How does tire pressure vary with altitude?

True enough, but the author does not also factor in Temperature which also affects psi. So as the ambient temp increases 10 degrees, tire pressure will increase 1 psi, assuming no change in altitude. But that increase in psi is off set if you are increasing in altitude because atmospheric pressure decreases as altitude increases.

So if your psi is say 40 at sea level, it will be almost 46 psi at 8,000 feet above sea level. But it will also probably be colder at 8,000 feet than at sea level. So assuming ambient drops from say 80 at sea level to 40 at 8,000, temp alone would drop your psi about 4 psi, so adjusted to altitude, your net change in psi is only 2 psi more after factoring in BOTH temp and altitude. And in the winter, ambient at 8,000 feet could easily drop to 20, so your net change in psi would be 0.

How does measured tire pressure vary with altitude? If I inflate a tire to the recommended cold pressure of 30 PSI in Yellowstone (elevation 8000 feet), then drive to Big Timber (elevation 4000 feet) and measure the pressure the next morning at 26 PSI, does this mean I have a slow leak, or is this due to the change in atmospheric pressure?

The important thing to notice is that tires (sans leaks and temperature changes) have a constant absolute pressure inside, but what any gauge tells you is the pressure difference.

Example: I have a fat-tired bicycle that uses around 0.5 bar pressure (gauge reading). If I inflate it at room temperature to 0.5 bar (gauge reading), it actually has 1.5 bar. Pressure is proportional to temperature so 22 degrees Celsius room temperature (295.15 Kelvins) reduces to -10 degrees Celsius (263.15 Kelvins) so pressure is now 1.5 bar * 263.15 / 295.15 = 1.3374 bar. The pressure difference is thus 0.3374 bar. So for these kinds of bicycles, you have to be precise what your intended working temperature is. Inflating the tires at some other temperature is a problem.

A similar problem occurs with altitude. If you have 30 PSI at 8000 feet, it's at 10.91 PSI ambient pressure. Thus the pressure is actually 40.91 PSI. Then lowering to 4000 feet (12.68 PSI) you have 40.91 PSI absolute or 28.23 PSI relative.

Thus, the possibilities are as follows:

• Your tire had 30 PSI relative, it reduced due to altitude to 28 PSI relative and then you lost 2 PSI due to a leak.
• Your measurements are not precise and the apparent 2 PSI leak was due to imprecise measurements
• Temperature had an effect. For example, if the 30 PSI was measured when the tire was hot, and the 26 PSI was measured when the tire was cold, it is very well possible that of the 4 PSI difference, 2 PSI was due to altitude and the remaining 2 PSI was due to temperature. (See the fatbike example -- car tires have a far higher pressure than fatbikes so the problems are not as prominent as for fatbikes, but the problem is that temperature still has an effect on tire pressure.)

The apparent 2 PSI leak can for example be caused by 15 degrees Celsius reduction in the tire temperature. If the ambient temperature reduced by this amount, there's your problem! If not, it could be that the 30 PSI was measured when the tires were warm from driving, and the 26 PSI was measured when the tires had not been driven for a long time and were thus cold.