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inside lane vs. outside lane
Does anyone out there know how much further it is to run 1 mile in the outside lane of a standard track vs. the inside lane? Or if you know the difference for one lap, I can do the math myself. Just curious. Zilla
i don't know. however, the answer to your question is but an equation away:
Circumference = pi multipied by the diameter of the track
the circumference of the track using the inside lane = 3.14159... * diameter of the track to the middle of the inside lane (or wherever it is that you run)
the circumference of the track using the outside lane = 3.14159 * diameter of the track to the outside lane
so all you'd need to know is how much longer the diameter is for the outside lane. so if the outside lane is ten feet away from the inside lane, that's 20 feet extra in diameter, and over 60 feet per lap. good luck!
The track is an oval (around a football field).............so maybe you know how to measure the diameter of an oval? I don't, got a D in college algebra. Thanks anyway
Zilla
I am pretty sure that one lap on the inside lane is 400 meters, that is why they stagger start races.
okay. so the formula for the circumference of an oval (according to some math homework help site: "We can find the circumference using calculus, but an easier method (although it only results in an approximate answer) is the formula circumference = 2*pi*sqrt[(1/2)(a^2 + b^2)]."
'a' and 'b' are the "semiaxis" lengths. so: 2 * 3.14159 * the square root of ((a squared + b squared)* .5). let's say your track is 100 meters one way and 200 meters the other way. then: 2 * 3.14159 * the square root of ((50 squared + 100 squared) * .5) =
496.72899 meters. remember, this is approximate bec the formula's an approximate formula. the semiaxis length of the inside lane is obviously smaller than the semiaxis length of the outside lane. just calculate the difference.
huh?
that is what i came up w/. you'd have to know the semiaxes lengths to calculate the actual numbers...
I stole this from somewhere else, but it applies:
"There is no such thing as a "standard" track. One look at the track at the Penn Relays and you'll know what I mean. Tracks vary, a little, according to the characteristics of the site. Older tracks were built to be 440 yards, rather than 400 meters, around from the point of the start/finish line against the curb in lane one. Some contractors who build tracks are a bit more precise than others and sometimes the contractor is required to "fudge" a little because there isn't quite enough room in the stadium to get all the lanes they need if they build a track that is exact. So, the start line in lane one for the 400 may be a little behind (infrequently in front) of the finish line to make up for the imperfection. But, if you look at the markings on the track you can generally decypher where the start line for the 400 is in lane one.
The 400 is run with a "one lap stagger." As you realize, each lane as you step out to the outside of the track is a slightly larger circle. To compensate for this, the start line for the 400 (which is run in lanes all the way) in lane two is slightly forward of the lane one start line, so that both (all) runners can run an equal distance and finish at the same line straight across the track. The same applies in each lane as you go to the outside of the track, so that the runner in lane eight is starting in "front" of everybody.
Got that? The distance around the track in lane eight is longer than the distance around the track in lane one by the distance from the lane one 400m staggered starting line to the lane eight 400m staggered starting line (measured in lane eight). The exact difference varries according to the width of the lanes. On a "perfect" track, the lane one staggered start line and the finish line are the same, so there is a line all the way across the track to measure form in lane eight... easy!
Unless you are running for a sanctioned record, in which case you would be running in an event where the officials are responsible for certifying the distance... just figure a lap is about a quarter mile and let it go at that!"
A track isn't an oval. It's straight lengths with a semicircle attached to each end. The only distance you need to get an exact distance would be the width of the track.
Assuming a 15' track width, you just use:
15' * 3.1416 = 47'
Hope this helps.
ddfletch, that's what an oval is. see merriam webster: http://www.mw.com/dictionary/oval
some ovals aren't ellipses, but the formula provided is for an ellipse (like a track).
Original Post by caloriecountingme:ddfletch, that's what an oval is. see merriam webster: http://www.mw.com/dictionary/oval
some ovals aren't ellipses, but the formula provided is for an ellipse (like a track).
Your confusing a mathematical definition with a common use definition. The ellipse and any formula involving a major and/or minor axis is not applicable since the only portion of the track that involves more distance are the semicircles capping the ends. The lengths on the outer and inner edges of the straights are of course identical.
2 semicircles = 1 circle so the extra distance is:
The length of the circumference of the outer edge  the length of the circumference of the inner edge.
Luckily we don't have to know the absolute diameters of the circles, just the difference between the inner and outer.
The formula for a simple circumference is pi*diameter. We know the diameter defining the difference is track width*2 so the final formula for the difference is:
track width * 2 * 3.1416
Hope it was a bit clearer this time :)
don't know what it is in feet or miles, but most tracks are usually 400 meters around for the inside lane with each additional lane being 7 meters longer. (1st lane is 400, 2nd is 407, 3rd is 414, etc..)
Fianlly a straight answer! Yay!
Braodzilla  The straight anwer to your question is that running a mile in the outer lane is the same distance as it is in the inner lane (it's just not quite 4 full laps). I am glad someone finally came up with a number for difference per lap. Just from seeing staggers, I would have guessed 50 meters between the inner and oute lanes, which turns out to be pretty close.
LOL it took you over a year to get your straight answer!
Which I am glad of because I was STILL working on that math formula!!!! LOL
SO........if I run four miles (or 16 laps) in the inside lane it is just four miles but if I run 16 laps in the outside lane it is four and a quarter miles.
I guess I did knid of ask for the math thing. ;)
It doesn't matter how long the straights are or even if they're equal or straight, nor does it matter if the curves are smooth, all that matters is that you make one 360 degree revolution and the lane width is equivalent. The radius of the arch doesn't matter either.
The answer is 2*PI*d, the difference in length between the first lane and any other lane is 2*PI*d.
The track could be crooked, and meandering, or be a figure 8. It could have looptheloops in it, as long as the net result is that the track turns 360 degrees, the difference will be 2*PI*d.
IF you walked around the world in any direction, eastwest or northsouth, across mountains or on flatland, your head will travel exactly 2*PI*d further than your feet.