 So, the last class and the class before that we were looking at or we are beginning to look at the force development, right. So, that is what we were looking at. It was very clear from a very simple analysis of our free rolling that force development depends upon the deformations in the tread blocks. When we say tread, it includes belt, it is a very loose term that we are using, okay. So, in other words, all that stiffness in the longitudinal direction put together, we call that as a tread or a tread block here, right. Yes, stiffness of the tread is very, very important. You saw what is a tread, that is a tread. Even if it is continuous, it does not matter. It does not matter because we can assume that as if it consists of a number of what we called as bristles, okay. We represented these treads by means of bristles. It does not matter that even if it is a continuous piece. Incidentally, there were some questions in the last class at the end of the last class. Please note that this is the cut section of a tire, right. It is a cut section of the tire, right. And that section when you expand it, you know, it becomes the tire, right. It is big. One of the questions is, it is big. It looks very different from what we see in the cars. Yes, this is not a passenger car tire. It is a truck tire, right. What we are talking about is a truck tire. Passenger car tires are much smaller. Maybe in the next class, we will get the passenger car radial tires. One of the key things that you would have noticed is what is called as the aspect ratio and we will look at the aspect ratio effect on rolling resistance shortly. So, the aspect ratio you know what we mean by aspect ratio, the height to width of the ratio, right. So, this is typically of the order of 50 percent in the passenger car tires. It can be 45. When you go below, you can also go up to 35, 30, then you call these tires as low aspect ratio tires. These are almost one, almost one. So, these tires aspect ratios are much bigger, that these tires in sense, these truck tire aspect ratios are much bigger. So, that is one of the things that I wanted to say. The other thing, other question that was asked is between this, what we called as a rip tire and the luck tire. What is this front axle, rear axle and so on? I skirted it a bit because I wanted to finish this topic and you may understand it more as we go along, especially when we talk about stability and so on. Since there was a question yesterday, so I would answer that question with, you know, in such a fashion that with your knowledge right now, you will be able to understand the answers. Luck tires or I would say grip tires, you know, they have grip. They have what is called grip and hence they are supposed to be used in the rear. Now, what is grip? Why is that the luck tire has grip? Does it really have a grip and what is, what is it that gives this grip and so on? Now, this is a question which you have to answer very carefully. If you go to most of the websites of the tire manufacturers, they would call this rip tire to be the steer axle tires. They would recommend that they would, that you can use this in steer axle and many of them would recommend that the luck tires are used in the drive axle. This is what they would recommend. Is there a difference between the two? It is the first question. They would also add some things like this. Rip tires have steering stability. They would use the word stability. Steering stability is what they would use. And correspondingly, they would suggest that the luck tires are high grip, wet grip tires. Many of them would say it has a good wet grip. All of them, these statements, all these statements and then there would be tires, which I called as hybrid, which is, which they would call as all wheel tires and so on. All of them should be taken with the carrier, with the rider. Basically the most important thing here is this wet grip with a luck tire. Because of the fact that there are channels, if you look at a, if you look at a luck tire, you would see a number of lateral channels for taking or removing water as it goes along. What is called as hydroplaning is avoided in this kind of luck tire. Hydroplaning, here I am using in the sense that there would be a water film that is formed and the friction coefficient reduces and so on, which we will see again in the next couple of classes. So there are channels for the water to be carried and hence the grip is enhanced by that process and hence you would say wet grip is high. Strictly speaking, dry grip is not necessarily higher than a rip tire. In fact, many experiments show that rip tires have good dry grip. Dry grip in sense that when there is no water, no fine sand and so on, then we say that we have a dry grip and the dry grip is actually better in a rip tire because you have lot more rubber that is sitting on the road. Strictly speaking, that is the case. So now, a lot of research going on and there are tires where you have a rip like tire with a lateral groove in order to carry this water and so on. The grooves are very strategically put. I mean, lot of analysis is done. There is a fluid structure interaction analysis done in order to understand how the water flows. These grooves are put so that the water is carried. Usually, the rip tires, there is nothing, there is no rule. I am talking about the usual practice. Usually, rip tires have lesser what is called as the non skid depth. This is called as NST, non skid depth. Non skid depth is this depth, this depth which is in the groove. This is the non skid depth. Do you understand? That is the non skid depth. So the non skid depth or NSD as it is called is usually for a rip tire lower than that of the luck tire. This is usual practice. In other words, again under most instances, rip tires have much less rubber mass when compared to the luck tire. Basically, because of the fact that this is being used in drive axle, because of the fact that the wear rates are higher, they use it in the and they want it for a higher mileage and they use lot more rubber there. Because of the fact that these tires have less rubber and because of this kind of construction, usually the rip tires have much or less rolling resistance and their noise characteristics are much better, much much better. Rolling resistance is slightly you know here and there. You cannot make a statement out of it. Why I am being very careful in making the statements is because all these statements are maybe in variance when you have different non skid depths. In other words, you have to compare apples and apples. If one tire has worn out more and the other tire has not worn out, then these sentences are not valid and so on. So, you have to be very careful in these sentences and hence all these things you have to understand it with that theoretical background. Clear? This was the noises concerned again. The rip tires have much better noise characteristics when compared to the luck tire. I would not have, that is another course I cannot, I would not be able to go into the noise aspects. But now the let us just understand that the noise levels of a luck tire is much higher than the rip tire. The decibel scale can be as high as 4 to 5 dp. What is noise? What do I mean by noise? Obviously all of us have stood near a truck. Do you hear the noise as it goes? I passed you. Now there are number of sources of noise in a vehicle and one of the major source of noise, especially what is called as pass by noise, as it passes by you will hear that noise is from the tire. We will sort of indicate this towards the end of the course. So, it is the noise generated from the tire is what we are talking about. We will indicate may be a half a class what we mean by noise towards the end of the course, but it is a separate topic by itself. You have a question? Yes, that is exactly what I am saying that what are the tires used in, there are two things here. What we are talking about in those kind of trucks? We have drive axles, we have dummy axle, dummy axle and we have what is called as a steer axle. These are the three different types of axles you have. So, the first rule is that especially in Indian conditions, unfortunately many people mix tires. For example, they would put a nylon, nylon is a loose colloquial term for bias tires. So, they will put a bias tires and they would mix it with what is called as the radial tires. It is a usual practice to put bias tires in the front and the radial tires at the rear. In other words, rip tires are still not very popular in especially in the Indian market. They usually put a bias tire in the front basically because rip tires are extremely sensitive to the camber of the vehicle and as well as the tow. Tow and camber has a large effect on the tire performance and in fact the vehicle parameters as we would call suspension parameters such as tow and camber as well as what is called as the axis of thrust which we will define later. These things have an important effect on the wear of this rip tires and these factors usually make the tire not to wear uniformly. There would be an uneven wear in that tire. Why is it so? Quickly look at. So, you can see the difference between that is the contact pressure distribution when you have a camber. The camber is a very tricky business. The whole it changes the whole contact pressure distribution and hence it changes the wear the way the wear takes place in these in these what are called as the lips. It is a very tricky business because you have two things. One is the camber of the road. Road has its own camber may be a one degree most roads in this country has one degree but it depends upon it varies from country to country and is governed by certain standards and you also have what is called as the vehicle camber. All of you know camber you have studied this in your earlier classes on automotive systems. So, these two combine the road camber and the vehicle camber combine sometimes it neutralizes sometimes it makes it or in sense one side it makes it neutralize other side it makes it more and so on. So, this camber actually affects that is the pressure distribution. Remember last time it was such a you know nice symmetrical pressure distribution that you had and the distribution is completely affected when you have a camber and when you have a toe then the again there are differences and the wear is not uniform in these lips. So, when the wear is not uniform in this lips. So, uniformly it does not wear out what I mean is that this NSDs do not go down in an uniform fashion. Usually what happens is one side say one side this side the wear may be more and this side the wear may be less. So, the tire ultimately assumes a shape something like this. So, that is the groove. So, let us say that it would be I am just exaggerating it. So, it would be something like this. So, there is a one sided wear one sided uneven wear that takes place and so the tires are usually rotated from one wheel to the other. This is what is called as a rotation plan which the vehicle manufacturers or the tire manufacturers more importantly give you. So, that it is it is rotated. Yes, usually the lactire since it is at the at the rear you do not have this problem. So, you have a semi what we call a semi lug tire or a hybrid tire between a lug and a rim. It is something like a semi lug tire a typical example I would not call this, but typical example here is something like this. You have lugs as well as ribs here a semi lug tire is used as a all wheel vehicle even there many times you would see this kind of uneven uneven wear. Due to certain reasons which we would not be able to discuss now the bias tires because of the contact pressure distribution and so on. The bias tires contact pressure distribution is very different I said that we are not going to go into the details of pressure contact pressure distribution in a bias tire, but because of that these tires are not very prone to the vehicle geometry and hence people prefer to put the bias tires in the front and when they put the bias tires in the front their rolling resistance definitely is higher than the radial tires and hence there is a fuel consumption which is which they have to pay the penalty which are they have to pay because of this factor. It is a very tricky business to actually design a ribbed tire with a uniform uniform wear. The course is not on tire design so I would not be able to again sorry that I have to digress how to go here and there, but nevertheless it is a very interesting and a tricky business to design a ribbed tire. People who are interested the best place is to look at the patents the number of patents that have been there are filed in ribbed tire design huge numbers which does all sorts of things in order to mitigate this problem of camber and tow, but anyway camber and tow are reality and they have an effect both of them have an effect and it is very important that the truck owners and the guys who drive the truck they actually look at the what I would say changes in the camber and the tow. Let us come back to this a lot more to that question and anyway quick answer to that question is this and the contact pressure distribution as I said is local bending that is instead of understanding every all these you know niceties inside local bending is better to look at contact pressure distribution from a finite element analysis which you would understand it quite well. Now we have lot more to cover so let us go a bit fast let us understand three things the traction breaking and contouring before we derive simple formula in order to appreciate the physics that we are going to bring in here. One thing is very clear from what we did in the last class or the classes before that there is a difference in velocity difference in velocity what is the difference velocity between the tangential velocity and the ground velocity there is a difference in velocity this is what causes deformation if the ground velocity vx happens to be happens to be the same as that of the tangential velocity say let us say that omega re is equal to v that is how we defined and that both of them are the same remember that we had it at a point then what would happen to these tread elements so let us say just look at this one tread element let us say that it is rotating in such a fashion that there is no difference in the tangential velocity due to rotation omega versus I mean difference when compared to the v of the road there is no difference these tread elements are not going to be subjected to any force they are not going to be subject to any force so it is this difference which is responsible for breaking traction and as well as a similar thing we would extend it for what is called as the lateral force so it is the deformation which is responsible for all these things and we are going to define a quantity called slip after some time so we understand first the physics and then we put this in the difference between the tangential velocity the velocity of the ground so that would give raise to a quantity which we would call as slip so we can define the slip to be let me define it so that is the first quantity that is of interest what we would call as vx you will see why we have put a minus there vx minus omega re that is the difference and that is what causes the what we call as the deformation and then hence the force that can be divided either by or normalized either by vx or by omega re either by vx or omega re right okay so let us look at what this quantity means what happens when omega is equal to 0 what happens when omega is equal to 0 omega is actually the angular velocity okay so what is the condition we are breaking worst case of breaking where I have jammed the brakes and the wheel is no more rotating okay in which case what happens to that slip maximum slip value or a minimum value rather because there is a minus 1 so minus 1 is the I mean what is the minimum value that happens to be minus 1 right so the breaking condition which is worse is has a slip ratio it is slip of minus 1. Please note that when we break okay we are not talking when the vehicle completely comes to a halt when we break okay we are applying the brake jamming the brake there has to be a force generated okay that is why we have f is equal to ma okay that force generated has to stop it and the force is generated by this pulling remember that we are going to explain that again here okay pulling of those bristles okay when they are stuck to the ground right that is what causes the force because I have a wheel okay of a vehicle right let us say that it is going in this direction I am going to stop it so I have to have breaking force how do I create the breaking force okay so I have to that breaking force creation is what we are talking about so we are not talking when the vehicle comes to a halt nothing happens after that so when I jam the brake worst condition my wheels stop rotating does not mean you would have seen severe breaking conditions does not mean that the vehicle immediately comes to a halt right so the worst condition is omega is equal to zero okay in which case this becomes minus one what is the other condition the other side the other side is the vehicle stationary okay and then the wheel just keeps rotating so in other words v is equal to zero vx is equal to zero so in other words that condition is infinity and that is the we are trying to drive the vehicle but not able to drive it because it is it is it is not have it is not able to have what we call as a grip right so these are the two extreme conditions but before we go there let us understand the mechanics first and we will put down we will spend a class to understand these things from a mathematical perspective okay right yeah because this is equal to zero here wheel is wheel is rotating okay so omega is present but there is no grip so the vehicle is not moving you would have seen this many times you know if you have water wheel rotates the vehicle is not moving or in sand okay does not develop enough force for the for the vehicle to move right so that is the condition right okay. Now let us let us now understand this and appreciate that there is a very beautiful micro mechanisms that are happening in the tire okay in fact there is a there is a lot of I would say race between various quantities which decides how the tire is going to behave clear okay now the first thing is pressure we know this I am not going to repeat anything out of this there is a contact pressure okay the vehicle is moving in that direction right and there is a contact pressure no problem. Now let us analyze the braking condition let us analyze the braking condition let us look at that that bristle okay which is called as brush people call this as brush model and so on looks as if they are the comb you know combed brush or the comb so it is called as a brush model right okay there are number of actually number of these guys who are going to come and sit and that is the ground let us just understand one of them and then we will we will extend it or we will put a much larger thing right okay now my velocity is in this direction so I would my ground my ground velocity is in this direction okay now ground velocity is in this direction velocity is in this direction but my acceleration is in this direction right because I want to decelerate so in other words I have to produce a force which is going to act like that yes yeah that is exactly what we said the last class that we can have two views one is the vehicle is moving ground is stationary the ground is moving the opposite direction in vehicle station that is what okay so please remember that I am going to repeat that again and again right okay now just let us concentrate on one bristle I am breaking now what is the condition under this let us call this as the head and that is the tail of the bristle the head has hit the ground okay and there is a contact patch pressure that is built on the head okay this fellow is actually under pressure according to what we have seen now what is the condition the ground okay the ground velocity which is opposite of the vehicle velocity will it be more or less than the wheel tangential velocity it will be more okay so in other words what would happen to this how would this this bristle look like okay if you now look at the relative thing it will be in the that direction okay so let me remove that so it will be in this direction okay the guy is going to the ground is going to run away as if it is going to run away with the head right it is going to go run away with the head the leg of the tail is still sitting on the dial on the wheel rather right okay so what happens now this guy is going to develop tension and is actually going to pull the V and that is what we saw in the law one of the earlier classes and that is going to give rise to the breaking force it is not one actually one bristle just to illustrate it we said this as one but there are a number of guys who are going to participate okay now let us extend it let us extend from one to seven let us make it flat so the ground is moving like that it hits let us say it hits just hits just realize the ground so slowly it will the number of this bristles okay just for illustration we are saying this they are now going to develop these are the ones which are going to give you the breaking force fine but then but then that force there is also a force you know this guy is not going to leave this is going to be a equal and opposite reaction right okay so in other words there is a tangential force which is generated at the interface between this bristle head what we called as bristle head and the ground right so there is a tangential force that is generated that is the opposite reaction if this force over comes the friction force what would happen the guy would slip this is what we called as micro slip I am just repeating it so that things are clear so he would now slip keep on holding now as long as the ground is able to hold him he is going to be stuck to the ground once the friction coefficient multiplied by the normal force that is exceeded by the tangential force the guy is going to slip now okay so at one point of time in this race between the tangential force and the normal force the tangential force wins okay the guy is going to now slip he has got a slip okay so an oxymoron that unless unless there is a deformation unless there is a slip note this a force is not generated okay you would think that when it slips you know there is no force but actually in attire when there is no slip there is no force generated number one okay when the tangential velocity and this are the same they are they are not going to generate the bristles are not going to generate the force this point number one point number two I want to distinguish between when I say this slips I have just defined a slip quantity here so what is this slip and what is this slip so I would call this as a micro slip right there is a micro slip okay this motion is a small motion just this bristle just moves okay moves in such a fashion that it comes under again to an equilibrium okay now this is what we studied before on how mu is developed now yeah so this is what we are talking about here breaking force development rolling resistance is any way present okay even we said even in the free rolling rolling resistance is present and it opposes this motion okay yes okay so that is a good question how do I characterize this friction in other words how do I characterize this friction or you know I know that quantity called mu which is coulomb friction can I just write mu into n okay is the limiting tangential force case is mu a constant that is the question right good question and it is a difficult question because strictly speaking this is not a correct model if you ask any researcher who works on an elastomer friction he would say this is nonsense okay because the friction coefficient depends upon interestingly the contact pressure p is a function of contact pressure p it is a function of that slip velocity v okay because v is proportional to omega of omega of x viscosity keep on building and so on temperature very important and so on but it is a very difficult factor to take into account this these things so what people do is to follow coulomb friction and say that the coulomb friction for example for a truck tire is 0.75 coulomb friction for a motorcycle tire is 1.02 and so on right so we sort of have an approximation which is not necessarily correct but somewhere we have to start working and hence we follow coulomb friction if you go and look at the literature there is a number of papers on how friction is developed and so on yeah I said there itself that we will dump everything we called at that time and I gave one of the previous lectures I said we will call this as friction right so the friction as I said then itself that viscoelasticity plays a great role right so pressure, velocity of slip all those things it gives rise to a number of other phenomena let us let us just move on okay we will look at this thing quickly. So the first thing is that there is summarizes a race between the two so there is a normal pressure okay then there is this Fx which is this guys pulling okay so remember that these are actually different you can view it as a different conditions also of the same bristle time this same bristle goes through that kind of variation in the tangential force clear so if I now plot the tangential force variation okay to be something like that something like that I keep varying I keep increasing I come to a position where the normal forces no more able to sustain this tangential force so at that point things are going to change undergo a micro slip when it undergoes a micro slip okay so again the forces start now dropping because micro slip brings it back the bristles brings it back and so this elongation reduces so as it happens there is a drop in the tangential force and so on okay so that is what happens so that is what happens of course under all these conditions under all these conditions the omega re or in other words the what we plotted as velocity changes okay to similar to what we had done before and what we had seen before there is a compression okay and the compression reduces the radius so all those things happen like what we had seen before so you can interpret that from our previous free rolling condition okay now what happens is exactly similar in the case of acceleration or traction conditions people call this as traction whenever there is an acceleration okay now the scene is just other way okay. You are accelerating that means that you have given the acceleration torque is generated okay the torque moves the revolts or rotates the tyre faster than what the ground is moving and hence this whole thing is the other way okay the bristles are now in this in this direction okay and hence the force that is generated removes the force that is generated remember that is the velocity and I want the traction force to be in this direction now the force that is generated is like that pulls okay and so there will be a traction force both braking and traction force is hence generated by that difference okay been telling that again and again because that is a very important concept right this graph and this are exactly similar only thing that force directions are different again there is a slip there is a micro slip and again there is a variation of velocity and so on right. So that slip gives raise to a very important and interesting phenomena let us now look at I think I have some slides which gives you yes so that is the the longitudinal force development you know in braking that is the longitudinal force development in braking reaches a maximum and then you see that towards the end it comes back yeah because there will be when there is a change it is not it is a velocity is not negative in sense it drops below omega r not you know r so it is not that r becomes negative obviously not from omega r what it starts okay it goes to omega re and then again goes to omega r and there is a variation in the see it is the whole thing is very simple it is what is the basis for this graph what is the basis for this graph the basis for this graph is nothing but no what is the basis for that graph the basis for the graph you remember in one of the earlier classes we said is the compression expansion along the circumferential direction I said I asked you to go and lie down here okay and compression expansion right so that is exactly what is depicted here it is not that it becomes negative okay omega r not becomes omega re then goes below omega r not and then goes again okay now why is this very important this is this is very important from one perspective this is what gives where to attire people keep a lot of in there is a lot of sanctity to this what you call as contact pressure in the tire community okay looking at contact pressure they usually say this is a good contact pressure this is a bad contact pressure and this is this gives you where and this and that and so on but unfortunately they do not really understand or I would not say understand they do not want to go into the details of how actually there is a race and there is this micro slip and there is a micro slip the micro slip is responsible for where right so there is a slip and force multiplied by that displacement that gives the work done by this friction or friction energy which is responsible for where in other words the interesting point I want you to note is that all that that energy friction energy that is what causes friction okay is concentrated at the rear of the contact patch on either side okay is concentrated at the rear of the contact patch because whatever be it this is the reverse direction so do not look at the right hand side look at the left so you would see that whatever be the condition it is that is micro slip that causes or that gives the energy for where and that is responsible for where that is why very important to understand this race and how where is created in a tire clear okay whenever this where rates are are different in different what we call as ribs or different positions then we have uneven way okay these blocked tires this these tires are prone to what is called as wheel and tow where you know wheel and tow where you know heel is or heel and tow where these wheels are these tires are prone to what are called heel and tow where because of this distribution of pressure we do not have a graph here you would see that each block one side of the block has a one wear rate at the other side another and so on so there is an uneven where even in that blocks should give rise to what is called as the heel and tow where okay we will get into the match behind it but before that we will explain what happens or how is force generated in cornering okay how is the lateral force generated in cornering right so let us say that that is the lateral force that is generated that is actually quite interesting and slightly more complex than what we have seen till now after all I need a centripetal force if I take if I corner a vehicle I need a centripetal force okay let us say that is the centripetal force that needs to be generated okay and of course this is the D'Alembert's force which you would call as the centrifugal force okay so the centrifugal force what does it do it tends to push the wheel and the centripetal force would now pull the wheel or oppose that okay M omega squared R versus the F or equal to F right let us see how this force is generated this is you have to be very careful in understanding imagine that there is also rotation okay this wheel is actually rotating so part of the wheel gets stuck here okay so the guy again my good old road is going to hold it here is going to hold it right and the wheel is now pushed out the wheel is now pushed out and it now rotates now rotates so now what happens if you are a material element if you are an element sitting here if you go and sit in a material element and as you go now down you are going to go towards to the I mean towards the right so as you touch the ground okay because these dread guys are going to sit there and they are going to be held by the ground okay you are going to drive a very complex path okay you are going to drive a complex path in other words your head which is in the ground and your leg which is say and the carcass okay will be like this right because this guy has been pushed out so will be like this right in other words this inclination which is going to increase which is going to increase as you travel the contact patch you see travel inside the contact patch gives rise to that pull our good old pull which we saw there and that pull results in what is called as the centripetal force and in that whole process the tire is completely twisted it is just not that it is going to be in one plane that whole process the tire gets twisted right will stop here and continue in the next class.