NASCAR drivers drive close to the inside of a track (close to the center) to save their total distance traveled when they can. Runners run on the inside track for the same reason. Is the distance saved a meaningful distance when it comes to, say, 10 laps?
1.
Assume the turns on a track are a semi-circle. The radius for the
inside track is approximately 32 meters and the radius for the outside
track is approximately 40 meters. How many additional meters does a
person run 10 laps on the outside track as the person who runs 10 laps
on the inside track?
We can calculate the extra distance required for one turn, then multiply the result by 20 (10 laps, 2 turns each lap). We do not need to include the straight parts of the track as the inside and outside runners both run the same distance for each of these.
The length around a circle, the circumference, is \(2 \pi r\). The length around a semicircle is therefore \(\pi r\).
The length run by the inside runner is
\[\pi \cdot 32 \text{ meters} \approx 100 meters\]
The length run by the outside runner is
\[\pi \cdot 40 \text{ meters} \approx 126 meters\]
The outside runner runs \(26\) more meters per turn than the inside runner. There are two turns per lap and 10 laps total. That means the outside runner runs
\[26 \text{ meters } \cdot 20 \text{ turns } = 520 \text{ meters}\] more.
1. Assume the turns on a NASCAR race track are a semi-circle. The radius for the inside space of the track is approximately \(0.5\) miles and the radius for the outside space of the track is approximately \(0.51\) miles. How many additional miles does a NASCAR driver have to drive if they drive on the outside of the track, when compared to a driver on the inside of the track?
1. What can race officials do to ensure a fair start for these types of races?