Temperature change & Altimeter indication

Question

Ref: FAA Pilot's Handbook of Aeronautical Knowledge 2023 (faa-h-8083-25c) Page 8-4, column 2, paragraph 3 (including figure 8-3) through page 8-5, column 1, paragraph 1.

As a background to my question, the statements on Page 8-4, column 1, paragraph 3 through column 2, paragraph 1, related to flying from a high-pressure area to a low-pressure area without adjusting the altimeter make perfect sense (it is implied that the pilot maintains the plane’s indicated altitude in the process). Clearly, the atmospheric pressure drops in the process and, as a result, the true altitude decreases if constant indicated altitude is held constant. Said another way, if the true altitude were maintained in the process, the altimeter would display a higher indicated altitude as it would register the lowered atmospheric pressure.

By similar logic, I would think that traversing from a warm air mass to a colder air mass would result in entering into a denser air mass. A denser column of air would therefore produce increased atmospheric pressure. If one were to maintain the same indicated altitude during that part of the flight, I would think that the true altitude would increase. Similarly, increased atmospheric pressure would show a lower indicated altitude if a constant true altitude were maintained through that portion of the flight.

Clearly, my logic in the above paragraph shows me to have my head on upside down! The question is, what am I missing in the big picture to have drawn such an erroneous conclusion? Does it have to do with where the temperature is warmer / colder than (adjusted) standard; i.e., at sea level or at the altitude at which the plane is located (my assumption)? It has been suggested that I am thinking about Boyle’s Law and that is giving me an incorrect perspective on the situation. But, even in free air, won’t colder air have increased density and therefore greater air pressure at the bottom of the air column compared to warmer air?

I’m totally confused and suspect I should just stay on the ground and taxi around!

Answer 1

I made a nice picture for you:

Now, as we know, the air pressure can be thought of as the weight of the air above you.

We also know that temperature of any matter is simply the kinetic energy of the particles of that matter: The hotter something is, the more kinetic energy the particles of that matter have.

In atmosphere the kinetic energy of the gas molecules makes them bounce against each other, pushing them apart and expanding the gas. This expansion will also "push" the pressure gradients away from each other, so in hotter weather the pressure gradients are further apart from each other as shown in the crude presentation above.

A given volume of cold air is denser than the same volume of hot air, but in atmosphere the pressure gradients are also placed closer together in cold air.

This will manifest itself as the "from high to low, look out below".

_{P.S. the atmosphere is a VERY complex system. Local atmospheric pressure is not in fact simply a product of the height of the air column above you. Vertical movements of the air and deviations from standard atmospheric lapse rate also play a significant role in local atmospheric pressure. I personally found meteorology the most demanding and fascinating subject during my PPL studies due to the complexity of the subject :)}

Answer 2

You're actually closer than you think: it's not where the temperature is adjusted, it's where the pressure is adjusted.

The reason is that colder air above a ground pressure has a steeper pressure loss gradient with altitude than warmer air. Because of its greater density near the ground, it needs less volume to make the same weight (pounds per square inch =pressure).

The column of air above a warmer place (at the same ground pressure) will be taller and have higher pressure at altitude.

Look at weather. Cold fronts roll forward on the ground due to greater density, warm fronts ride up over cold air at altitude due to greater temperature.

To further understand this phenomenon one can compare pressure change differences to temperature change differences in passing fronts. Pressure change differences occur gradually over many miles, whereas temperature change differences occur in a frontal passage over only a few miles.

Using the Gas Law P is proportional to Density and Temperature (Kelvin scale), one can see, with a passing front dropping temperature 30 degrees$^1$, we have (273+30)/273 = an 11% difference in temperature at a similar local pressure$^2$.

So, local pressure gradient "stacking" with altitude, as confusing as it is, must be accounted for, as the altimeter only reads pressure.

$^1$ Celsius and Kelvin units are the same, 273 Kelvin = 0 Celsius, 303 Kelvin = 30 Celsius

$^2$ Even a hurricane pressure gradient can be as little as 960 mb/942mb over 100 miles, or around 1 percent!

What we need to know as pilots is the:

altimeter error relative to the ground pressure reported at a take-off/landing site based on deviation +/- from standard temperature

altimeter error relative to passing through a warm air mass into a cold air mass from temperature change and

altimeter corrections based on changes in reported ground pressure as we fly deeper into the cold air mass (they're bound to increase).

More reading here.