Measurement technical question from another sport

For a square circuit of 500 meters length, a 5 km race will take 10 laps. The skater will make forty 90 degree turns. If he skates on the centerline of a 10 m wide road, he will be 4.7 m farther out that he would be if he was skating 30 cm from the curb.

Forty 90 degree turns is ten complete circles. Each circle taken 5 m out rather than 30 cm out will be 29.5 m longer than the 30 cm path. Over ten circuits this adds up to 295 meters.

If the 500 m course is measured on the centerline, a skater using the shortest route (30 cm from curb) will travel 295 meters less than 5 km when skating 10 laps.

Other configurations will lead to other differences.

Where can one access in-line skating measurement rules? I was not aware they had any.

In-line skating races seem to be increasingly piggybacked on top of regular footraces. The people who measure the courses can have more work to do if the definitions of the proper measure lines for running and in-line courses are not the same. First, measure the course using the SPR. Next, do it all over again using the middle-of-the-road.

It would be perplexing to both the runners and skaters in a 10 km race if there were two different start lines and a common finish for the same supposed 10 km race.

If the in-line skating event is a stand-alone event, there will be no problem. If it’s combined with a running event, somebody’s got some thinking to do.

Sounds nuts to me. The error you calculated assumes the course has no concave sections. In real life the errors would be larger. It's not just the outer corners of the course. Inner curves, or concave sections, would also shorten the distance. On a wiggly road, and even in Florida we have many, the SPR would be much shorter.

What would be the maximum possible difference?

After thinking about it, taking it to extremes, if the SPR was a straight line, and the road wiggled like a snake, taken to the max without disturbing the straight line SPR, the road edge would look like a continuous set of alternating radius curves, with the curve’s radius bing the road with.

Did a little thinking, if my math and theory are correct, in this case the max difference in measured length is independent of road width. It is 2/pi. An error of 1867 meters on a 5K course. That's quite a bit.

Then I thought of another extreme example, that takes the error to infinity. It's a bit silly but what if the course round and round in a circle. How about a tiny circle? Round and round the circle at the end of my road?
The SPF would be just wrapped round the nail in the middle of the circle and the center line distance would be a circle around that at 1/4 the radius of the circle. The math error gets impossible. Also the same course, moved to a different venue with a larger circle, or dumped in the middle of a large parking lot, changes length.

Why are they so silly as to assume that the blader will not take the SPR? I would if I was in front.

It also seems to me that elevation gains and drops would be a lot more critical to records in that sport. How to measure them accurately is an ongoing problem.

I think they need to take the Triathlon approach. Not comparing records on different courses but records on the same course, year to year. The way to settle the record holder is to have a world meet once a year that is run on the same course each time. This also equalizes for the ongoing upgrading of technology, wheels, bearings, titanium and carbon fiber thingies.

James, you said:

" Sounds nuts to me. The error you calculated assumes the course has no concave sections. In real life the errors would be larger. It's not just the outer corners of the course. Inner curves, or concave sections, would also shorten the distance. On a wiggly road, and even in Florida we have many, the SPR would be much shorter."

I gave the answer to the problem Seutter proposed, not to the problem he didn't propose.

Propose a different problem, get a different answer. The more the curvature, the more will be the difference between the SPR and the middle-of-the-road route.

quote:

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I gave the answer to the problem Seutter proposed, not to the problem he didn't propose.

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You are right, The answer you gave was for the theoretical rectangle. It's just that the math problem seemed ripe for further extrapolation, to see what the limits on the errors were.

From the extreme snaked road case, it appears clear that midline method is not just a little wacky, but totally devoid of any reasonable precision... 1,817 meters in a 5K.

Even with a simple rectangle they end up with an unacceptable error, as you point out.

Regarding his other example, an oval. Since I don’t know the dimensions, I used a classic case, the circle. With a circle, the error on a 10 lap course would be about 314.2 meters. Similar to the 295 meters in your solution but interesting because by rounding out the 90 degree turns into a circle it adds more error, not less. Not what I would have expected.

The difference between the 314.2 and the 295 comes about because the measured line is offset 30 cm from the curb. Thus the circular course (measured at the center of a 10 m wide roadway) will have a diameter (5-.3)x2=9.4 or a circumference 9.4xpi=29.5 meters. Or, for 10 laps, 295 meters. No conflict here.

Tom Knight first proposed using the idea of "degrees of curvature" when describing a course. Add up all the right and left turns in a course, and the result is the degrees of curvature, a good index of twistiness.