The maximum combined cornering force that can be generated by the tyres is , equating this to the centripetal force shows that the maximum cornering speed is
We can drive around large radius corners more quickly (Tipler, p. 114).
Figure 9: Three possible routes around a corner connected by two long straights. Although route A is shorter, the cornering speed is slower. Route C has largest radius and is fastest.
Figure 9 shows three possible lines around a corner. Consider the time taken to complete the curved parts of routes A and B.
Although she takes the longer route, it takes driver B only a factor longer to cover the curved part. Further more, she needs to brake less before the corner, and will start travelling down the straight with a larger initial speed.