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Sixth grade mathematics starting line formula
To determine the starting line, it is necessary to determine that the first runway is the innermost runway, and then calculate the starting line according to the method that the running line extends forward, that is, subtract the curve length of 1 lane from the curve length of a lane, which is the number of starting lines that this lane extends forward. The formula is as follows: wn = 2π [r+(n-1)+0.20]-2π (r+0.30).

1, calculate the runway perimeter (lane perimeter number 1)

(1) Calculation of bend length: The sum of the lengths of two bends in a semi-circular track and field is exactly equal to the circumference of a circle. According to the circumferential formula C=2πr, the length (calculated line length) of two bends in the first lane is 2× 3.1416× (36+0.30) m = 228.08m, and the length of one bend is 228.08 ÷ 2 =/kloc-0.

(2) Calculation of straight line segment

Two straight lines = total length of runway-two curved lines = 400m–228.08m =171.92m;

A straight line segment is171.92m÷ 2 = 85.96m;

(3) Runway length calculation: Runway length = two bends+two straight lines = 228.08m+171.92m = 400m;

2. Calculation of bend length of each branch (taking lane width1.22m as an example)

According to the circumferential formula c = 2π r;

Cn=2π[r+(n- 1)d+0.20] (C stands for curve perimeter, n stands for passing times, r stands for site radius and d stands for lane width);

3. Calculation before the start line extends forward

If two athletes with lane separation run 1 week according to their own lane separation, the athlete with lane separation 2 will run 7.04m more than the athlete with lane separation 1. In order to make the distance of the second lane equal to the distance of the runner running 1 lane, the starting point must extend forward for a certain distance. The distance that should be extended forward is called the number of times to extend from the starting line.

The method of calculating the start line extension is to subtract the curve length of 1 lane from the curve length of a lane, which is the start line extension number of the lane. The formula is as follows: wn = 2π [r+(n-1)+0.20]-2π (r+0.30).