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In motorcycling, Apex can be defined as:
In motorcycle racing, the racing line is the route the motorcycle must take in order to minimize the time taken to complete the course.
When looking at a single corner, the optimum line is the one that maximizes the motorcycle's speed throughout the whole corner (please note, this does NOT mean entering the corner as fast as possible). If one used the path with the smallest radius, that would minimize the distance taken around that corner. However, by fitting a curve with the widest possible radius into the corner, the higher speed which can be maintained more than compensates for the extra distance travelled.
The apex is often, but not always, the geometric center of the corner. Within the context of motorcycling, the apex is referred to the point where the motorcycle is closest to the inside of the corner and not necessarily the center of the corner. Because of motorcycles' need to lean through corners and the risk associated with the lean, it is desirable to limit the time leaning over as much as possible, as such it is a popular technique to delay the apex, the point where the vehicle is closest to the inside of the corner, until some point in the second half of the turn. Passing over the apex allows the motorcycle to take the straightest line and maintain the highest speed throughout the whole turn. The apex is also the tightest section of the corner.
In order to maintain optimal line, the motorcycle rider will position the motorcycle on track toward the outside edge of the corner before entering the corner, and turn into the corner intending to follow the path he/she plans to take through the apex. Depending on timing and speed of turn in, as well as steering input, the rider attempts to guide the vehicle through the chosen apex, often on the innermost edge of the corner. After hitting the apex, and upon exit of the corner, the rider lets the vehicle move back to the outside edge of the track, allowing the motorcycle to follow the widest, straightest path through the corner.