Please help settle an ongoing arguement  when an athlete runs wide around a bend  ie on the first lane line marking , how much further do they run per lap , for an outdoor 400m track ,and a 200m indoor track ? Over the course of a 800 1500 5000 10000 race ,this must add upto a significant distance .
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Run the bends wide how much further run ?
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Re: Run the bends wide how much further run ?
It's not quite as far as you might think, as I believe the track distance itself is measured out about 1 foot from the rail. So it's about a half a lane wide if you run on the first line around both turns. As for the extra distance around two turns per lap, it's easy math for math types so I'll leave that to others.

Re: Run the bends wide how much further run ?
Conor Dary is correct. I believe your 200m track calculation is incorrect. Its twice as many curves but each curve is half the distance.
The following is quoted directly from the "Big Green Book" (its the same in all the previous books (little green, brown,etc.)
As Quoted: Running one foot farther from the curb adds an extra 1.9m (6'3") per 400m. A runner ho is 2 feet farther from the curb will cover an additional 15.3m (17y) in a onemile run. Rounded to the nearest foot:
1ft out: 200m3ft, 400m6ft, 1600m25ft
2ft out: 2006ft, 40013ft, 160050ft
3ft out: 2009ft, 40019ft, 160075ft(Conor Dary)
4ft out: 20013ft, 40025ft, 1600100ft
As easy to remember rule of thumb: Multiply the additional distance from the curb by 3 to obtain extra distance run on each curve. For instance, 3ft out from the curb will cost 9ft per turn9ft for 200, 18ft for 400. End Quote.
It's the same for a 200m track: 2 curves at 1 foot out from the curb = 3 extra feet for the one lap (200m). Hope this helps.
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Re: Run the bends wide how much further run ?
'Conor Dary is correct. I believe your 200m track calculation is incorrect. Its twice as many curves but each curve is half the distance.'
Sorry, Jim but it is the same for a 400 meter track or a 200 meter track, since both consist of 2 semicircles and two straights, the latter of which can be ignored.
We know, 2xpixR = C, thus 1 meter out the additional distance run per lap is
2xpix(R+1)= 2xpixR + 2xpix1
= C + 2xpix1
= C + 6.28.
So the additional distance per lap is 6.28 meters per lap as noted before. And it is irrelevant what R the radius. Therefore, it is the same for any track regardless of its length or length of the curves, i.e. a track made up of one Circle or a Ben Hur type of track with extremely long straights and very tight turns.
Q.E.D.
Jim, after rereading your post again, I realize I had misinterpreted what you had said. Thanks for the comments. Cheers.
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Re: Run the bends wide how much further run ?
Conor, I agree with you and I believe what I stated agrees with you. However, it's possible that I my actual wording wasn't clear enough to eliminate the possibility of a slightly different interpretation. I didn't mean to emphasize the word "distance" when referring to the difference between a 200m and 400m track. Either way, 360 degrees is 360 degrees,regardless of the size / shape of the track. Nice work on the actual mathematical formula.
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