N2 FAQ List:
Some folks have asserted that racers use dry nitrogen in their tires because the pressure of nitrogen varies (with temperature) less than air, or less than moist air, or more predictably than some random mixture of air and water vapor. With the aid of some thermodynamic software, I decided to see just how tire pressure varies over a range of temperatures for different gas mixtures.
If you only want to see the case studies and understand what is happening when a tire is filled with different gas mixtures, skip ahead to the Case Study section. If you are interested in understanding why different tire fills behave differently, keep reading.
Before we get rolling, I need to explain some terms and concepts that are used in discussions of gas pressure. Engineers and chemists will already understand this stuff, but other folks may appreciate the following information.
”Gauge” and “Absolute” Pressure
When we measure tire pressure with an ordinary tire gauge, we are measuring “gauge” tire pressure. This is the difference between the pressure inside the tire and the ambient (atmospheric) pressure. So at sea level, where atmospheric pressure is 14.7 psi, if you measure your tire to be at 40 psi-gauge, it’s actually at 54.7 psi-absolute. If you get a flat and measure 0 psi-gauge, your tire still actually has 14.7 psi-absolute in it. This is why the gauge-pressure in your tires actually increases when you ride to high elevations. Drive to the top of Loveland Pass (11,000 feet), where atmospheric pressure is only 9.8 psi; your tires, which were 40 psi-gauge at sea level, are now at 44.9 psi-gauge, but their absolute pressure is still 54.7 psi. This is even before considering any temperature differences. Most people will only ever deal with gauge-pressure, but in engineering analyses – particularly when dealing with pressure ratios and assessments of gas behaviors – absolute-pressure measurements are important.
The total pressure of a mixture of gases can be understood as the sum of the partial pressures exerted by each component gas. For example, in the atmosphere (by volume: 78% nitrogen, 21% oxygen, 1% other stuff), the total pressure is 14.7 psi at sea level; the partial pressure of nitrogen is about 11.5 psi; and the partial pressure of oxygen is about 3.1 psi. The great thing about this is that in a mixture of gases, you can analyze the pressure behavior of each component gas independently of whatever other gases are there. If I have a container full of neon at 100 psi, and I add helium until the total pressure in the container is 200 psi, the partial pressure of the neon is still 100 psi. This idea will come in handy later when trying to understand the behavior of water vapor in a tire full of moisture-laden air.
Every substance has a property called vapor pressure. If you have an exposed liquid surface, the substance will continue to evaporate until the partial pressure of that vapor reaches the vapor pressure for that substance. At that point, no more liquid will evaporate, and if the system is cooled, some of the substance will condense back into liquid. Note that this behavior is entirely independent of whatever other gases might be present. So the vapor pressure of a substance is the maximum possible pressure at which that substance will remain in a gaseous state. As the temperature is increased, the vapor pressure also increases, as in this plot:
Note that at 212 degrees F, the vapor pressure of water is 14.7 psi; this is the temperature at which water boils (at sea level).
A practical example:
At 70 degrees F, the vapor pressure of water is 0.363 psi. A mixture of air and water vapor at 70F in which the partial pressure of water is 0.363 psi is said to be at 100 percent relative humidity. A bowl of liquid water left out in this environment will not evaporate at all, and if this moist air is cooled off even slightly, fog (suspended droplets of liquid water) will form.
Again, note that this behavior of water vapor is independent of whatever other gases might be present, no matter the total pressure.
Another practical example:
Run a compressor on a 70F day with 100% relative humidity, and fill a storage tank to 150 psi-gauge (164.7 psi-absolute). In addition to compressing the air, you’ve also compressed the included water vapor. The total pressure increased by a ratio of 164.7/14.7 = 11.2, so the partial pressure of the water vapor has been increased to 0.363 * 11.2 = 4.1 psi. Compressing the air also heats it up a lot, so that water remains in a vapor state. However, the air eventually cools down to 70F; when it does, water vapor will condense on the inside of the tank until the partial pressure of the remaining water vapor drops to – you guessed it – 0.363 psi. (This is why you have to drain condensate from the tank on a regular basis.)
Now take that air and let it back out to the atmosphere; the expansion results in a water vapor partial pressure of 0.363/11.2 = 0.0324 psi. The expansion will initially cool this mixture off, but after it warms back up to 70 F – where the vapor pressure of water is 0.363 psi – the relative humidity will be 0.0324/0.363 = 8.9 percent. What this means is that filling your tires from a high-pressure storage tank is the equivalent of filling it directly with ambient air at 8.9% relative humidity.
Some compressors don’t have a storage tank. Most notable among these are the little ones you carry on your bike so that you can repair a flat tire by the side of the road. In this case, you can regard your tire as the storage tank: you squeeze moist air into the tire, and as was just described, unless it’s a very dry day some of the moisture is guaranteed to condense into liquid in there. Won’t be quite as much, since you only fill your tire to about 40 psi instead of 150 psi, but you get the idea.
Now that we all perfectly understand gauge/absolute pressure, vapor pressure, and partial pressure, let’s move on to the case studies.
I simulated six different tire fills. In all cases, the tire begins at 70 degrees F, 40.0 psi (gauge). The cases differ only as follows:
Here’s an overview of what happens to tire pressure over a very wide range of temperatures:
As was explained, all six cases are set up so that at 70F, they are at 40 psi.
As the temperature drops below 70F, the water vapor in cases #4, 5, and 6 condenses, lowering the water vapor partial pressure and causing these cases to deviate from cases #1, 2, and 3 – but not by much, only about 1/3 of a psi as you approach 0F. In fact, the deviation will never exceed 0.363 psi, and that extreme will only happen if you somehow manage to get all of the water vapor to condense out (for example by cooling to cryogenic temperatures). In case #3, the amount of water vapor is so small that you don’t actually get any condensation until about 40F.
As the temperature climbs above 70F, case #6 climbs steeply, especially when we get well past 100F. The puddle of water in the tire adds more and more water vapor to the gas mixture as the temperature increases. If a ridiculously high tire temperature of 212F were achieved, the partial pressure of the water vapor would be 14.7 psi, resulting in a huge discrepancy between case #6 and all the others.
OK, so now we’ve seen what happens in the extreme temperature limits. What happens in the normal operating range of a typical street-legal car or motorcycle tire? Here’s a detail plot of tire pressure behavior within the range where it’s likely to operate most of the time, i.e. start at 70F, and work that tire until it’s somewhere around 110F-120F:
The first thing to notice is that throughout the entire operating range of the tire, cases #1, 2, and 3 are virtually identical, differing by no more than 0.04 psi at 110F. In other words, it doesn’t matter whether you’re using desiccated-dry air, moist air from a 150-psi storage tank, or dry nitrogen: all three mixtures respond the same, with negligible difference, to temperature changes.
The rule of thumb one often hears is that the cold tire pressure should be set so that when the tire warms up during the normal course of operation, the gauge pressure increases by about 10 percent; for this study then, we’re talking about an increase of 4 psi. Note that for cases #1, 2, and 3, this corresponds to a final gas temperature of about 109F (though the tread surface may be significantly warmer than this)]. At this temperature, case #4 pressure has risen (from cold) by 10.8 percent (an extra 0.3 psi), and cases #5 and 6 have risen by 12.2 percent (an extra 0.8 psi). For a typical motorcycle front tire, if you take the water vapor present in cases #5 and #6 at 109F and condense it down to liquid form, it’s a cube of liquid water 5/16” on a side – about 2/3 of a gram. In other words: no matter what you fill your tire with, if you (or your tire-mounting mechanic) got even SLIGHTLY sloppy with the tire bead lube when you mounted your tire, it’s going to behave like case #5 or 6.
So the bottom line on temperature versus pressure: if you’re sloppy with the lube when mounting the tire on the rim, it won’t matter what you fill with. And even if you’re fastidious about using just enough lube to get the job done, it doesn’t matter whether you fill with nitrogen, dry air, or compressed atmospheric air from a high-pressure storage tank: they all behave the same way.
Now that we’ve dealt with the whole pressure-versus-temperature thing, let’s check out some of the other assertions that are frequently made regarding the benefits of nitrogen in tires.
Questions? Comments? Email me!
Copyright ©2006, Mitchell P. Patrie