# Car and tire dynamics at the limits of handling (Part I)

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Formula 1 cars can swift through corners at more than 5g, and after twenty years watching the sport, still fascinates me. Really. And it gets even more mind-boggling once you realise that this acceleration is entirely produced by the grip of tires. To push the tires into their operating window and extract their maximum performance is key in Formula 1. All the dynamics, the power of the engine, the energy of the brakes, ultimately is imprinted to the asphalt by the tires. So we need to talk about tires!

In this blog, you will read about how tires generate grip, about what parameters dictate the grip levels, how this grip can be modelled mathematically, how it is effectively controlled by the drivers, and how it affects the car dynamics. This blog is the first part out of two, which covers straight line acceleration and braking. Cornering and lateral forces will be covered in Part II.

There are many articles on internet about tire modelling, but what makes this one powerful, is that through simulations you will see them in action fitted in cars, which gives you a broader insight on how they really work.

# Understanding straight-line acceleration and braking

A tire is free-rolling when it rotates at a rate, ω, such that the points at the contact patch move with the same velocity of the tire hub, v. This rate is ω=v/R. Under these assumption, and if we neglect the rolling resistance, the tire produces zero grip…

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I am an aerospace engineer PhD. passionate about motorsport, learning about vehicle dynamics and optimal control