okay good morning good evening wherever you are in the world uh thank you for being part of this canada kinematic march which will be four sessions each tuesday at 10 a.m colorado time which is noon on the eastern part of the united states i'm going to present the first one which is the vehicle damage aspect that and the performance of the car that i influenced by kinematics the next three session will be presented by ariel avi who is an optimum g engineer he will speak about how to use a kinematic software than the force model and then the optimization because until a few months ago uh optimum kinematics for example i was able to tell you uh what were you camber variation new aqua money roll center movement your motion ratio with uh given points but it didn't tell you where the bigger point had to be that's what we call uh optimization so let's go straight away we are going to speak about uh wheelbases and track um definition uh scrub bridges and mechanical trail and caster and kpi guild so two and three are about uh two of the pickup points uh on the upright the third one being for the towing um we're gonna speak about outboard pickup points that's what it is on the uh on the upright uh the front view virtual swing axle the instant center position and the road center all goes together same thing view from the side side virtual swing axle position of the instant center and pitch center position also um inboard wishbone pick a point so we will go now uh trying to define where you want to have you pick a point on the chassis um then we're going to speak about steering rack inboard and all about holding position which means that inevitably that will influence you bumste and your ackermann um the spring and the n2l bar motion ratio and then we'll speak about integration of the kinematic with the vehicle design and then we will give you some i would say 90 of the passenger car these are decided already first of all because you cannot make cars which are three we three meter wide and because depending if you're in class a class b calm these dimensions are probably probably very much decided but in racing things are a little bit different you have to consider the inertia the circuit you are running over i mean is it fast circuit is a tight circuit um the driver skills the tyre characteristics obviously the rules all the templates and so on uh the weight target because obviously a long car will be heavier than the short car and the down force and the possible rollover and when i say the downforce is important a few years ago in formula one the maximum width of the car was uh 200 millimeters shorter than it was now so the truck was about 200 millimeters shorter from the inria than it is now and guess what they had so much downfalls that the difference in the way transfer was not making a big difference but anyway so um let's speak about that first when you speak about a formula one you need to know that the diffuser is doing 60 of the downfalls and the front wing and the rear wing about 20 percent uh things are going to be even more for the diffuser this year and uh in f1 and in indica at indianapolis you have about 85 percent of the downfalls coming from the underway so that's not negligible so um if you take a formula one the maximum wheelbase oh there is a little yellow line and not in the right position here but um which is uh 3600 millimeter 3.6 meter so the good news is that uh you have a maximum of the downfalls created by the lung and the wing no the negative is that necessary the weight and the your inertia thinks about tight circuit so a lot of your inertia improve the stability but re reduce the response and when you go on the circuit like monaco for example uh it's going to be difficult now the minimum wheelbase for a formula student for example is 1525. so the short wheelbase has an advantage first the weight because the cheapest way to make a light car is to make a small car and then the inertia in formula student circuit do not demand a high stability but they mean they demand a lot of response and the best proof of that is that you have go cart which are way smaller and way lighter and the driver can still maneuver the car in with good confidence so that means that for a formula student um your inertia has to be at the minimum um i do not understand why formulas can team would design a car with a wheelbase longer than 15 28 i'll give you three millimeter more uh just uh for the safety there or just to be sure you are passing the rules uh the technical inspection another thing let me give you a little example here i take a car with mcpherson and i made simply four times three kilo for the call over so spring plus damper and so on and i calculated the inertia versus the center of gravity okay i made my life easier i put the center of gravity in the middle here and i have 31.2 kilometers square of the inertia and we're going to consider the same weight whether you have pushrod or mcpherson and so on so now if you take a double arm look at that what i made is making sure that the front damper are to the rear of the front axle and the rear damper on the front of the reaction and then look at that the inertia is now 20.3 instead of what did we have 31.2 so the difference is 35 less inertia and that's the goal that if you are looking for a formula student you the three things that needs to be uh achieved are the lightest car uh the lowest cg and the minimum your inertia because in formula student you are using mickey mouse circuit there that stability is really an issue you need to enter the corner and the maximum speed is very low compared to many other racing circuits for race car i'm giving you another example this is uh an engine and this is for non-non-suspended mass and look at that i calculated the distance between the center of gravity here and the engine center of gravity the non-suspended mass and the distance between the front suspended mass and the cg one meter and 0.9y because uh the which the weight distribution is slightly more to the rear and look at that i calculate the new inertia of one front suspended mass one rear all four of them so twice 8.4 and twice seven pollen and the inertia of the engine an engine of 50 kilo so four non-suspended mass of 90 load contribute to the uranus of 15 times more than a 50 kilo engine obviously the worst contribute to the real inertia are the wings because they're even further away uh the wheels all right um let's speak about the outboard pickup point which is caster and girl mechanical trailer kpi and girls say square bridges so when you have here uh when you design your pride of course the cast or the mechanical trail or the square bridges have been exaggerated for the sake of the um the visualization normally with that much offset the car would be very difficult to drive um the choice of the thunder pride and kpi cast an angle entrail will influence four important things number one the right eye changing steering and if you have a one or two millimeter of difference could make a serious difference in term of aerodynamic behavior because on race card the the rider is extremely sensitive um and influence the dawn force and the dawn force distribution in the drive then the camber variation in steering then the steering wheel torque and then the cross weight in steering which is very very important this is something that a lot of people are ignoring and i'm already going to give you two pieces of advice you want at most 10 newton meters of torque at the steering wheel at most if you take a passenger car it's rarely uh going over five newton meter and it has power steering so if you come with 20 newton meters of torque and steering wheel mamma mia you're going to have to uh send your driver to the uh gym very often and then you want this kingpin axis to cross the tie roughly at the center uh you're going to tell me yeah but there is no steering torque on the rear yet there is no steering car correct except that the torque that will be created by the fx or the fy multiplied by the offset will put a big load on the tolling so you will need a bigger tube bigger rodent and more bigger tube or stiffer monocoque for the inboard pawn of the tolling so i be careful with that all right so let me give you an example here that's pretty scary when you see the um the uh the camber on the outside wheel there and the question is that is that okay if you have a tire model i would be very surprised that the thai model tell you that the best camber is positive i'm i'm i don't some ties are more some are less sensitive to camber but you really have more grip with positive and the question is that is this uh the reason for that isn't it a part of kinematic or part of compliance okay uh for this big camber so uh i want you to know that uh let's speak about canva variation here if you have a large mechanical trail it's going to be a lot of torque on the steering wheel but you're going to have a lot of camber variation on the other end if you have a small mechanical trail you are not going to have a lot of camber variation but uh you you will be a less talk in the steering wheel well guess what it's possible to have the best of both worlds by having a small mechanical trail and a large caster angle nobody told you that the kingpin axis had to go through the center of the wheel except for phone front-wheel drive when when you steer the wheel in the paddock if you have a bigger angle between the drive shaft and the uh the hub axis you are going to have uh i have it yeah uh you are going to have um an angle and you could hear the uh cv john you know but that's an exception okay this is an example of the vertical load that you have on the uh on the tires and you see that's interesting that when you turn left for example the vertical load increase on the when you turn left yeah the vertical will increase on the inside decrease on the outside and it's interesting that we have a diagonal weight transfer because when you increase the load on the left front sorry left front you increase the load also the right way when you decrease the load on the right front you decrease it on the left rear and it's not negligible because when you look at this we have about 24 70 something like that and if you turn the wheel 95 degrees 90 degree you go from uh let's speak in kilo 247 to 262 not negligible correct and that will influence very much the real magic number um the tltd uh will be different because of that and it's important because if you have weight transfer you're in a corner and if you're in a corner you turn the steering wheel so inevitably that's going to make a difference the other one is the camber variation usually you have more positive variation so you still you start at 2.8 and you have less and less negative so it's a positive one and you have a negative one on the inside wheel we are turning left and here uh negative on the outside wheel and you will notice that there is also a chem variation on the left rear and the right wheel yeah the reason look at the scale here we are speaking about uh uh less than one tenth of a degree and the reason for that is that when you change the oops sorry when you change the vertical load well you have more vertical load on the right wheel less on the left rear well guess what you're going to have tight deflection and a little bit of roll angle and therefore the camber is going to change um now i'm going to give you an example this is a very good idea of what you can do with infrared temperature sensor i'm going to give you a simple example you have a car like this you have the internal temperature of the right front so this tie 105 90 70. what what's the problem you have too much camber correct okay now you go at the apex and the temperature is 120 130 150. so why is the average uh higher deal where you're the braking zone then you you break and you enter the corner so you put more energy in the tire so the problem is this if i have too much um camber and i reduce the the camber the negative camber on the right front i'm gonna solve this problem but i'm gonna make this one even worse or if i put more camber i will help with this one but not in that one well so what's the solution where the solution is to have less static camber and more caster but caster i'm not going to go through all the formula but accounts deeply influenced the camber variation in steering and that's even more true in a very tight corner because guess what on a very tight corner you turn the steering wheel even more and then the right eye variation in steering there could be very different if you have a push road for example which is directly connect to the wishbone or if you have a push rod which is directly connected with the air pry and you have an example here all the straight line are with pickup point on the a-arm on the lower arm and here they are connected with the upright and it's not negligible because when you turn the steering wheel let's say 180 degree you go from 41 to 36 millimeters five millimeter more uh unless sorry so i can tell you in term of aerodynamic that's going to make a huge difference positive negative give me your room up and i will tell you which rider a new tire model and i will tell you which ride that you need to be in which corners okay um then we are going to calculate the focus so we spoke about camber variation vertical load right eye and now we're going to look at the steering talk so i'm going to give you a very simple appreciation you are going to look at the kpi here so the lateral force has a little offset uh compared to the center of the wheel that's going to create an mz mz but you have also the mz from the tire itself then you have to consider the steering arm of the upright and then you have to look at the distance between the axis of the corner steering column and the one of the steering rack so there can be steering talk uh coming from the fy from the fz ah yes a car with modern force will have more steering torque because the vertical load is as an offset compared to the kingpin axis and then you even have the ethics when you break when you accelerate and even the amex which is called the camber torque by some people and then of course the length of the steering arm and the steering rack trail as we call it here so i'm going to give you a simple example so you have an example here where in blue in blue you have the grip versus the slip angle so more and more grip until you go through a maximum and then the grip diminished then you have the one from uh the mechanical tweet so that's the fy multi multiply by mechanical trail and then you have here i don't know sorry the purple one was the fy versus alpha okay that is the mz and as usually the slip angle at which you reach the mz is smaller the sleep angle at which you reach the maximum fy then you have here um the fy versus the the pneumatic trail and that is the fy versus the kinematic trail and that is the total so i made a calculation for you with you i have 1984 newton meter on the outside wheel uh 1178 newton that i multiplied by a trail of uh sorry uh a steering arm of let's say 100 millimeter uh sorry a steering um the pneumatic trail which is ten millimeter here pneumatic trail sorry and then divide by the steering arm on the upright and multiply by what we call here this 40 millimeter there okay steering trail and so i have 9.73 on the inside well i have less grip and i have less mz because the tie is very unloaded so 0.2 instead of nearly 20 so 1 10 you have about one fifth one six of the lateral grip of course the steering rack in the upright have not changed and you have 0.75 so if you do the calculation 973.005 that's 1048 that's already way too much to do it so one solution is you send the you ask schwarzenegger to drive your car or you put power steering and of course power steering is demanding uh power and it's weight and it's it's it creates more complications no on many race car there is so much down force that we voted you cannot turn the steering wheel and power steering is mandatory i would say not by the rules but necessary let's say this way except in indica in the car produce a lot of dawn force within the knife power steering ah note that we have decide um uh the kingpin axis angle the caster trail the trail uh view from the front of the script bridges from the synonym we need to decide on this axis here where are you going to put the top wishbone in the bottom wishbone pickup point okay so we are going to have a packaging challenge here uh because we have to look at the tire the rim the hub the bearing around the hub the brake caliper the brake disc uh maybe some cooling ducts ah it's already pretty uh cramped over there you know you're gonna have to be uh and even worse if you have a outboard electrical motor that's not going to make your life easy but um there is one thing that you have to be very careful and a lot of people don't uh care about that enough that's the distance from the non-suspended mass cg to the kingpin axis why because when you are breaking the non-suspended mass is not zero and when you are breaking the wheel wants to i'm gonna make an image here wants to continue forward or when you accelerate they want to go backward relatively to the chassis and that is going to create an mz that is even bigger for this inertial force on the non-suspended mass then the distance between the center of gravity of the suspended mass and the key keeping access is so you're gonna have to be extremely careful with that you try to reduce the distance between non-suspended mass cg and kingpin axis i received formula student people putting here a big inboard electrical motor and the center of gravity went from roughly the center of the wheel to the outside first test they break boom they put the tolling on the front in buckling if if you don't pick uh take care about that uh initial force from lateral and longitudinal acceleration non-suspended mass will create a huge talk around the kim being axis and therefore huge forces on the tollings so you have to be careful with that okay now um little example sorry bad example here what's the problem here you should use the maximum space that you have in the rim so that pickup point should be there and you would like to put that picker point there and basically the tolling to be nearly perpendicular to longitudinal axis of the car same thing here it's absolutely ridiculous not to use the space in the rim if you multiply if you put that point here you multiply the leverage by five and all things being equal you are going to um uh have five times less steering um you have a less steering talk same thing here you know this thing should be there by the way okay um so uh two basic principles try to always have the longest possible steering arm if you look any good race car they always use the maximum space that they have on in the rim and the upright steering ram will define your steering rack ratio not the other way around so it's only when you have your tire model you know the forces in moment acting on your tire and you have decided the steering arm length that you can decide what's the steering rack radio ratio that what the steering rack that you want to manufacture or buy and also is i have the tolling perpendicular to the longitudinal axis of the car now we're going to speak about front view kinematics okay you have the wheel like this so the distance between the instant center and the contact patch is what we call the front view virtual swing axle and that is the instant center position there that you have to be careful and take into account and that necessary the role center will be here if the suspension is symmetrical so most the biggest influence here is that the camber variation in roll and eve will be influence so obviously if you have a very long virtual swing axle you're going to have minimum camber variation in heave when the car goes up and down but unfortunately you're gonna have a lot of camber variation involved and that's very important i will explain to you why so um uh the instant center will have also an influence of the thai later if if my wheel is here my instant center is there okay and if you put it there you're gonna you're gonna have a lot of scrub and that's gonna be tie away and higher temperature in many uh automotive institute in europe in the united states they ask you to diminish your script of the tie because they hope that you can do 50 000 kilometer with the same tyre in racing that's different we change the tire sometime every 100 kilometer and you want to have temperature at the risk of wear so it's a question but obviously if the instant is very high you're going to have a higher roll center all right so you have camber variation in heave in roll and in steering and you you need to take all of them into a cone so camber variation bomb i'm not going to demonstrate the formula here but the camber variation bomb is an arc tangent of h divided by the lateral virtual axon h being the wheel movement so if you have a suspension like this with the wishbone parallel like this the instant center is at the infinite and therefore whatever wheel movement versus the chassis you will not have any camera variation well we know that as the wheel goes up and down or the chassis goes up and down the convergence will not go to the infinity all the time they could be changes but they will be no instant center it will always be in the infinite if the top and bottom which bond are the same length now so if your goal is to decrease the camber variation burn we need a suspension like that however the camber reaching roll is uh the roll angle multiplied by one minus strike divide twice virtual singapore i'm not going to demonstrate that formula that means what if the car is like this that's the middle of the car and you extend the two-wishbone and they meet right there that means that the instant center is the middle of a car uh same thing symmetrical you're gonna have that the half track is the virtual swing axle so if the half track is equal to virtual axle that parenthesis is one one minus one equal zero and guess what you're going to have uh no can variation in raw is it a good thing well let's discuss that so um if you have a long virtual swing axle this is what's gonna happen you're gonna have a lot of camber variation in raw if you have a very short one you're gonna have a lot of camber-ish in here so you're gonna have to make a compromise okay so the circuit let's think about formula student do you want to win uh the skid pad mainly camber variation roll a little bit in here because of the downfalls you want to win the acceleration you don't care about lateral acceleration you're going to look at mastering your camber variation in acceleration uh it depends on the tie sensitivity because the ideal camber for michela is not the ideal camber for goodyear so you're going to look at the sensitivity of the lateral grip and the longitudinal reverse of the camber um you're going to have to look at the driving style yeah because if the guy is very sharp i had an example let's see bring a guy brake leg and turn right so boom big camera variation um braking boom camber ratio uh in roll and steering and the other guy was kind of trail braking and mixing a little bit the roll the steering and and the pitch that could make a difference also and then the ambient condition we are speaking about the track temperature and the tire temperature and what is it wet or dry condition so let me give you here is a very important point here i'm gonna go to monza and i'm going to change the lateral grip here i'm going to reduce the lateral grip from 155 to 152. there's a change here of 0.03 how much do i need to combat up these are the iso line of the laptime i forgot to tell you how much do i need to compensate the reduction of the lateral grip by an increase in the longitudinal grip look at that 0.17 so that means that at monza 0.17 divided by 0.3 5.7 56 57 5.7 that means that the lateral grip is much more important than the launch delivery um you're going to tell me to get the same lap time okay you're going to tell me oh close that's monza it's a fast track well let's go to monaco and that's a little simulation here and i'm going to look at this when i change my lateral grip or lose 0.5 i need to increase the longitudinal ground by 0.16 so you go 0 16 divide 3.2 that means that even with a lot of break in monaco and long beach street circuit and so we have a lot of braking and a lot of acceleration the luxury grip is still four times more important than the launch telegraph so so why am i saying you that what camber variation do you want to uh uh look at the most the one in here or the one enroll okay i think you start to have a uh an idea there that uh mastering the camber rich in rollins may be more important so you need to understand your time model let's take an example that's the natural force with camber equals zero let's put two degree of camber and you see that you are a winner here and even more winner there so you have to understand that the advantage of the camber could be bigger at the apex than you are at the entry or the exit of the corner so in that case what you do is that you are looking at this one for example you see more advanced advantage everywhere on the outside wheel i'm only looking at one wheel but bigger on the middle of the corner and the entry when you have something like this that's the other way around you are a winner everywhere but you are a bigger winner on the entry uh then in the middle because the camber stiffness as we call it the number of newton of lateral grip that you gained per degree of camber now imagine something like this you have a plus in the middle but you have a minus in the uh and the entry in um uh and the entry so uh that's an inversion i think that the minus process has been inverted here i apologize so you would have a minus here minus c and a plus there sorry need to correct that all right um let me give you a little experience there this is entire a team that we worked with and um you could see that there was a lot of graining here the ties being cleaned from all the marbles as we call the pickup the tie is working decently there and um the problem is that they were using a lot of negative camber a lot of negative camber and why did they have to lose a lot of negative use a lot of the negative camber because the virtual swing axle was very long and when you have a lot of camber variation and because of long virtual swing axle the roll is going the same direction and nearly equal to oh sorry the camber variation is equal to the roll so this is after some variation the virtual syntax and look at that we had too much convergent role to get a good dynamic camber on the outside wheel the team had to run a lot of negative camber because they had a lot of variation um a new child whale and lost of lots of lots of graining uh pull grip much shorter now with a much shorter vertical much less camber variation you could run uh less static camber and more lateral and longitudinal grip so at the end you were a winner because you had less higher wear you had even actually better braking because you had more cam variation in pure heath but you started with so much less negative that dynamically you add even less so you will win on both sides and less thai wear and much less graining so you see the schematic influence on the tyre wear and the distribution of the wear and temperature also now where do you put the you roll center altitude okay um when you put your roll center high above the ground and the ground so i'm going to give you a very quick demonstration here that's your suspended mass in the center of gravity you non-suspended mass you're going to have first a non-suspended plus weight transfer you're going to have a non-suspended load transfer we shouldn't use the word weight transfer but load transfer you're going to have a suspended mat which suspended mass load transfer that is going to be split in a geometric load transfer and the elastic one geometric load transfer an elastic one so you know that a force applied at one point is equal to a force applied at another point plus a torque so the geometric weight transfer is there and the geometric weight of answer is going to go through the wishbone for all the suspension link while the elastic weight transfer is going to be going through the spring the bump stop maybe the anchor by an intro engine the damper so it doesn't matter uh blue plus red is always uh sorry yellow plus red is always equal to blue if you put a lower roll center you're gonna have less geometric but more elastic we call that geometric because who decide the role center position the geometry of the car and why do we call the yellow one elastic but because it's very recuperate by elastic things like spring bump stop and dual bar damper okay so um with that in mind um i'm going to make a an interesting thing i'm going to decompose the outside tyre force inside force and i'm the action reaction of course and i'm going to decompose that in the geometric which one so let's look only at the geometric red up and red down so for the moment the red up and the rock the wrap down are equal so there is no jacking force you're gonna see that in the next slide you're gonna tell me uh so what's the point well ladies and gentlemen there's something fundamentally wrong on this picture is it possible that the green grip is equal to the per or the magenta one is it possible that you could have the same inside and outside trilateral force no so let's keep the roll center in the in the middle and now let's make more a little bit more sensitive more grip on the outside less grip on the inside re-decompose that i find my geometry weight transfer on the outside wheel haha and the inside they are not um equal anymore so you're gonna have a negative you're gonna have a positive and if you look at this boom you're gonna have some jacking force there and this jacking force can put the car up or down um all right no that's only uh we keep the roll center on in the center now let's be put at the roll center moving towards the outside wheel so let's say the roll center is here you have the same uh force variation and you see that if you look at the geometric way to answer you're gonna have more geometric up than done that is going to create a jacking force which gonna lift the car now let's put the roll center on the inside of towards the inside wheel the inside of the corner also uh the roll center moving toward the outside wheel jacking force pushing the car let's put the roll center towards the inside wheel and look at the decomposition here you see that actually you have more done than up and you see that the car is going to be jacked down which could be an advantage in terms of central gravity position and definitely right eye then for definitely downfalls so um you you have to uh you have to be careful with that there are people saying the royal center should not be moving sideways well when i asked them i said why and said they tell me an expert told me that then you asked the expert and the same expert tell you me uh that he got it from another expert the people who say that role center should not be moving are the same people who said that bumpsteer is wrong bumpstee could be a good thing because it will help you to have the slip angle you want when you want it okay um so be careful the altitude and the lateral movement of the roll center lateral detonator jacking force and the dynamic rider which could write heights or which can influence the iron don't force and don't force distribution now i'm going to show you an example what the role center is doing here look at that you have a lateral acceleration it's a open loop so i increase the uh i increase the the uh lateral acceleration decrease so i take 2g here between 0.5 and 2.42 seconds and then you have the decomposition here of the force going through the the anterior bar the force going through the spring and you see by the way there's a little delay compared to the peak of the lateral acceleration why because of uh inertia the geometric rate transfer is there and it's interesting because the geometry which also does apparently much more than the spring that's with a 75 millimeter high roll center and that's the damper and you see of course that the damper doesn't do anything in the middle of the corner because the roll is maximum the road speed is minimum you roll then you d-roll and then you are going to have here uh uh the damper which is much more important look at this if i look at the very beginning of the corner which could make a big difference you have 65 percent of the weight transfer of the non-suspended mass the low transfer not suspended mass which is coming from the geometric and elastic 34 but in this 34.7 the majority is from the damper so it's telling you that um the roll center play a big importance at the entry of the corner because that you have a maximum of weight transfer coming from the damper and from the uh roll center from the geometric wave chances you have the same thing here in uh roll center below the ground and except that no the geometric weight transfer goes to the bottom and [Music] and then you have the damper and i look at the percentage here and you see no it's a negative geometric way to answer but you still have a majority of it in the five first hundredth of a second okay so that's giving you an idea where the role center should be last recommendation um what is going to do in terms of transient behavior you are know what we call the parallax axis theorem in europe they call it the steiner for the german and uh the dutch call it the huggins uh wiggins as the franchise uh theory that um the inertia of uh of solid going uh through the center through around another axe is going to be the inertia uh of the inertia around another x will be the inertia of the complete mass around his own cg plus that must multiply by the square of the distance a b so you have an example here of a car like that and the longer the distance between the suspended massive g in the royal center the more you're going to have inertia because the inertia is going to be the suspended mass around its own center suspended mass inertia around its own center of gravity plus the suspended mass multiply the square of the distance of the suspended mass to the uh cg to the role center there is another way to explain that you look at the inertia and you multiply by the role acceleration but the principle is the same and guess what when you have a very talented driver who can have a very responsive car you need a high roll center but we have an amateur driver maybe you want to have a lot of inertia do you have a little more stability and less restaurants tight circuit high roll center more geometric more quick more responsive and uh low roll center for fast corner and then depending if you tie a high corning stiffness you maybe want to put the lower one why to calm down uh because maybe if you have an amateur driver and the tie is very racy you need to compensate by a roll center high or the other vibrator vice versa low a high roll center with low corning stiffness and high volts low roll center for low high cooling okay iconic stiffness low roll center low connectedness high roll center okay and last thing i need to explain to you um you have to be very careful that the roll center doesn't cross the wheel because if the roll center is here that's all the rolex is there but if the roll center is there the relax is there the car will be jacking too at the moment the roll center cross the wheel you are inverting the uh the outside dampers and compression and now they are in rebound um on the other end i have no problem it could be actually an advantage uh to have the roll center moving laterally especially towards the inside be extremely careful know that you don't have a roll axis which is moving with the front roll center going to the left and the rules re-rolls and going to the right not good all right let's go further side view virtual swing axle and also instant center height and that is going to determine many things so first of all uh it will have a wheelbase and cam caster variations a big debate in formula one now they have very short front virtual swing axle so they will necessarily be a lot of cam uh caster variation which itself could influence the bumpsteer and pitch center is the same story as the role center when you have a high pitch center you have lower inertia you have a quicker response and probably a higher tight temperature because you have a lot of anti-dive in this squad so you put more and more uh effort in the tires quickly now if you have a low pitch center you have high inertia slow response and lower at high temperature so um long virtual axle smaller caster variation uh in here but last calf duration in pitch and same thing uh but the other way around with a short virtual swing axle once again without knowing your tie model that's going to be very difficult no you see the title of this thing the ntnt i'm not a fan of anti-squat anti-lift anti-dive and so on i'm going to explain to you why but let's speak about how people are defining that first of all you take the axes going from the inboard axis and the parallel to these axes going through the oddball yeah why in the hell would you speak about the instant center of the wheel by taking pickup point belong to the chassis you need to take the picker point there and so if you go the same way on the rear you go from the instant center to the contact patch like this front and rear and you find your pitch center okay so pitch enter controlly to the front where the roll center is most of the time in the middle of the car the pitch center is not necessarily in middle of the car because the rear suspension is not the mirror of the front one okay so be careful here let's speak about anti-dive and go through this you have the contact patch you have the braking and you see you break more with the front and the rear you have here an instant center and that is going to define the angle a then you're going to have a load transfer and that load transfer is going to be split in a geometric red and elastic yellow and that is going to be the composition of breaking and uh load transfer and you are going to have here that force going above the incentive so it will help the wheel will go adverse to the chassis or the chassis down versus the wheel but if um this instant center would have been on that line you can push as much as you want the wheel will not move there will still be right eye variation because the tie deflection but no suspension movement so uh that is the angle b and the one the way we define the anti-dive is one drop multiplied by tangent a divided by tangent b and so the angle a is a function of the instant suspension geometry at that moment because it's gonna have to be iterative solution and the brake distribution load transfer yeah yeah yeah when you change the distribution between the front and rear braking force you are effectively changing the angle b so you change the anti-dive that is for breaks which are inbound in the wheels okay if you have oddball breaks it's the same calculation but the angle a and b are not the same so angle b same thing functional distance uh suspension geometry angle b brake distribution load transfer but look at this you have now the wheel center there and i'm going to find the instant center i do the uh the line from the instant center the wheel center because the you have all uh uh uh oddball break wait a moment here i made uh no no no sorry i want to make no no that's that's um uh that's the all the way around i need to correct that i do apologize so i need to correct that very quickly and i i'm sorry uh sometimes you still have okay with my mouse okay so it's here all rolled out both brakes and on the next one inboard brakes i'm sorry very sorry guys so inbold brake is uh um in the ball break sorry i apologize for that so inbold brakes like this so the brakes are in the chassis near the differential so let's calculate it now the angle a is not the same you have braking force you have load transfer that is going to decompose geometric and elastic same thing and that's going to be the angle b so in the previous example the reference is the ground no it's the uh longitudinal line the the the horizontal line going through the wheel center okay um and so you're gonna have here the same thing now you have to be careful with this because um when you have a car with um hybrid you have brakes in the wheel and you have inbound brakes so you're gonna have to calculate unt dive twice very important and the um so same thing for the uh uh anti-lift for example in the rear or this is braking but we could have done it with anti-squat and it's going to be the same thing also okay and why i call that the anti-anti is it funny that when you look at the car view from the front you look at the role center to but you uh when you look at the side and you speak about anti you look at the front with ignoring the rear and you look at the rear ignoring the front so why in the hell don't you speak about the anti-squat of the outside wheel view from the front and the anti-lift of the inside wheel you cannot look at uh roll center view from the front and ignoring the pitch center under it so for me i'm not a fan of this uh definition of anti-dive and t lift and d squat and so on because a car is four wheels and in roll it roll around a roll axis and in pitch it roll around a pitch axis okay so let's go back to the main course here we have discussed we have here you um kingpin axis there you remember all the issue of the packaging there's this side about the caster trail the mechanical trail the caster angle the kb angle so we decide that the point in red are going to be here okay this is the instant center view from the front this is the instant center view from the side so do you agree with me that the top wishbone plane will be there from the lower which boat plane sorry will be there and the top which born plane will be there inevitably so because you have an instant axis you have a top push bomb one axis and one point define a plane and you have same thing on the bottom so on the bottom so necessarily the in the pickup point of you um which born on the chassis will be on that plane and you remember that a plane is inspired by a point and a line and which is the plane of bottom which bone pick a point on the upright instant axis same thing for the top which bone and by definition the plane is described by the following equation ax plus b y plus z plus d and you have the inboard uh you have the plane equation you have the outboard so if i have the x and the y is giving me the z if i impose the y because uh i don't know template for example or packaging um and i impose the set automatically the x will be given there so it's it's depending on what you want you static kinematic you issue with packaging the rules and so on but at the end think about this um the guy who's designing the chassis doesn't care about how much caster angle you put doesn't and the guy who is designing the upright doesn't care about what the chassis pick upon is except that where do they meet right there and uh that will have a serious influence by the way on the point that you have the the force that are in you in your chassis so it's interesting the chassis guys goes toward the wheel the wheel goes guys goes toward the chassis where do they meet the inbound pickup point so that's why you have to two guys need to work together and you need to know this point before decide designing your chassis and the four and the force and that will be explained in the first module uh example steering rack position uh do you put it ahead or behind the front axis there are plus and minus of that and you're going to speak also about the acumen uh front or rear of front axle uh pro or anti-acumen high or low mounting do you put it high low center of gravity could make a difference and why so have you already selected the outboard pickup point okay um to be considered weight distribution inertia yeah a steering rack modeled inside the spinners but on a race car everything is spinning you know there is no magic bullet it's 200 of a second here and 300 there and 100 there and at that time you at the end you have three or four tenths steering column packaging template bumpstee and the bloody compliance which i will speak about at the end so um ackermann or language speaker spurgo or gento actually ackermann is the guy who uh still did steal the uh all the work made by uh langesberger and actually it was created uh by jonto even a french guy be before even uh the english american took care of it so you can have a acrobat a parallel or reverse and you're going to say how do you decide it well you cannot do that unless you have uh your thai model so this is an example of an acronym geometry where the extension of the in the steering are made behind and if you turn the in the left corner the right wheel 10 degree the left wheel will turn a little bit more 12 13. and that is an example here where you look at the anti-acumen where when you turn the steering on the right 10 degrees the inside is gonna run eight degrees so the outside is turning more than inside how do you make the decision well you need to have a time mother here's an example where you increase the load from the blue to the brown you have more and more load and if you want to use the type the peak of the slip angle you need to be at the peak of the curve if you have another tire michelin ties are often like this you load the tie more and more and if you want to induce more and more grip on the tire you need to mo more and more slip angle you agree with me that's the last load the tire so that's typically the inside wheel that is the more loaded that's definitely the outside wheel and you realize that you want to have uh more slip angle on the less load attack inside and uh you want more sorry sleep angle on the inside wheel and less depending on the side really that's the procurement now here the more you load the tire the more slip angle you need and uh that means that you're going to need more sleep angle on the outside then less loaded inside and that's going to be entire command but that's a little bit easy okay um there are a way to uh in good time modeling software to know what's the peak sleep angle so that's an example here where i have uh the normal load and i have even three different lines depending the inclinance angle which is the camber different um nomenclature different uh sign convention but anyway uh let's say my load is four hundred kilo for for the newton like this i have a need of slip angle of seven 7. 6.8 degrees something like that so this is an example where um you have a car at 100 kilometers an hour you have 36 newton on the inside wheel taking them i need a degree of sleep anger and here on the outside we take them i need 6.7 but if you are at higher speed 200 kilometers an hour you're gonna look at this uh 12 000 newton i need 6.7 and here i need 5.9 okay so you know what slip angle you you you want if you want the tie to be used at the peak slip angle but very quickly there are three calls for the slip angle one because you steal the wheel number two because you have a your angle and therefore that change the wing and there is a third one that a lot of people uh uh mistaken or ignore sometimes the gyro uh will show you that when you have a car going on a circle in 10 seconds well the your velocity is 36 degree per second 360 divided by 10 okay and let's look at what that does look at this when you have your velocity like this you are going to have a tangential force uh on the rear and on the front and longitudinal force add or restricted so you have here r multiplied by b be the distance between center of gravity axle r your velocity in radian and then you have the half track and the half track on the front and the rear are not necessarily the same and then you have a tangent speed going down here on the front which will change the slip angle so i'm not going to go into detail of that but at the end you have this formula where if you know um the left front if you know sorry the front and the right track therefore the half drag the wheel base the weight distribution so you know the distance a and b the cg sleep angle better the steering angle delta front and rear you can calculate the front uh the two front sleep angle yeah but now if i'm gonna go backward if you and know which sleep angle you want here with which camber then you can calculate the steering angle uh that you need so here we're going to go the other way around where the the target here of the slip angle are becoming an input and here the steering angle are becoming output so be careful because you have to do that for many different speed many different new angle but it's gonna give you an idea okay so um you're gonna have to make that calculation at different slip angle different speed different ranges different your angle to find the ideal steering left and right inside outside be careful now because you can have a given ackermann the initial toe is a big part of it and you're going to carry this initial toe in or old uh so akiraman is a variation but what cone is the dynamic slip angle so what's the static slip angle that you start with grip and balance are going doing two different things you could do such a good job exploiting in any condition the front slip angle the tie at the ideal slip angle that the driver could be yelling at you why because the front are going to be too good and the real doesn't follow so you have to be careful grip expectation of slip angle is good id but balance is another one okay and all this calculation you have to be careful is going to be are going to be washed away once you take the compliance into a car nothing is rigid um remember also that there are other sorts of compliance effects if i if i have a lot of steering on the inside wheel they're going to have a lot of effects yo in the car and the m side also so uh it's a little bit more difficult than you want that being said makes a big difference again to you take a formula student try different pro parallel and anti-acumen and ask the student to push the car on the skid pad you will see the difference huge all right ah that is a mistake that a lot of people are doing non-linear steering ratio like this you're gonna have to take into account that the angle are correctly assembled that's a bad example that's a good example they have very good information there on the steering column angle that you can find on uh google and the correct phasing and you know if you put the um the the car down the cvg on like this or like that you are going to have a very big difference and that is going to play a bad role on the steering ratio so let me show you a bad and a good example of real car you have an example where you have in blue the k and c and in red the simulation so pretty good the simulation is giving you uh something correct and then we vote in intermediate chart on the passenger car is very difficult because uh steering column you know you go to the steering wheel to uh towards the steering rack you have an engine you have especially traversal engine so you need to have an intermediate shaft so without intermediate shaft you would be a perfect situation direct connection between steering and steering rack just by changing the inclination of the steering wheel you change that searing ratio that is bad when you have this kind of variation the the the tire are not speaking to the driver is very discontinuous there very bad so let me show you a better one where simulation and uh with and without intermediate shaft you have something very very constant i implore you to look at that it's going to make a big difference in the driver control and confidence that's another one that you're going to have to take into account let's say that i'm going to lock the chassis i'm going to put two dial gauges uh on the left and the right wheel on at the rim and i'm going to put a talk normally in a perfect world the only thing which should be changing is twisting the tire look at that you're going to be scared look at this this is at zero torque you have something like point six degree toe into hot and so on but as soon as you see the wheel you see the variation there and not only there is a variation but there is there is it's not the same when you turn or de-turn the steering wheel so i impo imply you to be careful with that last thing last few things motion ratio very important um that's the ratio between the spring and the damper movement the spring damper or damper most of that they are the same so let me give you an example here the wheel rate which is the effect that that spring airs on the wheel and that wheels that will uh uh bring um uh as i have a phone ringing here yeah yeah hold on no it's here my cell phone is ringing sorry it's going to stop very quickly i guess sorry thank you sorry um okay the wheel rate is the effect that that spring has at the wheel and it will be in series with the tire rate so let's say my motion ratio is 0.9 and my wheel rate will be 11.5 divided by zero point square no i'm going to put a 0.9 square 14.2 let's put a softer spring yeah but if the old spring has the same free length and you don't change the suspended mass guess what you are going to compress the spring that means that you are moving the rocker and that means that you have no uh a motion ratio of 0.8 and if i do the wheel rate calculation is spring by the square of the motion ratio ta-da look at that you have a softer spring but you have a stiffer suspension be very careful with that okay so by decreasing the stiffness of the spring you could have actually an increased wheel rate okay uh variable rate motion ratio rocket ratio a and b here you can see that when the rocket is moving the ratio a divided by b is nearly the same okay and um here a divided by b is very very different okay you have something extremely different there and that could be a good thing because you could use the motion ratio um variable to have a stiffer and stiffer car as you go faster and faster so you soft car for mechanical grip at low speed the car goes down stiffer car with the same spring to resist the down force so it could be used to obtain a rising rate wheel rate so it could be a good thing if you know what you are doing okay all right anti-roll bar motion ratio when the wheel goes up you are going to twist the anchoval bar so you have a ratio here of h wheel movement divided by little d uh anterior by motion ratio some people could that but i have a problem with that because if you have a u bar and which displacement are going to have uh vertical or tangent well if you want your bias like that you're going to move like this or like like that it's going to move like that so i'm a little bit not happy with that ratio between wheel movement and the edge of the leverage of the anterior bowel movement now if you have another solution here is to use the roll angle versus the anterior body or angle so in other words when i roll one degree how much do i twist my enture bar i prefer that solution now be careful because the angular bar stiffness could be uh expressed in newton per millimeter sometimes they put force in newton per degree dalara is doing that i still don't get it they have even kilo per degree of torsion or the newton meter per degree but be careful that if you are using f uh a force which is um uh versus a deplacement then the motion ratio must be wheel movement divided by entualba edge movement if you are using newton meter per degree to characterize the anti-robot stiffness you need to use degree per degree of roll angle versus anterior by angle finally integration of vehicle design you need to know in this example that's a professional car that the bottom wishbone outboard picker point the lower low boy uh the the low bone of the the the push rod pick a point off the on the wishbone the top point of the pushrod on the rocket the center of the rocket the position of the damper on the rocket the position of the damper on the chassis and also the dropline position on the rocker and the entire bar all this thing must be on the same plane why to avoid compliance because if your rocker is like this pivoting around that axle and you have a push world like this of course you're going to bend the pushup that's not very smart okay and i'm going to view bad thing that i've seen and good thing that i've seen in formula student to get an example formula student um uh same thing uh you need to know that uh the push road must be sorry the the little circle should be there uh from the oddball bingo john uh that is not not good because here you have the pool road uh which is not going through the center of the ball john that's guarantee is this thing is going to break it's going to be right here let me give you uh do and don't do let's start with don't do that sorry that's pick a point arriving at the uh node of the chassis less compliance that is a no no no no no you have the rock the the damper in the middle of your tube and you have the anchorage of the rocker in the middle of the tube that is a yes double she a single a double shear that is a no in formula student by the way that is not allowed anymore you uh tolling must be uh double shear on the upright conclusion um this is the way you're gonna work track and wheelbase scrub and make reduced mechanical tray caster angle kpi trailer outboard pickup point roll center pitch center inboard pickup point on the chassis steering rack position which influence uh the acumen and also the bumpsteer and you're gonna have to refine the loop the one thing that you need to know is that we didn't discuss how we have to put the turning to avoid the bumpstee or to have the bumps to u1 that is going to be discussed in one of the next session about optimization so that's it guys thank you very much and i think we have hola we have a lot of questions here so um okay why do rear wheel need to have a caster angle you don't necessarily need to have one but you have to understand that if you have anti-dive and anti-squat the wheel will not go up and down so if you have anti-dive in this squad there will be variation of the cast and what can't is the dynamic caster not the static one so you want to kind of take that into account for your cast angle remember also that the cast angle on the rear the kp angle on the rear the scrub radius and the mechanical trail will influence the torque that you have around the kingpin axis which is going to influence forces on the tolling and therefore on the upright and on the picker point inboard of the tolling of the suspension of the chassis sorry um shifting the oddball toe out to the center of the tire will increase the amount of rotation made by c or can we counter this shifting the oddball trolling to the center of the time why would you do that shifting the odd part toe length point to the center ah for the rear suspension uh uh i i don't know i'm not sure i don't understand that question if it's for the front it's very clear that you want maximum uh steering arm leverage so you want to use all the space do you have on the rim so you want to have the longer one so the toe link uh on the outboard should be as far as possible from the wheel center if um i don't understand it i and same for the rear shifting the outboard toe point to the center of the target increase the amount of rotation angle made to steer at the rotation angle of the steering wheel yeah right how do you come to that put a good steering ratio and calculate the steer ratio after having tried to make the longest um uh uh the longest steering arm last question i have here is that apart from the obvious effect of aerodynamic are they uh any downside of upward jacking force well yes because if you have okay i'm going to take an example i go on the scale i measure my weight okay then i put two uh weight in my hands of 10 kilo okay so my weight is 20 kilo 10 kilo initial so my weight is already 20 kilo or more okay and if i move the wheel at my arm up at constant speed the scale will still measure my normal weight plus 20 kilo but if i do this in other words there is a variation of the speed you are going to have an acceleration and this inertia and you're going to see on the scale that there is a variation of the load momentarily so the uh the jacking force will increase or decrease depending where your roll center is in altitude and lateral position uh the vertical load on the tire you have to take that into account so apart the obvious effect on iron make the any downside of upward jacking force well the other one is that you're going to put your roll center higher a lot if you have soft spring literally if you're a stiff spring okay do we have any other questions no okay good so i want to uh some of the answers that uh uh have been asked has been uh given by um ariel uh online um i want to uh we have more questions there okay sorry all right so uh thank you um the air arm of the suspension need to mount either vertical or horizontal like the picture in slide 11 okay we're gonna go to i mean my glasses here slide 11. [Music] slide 11 11 11. hmm the air of the suspension need to be mount either vertical or i mean i guess you speak about the rodent being like this or like that like the picture on slide 11. i i don't see the i have one if i one vertical one and one horizontal one i'm not sure what you mean by vertical and horizontal i guess you speak about the rodent well when you put a okay let's say this is your chassis and you put your rodent like this there will no be any missile in mine but if you put your rodent like that and you have a local movement at a certain time the spherical joint then is going to be bending so you need to take into account if you don't have enough uh misalignment angle potentially in the road and that is good to put the steering arm sorry the road then of with the plane let's say nearly perpendicular to the other it's not on site 11 it's on page 69. oh and on page 69 like this one oh this point here well i think i uh i answered that question in that case um that's that's the number one uh solution that i'm thinking uh is mr will going to formula student in gary this year i hope so i already have a busy busy schedule and uh do we need caster at the rear i answered that question uh previously uh from another person if the dynamic cast of variations is let's say 0.3 degree in the read the static caster need to be adjust enough to take into account guys you have to understand that if you have cast a variation when the wheel goes up and down that means you pick a point with the car it's not only going up and down it's turning that mean you modify the oddboat point of the turning that means you are creating bumps to you if that is not taking into account be very confident you need to look at the car view from the front camber creation heave and rolling steering you know look at the car view from the side camera very a wheelbase variation and caster variation but you also need to look at the car view from the top how much do you have um uh bump steer once again bumpstee is not necessarily a big bad thing it could help you to have the the slip angle you want when you want but uh that's not good on bumpy track on bumpy track then the slip angle keep changing and and and the tire doesn't know where it needs to be but on the smooth circuit it could be a good thing so you have to look at that um more question here thank you for your question guys i appreciate that when calculate the motion ratio of the push rod should be calculated from the l beat lower uh no no no no no no a motion ratio is okay let me uh it's good that we are speaking about that here when we speak of it that is the not the motion ratio that's the rocker ratio and the rocker ratio is um one of the element in the chain of the motion ratio wheel versus spring and damper so the you have the wishbone the top which bond the tolling uh the um uh the kpi believe it or not the kpi will influence your motion results when my wheel goes up x millimeter how much is my spring moving y min that's the motion ratio uh you you everything has to be taken into account you cannot calculate the motion ratio by looking at the top of the bottom wishbone vertical movement is kpi necessary and why the consequent zero kpi well i'm going to good question good good question if your kingpin axis go through the center of the contact patch that means the ethics whether it's breaking or acceleration will not create an mz so look at that uh you are in the let's say you're on a not a formula one not a single city car you are in a covered covered wheel car you turn the steering wheel and one of the wheel is locking and you don't see it you don't you don't see the wheel the wheel is locked and you are not going to think any difference in the steering wheel so you need a l it's like this the car is to trail the mechanical tray you don't want too much of it because if you have too much fy multiplied by a long mechanical trailer or too much fix multiplied by a long scrub radius you're going to need schwarzenegger to turn the steering wheel if you have a too small one then you don't feel any erection so it's all about the steering torque guys it's all about the steering talk you don't want no steering talk and you don't want too much steering tower try to get four five six seven newton meter that is designing and the fix and the fy versus the cast of trail and versus the scrub radius will make a difference so that's the question about is the kpi necessary can you show some example of some geometry which can be implanted to quickly change the camber on the truck rather than those can you show some example of some geometry which can be implemented to quickly change the camber on the track rather than those threaded rods yeah of course shims guys we'll go on the internet the shims you put shims and the that's going to change the the camber no that's an interesting question which gonna make you think think about that you have a given camber that's your top wishbone okay so let's turn the road end and make the top wishbone shorter but put more shims and you come back to shorter which bone more shims same static camber yeah except that no you change the kpi angle and the kp angle will have an effect on the steering talk and the kpi angle will have i was surprised i learned that 15 years ago i were very surprised how much the cape a variation the kpi kpi angle changed the motion ratio yeah because europe right now is moving uh with a same length bottom which bomb the shorter one on the front so it's gonna change your motion ratio i was very surprised and do not forget the wheel rate is the motion ratio divided by the string divided by the motion ratio square squared that means if you change your motion ratio 10 you change you will rate 21 because square 1.1 is 1.21 okay so i think uh ariel do we have more questions two more questions as i'm waiting for the question let me put a little bit of advertising here um we are going if you go to the optimum gi website we're gonna have a several seminar we are going to have two applied vehicle dynamics seminar one in eindhoven beginning of april and over in the netherlands at eu and oven and one at michigan state university in may so beginning of april and oven and michigan state university in that case just after formula student competition now we're going to have one two three four five data driven engineering semi data driven performance injury the applied vehicle dynamic seminar is i would say 70 percent of theory and 30 of practice and the data driven is that we're going to give you data of real car and we are you are going to make kpi key performance engineering from the data acquisition that is about 65 practice and 35 theory and you need to come with your laptop and ahead of time we will send you data so that you can practice that and we will be using the motec system why because motec is free of charge and software so it makes things easier and we will send you a head of the seminar suit that you can practice now uh last question uh sorry sorry yeah i think this one yeah i want to know what's the way to i can calculate the spring rate and what's the parameter i need to add the spring rate to get yeah okay so ah okay i'm going to repeat the question the simple way do you want a heavy a stiff spring or a soft spring and my answer is i cannot discuss that in the kinematic march this is much bigger if i want you to explain that to you i'm going to need one hour because there are so many important things but i'm going to say it in a simple way when you test the car go stiffer and stiffer and stiffer in the spring and the end your bar until the driver will tell you i cannot handle it then you go one step backward do not forget though that the critical damping is two square root of k multiplied by m so that means when you increase your spring five percent i don't care too much if you increase the spring 50 percent then the damper is not following okay so if you want a good um critical damping a damping ratio 0.7 would be i don't say the car will be perfect there's a good way to start you're not going to be stupid on the racetrack or test track so if you increase the spring uh you need to increase the damping by ratio of square of that variation the damper need to go there but that that's my um and you you need to calculate the frequency the critical damping and so on um so it's a it's a simple question it's a longer answer which is not purely kinematic uh if you want to know more maybe you want to come to the one of the seminars that i will and by the way the seminar are only until the end of spring we're going to come with more seminar in the summer and the fall um is it necessary that am linkage on front and reach should be in line in line with what is it necessary that arm linkage of front and rear should be in are inside you well good question if you wish bones are parallel to the ground your instant center is on the infinite for the front wheel is on the infinite on the rear wheel and then ways you pitch center uh you know one thing it's on the ground because you go from the instant center to the contact patch which will be a parallel to the inboard access parlor so the pitch center is on the ground but where is it you cannot calculate that unless you know the spring stiffness okay take a beam like this two spring under the beam same stiffness you push in the middle the beam will move parallel to itself put a stiffer spring on the rear and push in the middle you will create heave and pitch okay so kinematic is one thing but kinematic is good it's important but it's not the solution to every problem it's a good solution to be honest with you archimedes said um give me a leverage and a point where i can put the leverage and an arm long enough and i will leave the world in school you remember that you define a force by an application point a direction and an intensity i would worry if i was you more about the application point in the direction before you uh worry about the intensity and i'm going to tell you i've been working on race car where we changed the spring the interior about the tire pressure the toe the caster and so on practically nothing and suddenly we change the pick up a few picker point by five ten millimeter boom the car starts to be working so i don't say kinematic is more important than iron maker load transfer spring damper tire pressure i don't say that i see it's an essential thing and that's one of the things that you should discuss before you [Music] work on the on the spring stiffness anymore question okay so i would like uh you to make sure ariel come here so that you will they will see your face okay so this is ariel who will be yes it will be at uh my uh you want to learn a little bit maybe yeah yeah i'll be at your place last week ariel what are we going to speak in the next three years next week we are going to speak about optimum kinematics so how do you put everything that you learned today and everything that learned that cloud presented how do we put that in practice and how do we use optimum kinematics to get the most out of your car so i think that's all okay the next one will be false model no the yeah the first one is going to be optimum kinematics standard you know how to run simulations uh how to view your world centers your pitch centers and so on the second one which will be two weeks from now will be about the forces module and the last one will be the latest development which is the optimization module which is the most powerful kinematics tool that we have today okay guys well i wish you um uh a good year i wish you that um you're gonna have a good season whether it's in racing or in formula student and even i think that for passenger cars some of the advice i shared with you i'm going to say one more thing compliance all kinematics will be uh purpose a design will be ruined by compliance inevitably um and i want to tell you there is no such things as a little bit of that is compensate a little uh a little bit of that one into the other you cannot compensate by the kinematic of bad compliance it can only go worse as one of my teacher in mechanics said the gods are against you don't expect that the compliance will be a patch on a bad kinematic the the gains are good they go against you both okay so be careful about it all the compliance very very important okay thank you guys and i will see you uh uh later uh on the circuit and uh with ariel next to a week in the next two weeks after that for optimum climatic uh