I have seen descriptions of this before but I am not sure where. I am measuring an out and back mile course. I would like to use some sort of arc turn. What is the best way to lay this out?

Thank you.
Original Post

Jon:

There're probably many other methods, but here's one.

PK Nails separated ____________ o
by a distance ____________>
convenient to ride o o
over, mark and
locate exactly from
permanent
landmarks

______________
Start / Finish ______________> o
Sorry Jon, It didn't post as it appeared on the reply. I can email it if you wnat.

Pvolkmar@snet.net
Using your calibrated bike, lay out your TA as though it was a single point, and there was no arc. Now see how much room you have and what you want your arc radius to be. Call the arc radius “C.” Remember than the runners will run 30 cm (1 foot) outside the arc. This radius is R (=C+1 feet)

The runners, running around the arc, will add distance to the true out-back. This will be equal to π (pi) times the radius they run. The deduction from the original TA point will be half this value, as it is this short out-back which you are removing and replacing with the arc.

The offset will be:

Offset = πR/2

Example: If the cone radius is 15 feet, the runner radius is 16 feet. The offset is π(16)/2 = 25.13 feet. Thus the arc center will be 25.13 feet short of the original TA.

Mark the new center and lay out an arc of paint dots where the cones should be.

The length of the arc will be πR, or 50.26 feet added to the course.
The deduction from the original TA is 2x25.13 feet, or 50.26 feet.
The two turnarounds at the Women's Olympic Team Trials Marathon in Boston were marked this way. Here's a nice map detail of how they were laid out. Justin Kuo can probably elucidate.

Also, if you want to follow the letter of the law as spelled out in the Measurement Manual, you measure to the TA point, freeze your wheel, then ride back, assuming the runners can turn on the proverbial dime (or PK nail in this case). This results in a long course, probably significantly in the case of a mile.
I don't think it's the letter of the law to lay out a TA as a single point. It's simply easier to do and document, and generally doesn't make much difference in the overall length of the course.

Anybody who wants to lay out an arc has always been free to do so. Most don't.
Pete-Doesn't your course actually end up at about 20 ft longer than 1-mile with the SCP using the hypotenuse? Following the letter of the manual, a 3-nail (or more if more accuracy is desired) method for measuring and marking the T/A could be used. A nail could be at the beginning and end of "the arc" and one at its apex. The nails could be placed for ease of riding and could mark the cone locations. The Start/Finish could be adjusted as needed to obtain the desired distance. I agree that this method probably requires more riding, but its only a mile.
Guido - I don't see what you mean about the hypotenuse. Usually a TA is at the end of a straight section that's long enough that the difference between the direct line to the TA and the distance to the arc end is trivial.

Cound be I made a math or geometry error, but haven't found it. As I see it, you gain the length of the arc, and you lose twice the difference between arc center and original TA.

My method works for any course with a TA, not just one mile. I think it's a lot easier, and more accurate, to lay out a single out-back point and revise it than to try to measure around an arc of cones. You can also incorporate the final adjustment of the course in the layout of the arc, but that's beyond the scope of this discussion.
Pete: Don't you add a little distance by running from the Start/Finish point to the point that is the begininning of "the arc" because of the small angle involved? This is as opposed to running from the Start/Finish point straight to the offset T/A. I agree it may be easier to layout and measure a straight course and then adjust it. I think the trade-off is that with the 3-nail method the measurer can ride directly to each nail and get a pretty accurate measurement following a path almost what the runners will.
It makes a difference, but it’s so small that it can be ignored. Consider a one-mile out-back course on a straight road. On the single-point TA course it’s 2640 feet to the TA. On a course with an arc of 15 foot radius (16 feet for the runners) the center of the arc is 2614.87 feet from the center of the start line.

If the runner takes the diagonal from the center of the start to the end of the arc, he runs 2514.91 feet. This is indeed greater, but only by 0.04 feet, or half an inch. I don’t see where “20 feet” comes from.

Pete: My mistake! That sneaky little factor of 2 got me. I calculated the distance around the arc using 16-ft not 32-ft.