Math is Easy wrote:
Based on the numbers you posted in your comparisons, it looks like the cheap wheel was off by about 3.822 metres over 600m. Using that as your calibrated working value. Your cheap wheel and gold standard are the same, you just failed to calibrate the wheel.
However, there does appear to be additional under variance with the wheel, because a properly calibrated wheel should show a value longer than the tensioned steel tape if truly stretched in a 600m straight line. There is zero measuring error associated with a properly stretched steel tape, whereas much measuring errors may occur by the user picking up slight ground imperfections (bumps) and the nearly impossible task of roiling a truly "straight" line.
The problem with the wheel was that we got significantly different calibration numbers on the grassy parts of the course versus the firm dirt parts. This made it impossible to calibrate accurately because the wheel's precision would be changing throughout the course in unpredictable ways, and we had no way of finding out what the average correction number should be without measuring the whole course with both the tape and wheel. At that point why do the wheel at all?
The On Course Ratings guys warned us that the time of day would change the wheel measurement as well because of dew on the grass in the morning, etc.
With regard to your second paragraph, I thought the wheel would measure long as well, but it doesn't. The slipping error dominates the straight line deviation error. Maybe if you went reeeeeal slow and put a lot of pressure on your wheel, then maybe you could get a more precise calibration, but who can maintain that discipline over a 5k course? And how would you know you got it right without calibrating over the entire course?
Remember, our wheel measurements were supposed to represent the amateur who shows up with the $50 Home Depot wheel, and then declares that they have "the real measurement". They don't and they never did. They had an approximation good enough for PR purposes which was probably too short.
It comes down to this. If you can't make reliable calibrations which correctly reflect the behavior of your measuring device over the entire length of the course, then that measuring method is inaccurate and should only be considered an approximation. All wheeled devices have this problem on anything but smooth paved surfaces, and GPSs have this problem because many courses alternate between open stretches and wooded areas. GPSs are problematic around turns as well.
The steel tape method introduces errors, but those errors are very small compared to other methods and will be consistent from one course to the next, no matter what the surface is or how much tree cover there is. The error of the steel tape is a couple orders of magnitude smaller than the error for other methods. No matter how you look at it the steel tape is the best way to go.