The Karussell (Carousel) is a famous hairpin corner on the 22km long Nurburgring

Question

The Karussell (Carousel) is a famous hairpin corner on the 22km long Nurburgring Nordschleife (North Loop) racing circuit in the Eifel Mountains of Germany. The corner consists of two racing lines: A bumpy, but heavily banked (20degree) inner concrete surface, and, A smooth and more mildly banked (10degree) outer asphalt surface. The inner concrete surface was originally designed as a drain, however people soon realised it was the quickest way around the corner. Most cars drive on the concrete, however it is quite bumpy and a reasonable amount of ground clearance is required. Assuming that the coefficient of static friction between the tyres of a car and the road is 1.0 (concrete or asphalt), calculate the fastest time possible to drive around the Karussell on each of the two lines. You can assume that a car has a constant speed all the way around the corner, and measure any relevant dimensions directly from the Google Maps image above.

Explanation / Answer

From the Google Image, we can approximate the radius of the asphalt road to be 25 metres and that of concrete pavement be 15 meters.

Coeff. of static friction = 1.0 for both surfaces

Maximum Velocity (V max) around a banked corner is given by the formula

Vmax = [ rg*(sin? + ?s cos?) / (cos? - ?s sin?)]0.5

For Asphalt ( r = 25 m, ? = 10 deg) Vmax = 18.7 m/s or 67.3398 km/hr

For Concrete ( r = 15 m, ? = 20 deg) Vmax = 17.75 m/s or 63.91 km/hr

Considering the difference in the turning curve distance, it will be timing on concrete will be quicker than that of asphalt.

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