I have been having fun with my new electric bike measuring how the calibration constant changes as the temperature changes and the tyre slowly deflates over several weeks after being pumped up. In fact I have not had so much experimental fun since the 1990s when I reported on
The Temperature Sensitivity of Pneumatic Tyres (report of an experiment on 12 tyres by 6 measurers)
This was published in Measurement News at the end of 1999. A copy of the article is available for download as a pdf file (142kB).
For the last 11 years I have continued to use for measuring the 32mm Michelin World Tour Tyre which was one of those which I characterised then. However with the arrival of my new electrically assisted bike on 1st April, one of the early things I did was to start to measure the temperature coefficient of its Continental Townride tyre, and I reported a coefficient of -1.98 counts/km per C.
As you can see above when I corrected the counts/km to 10C using my average value of -1.98 counts/km per C. I did not get steady trend showing the deflation each day.
However, it turns out that when I continued the calibrations during April (all using the same 550 metre calibration course near my home) I got a clear pattern showing a somewhat lower temperature coefficient -1.62 counts/km per C and a steady deflation resulting in a calibration constant change of +1.55 counts/km per day. Here is my later data plotted against temperature
However a somewhat different picture emerges if one corrects for deflation and temperature as shown in the following two plots.
These last two plots are derived iteratively using the gradient of one to correct the data for the other. After a few iterations one gets the steady values of
temperature coefficient and deflation. It is quite a validation of the appropriateness of the underlying linear models that the data fit the straight lines so accurately within about 2 counts/km, implying that the calibration constant can be predicted over long periods by just measuring the temperature and recording the day.
The tyre does not have quite as high a temperature coefficient as I had first estimated using the 2 - 9 April data. In fact if you look at my 1999 publication you will see that this tyre with 1.5 inches diameter of cross-section will fall very nicely in figure 3, exactly midway between the "best" and "worst" tyres. So this Townride tyre is very typical of a 37 mm tyre.
So why did I get a coefficient of 1.98 counts/km per C for the initial period 2 - 9 April? I think this was probably due to creep after the initial inflation of the tyre. The effect of creep is that the tyre continues to expand for a few days after being inflated before the deflation due to air permeating through the rubber inner tube comes into effect. Section 3 of the Appendix of my 1999 report describes creep. Hysteresis mentioned in section 4 of the appendix may also have an effect. Thirdly in contrast to the last part of this April which has been completely dry, there were some slightly damp days early this April. When a tyre picks up some dampness from the road, this can evaporate as the tyre whizzes round. The temperature of the tyre is thus reduced towards the wet bulb temperature.
So here is what I suspect happened with my new bike. It had been stored for me in the supplier's warehouse since January, awaiting the arrival of a large capacity battery (453Wh) which I judged that I would need for measuring the London Marathon. On the 31 March I called for delivery since I needed to start using the bike, and a large battery was fitted from a different bike. The supplier must have then checked the bike and pumped up the tyres. When it arrived on 1 April the tyres felt very hard. I did not measure the pressure and used it as supplied. I have not touched the front tyre at all since receiving the bike. The tyre had probably been pumped from a fairly soft state by the supplier on 31 March, so for the next few days it expanded slightly due to creep, and it was not until more than a week had elapsed that creep dropped to zero and the steady deflation predominated. This really highlights the rather unpredictable results on can get if you pump up a tyre and then immediately calibrate and use for a measurement. I really like to pump a tyre a day or twos before use. In view of this result, I think I shall in future pump up at least a week before measuring!
It is pleasing after 11 years to see that the method is still applicable to a new tyre, and I recommend it to measurers prepared to do a bit of work to understand and measure their tyre. However, the cautious method of calibrating immediately before and after a measurement and using the largest constant is simpler and should nearly always be reliable in avoiding short courses.