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Crr of water inflated tires
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TOPIC: Crr of water inflated tires

Re: Crr of water inflated tires 5 years, 5 months ago #27013

  • howardjd
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I'd love to run the test but Im still not ready to start riding again. I honestly don't know exactly what I damaged or tore in my pelvic/groin area and whether it will ever return to normal. I fells alright now but as soon as I start doing any riding on the bike(just a couple miles) the soreness starts coming right back. It has improved tremendously over the last two years and hopefully it will continue to do so and in the future and can continue being crazy and riding heavy wheels.
Last Edit: 5 years, 5 months ago by howardjd.

Re: Crr of water inflated tires 5 years, 5 months ago #27014

  • kraig
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howardjd wrote:
I'd love to run the test but Im still not ready to start riding again.

Sorry to hear that your injury still has not improved significantly.

You can run a virtual test of your alp d'huez up/down scenario (simplified) using online, free tools. Give it a shot.

Re: Crr of water inflated tires 3 years, 8 months ago #27129

  • howardjd
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Well this past year I finally got to the point that I could ride enough to answer my own question. I conducted rolling resistance trials on rollers in a temperature controlled room over the winter and did infield trials during the spring.

For rolling resistance trials I used a 25mm Hutchison equinox tires inflated to 90psi. I did seven trials each of water and air and got the following results for crr rollers

trials conducted at 40kph

Water {0.0206 0.0204 0.0201 0.0217 0.0214 0.0187 0.0204} ±
{0.0015 0.0015 0.0015 0.0016 0.0016 0.0014 0.0015} watts/(Newton*m/s)

standard deviation 0.001 watts/(Newton*m/s)

Air Air {0.0190 0.0196 0.0179 0.0199 0.0193 0.0173 0.0187} ±
{0.0014 0.0015 0.0013 0.0015 0.0014 0.0013 0.0014} watts/(Newton*m/s)

standard deviation 0.0009 watts/(Newton*m/s)

Average water 0.0205 ± .0004 watts/(Newton*m/s) (note: error orginally posted as +/- 0.0015)
Average air 0.0188 ± 0.0004 watts/(Newton*m/s) (note: error originally posted as +/- 0.0014)

Note about error:
The changes to error propogation were made because I kept thinking something was wrong with the error because they where about the same for the average as the data points. I thought error was suppose to go down as you collected more data so I checked the equations I used and found I had been calculating the error for the average wrong.

For purposes of later comparing to infield data I took the ratio of the two

The ratio of average crr air/average crr water
0.92 ± 0.024 ( note: error originally posted as +/- 0.096, it is now calculated from the new errors for the average crr roller values )

Infield to determine an effective crr I completed sets of 4 loops on a .5 mile course with air and water back to back to get as similar conditions as possible. I again used 90psi inflation and tried to hold 150 watts as best I could. I had 50m acceleration zones(I used 250watts acceleration power) that I trimmed off from the data then took a time weighted average velocity and power of the four segments. I then used a value of cda I had from a wind tunnel visit along with a bike modeling program we made in class and programmed it to find the crr that would give me the avg velocity for the given avg power for each trial. I conducted 7 of these trials. I wanted to do more trials but because of time and weather was unable.

For each pair of air-water data I took the ratio crr air/crr water then averaged. The results are as

the first entry of water and air correspond to data taken on the same day very close to each other on so on for the second, third, ext.

Water { 0.0085 0.0090 0.0086 0.0087 0.0079 0.0088 0.0077} watts/(Newton*m/s)
Standard deviation 0.0005 watts/(Newton*m/s)

Air { 0.0086 0.0080 0.0079 0.0078 0.0078 0.0074 0.0079} watts/(Newton*m/s)
Standard deviation 0.0004 watts/(Newton*m/s)

Ratios (crr air)/(crr water) {1.01 0.89 0.92 0.90 0.99 0.84 1.02}
Standard deviation 0.07

Average of ratios 0.94 +/- 0.03

Although I wanted enough data to form a Gaussian distribution the average of 0.94 +/- 0.03 infield to the average 0.92 +/- 0.024 on the rollers seems to indicate the water inflated tires are performing as expected.

I went back and used the conversion factor outlined in Tom A.'s blog for converting roller crr to infield crr (along with the X1.5 approximation for real road conditions) and got the predicted crr's as

predicted water crr 0.008 watts/(Newton*m/s)

Avg infield computationally determined crr water 0.0084

predicted air crr from rollers 0.0074 watts/(Newton*m/s)

Avg infield computationally determined crr air 0.0079 watts/(Newton*m/s)

I just corrected my infield crr's according to temperature from Tom.A's 1.4% per deg C (I recorded temperature on test day although at my house and not at the test site but better than nothing) and corrected them to 21 deg C, my roller testing temperature.

Avg infield computationally determined crr water corrected for temp 0.0077 watts/(Newton*m/s)

Avg infield computationally determined crr air corrected for temp 0.0072 watts/(Newton*m/s)

Which I think is pretty revealing in its predictive capabilities.

I theorized that the increase in resistance was from having to flatten a small element of water as the wheel rolled. I made a made an estimate on the size of this element from the amount of deformation in the contact patch. I calculated how much work would be required to flatten this element of water in a time calculated from how many of these elements there where in the circumference of the bike wheel and how fast the bike was moving. The results came to the same order of magnitude as the measured losses. If I remember correctly I think I got 8watts from the calculation for riding a 17mph which is a about twice the amount of increase in power requirement from the measurements.

note: the above applies for steady state, during accelerations there is likely quite a lot of turbulence.


Anhalt, Tom. “Blather ‘bout bikes, tire crr testing on rollers-the math”. Internet, February 9, 2013

Wilson, and Papadopoulos. “Bicycling Science third edition”. Cambridge MA: MIT Press, 2004. print
Last Edit: 3 years, 8 months ago by howardjd.
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