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In this picture:

figure 1

it states the tops and bottoms of the 3 columns of air have the same pressure.

This explains the error in altitude indications given in a non-standard temperature.

Pressure only drops 1 inHg per 1000 ft. when temperature is standard.

Assuming that the bottoms of the column of air are at sea level, why aren't pressure altitude readings (setting altimeter to 29.92) affected by the True altitude formula, TA = IA + (4ft. x (1000s of ft) x (OAT - ISA))?

I was always told temperature does not affect pressure altitude readings because the atmosphere is not a fixed volume of air. If temperature increases, it will also expand in volume, like how the picture explains.

I could see how pressure altitude wouldn't be affected by 4ft. per 1000ft per (delta°C ISA) only if the picture assumed the bottoms of the pressure started at ground level.

Or does it affect pressure altitude, just very slightly and non-significant? Not as much as if you were in a fixed volume of air...

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The picture you have displayed is correct. But, your understanding of what it is saying is incorrect. The picture is explaining the reason your Indicated Altitude will change with temperature for the same True Altitude. And, your True Altitude will change with temperature (a potentially dangerous situation) for the same given Indicated Altitude.

Your misunderstanding may stem from the fact that the Indicated Altitudes and the field level barometric pressure (or at least the Altimeter Kollsman Window) setting are the same in all three temperature scenarios. This is not the case for the pressure at 10,000 feet MSL True Altitude. The atmospheric static pressure at altitude for the three scenarios is not given. And, they can not be equal to 29.92.

The static atmospheric pressure is higher for the cold scenario and lower for the warm scenario at 100,000 feet MSL True Altitude. You would think that this would be the opposite way around. And, it is for air confined in a container. But, not for unconfined air or air confined in different sized containers.

Atmospheric air will become less dense and rise when warmed. This will create a partial void of air below it. This partial void is an area of low pressure since the surrounding air has yet to move in to fully replace the vacating air. If the air were to be cooled, it would sink onto the air below it. This would create an area of high pressure as the existing air has not moved outward in sufficient quantity yet.

How does this affect the different types of Altitude? Like this:

  • True Altitude is the height above MSL measured in actual feet of distance.
  • Pressure is just a measurement of the amount of air interacting with the measurement device and the average amount of energy each air particle has. Temperature will affect the amount of energy possessed by each air particle proportionately. This will either cause the pressure to change proportionately. Or, it will cause the volume and density of the air parcel to change proportionately.
  • Barometric Pressure (Altimeter Setting, Kollsman Window Setting) is just the static atmospheric pressure at field elevation adjusted to show what the pressure should be at Mean Sea Level.
  • Indicated Altitude is just the reading you receive from your Altimeter. Your altimeter is just a very accurate pressure gauge (a barometer) calibrated to show the height above a specific reference line of pressure. The pressure and density of air at lower altitudes are greater than they are at higher altitudes. This is due to the sheer weight of the air from above pushing down and compressing the air below. The amounts of changes of air pressure and air density are known. This is based on observationally, scientifically and mathematically derived formulae and estimations that are based on the International Standard Atmosphere. On an ISA day, that reference line is equal to the Mean Sea Level. That is not always convenient since the atmosphere is not always at standard pressure and temperature at Mean Sea Level. So, most altimeters can be adjusted to account for non-standard barometric pressure.
  • Pressure Altitude is just the height above the mathematically derived line representing where the International Standard Atmosphere pressure of 29.92 inches of Mercury should be felt. Pressure Altitude is the height in feet you would feel the same pressure on a non-standard day as you would on an ISA standard day in feet MSL. If the atmospheric pressure at MSL (or the barometric pressure at field elevation) is not standard, the two beginning levels will not be in the same place. You would have to make an adjustment to the height of MSL to derive the Pressure Altitude. The pressure of air is derived from its volume and energy content. Temperature is a factor in this only if the air is confined or in a container.
  • Density Altitude is just the height above the mathematically derived line representing where the International Standard Atmosphere density. Density Altitude is the height in MSL where you would feel the same density on a non-standard day as you would on an ISA standard day. If the atmospheric density at MSL is not standard, the three beginning levels will not be in the same place. You would have to make an adjustment to the height of MSL to derive the Density Altitude. The density of air is derived from its weight and volume. Both pressure and temperature are factors in this only if the air is unconfined or in a container.

You derive Density Altitude by adjusting Pressure Altitude by atmospheric temperature. You derive Pressure Altitude by adjusting the True Altitude by the atmospheric pressure. You have to have each to get the next.

Case in point. If the air were confined to nice, neat, little columns with defined and rigid lateral boundaries and adjustable vertical boundaries, the average pressure in each container would remain the same. The heights of each column would be different based on temperature. For extremely tall columns, the pressures at the bottoms would all be equal. And, the pressures at the top would all be equal. But, the rate at which the pressures would change with height would be different. Since Indicated Altitude is just another way to represent the static atmospheric pressure at altitude, the Indicated Altitude of 10,000 feet MSL would be at different True Altitudes based on temperature.

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  • $\begingroup$ In your 3rd bullet, you say that your altimeter setting is static pressure at field elevation adjusted to show the pressure at 0 MSL. If the airport is 1000 ft. above MSL, then the actual pressure on ground should be lower than the kollsman window right? For example, in the picture provided, if they were all set to 29.92, why would being at the field (1000ft) give the correct pressure altitude without being affected by temperature compared to being at 10,000 ft. MSL? My understanding of the gradients being stretched out is what causes the 4ft per degree per 1000ft. $\endgroup$ Feb 26 at 18:00
  • $\begingroup$ The easiest way to explain my question is say the airport was a quarter way up in altitude on the middle column in the picture. Why isn't it affected by temperature when setting it to 29.92 even though the actual pressure would be slightly lower than MSL? $\endgroup$ Feb 26 at 19:13
  • $\begingroup$ @user7828137 - I can see how my wording is a little confusing. The barometric pressure that is used to set your altimeter Kollsman window would be the barometric pressure at Mean Sea Level. If you are at an airfield whose field elevation is above Mean Sea Level, there is no way to measure the actual barometric pressure below ground level. The static atmospheric pressure at field elevation is measured. Then it is adjusted for the higher than sea level elevation. The static pressure measured will be lower than the barometric pressure. But the adjustment is fairly predictable. $\endgroup$
    – Dean F.
    Feb 26 at 20:20
  • $\begingroup$ @user7828137 - If you set your Altimeter to the correct barometric pressure at MSL, it should show you your correct field elevation to within 75 feet. Even though it is actually reading a lower static atmospheric pressure. If you were set your Altimeter to the static pressure measured at field elevation by a non-calibrated barometer, your altimeter would read zero feet. If you were to set your altimeter to zero feet, your Kollsman window would read a lower setting than what the current setting would be for that field if the field were above MSL. $\endgroup$
    – Dean F.
    Feb 26 at 20:33
  • $\begingroup$ The picture you have given does not represent three airports at different field elevations. It represents the same airport or three airports at the same field elevation. True Altitude references MSL. Absolute Altitude references AGL. The actual field elevation is irrelevant in this picture. Your idea on temperature affecting pressure is correct if the air were in a rigid container. Instead, the air is unbounded. Think of the columns as cylinders with movable pistons. So, instead of the pressure changing with temperature. The volume changes. And, weight stays the same. $\endgroup$
    – Dean F.
    Feb 26 at 20:42
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Because Pressure altitude is a measure of the weight of the air above you. Temperature does not affect that. Heating the air just makes it expand. It still weighs the same.

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  • $\begingroup$ I'm confused on when temperature affects the pressure vs. When it doesn't, because it does change 4 ft per per degree from standard temperature per 1000 ft when flying. I understand (I think) that at 0 MSL, the weight above is the same, but for an airport at 3000 ft., why does it not change there? You are already 3000 ft up in the pressure gradient so isn't there room for error in those 3000 ft.? $\endgroup$ Feb 26 at 18:16
  • $\begingroup$ @user7828137 - The altimeter setting is not the static atmospheric pressure at field elevation. It is what the static atmospheric pressure would be if the field were at Mean Sea Level. If it were not consistently given referencing MSL, aircraft Indicated Altitudes would show AGL instead. Two different aircraft flying in the same general area with 1000 foot separation and the same altimeter setting would be in conflict if one were flying above an area with 1000 feet of difference in field elevation. $\endgroup$
    – Dean F.
    Feb 26 at 21:07
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    $\begingroup$ @user7828137 - From your comment, I can see that you are putting the cart before the horse. It is not the temperature that is affecting the pressure (not directly at least). It is the pressure that is affecting the temperature. If the atmosphere has a standard lapse rate, the temperature of the air will decrease by 2°C for every 1000 feet of altitude increase. This is due to adiabatic cooling (cooling due to decreasing pressure). $\endgroup$
    – Dean F.
    Feb 26 at 21:16
  • $\begingroup$ First of all, why would anything in the 3000 feet below you affect the pressure? That air cannot be pressing on you. It is below you. You can stand on a 20 ton block of concrete without ill effects... But put the block on your head ... The formula you reference is a part of a shortcut used to calculate pressure altitude when you know the local altimeter setting. It assumes that the altimeter setting is the measure of the air that would be above you if you were at Sea Level at the same place. You cannot draw any inference from this as to how pressure altitude changes from temperature. $\endgroup$ Feb 27 at 15:18
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By definition temperature is not factored in to calculation of pressure altitude. Pressure altitude is always the indicated barometric altitude with 29.92 used as a barometric offset. Temperature will affect the altitude of aircraft flying at pressure altitude though.

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  • $\begingroup$ If you were at an airport on two different days at 5000 MSL with the exact same barometric pressure say 30.92, but one day was freezing cold and the other day was very hot, would you have two different "pressure altitudes" then? $\endgroup$ Feb 26 at 20:31
  • $\begingroup$ @user7828137 - No. You would have two different density altitudes with the same pressure altitude. That is why density altitude is taken into consideration when calculating aircraft performance. Pressure altitude is only a way of deriving density altitude. Pressure altitude can be easily measure by setting your altimeter to 29.92 inches of Mercury. Pressure altitude is the altitude at which your ears think they are it will affect the pressure gradient of your body. Density Altitude affects the oxygen absorption of your cells and the performance of your engine. $\endgroup$
    – Dean F.
    Feb 26 at 20:46
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As already stated, pressure is effectively the weight of the air above the aircraft. If you were (for example) to double the absolute temperature of the entire atmosphere (from say 300K at sea level to 600K then the atmosphere would double in volume, assuming it’s an ideal gas, which isn’t a million miles from the truth, and pressure altitudes would increase by almost a factor of two (but not quite, with the Earth being spherical). However, a localised temperature change would tend to result in expanding air spreading out into the surrounding airmass rather than generating a localised lump in the upper atmosphere.

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