How far is 1 lap in lane 8 on an outdoor 400m track

flatfeet wrote:

So, if I want to run miles on a standard high school 400m track (with no curb) ... AND get my 440y splits at the same spot on each lap ... I would run in the outside two-thirds of lane one.

Exactly correct. The line of measurement for the 400 meters lies exactly 10 cm (I think) to the right of the inside (left side) of lane 1. The line of measurement for the 440 yd distance (thus make 4 laps exactly a mile) is about 2 feet to the right of that, BUT STILL INSIDE LANE 1.

dukerdog wrote:

All curves are made up of circular sections at the differential scale.....

What happened to kartelite?

Yeah that's basically what I meant...you had mentioned earlier that it didn't matter the shape of the track, and it doesn't as long as at every point the shape is differentiable (curved). You may be able to get away with not being differentiable, as lanes on a track technically aren't the whole way around (where the turn becomes a straightaway)--but I'll have to think about that.

Malmo, I wasn't disputing what dukerdog said, I was just conditioning it on curved turns. Obviously, lanes around a square will not be of uniform length, as the corners will be sqrt(2) times as long. If the general shape is square or triangular, that's not a problem.

Not sure what you meant by what happened to me...

And so how far IS lane 8?

Just wondered...

Ya know (no joke), I went to bed last night and two thoughts hit me: First, this entire non-normal track shape thing is just ridiculous as it is so impractical.

Second (and directly related to the first), if you started adding lanes to an elliptical base lane, you wouldn't necessarily get larger and larger ellipses if you created them by keeping the line width constant, as measured by a line perpendicular to the tangent of the previous lane (although it looks that way if the eccentricity difference isn't too great). In other words, you can't make a true elliptical track this way (all lanes elliptical), so WE'RE ALL WRONG. We're arguing about something that doesn't exist, not to mention something that the original poster doesn't give a rat's behind about.

Did someone out there with an advanced math degree point out that triangles don't have 360 degrees as was implied?

thank you to everyone who posted on this question I had. I'm going to use the 446m's to work out my training times.

alot of responses to the question...huh handy

Anyone else ever run at the 1st modern olympic track in Athens? That is the track with the shortest turns ever (and only 4 lanes if I recall correctly)...they are going to finish the marathon on it next summer.

Only that you were the first person to agree that the track shape doesn't matter, but then you disappeared before helping to argue the point.

The discussion is about the fact that with any shape track the difference between lanes 1 and 2 is given by

2*PI*w, where w is the width of the lane. The "concentric" ellipses was just one case that we thought was an example of this, but as we have both pointed out, is not, because the lane width would not remain constant. If you also believe that 2*PI*w is valid for any shape track, I don't think there is anyone still arguing against it.

I think we can all agree that we stopped talking about anything practical a long time ago.

HS Guy wrote:

Did someone out there with an advanced math degree point out that triangles don't have 360 degrees as was implied?

WRONG

The three inside angles that make up a triangle always add up to 360 degrees (assuming Euclidian geometry - ie: flat surface). Just as the 4 inside angles of any rectangle always add up to 360 degrees and the 5 inside angles of any pentagon always add up to 360 degrees, and the six inside angles of ......

and so on and so on.

From:

http://www.mathsisfun.com/proof180deg.html

This is a proof that the angles in a triangle equal 180°:

From the rules of angles when a line cuts two parallel lines we can show that the angles of the triangle

a + b + c = the angle on a straight line = 180°

Martin

Snowbear wrote:

HS Guy wrote:

Did someone out there with an advanced math degree point out that triangles don't have 360 degrees as was implied?

WRONG

The three inside angles that make up a triangle always add up to 360 degrees (assuming Euclidian geometry - ie: flat surface). Just as the 4 inside angles of any rectangle always add up to 360 degrees and the 5 inside angles of any pentagon always add up to 360 degrees, and the six inside angles of ......

and so on and so on.

My bad. The sum of interior angles in a triangle is 180, not 360. I will now shut up and go crawl in the corner.

HS Guy wrote:

Did someone out there with an advanced math degree point out that triangles don't have 360 degrees as was implied?

No one "implied" that the sum of the angles of a triangle is 360 degrees. That's just silly. We were talking about the sum of the arcs on the OUTSIDE if you were to, for whatever reason, construct a triangular track. Each of the arcs at the turns would start at a line drawn perpendicular to each side of the triangle.

The formula 2*Pi*W is irrefutable. For 42 in lanes the answer is 46.93 meters.

dukerdog just took the thing to the next level, suggesting that it doesn't matter what the shape of the track - just as long as you make a 360 journey. He right. SO simple yet so complicated to some.

I think I have a way of illustrating this for you. IF your arms were 7.469 meters long (the width of the track from the inside lane to the inside lane of the eighth lane..42 in = 1.067 meters x 7 = 7.469). If you extend your right arm out and rotate to the left 360 degrees you hand would travel 46.93 meters further than your shoulder. 2*(Pi)*7.469. AGREED?

Let say you go for a walk around the track, holding your arm out to the right, your hand travels 46.93 meters further than your shoulder.

Make a turn and cut across the infield? Doesn't matter - the result is the same.

Now, hold your 7.469 meter arm out to the right and go for a random walk, turn right, turn left, go ten miles and not even return to the start if you choose - JUST as long as the net result is a 360 degree turn, relative to the starting point, the difference between the journey traveled by your shoulder and hand is still 2*Pi*W or 46.93 meters.

How the heck can this still be going? I thought I'd seen it all on these boards. Guess not.

I agree

At the risk of sounding arrogant -- I thought I'd answered the original question on the second post of the thread ... and here we are 77 posts later.

Still, Socratic debate and all that ...

Martin

You did answer it right away! This is Letsrun - no one wants to believe the simple answer. 78th post.

Has anyone seen a double-bend track before? Assuming an equal quadrant makes the calcs easy but most tracks aren't equal!

http://www.ustctba.com/guidelines-track/section3a.html

1. Equal Quadrant Tracks - which are 400m or 1312.34? (minimum distance) tracks with 100m along each curve and 100m along each straightaway, measured along the measure line of lane one.

2. Non-Equal Quadrant Tracks - which are 400m or 1312.34? (minimum distance) tracks, measured along the measure line of lane one, with two curved ends of equal radius and two straightaways equal in length but longer or shorter than the curves.

3. The IAAF Track - which specifies a 400m or 1312.34? (minimum distance) track, measured along the measure line of lane one, with two curves of equal radius measuring 36.80m and two straightaways measuring 84.39m.

4. Double-Bend Tracks - which are 400m or 1312.34? (minimum distance) tracks measured along the measure line of lane one, with two straightaways of equal length and two curves that are formed with two different radii. This configuration allows for a wider infield to accommodate a broader range of sports activities.

Track aren't measured on the line. They are measured 7.87 inches outside the line.

I think somewhere around the top of page 3 I warned that this was getting pedantic. Well, we definitely crossed that line! What threw me was when we started talking about an "elliptical track". There are at least two possible definitions of this. As an example was given using a calculator to find the circumferences of two ellipses, I assumed that we were talking about a track in which all lanes were ellipses, and in such a case the formula doesn't hold (as shown). Of course, to make such a track you'd have gaps between the lanes at certain spots in order to keep the actual lane width constant (imagine the lane stripe getting wider and thinner). Amazingly impractical. OTOH, if the definition of an "elliptical track" is "first lane is an ellipse and all other lanes simply wrap around it keeping the distance between lanes constant" then the formula does hold. That makes perfect sense because by a simple extension in this manner, you are basing the new lane on circular subsections of the first.

My point was always that if all the lanes follow some curve other than a circle, the result will be different than 2pi*diff. BUT, I never meant to imply that drawing an arbitrary simple closed path and then wrapping the other lanes on it wouldn't work. If each lane is described by the same general equation (such as an ellipse, or even something weird like a couple of 3rd order polynomials) then in general, it won't work. Why would it? Each lane wouldn't be related to the other via 2pi. I think most of the argument here has been over misinterpretation. That, and a perverse desire to "prove the other guy wrong".

As long as we're talking about impractical tracks, I think we should consider over-and-under style tracks, bridged figure-8 being the most simple. We can then extend the idea into the third dimension by adding hills, ramps, and up/down spirals.

Here's where it gets interesting for the mathematically inclined. Flip the problem backward: We can, of course, create a track whereby each lane has the same circumference by adding appropriate twists and hills! In perhaps the most simple case, we insert a hill in lane 1, a somewhat smaller hill in lane 2, and so on until the outside lane is perfectly flat. Although the distance is constant, the effort won't be because you never get out of a hill what you had to put into it. Thus, the better question is how do we make a flat track where all lanes are the same length? I'm thinking in terms of an infield "bulge" that gradually disappears toward the outside lane (think kidney bean). A flat figure-8 track would work too, but collisions might be a problem.

Imagine a track where all lanes are the exact same length and include the same number of turns of identical radius and also hills and twists, each lane intertwined with the others. Everything is equal. Everybody runs in their own lane, always. Yet nobody would have any clue as to positioning until the finish line. Yeow!

Figure 8 tracks and crossovers - this is sounding a lot like speedskating. While we're at it, let's put ice on the track and make the athletes wear spikes. Then we can get the ESPN guys to market it. Hell, track might become a spectator sport again!

Wayne