Triathlon: should I deflate my tires in the sunny bikepark?

So what’s the ritual all about?

Competitors deflate their tires to prevent a possibly explosion, due to high pressure building up, itself due to the air getting really hot in the inner tube, thus reaching a pressure exceeding the resistance of the clincher or the tube.

The physical law behind

Fundamentally, it all starts from a perfectily founded observation.  Indeed, the black rubber of the clinchers or the tubes get energy from the sun, thus heat up the air inside, which wants to expand, due to dilatation, a natural physical phenomenon that nothing can prevent.  Since the air inside has a limited volume to take up (the inner tube’s); it can’t expand freely, so instead its pressure increases, much like inside a pressure cooker.  Except the resistance of the tire has a limit that is much lower than a pressure cooker, and may blow up past a critical pressure.
What sounds like a wise precaution first, may be an overreaction from the actual risk in presence.

So, could the tires possibly blow up?

What final pressure are we really looking at in practice?

Let’s go back to the fundamentals of static gases (as in, not flowing, which is the case in a tire).  What have we got?

In this equation, P is the pressure of the gas in the tube, as an absolute pressure (i.e.  including the atmospheric pressure, see below), V its volume, equal to the inner tube’s, since it fills it with no escape; T is its temperature, expressed in Kelvins (see Reference #1 down this page), that we will consider to be consistent in the inner tube, for simplicity’s sake; n is quantity of moles of the gas, basically the quantity of gas, in a special unit we will explain below; finally R is a constant, called the constant of perfect gases, equal to 8.31 J/(mol·K), that is, Joules per mole and per Kelvin, we will detail this too at the end of the topic, in the References section, although we don’t really need to make n and R intervene in the calculations here.

Immediate results

Since we have an equality, we can divide each member by another equality, in particular, we can stack these equations, the one above will be at state 2, after a couple of hours of the sun beating down on the tire, and the one underneath will be at state 1, when the competitor has just finished inflated his tires.
We can eliminate n and R from the equation, since we find them both in the numerator and in the denominator.
Two, we can eliminate a further term: The Vs, since V₂ is practically equal to V₁, since the tube/clincher barely expands despite the inner tube getting tighter underneath.  This is a direct practical observation from the experiment, we won’t need to demonstrate this.

Myth 1 : T₂/T₁ is not that impressive

The first conclusion that this equation leads to, is that P₂/P₁ ratio varies exactly as T₂/T₁ does.  So, to have a meaningful growth of pressure in the inner tube, it would need T₂ much greater than T₁.  But, do we have this?
The bike has been hanging around the bikepark anyway.  It was not in a fridge or a refrigerating van just before, was it? So why, when the bike got inflated at 8 bars (116 psi), in the hotel room, or near the car that brought it to the bike check-in, would it have tires that were much cooler than after 2 hours of sun beating down on it in the bikepark?
We can accept, that in the worst case scenario, air was inflated to 8 bars (116 psi) or so, in a 21°C (70 °F) air-conditioned room at the hotel, then the bike got brought to a bike park that is seriously heated up by a strong summer sun, and there air may get to 50°C (122 °F), due to tar reflection.

So, what is the T₂/T₁ ratio worth in this worst case scenario?
Let’s see:
All temperatures must be handled in Kelvins (see Reference #1 down this page)

T₂/T₁ = (273.15+50) / (273.15+21) = 1.10 = 10%

Conclusion: despite the greate apparent temperature difference for the human, T₂ is only 10% greater than T₁ for physics.  Not really impressive.

Myth 2 : P₂/P₁ is not much more impressive

Given the formula we’ve shown earlier, P2/P1 equals T2/T1, meaning P2 is only 10% greater than P1 too.  Not exactly impressive.
Beware though: this works with absolute pressures.  Your pump gauge displays the pressure above the atmospheric pressure, so 8 bar (116 psi) on the gauge means about 9 bar absolute inside the tube.  After a 10% increase, we get about 9.9 bar absolute, i.e.  about 8.9 bar (129 psi) on the gauge; whoa, do you think your tire will create a nuclear blast at 129 psi instead of 116?

What the rubber really endures

What matters to the rubber is not the ratio between the inside and outside pressures, but their difference: this is what pushes on every square centimeter of the tire wall, from the inside out.
At sea level, the outside pressure is 1013 hPa (about 1 bar).  With 9 bar absolute inside, the rubber withstands a difference of 8 bar, which is exactly what your gauge shows.
In the bikepark, the inside goes up to 9.9 bar absolute, so the difference grows from 8 to 8.9 bar: the stress on the rubber increases by about 11%.

Could altitude do the same?

As you climb, the outside air gets thinner, which also increases the pressure difference across the rubber.  Wikipedia supplies a good formula linking pressure and altitude: at 900 m, roughly half of Mt Ventoux, the outside pressure drops to about 912 hPa.
The difference becomes 9 - 0.91 = 8.09 bar, only about 1% more than at sea level.  To get the same 11% increase as in the bikepark, the outside pressure would have to drop by 0.9 bar, down to about 0.1 bar: an altitude of roughly 16 km, nearly twice the height of Mt Everest.  No road goes there, not even on the Tour de France!
So climbing a mountain is a much milder test than the bikepark, and proves nothing here.  Let’s look at it from another angle.

What does an extra 0.9 bar really mean?

Plenty of riders inflate their tires to 8.5 or 9 bar (123 to 130 psi) in the morning, and nobody worries about it.  In the bikepark, after hours of sun, you end up with about 8.9 bar on the gauge: the very same stress.  Tires are designed with a comfortable safety margin above the maximum pressure printed on their sidewall, precisely to absorb heat, potholes and the odd overinflation.
Enough nonsense! Nobody would worry about a tire inflated to 8.9 bar in the morning, so there is no reason to worry about the same tire reaching 8.9 bar in the afternoon sun.  The laws of Physics do not support the ritual, meaning there are no physical reasons why you should deflate your tires in the bikepark.

Legend / References

Kelvin

It’s the International System Temperature Unit.  Add 273.15 to Celsius degrees to get Kelvins.  For Farenheit degrees, convert to Celsius degrees and add 273.15 .  Under a normal pressure of 1013 hPa (sea level), water freezes at 273.15 Kelvin.  Note that we don’t say“Kelvin degrees”, but just“Kelvin”, since this is a unit, not a scale.