# 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 outer lanes would have to run further than the athletes in the inner lanes, because of the semicircles at the top and bottom of the track.

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 (approximately 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

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

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 will be 36.8 + 1.22 = 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

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.

However, 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 radius of the edge. The radius of the inside of Lane 1 is 36.5 m, so the radius of the outside of Lane 1 (which is the same as the radius of the inside of Lane 2) must be 36.5 m + 1.22 m = 37.72 m Area = π × radius2 (read more on the page Circle)

And the area of both straights = 2 × 1.22 m × 84.39 m = 205.9 m2 (to one decimal).

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

 Lane Inner radius Outer radius AIn = Area of circle with Inner radius AOuy = Area of circle with Outer radius AOut - AIn Area of both straights Total area of lane 1 36.5 m 37.72 m 4,185.4 m2 4,469.9 m2 284.5 m2 205.9 m2 490.4 m2 2 37.72 m 3 4 5 6 7 8