Several people in this thread have referred to the "Baumel method" of measuring a track. This refers to a document I wrote which is posted at
www.usatf.org/Products---Servi.../Taping_a_Track.aspx and it's also linked from
www.rrtc.net -- And now, to make it still easier to find, I've made the shortcut
www.rrtc.net/taping_a_track which redirects to the same pdf file as the long URL above.
As one important point, the above document describes methods of
measuring a track using steel tape, but says nothing about
certifying it. I'll return to the question of (RRTC) certification of a track later. But first, let's discuss the accuracy obtainable using the methods in this document. And here I'll point out a fundamental difference between the measurements made by surveyors in officially surveying a track, and the measurements we make. The official survey measurements, following procedures specified by IAAF, are based on knowing the exact locations of the radius centers. Our task is rather different, as we're given an already constructed track, for which we
don't know the radius center locations, and we want to determine a single number--the distance covered in running a lap of the track.
The document at
www.rrtc.net/taping_a_track actually describes
two methods. It states: "If curb is suitable, then tape circumference directly along outer edge of inner curb. If not, then use “Length-Width” method." I think we'd all agree that the first method (direct curb circumference taping) is highly accurate. In fact, its accuracy should match the accuracy obtainable in any careful steel taping. There was a time when many tracks, with either an asphalt or cinder running surface, had a permanent concrete curb that provided a good support for stretching a tape along. However, most tracks of that type have been replaced with more modern synthetic surface tracks, which don't have permanent curbs. Either they have no curb at all (typical of high school tracks), or they have a removable curb, which wouldn't provide suitable support for taping along, even when the curb is in place. Generally, the tracks with removable curbs are intended for higher level competition (e.g., university level or above), so a surveyor's certificate ought to be available. Thus, we're concerned mainly with uncurbed tracks, and the accuracy of "Length-Width" measurements for such tracks.
The Length-Width method described at
www.rrtc.net/taping_a_track involves measuring two widths, W1 and W2. There is, however, a simpler Length-Width method that would involve measuring only one width (which might be measured along the 50-yard line if there's a football field marked on the infield). Here, if we've measured length L and width W, the circumference would be found by:
Circumference = 2*L + (pi - 2)*W
This ought to be accurate if the track has perfect geometry consisting of straightaways and semicircles at each end. The formula at
www.rrtc.net/taping_a_track is obtained from the simple formula above by replacing W with the average of two width measurements, W1 and W2, in order to account for minor departures from perfect track geometry. As far as I know, the idea for doing this was originally due to Bob Letson. The widths W1 and W2 should be chosen near the ends of the straightaways, but clearly within the straightaways - don't waste time trying to locate junctions of straightaways and curves (if there's a football field marked on the infield, you might measure along the 5-yard lines).
How accurate is this refined Length-Width method (with the two widths, W1 and W2)? Back in 1986, Glen Lafarlette and I measured a track which had a permanent concrete curb, using
both this Length-Width method and direct circumference taping. I wrote it up in the article "Measurement of Memorial High School Track, Tulsa, OK" in June 1986 Measurement News, which you can access at
http://www.runscore.com/course...mentNews/017_86a.pdf (and if you don't know who Glen Lafarlette was, see
www.rrtc.net/lafarlette_tribute.pdf). We found that, when using the same steel tape, the two methods agreed within one centimeter. This was true even though the track geometry obviously wasn't perfect - e.g., if you sighted down the straightaways, you could see that they weren't perfectly straight.
I compared Length-Width measurement and direct curb circumference taping again in 1989, on a different high school track (which also had permanent concrete curb). I don't seem to have preserved the data, but my recollection is that the agreement was again extremely close.
I conclude that the Length-Width measurement is very accurate, comparable to direct curb circumference taping, for tracks with the "standard" geometry of straightaways and semicircles at both ends.
Unfortunately, there are also "double bend" tracks, where each end of the track is a compound curve built with two different radii, resulting in a track with a somewhat more squarish shape. These are often used when it's desired to include a wider playing field, such as a soccer pitch, in the infield area. According to David Katz, it can be very difficult to tell by simple inspection that a track has double bend geometry instead of the standard geometry with semicircular ends. And if a track does have double bend geometry, the Length-Width method will significantly underestimate the track length.
The IAAF Track and Field Facilities Manual that can be downloaded from
https://www.iaaf.org/download/...ition%20-%20Chapters includes diagrams (Figures 1.2.3b, 1.2.3c and 1.2.3d) showing dimensions of 400 meter tracks with three variations of the double bend geometry. From those dimensions, we can calculate that a Length-Width measurement would underestimate the track length by amounts ranging from around 5 to 10 meters.
From this, we conclude that, even if it can be difficult to distinguish a double bend track from a standard track by visual inspection, the difference should be readily apparent if we do a bike measurement (or other calibrated wheel measurement) in addition to Length-Width tape measurement, as those measurements will differ by at least 5 meters if it's a double bend track.
Now, my recommendations on certification where, based on previous discussion, it should be clear that we're certifying it as a "road" course, not a track.
First, since it's a road certification, we always have the option of measuring it by calibrated bike (or similar calibrated wheel method), just as we would measure any other road course. The only difference is that, if the track is uncurbed, we should measure/calculate it for an assumed running path 20 cm out from the inside edge (more on this later). As in any other bike measurement of a road course, the 1/1000 short course prevention factor would be used to ensure that the course is at least the stated distance.
If the track has a permanent curb suitable for direct taping of the curb circumference, this can provide greater accuracy and would allow use of a smaller SCPF (more on this later). Unfortunately, very few current tracks have a permanent curb of this type.
If the measurers wish to do Length-Width tape measurements, this can also provide greater accuracy than a wheel measurement, allowing use of a smaller SCPF. However, given the possibility that the track might have double bend geometry, we should never certify based
only on Length-Width tape measurements. We should always require a wheel measurement in addition to the Length-Width tape measurement. Then, if the tape measurements and wheel measurements agree within a meter or so (for a 400 m track), we can take that as evidence that the track has standard geometry (with semicircular ends) and certify based on the tape measurements. If not, we'd have to certify based on the wheel measurements.
On use of SCPF: If certifying according to tape measurements (either direct curb taping or Length-Width method), the SCPF can be smaller than the 1/1000 used in normal road measurements. But an SCPF is definitely needed! All course certification and record keeping follows the principle that the course must not be shorter than advertised. When IAAF certifies a 400 m track, they specify a one-sided tolerance of 4 cm, meaning that its length must be between 400 m and 400.04 m (i.e., it can be up to 4 cm oversized but must not be shorter than 400 m). Thus, a track builder would aim for a measurement of about 400.02 m, to ensure it's within the window, given the accuracy of their measurements. RRTC has always used an SCPF for road course measurements, but curiously, when RRTC wrote certificates for tracks, we simply reported the raw results of tape measurements without any safety factor. This may have been done by analogy with calibration courses, but it's a false analogy. Nobody runs races on a calibration course. The only purpose of a calibration course is to calibrate a bike. Then, when we calibrate the bike, we apply the SCPF, so it gets incorporated in measured race courses. But people do run races on tracks, so when we certify a track (albeit as a "road" course), we must ensure it's at least the stated distance.
In a bike measurement, we apply the SCPF by multiplying the "constant" by 1.001. This has the effect of increasing the course length when laying out a course to a desired intended distance (such as 5 km). Or, when measuring the length of an existing fixed course, it reduces our stated result for the length of the course, below the result we would state without the SCPF. When measuring a track by steel tape, we must similarly reduce our stated result for the track length. But by how much?
With extreme care and ideal equipment, steel tape measurements can be accurate to better than 1 part in 10,000. Our measurements don't reach that standard, due to factors such as calibration error of the tapes and uncertainty in the temperatures used for temperature correction. It's often stated that "ordinary" steel taping should be good to 1 part in 5000. I'm not sure our measurements always reach even that standrd. But I'd be comfortable using a slightly bigger SCPF of 1/4000 for tape measurements of a track. Thus, for tape measurements of a 400 m track (by either Length-Width or direct circumference taping), the length written on the certificate should be 10 cm less than the original measurement result.
On 20 cm clearance for uncurbed tracks: Track rules state that the assumed running path is either 30 cm from the curb or 20 cm from a painted line defining an inside edge. For road course measuring, we normally specify only the 30 cm clearance. Historically, when Ted Corbitt sent letters in Sept 1982 introducing the SCPF and tighter SPR procedure, he said to measure 30 cm from curbs and 20 cm from uncurbed road edges (see one of Ted's letters at
www.rrtc.net/SCPF_Adoption_1982.pdf). This was by analogy with the track rules. Then in 1985, when I was working with Ken Young and Pete Riegel on the first edition of Course Measurement Procedures, we decided it made no sense to keep specifying both 30 cm and 20 cm clearances for road measuring, especially since actual uncurbed road edges are nothing like painted lines on a track (they may be broken up, have dangerous drop-offs, etc.). But now, in the context of measuring on an uncurbed track, there is really a well-defined line marking the inside edge, and runners are really going to run closer than 30 cm from that line, so we really ought to measure/calculate at 20 cm. And, as pointed out previously in this thread, there's a huge difference between the lap distance at 20 cm and 30 cm -- about 63 cm, which is more than 1/1000 for a 400 m track.
As additional subtleties, even when measuring by bike, it's probably best to measure right at the inside edge, and then correct for the 20 cm clearance by calculation (by adding about 1.2566 m). To measure the proper path by bike, it's probably easier to walk the bike instead of riding it (Of course, if it's walked on the race course, it also needs to be walked on the calibration course). As one more point, if it's an uncurbed track, we'd need to decide exactly what defines the inside edge. If you want to use the painted line defining the inside edge of lane 1, that line would have to be coned during the race, and that would have to be written on the Certificate. The track surface probably extends some distance inside of that painted line. If the line won't be coned, we should assume that runners will use the entire track surface, so the assumed running path would be 20 cm out from the very inside edge of the available track surface.
