Hello everyone. Thank you very much for being here. Uh we're going to start off in just a second while we let everyone come in. In the meantime, can we please have everyone let us know where they're watching from? Uh in the world in the chat, please let us know where are you from. Seeing a little in the UK, Canada, India, Spain, Brazil. That is a fast chat. How you doing today, Harie? Doing fine. What about you? Very well. Very well. Are you tired? No. No. Ready for this? Wales, Portugal, Italy, Sweden, Morocco, Pakistan. Oo, bas country. Niche one. Lot of people here. Egypt. Korea. Mexico. Florida. Florida. Jordan, Germany, Brazil. Very good. Very, very good. A lot. Oh, someone in Brackley. Really close to action, I guess. Good, good, good. We're going to get started really, really soon. 2 a.m. in Hong Kong, Dennis. Well, thank you very much for for being here. I remember someone on LinkedIn. It was their birthday today. Um, can't remember the name. Sorry. If you're here, happy birthday whoever that was. India, India, Singapore, Oxford. Good. Right. Should we make a move, Javier? Yeah, let's do it. So, welcome everybody to Formula 1 tire performance and modeling. Uh, today is going to be a 1hour session. Uh, we'll try to keep it within an hour. We'll have uh time for Yes, lights out and away we go. Very well. Uh, we we will have time for questions at the end. Um, this session we are recording it. Uh, we will um publish certain bits of it online. Uh we're not deciding exactly how we're going to do it, but it will be recorded and if you need a link to re-watch it or whatever, you can ask us uh via email. Hello everyone. Last last few of you entering the the chat here. Uh we're going to we're going to go now. So Formula 1 tire performance and modeling. We're going to start off with uh us. Oops, not this. Sorry. Vial Dynamics. Uh so my name is Alex. Uh a lot of you might already know me from LinkedIn or the social media uh Instagram and so on. I effectively do the managing side of Rachel Dynamics. Uh I do the effectively the the running the this project that we have. We I you know I contact different uh you know I do all sort of contacting people making sure it all runs smoothly organizing these kinds of events going to universities and and so on. Uh here's a picture of me uh back at Red Bull. And to my right, I've got uh Javier, who is the lead instructor of this exciting project and is our our top expert here, which is a picture of him right next to Nico Hulenberg. This was at the Austrian Grumpy, wasn't it, Jav? Yeah, it was. It was. So, yeah. Uh Jav is, you know, he's been doing this for basically 10 years now. Uh he's now a performance engineer for Saur. He went through Red Bull Racing as a vehicle dynamics engineer and has also worked in Formula 2, three, and four as well as lots of automotive companies including Bridgestone and uh some of the teams. So, I'm going to hand it over to Javi. Javi, take it away and let's let's do this. Thank you very much, Alex, for the warm uh introduction. So, I'm very excited to be presenting today one of my favorite topics in vehicle, which are tires. Uh I believe tires are the uh are the middle of everything. That's where the forces and moments um re are are happening to the car. The car is a dynamic dynamic body. It's moving constantly. So all this interaction of forces and moments are happening there in the tire. Um we usually see a lot of talk about the um about complex and sophisticated wings and power units, but uh the tires are no different to that. uh they're really black magic and uh we're trying to lay some foundations on that today and u yeah let's try if we can uh understand a little bit more about this um about this word for everybody. So essentially um the target in posting motor racing is to minimize lap time and this is achieved commonly by uh having the maximum acceleration in the right direction. So this can happen by increasing longitudinal acceleration uh in braking which allows us to break later. If we break later and we're matching corner corner speeds, um we're effectively breaking later. We're carrying more speeds at the end of the straight. Uh we're increasing this lap time delta. Uh we can also use this longitudinal advantage, a longitudinal grip advantage to build up speed faster and to carry more speed during the straits, which is also going to result in um reduced lap times. And of course um if we have a given corner radius and we're able to uh maximize our lateral acceleration there it means as a consequence our um minimum speed or speed negotiating the corner is going to be higher and resulting in overall uh smaller lap time. Um it's not quite straightforward where the direction of this all accelerate of this longitudinal lateral acceleration needs to happen. Sometime it's pure longitudinal, sometime it's pure lateral and sometimes it's a combination of both. And spoiler alert, this happens most of the time because there is no such a situation as I mean there verely is a situation where we have pure longitudinal pure lateral. So we we'll be talking about the combined regime. So um essentially for a car to for a tire to generate forces it needs to slip. It happens longitudinally and it happens laterally as well. Uh there is no force without slipping and there is no slipping without force. So this binomial needs to exist at any given time. Um anytime we are we are accelerating the tires longitudinally, we need to build this slip ratio. So the tire is not going to be uh free rolling. It's not going to be locked. We need to kind of produce a slip this um percentage of slip which we'll be covering in a minute. And laterally um this slip that we measure it's the slip angle which is the it's expressed in degrees and it's the difference between the direction where the tire is heading and the direction where the uh car is actually going. So these lateral longitudinal forces as we said they can be combined as per the friction ellipse which means you can get one token of lateral you can get one token of longitudinal but the time you try to combine both the uh you will not get both one tokens individually so they're going to be reduced as per the ellips is telling us going into a little bit more of detail um we essentially see three forces and moments that cover make it for a six degrees of freedom of the rigid body of the tire. We got FX, we cover that longitudinal force that happens under braking acceleration. We got FY which is the lateral force that keeps our our tire or our car following the path of trajectory in the corner. We got FZE which is the vertical load that is happening to the tire. Uh this is changing constantly. Uh when the car breaks, when the car accelerates, there is a weight transfer. Um there is of course the loads that act in the tire as well. So this is dynamically changing um with an asterisk. We want our fset to be higher there. Um because remember that f_sub_x and fy there are nothing but fz times the friction coefficient. So for a given friction coefficient if we increase fz we'll increase fx and fy. If there there is anyone a little bit more advanced here watching and knows about the tire load sensitivity concept that will be dealt in more detail uh in the course. But going back to our um to our webinar, we also got the MX or the camber moment which is the moment that is trying to put our our our tires more or less stood up. This is a direct consequence of the lateral force that is acting in the longitudinal sorry in the contact patch of the tire. We got the myy which is the torque applied to the tire which is trying to accelerate it or to break it. Um when we have a rolling sorry when we have a free rolling tire this my u moment equals directly um the rolling resistance of the tire. Um and then finally least but not last but not least we got m which is the self-aligning moment. Uh this is the self this is m the moment that is trying to steer back the wheels. So the way that you feel on your on your steering wheel when you are negotiating a corner that is trying to put it back straight. It is one source of driver feedback and returnability but not the only one as we can see also in the course. Um so there are other components associated to that like suspension geometry and uh steering assistant characteristics but it all starts there in the tire. Talking about the lateral forces that the tire generates we can see three different regimes. elastic or linear, transitional and frictional. Um in the elastic sorry in order for the tire to generate the force uh we said that we need to have some degree some certain degree of slip. Um the tire force is going to be to be um to be building up as we um as we slip more and more and more. there will be this elastic or linear um window where this slope is going to be um just straight. Uh this is the operational point for road vehicles because they don't usually operate at the time uh sorry at the at the peak most of the time. This derivative of the force with respect to the sleep angle is called the cornering stiffness. And this is very important. Uh it's a very important concept in vehicle dynamics to understand balance, stability. And for the motorsport lovers, I know what you're going to say. I know you're going to say that um a motorsport tire is usually operating at the at the peak at the peak lateral force. And that's true. But remember that whenever you are straight in a in a straight line and you're trying to negotiate the turning, you're trying to steer your car towards the corner, um you need to build up that force. So that initial turning phase that balance the driver will feel. So that's also happening through that linear rate uh range. So that's also important for for driver confidence. Moving on, we got the transitional window. This is where the beginning of the nonlinear behavior of the tire starts to happen. Um we start to approach slowly um to the to the peak lateral force. Um what the shape of this curve, how this how fast we approach this peak lateral force uh is going to be dependent on tire construction, pressure, load, so many other factors. Um usually tires that are more reactive with higher current stiffness approach this peak. They reach their peak sooner than others than there are not. Finally, we got the Sorry, that was two slides. Finally, we got the frictional area. And here we basically exceeded or max all the force that our tire has to offer us. Um, there is a performant loss. Um, and then there is, you know, we're losing just the lateral force, the potential lateral force that our tire can generate is just losing. We're losing the potential. The tire starts to slide. We start to see degradation, increase in temperature. um we start to see a lot of things that we don't want to see. This is a very common thing when we we are go-karting. We see we can hear our tires squeaking. We think it's a good sign that we're doing it very good. We're good drivers. But what actually is that means is that we're losing we're sliding too much. We are past the peak performance of the tire and the tire is starting to squeak and then we're effectively unable to follow the trajectory and we are being pushed out by the centrifugal force. Um, a question for the crowd. Alex, what do you think? Um, this drop is going to is going to look for a tire. Is it going to be flat? Is it going to be an abrupt uh clear? You mean around here, right? As as we go past the peak, you know, does it does it go down really quickly? Does it sort of go down quite horizontally? Does it plateau? Um, you know, can we get a few people on the chat sort of giving us their thoughts? What do they think it's like and what does it depend on? People say gradual drop, fracture point, plateau, abrupt, sudden drop, depends on the tire, depends on the tire, depends on the temperature. Some people say as some people mention under steer already dealing with more advanced concepts. Love inverse inverse quadratically. There's gan gradual insert an exponential drop. That is a really fast chat. Uh okay, Alex, do you want to give the answer to the crowd? Um yeah, the answer is that effectively it really depends. Um it depends on a lot of factors which Jav will go into in a bit of detail but it can be it can be a lot of things. Generally there is quite a penalty you know in general motorsport and so on there is quite a penalty for um for going past this slip angle um threshold meaning it will drop off quite a bit. Uh but whether that is you know a specific angle or another you know a specific gradient that will depend on a lot of tire parameters uh as the rubber itself and um the temperature and so on. Is that right? That's right Alex. Very good answer. So um shall we move on? Yes go for it. We've covered lateral forces. Let's go through the longitudinal forces. Uh similarly to the generation of lateral forces uh in order in order for longitudinal forces to develop we need the tire to slip a little bit. Um there are many definitions of this slip slip slip ratio as we call it. Uh I'm quoting here the standard SIAA which defines it as it I like to call the amount of slip divided by the free rolling velocity. So how much the tire is really really slipping compared to how fast the tra the really the the tire will be traveling free rolling. So it can be you can see this expressed as a as a number as a ratio 0 to one 0 to 100 it's just the same thing. Um so what happens here so effectively all the ABS all the traction control system what they're trying to do is optimizing the slip ratio that our tire operates at. So we're maximizing the peak longitudinal force generation without going on the cliff without um including in increasing degradation and all the sorts of things that we want to avoid. So moving on sorry we got a little bit of a delay uh we need to understand um what what time models are uh how they are used in the industry. uh you know it's very very common that I hear this question what is a model is it a michelan pilot sport is it a bridges stone p 0 what is a tire model so a term model is nothing but a mathematical representation or set of equations that's trying to capture and describe how a tire performs um they are needed to simulate um if we don't know how the tire is going to if we cannot model the tire we cannot model the full car um in motorsport and in automotive industry in general we need to simulate stuff we need to predict we need to understand how things are going to to to uh to um to perform before we actually get the the real product. So another thing that we need to characterize is the tire. So I'm quoting here in some of the most what I consider the most commonly spread uh type of models in the industry. We got semi-impirical, semi-physical and then physical or FM. Um semi-impirical model uh we got a good example in Pasheska's equations. The equations are published and they describe det forces sorry responses and forces um based on measurements uh during test date based on measurements on test data. Um so empirical means we're trying to fit we're trying to understand how our our how our system works based on experiments that we do but we do not really understand we don't have a physical explanation for all of that. So we add the semi empirical we add semi to that um semi-empirical because some of the coefficient and some of the equations that we use to describe um the tire as per peska they have some physical sense so they are somewhere in between um then we got semifysical which is another step towards going physical towards really understanding the not just putting the tire in uh we'll see about tire testing later putting the tire in a bench measuring stuff okay we understand how this is performing and then we try to put our model to work based on that but really understanding what are the physical properties of the tire. Um there are private companies like um Coin that offers these kind of uh models. Examples can be F tire, CD tire. Um now we are going as we said another step towards physical um we are um discretizing our tire in different sections in different sections or thread blocks. Every block has its own properties. So that's why it's more towards physical. It has um uh lateral stiffness, longitudinal stiffness, radial stiffness, uh damping. So all these properties that really add up to capture the behavior of the tire. Um as we go towards physical, of course, because we're really um not just measuring the macro forces and moments of the tire, but really more understanding what's happening inside, how the tire per se is deforming and all these sorts of things. Um they are more suited for dynamic simulations which are ride and comfort stuff to understanding what's the level of vibration we get in our car to understand what is the right um suspension that we need to run in a truck uh right dump dumping levels all the sort of things um and then we go a step more towards the physical in which um I'm pretty sure you most of you have known of FM stands for finited element element methods uh it basically consists on discretizing the full tire in small small cells like and and a big amount of cells assigning properties to the cells that comes from testing testing um the rubber and then uh it's just a multi-body simulation just this full model capturing the full um the full behavior of the tire uh we will be covering mainly passage magic formula uh because probably the most widely spread in the industry and the golden standard so moving on what is a tire model. So I like this example to make it easy than complex. So I'm sure pretty sure all of us have done this linear regression exercise. We got a scatter uh we got some points and then we just feed our linear regression. And in this exercise what we're doing is um finding the values solving the values of m and n that minimize the error through the full range of um of test data. Um, so this is uh really what we're doing here with our term models. Uh, we got all these points. I don't know if Alex can uh mark them on the screen, but they are all these uh black dots you see here, they are really um they consist on these ones here on the right. No, on the right on the Yeah. So all this black all these the thick the thick traces they are just um experiments that we've captured where we have tested our tire and then all the thin line that is going through all of them is just our tire model uh doing something similar as what we were doing in the left uh linear regression example. So this is it we've understood uh what is a tar model. Uh here we have two coefficients. It just gets a little bit more difficult than that. So we got to from two to more than 100 coefficients but essentially this is the idea. All right. Um the idea is for us to understand what are the value of this coefficients that um for a set of equations that are described in this case by peska uh are going to minimize the error um and represent the tire properly. So once we do it, we will find we will end up with a model with a representation of the tire uh which we can use and run as lap time simulation tools, vehicle simulators, any sort of simulation we want to do really with that. And um yeah, this is really useful uh to understand our tire also when we run it live. Um so we will end up with something like this. we will end up with a black box uh in which we enter with our vertical load. We enter with our slip angle. Remember the lateral slippage of the tire, our slip ratio or the longitudinal slippage, our inclination angle and the pressure uh if our model is capturing the pressure uh effect and then uh from there we are able to predict the three forces and moments that are producing our tire. And then that can can be used in our um in our full vehicle model to understand uh you know to to really represent the behavior of the full car. Um so here I've marked uh inclination angle in blue. Uh I want to ask something to the crowd. Does anybody know what other name does inclination angle go by? Let me see camber toe mostly camber camber camber angle someone said rake angle I think camber kpi uh someone said caster toe defle def deflection angle clink pin inclination most of the people are thinking they're getting it right when we talk about inclination angle we're talking about the camber angle the main difference between both of them is not being pedantic is because the inclination angle is when we refer to the tire as a standalone um body and the canvas when we look at it uh in the full body in sorry in the full car um uh environ in the full car uh frame. So uh a negative camber uh is going to be is usually going to be positive um inclination angle in that case. So we know what is a tire model. Uh now we need to understand how we're going to get the tire data that we need to to fit our model to it. So there are essentially um two types of um tire testing which are indoor and outdoor. Uh the one of the most common indoor flat uh indoor tire testing procedures is the flat track in which the tire is put on on a control in a control environment in a belt. the belt is is is rolling spinning and then we're able to measure the forces and the moments. We have our test program which is also dealt with in in the course and once we collect our tie data we can fit our models understand everything that we need. Um the problem with this uh although repeatability is is quite good because it's a control environment. We can have our good sensors, good everything like pretty expensive equipment uh no wind like consistent grip all it's it's a laboratory right. So uh the main problem being um the sk the the friction is it's a at the end of the day it's a property between two bodies um a piece an asphalt the asphalt and the tire. So here we're faking the asphalt um by using sandpaper. So this is going to usually um result in um unrealistically high levels of grip which will need to be considered and scaled down after. But yeah, as we say, no tire tire testing method is perfect. Uh we got then outdoor testing which is one step towards um um towards um something more realistic but we're losing this repeatability. We got some different examples. We got um a trailer test in which the tire is put in a trailer then that's real asphalt. So we said it's more realistic but again data quality is usually worse and there are inconsistencies in the asphalt and everything. So similarly we got the on car test in which sensor are equipped to the car which is used as a running lab to capture the the information that we need to to fit our models. Then all right we got our tile model. So what is this used for? So we need it we need it to understand our tire characterist characteristics because only then we need we know how much camber we want to run how much toe uh how much sliding is too much uh we know how the balance of the car is going to feel uh we can put it in our driver in the loop simulator the driver can have a go can see if we need to adapt anything uh as well as realtime monitoring because we can capture all the information from the car we measure all the um we can infer the for the lateral and longitudinal forces on the tire and we can measure temperature. We see where we're operating. We see if we are extracting the tire perform the maximum of the tire performance. We see if there is anything we can do if we need to manage more this or that corner. Uh we see where we are operating with a little bit more of detail than just relying on uh driver feedback if that makes sense. So talking about oops talking about um tire performance we've been we've been describing the equations more or less we've talked about the tire testing procedures but we haven't mentioned anything about the the temperature um so interestingly um temperature although it's alite being one of the most important aspect in tire performance in motorsport was not captured in Peska's work um at least not at the time. Um, so what what what is usually done is the tire is warm up to the operating temperature, the most representative temperature and then all the tire uh tie data is collected around that point. But really it doesn't capture how the temperature evolves, how the temperature affects the performance of the tire. So generally when we go in a corner uh we got left and right hand corners um all the time the outside tires they they produce more lateral and longitudinal loads because there is more load there because of what we transfer. So they are more stressed. This is going to influ to cause a split left to right. Um tire energies are the main drivers of um tire temperatures. uh which as we say they are driven by these forces and the sliding velocity components of them. So it can happen and it does happen quite frequently. Then in push labs it's quite tricky to set a um the good to strike the good balance the good compromise between what is the real good the the optimal um temperature to open the laps. So if in particularly in long tracks, uh what happens if if you set your t your your temperatures too hot to start the lap, um you might have a very good first sector, sector one, but then as you progress to the lab, sector two and sector three, temperatures are going to overheat and then you're going to start losing performance and you're going to uh struggle. So how do you set up your your opening the lab temperatures on your tire your surface and carcass temperatures depends really on what is the temperature a bit the best compromise of the full lap that minimizes the overall lap time um lap time u problem. So generally speaking, um straight do cool down the tires and braking builds temperature in the front axle while acceleration does it in the rear. And uh it's not strange to see brake balance as a tool especially in safety car uh situations to alter the temperature split front to rear. Um here we can ask another question to the crowd. Um does anybody remember Hamilton 2021 if my mind is not failing me? Uh it was right in Baku which is this precise event that we will go uh in a couple days. So that's a big coincidence. Um so I'll leave it as a hint. But what happens when um how do you how would you how would you build more temperature on your rear tires if you are in a safety car condition? What would you do with your brake balance and why? Let's see what the what the crowd say. Magic button on. I see someone knows what we're talking about here. Local. Correct. We see break balance. Break bias. It's in that direction. Break bance. Break bias. Yes. Break bias. Precisely. This Jav uh this question actually reminds me a lot of um situ. Oh, I mean we might as well ask ask the ask the crowd. Um, who here has been watching F1 for quite a while? I'm guessing quite a few of you, right? Yeah, a lot of lot of people. Who can tell me what happened to Fernando Alonzo in Monaco 2005? Quite quite a while ago, but it was it was quite related to this as well. Does anyone know what happened to Fernando Alonzo in Monaco 2005? I was three, says Michael. Born in 2005. Uh guess people people are not not that old then. Um no his his front tires were really really uh worn out due to the temperature in Monaco and so on. Not enough straight to cool down the tires. Uh so he ended up having to move the the brake pliers really really rearwards. Uh and he ended up crashing because it was it was it was far too much and it was back in the days where you couldn't. So someone says I was born in 2005 along 2005 race. Um but yeah, effectively he, you know, it the brake pilots was way too far rear was to try and keep the front tires cool. Uh um and it was back in the day where you couldn't uh swap tires. Uh you couldn't, you know, go for a pit stop. It was only for uh for refueling and Yeah. Gosh, everyone's really young here, Harry. Yeah. Yeah. So yeah, essentially I think people, most of them, they got it right. So we want to do is to to move the split towards the rear. We put more energy in the rear tires by we actually put more energy in the more energy more heat in the rear brakes that is going to heat up as well our tires and that's how we um how we play with that as well. Left and right balance as we said is also important as if we got if we're dominated by left hand corners that's going to put more stress and on the right hand on the right on the on the right tire it's going to build up more temperature. So that's going to also uh if the you know every time we jump from left to right uh if we had a very different split left and right in the tire it's going to also change a little bit how the car feels and affect the tire the driver confidence but essentially that's it uh that's it for uh for thermal for today. Um now I pass it to you Alex just a few sections and a bit of a summary. Uh there's a lot of things that we still uh haven't covered here. Uh so for example we haven't properly dive don dive we haven't probably gone into uh peska's equation um we know which are the pretty much the the the gold standard for tire modeling in F1 and motorsport and so on uh haven't looked at how longitudinal and lateral uh grip budgets are assigned uh in sort of combined load cases. So, it's it's fairly simple to analyze how much a tire can give you longitudinally or laterally, but as you start to combine them, such as when you've got a, you know, you're breaking at the same time entering a corner at the same time as you're turning in. Uh, when that happens, you've got a combined load case where uh, you know, it's it's not purely longitudinal or lateral. So, you need to figure out exactly what is the what is this, you know, this budget that you have. Uh, we also need to figure out how variable loads can affect tire performance itself. Um, so for those of you that didn't know, Jav mentioned it very briefly, the FSED of your of your car on your tire will actually affect the grip uh that your tire can generate. It can actually affect um the actual coefficient of friction and that is something that is really important in you know in in in general in building cars and racing them and uh vehicle dynamics and tire performance. Understanding that and how that changing the balance of a car can change the overall grip of the car is extremely important. Uh we also didn't cover um exactly how to set parameters such as camber, toe uh and how these impact vehicle performance. And we also haven't yet learned uh how to properly design a a car according to all of this tire behavior. And that puts us in in a bit of this uh you know this road map that we made for how to become an an F1 engineer starting from an F1 fan. You know this this web this little webinar was just a you know a super condensed down version of you know a few of the parameters and a few of the performance techniques I used in F1. There's so many more things. Uh first thing you would look at is time load sensitivity. Uh really important. We just gone in went into understanding the corner phases is also extremely important. Then as you start to build your knowledge in tires and vehicle dynamics and so on, you start looking at aerodynamics which is a whole new dimension. It's a whole new um you know parameter to account for which varies with velocity and it's never a linear thing and there's a lot of things to take into account. Then you go into load transfer which is one of those things that can completely make or break your car. Is that right, Abby? That's right. Yeah. you can make a car from catastrophically good to to really really bad depending on how you how you set these up. Uh brake phase optimization is also extremely important. Um you know you need to always ensure that your tires are giving the maximum potential that they can possibly give and by that you need to always keep them on the edge uh by optimizing your braking phases under steer over steer angles and your under steer gradient. It's a set of equations and so on. Uh that will determine how much steering input you need and and so on. And it's alo extremely important. Then we get to a really a really cool one which is ride versus arrow. It's a stiffness problem where you have the aero team pulling in one direction to maximize a performance and you've got the ride and the vehicle dynamics performance team pulling in a different direction. And you know these are effectively the better you make one the worse you you you you make the other. And it's, you know, finding this problem, uh, is super interesting as well. And we've got the force-based RO center, which is slightly different to, you know, every book you will ever read will talk about the kinematic roll center. Um, but there's so many more things around it that and there's this other nuance version of it, which is the four-space roll center, which is extremely important for actually understanding how a car properly works. Then we've got the anties, anti- geometries, and performance. extremely important. Uh we've seen quite a lot of it in in F1 testing. I think it was Mercedes a few years ago. Have you that had some extremely cool anti-geeometries experimenting a little bit? Yeah. Yeah. Advanced load transfer strategies again super important stuff. Load transfer is extremely important. Uh then we go into the transients because stuff is never static. Um you know out of an entire lap, how much is the car in sort of steady state conditions? almost you know almost nothing extremely extremely little. So the entire almost the entire set of um of a lap is transient performance which you need to look and then only when you know all of that you know at the end of that is when you can actually design your suspensions. Uh this is something that most people get the other way around and they start designing suspensions from the start and they start putting points here and point there and look at roll center and so on. Uh but it's it's the other way around. You need to understand the rest of vehicle dynamics. You have to understand everything else before you can actually make a car properly work and design accordingly. This is how you go from an F1 fan to being an F1 engineer. And that is exactly why we created the complete guide to vehicle dynamics in F1, which is our 12-hour online seminar, which covers everything that we've just covered here. Uh it covers everything that Jav has learned, condensed down into 12 hours. It contains information on tire performance, later a dynamics, weight transfer, suspension design, performance, and simulation. Everything packed over a weekend. Includes a free one-to-one session with us where you can ask us any sort of question, technical, non-technical, career advice, CVS, anything that you want. Certificate of completion for you to brag on on LinkedIn. And you get to keep all of the slides forever. Uh they're yours yours forever. You download as a PDF and uh they're for you to keep. Uh the next one is happening on September the 27th and 28th via Zoom. Uh it will be an afternoon in Europe session. Uh so it will be the morning of uh the states, the afternoon in Europe, uh a bit later night in the sort of India, Australia part of the world. Uh it condenses Jav's 10 years of experience into just one seminar. Uh so it will be six hours and six hours on each day containing everything that Javier has learned and is suitable for anyone with a high school background in maths and physics. Uh I think you'll agree Jav um effectively as as things become more complicated in vehicle dynamics. It's only the concepts themselves that get more complicated. The maths don't really change that much. Um agreed. Uh but as we said this is entirely you know meant for understanding how you know how a car properly works and this session was only a bit of an introduction and we didn't really dive into any of the formulas or any of the equations that do it. Uh but this this online seminar does uh we dive into all of the equations. We derive a bicycle model. We do a lot of um math and equations. Uh but in itself it's not a math heavy or physics heavy content and anyone with like a high school background should be able to understand it. If not that's on me. Yeah. If not that is on Jav. He does spend a lot of time and we do get really good feedback of Jav spending time on you know on making sure everyone properly understands it. Uh this seminar is also something taught by universities. Uh so there's we've we've got partnerships with certain universities and we teach our seminar as their master's degree vehicle dynamic subject. Some of these cost thousands and thousands of euros and dollars and so on. We only you know we only charge 299 because we want to make this accessible to anywhere in the world uh for you know people to enjoy. You don't need to be super rich to go to a top university and and learn from from these kinds of teach you advanced teachers with so much experience. these two 999 I think it's you'll all agree it's exceptional value uh for the teacher that we get his expertise um you know his time at the racing his time at SA now you know he's man's man's on TV every now and then um we think it's exceptional value especially when you know other universities will charge thousands and thousands for mast's program that will uh contain exactly the same information with the same exact teachers And as a thank you for being here, we're going to offer a discount. Uh so for the first three people to book onto it, uh it's going to be just 249 down from the 299. for the fastest three people to book. We are going to send an email uh in the next sort of 20 minutes or so on with a discount code which will um which will give you a two a discount down to 249 for the first three people to book and then it will be 279 for the fourth person onwards for 48 hours only. Uh, as a word of caution, uh, from our main sale that we do, our main package offering, uh, we only have five seats left and we allowed 20 people, you know, we've allowed an extra 20 slots that we had reserved for this webinar. Uh, we're going to be releasing them now. So, there's only about 25 seats left. Uh, so if you wish to book onto it, uh, for the 27th and 28th of September, uh, this is your opportunity before they sell out. We will send the link via email uh in again about 20 minutes. I think that is everything for for now. Uh thank you very much for being here. We really appreciate it. Uh thank you for investing your time in becoming a bit of a little better engineer. And we are now open for questions. Right. Questions. Question. Questions. drop them in the chats. That's a really fast chat. Okay, this is a bit difficult. So, FYI, there's uh just over 760 people in in the chat right now uh in this uh meeting. So, it's it's going quite quite fast. Uh some of the recurring questions were how do we get the recording? Um we will post it on social media. You can ask us for a link if you send us a DM here on our email or our social media, but you can uh we we will share with you. It's not a problem. Uh a question that I saw earlier, Jav is um what type of tire testing is F1 allowed to do and how much of the data do we get from uh from Pirelli as opposed to their own internal testing? So, Pirelli is currently limiting the amount of hours that uh we can test our tires. I believe at the current year it's eight hours. Um we do receive data from their models but then uh of course every team wants to uh to have trust on the data that uh we receive. So then we always keep up you know we end up testing it even more uh in the procedures that we see fit to capture uh the information that we need for our models which might be different to theirs. So yeah that's essentially it. Um, someone says, "I'm creating my own lap time simulator tool and I want to nail the time modeling aspect. Any advice in particular," says Federico. Um, I will say you you're just fine starting with the equations from Pasheska. I mean, you got you're up for some fun there. There are plenty of them. Plenty of coefficients to to code to make sure it works. Um, I don't think you need more than that really. Just find the equations, put them in the right order, go through Peska's book, and yeah, just integrate it in your model. Okay, next question. [Music] So, um, Raphael will ask, uh, how can I validate my tires cornering stiffness? Can you repeat that question again? How can I validate my tires cornering stiffness? That's uh it's a very difficult question, isn't it? Um there's a lot of testing involved. There's a lot of simulation involved. Um depends really of I mean if you depends what access you have to different sensor what you can measure. Um I mean it really depends on the series depends on the category and the access of the data that you have. I mean it's very different. It changes a lot from one category to another. Um I mean for sure the more axis if you got if you are able to measure the forces directly in your um in your wishbones in your suspension elements you're able to get a better estimation of what the forces are really uh happening in the tire with your with a proper um full car model. Uh but some others you need to just trust your model using other other inputs just accelerations and and and things like that. So depends really on the information you count with. Cool. Uh Ro asked um effectively is Mat Lab and Simulink used for time modeling? Is it other types of software that companies develop internally? Is it commercial software? How is that done? At the end of the day, term modeling is just finding the coefficients that satisfy that the equations are just working to this to the data you've collected. So you can do it in any programming environment. You can do it in Python, can do it in MATLAB, uh whatever you are confident with. Um the process doesn't change. what you're trying to find is the numerical value of 10 and something coefficients or whatever your your model is. So um there was a question by gven on um what advice would you give someone who has no experience in F1 industry who wants to work in performance or track roles? Uh I have 10 years of experience in automotive tier one companies and working as a senior quality engineer. How can I make it into F1? Oh um I mean it's difficult to know without knowing the person, without knowing the background. Uh every everybody's different. I mean um but there is a lot of theoretical knowledge to go through. Uh you can go through books. Uh there are a big list that there is I believe in our website. uh our course summarizes most of this in in as Alex says in a in a very accessible fashion for for everybody. Uh but yeah, I mean I guess there is still like a big theoretical gap to take. Um but I guess nothing prevents you to start the journey today. It's just passion and commitment what you need and uh some people need to do it and some someone needs to do and everybody that does it started at some point you know from the from the bottom. Uh I did it myself, Alex did it himself. uh everybody that works in the in the industry did it himself. So, um that's just it. Grab a book and and start doing that. It's never too late to make a change. It's never too late to to uh pursue your dreams. So, yeah. Cool. Thank you. Um uh another question. We got one for you actually. What advice would you give to people trying to get an indust industrial placement this year, Alex? Okay, so industrial placement that's that's a big one. Um I think well first of all the thing you should do is you should check his LinkedIn because we posted the top five tips uh that we recommend on there uh that no one's ever told you before. Uh so that's a really interesting post which contains some of our best advice. Um everything else I would say is don't ever stay still. Uh don't ever you know in university uh it's probably going to be one of the best years of your life. Don't just lie around and not do anything and you know wait for someone to give you homework. It's all about what you do outside of the classroom. Uh you know if you can do formula student do that but you know some people can't do formula students or there's not a good team or whatever in the university. There's so many things you can be doing. Um, it depends really what you're into. But, you know, let's say someone really uh is really into aerodynamics, right? Let's say you want an aerodynamics placement or internship or graduate program and you can't do formula students for whatever reason. You go out to the world and you show them that you are the best at aerodynamics and you show them what you can do and why they should hire you. I mean, uh, some of you saw probably saw it on LinkedIn. There was a guy from uh Bath University that reverse engineered a an RB16B from wing uh just you know doing his own CFD and his own analysis. That's a brilliant piece of work. Something else you can do is let's you know grab a master's thesis grab a PhD dissertation or something on you know some CFD or something. Learn to do the CFD yourself. Learn what things they've done right, what things they've done wrong. Write a paper yourself. Critique you know make make a critic of it and post it on your LinkedIn. and post it online and post it on GitHub. Uh if you're into vehicle dynamics, make a tire simulator, make a lap time simulator, do all these kinds of projects. Put them on your LinkedIn, put them on on your CV. Uh and that will really make you stand out because there's nothing you know there's nothing more frustrating for someone uh and which is something that a lot of F1 teams get is someone who is an F1 fan is incredibly passionate but they haven't done anything in their entire life to do with you know with the engineering of it. There's so many things out there. Learn programming, learn vehicle dynamics, learn aerodynamic, learn CFD, finite element models. There's so many things you can be doing. It's all about showing that you are the best possible candidate for this. Very good answer, Alex. Thank you very much for that. Uh we got another question here. Uh can you share names of some books that will be helpful for someone who is a beginner? I believe that's already on the website, isn't it, Alex? Yes, it's on our website. If you go to the very very bottom in the footer of the website, there is a section called best resources and books or something like that. Uh there's a it's a whole website on uh the best recommendations we have. Yeah, we got another question from uh from someone actually from Spain. What do you want to focus on when studying the linear range? So the answer to that what you're trying to focus there is essentially the current stiffness which is the um the slope of the force um how rapidly forces are generating for a given lateral force. how much slip angle you're going to have which is going to dictate your balance. It is your split front to rear uh which matters alongside any other many other parameters such as a weight distribution um and so on. But essentially what we're after here is uh corning stiffness. That's the number one thing. [Music] Uh we got another question people asking about the content of uh the 12-hour course. Um, I believe the full description of that should be in the website, right, Alex? Yes, it's all Yeah, if you got any specific questions about it, you can ask us here. Uh, but yeah, the content it's it's all on the website. Uh, we cover Yeah. what we what we what we cover really. All right. So, it becomes really impossible to answer uh all of the questions. Uh, some of them will take ages to really answer. Um there will be great um great questions for the uh for the extended seminar. Um let's see if we can find something we can uh can I apply this to Vasai or is it different there? I don't see why any reason a tire uh an F1 tire is different to a road car tire to a Basai or Formula Sai Formula Student. Um I mean it's just the same physics and equations, same principles. A tire deforms, produces forces. Um it's just yeah maybe the performance is a bit different but a little bit more oriented towards the category where uh we're talking about but uh yeah I don't see any any big um for sure there are some concerns some things that will change for sure in VA temperature is not going to be one of your main uh your main things you want maybe to keep your tire much more um to your camera much more controlled because there will be a lot of wheel travel and everything but at the time of tire model at the time when you need to model your tires don't I think it's going to be uh big difference. Um can you suggest a book for tire study? Yes. Um tire veganomics by Hans Sebastian Peska who is the um the man behind all these messy equations. What is the Bible for veganomics? Uh I believe I need to quote Milikin as everybody does. Um yeah. What is the purpose of anti-dive and anti-quat suspension? Not really related to the topic but thought I can give my insight here to this very one very fast one question. Um so essentially what we're doing with anti-dive and anti-quat is making sure that part of this forcing and acceleration forces that you know some of them will travel will they will have a load path. They will go from the tire then to the elastic elements through the links you know they will be decomposed. So we're trying to redirect as much as we can of them through the suspension links and not through the elastic elements. So what we're trying to do there is um just to minimize this uh diving and squatting movement of the car by effectively uh directing the the forces that we see in in this um dynamic events. Cool. Um next seminar is probably happening. Uh, we haven't put a date yet, but we will, right, Alex? Yes, it will probably Yeah, we need to look into it. Um, yeah, we will announce it on our LinkedIn social media. Uh, also be sure to sign up to our mailing mailing list. So, if you go on the website, there's a section called register your interest. Uh, if you're not available for this seminar, you can come to some of the future ones. We will send you an email about it. Uh, final things to mention and I think we can call it a day here. Have you? Um, as we said, uh, you will receive an email in like 5 minutes from us, uh, with some discount codes. Uh, additionally, if you would like some one-to-one sort of sessions with us for CV, uh, reviews or career advice or practice interviews, uh, we've got a huge bank of F1 questions that we've collected over the years from us and our friends. Same for a big bank of CVs that have made it into F1 from us and our friends. Uh, so we can help you out with that. again on our website. It's under individual consultations. Any final things from you, Jav? I think I'm good. Cool. Well, thank you very much for coming everyone. Uh we're sorry we couldn't answer every question. We would be here for hours. Uh the biggest number I saw was 980 people. Uh which is really good cuz the limit was a thousand. It wouldn't have let us get any more people in. Uh so that was really good. Thank you very much for being here. Thank you for investing a bit of time in your own future and your own engineering. and let's unleash performance together and turn people from F1 fans to F1 engineers. Thank you very much.