Cold Air Altimetery

[Donsa320]

Umm, no, it won't. Not necessarily. You seem to be adamant that the behavior of the atmosphere is absolutely and completely described by the ideal gas law. It's not. As I said before, extrememly cold temperatures are more often than not accompanied by higher than standard temperatures. Now, this is not predicted by the ideal gas law, so you have to conclude that either a) the ideal gas law is incorrect (it is not) or that b) the atmosphere is a little more complicated than one simple equation can completely account for.



because the pressure lapse rate is directly proportional to the densiy ofh te gas or fluid. I don't have time to give a more complete description right how. I'll try to get back to you a little later, but in the meantime, go back to my description of the altimeter underwater and think it through.

A-Squared I never did get back to you on how the aneroid wafer altimeters manage to follow the non-linear standard atmosphere pressure lapse rate so consistently. I managed to get to a licensed overhaul tech and he said... "I don't know". We will have to wait until a design engineer comes along to educate me/us, I guess. <bg>

DC

 

[A Squared]

A-Squared I never did get back to you on how the aneroid wafer altimeters manage to follow the non-linear standard atmosphere pressure lapse rate so consistently. I managed to get to a licensed overhaul tech and he said... "I don't know". We will have to wait until a design engineer comes along to educate me/us, I guess. <bg>

DC

Yeah, if you ever do hear how that works, I'd certainly be interested to hear.

 

[Alamanach]

A-Squared I never did get back to you on how the aneroid wafer altimeters manage to follow the non-linear standard atmosphere pressure lapse rate so consistently. I managed to get to a licensed overhaul tech and he said... "I don't know". We will have to wait until a design engineer comes along to educate me/us, I guess.

I don't know anything about the construction of altimeters beyond what's in the Instrument Flying Handbook, but I do happen to be an engineer. There's probably non-linear gearing between the aneroid wafer and the altimeter dial. If we have a mathematical expression for the pressure change of the atmosphere, then a geometric equivalent of that mathematical expression isn't hard to find. The actual mechanism is simply built to that geometery. Be advised, that's just a guess.

A Squared, the ideal gas law is generally reliable to about 10 atmospheres of pressure or approaching -350 degrees F. I look forward to reading your full answer about pressure lapse rate.

 

[UndauntedFlyer]

Here is the simplest way to understand the corrections for colder than standard air (true altitude.)

First. The error is based on your height above where you got your altimeter setting from.

Second. The error only causes you to be too low if the temperature is below standard for that altitude. A little below standard from ISA causes you to be a little low maybe 1% lower than you think you are from where you got your altimeter setting from. Way below standard causes you to be maybe 10% lower than you think you are above where you got your altimeter setting from. For example let's say you are landing at a 5000 foot elevation airport on a very cold day and flying an ILS. As you pass 6000 feet above MSL you may really be 5900 feet above MSL because there is a 10% error. (6000-5000=1000, 1000x10%=100) But when you descend to a DH(A) of 5200 feet above MSL (200 feet above FE) the amount of error is only 20 feet, an insignificant amount.

Now it is important to understand, based on the above example and explanation that this altimetry error isn't really a big problem on instrument approaches because the error is always diminishing to zero as you get closer to the airport where the altimeter setting was obtained. It is only a real problem; for example, if you were flying at say 16,000 feet above MSL with an altimeter setting from say a 5000 foot elevation airport on a very cold day. In that case the error would be 1,100 feet (16,000-5,000=11,000, 11,000x10%=1,100) And in this case when the pilot thinks he is at 16,000 feet he is really at 14,900 feet. This is a serious problem if there is terrain such as the Rocky Mountains with a 15,000 peak in the area. This is why the IFR obstruction clearance criteria is 2000 feet in mountainous areas instead of the usual 1000 feet that applies everywhere else. Now if the top of that mountain was giving a local altimeter setting then there would only be 100 feet of error instead of 1,100 feet of error but since that is not the case, the 2000 foot separation standard is used.

It is also important to understand that it is impossible to really compute "True Altitude" with just a temperature correction unless you could sample the atmosphere by the foot from the airplane all the way to the ground. Any chart that tries to give a correction is really only giving an estimate, assuming a standard lapse rate increase from the sample point to the ground.

In summary, true altitude is not a problem unless it is a very cold day and even then the amount of error gets smaller and smaller as you get to where the altimeter setting was taken. So on instrument approaches it is hardly worth correcting for except on a procedure turn that is maybe 4000 feet above the airport elevation. In that case the error would about 400 feet which is dangerous if your are that much lower than you are suppose to be.

So the saying, "Warm to a Cold" , as “Flybiewire” asked about, is very misleading to people learning about the altimeter. The altimeter’s temperature errors have nothing to do with where your took off from. The error simply applies whenever you are flying in colder than standard air, and the most error is usually about 10% of your calculated height above where you got your altimeter setting from.

Your questions or comments are welcome......

 

[Alamanach]

Your questions or comments are welcome......

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.

 

[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....