[Guest]

Congratulations, you made the 200 meter sprint final in the Beijing 2008 Olympics, competing against 7 other runners, and are given the choice of lanes. Is there a lane you can choose that will give you an advantage? If you think there is then you must be able to show this mathematically, and not formulate potential advantages such as running in the center lane gives you the best view of the field, or in the past most runners who won the race started in lane x. If there is no advantage to lane assignment than hopefully you can state a logical convincing reason why this is so. To put this into perspective you can assume the lane width is about 1 meter.

[TwoaDay]

it depends on personal preference, and i think lane 1 usually has the best view

[Guest]

yes, the innermost lane.

when you run, you move through the air in between each step. you jump from point to point rather than constantly follow your lane's curved line. so, if you run perfectly, your path will not form an ellipse; rather, you will trace the sides of polygon whose vertices are shared with that ellipse. you will inscribe inside the ellipse a polygon with side lengths equal to your stride lengths. not only will the perimeter of this polygon be less than the perimeter of the lane's ellipse, it will be less than half than that of a polygon of equal side lengths inscribed within an ellipse having twice the perimeter. essentially, by jumping, you are able to cut out a bigger chunk of that ellipse than would be possible in a larger ellipse. (imagine a small ellipse, perhaps the size of a table. you can technically run around it in two quick steps-- just jump from one side to the other. you have reduced your running distance from the perimeter to the distance across. now imagine a much larger ellipse. you can't cheat to quite the same extent.) i'll leave the math up to the rest of y'all.

Edited August 19, 2008 by HotMarmalade

[Guest]

Lane 7. Because the 200 meter event takes place on approx. 115 meters of curved track, your feet will have to cover a slightly different distance. Your inside foot will run the inside measurment of 115 meters, but the outside foot will have to cover just a bit more. In lane 1 the difference between the outside foot and inside foot is over 3.1 meters more. In lane 7 your still running the same 115 meters but on a smaller fraction of a larger circle, thus the difference between your outside foot and inside foot is only 2.7 meters different in distance. I would choose lane 7 for that reason.

[Guest]

Well, it is the Olympics...

A bunch of smart people probably calculated the distances a while ago, when they decided to have the runners start along a curved section of track. It's the Olympics, of course everyone has an equal chance! I'd imagine that they calculated the distances (assuming 1m lane width) at about 0.2m from the inside radius of each lane, which is about where the runners run to minimize their distance (but avoid stepping on the lines).

I would choose lane 7. While the distance is the same, lane 7 is the outermost curve, meaning a larger radius. I think I can run faster in this lane because I don't have to turn as sharply.

Maybe I'll get a better time in lane 1 because my strides "jumping" will have more of an effect. Smaller radius, easier to cut corners. But, if I were an Olympic sprinter, I would be out running instead of typing...

[Prof. Templeton]

Hmmm...I might be able to plot a shorter course on the inside lane, however,maybe there's less centrifugal force in the outside lane. I don't think it more beneficial to chose a track. The inside lane might be the shortest plotable route by taking tangetal lines along the inner track lane boundary, but the angles between lines might slow you down, and centrifugal forces may not be a large factor. Takes pencil out from behind his ear. Ummm, I'll get back to ya.

[Guest]

I was just asking my fiance this question only hours ago.

The inner lane has an advantage. Despite the fact that each starting line is staggered the outer lanes require a greater distance to be ran before the winner crosses the finish line. Staggering the finish line would not balance the distance to be ran because each outer circle is progressively larger. However, the finish line does run straight across the track.

I do not know how to put that into a mathematical equation.

That's GOTTA be right, I used to run track and when I presented the idea to teammates/rivals, it was not conflicted.

Edited August 20, 2008 by mswelldone

[Guest]

yes, the innermost lane.

when you run, you move through the air in between each step. you jump from point to point rather than constantly follow your lane's curved line. so, if you run perfectly, your path will not form an ellipse; rather, you will trace the sides of polygon whose vertices are shared with that ellipse. you will inscribe inside the ellipse a polygon with side lengths equal to your stride lengths. not only will the perimeter of this polygon be less than the perimeter of the lane's ellipse, it will be less than half than that of a polygon of equal side lengths inscribed within an ellipse having twice the perimeter. essentially, by jumping, you are able to cut out a bigger chunk of that ellipse than would be possible in a larger ellipse. (imagine a small ellipse, perhaps the size of a table. you can technically run around it in two quick steps-- just jump from one side to the other. you have reduced your running distance from the perimeter to the distance across. now imagine a much larger ellipse. you can't cheat to quite the same extent.) i'll leave the math up to the rest of y'all.

Wow, great answer and I did some of the math before posting the puzzle. Based on some assumptions regarding lane width, determination of distance in each lane, radius of curvature, stride length and angle of curvature, I roughly think the inside lane gives a .005 meter advantage. This could relate in a decreased time of about .0005 seconds. Unfortunately I think they are displaying times to only the one hundreth of a second but this could allow an advantage when the one hundreth is rounded from the thousandth to become significant. I doubt the race officials are too concerned about this. I also have noted that when there are only 8 competitors they use lanes 2 thru 9 and leave lane 1 open, so maybe they are aware of this minute advantage.

[Guest]

I think that 5mm difference would be much less than differences in the way your leg muscles and joints are in action when you are running around a smaller radius. It would probably even be smaller than the differences in the air resistance caused by your position in relation to the other runner.

[Guest]

I think that 5mm difference would be much less than differences in the way your leg muscles and joints are in action when you are running around a smaller radius. It would probably even be smaller than the differences in the air resistance caused by your position in relation to the other runner.

I agree with Chuck, not an exploitable advantage, but still an interesting outcome. Thanks to all who chimed in on this one.

[Guest]

I think that 5mm difference would be much less than differences in the way your leg muscles and joints are in action when you are running around a smaller radius. It would probably even be smaller than the differences in the air resistance caused by your position in relation to the other runner.

I would say air resistance has the most importance in how fast your time is. For this reason, I would say one of the middle lanes gives the best performance, where the air is being cut into by the outside runners at first, but the tight curvature of the innermost lane doesn't impede your performance too much. My choice for ideal lane would be about 5 or 6.

[Guest]

while we're on the topic of negligibly minute advantages in track and field:

http://www.cbc.ca/olympics/athletics/story...l-research.html

[unreality]

^ interesting I like the speaker-behind-them idea

anyway, for the original problem, as someone said, it IS the Olympics and each lane is staggered to be the same distance to the finish line. The only other thing is your personal preference based on how you run and you want to run the race. Sharper curves or wider curves or middle curve, it all depends on the individual's running style, even though the changes between are pretty minute. To whoever said that the distance is more in the outer lane: it's not. Track lanes are staggered mathematically for the same distance. I think the OP was focusing on factors like wind, joints, running style, etc, which would vary with each athlete

[Guest]

^ interesting I like the speaker-behind-them idea

anyway, for the original problem, as someone said, it IS the Olympics and each lane is staggered to be the same distance to the finish line. The only other thing is your personal preference based on how you run and you want to run the race. Sharper curves or wider curves or middle curve, it all depends on the individual's running style, even though the changes between are pretty minute. To whoever said that the distance is more in the outer lane: it's not. Track lanes are staggered mathematically for the same distance. I think the OP was focusing on factors like wind, joints, running style, etc, which would vary with each athlete

I wouldn't say that it is all personal preference. It is a generally accepted fact among the trackies of the world that the innermost few lanes are pretty crappy draws.

For this, I like the Prof.'s explanation of centrifugal force (or more specifically, centripetal force). To keep yourself at the same speed on a tighter radius curve requires more inwards force, which is proportional to one over the radius squared. All the effort you put into maintaining that inwards force to keep you on the track is a little less effort you can put into driving yourself forwards.

[Guest]

I think also, you need to rember mental. I would choose either 4 or 5 to give me the best view of my competitors. But this question is only relevent IF every single competitor is identical (i.e. same tactics, same speed, same acceleration). Personally, i don't think it makes too much of a difference. Also aren't lanes worked out on qualifyiing?

[Guest]

another interesting variable to add to the mix: "Rules specify that a lane's length is not measured around the outer edge of the lane's inner boundary but around an undrawn curve, called the measure line, which is 20 centimeters outside that outer edge." the lane measurements make an effort to trace the path that runners tend to actually follow, rather than the lane boundaries. this leaves open the possibility that somebody could run less than 400 meters by running less than 20 centimeters off their lane's inside edge. theoretically, of course, they could even make every step a fraction of a millimeter off the tape. by doing so, an inner-lane runner would achieve an advantage over an outer-lane runner by "cutting out" a greater proportion of his/her "measure line".

but i agree with those posters' previous statements that these considerations are quite minute compared to the psychology and range of vision involved with lane assignments. and for that reason, yes, i believe that lanes 4 and 5 tend to be most preferred.

[Guest]

another interesting variable to add to the mix: "Rules specify that a lane's length is not measured around the outer edge of the lane's inner boundary but around an undrawn curve, called the measure line, which is 20 centimeters outside that outer edge." the lane measurements make an effort to trace the path that runners tend to actually follow, rather than the lane boundaries. this leaves open the possibility that somebody could run less than 400 meters by running less than 20 centimeters off their lane's inside edge. theoretically, of course, they could even make every step a fraction of a millimeter off the tape. by doing so, an inner-lane runner would achieve an advantage over an outer-lane runner by "cutting out" a greater proportion of his/her "measure line".

but i agree with those posters' previous statements that these considerations are quite minute compared to the psychology and range of vision involved with lane assignments. and for that reason, yes, i believe that lanes 4 and 5 tend to be most preferred.

I also heard the NBC Beijing Olympic commentators mention, just before the start of the 200 m final, that a world record has never been set running an inside lane. During the race 2 runners got disqualified for stepping on the inside lane boundary, obviously trying to shorten the distance they had to run.

[Guest]

it is posssible to set up a straight 200m like the leter p - straight addition instead of oval - like the 100m but extended

[Prime]

If I made finals, I would choose the line in which I already ran and won. Another possibility is to make a note, which is the preferred line of the favorite in the competition, and grab his line. Another more serious, variation -- to choose the line next to favorite (if he gets to choose after you), so that you can compete close to him.

Also, isn't 200 m run in a straight line without any turns?

[Guest]

Great post regarding loudness of starter gun resulting in a kind of instinctive start. Not only would I, as the inner runner, hear the loudest report, but I would hear it first. I'd take the inner lane for sure.

Edited August 24, 2008 by Geneass