I'm developing my first game containing player controlled cars, and therefore ofcourse I need proper car physics. I've got basic car accelleration and turning done, however, no skidding is currently done.
Basically, when a driver drives a car at n speed and applies the brakes 100%, the car will skid IF the friction between the tires and the road isn't enough to hold the car that is still going forward. If the friction is large enough, it would stop at once (like when driving at very slow speeds). When you turn a force is trying to press the car out of the road (when you turn left, the force is pressing the car against right; out of the road). If the friction between the tires and the road is enough to hold it back, the turn goes smoothly, if not, the car will skid against right, uncontrollable if not ABS brakes. That's what I know, so no need to teach me that again.
What I wonder about is ways to calculate this properly (please give me nothing but proper equations/values, otherwise i get a problem getting this done). Basically a way to calculate the breaking resistance (percentage of speed before calculation is the result? per second?) when skidding (time=v*friction, however, that's the time), and to calculate when the breaks are applied too hard, so the car starts skidding (force pushing car forward too much for friction between tires and road to handle). I take things like grass, asphalt, wet asphalt, sand, snow and ice does have different friction values against a normal tire too. Also at some angle, at some speed, the car will probably also stop skidding before it has stopped fully after the breaks are released, so some algorithm to find out about that would also be nice. I don't need more values than velocity and how hard the breaks are applied (percentage 0-100% maybe) I hope, or? Air resistance is done later, and will be applied globally.
That's one of two problems, the next problem is (sharp and fast) turning. I need a way to find if the force pushing trying to push the car out of the road is higher than the friction between the tires and the road, to trigger skidding (accelleration on unrelieable surface; ie ice, can trigger this too I know). The velocity, and the frontwheel angle would be nice values to calculate this from I guess.
Please don't come with waaaay toooo complicated answers, as I'm only 15, and haven't learned anything about this on school (none of my teachers knows this stuff either).
Help is appreciated :)
Added: It's a 3D game!
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try these 2 links
1. A pdf about realistic trans/rotation of a disc
http://www.physics.emich.e
2. http://www.innerauto.com/i
has an overview of car brakes and animations
I've never done a racing game before but I always wanted to.
For a first step, try to write an algorithm that calculates the car's lateral G's as a whole. When the lateral G value exceeds .9, for example, switch the car into a partial slide (sliding more & more depending on the lateral G value). When the car starts to slide and you straighten the steering wheel a little, the lateral G's which naturally fade until the car falls beneath .9 G's for example, then you can switch the car back into a straight path. Those transitions between sliding and not sliding will take a lot of tweaking to get it right.
After you pass that hurdle, then you'll have to use the same technique with all 4 tires independently and do a lot more calculation to get the car to drift, powerslide, etc.
This task will take a lot more than simple formulas... it'll take lots of time & experimentation.
(for the diagrams you need to copy and paste this into a text editor and use a fixed width font such as courier for it to line up properly)
Friction
max Fr = μR
max Fr = the maximum force due to friction
μ = the coefficient of friction
R = the reaction of the car on the road
For this it is easier to think of the car, C as a particle rather than an object with 4 wheels, ie the car has a constant centre of gravity.
R
^
|
----- --> v
| C |
-------------- μ
<-- F
eg a car C travelling at velocity v
ie
the maximum Force due to friction =
the reaction of the car on the road (which will be equal to it's weight)
* the coefficient of friction between the car and the road
μ will be different for each type of surface but is typically a small fractional value
Acceleration / breaking
You will begin to skid when the force due to breaking exceeds the maximum force due to friction.
This can be worked out by the change in momentum of the car.
F = | mv - mu |
| ------- |
| t |
F = the breaking force
m = the mass of the car, C
v = the final velocity of the car
u = the initial velocity of the car
t = the time taken for the change in velocity
This can be applied to acceleration as well as breaking (ie wheel spin when accelerating). Don't forget to take the modulus / absolute value as it's the value of F you are after to check against the maximum frictional force rather than the sign (eg breaking will give you a negative value).
Turning
Turning effectively makes the car C travel in a circular motion and therefore centripetal forces apply.
(bah! you try drawing a circle using text :p)
---------- v
/ \ ^
/ \ |
| | |
| |---|
| max Fr <-- | C | ---> F
| |---|
| |
\ /
\ / (circle has radius r)
----------
F = m * v^2
-------
r
(v^2 = v*v)
F = the centripetal force pushing the car outwards
m = the mass of the car C
v = the velocity of the car
r = the radius of the circle that it's travelling round
max Fr is the maximum force due to friction
When F is greater than max Fr you will spin out
Here's a proposal for a SIMPLIFIED physics model
2 variables:
lateralG (positive=G to the right, negative=G to the left)
slidemovement (positive=slide to the right, negative=slide to the left)
lateralG is the lateral load applied to the tires. for our game, we'll make it a function of speed an steering wheel position.
slidemovement is the speed of the sliding motion.
as long as lateralG is whithin the max lateral load of the tire (say 6G), slidemovement will stay 0.
when the max lateral load is exeeded, stop increasing lateralG and start increasing slidemovement instead.
It's like having 2 glasses of water. When the 1rst glass is full (lateralG), go to filling the 2nd glass (slidemovement).
i'd make a 2 wheel model of the car (front and rear) instead of just a one wheel model. this way you can change the maximum G of the front and rear of the car during acceleration/braking to simulate the effects of wheight transfer. you would have a car that oversteers (tail slides) during heavy braking. oversteering will make the player happy :-)
Wheight transfer means that in real life, when you brake, you'll have more weight on the front tires and less on the rear tires. this will effectively increase the max G load of the front tires and decrease that of the rear tires, which will result in tail spin if you turn hard while braking. The inverse effect is observed during accelaration.
You should also decrease the max G of the rear under low speed heavy acceleration to simulate the effect of loss of traction under heavy acceleration on a rear wheel drive car. do the same with the front for a front wheel drive car.
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by: ozoPosted on 2004-07-25 at 01:15:06ID: 11631017
to first order, skidding will start when the accelleration exceeds the coefficient of friction of the surface.
On wet surfaces, you can also hydroplane above a critical speed.