tia
tia
Similar questions have been posted many times before. Quick answer is to use the standard lap formula. Works for any well-marked track.
S_L = S_1 + 2*pi*W*(L-1)
Where:
S_1 = Distance around lane 1
S_L = Distance around lane L
W = Width of each lane
L = Lane number
pi=3.14159...
W's can vary, but standard 400m track is supposed to be W=1.22m.
So if you are on a standard track: S_5 = 430.7m +/- 0.1m (assuming lane 1 distance is accurate to better than 1/10th of a meter, and lane widths are accurate to 1cm with no cumulative effect). Of course, how far you actually run depends on where you run in your lane.
What I mean by "with no cumulative effect" is that each lane should be marked-out with respect to lane 1, not with respect to the previous lane.
Buy a Wheel and measure it
Measure the distance from the staggered start line back to the finish line and add to 400m.
I was told it is 28 ft. per lane, per lap. So, if you ran a 400m in lane 5 it would be 400m + 112 ft. which comes to about 437m.
This is what I was taught long ago.
Anyone else?
UPMC wrote:
I was told it is 28 ft. per lane, per lap. So, if you ran a 400m in lane 5 it would be 400m + 112 ft. which comes to about 437m.
This is what I was taught long ago.
Anyone else?
The lane width must be taken into account. All tracks are not created equal.
28ft/lane would be about right if the lanes were 4.5 ft wide. Most tracks, the lanes are closer to 4ft (48") wide, in which case, 25ft/lane would be more appropriate. But I still stand by my original answer, and I don't see that any further discussion adds to it.
Your formula assumes the curves are congruent semicircles. This is not true for all tracks, especially many indoor ones.
depends - are you running relaxed?
There used to be a sign at my high school that said "three laps in lane three = 1 mile", to encourage people not to use lane 1. Haven't beaten my mile PR since. Off topic I know.
Math Mann wrote:
Your formula assumes the curves are congruent semicircles. This is not true for all tracks, especially many indoor ones.
Not true. It only depends on maintaining constant lane widths. You'll note that the formula doesn't depend on the radius of the track. As a result, it can be shown mathematically that, as long as the lane widths are faithfully maintained, the actually shape of the track doesn't matter. Even works if lane one has perfectly square corners, but remember that each lane beyond that will have filleted corners to maintain constant lane width.
Math Mann wrote:
Your formula assumes the curves are congruent semicircles. This is not true for all tracks, especially many indoor ones.
Not so. It doesn't matter what the shape of the track -- as long as the lanes are uniform in width.
ovaltine wrote:
You'll note that the formula doesn't depend on the radius of the track.
S_L = S_1 + 2*pi*W*(L-1)
The final term of your equation is the formula for the circumference of a circle. Doesn't that include the radius?
ovaltine wrote:
28ft/lane would be about right if the lanes were 4.5 ft wide. Most tracks, the lanes are closer to 4ft (48") wide, in which case, 25ft/lane would be more appropriate. But I still stand by my original answer, and I don't see that any further discussion adds to it.
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Yes. I agree.
i measured a typical outdoor 400m track for this same thing last year.
It came out to around 27+ ft. per lap. I rounded it to 28 feet
So, the post stating 28 ft. would be my guess / per lap.
No, it is not the circumference of any circle in the problem. W is the lane width, which is not a radius. Just because there is a 2*pi*width doesn't make it a circumference. pi is just a mathematical number that appears in many mathematical expressions, too many to be enumerated. The fact that the formula can be easily shown to be true for semi-circles doesn't mean it only works for semi-circles.
Then why use pi if the track is square?
Even if lane one is square, subsequent lanes mst be rounded. If they weren't rounded, then the width of the subsequent lanes would not be constant width. They'd be widest in the corners (by sqrt(2)) than on the straightaways.
So we are talking about the circumference of a circle (the rounded corners)?
Simple answer wrote:
Measure the distance from the staggered start line back to the finish line and add to 400m.
The thread should have stopped with this post.
wondering wrote:
So we are talking about the circumference of a circle (the rounded corners)?
A square with rounded corners is not a circle.