Vehicle rollover threshold ($v_{\max }=\sqrt{ga{R}_b/h}$)

For a rigid vehicle turning on a level road, with centre of mass height $h$, half track width $a$ and turn radius $R_b$, sufficient static friction supplies centripetal acceleration $v^2/R_b$. The inner and outer wheel normal forces obey $N_i+N_o=Mg$ and $a(N_o-N_i)=Mh{v}^2/R_b$. The inner contact force first vanishes at the displayed speed. The approximation neglects suspension movement and extra torques; inadequate static friction can cause sliding before rollover.