simple. So, we will go over to how to apply all these things, whatever we have studied in order to look at handling. Is this clear? Any questions? Yes. Numeric trail. Numeric trail, we already saw that. The force, lateral force does not act at the center, acts at the rear. You know, that is the, the moment that is created, that distance at which this acts and gives the aligning torque. The force multiplied by pneumatic trail gives the aligning torque. So, that is what we saw long ago as the pneumatic trail. It is a, yeah, we will, we will talk about steering right now. Okay, there are lot of things which are going in the steering. We will talk a lot more about steering, okay, right now. We saw that already that the force that acts, okay, will have a tendency for the vehicle to yaw. The force that acts at the rear or the front will have a tendency for the vehicle to yaw. Depending upon whether the yaw that is produced due to the lateral compliance, which is in the sense that the force that acts, okay, depending upon whether it helps you, aids you in turning or prevents you from turning easily, okay. So, when I am taking a turn to the right, if my lateral compliance, very simple terms, when I am taking a turn to the right, if my lateral compliance aids me in that further turning, okay, I have a oversteer characteristics. If my, that lateral compliance is going to be making me go in the other direction, then I would have a tendency to understeer, right. So, depending upon, so why is there a difference between front and rear? Because the yaw of center is different, the front and the rear, you know, the way it is going to yaw with respect to the front and rear are different. So, that is why if I use the same notation, positive notation, you would find that there is a positive to front, okay, and a negative to the rear. What is positive to the front? The same force is applied at the rear because the yaw center is now shifted, you will have a tendency to go to the right, okay. So, there is a difference, that is why we have, okay. So, here also the compliance of the steering system comes into picture, okay, that is very important and we are going to see that as well, all right. In fact, I have to spend a lot more time, I do not have that time now. So, I refer to Gilles B, the chapter on steering, but we will move now, we will move away and we will look at subjective and objective evaluation, okay. Let me finish this and then I will take the questions, okay. Now, other number of references, this is a topic which I would say has been very well researched, a lot of work has been done. So, let us look at a few of the work that from where we are going to pick some concepts to understand what is subjective and objective evaluation. Before we go further, these are the references, reference SAE 980226, a group from, you know, by Krohler and others, Professor Krohler and others. So, that is, then I think that is the topic is vehicle handling and assessment using a combined subjective-objective approach. An important, very interesting paper, lot of data available. It has gone into a PhD thesis as well, Correlation of Subjective and Objective Handling of Vehicle Behavior by Ash from Leeds University. This Leeds University group has done lot of work on this with the help of MIRA, Motor Industries Research Association in UK. A very interesting article recently published in a book titled Road and Off-Road Vehicle System Dynamics Handbook. One of the chapters there is Subjective and Objective Evaluation of Car Handling by Jim, G. Jim. That has a lot of information on subjective-objective evaluation. So, basically we have, we are going to follow these people on subjective-objective evaluation, not to say that there are not others, you know, there are a number of references, other references, but which is going to scratch the surface as far as the subjective-objective evaluation is concerned. Huge topic, okay. Let me go back. If you know further things and you have a question. Yes, no, we are, we are, that is a, that is a grip. We are not talking about that. We are only talking about, that is what is called, we will come to that, what is called limit handling, okay. So, we are not talking about that. We are not talking about total grip. This gives us an idea, okay, that in other words, we are, when we talk about this, we assume that we have not reached the limiting grip, okay. So, we are going to talk about limiting grip and at limiting grip, what is the problem, okay. We are going to do that. Still, still, see there are two things. One is stability, okay. Safety is not just stability. The other is the driver's ability to follow a manoeuvre, okay. It is very or follow or follow a path rather, manoeuvre to follow a path. He does not want surprises, okay. This is very important. How much steering I have to give, that field should be clean and clear, okay. So, it is not that we all the time talk only about stability. Handling, as we are going to see now, that is why this is the next topic. Handling is about lot more things than just stability, okay. So, we are going to see the feeling. In other words, what is that you want? You want easy driving. Someone is going to drive for you, fine. That is the best thing that can happen to you. But if you are going to drive, then comfort is very important, okay. Safety is very important, okay. Then limit grip, stability, all those things, okay. So, all these things, no, we are right. I understand your question, okay. We are going to talk about that in a minute. In other words, what you are asking is whether this will steal some of the force for Fy. Of course, it is going to steal, okay. Of course, it is going to steal. This formula does not bring that out. Of course, it is going to steal. In other words, that is what we called that as a friction ellipse. Friction ellipse is going to have an effect. We are going to see that, right. Does that answer your question? So, we are not yet there in that friction ellipse where we are not using this formula. In other words, we are not using this formula in order to analyze friction ellipse. No. I am only talking about how much delta I have to give and so on, right, okay. What is the effect of this friction ellipse? We have to wait, yeah. I am only for the steady state learning case or is it the end result? Yes. That is a good question. You know, we had started on this, okay. Understeer and oversteer, all these things are derived for steady state. So, that is why we introduced what is called as the transient understeer and transient oversteer. This becomes a very important test for subjective evaluation. In fact, this becomes so important that there are power of power on test, okay. That becomes a bread and butter of some of these tire companies, okay. Most instances, in fact, tire companies are at the forefront in order to understand the subjective evaluation basically because they are the people who are going to provide many of the field, which we are talking about, okay. So, there are three things now. I had done that before, but let me repeat this. So, I have a subjective evaluation. What is meant by subjective evaluation? We have expert drivers. Not one may be a number of drivers. There is a jury may be available. So, these subjective means that it is the perception of these drivers, okay. So, they have a questionnaire. In fact, questionnaire design, okay. There are standards now. The questionnaire design is important. So, you can go and ask him, obviously, you are all students, you know. So, you do not care, hey, how was the car? Did it go well? No man. It is a damsquare. You know, this kind of thing would not work, right. I mean, so, you have to have a proper questionnaire and a proper test procedure. So, you have to say that I am doing a steady state cornering on a smooth road, okay. Or you are able to hold the line, okay. This kind of things. In fact, Krohler and others have got into about 39 questions, okay. And then there is a rating may be 1 to, you know, 1 to 10 scale and so on. Some people may differ, some people may agree. You know, like all questions, everyone would not agree, okay. So, we will typically see these questions a bit later, but I am only telling you that there are a number of questions, okay. So, there are tests and there are questions and there are ratings, okay. There are ratings. Ratings may be 1 to 5 scale or 1 to 10 scale and so on. Now, this is subjective. So, subjective evaluation has to be interfaced or correlated with objective evaluation, okay. So, there is a test procedure, of course. And there is an objective. What do we mean by objective evaluation? Remember that we saw one of the models, Memuro model, okay, which many, there are many tests which shows that the Memuro model is good model and it brings out the effectively the handling of the car, the area of that rhombus. Memuro rhombus is good enough to tell us whether the car is good or not. Now, this is, but there have been a lot of tests or a lot in the literature, especially in this group from Leeds itself who says that this is not adequate. This is not adequate, okay. There is a Japanese group which says that this is adequate, some group which says that it is not adequate. In other words, these four parameters which this Memuro model considers may not be adequate representation is one of the things. Yes, to start with this is good, but if you want to go into niceties, this may not be adequate. In other words, this parameters start expanding now, okay. So, you are at gain at some say 0.4 hertz, 0.7 hertz and so on. They become important. So, objective evaluation is many times in the frequency domain, most of the times in frequency domain, one or two in the time domain. Now, that becomes, they are values which can be derived from the measured, from the car, okay, a quantitative value which can be measured that is the objective rating. So, the whole idea in subjective objective evaluation is to look at that correlation. For example, this correlation in these papers is given by a formula, okay. This becomes very important. It is not very easy. It is very easy to say this, but this is not very easy to actually correlate the subjective evaluation. Why is this guy saying that during cornering, the car is not holding out? You know why? You have to know it. So, you have to have an objective evaluation or objective or a reason from what you can measure, the characteristics of the car, okay, from a model. Then, the third step which is important is this objective evaluation is then correlated with the design, with design. Now, what should I change? If your damping is not good, what is having an effect on your damping? Okay. So, what is having an effect? So, that this whole thing is clear. So, you know the words, if a driver, an expert driver comes and says that this car has a problem, what is called balance F A R A or something like that, then why is that happening and how can I correct it? So, that is the complete route, okay. Now, let us look at subjective reading. So, as I told you last time that if you want to buy a car, let us see what all you will do, okay. You know this already, many of them, but it is fun to look at how to evaluate a car. We will come to a very specific manoeuvers later. Let us look at a very broad, you know, perspective of subjective reading. So, we follow Jim in what we are going to see now. We already saw that. Please link what we have done so far to what I am going to present now. Yes. But it is not, your question is well taken. This is not like, look at this carefully. This is not like design. For example, you did a course on finite element analysis or mechanics of materials. So, there for example, in finite element analysis, you are told that calculate the formice stress, okay, or equivalent stress and then compare this with your yield, okay. And then you are told that if it is less than the yield, say maybe yield divided by factor of safety or permissible stress, then it is fine. So, in the words, there you calculated it and you had a fantastic, you know, criteria function which told you that look, compare these two if they are less fine. Here I do not have a criteria function because I have too many parameters. It is not one stress, one formice stress and then done with it. It is not like that. I have so many parameters and I do not know whether it should be less than this value or greater than that value or between this value. I do not know. That is the difficulty of design, okay. That is why we are looking at all these things. So, running straight, what is it that you will look at? We have seen all these things. So, running straight, the first thing you will see is pull. Remember, we did that long ago and we had put the blame on the tire and we said that, okay, the car will drift. There is a, forces are different, corner city, light steer, right. So, the first thing you would do when you take a car is to find out whether, okay, imagine that you are going to buy a car, okay. If you do not have the money, ask your dad. So, you are a mom, okay. Whoever has more money, they can pay. Now, you have this, you go, you see how much it is drifting, okay. This is straight away drift, right. This is what we call as residual pull. Then running straight, this is one of the reasons for it not to go down or not to go to one side. Then there can be other things. This, when you run straight, okay, the tire may not be the reason for it to drift. There may be other reasons where, if I, now, if there is a pull, it may so happen that the vehicle can go like that, what is going straight may go like that and that is drift. But the vehicle can also go like this, okay. It can go straight. Here, what is the difference? Here, it can turn like this. This is the pull. You know, this can be drift of the vehicle, okay, as you go down. It may be due to steering system and so on. Then it can wander. It can wander. What is wander? It can go like that and remember that when we go over a bump or a rough road or whatever it is, okay, there can be, it is possible that the steering is not steady and it can wander or it can wander and be sloppy. All these things may be due to external disturbance like, say, a crosswind flowing and so on. So, in other words, we are expanding the first thing called drift to take into account a motion away from the straight line due to a crosswind, okay, due to road roughness and so on. The lower it is, it is better. So, the first thing you do is to take a car and drive straight. Hey, it is not going straight. I have to keep my steering all that time, okay, engaged so that I do not, I do not get into trouble. That is not a, this is not a good situation, right, okay. So, that is the first thing we have to do. The other one is what is called as torque steer. Oh, steering happens not by only you. Steering happens by so many things, okay. So, what is torque steer? So, most of the cars that you drive, for example, are front wheel driven cars, okay. So, the torque for the wheels are given to the front wheel. Sometimes it may have, why sometimes, you know, due to so many reasons that the left and the right torque may not be the same and there can be a difference because of which there can be a steer, okay. There can be an unbalance in the torque that is given to the front wheel and because of that there can be a steer. So, I will have to do tests to look at whether when I accelerate it is going the other direction, when I decelerate afterwards, whether it is coming back and so on, right. So, what happens during my acceleration decelerate? First I will go straight. I will not even accelerate. I will look at how this vehicle goes. The dancing here and there, that is the first test I will do. Then I will take the car and accelerate, okay. See whether, okay, lose, hold the steering, see whether it is going to one side because of torque steer. It is steering on its own because of this acceleration that I am giving and because of the torque that is available at the wheel, right. When I decelerate is it coming back, okay. In other words, is the car having a path like that. First part is acceleration, second part is deceleration. So this is what is called torque steer, okay. That is the next thing I will check, right or you will check. The other one when you go straight is braking and the performance of the vehicle when you brake. What do I mean by performance of the vehicle when I brake? When I go fast and brake, I would like it not to lose the attitude. In other words, when I go and brake, it should straight be, straight the nose. See one of the major things in the driver's feel subjective is they look at that nose angle and they look at the feel in the steering. See these are very, very important, okay. Though we talk about wander and other things, actually the driver would not allow it to wander. You know, they will keep on correcting the steering, okay. This is I am talking about testing and even when you drive, there can be a wander and what does the driver do? He keeps on adjusting. So he knows the nose of the vehicle, what is its attitude and he keeps on correcting it. The problem is either the tire wear will be high or fatigue of the driver will be high. So he does not want his attitude of the car, okay, the nose angle, does not want it to go up and down. So braking straight is the deviation of the vehicle attitude, whether it is going to turn or it is going to remain straight high. We look at then steerability, okay. There is what we call as, look at that on center feel, okay. What is on center feel, right? We talked about steering. We talked a lot about steering and on center is a very practical approach to the steering performance. As it is written there, it is a feel, a perception about the steering torque and vehicle path, okay. What do we mean by this? What is the, what is responsible for this? You know, let us understand that. So now if I plot, say for example, steering angle versus the torque, steering torque, okay. This friction, a line of warning, whatever we are talking about is evaluating a car, not that you would, you are going to, assuming that you are not going to drive at 30 kilometers per hour in this crowded roads, okay. So do not tell me that why are you doing all these things in here. I am not going to drive beyond 30 kilometers. Subjective evaluation is not there. It is to understand the limit of the car, okay, right. So there are a lot of subtleties, right. Now if you look at the, the torque versus steering angle, the first thing that comes to our mind is that steering having so many moving parts, okay. So before the steering angle changes, I have to overcome those friction, okay. So it does not start here. I cannot plot zero versus thing. So it will start here, okay. After this, there is a compliance of the, we go into the compliance of the steering system, okay. So the steering angle versus steering torque takes that kind of turn and so we have, so this region we have what is called as the steering effort, the steering effort, okay. So I have to overcome friction after which I will then look at how much is the effort that I have to give in order to drive. I can plot another graph which is very important, which is the angle versus, versus the vehicle path, angle versus the vehicle path, okay. How is it going to look like? It is going to look like this. Yeah, any questions? This is the steering, this is the steering, okay. Okay. So you would see, I mean, let us say that it is symmetrical about the center. You would see that, look at this. There is an angle of the steering after which a path change is going to take place. This is very important, okay. This is called as the dead length. This is called as the dead, dead length. Look at the subtlety. This is very important. So this, the friction is very important, okay. Lot of friction and lot of compliance, my driving effort, my steering effort is going to get affected. After all, everything depends upon steering for the subjective ratings. In other words, driver's feel, all depends upon the steering. So this is called as the dead length, okay. So what does it mean? It means that if I, if I now play with my steering within that, within that length, the car's attitude will not change, okay. Why is this important? What should it be? Difficult question to answer but you can look at the plus and the minuses of this. Assume that the dead length is large. What happens? Then I, I turn the vehicle attitude will not change, okay. After sometime, after I turn a bit, okay, then it will start changing. Oh, that is not, that is not good. In the words, the feel is not going to be good, okay. So the larger it is, I am not happy with it. Now, what happens if it is 0? Smaller, bring it to 0, right. Yes, that is correct. So if there are disturbances, small disturbances in the road and it is going to have an effect on my, on my steering, small vibrations due to that, okay, small disturbances on it is going to change my vehicle attitude or vehicle path and hence I have to keep on adjusting it. So this is, this, this is together the perception of the talk to the vehicle path, you know, this is what is called as the on-center feel. The path you want to take, usually the path is measured by the nose angle to your path. Now, how much is the nose angle different from the path you want to take? Deviations. Deviations, okay. That is it. The deviation sense that you want to, you can plot that as an angle of the, you know, nose angle of the. So as I told you, most of these things, when I say that there is a path and deviation from the path, we talk about the nose angle, okay. Even when you look at the understeer or oversteer characteristics of the car, we look at nose angle, okay. Nose angle is simply the attitude of the car, okay. So if the car is going to go, it has to go like that and if the car goes, if this is the car and goes like this, that is the, you know, attitude or the nose angle. Simply the nose of the car, how it is with respect to the path you want to follow. No, no, no. Please note that. No, no, no. We are not talking about oversteer or understeer. No, that is, that is exactly what I am saying. This is the characteristics of the steering, okay. Yes, you can interpret it in that language. That is why we have this guy here, right. So that is why we said that the case steering has an effect, okay, right. That is why we have one effect. So in other words, in a broad sense, steering has an effect on understeer and oversteer, clear, okay. But this dead zone is not understeer characteristics. It is the compliance which affects the understeer characteristics, clear, okay. Sir, so that disturbance in the vehicle, if that disturbance happens when the steering angle is not at the edge like... No, that is that. If it is off, that is what is called as off-center. If it is off-center, okay, and if there are disturbances, you have to control. No doubt about it, okay. But when you are going straight, I do not want the disturbances to be affecting. See, that directly impacts your fatigue, right. Because when you go straight, you keep on turning, you know, fun is lost. That is what I said. It is very difficult to say what should be the value. See, actually if you look at the total steering input, it runs to 300, you know, degrees. It is not that it is 5, 10, 20, 30. So this may be of the order of about 8, 10 or may be much less than that, okay, plus or minus 4, 5, that kind of thing. So it is a very small value. Because you would see how much the angle, actually the steering changes, okay, because when you go straight. So actual steering, you would see, you go and turn, you know, the turning is, the angles are so high, okay. The ratio, for example, between the wheel and this may be in the order of 30s. How is this dead length? How is it dead length realized? That is what I said. That is the steering. It is a part of the steering characteristics, okay. That is a part of the steering character. Compliance is due to so many things in the steering and so on. Yeah. That is exactly what I am saying. So that is related by this one, okay. So there is a difference. There is a subtle difference between this and this. Here we are looking at the change, okay and torque is not produced to change the vehicle angle. In other words, here we are looking at the correspondence between the steering angle and the wheel, okay. That is what we are looking at. Here we are looking at how much the steering angle changes required in order to get the steering torque going, okay. That is what we are talking here. In other words, here this is due to the friction, okay. So that would be the type of, so that is why I distinguished between the two that drew it in such a fashion that this is the angle and that is the, you know, attitude that you look at. Then you have what is called as the steering response and linearity, okay. How linear is the steering with respect to the path that it is going to follow? Is it linear or non-linear? In the sense that if I progressively increase the steering, is it that my, what I want is there is a corresponding radius which is followed, okay, correspondingly for the same velocity. We are not bringing into effect the concept of understeer as we had learnt now, okay. It is a question of as I change the angle, am I into surprises, okay or the change is progressively linear. So that is what we call as the linearity of this one, okay. I left that steering response. One of the other things that apart from this is that we can look at this response in a time domain, okay, in a time domain. In other words, if I now change the steering, okay or the steering angle, now what is the path change and after how long does this path change take place? In other words, if I now plot the time, you know, here I do not have a time. I am now plotting it with respect to time, okay. Time versus angle, steering angle, okay. I give, let us say that it is like that. It takes time for me also to give an input, right. That is what this is. Now, I want to look at after how long does my car start negotiating this maneuver, okay. So it may happen that the car which is going straight will keep going straight for some more time which is that response time after which it will start going, right. So if it goes, this is, this is, how much it goes is what we call a steering gain but this time after which that vehicle realizes that there is a steering input and starts changing the course, okay. That is what we call as steering response. Time, time. This is time. That is the path. No, okay, fine. It does not matter because I am just going straight. That is all. You know, this is only a subjective representation, not a very objective representation, okay. I am going straight, I am changing it. That is all. After how long I change, that is all it is like, right, okay. So that is the steering response. Then we have three things, you know, steering precision, steering angle, steering effort, okay or this thing followed by what is called as returnability. So how do you test all these things, okay? We will look at the three things. It is the name indicates what they are. How do you test all these things? Let us say, let us give you a test. Let us not become too technical. Let us say the returnability. What is returnability? Steering has to come back, okay and so suppose I tell you, you design a test to look at returnability, okay. How, what will you do? If the steering angle is zero, okay, does it go back to the same course? Yes but how will you do a test? Of course we are looking at subjective test. No, no, no, no, no, that is all fine but what is that, see there is a difference between evaluation, okay and a test procedure, okay. So how will you do it? That is what I am asking you. What is the test procedure you think can be done in order that I can test, say for example, returnability. See that is how you look, you conceive a test. So each one of them will have a test, you know. So that is what I said. Subjective evaluation, then there is a test, then there is a feel, then there is a mark, there is a grade, then look at the objective. So what is the test? Simple, I go straight, I flick the steering, okay. This is called flick test, flick the steering, okay. Then how fast the steering comes back? What is my feel that steering comes back? It can also be measured, okay. So these are, so for everything there are tests, right and we will talk more about this, we will complete this, we will talk about a few of the tests at least in the next class.