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# A Timed Corner

Figure 10: Illustration of Driver A's speed through the corner. After the time-gate, he is able to maintain speed briefly before braking, turning the corner at a relatively low speed, and then accelerating once onto the straight. Driver C takes a longer path, but does not need to slow for the corner.

Example Drivers A and B have identical cars that can brake at 1g and accelerate at , and have tyres with coefficient of friction of 1.1. They are timed over section of the circuit, starting 12m before a corner and finishing 12m after it. They pass through the first time-gate travelling at 41.8 mph. Assuming the inner and outer radii of the corner are 15 and 20m, which driver will make the fastest time?

Comparison of cornering times of Drivers A, B, C.

Notes: max. cornering accel. 10.78; accel. during braking -9.8; accel. 4.9; distance from timing gates to corner 12m.

This is how I calculated the table entries.

1. Calculate max cornering speed and time to turn corner.
2. Calculate time to slow to this speed () and distance travelled ().
3. Calculate time to cover remaining distance from first timing point at constant speed.
4. Calculate time to accelerate towards the second timing point (solve for t). Final speed is v=u+at.

After allowing for acceleration and braking times, B is only 0.15 sec (4%) slower despite travelling 30% further. Also, B passes the last timing post moving faster.

Richard Bower
Thursday October 8 16:09:30 BST 1998