How much shorter is the total distance I run if I'm in lane 1 compared to lane 5 on a high school track?

Question

Given that the track is 400 meters and each lane is the standard width - is that 3 feet or 4 feet?

Answer 1

If the track were a true circle with radius r, then the distance run on the inside track is 2 x pi x r. If the outside lane is s feet from the inside lane then the radius of the outside lane is r + s, so the distance run is 2 x pi x (r+s) or 2 x p x r + 2 x pi x s, do the difference is 2 x pi x s. In other words, it doesn't matter what the radius of the track is, the extra distance is always 2 x pi x the difference between the inner and the outer track.

Measure the distance between lane 1 and lane 5 and multiply by 2 x pi. You will find in practice, though that either the start lines are staggered or the finish lines are, so that everyone runs the same distance.

Notice that, since the only significant variable is the distance between one lane and the other, it doesn't matter if the track is an oval, the only criterion is that you run through 360 degrees - in other words, a full circle and, of course that the two runners stick to their lanes.

Answer 2

If it is a perfectly circular track and the middle path of Lane 1 (outermost) is situated R1 feet from the circle's center and Lane 5 (innermost) at R2 feet,

the difference in your actual running length will be

2 x Pi (22/7) x (R1-R2) feet

If an eliptical or other track forms, the calculations will be a bit more complicated.

Answer 3

Okay for SIMPLICITY sake, lets take it like a circle.

The 'diameter' of Lane 1 will be x metres.
Adding the lane width per lane, on each circular end of the track.
Lane 5 will have a diameter of x + 5*3ft*2.

That is the additional distance you have to run per round.

So by calculation, technically, you would have run approximately 10 more metres than thn running in Lane 1.

happy trying.

Answer 4

3 feet.