Trailbraking is a term used to describe carrying the braking action of a vehicle past the turn entry.
In motorcycle parlance, the rider applies either or both brakes at varying braking pressure between the front/rear. The pressure to use is determined by the rider's entry speed, lean angle, and other factors. The use of trailbraking allows the rider to adjust speed all the way through a turn, and can allow the rider to set the motorcycle's cornering speed at the apex of the turn -- the slowest point of a corner -- or even past the apex, if necessary.
This technique is commonly used when racing, but can enhance control and add more evasive options for advanced street riders.
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