This dissertation is on the significance of realistic physics in simulation games.
Physics in games has changed a lot over the years from arcade games having no physics to Need for Speed: Shift having world class physics. As the years have progressed so has the technology giving ways to make the game more realistic to a point which makes them almost as real as in real life. The question here is that do we need such good physics in games cause in the end the players need have a good time playing the game while having a realistic experience, pushing the realism a bit further can cause problems with the game being excessively difficult the daily gamer.
The oldest form of racing games would be arcade games where there was no physics but the games were still fun to play for the casual gamer. They can be called the classic example for physics-less fun games like outrun, Virtua Racing by SEGA. With time games like ‘The need for speed’ came out with realistic acceleration top sped etc. they built up on car personalities with different cars having different type of grip, speed etc. with more advanced Physics processing units came better physics with destructible models, actual car damage and very realistic handling etc. as seen in ‘Need for Speed: Shift’ and ‘Need for Speed: Pro-street’ these games reached the benchmark for physics at their time but were not as popular as the ‘Need for speed: Most Wanted’ and similar Titles with intermediate use of physics. But the physics in games now days have totally changed the driving experience in games.
My thesis is on how this can be improved and what type of physics should be added and what type to be controlled so as not to make the game extremely difficult but also improve the gameplay and give a better ‘feel’ of realism.
C.1 The Statement of Problem
The statement of problem in my dissertation is the fun factor in racing games with realistic physics.
Racing games are played for fun and are not viewed as some physics prototype so a game with exceptionally good game does not have to be an exceptionally good game and vice versa. There has to be a balance between fun and physics in game. A game with very realistic handling will make an immature player crash a lot which is not very impressive to the player, whereas in a game without friction or skidding, the player will not have the feel of physics or realism in a game making it boring again. How to get this balance in a game is my main objective.
In a racing game there should be balanced handling and to make it more realistic new improved effects for drag can be added. Better collision and realistic damage which effects the players driving can help make the game look more realistic. Things like this are very important nowadays as the competition between games is rising and most of the games are coming out with good physics so it becomes a common ground between most games. New type of physics including centre of gravity, collisions effecting the player, g-forces on the player causing loosing handling, blurred vision can be a thing of the future also player fatigue while driving can be added in the games in the future to make them stand out.
This study is aimed at accomplishing to implement new type of physics in the game, making them more realistic while still being fun to play.
The purpose of this study is that when we are adding new type of physics in a game, it should not be so much that it looks more like a physics prototype than a game.
This chapter explains how the research for this dissertation is done.
This dissertation is based on experimenting on different type of games arcade and realistic alike and also based on articles related to this subject.
D.1 Study of Existing Information
Existing information was collected over the internet mainly from www.google.com and www.gamespot.com.
Different type of physics used in current games was searched and also about arcade games. The information was used to understand the working of present day physics realistic games.
Information and ideas for different type of physics were also gathered from different forums and articles.
To better understand how physics actually works in a game different reference articles which explain how physics is implemented in games with code were studied go get a better understanding about the subject.
Experimentation was done by testing different racing games from arcade games to realistic games to understand the difference in physics and to understand what type of physics is implemented in present day games.
Case study in done in ‘Need for Speed: Undercover’, ‘Burnout paradise’ ‘Dirt’, ‘Need for Speed: Shift’ and ‘Virtua racer’ to understand the physics in those games and to understand weather they were successful or not and why. Different types of physics modules were studied in each game, understanding what game used what and to how much realism and how it affected the outcome of the sales of the game which tell which was more popular.
This chapter will discuss the articles significant for this research and what use it has in my dissertation.
This chapter is in two parts, one discussing the physics aspect behind making a game and the other one discussing about different games, their popularity and what type of physics they used.
E.1 Physics Review
Reference: [Title ‘Motion along a straight line’ by author Michael TanczosÂ http://www.gamedev.net/reference/articles/article434.asp ]
This page is about basic motion along a straight line which is required to make a game about any moving body. This helps with the basic physics that require programming of moving objects.
Reference: [Title ‘The physics of racing’ by author Brian Beckman http://www.gamedev.net/reference/articles/article1610.asp ]
This is a comprehensive guide about how to make racing games. This helps with understanding of present day physics and how they are actually implemented in a game. This also helps me to formulate my own ideas to how to add new physics to the game.
This page helped me understand about braking systems in cars.
Reference: [Title ‘Motor Sports Setup’ by author Carroll Smith http://needlesslyobscure.wordpress.com/motorsports-setup/]
This is a series of tutorials of how to setup a car. I used this to make compute my own vehicle simulations.
This article gave me a better insight of how slip works on a car.
E.2 Game Review
Reference: [http://en.wikipedia.org/wiki/Racing_video_game#1970s Title ‘Racing Video Game’ by Wikipedia]
This is where I started researching about history of video games and looking into what types of racing are there and how they developed over time.
I visited this website which had old arcade racing which I played and also read about them to get a better understanding of how racing games were back then.
This is a forum where i read about Atari arcade games.
In order to understand the exact nature of physics of present day games and games from the past, I tested out a few games to understand what different types of physics were applied to them and how they are different from one another. This also helped me to understand how the physics evolved from the past to until now. Another aspect of this study was to understand how the popularity of the game was related to the physics it.
F.1 Virtua Racing
Virtua Racing was released in 1992 by Sega. This game had excellent and clean 3D graphics for its time. It was based on F1 racing and was one of the best arcade racing game of all time. This set the base for racing games that came after this. It had features like minimap track, speedometer etc. basically it had a fully functional HUD for its time. It had 2 views, one third person and the other was first person inside the car. It had time chase and also the player could race against the AI cars in the single player mode. In the multiplayer mode, two players could race against each other. It had also implemented different cars so the player could choose between them. They were not just artistically different but also were also different in the way they handled. This was a change from the old racing games before this which had only artistic differences between different cars. This game had simulated physic s, there was not an actual simulation engine deciding what the car would do. It was just programmed to skid if the player was taking a turn over a certain speed. It gave a very good feeling of realism.
F.2 Need for Speed
Need for Speed for first released in 1994 by Electronic Arts. This game went on to be the most famous game series of all times. Need for Speed was based on street racing. It had good load out of cars which performed very differently from each other. The players had to race in the street with oncoming traffic and against AI player; it also had a multiplayer mode which 2 player could play simultaneously. It had a very smooth camera system which allowed the player to play in a third person view or a first person view with the player sitting inside the car. This game had implemented gearing system which the player could manually change or set it to automatic where the computer would take care of it. This game had very good physics simulations which was quite different from its predecessors.
Need for speed has impressive graphics getting better than anyone before them. They had open seamless outdoor worlds. These worlds gave an effect of a 3D world unlike the past games. The cars were also very detailed, which ranged from Lamborghini, dodge viper to Mustangs. They were replica of real life cars with all the details in them that could be put at that point of time. The race tracks also had a lot of variance in them which were set in a realistic environment. This game also had weather effects which added more realism to the environment.
The sounds implemented were also awesome. They were very accurate and added to the realism of driving a vehicle as a driver depends on sounds a lot when driving a vehicle. For a game to achieve this, the sounds had to be very accurate which EA achieved with NFS. The simulation engine for this game was also very nice, it gave a clean difference felt in power, speed and handling when driving different cars. Different cars had different statistics and performed better on different tracks.
F.1 Need for Speed: Shift
This game of the NFS series was a circuit based game and had more advanced physics to its predecessors. Physic-wise, Need for Speed Shift starts to sound really promising. If done right, the 3 different physic models can really make the game enjoyable both for the usual Need for Speed crowd as well as simulation enthusiasts.
At first, the driving physics in Shift take some getting used to. You can’t go into a corner, hit the apex, and then pump 100% throttle on the way out. Without a doubt, you’ll inevitably end up facing the wrong direction, or planted into a wall.
Throttle control is absolutely mandatory in Need for Speed Shift. There’s no way around this and if you haven’t got a racing wheel handy, the controller does little to favour irresponsible throttle application or violent steering input. A lot of importance is given to the throttle of the car making it one the most tweaked feature which takes some time getting used to.
Due to the high end physics in this game it made it quite difficult to play for the casual gamer so the game had features like 10% extra grip for the newcomers etc.
The car could be customised in a lot of ways to make it affect the physics of the car, this helped out the professional players a lot, but in this game doing anything wrong to the customizations without knowing what the person is doing would make the car difficult to handle making it again unfriendly to the casual gamer.
One glitch that you often encounter later on in the game when dealing with high performance cars or extensively modified tuned cars. Due to the lowering of body work, additional front splitters, under body modifications and different wheel/tyre combinations, cars seem to run far too low, removing ground clearance and effectively making a car bottom out over even the tiniest of bumps. This results in a ridiculous and uncontrollable glitch where a car will continue down a straight path.
This game boosted of great physics giving realism to the circuit/professional racing and tried to make the game real but they failed in a way. The professional player didn’t like the game so much because of the physics not being to real life like with some glitches here and there. Also the car would sometimes out or under manoeuvre in an awkward manner as not expected by the user. As for the casual gamer this is not the game for them, this game is very intense and requires decent amount of racing knowledge of knowing when and how to turn/corner at high speeds, tune the car properly according to your personal needs. So in all it was not a great hit either ways.
F.2 Need For Speed: Undercover
This game does not have realistic physics but it has type of physics which helps the player a lot. The game is made in such a way to make the physics work in the way of the driver to give him/her an awesome driving experience this does not have to be entirely as in the real world. This game allows you to pull of the craziest of stuns with easy, this game is built only to give the driver awesome driving experience with computer guidance to accomplish stunts which would not be possible in the real world giving an adrenalin rush to the player.
Key to Undercover is what EA is calling the ‘heroic driving experience’. In Undercover this physics system has been given an injection of cool. Think of all the best car chase scenes in movies from the last ten years and you’ll get an idea of what to expect. EA want you to feel like a skilled stunt driver, and it works. By using a combination of the gas pedal, brake, e-break and gear stick you’re able to pull off stunning looking manoeuvres like reverse 180 degree turns. It’s like you are Jason Statham from the Transporter movies.
While we were quite looking forward some potentially funny moments, it seems EA has gone down a more serious route and it works very well indeed. Your goal in the game is to take down the various captains before taking down the whole operation, which is obviously done while driving at insanely high speeds.
The game involves high speed chases over the highway, battling enemy cars, the good old cop chases etc.
According to EA the traffic in Undercover is modelled realistically and reacts to your actions. While you can simply push a car over into the way of your target, you could choose to spook a driver of a bus, causing him to jack-knife in the middle of a dual carriageway. Racing at high speed, weaving in and out of traffic appears to offer the kind of thrills that were severely lacking in the more down to earth and structured ProStreet.
As EA repeatedly pointed out during the publisher’s Games Convention 2008 demonstration, Undercover is all about heroic driving, and there’s no better reason to drive like a stuntman than trying to outrun a swarm of angry police cars. Police chases thankfully return to Need for Speed in Undercover and these guys are aggressive, very aggressive. To begin with they’re not pushovers, but as you progress through the story and increase your level; your notoriety amongst the police also increases. Before too long they’ll spot you on the streets and go after you, hunting you as a pack. If they get you – which seems like it’ll be a regular occurrence for less skilful drivers – you’ll have a strike against your car and it’ll be impounded.
Being able to take pictures of the game during gameplay situations is becoming increasingly common, and with the amount of action on display in Undercover it’s no surprise to find such a feature here. We didn’t see it in action but EA says that the snaps taken have been dubbed ‘Movie Poster Action Cinematic’ – sounds good to us.
Undercover still has some way to go in development (it’s not out until late November) but it’s already looking very impressive. Car models are incredibly detailed and procedurally deform based on collisions. The areas of the city demonstrated to us were bathed in a gorgeous yellow light that gives the game a highly stylised appearance, and the camera often uncouples from the rear of the car in order to give a better, more cinematic view of the action. With months of development left there were obviously a few technical issues, but on the whole we can’t wait to see how the final game looks. As in previous Need for Speed titles the audio is often dominated by the sound of police chatter. We only saw one police chase so can’t say how it’ll sound hours into the game, but they said all the right things to convince us they were on our case.
To sum it up, the game is made for the player to have a free stunt filled game which could be easily be pulled of which was not like by the old NFS users. The game wasn’t such a big success like the old NFS Most Wanted due the reason that it lacked realist9ic physics but it had player friendly physics which made the game very to finish which much challenge.
F.3 Burnout Paradise
This game was made for its stunts. It had some realistic physics with a lot of importance given to the car damage. The game was a stunt mania. Though it is not correct to say It had realistic physics but it had good amount of it and put to use in the correct places, the made a game for stunts and it was good for it. The car damage actually affected the car performance. Though it did not have really good physics for driving, it had awesome crash physics.
Burnout 5’s speedsters will atomise stupendously during crashes, with more than six times as many breakable pieces in each car compared to Burnout Revenge. This will mean you can tear your car in half, rip the roof off or achieve other satisfying shunt stunts.
The biggest change introduced in Burnout Paradise is the move to an open world, the streets of Paradise city. The entire city is open at the start of the game, with the idea being that you can do whatever you want, whenever you want. Not all of the events are present at the start, mind you, and you’ll have to put in a lot of time to unlock the game’s roughly 75 cars, but you’re never limited in the options before you.
The main downtown area of Paradise City is very reminiscent of the downtown tracks in the last couple games, while the western section of the city harkens back to the long, winding, countryside courses of past games as well. A couple of highways will put you dead in the middle of traffic and give you plenty of roads to get up to speed on.
In all the game was a success and was loved by crash maniacs but was hated by the driving fanatics. It stood to what it was designed for and achieved excellence in stunts and crash driving.
Dirt 2 as Dirt is an off-road racing game. I chose this for my case study because this game is somewhat like my project. The game had a lot of focus on suspension and grip, any wrong move by the player could make the car skid off the road, in general the game physics were not player friendly but realistic to give the feel of an off-road racing game with the difficulties involved in an off-road racing game.
The physics in Dirt 2 are impeccable. When a truck tumbles after taking a hard landing off a jump, it looks and behaves exactly as it should, which is critical if you’re behind the truck anticipating its motion across your driving line. The physics are so realistic that the vibration from my idling engine would shake the skirt on my dash-mounted hula doll. Physics also come into play in the water hazards that now dot many of the courses. Driving through water will slow you down (though this can be advantageous if used strategically), and if you’re driving from the cockpit view, my preferred perspective, it will obscure your vision for a few crucial seconds. Dirt 2 also features night-time races, confined to Rally Cross events, which add a whole new dimension to the game. You will have to avoid smashing your headlights on those tight corners if you want to see, and decide if you want to overtake the leader and risk underestimating a dark turn or let him show you the best line through the corners.
Dirt 2 takes the series in a new, quite risky, direction, by taking a more Arcady, fun feel. Although this may have upset some of the hard-core fans of the series, it still kept enough difficulty to please all, even the most casual gamers. It blends the realism of off road racing with the enjoyment of a street racing game and it works perfectly, making one of the best racing games
To summarise the game is on the best off-road racing game, like burnout paradise they concentrated on the particular type of physics needed for an off-road racing game.
History of Racing Game
The old 2D racing games like ‘Speed Race’ 1974 where generally black and white and were simple arcade games rather than proper simulations. In this era some basic concepts for racing game were developed like collision detection, HUD displays like Tachometer, speedometer etc. were developed. They were all vertical scrolling games and the player had to race with other AI cars or setting a high score. This was the base in the 70’s for racing games and racing games evolved from this slowly over the course of years.
In 1974 ‘Atari’ released ‘Gran Trak 10’ which was the first racing game to implement ROM (Read Only Memory). This was a black and white game with an overhead view where the player raced against the clock which made the game non-competitive.
The next concept came up was a sort of multiplayer where the player played against each other turn wise by competing against each other’s scores. This slowly evolved to a proper two player multiplayer where the players were able to play with each other simultaneously in a split screen view.
In 1976 ‘Crashing race’ was released which was a multiplayer capable arcade game where the players had to crash into other players to gain score. In this game the collision in racing game was reworked but this was still not a simulation game. The same year ‘Moto-Cross’ was released which introduced Third-person perspective view into racing games. It achieved this by scrolling the track forward as the player moved and the scene closer to the player kept scaling so that it gave an illusion of perspective. Another game released this year called Fonz introduced feedback in controllers. The next game called ‘Night Driver’ introduced the first person perspective in racing games. By this time the games were in colour rather than black and white. From 1970 to 1980 the games generally improved in graphics a little bit.
In 1980 ‘Namco’ released ‘Rally-X’ which was the first racing game to have background music. The game also had a feature to Scroll the screen to either direction giving actual control over the players view. Then in 1982 ‘Namco’ released ‘Pole position’ which was the first game to have a track based on an actual circuit. The game had high resolution colour graphics for its time. The game was designed in such a way so that the player had to brake and use controls to manage turns; this is where some kind of simulation started in racing games. The player had to race against AI drivers and also had to race against time which made the game interesting. The game also featured collisions with boundaries and other cars which caused crashes which were first time implemented in a racing game. The game was the first of its kind to implement simulation at the most basic level which is where racing game simulation started from. The games after this adapted this concept and the racing game simulation started increasing giving a more sense of realism. The players had to manually shift gears and use brakes on turns to get turns correctly. ‘Pole position 2’ in particular had 3 screen display of the game giving a sense of 3D. In 1980’s the this was the general trend in racing games and the simple car simulation were upgraded slowly as new hardware came, with this the graphics of the games also improved
In 1984 ‘Geoff Crammond’ developed a racing game simulator RVES for its time on BBC Micro Computer platform. This was the first step in game to really simulating driving. Though this is primitive from present standards but for that time this was huge step in racing simulations. In 1985 ‘HangOn’ was released which was the first game to use 16 bit graphics and also had an improved simulation and AI system compared to the other games out there at that time. In this time more concern was given on improving graphics rather that the simulations. In 1986, Red Racer was the first stereoscopic 3D game. In 1989 ‘Atari’ released ‘Hard Drivin’; this was the first game to use 3D polygons in a game.
In 1990 Papyrus Design Group made the first actual 3D racing game simulator and they actually concentrated more on the simulations rather than the graphics. This simulator simulated realistic physics and telemeter.
In 1992 ‘Formula one Grand Prix’ became a hit racing simulation game which had all the drivers from the actual Grand Prix. From 1993 onwards polygons were highly used to make games and each and every game that was coming out had better graphics than the last one. In 1992 the other game which made big news was ‘virtua racing’ which was not the first 3D racing game but it had the cleanest 3D graphics for the time. It did not have a pixelated look, rather all the textures were very neat and clean for the time.
In 1993 ‘Sega’ came up with ‘Daytona USA’ which was the first racing game to feature filtered texture-mapped polygons. In 1994 ‘Electronic Arts’ came up with ‘Need for Speed’ which became the most popular racing game series of all time. This game had the most realistic audio for its time, detailing sounds of engines, gearshifts and tyre squeals to perfection. It also featured vehicle traffic in races. This game had both multiplayer and single player capability.
In 1997 ‘Gran Turismo’ was released for play station and was the best game at that time for its simulation and graphics. This was considered to be the most realistic game of its time.
In 1999 ‘Midtown Madness’ changed the face of racing game with free roam in games.
After this racing games improved generally on the course of time with better and better graphics and simulations. The latest racing game that is supposed to come out in 2011 called ‘Need for Speed: Shift 2’ uses data from actual cars by attaching computers to it and computing every minute detail of the car and driver and have gone so far that they start to bridge the game between real life physics and simulated physics.
The very basic idea behind moving a car or any object is F=ma, where F is the force applied, ‘m’ is the mass of the object and ‘a’ is the acceleration generated. For a car, the force comes from the engine and the mass of the car is a constant, therefore rewriting it we would get a=F/m. This would give us the acceleration. This is the base idea which would be used over all in the game. For example, even when the car takes a turn, would be a force applied in a direction from the centre of mass of the car.
H.2 forces applied in Linear Motion
Torque: To keep it simple at starting let’s consider the car to be going just in a straight line and see what all we would require for the car to run. Now the car engine generates a force which is from spinning motion of the engine shaft through the gearbox, to the axle and finally to the wheels which would drive the car. This gives an understanding that there is a torque applied as a form of force.
F=ma: This tells us that the acceleration on the car depends on the mass of the car directly considering the force is constant.
Equations of linear motion:
v=Final velocity of the car
u=Initial velocity of the car
The force generated will give us acceleration of the car and thus the speed of the car can be calculated from this.
This equation will be useful to get the position of the car in X, Y, Z direction in 3D space based on the velocity and direction of the car.
S= Distance travelled
This equation calculates values independent of time.
For all the above equation the time will be considered as Î”t, which is a small change in time. All our calculations will be based on these getting small points on a graph thus getting the whole motion.
Friction: Considering the car stops Appling force on the tyres, by newton’s second law it would still be in motion as no negative force is applied to it. But in the real world this is not true; the car decelerates if there is no force from the engine. This is due to the frictional forces present which act in the opposite direction of the car thus acting as negative forces. This can be categorised in 3 parts in general for a car in order of how strong they are.
Internal Friction â€“ This friction comes from the moving parts of the vehicle and is very minimal compared to the other two.
Ground Friction â€“ This friction comes from the friction between the tyres of the car and the ground. It depends on a few things, the larger the tyre of the car the more friction it will have. Also this is also related to the smoothness of the ground and tyres, the smoother tyres give less friction but it to be kept in mind that higher friction tyres have higher grip.
Air Friction â€“ This is the strongest frictional force of the 3 and exponentially the in depth calculations based on this would come later, for now it is this is just to get an understanding of what all basic forces are applied on a car.
This is the air friction experienced by the car when it’s driving. The drag is a force value acting opposite the direction the car is travelling. This is the force required by the car to overcome to be in motion.
=Density of Fluid
After going through a lot of Drag Coefficients, that value for our car fit to be 0.50
Ford Mustang 1976
*List from Wikipedia.org
Air density which is fluid density here is 1.29kg/m^3 at sea level, which will be our density.
The frontal area of cross section for our car came out to be 2.5m^2 which is our area of reference.
Putting the values in the equation of drag
All the calculation is are done in metric system.
Table for Drag force for our car
This shows that as the velocity increases drag force exponentially which increases the force required to overcome it.
H.4 Centre of Mass
The centre of mass (COM) of an object is the mean location of all the masses in the body. When a force acts on the cars, it acts on the centre of mass of the car and the car moves along with it. Consider the COM to be a point inside the body of the car, if this point was to move out of the car’s body, the car would topple over. This is what determines the momentum of the car and the direction of momentum. Gravitational forces also act from the centre of mass of the car.
To make calculations easier, consider the density of the car to be constant at all the places, and then the COM would be equal to the geometrical centre of the object. This doesn’t stand completely true as the engine is very heavy when compared to the empty body behind therefore after calculating the Geometrical centre of the car, the COM should be moved a bit forward towards the engine to make the assumed COM closer to the actual COM of the car. This will be done based on assumptions purely.
A little more accurate version of this would be to get the get the geometrical centre of all the components of the car separately. Give them a specific assumed mass based on what material they are made of. A main COM based on the geometrical COM can be calculated by taking the medians of all the component points; this can be called as the temporary COM. All the individual points can be plotted as vectors pointing to the temporary COM with their masses as magnitude of the vectors. The temporary COM is to be pushed closer to a point with higher mass value and this should be done for all the points present to get the final COM of the car.
H.5 Weight Transfer
The car’s mass is balanced on four wheels of the car, when the car accelerates or brakes, the weight is pushed front wheels to the back wheels. The same thing happens in a lateral way when the car is taking a turn. This happens due to the COM of the car shifting inside the car. This is also responsible for car skidding when taking sharp turns.
Consider this car braking at 1 G. This means that the braking force is equal to the weight of the car. The Black and white circle in the centre of the car is its COM and G is the gravitational force that is pulling the car down. is the lift force exerted by the ground on the front tyre and is the lift force exerted by the ground on the rear tyre. These forces keep the car falling through the ground to the centre of the earth. The imbalance of these forces results in oversteers and understeers.
When there is no motion the weight distribution can be considered to be equally distributed, therefore
=Braking force on the front tyre
=Braking force on the rear tyre
Braking causes the COM to be pushed forward thus increase the weight on the front tyres and lifting off weight of the rear tyres. Braking force acts at ground level on the tyres but the COM is in the centre of the car which gets pushed forward; this causes a turning effect or torque. It is for the same reason that low cars have less chance of toppling over at turns because their COM is closer to the ground therefore reducing the distance between the braking force and the COM.
Breaking Torque is proportional to and Height of COM
Counter Torque is proportional to
For example (not specific to the car in game) consider the height of COM h to be 20 inches, wheelbase to be 100 inches and the mass of the car be 3200 pounds.
As Described above,
Substituting above and solving gives =960lb
Therefore an extra 640lb is put on the front tyre and 640lb of weight is removed from the rear tyre.
From this, I conclude that when the car is turning, the wheels on the outer side of the run get heavier and get more grip and when the car brakes, the forward wheels get heavier and get more grip. This also tells that when the COM is moving in the above described positions, it is creating a torque force which if exceeds a certain limit would topple the car.
H.6 Tyre Grip and Braking
Tyre grip is based on two factors; the first one is the coefficient of friction between the tyre and the surface and secondly on the weight applied by the car.
The slip of the tyre can be measured on different surfaces as g values. A tyre with higher g will slip lesser that a tyre with lower g. This means that it can hold up to g amount of force in the sideward direction.
This frictional force is applied as a negative force in the opposite direction of the car’s direction which the car has to overcome to move forward.
The frictional force can be calculated by
=Coefficient of friction between the tires and the surface
=Normal force, which is the weight of the car acting downwards
From this it is understood that frictional force depends on the weight of the object, so when the car takes a turn the outer wheels get heavier and have more frictional force.
Tyre grip between different surfaces is approximated and the values can be used to calculate the slip of the tyre. For average tyres this value ranges from 1.2g to 1.7g on tar roads.
Consider if our tyre has a grip of 1.2g, then it would decelerate the car at the rate of
1.2*9.8 = 11.76 . This value cannot be considered static as the weight transfer would change the grip on tyres and therefore also affect braking force.
H.7 Centripetal Force
When a vehicle takes a turn it pushes the COM of the car outside due to inertia. This is a force away from the direction of the car and pushes on the tyres towards the side. If this force becomes greater than the tyre’s grip force the tyre slips.
The Acceleration needed to keep a vehicle at velocity V to go in a circle or radius r can be calculated this way (Below)
Consider a small change in time dt to move a small distance dx. Then from the speed distance equation
Consider a small change in sideways distance ds, then the side velocity will be
The sideways acceleration for this would be Equation 1
If we go forward by a fraction of radius then we must go sideways by the same fraction of dx to stay in the circle.
Substituting equation 2 in 1 we get
This again tells us that tyre slip is a square function of velocity and greatly gets affected by a slight increase in velocity.
For example consider two tyres of grip 1G and 2G, and then we can calculate their minimum turning radius before they slip off.
Minimum turning radius->
Graph at 1G
Speed in x10 m/s->
These calculations are not accurate as the grip of the vehicle tyres does not remain constant at turns and braking. The grip of all four wheels is dynamic and this change has to be taken into account. To keep the vehicle simulation very simple, we can calculate the weight on every tyre and calculate weight transfer. If for example all tyres have 600kg weight each on them. Consider all tyres to have a grip of 1G. Then it can be said that at 600kg the tyre has 1G grip. Then from the weight transfer we can get how much extra weight has been put on the tyre and from that we can get the increased grip based on that. Example the side tyres get an extra 300kg weight on them, then their grip would be 1.5g and the others tyres grip would fall off to 0.5g. From this it can be noticed that weight transfer causes grip transfer also at the same ratio.
H.8 Rolling Resistance
Rolling resistance is the resistance or frictional force of the wheels with the surface when they are in motion. Coefficient of rolling resistance is a constant which depends on the friction between the two surfaces.
Force of rolling resistance can be calculated by
=Force or rolling resistance
=Coefficient of rolling resistance between the two surfaces
= Normal force applied which is the weight of the car
This is force acting in the opposite direction of motion of the car; the car also has to overcome this force to move.
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