Hey give the guy a break, the title of this thread is "LANE FORMULA" that's exactly what he supplied with a little sarcasm added for flavor.
Hey give the guy a break, the title of this thread is "LANE FORMULA" that's exactly what he supplied with a little sarcasm added for flavor.
You should ask the walkers to move to lane 2-3 where they belong.
mrr82 wrote:
Actually it does make a difference..you could have turns that are 1 meter long which leave for 199 meter straight aways...and the different would be less then a meter...and this changes as the turn gets bigger or smaller...The size of the curve is an important variable despite what you think.
Even if the turn is 1 meter long, if you move to lane two (assuming the lanes are a standard 1.25m wide), then you have added 2.5m to the diameter of the circle.
PI*d = circumference. In this case 2.5*3.14159=7.85m(approx), no matter how "long" the turn.
The point here is that it is the width of the lane, not the diameter of the circle that is important.
Of course, you are correct if you are saying that if one had an 8 lane track that is only 1 meter wide (silly, but nonetheless), then the difference between running in lane one and two would be 0.785m (assuming equal lane widths).
However, this example shows that the extra distance run is a function of lane width, not length of the turn.
It's 2 times the width of the lane times pi. It doesn't matter the size of the circle or the length of the straights. If you fly 1.25 meters above the earth, you add the same 8 meters to the distance around.
Okay, new math lesson:
You want to run on a track for which 1 lap is 26.2 miles instead of 400 meters. You move out a lane to avoid the walkers. How much farther do you run?
Change in distance for each lane = 2*(pi)*w
where pi=3.14159265358979
w=lane width
Note that the same formula works for a 200 meter track as for a 400 meter track, as long as the width of lanes stays the same around the track (this precludes lanes with sharp corners).
Pete wrote:
malmo, where are you? We need you to sort out the math for us again.
i thought that you claimed to be an engineer, Pete?
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 loop-the-loops 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, east-west or north-south, across mountains or on flatland, your head will travel exactly 2*PI*d further than your feet.
Yep, where "d" is the distance between the lanes (lane.width*#of.lanes.away). The ONLY requirement for the 2*pi*d formula is that the lanes be a constant width. Unless the custodian who applied the paint/chalk was drunk or had a warped sense of humor, this should be the case.