Cold Air Altimetery

[UndauntedFlyer]

Yeah, if you can give us a similarly lucid explanation as to why this happens, I think we'll have another thread all wrapped up.

Thanks for the opportunity to better explain my reply.

The air is more vertically compacted on a cold day (because it's heavier) and it is less vertically compacted on a warm day (because it is lighter).

If you climb to the top of a 1000 foot tower with an altimeter in your hand and the temperature is below (ISA) standard at the top of the tower the altimeter will read greater than 1000 feet because the 1000 foot pressure level is below the top of that tower. In other words, if a pilot is reading that altimeter he might think he is at 1100 feet when in reality he is at 1000 feet (lower than the thinks and in a dangerous position).

Conversely, if you climb to the top of that tower on a warmer than standard day the altimeter will read an altitude of something lower than 1000 feet because the 1000 foot level is above the top of the tower.

This is as lucid an explaination as I can give.

Hit the EASY button.

Your questions or comments are always welcome.

 

[Alamanach]

The air is more vertically compacted on a cold day (because it's heavier) and it is less vertically compacted on a warm day (because it is lighter)...

...if a pilot is reading that altimeter he might think he is at 1100 feet when in reality he is at 1000 feet...

So you're saying that cold air is denser and (by inference from the altimeter) at a lower pressure. That's pretty much what A Squared is saying. There's only one way I can get this to jibe with basic thermodynamics, and that is if the temperature drop has a greater effect on the pressue than the rise in density does.

And as it happens, the temperature lapse rate is linear while the density lapse rate is not. If I could superimpose plots of T and D, both as functions of altitude, I think I could show how a change in temperature will have a bigger effect than the comprable change in density (in some regions of the plot, at least). I'm sticking with my ideal gas law on this one.

 

[UndauntedFlyer]

So you're saying that cold air is denser and (by inference from the altimeter) at a lower pressure. That's pretty much what A Squared is saying. There's only one way I can get this to jibe with basic thermodynamics, and that is if the temperature drop has a greater effect on the pressue than the rise in density does.

And as it happens, the temperature lapse rate is linear while the density lapse rate is not. If I could superimpose plots of T and D, both as functions of altitude, I think I could show how a change in temperature will have a bigger effect than the comprable change in density (in some regions of the plot, at least). I'm sticking with my ideal gas law on this one.

I really can't comment on the plots of the T and the D, all I know is how the altimeter works and what the errors are. I can not make my explaination any simpler because the concept is already simple.

My advice it to forget about the engineering stuff and the thermodynamics, then just re-read what A-squared and I have written. Trust us, it works just as explained.

Questions, comments are always welcome.....

 

[Alamanach]

My advice it to forget about the engineering stuff and the thermodynamics...

Too late! I typed the relevant numbers from Aerodynamics for Naval Aviators into Microsoft Excel, made a few plots, and crunched a few numbers. Here's what I found:

First of all, the Ideal Gas Law most definitely works for standard atmosphere. In fact, the fit is so good, I suspect the Ideal Gas Law may have gone into the definition of standard atmosphere.

Secondly, it is possible, as I speculated above, for the increase in density to be overcome by the decrease in temperature, resulting in a drop in pressure. As UndauntedFlyer and A Square have insisted, there is some shrinking of the atmosphere. However, it should be emphasized, that this vertical compaction is a smaller effect than the drop in temperature, and it tends to mitigate that temperature drop. We could say that the temperature drops so much, it actually causes some collapse of the atmosphere-- but not enough of a collpase to prevent a drop in pressure.

To steal a line from Undaunted Flyer, the Ideal Gas Law is the only correct way to understand this phenomenon.

 

[UndauntedFlyer]

Too late! I typed the relevant numbers from Aerodynamics for Naval Aviators into Microsoft Excel, made a few plots, and crunched a few numbers. Here's what I found:

First of all, the Ideal Gas Law most definitely works for standard atmosphere. In fact, the fit is so good, I suspect the Ideal Gas Law may have gone into the definition of standard atmosphere.

Secondly, it is possible, as I speculated above, for the increase in density to be overcome by the decrease in temperature, resulting in a drop in pressure. As UndauntedFlyer and A Square have insisted, there is some shrinking of the atmosphere. However, it should be emphasized, that this vertical compaction is a smaller effect than the drop in temperature, and it tends to mitigate that temperature drop. We could say that the temperature drops so much, it actually causes some collapse of the atmosphere-- but not enough of a collpase to prevent a drop in pressure.

To steal a line from Undaunted Flyer, the Ideal Gas Law is the only correct way to understand this phenomenon.

With all due respect, the "ideal gas law" sounds great to you and other engineers but to just ordinary tripple 7 captains and DPE's like me, much less FLYBIEWIRE who is 15-years old and made the post, the "compacting of the atmosphere" in cold air is a much simpler and yet a totally correct answer. In fact, even in the FAA's Aviation Weather book it uses the "compacting" explaination to explain errors of cold air on the altimeter.

More questions or comments are always welcome....

 

[Alamanach]

...to just ordinary tripple 7 captains and DPE's like me... the "compacting of the atmosphere" in cold air is a much simpler and yet a totally correct answer...

As coincidence would have it, you were my DPE about ten years ago.

OK, I think we've wrapped up another one.

 

[FL420]

Alamanach, you know your stuff and that's good. OTOH, your explanations make my head hurt; but I guess that's my problem, not yours.

 

[UndauntedFlyer]

As coincidence would have it, you were my DPE about ten years ago.

That's all interesting. I hope I was a good guy and passed you?

 

[Alamanach]

That's all interesting. I hope I was a good guy and passed you?

You did. Your exact words were, "You're an excellent pilot."

 

[A Squared]

First of all, the Ideal Gas Law most definitely works for standard atmosphere. In fact, the fit is so good, I suspect the Ideal Gas Law may have gone into the definition of standard atmosphere.

Yes, of course the standard atmosphere is based on the ideal gas law. I've never said the ideal gas law was invalid. That is something you read into my words, repeatedly. What I did say is the the ideal gas law does not completely explain all that is going on. remember we're not talking about the standard atmosphere, we're talking deviations from the standard atmosphere.

If the ideal gas law is the "only the only correct way to understand this phenomenon", explain why barometric pressure doesn't vary in perfect proportion with temperature, every time, all the time?

Why are exceptionally cold temperatures usually associated with exceptionallyt high barometric pressure.

Example, the lowest barometric pressure ever recorded on the north american continent was 31.85" hg, at a time (jan 1989) when all of alaska was experiencing record low temps.

According to the ideal gas law, exceptionally cold temps are always, without exception, accompanied with low barometric temps, yet the reverse is usually true.

Explain this using *only* the ideal gas law.

 

[Alamanach]

According to the ideal gas law, exceptionally cold temps are always, without exception, accompanied with low barometric temps...

I assume you meant to say barometric pressures-- and it is not the case. By our simplified form of P=DT, we see that low temperatures would accompany high pressure if the density is higher than the temperature is low. Those would be some pretty exceptional conditions, to be sure, but still within a range that makes Ideal Gas Law error negligible.

Why are exceptionally cold temperatures usually associated with exceptionallyt high barometric pressure.

If this is true-- and we get back into something you would know about more than I-- then why are we worried about cold air causing our altimeters to read high? Is this something different from the usual cold air stuff we've been discussing?

 

[Alamanach]

A Squared, I have just now come across something interesting-- Part 2-4 of Chapter 7 of the AIM. It says:

Cold, dry air masses produce barometric pressures in excess of 31.00 inches of Mercury, and many altimeters do not have an accurate means of being adjusted for settings of these levels. When the altimeter cannot be set to the higher pressure setting, the aircraft actual altitude will be higher than the altimeter indicates.

It goes on from there. The word dry is crucial. If we remove water vapor from the air, then the composition is not what it was, and we are not dealing with quite the same substance. This means that the r of PV=nrT will take on a different value. (I believe I mentioned in my second post in this thread that r is specific to a substance.) The arctic air is certainly going to be a lot dryer than what we see here in the temperate zones (and by the way, it will be absolute humidity that matters here), and that could account for these extraordinary densities.

So, humidity plays an important part in how we can apply the Ideal Gas Law. I confess, I hadn't really paid any attention to that in my earlier posts.