Do foam tyre inserts get smaller when tyres are inflated?

The previous foam tyre insert testing I did (see previous blog post here) gave some interesting and surprising results.  I was expecting the foam tyre inserts to cause a small rolling resistance penalty, especially at very low tyre pressures of around 15 psi. However, they didn't.  The effect of the foam tyre inserts on CRR (coefficient of rolling resistance) was within the precision of what could be measured in the test, so the effect was very small or nothing.  The results are re-shown in the plot below (the green symbols versus the blue symbols). 

This surprising result got me thinking about the causes.  Why don't the foam tyre inserts have an effect on rolling resistance?  At low tyre pressures, the compression of the foam insert at the contact patch should generate hysteretic losses that manifest themselves as additional rolling resistance. Why is that not seen?  It got me thinking.

One possible explanation, and one that I mentioned at the end of my previous post, was that the ends of the inserts were (unintentionally) not connected when I did the testing, so the foam insert was 'free floating' in the tyre cavity, rather than held tight against the rim.  This is a plausible explanation for an absence of any effect at higher pressures.  However, I would still expect the foam insert to get compressed at 15 psi, when the tyre drop (the squish) should have been enough to compress the foam insert.

There is a second possible explanation for this observation, though, for the lack of a measurable effect of the tyre inserts.  I remembered that when Vittoria launched their Air Liner Road tyre insert for road bikes, they explained that their inserts compress into the rim bead when the tyre is inflated, because the foam is closed-cell foam.  The effect of the tyre pressure on the Vittoria Air Liner was demonstrated nicely in their video below:

This is the reason why the effect of the Vittoria Air Liner on tyre rolling resistance measurements was negligible when it was tested by Bicycle Rolling Resistance here.  It might be the same reason why Aerocoach reached the same conclusion, but for the Tubolight Road insert in their rolling resistance testing here.

Could the same thing be happening for my gravel/cyclocross tyre inserts, that they are shrinking when the tyres are inflated?  I didn't even know whether the foam inserts were constructed from closed-cell foam or not.

I decided to do an experiment to find out.  The method and results are shown in the YouTube video below:

Results

So, the answer is a YES, they do shrink, and quite a lot!

It confirms that my budget Planet X foam inserts are indeed made from closed-cell foam, and so they were subject to the same compression mechanism as the Vittoria Air Liner Road tyre insert.  The picture to the left shows the cross section of the tyre insert as the pressure is raised from zero to 34 psi.  At 34 psi, the insert has shrunk to about a third of it's original size.  At 15 psi, it would have been approximately half it's original size.

So finally, this is plausible explanation, and the most likely reason why I saw no effect on rolling resistance when I tested at 15 psi:  The tyre insert had already shrunk enough that it wasn't actually getting compressed at the tyre contact patch on the rollers. 

Do tyre insert companies know this happens?

We know that Vittoria have figured this out, but what about other tyre insert companies?  I'm not convinced they have.

If I look at some of the promotional pictures on the websites of the various companies selling foam tyre inserts, I get the impression they don't realise this compression is happening.  For example, I have shown on the left a few pictures taken from some of the company's websites. These all show the foam tyre inserts inside the tyres rolling over objects, but the inserts are the same size and shape as their pre-inflated size.

Either the tyre insert companies don't realise what's going on, or they are trying to mislead people.

It could be argued however, that this doesn't matter, and that it's the performance of the tyre inserts that matters.  I would agree with that, and the testing done by PinkBike shows that these tyre inserts do still work (for rim protection), regardless of them probably shrinking when the tyre is inflated.  

However, I think it's still important to understand what size and shape the insert becomes when it's inside the inflated tyre.  For example, is it still going to be wide enough to cushion and protect the rim flanks, or will the insert become too small for that, and instead get pushed down into the rim well and central channel?  That will affect how impact loads are taken by the rim structure.

What many of these companies show is happening, and possibly what they think is happening, inside the tyre is probably not what's actually happening.  It will depend on the construction of the tyre insert though, and how much air is contained in the tyre insert material.  Nevertheless, what's important is to check what size and shape the insert becomes when it's inside an inflated tyre.  Apart from Vittoria, I haven't seen other companies address this.

The physics behind what's happening

This final section may not be interesting to many people, but as an addendum, I can explain why a closed cell foam tyre insert shrinks when the tyre is compressed.

My foam tyre insert has a volume of around 1280 cubic centimetres and weighs 34g.  That means its density is 26.6 kg per metre cubed, which shows that most of that volume is air; air inside the closed cells of the foam.  In view of the density value, I would guess that more than 95% of it is air.

Before installing the tyre insert, the pressure outside and inside the foam insert is at atmospheric pressure, which is 14.7 psi at sea level.  When the pressure outside of the foam insert increases, however, as happens when the tyre is inflated, that external pressure causes the air cells inside the foam to compress to the same pressure.  This is the same principle as when you sit your 80kg backside on a chair: The chair and floor has to push upwards with a force of 80kg.

The volume of the air cells reduces under this increase pressure, as dictated by Boyle's law. Boyle's law says that the volume of a gas (air in this case) is inversely proportional to pressure, for a fixed mass and temperature of gas.  This means that if the pressure doubles, then the volume must half.

For our particular application, a doubling of the pressure means putting 15 psi into the tyres, because remember, the pressure started at one atmosphere, which is about 15 psi.

And what happens if 15 psi is applied?  The volume of the foam tyre insert approximately halves, as shown on the left.  This is a good demonstration of Boyle's law.  Another demonstration of Boyle's law, very similar to this, can be found here, which is the link on the Wikipedia page.

People very familiar with these gas laws may already realise that for the case rapid inflation or deflation, as shown in my video, the expansion is not strictly following Boyle's Law.  This is because Boyle's law assumes an isothermal (constant temperature) expansion or compression.  A rapid expansion or compression is an adiabatic process (no heat transfer) instead of an isothermal one, and is therefore subject the Ideal Gas Law instead, which considers temperature changes on pressure and volume (whereas Boyle's Law assumes temperature is fixed).  In the case of a tyre being quickly inflated, if the pressure is doubled, the volume won't be halved but will be 61% instead. This 0.61 value come from 0.5 raised to the power of (1/gamma), where gamma is the specific heat ratio for air, which is 1.4.

What's important though is what volume the foam tyre insert will be when it's in the inflated tyre being ridden.  In that case, the foam insert and the tyre will have reached thermal equilibrium after half an hour or so, so in all practical riding cases, where tyres would have been inflated in advance of the ride, thermal equilibrium would have been reached, and so Boyle's law is appropriate.