VeTeR Опубликовано: 3 марта 2018 Share Опубликовано: 3 марта 2018 Обширный доклад от Дейва. http://members.iracing.com/jforum/posts/list/3596425.page https://www.iracing.com/physics-modeling-ntm-v7-info-plus/ Скрытый текст It’s been quite a while since I’ve written about the tire model, and I know some of you are eager to hear more about it. It has gone through several iterations since the new tire model (NTM) was first unveiled and I wrote the first incomprehensible blog about it. I am wrapping up the work on the seventh update to the model (V7). Because I haven’t written about it since about the first or second iteration, I’ll include info about version 6 as well. All the cars in the service are currently running on the V6 tire model. All versions prior to that are not worth remembering (except a modified V5 tread rubber model which is used in the V6 tires), so there will be very little here about those. For those of you who haven’t been here since 2010, you can find some basic information about tire modeling and my approach here: https://www.iracing.com/the-sticking-points-in-modeling-tires/ If you haven’t read that post, it’s worth reading before going on because it covers some of the terminology that I’ll be using later, as well as some basic information about what a tire model is. As those of you who have read that post already know, the tire model I’ve been developing is a physically-based modelas opposed to an empirical model. An empirical model doesn’t try to model exactly what’s going on in a tire, but simply tries to reproduce measured data and predict what will happen in some new situation by assuming it will be similar to what happened in the lab experiment. This involves a mathematical model, which has certain parameters (also known as magic numbers) that control its fit to measured data. In the tire industry, the most well known empirical model is Hans Pacejka’s Magic Formula. Google it! And it is pretty awesome at fitting tire curves measured in laboratories, especially when augmented with a couple decades worth of improvements. But fitting tire curves as measured in a lab turns out not to be very useful when modeling (and therefore having to test) many different tires, and especially tires that are being pushed to the limit, i.e. racing tires. There are many parameters that need to be determined for each type of tire. And many of those parameters don’t have a real physical meaning, so without actually performing a tire test there is no way to predict what they might be, or how they would change with pressure and temperature changes or changes in speed. Further, while empirical models might fit part of a tire curve (usually they are fit to the initial part of the slip curve, before the limit), they tend to not reproduce what’s happening over the limit well. They also don’t do a great job with all the little transient behaviors that real tires exhibit. All of this is okay for most of the tire industry, where the focus is on passenger car and truck tires. Out on the highway, tires don’t undergo massive temperature swings, and they don’t often drive beyond the limit of the slip curve (except in the rain), so an empirical model works fine. A physically-based model, on the other hand, tries to simulate the physics of a tire from first principles. That means it is based on the materials and the structure of the tire, and on the physics that apply to those materials and structures. In order for it to work, it has to model every real-world effect that determines how a tire behaves. Or to make it more do-able, it has to model at least all the effects that make a noticeable difference to that behavior. It becomes important to understand exactly how and why a tire generates the forces that it does. This is a hard problem, but in the end it is possible to predict tire performance knowing only how the tire is constructed. We can learn how a tire is constructed by cutting it up, and we can learn how all its bits behave by sending various bits off to a lab for analysis. Once we know its construction, i.e. what its tire cords are made of and how its cords are layed up, and we know what its carcass and tread rubber are made of, we can predict how it will behave on a racetrack under a great variety of conditions. So what have I been doing on that front through the various versions of the model since the NTM was introduced? The short answer is two things: studying and improving the modeling of carcass constructions, and studying and improving the modeling of rubber. I tend to move back and forth between the two, as they are somewhat independent of each other. Usually when I have improved one, then I want to improve the other. In that spirit, the rest of this tome will go back and forth between carcass information and rubber information. It will keep getting more detailed until you don’t want to read anymore! Or until I’ve reached the limit of what I’m willing to reveal. First I am going to describe how tread rubber is made, and how a real tire is constructed. Once we have a set of numbers that allows us to specify that construction for a particular tire, both rubber and carcass, then we are at the starting point. The goal from there is to calculate the tire forces and all the tire’s behavior using only those numbers (as well as knowing the position, orientation, linear and angular velocities of the wheel rim, and numbers describing the surface characteristics, of course). Let’s start with some background on tire rubber. Tire rubber compounds consist of just a few basic things mixed together: raw rubber, oil, carbon black filler (soot particles), and sulfur. That’s an oversimplification—real rubber also includes stearic acid and zinc oxide (catalysts for curing), some accelerators for the cure process, as well as chemicals to protect the rubber against oxygen and ozone, and to make it tackier, if necessary. We don’t really care about those, but thank goodness someone does. In addition to or instead of carbon black filler, many tires are now made with silica filler, although that is less common in race tires. The first four ingredients listed above are the most important for determining the characteristics of the rubber that we need to know about. The raw rubber is usually SBR (styrene-butadiene rubber, invented during World War II), although natural rubber (or isoprene rubber) is also common. The oil mostly just dilutes the rubber, which makes it softer. I treat the oil simply as a diluent. The oil actually affects the glass transition temperature of the compound. The glass transition temperature (Tg) of a polymer (and rubber is just a polymer) is the temperature at which the polymer starts to change from stiff, plastic behavior to soft, gooey, rubbery behavior. Any effect the oil has on the Tg of the rubber compound is taken into account by the fact that we simply specify the Tg of the whole compound, including rubber, oil, and black. That’s what we get back from lab measurements anyway. Typical Tg’s for tire rubber compounds range from -100 deg F (-75 C) for a snow tire to -60 F (-50 C) for a typical passenger car tire (or a high speed oval tire), up to -30 F (-35 C) for a typical racing slick, even as high as 14 F (-10 C) for an F1 tire. Given that rubbers typically only approach rubber-like behavior at about 90 F (50 C) above the Tg, you can see why F1 uses tire warmers. Without them the tires would start out like plastic water bottles. The carbon black is an essential ingredient to make the rubber a worthwhile tread compound. Raw rubber by itself is too soft and weak to be an effective tread. Carbon black comes in the form of soot particles, and the size of the particles is important. Think of them as little spheres with diameters ranging from 15 nanometers to 250 nanometers. Most tire tread compounds use the smallest particles, up to about 30 nanometers. To the rubber polymer (and the oil), these little particles are very sticky. The polymer really likes to stick to the carbon black surface. A lot of things like to stick to the surface of carbon black, which is why carbon filters are so widely used and why it’s so hard to get the soot off your hands after touching your fireplace. In fact, even the carbon black really likes to stick to the carbon black. This requires careful mixing of the rubber, oil and black to make sure the particles are well dispersed, i.e. not in a bunch of clumps. Once you have black in your rubber compound, it has some startling properties. One, it’s much stronger. Two, it’s much stiffer. And three, it’s much more dynamically complicated, because it’s no longer possible to use standard polymer theories to determine how it behaves. Sulfur is the last ingredient I need to talk about. It is used to crosslink the rubber. This consists of chemically attaching the many polymer strands to each other with sulfur bridges. Sulfur is mixed into the rubber compound along with the black and oil (and those other things we don’t care about), and waits, relatively inert, until the temperature of the rubber is raised in the tire mold after the tire is formed, to about 280 to 300 degrees Fahrenheit (140 – 150 C). At that point, the little rings of 8 sulfur atoms that make up the most stable form of sulfur at room temperature begin to break into little chains of 8 sulfur atoms. And those attach to the carbon-carbon double bonds in the rubber polymer, turning them into single bonds with an attached chain of sulfur. Eventually the other end of the sulfur will attach to some other bit of polymer and a crosslink is formed. On and on this process goes until the mold is cooled. The sulfur crosslinks also break during this curing phase, and then reattach to still more polymer, forming more crosslinks, until eventually there are crosslinks with anywhere from 2 to 8 sulfur atoms. At the end of the day, the only thing of importance is that the sulfur helps give us the number of crosslinks that the compound will have. Twice as much sulfur leads to twice as many crosslinks (roughly), and twice as many crosslinks means the rubber is twice as stiff. Crosslinking the rubber basically changes it from being a (very viscous) liquid into a solid that will hold its shape. A rubber compound is specified with a recipe, which spells out how much of each substance is added to the compound. The raw rubber polymer is always specified as 100 parts by weight, and all the other additives are specified as phr, or parts per hundred rubber by weight. So for example, a compound recipe might be specified as: 100 phr SBR, 30 phr aromatic oil, 70 phr N330 black, 1.8 phr sulfur. And there would be other additives as well, as mentioned earlier, but we’re ignoring those because they won’t greatly affect the rubber’s dynamic behavior. N330 tells what grade of soot we’re using, from which we can determine the size of the particles. You might be asking yourself, “how on earth would you even find out this information?” Well, we can ship a piece of tread rubber off to a lab and get back a report which gives a pretty good guess as to the original rubber recipe. So it is possible to find out this information. Also, there are a number of standard rubber recipes published, although the tire companies guard their recipes more closely than Mrs. Field’s Cookies. While there are typically many different compounds in any given tire, the only ones that really concern us are the tread compound, and the carcass compound, which surrounds the tire cords. I assume that all tires use a similar carcass compound, and only specify the recipe for the tread compound. This is reasonable, because the requirements for the carcass are the same no matter the tire, really. And as far as the carcass itself, the tire cords are far more important than the carcass rubber. So now you have an idea of how we specify the tread rubber, with a standard (but simplified) rubber recipe. Along with phr of rubber, oil, black, and sulfur, we also specify the Tg of the compound, and the mean diameter of the black particles in nanometers. We also specify a cure level from 0.0 to 1.0. Curing less than 100% gives an initially softer rubber that will continue to cure while at temperature on the race track. This is a simple dial that lets us control for different curing times and temperatures, and different amounts of cure accelerators. The tread rubber model gives us most of the slip curve behavior (a bit is due to the carcass), as well as the ultimate grip and the feel over the limit, so obviously it is quite important to get the details right. Well that’s neat, but I’m sure you’re now dying to know how we specify the carcass construction! So let’s talk more about the carcass model. We’ll start with some background on how tires are built. You could not make a decent tire using only rubber. If you’ve ever inflated a bicycle inner tube with a hand pump you’ve seen that long before you get enough pressure in the tube to have it work as a tire, it will balloon out and pop somewhere around the tube. That’s because rubber isn’t really stiff or strong enough to hold its shape against the inflation pressure. So some clever chap came up with the idea of coating some cotton cloth with rubber, wrapping it into a tube, and curing it! The cotton fibers provide the strength to counteract the inflation pressure, and the rubber both holds in the air, and grips the ground. This worked great at alleviating the headaches of John Dunlop’s young son as he rode around on his tricycle, but as this pneumatic tire idea spread to automobiles, some problems arose. First of all, woven cloth has a tendency to chafe and wear through itself when subjected to the many thousands of deflections of a car tire as it rolls across the ground. Thus the cotton fibers break, and the tire pops. Flats were very common in the early days of motoring. Solution? Don’t weave the fibers over and under each other! Just lay a parallel set of fibers in a rubber sheet, then put another layer of parallel fibers in its own rubber sheet and lay that sheet on top of the first, rotated by 90 degrees. Now you have all the strength of woven cloth, but the fibers don’t chafe against each other. They are all separated by a little bit of rubber, which allows the fibers to move slightly relative to each other as the tire rolls, so there is a lot less chafing, and therefore less breaking of the cotton fibers. Second problem is that cotton is not a great tire cord material. It’s not terrible, but the chemists of the twentieth century soon made much better ones. First rayon, then nylon, polyester, fiberglass, steel , and aramid (carbon fiber) cords were developed. Today all these different types of cords (depending on use) are found in cross-ply laminates of the type I described above, with parallel cords held in a rubber layer, and cords in a second layer laid on top at some angle (not necessarily 90 degrees) relative to the first. These cross-ply laminates are the building block of tires. A single layer (ply) is not useful unless it either is wrapped around a tire completely circumferentially (i.e. the cords are parallel to the direction of travel when rolling), or radially (they are perpendicular to the direction of travel). That’s because if you take a single ply sheet of rubber/cord and stretch it along any angle other than parallel to the cords it will change shape in a way that is not helpful in keeping the tire stable when inflated. However, if you take two plies, and they are rotated so that one is plus some angle relative to the tire’s crown (the circumference around the center of the tread), and the other ply is rotated to minus the same angle, then this 2-ply laminate (as the two layers are called) is quite useful. Depending on the angle you choose for the laminate, it can have very different stiffnesses circumferentially and radially. In the early days of making tires, manufacturers tended to stick to 2-ply or 4-ply construction, and the angles were fairly large, plus and minus 35 to 45 degrees (approaching 90 degrees total as in a piece of cloth). These tires are called bias-ply tires, because the cords are laid along a bias angle relative to the crown (English dictionary definition of bias: n. 1. A line going diagonally across the grain of a fabric). If you take a handkerchief and stretch it with the grain of the fibers (pull at the middle of opposite sides of the square cloth) it is pretty stiff—cotton isn’t very stretchy. If you stretch it from opposite corners, though, then you are stretching it on the bias, and it is quite stretchy (using either pair of opposite corners). A 2-ply laminate is just like this, except that it is possible to lay the two plies at an angle other than 90 degrees as in typical cloth. If you could do that with the cotton fibers in a handkerchief you’d be able to make a handkerchief that is more stretchy when you pull one pair of opposite corners, and less stretchy when you pull the other pair of opposite corners. It is important to have a material that is stretchy, because of how tires are built. A great video can be found here, thanks to Michelin: In it, you can see that the tire casing is first wrapped around a drum that is the diameter of the wheel rim the tire will be mounted on. Once enough of the tire’s bits are added on this drum, the center of the drum inflates and pushes the tire out into a rough tire shape. In order to do that, the casing plies (or body plies) must be able to stretch from the rim diameter out to the tire diameter. They can do this only if the casing plies have their cords lying at plus and minus some significantly non-zero angle relative to the tire centerline. As the tire casing is expanded into the tire shape, the cord angles have to get shallower as they go from the bead up to the centerline (unless the cords are perpendicular to the centerline). So, for example, if a 2-ply bias-ply tire were being constructed, and the two plies start at plus and minus 45 degrees to the centerline on the drum, then when expanded the cords at the crown centerline would need to change to plus or minus some smaller angle, like 30 degrees. This is a fun thing to try to visualize—and even more fun is the math involved. So a bias ply tire is stiffer circumferentially than radially. This helps to flatten the tread area a bit relative to the sidewalls, but a bias-ply tire’s cross-section is still usually more rounded than a radial tire’s, and bias-ply tires grow more with pressure, generally. Today bias-ply tires are rare, except for off-road vehicles and motorcycles. And some types of racing, notably dirt. A bias ply has a basic trade-off if you are trying to make wider treads. In order to make the crown ply angles small enough to control the cross-sectional curvature (i.e. to keep the wide tread area flat), you need to use shallower angles overall, which makes the sidewall less stiff, so less able to hold pressure. And, of course, wider tires give better grip, so racers want wide. The radial tire solves this issue, allowing for both a flat tread area and stiff sidewalls that won’t balloon under pressure. It does that by introducing another set of plies, the belt, which is wrapped around the casing plies after the tire is expanded into shape. A little secret: most radial tires don’t actually have purely radial cords, i.e. the body ply angle isn’t 90 degrees from centerline. In order to get enough longitudinal stiffness, the cords are often placed at a slightly smaller angle, say 85 degrees. Radial race tires more often use 65 to 80 degrees. This is key to determining the correct value of the longitudinal stiffness kx. More about kx later. One more ply is often added to a belted tire, the cap or overlay ply. This is usually a single ply with the cords lying parallel to the crown. It is used primarily to keep the belt attached to the tire at high speeds, although it can also add longitudinal stiffness. So finally we are at a point where I can describe how we specify a tire carcass construction. First, there are some basic dimensions that need to be specified: A reference pressure at which these dimensions were measured, the rim width upon which these dimensions were measured, the centerline circumference (with new tread), the section width, tread width, tread radius at the center of the tread, tread radii at the edges of the tread (tread radii are the radii of curvature in cross-section), the percent of tread width that has the center tread radius, and a bead apexpercentage (what percentage of the sidewall length consists of the bead apex, which is a relatively stiff section of the sidewall near the bead that acts for our purposes somewhat like additional rim radius). Second, we have to describe the body (casing), belt, and cap plies. Each of these consists of ply depth plus cord information: cord modulus (how stiff), cord density, the cord loss tangent from a carefully specified dynamic experiment (used for rolling drag and vertical damping), the crown ply angle of the cords in the as-built tire, and the volume fraction of the cords in the ply (the remainder is carcass rubber). Finally we specify the tread depth and the dimensions of tread blocks (if there are any). All of this information can be determined simply by looking, and measuring, and cutting, and by taking a deep dive into the textile world of fibers, yarns and cords, and how twist levels affect cord modulus in a quantitative sense. While that seems daunting, it’s really a fairly small number of parameters, each of which can theoretically be determined. Combined with the rubber recipe for the tread described earlier, we have the complete description of our model tire. Well, one more thing: we need to describe the rim on which it will be mounted. That’s very basic: a rim diameter, rim width, flange height, mass, and material properties—density, heat capacity and thermal conductivity. So how do we go about turning all these measurable numbers into tire forces? Short answer: with mathematics. Lots of it. For a couple reasons, I’m not going to talk too much mathematics here. One, much of it I’m not eager to reveal. It took a long time to derive all of it, and we consider it a key asset of iRacing’s. Two, I’d quickly lose most remaining readers out of the few of you still reading. I will cover some of the theory that underpins the model, but know that I am just scratching the surface. A complete description would be an entire book, mostly filled with equations. Since we’ve been talking carcass construction for quite a while, let’s return to rubber. The paramount thing we’d like to be able to compute for the rubber is what’s called its shear relaxation modulus. This is known as G(t) in the literature—since G is a universal mechanical engineer’s term for a solid’s shear modulus, and it is a function of time. Fortunately for us, the basic experiment we’re conducting over and over again is how the tread rubber shears as it passes through the contact patch. Shearing a rubber block (especially since the amount of shear isn’t too large) doesn’t require us to use the full mathematics of solid mechanics. And that is fortunate, because solid mechanics makes organic chemistry look like kindergarten class. Instead we can use the (simplified) notion that the shear stress exerted on the tread by the road is equal to G times the shear strain. Ok, the undefined terms are piling up. Here’s an illustration: ___________ ____________ |__________| /___________/ (a) rubber block (b) sheared rubber block Worth a thousand words, right? Shear strain is just the distance the bottom (or top) surface moves divided by the thickness of the block, essentially an angle in radians. Shearing a rubber block requires that a shear stress be exerted, which is basically a force parallel to the moving surface, stress being a force per unit area. Another simplifying thing about our experiment is that the shear rate (just the speed at which the shear strain is changing, in radians per second) is pretty much constant. Shear strain is usually represented by the Greek letter gamma, γ, and the shear stress by the Greek letter sigma, σ, both of which are used in the following integral equation giving us the stress as a function of time spent straining the rubber at the constant strain rate dγ/dt: t σ(t) = dγ/dt ʃ G(t-u) du 0 This is a well-known equation from viscoelastic mechanics. It actually contains a lot of information in its relatively simple form. Knowing only G(t) and the strain rate we can determine how much of the exerted force after a time t is due to elastic deformation, and how much has been lost to viscous friction. The sad thing is that reality is nowhere near this simple. The strain rate in reality isn’t actually constant, there is a lot more of importance going on in the contact patch than just shearing the tread. But this at least serves as an example of the usefulness of knowing G(t) for the rubber compound. For polymers, it turns out that there is a lot of existing theory for finding G(t). Except when you add carbon black to it, sadly. G(t) represents how stiff the rubber seems to be at different time scales. At very short times scales (on the order of a picosecond, a trillionth of a second), rubber will seem to be like a hard plastic. At typical temperatures, this holds true up to times as long as nanoseconds (billionths of a second). After a nanosecond, but before 10 microseconds (millionths) has gone by, the rubber softens rapidly. It continues to soften, but more slowly, up to quite long times, as long as several seconds to minutes. At colder temperatures, all these times are lengthened considerably. At hotter temperatures, they are shortened considerably. In the field of polymer mechanics, this is known as time-temperature superposition. All polymers (long chain-like molecules) behave this way. Changing temperature is like speeding up or slowing down time for a polymer. This is simply because at cold temperatures the polymer molecules are moving more slowly. At high temperatures they are moving more quickly. In most research in this area this shifting of times with temperature is described by the Williams-Landel-Ferry transformation, or WLF. The WLF transform is useful for temperatures from a little above Tg up to Tg plus 100C or so. That’s laughably inadequate for the purposes of the temperatures we see in racing tires. However, after quite a bit of work and research I have found a good way to model this shift over a greater range of temperatures, and knowing this transform allows us to collapse this complicated function G(t) into a single curve that can be used at all temperatures, as long as we change the time properly. Another secret: adding carbon black to the rubber throws that out the window—there is no longer a single curve. But after a lot more work and more research, that has also been addressed, although now our function is G(T, t), where T is the temperature and t the time. But let’s call it G(t), for old times’ sake. Lest you think this is all a waste of time, it turns out that G(t) plays the predominant role in how the tire feels over the limit, as well as to grip levels at different temperatures. Some of the improvements in V7 come from that work. Another set of improvements in V7 come from better carcass modeling, but first I’ll cover a bit of V6 carcass information, because that is a building block for V7. Fundamentally, the carcass model gives us the tire’s foundational stiffnesses as a function of load, pressure, temperature and speed, and also determines where and how large our contact patch is. The foundational stiffnesses are basically how strong of a spring the tire appears to be when the contact patch is moved in any direction relative to the wheel rim—longitudinally, laterally, and vertically. Just as suspension springs are labeled in pounds per inch of travel (or Newtons per meter for the metric crowd), so can the contact patch be considered to be mounted on springs that have different stiffnesses in the x (longitudinal), y (lateral), and z (vertical) directions. Those foundational stiffnesses can be measured, but we’ve found that the measured numbers for kx, ky, and kz (as they are referred to) differ quite a lot for different tires, and they differ in how they change with inflation pressure. Kx is usually quite stiff, but doesn’t grow rapidly (or linearly) with pressure. Ky and kz have a more linear response to inflation pressure, but they differ in magnitude as well. Ky is usually the smallest (though not always), and kx is usually the largest. As an example, a typical tire might have a kx of 2,000 pounds per inch, a ky of 800 pounds per inch, and a kz of 1,300 pounds per inch. A hot NASCAR right-side tire can have a kz over 4,500 pounds per inch! They can be pretty stiff. Just in case this still makes sense to you there is actually a fourth stiffness that is important, the torsional stiffness. That is how many inch-pounds of torque per degree of rotation the contact patch exerts as it is rotated relative to the wheel rim (metric is Newton-meters per radian). The torsional stiffness varies strongly with load and pressure changes. We have seen quite a lot of data for kz, a fair amount for ky and kx, and very little (but some) for ktorsion. The data doesn’t generally have any kind of predictability to it. Different tires can have very different numbers, even if they are similar in size and shape. A better understanding of where these stiffnesses come from is required. That was the bulk of the work for the V6 model. We have covered cross-ply laminates and how we describe the tire carcass by specifying those along with some basic tire dimensions. As a point of interest, the carcass code actually proceeds in an analogous way to how the tire is built on the drum in Michelin’s aforementioned video. We construct the body plies, change the body ply cord angles appropriately due to inflating the drum out to the tire shape, then we add the belt, then the cap/overlay ply, and finally the tread rubber. As the plies are added to the carcass (virtually, using C++, not a tire drum), some matrix math along with some formulas that approach solid mechanics a little too closely (and so probably burned off some of my hair) give us a way to describe the various stiffnesses in different directions of the carcass tread belt and the sidewalls. Armed with those stiffnesses, and a bunch more mathematics that I toiled on for a long time we can find our way to the foundational stiffnesses. Those are important because the contact patch doesn’t stay in a fixed spot with respect to the wheel rim when the tire is cornering, accelerating, or braking. Neither does it point in exactly the same direction as the wheel rim. We need to know how the tread belt (and therefore the contact patch) moves and steers relative to the wheel rim to know exactly how the road is moving past the rubber in the contact patch. Other goodies from all this work: we have a better way to determine the contact patch dimensions and pressure in the contact patch, and the stiffnesses all change properly as the tire heats up and the pressure builds. Most of all of that is already in V6, and you’ve been driving on it already, albeit with our older V5 tread rubber model. For V7, in addition to the tread rubber improvements I referred to before, there is also a sophisticated model for handling the dynamics of the carcass motion. Every tire has a critical speed beyond which the tread belt takes up a great wavy shape and much heat is generated. Generally, tire manufacturers want you to stay far below this critical speed, because any prolonged operation near or above it will quickly cause the tire to fail. Only exception here is drag racing. At the end of a Top Fuel run you can see how the rear tires become pentagons due to all the inertia in the tread belt, and how the belt bounces back and forth around the rim between each impact on the ground. Fortunately, the tire only has to do this for a few seconds. In all other forms of racing approaching the critical speed is a no-no. It will be a no-no at iRacing, too, for the same reasons. The belt dynamics equations provide a lot of information about the shape of the tire belt as it is spinning around, and that shape changes as you approach the critical speed. From the shape and the speed of the tire, the rolling drag (the energy dissipated by the tire while it’s rolling) is now also computed from first principles, using nothing but the tread, carcass, and wheel rim descriptions outlined earlier. The vertical damping of the tire is also computed from first principles, and also matches what real world data we have well. In addition, the amount that the tread inertia of the belt “lifts” the tire as speed increases is also calculated. That is important for changes in grip with speed. These effects change with inflation pressure—lowering pressure lowers the critical speed, which affects how the tire is going to behave at a given high speed. A tire may have higher grip in a 40 mph corner when pressure is lowered, but that will make the handling in higher speed corners a bit sketchier. So there will be trade-offs, and those should be similar to trade-offs you’d see at a real race track with real tires. If you’ve made it to here, congratulations, you now know a lot more about the V7 tire model that will be making an appearance on a few cars (we hope) next season (June, that is)! TLDR: With V7 the variation in laptimes from cold to hot temperatures is much better, there is no longer a “Golden Out Lap” syndrome, and the grip loss with temperature and feel over the limit has been improved. 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