With the Jones counter the best accuracy I could hope to get was 1/2 count, or about 1/50th revolution, and I believe that is what was causing much of the scatter in my calibration experiment. With the marked up rim I believe I can read to the closest 200th revolution, and this should eliminate much of that scatter.
In order to test that theory I repeated my calibration experiment with the marked up rim. After compensating for the increasing temperature, as I described in my previous post, the results of the 48 rides are shown below.
Below shows the resulting average calibration constants for the three different length cal courses.
Recall that in the previous experiment the mean for the 100m cal course was also smaller, although it was by a very small amount.
In my mind there are only two plausible explanations for the 100m course giving the smallest cal constant:
1) The difference is extremely small (less than 1 count on a 300m cal course) and isn't real. It is only due to the fact that even in these experiments we don't have enough data.
2) With the 100m cal course you can actually see the mark in the road at the end, so it is easy to follow the same path as the steel tape. With the 200m and 300m courses it is much more difficult to follow the shortest route to the end mark. If this is true it would mean that using a 100m cal course is actually more accurate! I'm not saying that is the case, but if the 100m really does give the smallest cal constant, I see no other explanation for it. Remember that any "wobble effect" would give the opposite result, the 100m giving a larger cal constant.
The chart below shows the 97% probability error for the three different cal course lengths using 4, 6, and 8 calibration rides. It shows this data both for the case where the rider uses Jones counts to record his data and where he uses a marked up rim. For example, if a rider does 4 300m cal rides and records data using his Jones counter, he has a 97% chance that his cal constant will be less than 0.028% away from the 16-ride average (yellow column).
The key thing to notice here is that the use of the marked up rim dramatically reduced the scatter that was seen in the 100m cal rides.
In fact, if we compare the conventional calibration method (4 300m rides using a Jones counter, yellow column) with the marked up rim method (4 100m rides using a marked up rim, light blue column) we see that they have nearly identical error.