INTERPRETATION OF A VALIDATION MEASUREMENT

Here is what is known from actual measurements:

Certified calibration course length = 1000.00 feet
The course was steel taped by the validator and helper. A length of 1000.00 feet was obtained at 80F.

Four precal and four postcal rides were done, with the average of the eight rides being 3590.75 counts over the calibration distance.

497825 counts were recorded on the validation ride of the course.

Question: If you obtained the above values, what would you report as the length of the course?

Different philosophies will come into play here. Discussion is invited.
Original Post

Pete, you are obviously trying to stir up another debate over the SCPF on validations measurements. The correct answer, in my view, includes the SCPF and is therefore 42.2202 km or 138,517.6 feet. The SCPF is there to allow for the inevetable errors that creep into our measurements. For example, was the tape really at 85ºF? Was the pull on the tape the correct force? Did you truly ride the SPR? What was the tire pressure fluction during the ride? etc. etc.
Paul,

US validations don't use the SCPF, so I'll chalk up your answer as 42.2202 x 1.001 or 42262.4 meters. Can't see how you got it though.

Was the tape tight? Was a good line ridden? Was the temperature measured correctly? What about tire pressure? We don't know. All we have are the data. This is about the best way to calculate it.
Pete, you don't say whether or not the proper amount was deducted from the cal course laid out at a temp of 80 degrees so I'll assume it WAS adjusted to 1000'. I don't think this is a trick question...altho I have my suspicions. Given that, I'll say the course was 26.258 miles. It passes validation for a marathon.
I assume the calibration course would measure as 1000.0774 ft ( 304.8236 meters ) at 68 degrees F.

The marathon course is 497825 counts / 11.779764 counts per meter = 42,261.03 meters

If the temperature is above 68 degrees F when I measure a calibration course, I may not adjust the length for temperature. A validation should always adjust for temperature.

Dale Summers
The cal course is 1000.0 ft. regardless of the temperature on the day the course is used.

The constant, without the SCPF is 3590.75 counts times (5280/1000) = 18959.16 count/mi

The course is 497825 counts

The length is 497825 counts / 18959.16 counts / mi = 26.2577561 mi

A marathon is 26.21876 mi

The course validated is 0.03899615 mi (205.899 ft) long

The constant with the SCPF is 3590.75 times (5280/1000) times 1.001 = 18978.1192 counts/mi

The course length is 497825 count / 18978.1192 counts/mi = 26.2315246 mi

A marathon is 26.21876 mi

The course measured using the SCPF is 0.01276462 mi (67.3919 ft) long

The question is “What would you report as the course length?”

I would report 26.22577561 mi as the validated course length.
Pete, thanks for suggesting this problem that does bring up interesting philosophical points.

As I see it, there are two slightly different possible answers: either 42257.76 m based on assuming the certified length of the calibration course (1000 feet = 304.8000 m), or 42261.03 m based on using the temperature corrected length of the calibration course as measured by the validator (304.8236 m). Of these, I would go with the second answer, which matches Dale Summers' result, although I don't like the way Dale stated the first sentence of his reply.

Before explaining my reasoning, let's rule out some obvious red herrings. The SCPF is irrelevant because we never use the SCPF in calculating the result of a validation. Also, the fact that the race may have been nominally a marathon wasn't stated by Pete, so is irrelevant. Assuming it was supposed to be a marathon, then by either calculation, it clearly "passes" the validation, as the validated distance is certainly greater than the nominal marathon length (42195 m).

Regarding temperature correction, some basic physics: We normally assume that the lengths of our calibration courses (and race courses) are independent of temperature. The reason for this is that such courses are basically fixed to the surface of the earth, and as soon as you go a meter or two beneath the surface, the temperature is nearly constant year round. While some cracking or buckling of surface roads can occur due to seasonal temperature variations, changes to the course length are negligible, not counting gross events such as earthquakes, landslides, etc. (There are exceptions, of course, such as a course laid out on a bridge, which may undergo greater changes in length when the temperature changes.)

Thus, we assume the calibration course length to be independent of temperature. To understand steel taping temperature corrections, it's just the length of our steel tape (the measuring instrument) which changes with temperature. We assume that the tape was manufactured so its graduations are accurate at a temperature of 20 °C (68 °F). If it's warmer when we do a measurement, we know that our tape is longer than its graduated length, so we conclude that our measured course is somewhat longer than the distance we read from the tape's graduations.

I felt Dale's first sentence to be somewhat misleading because, although correct, it suggests that the calibration course length may vary with temperature. Actually, as stated by Guido Brothers, the cal course length is the same regardless of temperature. But it isn't necessarily 1000.0 ft; that's just the length that the cal course was originally certified as.

Now, the philosophical question: The cal course was originally certified as 1000 ft = 304.8000 m, but the validator found a somewhat greater length of 304.8236 m. Possibly, the validator would feel a little uncomfortable using his own measurement of the cal course, which will make the race course look a little longer. I say to go with the validator's measurement for the following reason: It's the race course, not any particular calibration course, which is being validated. The validator is under no obligation to use the cal course that was originally used in laying out the race course, or any other previously certified cal course. The validator can just as easily pick an arbitrary stretch of road and lay out his own (possibly temporary) cal course to use for the validation. It's nice if the validator can check the cal course used by the original measurer, but this isn't required. In any case, the validator's measurement of the cal course should always be used for calculating the result of validating the race course. Afterward, assuming that the validator checked a previously certified cal course, the question may arise whether to recertify that cal course. In the present case, I don't think any change would be warranted, but if the validator had found the cal course to be shorter than its previously certified length, a change in that certification may be appropriate.
Speaking philosophically, it seems to me that 99 percent of our discussions are concerned with one percent of our courses. We have a smoothly-functioning bureaucracy in place which allows the creation of thousands of accurate courses, and this functions almost problem-free.

It’s the one percent that leads to misunderstandings and contention. All concern records and “important” races. I see several things that have been unresolved for a long time.

1) We are asked by the existing rules to state with an undefined degree of certainty whether a course is short. We wrestled with this in the past, and now seem to have changed our minds.

2) Various people round off data to different degrees, resulting in different results from the same basic data. Results are presented to varying degrees of exactness.

3) It remains unrecognized by many that measurement is inexact. The concept of measurement error seems to be hard to grasp and to deal with.

With regard to my posting, I noted from responses and other data that the length of the course was calculated in different ways, and results presented in different forms.

The issue of which value to use for the calibration length can be important in a close call. My own inclination is to use the certified calibration course length, as the checking generally involves only one measurement. Unless the checking shows a significant difference (it usually does not), I prefer to accept the certified value. I do not claim this to be right or wrong, but I think it is proper.

Rounding of numbers, if done prematurely, will lead to less precise calculations. My preference is to round nothing at all, retaining everything unrounded until the final calculation of length is made. At that point I round the result to two decimal places if metric, and to five if miles. I recognize that we cannot really achieve this level of accuracy.
Texts mention that a calculation has the precision of the number with the least number of significant figures. When we calibrate we generally get a series of four-digit numbers, perhaps five. I remain perplexed as to what this means to us. I do know that when I fill out a certificate for a half-marathon, I cringe when I put down the length at 21097.5 meters. Nobody on a bike can measure that well.

I’m proposing no changes. It is easy in these arguments to forget that we are doing very well at what we do, and the corrosive argumentation in which we sometimes find ourselves only involves a tiny fraction of the whole.