§ How it works

A car travelling in a circle is constantly being accelerated toward the centre of that circle, even at constant speed. The tires supply this centripetal force sideways through the contact patches.

a_{\text{lat}} = \frac{v^{2}}{r} \qquad\qquad g_{\text{lat}} = \frac{v^{2}}{r\, g}

$v$ : speed in m/s (km/h divided by 3.6).
$r$ : radius of the path the car follows, in metres.
$g = 9.81\ \text{m/s}^2$ , to express the result as a multiple of gravity.

Speed is squared: taking the same corner 10 % faster demands 21 % more grip.

The grip limit

Tires can generate a sideways force of about $\mu m g$ . Set that equal to the force required, $m v^{2}/r$ , and the mass cancels, leaving the fastest speed a flat corner can be taken:

v_{\max} = \sqrt{\mu\, g\, r}

Because of the square root, quadrupling the radius only doubles the speed. That is why racing lines try to open up the radius of every corner as far as the track width allows.

Friction circle

A tire has one budget of grip to spend on braking, accelerating and turning combined. Plot longitudinal and lateral g on two axes and the limit is roughly a circle of radius $\mu$ . This sheet looks at pure cornering, so the dot sits on the horizontal axis; any braking or throttle would move it off-axis and closer to the edge.

§ How it works

A car travelling in a circle is constantly being accelerated toward the centre of that circle, even at constant speed. The tires supply this centripetal force sideways through the contact patches.

a_{\text{lat}} = \frac{v^{2}}{r} \qquad\qquad g_{\text{lat}} = \frac{v^{2}}{r\, g}

$v$ : speed in m/s (km/h divided by 3.6).
$r$ : radius of the path the car follows, in metres.
$g = 9.81\ \text{m/s}^2$ , to express the result as a multiple of gravity.

Speed is squared: taking the same corner 10 % faster demands 21 % more grip.

The grip limit

Tires can generate a sideways force of about $\mu m g$ . Set that equal to the force required, $m v^{2}/r$ , and the mass cancels, leaving the fastest speed a flat corner can be taken:

v_{\max} = \sqrt{\mu\, g\, r}

Because of the square root, quadrupling the radius only doubles the speed. That is why racing lines try to open up the radius of every corner as far as the track width allows.

Cornering G-Force

Inputsdrag · tap · type

Fig. 17Skid-pad view and friction circle

§ How it works

The grip limit

Friction circle

Cornering G-Force

Inputsdrag · tap · type

Fig. 17Skid-pad view and friction circle

§ How it works

The grip limit

Friction circle