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Let us consider a bike wheel. Does anybody know a way to calculate how much does rolling resistance changes if the inner tire volume is filled with foam instead of air? Let's assume a foam hardness which equals a 2 bar inflation.

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    This will depend on the surface in a different way to an air-filled tyre; you also can't really define a foam as being equivalent to a 2 bar inflation in practice because a normal tyre uses the whole volume to adjust for load and absorb impacts, i.e. a foam that matches that pressure in some ways won't match in others. – Chris H May 16 '18 at 16:39
  • Rolling resistance depends on much more than just the inflation pressure so I don't really see how your assumption helps. – David Richerby May 16 '18 at 16:39
  • I don't quite understand your question. Any of the methods currently used to measure rolling resistance with a pneumatic tire would work with a non-pneumatic tire. Perhaps a better question could be "how can one calculate rolling resistance for a tire?" – R. Chung May 16 '18 at 16:41
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    @albus_c Calculating it probably requires approximation and finite-element analysis. People do whole PhDs in that kind of thing. Building one and measuring the rolling resistance would probably be much easier. – David Richerby May 16 '18 at 17:31
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    I can summarize some of the ways that rolling resistance is measured, but I'm pretty busy right now so I may not be able to provide a full answer for a couple of days. I'll upvote good answers. Basically, the methods involve controlling input power (whether zero or non-zero) and then calculating the drag that dissipates that power. Meanwhile, this bicycles.SE question talks about estimating drag. – R. Chung May 16 '18 at 19:34
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Even with a finite-element tool kit you would need a lot of physical data in order to be able to calculate the RR. In addition to data for the tyre casing and rubber you would need the visco-elastic properties of the foam. Deformation of a foam will certainly absorb more energy than deformation of an air chamber, hence result in higher RR.

There is a kind of foam tyre made of closed-cell polyurethane foam sold under the trademark name Amerityre Flatfree. You can find on the internet an investigation of this tyre by Thierry Larose Chevalier et al from the University of Ottawa. http://www.flatfreetire.ca/Ottawa%20U.pdf

The results of this study are a bit ambiguous. Based on in-shoe force measurements from cycling on training rollers the authors state that there is no significant difference in RR with a traditional clincher road tyre. However, the participant cyclists subjectively commented that they felt more resistance.

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  • I don't see how in-shoe force measurements can effectively measure rolling resistance. And certainly a purely mechanical test would be more accurate and easier to perform. – Daniel R Hicks May 16 '18 at 23:01
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    It's easier to bypass the FEA and just go to measuring the drag. There are lots of ways to do that, though some are more hassle or require more instrumentation than others. I know of pendulum tests, coasting tests, driven roller tests, and field tests with and without power meters. There may be others I'm forgetting at the moment. I haven't done the pendulum test but I've done the others. – R. Chung May 17 '18 at 0:25
  • @Daniel Hicks In principle an in-shoe force measurement is as suitable as a force measurement in the pedal (Look) or in the crank (SRM) to compare applied power. However, it will be more difficult to calibrate. – mathieu van rijswick May 17 '18 at 8:35
  • @mathieuvanrijswick - The thing is, the foot power meter scheme will have such high variability that that could swamp the real "signal" in a test such as this. The fact that this company chose to use this technique suggests that they wanted to bury the signal in noise. – Daniel R Hicks May 17 '18 at 11:35
  • The study was not done by 'this company' but by a research group at the University of Ottawa. Why do you believe that these investigators wanted to 'bury the signal in noise'? Please read the article! It was presented in a symposium of the International Society of Biomechanics in Sports, 2007, Brazil. – mathieu van rijswick May 17 '18 at 13:14

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