Abingdon Loop measurements

Measurements

I have used my ETREX H to measure the length of the Abingdon 4.5 km loop. So far I have had 16 rides. I expect to do more rides in the future and will add new data to the table below as it is acquired and analysed. Various settings and analysis methods have been used:

• Track recording setting - It is possible to set the ETREX to record one track point each second, or to select a longer time interval. It also possible to choose a distance interval. the smallest interval is 1m, but when this is selected and the bike is ridden at 4 m/s points are only recorded once every second. An auto setting is also possible with various resolutions - I tried the highest. Having tried out these various settings my preferred setting is 1 track point recorded each second
• The ETREX odometer reads with smallest digit corresponding to 10 m. However Mark Neal pointed out in his post of 28 March that 1 m resolution was possible, " 3. Since my GPS would show measurements only to the 100th of a kilometer, at the end of each ride I would slowly roll forward until the next 100th of a kilometer turned over. This gave me a GPS measurement down to something close to 1 meter. This wouldn't have been possible if I had measured a course of fixed length." For lap 12 onwards, I marked 20 1 m intervals centred on the lap start/finish point and followed Mark's method to obtain lap distances to 1 m from the odometer.
• Track points recorded at 1 per s exhibit a zig zag mainly caused by the track point recording resolution, which is only 1 m. Therefore, distances derived by Pythagoras from these points average about 1.9% long. I have used the GPSU software package to smooth these points. GPSU can be set to fit the points by straight lines and the maximum distance of any point from the fitted lines can be set as a parameter. For this analysis I set the maximum off-track distance to 2 m, which I judged best followed the track round corners with minimal distance added due to zig-zags.

Lap No	Date	Time	Track Recording setting	No of points in track	Distance from Odometer	Distance from auto track points	Distance from Track Points unsmoothed	Distance from smoothed track	No. of points in smoothed track	Smoothed with off route track distance
					km	m	m	m		m
1	28/02/09	17:20:00	1 s interval	1177			4659	4547	107
2	01/03/09	08:45:00	1 s interval	1026			4637	4542	87
3	01/03/09	09:10:00	auto - high resolution	141	4.54	4533
4	07/03/09	10:30:00	auto - high resolution	134	4.54	4522
5	22/03/09	07:59:00	auto - high resolution	120	4.52	4511
6	22/03/09		auto - high resolution	124	4.54	4521
7	22/03/09	08:40:56	1 m interval	992	4.54		4627	4531	75	2
8	28/03/09		1 s interval	1203	4.53		4609	4531	79	2
9	28/03/09		1 s interval	1118	4.52		4607	4527	71	2
10	28/03/09		1 s interval	1133	4.53		4617	4527	76	2
11	28/03/09		1 s interval	1154	4.53		4627	4536	81	2
12	05/04/09	07:00:00	1 s interval	1028	4.531		4607	4530	69	2
13	05/04/09	07:17:00	1 s interval	1077	4.526		4604	4524	71	2
14	05/04/09	07:35:00	1 s interval	1064	4.530		4608	4529	76	2
15	05/04/09	07:52:00	1 s interval	1024	4.532		4611	4531	70	2
16	05/04/09	08:09:00	1 s interval	1040	4.532		4606	4533	71	2
					m	m	m	m
Average lap distance					4531.5	4521.8	4618.3	4532.3
Standard Deviation					6.8	9.0	16.6	6.5
Standard Deviation as %age					0.15%	0.2%	0.36%	0.14%
Average for lap 12 to 16 only					4530.2
Standard deviation for lap 12 to 16 only					2.5

Discussion of Results

Very encouraging results are given by both the ETREX odometer and the tracks recorded at 1 point per second then smoothed using GPSU set to fit within 2m off track. The distance of the lap measured bt a steel tape is 4533.2 m, and the average of 14 odometer readings differs by only 1.7 m. The average of 12 smoothed tracks differ by even less, 0.9 m.

Many course measurers with Jones Counters have measured this course. Experienced (mainly grade 1 measurers ) obtained values between 4529.1m and 4535.1m in 1997 as reported in my Measurement News Article. In June 2006 during an upgrading seminar 14 measurers obtained values between 4532.0 m and 4539 m. Some of the longer values on this occasion were believed to be in part from grade 2 riders not following the SPR. So the average of the odometer readings or the smoothed tracks which I have obtained with my ETREX is not much worse than the Jones Counter.

I have calculated values for the standard deviation of the distance.

The smoothed track method gives standard deviation of 6.5 m which is perhaps about a factor of two worse than the Jones Counter when one takes into account all the potential errors such as temperature changes, surface variation etc. - we would normally expect all Jones Counter results to be within +/- 4.5 m

If I take all the ETREX odometer readings, the standard deviation is 6.8 m. However, much of this scatter may be due to fact that the odometer readings had 10 m digitisation error, before I adopted Mark Neal's method to read to 1 m. Taking just lap 12 to lap 16, which were read to 1 m, I obtained a length of 4530.2 with a standard deviation of about 2.5 m. If this performance is maintainted over more trials it would confirm performance comparable to the Jones counter in the hands of experienced measurers. However, it may be that I was lucky over the period of 85 minutes that the 5 laps took to ride, in that the satellites were in a favourable location and there was little in the way of atmospheric and ionospheric perturbations.

When I simulated this lap I obtained a standard deviation of 10 m. In practice the performance seems better than that. Perhaps this is because the simulation, which treats the error in each way point to be uncorrelated, over estimates the total error when there is a degree of correlation over time period of a few minutes. This needs further data to provide confirmation.

Conclusion

My ETREX H odometer gives results which are much more accurate than those obtained by runners ( avearge +2.2% +/- 0.8%) who reported their GPS distances in one half marathon. Obviously I follow the SPR properly which few runners do. But probably I have found an accurate method of operating my ETREX H.

The best results previously reported were those of Mark Neal. T he best of Mark's 13 course rides are similar to my results. Six of the courses that Mark measured exhibited deviations of more than 0.15%, However these were trail courses and from his descriptions it sounds that conditions were much less favourable than on my road course. My results indicate that better results can be obtained on roads in a fairly open town/country environment.

Mike Sandford - 5 April 2009