# Car Suspension

Hi All
I'm trying to creater online racing game based on car physics.
My car already running on the straight, but as you know racing tracks had some corners (doh !).
How my model pass the corner you can find in this tread https://www.physicsforums.com/showthread.php?t=117606"
But As i know suspension is not last thing in cornering process and thats a reason why i'm posting this message.
Can anyone can help with such equations that describe how suspension fluent on cornering ?

Thank you in advance

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## Answers and Replies

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Cliff_J
Its incredibly complex.

What happens is that a tire that is flat to the ground gets the most traction, you want the vertical force to push all of the tread area onto the road surface evenly.

Unfortunately, a car in a corner will want to lean, and when it leans so do the tires attached to independent suspensions. This means that one edge of the tire gets more force than the other, which means less traction. In addition, the tire is not a rigid body and flexes allowing more of the force to end up on one edge and not on the other edge.

To counter this, tires can be leaned in slightly (called negative camber) so that in a corner this lean offsets the lean of the car. In addition, spring rates and anti-roll bar springs are used to minimize these effects, and this assumes the center of mass is as low as possible and the suspension is desinged accordingly.

Tires have a grip coefficient where as you apply more vertical force they can generate more horizontal traction, but its not a 1:1 relationship. So if you double the vertical force, you might get 50% more traction. If you cut the vertical force by 30% you might only loose 20% of the traction.

Combined with aerodynamics and the varied suspension designs and settings that have a dramatic effect on those settings, the closest you will come is a rough approximation.

So for your kinematic model, it might be best just to assume that the suspension is an awesome compromise and instead model the traction curve of the tires and then figure in the side-to-side force transfers from the corner itself, any braking or acceleration that causes front-to-rear force transfers, and the exponential amount of force from aerodynamics.

Hi Cliff_J
Thank you for your explanations
I'm not planning to have exact thing, so all i need is just simple factor
that will be based on corner radius and spring\anti-roll bar springs settings

Maybe you can point me on some equations ?

Thank you in advance

Mech_Engineer
Gold Member
c00ler said:
Hi Cliff_J
Thank you for your explanations
I'm not planning to have exact thing, so all i need is just simple factor
that will be based on corner radius and spring\anti-roll bar springs settings

Maybe you can point me on some equations ?

Thank you in advance
Basically, there are no "magic equations" that will solve your problem. You'll have to come up with something simple, where the car's traction is a function of it's centrifugal acceleration or something like that.

You can look at "lateral g-force" ratings of some cars, they drive in a set-radius curve as fast as they can, and measure the maximum lateral g-forces. Sports cars are usually between 0.90g and 1.0g. Race cars can hit upwards of 2.0g depending on the road surface and tire combinations. You could look at a car's maximum straight-line (drag) acceleration and relate it to it's maximum centrifugal acceleration based on some constants.

Maybe just plug in numbers until you feel like it is kind of accurate...