There are three things that a runner can do to increase their speed and decrease their time when running a turn or curve. These are:
On the down swing, throw the outside (right) arm/hand down and back past the hip and out away from the hip. When the hand passes the hip it should be about a foot away from the hip. The inside (left) hand/arm should be kept in as close to the hip as possible. The reason for doing this comes from one of Newton's Laws: For every action, there is an equal and opposite reaction. The reaction to the right arm going to the right is that the left foot will go to the left, keeping the foot plant closer to the lane line.
When the left foot is in the air, turn it slightly to the left--the sharper the curve, the more the foot should be turned. When the foot is planted, the body will automatically align align itself over the foot. Most people automatically do this when they are walking, but not when they are running.
To accelerate when coming out of the turn, make sure that the body is leaning slightly forward from the feet. Almost no forward power can be generated when the body is erect or "standing tall". So, as in the last four or five strides of the sprint start, have a forward lean and then transition into the "standing tall" maximum running speed form.
These are simple, easy to learn techniques that will allow the runner to run a turn faster. However, they must be practiced until they are natural because in the "heat of battle", the mind tends to think of things other than running form.
Try them---they do work.