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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.
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Dear Mike,

I’ve been reading with interest, but one thing seems to be missing. As time goes by, the constant changes, presumably because of air leakage and expansion or contraction of the inflation air due to temperature change.

So, if I read correctly, you began with an unstated tire pressure and took more or less daily calibration readings, recording time and temperature as you did so. You did not do any inflating during the process. I see constant recorded by date and I see it recorded by temperature, with various corrected constants.

It would be a boon to see a chart of date, time, constant, and temperature shown without correction – in other words, the original recorded values. This might help me get my head around the figures.

I may have made a ridiculous mistake, and I will not be at all offended if you point it out, but nowhere do I see original recorded data.

You are absolutely right in your understanding: I have not presented the complete raw data. It is a bit more work to present in the form a graph, for two reasons.

Firstly, although the time is recorded in my notebook, I did not transfer this to my spreadsheet. I have treated all calibrations taken on a single day as taken at the single point on the time axis representing that day. To show how temperature changes during the day i would have to incorporate both the day and the time of day on the time axis. This is not hard to do, but I set out might spreadsheet on a simplified basis since I expected deflation during part of a single day to be of little importance.

Secondly, to display the temperature data as well as the cal const data against day+time, I either need a 3 dimensional graph or I could plot two series of points on the same time axis. I will experiment and see how best to show the raw data.

I have emailed the following to you as a .xls file.

Continental Townride 37mm tyre
No adjustment to tyre pressure apart from natural deflation
Date Temp C Cal Const
02 Apr 14.2 10913.9
02 Apr 14.8 10912.4
04 Apr 11.4 10918.4
05 Apr 10.2 10920.2
06 Apr 17.5 10905.1
07 Apr 9.3 10924.6
07 Apr 18.3 10903.8
07 Apr 20.9 10903.5
08 Apr 6.0 10929.0
08 Apr 12.3 10918.3
08 Apr 19.3 10902.1
09 Apr 6.8 10929.3
12 Apr 15.1 10908.7
13 Apr 7.4 10921.2
15 Apr 12.7 10917.3
17 Apr 8.5 10928.0
18 Apr 18.3 10913.9
19 Apr 21.3 10907.6
22 Apr 25.4 10908.3
23 Apr 19.0 10918.5
23 Apr 26.0 10907.4
25 Apr 11.8 10934.3
25 Apr 19.9 10920.8
26 Apr 10.1 10937.7
29 Apr 11.6 10938.2
30 Apr 14.8 10934.9

I can see how your corrections work now. Thanks for the data.

We have taken two approaches to our tire work. Your investigation involves an initial inflation with no subsequent re-inflation as time goes by and data is taken. My data was obtained by pre-pumping the tire to 100 psi before each daily precalibration, with the day's postcalibration falling where it might.

I have been able to wring some information relating to the change of constant with time and temperature changes between calibrations, but thus far I have not been able to make sense out of it.

I am not sure whether you had a specific goal in mind as you did your data collection. I had no specific goal in mind when I began. It was only as the data grew that I saw that it could be used as a fairly accurate predictor of the day's constant. All I need to know is the day's temperature and I have the constant quite closely.

Of course, it would work only for the specific tire involved, and would have no general application. Also, it took me seven years to collect all my data. This might be seen as an undesirable handicap to the usefulness of the method.
This was really the first time since the 1999 work which we did that I have changed to a new tyre apart from some occasional, one-off use of different bikes. So it was natural for me to go back to what we did in 1999 and take measurements in the same fashion and do the same analysis that we established then. The two factors deflation count change per day, and temperature count change per C. Are an excellent way of charcterising one's tyre. If you know those two coefficients as a result of this sort of measurement, you can go a long way towards understanding calibration constant variations.

I have shied away from the pump up to standard pressure before calibrating method for two reasons.
  • I have not been entirely happy that my pressure gauge will be reliable and sensitive enough.
  • I worry that if I pump up a lot just before calibrating, the tyre will creep and go on expanding for the next few hours/days
The Michelin World Tour tyre served me extremely well on my old bike from I think before 1995 until early in 2011. What finally put paid to it was in January/February this year I was doing some extra regular training rides on my old bike to recover some fitness prior to the arrival of my new Electric Bike and the London marathon measurement ride in April. On one fitness training ride I got a front wheel puncture and when I looked closely at the MWT tyre I figured that age had contributed to weakness.

Incidentally I ran that MWT tyre for all those years with a plastic protector strip inserted between the inner tube and the tyre. I only ever got punctures very occasionally and towards the side wall. In fact the inner tube when I dismantled it had only one patch on it. I can certainly strongly recommend such plastic strips for puncture protection.
I always inflate to 110 psi prior to pre-measurement calibration. I haven't noticed any "creep" and like Pete, my post-measurement calibrations are typically within 1 or 2 counts, which is what I expect due to temperature changes.

My Trek came with Bontrager RaceLite Hard Case 700x32 tires, which aren't a particularly expensive or high-tech tire. They have a slick tread and a recommended 110 psi pressure. As with all my measuring bikes, I always buy a spare wheel and set it up with a counter, so that when I do leisure rides, I can swap off the counter by just replacing the entire front wheel (saves wear and tear on the counter as well). When I set up the measuring wheel (with the counter), I bought the same Bontrager tire and used a thorn-proof tube and a kevlar tire liner (e.g., I'm paranoid about punctures, especially on the front wheel. As a result, I've never had a puncture on the front while measuring. I have had a few on the rear, but with tools, tubes, and a patch kit, I can continue with a measurement without having to return to a calibration course and start the day all over again. Anyway, the thorn-proof has very thick rubber where it faces the tread and with all that rubber and kevlar inside the tire, 110 psi inflates it as hard as a rock.
My tire is rated at 125 psi, and that is the pressure I used to pump to before each precal. I wanted to keep rolling resistance minimized to compensate for age.

On one hot day I had a blowout on the rear tire in mid-measurement. The bead popped out of the rim, and the tube gave a nice loud bang.

Since than I have pumped to only 100 psi before precal, and have not had another blowout.
Creep (tyre slowly increasing to a larger diameter over many hours after inflation) has only been noticed occasionally. I found it on some of my tyres including my new Continental Townride tyre as discussed above.

On page 7 of the article referenced above ( pdf file ) I analysed some data from Pete taken in September 1999 on his Kenda tyre. This clearly showed creep extending over two days after he pumped the tyre up. It was followed by steady deflation over the subsequent 5 days.

One would expect that small changes of tyre pressure would produce proportionally small amounts of creep.

The tyre is held together by nylon cords in the casing. These stretch as the tyre is pumped up. Most of the stretch is a normal reversible instantaneous elastic process. However unlike a springy metal, something else goes on in the nylon. The molecules can stretch a small amount extra slowly over a few days after the tyre is pumped, so we get what I have called "Creep". It does not seem to go on for more than a day or two. It is presumably caused by bonds between nylon polymers slowly being broken. Perhaps the period of creep completes more quickly at high temperatures than at low temperatures when one could imagine that bonds are harder to break.

By the way the principal reason why a tyre expands as the temperature increases is not due to the air pressure inside increasing, but the elasticity of nylon changes with temperature. It becomes "softer" as the temperature increases so it will expand more even if the air pressure inside is kept absolutely constant.

Our tyres are a miracle of engineering and have wonderful properties.
This post reports on 9 further calibrations of my 37mm cross-section Continental Townride tyre. All have been on my Long Tow calibration course and in dry conditions. The tyre has not been inflated at any time since I received the bike on 1 April and now. I had intended to measure the tyre pressure on 15 May when I decided to terminate this series of calibrations, however, on taking the valve cap off I realised that the inner tube had a Woods (Dunlop) style valve:

My two pressure gauges for Schrader and Presta valves don't work with a Woods valve. Indeed it appears that the only way to get an idea of pressure would be to inflate it with a pump which has an integral pressure gauge. However, I think this might be rather inaccurate since the pressure difference to force the air through the valve would not be measured.

Between 2 April and 9 April the tyre appeared to be settling down after being inflated before delivery to me. The 12 calibrations between 12 April to 26 April which I reported at first post in this thread showed the calibration constant was increasing steadily by 1.55 cts/km per day. The temperature coefficient was -1.62 cts/km per degree C.

I have now added the 9 further points to this series, which now extends for more than a month:
The daily deflation now seems to average a bit less: 1.35 cts/km per day. The temperature coefficient is unchanged; 1.56 cts/km per degree C

Note that all the points lie within about 2 cts/km of the fitted lines. So using temperature and deflation coefficients which I have determined for this tyre, I could, in principle, take a calibration on one day, and then predict the calibration at another temperature within say a week or so. However, I might be as much as 4 cts/km out. So, using these coefficients can not provide the precision and reliability that one can obtain by calibrating immediately before and after a measurement ride. Nevertheless it can be useful to know what one's tyre is doing and to be able to predict calibration constants.

Also, this type of analysis is useful for comparing one tyre with another. Tyres with lower temperature coefficients are preferable when one needs to measure on days with large temperature changes. Fatter tyres tend to have larger variation with temperature, so I have now fitted another wheel to my bike with tyre of 25 mm cross-section. I have started a similar series of calibrations, and I will report in detail when I have a few weeks of data.

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