# Activity: The Olympic Athletics Track

Have you ever watched some of the races in the Olympic Games and wondered why the athletes don't all start from the same part of the track? |

It is called a "staggered start".

## Why a Staggered Start?

If
they all started from the same line, then the athletes in the |

So each lane has to have a special starting position so they all have to run the same distance.

**Let's learn how to calculate the correct positions
for the 400 m running race**

## How Far?

### How far does each athlete run when he/she completes one lap of the track?

Let's look first
at the route followed by the runner in **Lane 1** (the inside lane).

The rules state that you measure 300 mm from the inner edge of the lane (about where the runner runs).

On the curved sections Lane 1 has a radius of 36.5, but we need to **add 300 mm** for the "running position", for a total of 36.8 m

And together the two curved parts make a See the page Circle to learn more about radius and circumference. |

So, how far would you have to run? Answer: the Circumference of the circle (plus the straight parts)

The radius is **36.8 m**

So the Circumference
= 2 × π × radius = 2 × π × 36.8 m **= 231.22
m**

**Add** the two straight section of 84.39 m:

231.22 + 2 × 84.39 m = 231.22 + 168.78 = **400 m **

Wow! The inside lane is exactly 400 m.

Well, that is how it is designed.

## But What About Lane 2?

Each lane is 1220 wide, so the radius for Lane 2 is 36.8 + 1.22 = **38.02 m**

The radius is **38.02 m**

So the Circumference
= 2 × π × 38.02 m **= 238.89
m**

Add the two straight section of 84.39 m:

238.89
m + 2 × 84.39 m = 238.89
m + 168.78 m = **407.67 m**

That is **7.67 m longer** than Lane 1 ...

... so Lane 2 should start **7.67 m after Lane 1** to be fair

## Your Turn

Can you complete the following table?

Lane |
Radius |
Circumference |
Total
distance |
Staggered Start |

1 | 36.8 m | 231.22 m | 400 m | 0 m |

2 | 38.02 m | 238.89 m | 407.67 m | 7.76 m |

3 | ||||

4 | ||||

5 | ||||

6 | ||||

7 | ||||

8 |

You should have found that the runner in Lane 8 starts about **53
meters** in front of the runner in Lane 1!

- Does that surprise you?
- Is it fair?

It's fair because, with the staggered start, each athlete runs exactly 400 meters.

But some people say that the athletes in the inner lanes have an advantage because they can see the other athletes, and know what work they need to do to catch up.

On the other hand, others argue that the athletes in the outer lanes don't have such tight curves to run. So, unless all races could be run on a straight stretch (like the 100 meters), it will never be totally fair.

## Bonus Activity: Area

You might want to investigate the **area** of each
lane (imagine you want to paint them different colors).

The area is made up of the circular area and the straights.

Remember the radius we used in the first table was 300 mm inside the lane (for the
path the athlete runs), but now we want the The radius of the inside of
Lane 1 is Area = |

And the area
of both straights =
2 × 1.22 m × 84.39 m = **205.9
m ^{2}** (to one decimal).

### You can do the rest! Will the areas be different? By a little, or a lot?

Lane |
Inner
radius |
Outer
radius |
A_{In} = Area of circle with Inner radius |
A_{Ouy} = Area of circle with Outer radius |
A_{Out} - A_{In} |
Area
of both straights |
Total
area of lane |

1 | 36.5 m | 37.72 m | 4,185.4
m^{2} |
4,469.9
m^{2} |
284.5 m^{2} |
205.9
m^{2} |
490.4
m^{2} |

2 | 37.72 m | ||||||

3 | |||||||

4 | |||||||

5 | |||||||

6 | |||||||

7 | |||||||

8 |