Cold Air Altimetery

[FlyBieWire]

I can easily understand errors in the altimeter regarding pressure changes, but the errors associated with cold air have me baffeled.

So I do understand, "High to a low, look out below," but not, "Warm to a cold, look out below." Is that true? If so it makes no sense to me.

 

[Alamanach]

As we go up, air density and temperature both go down at linear rates (usually). From Thermodynamics 101, we know that Pressure = Density x Temperature x (constant r), so pressure is going down as well. Under non-standard conditions, it is possible for temperature to drop faster than usual, while density stays where we expect. This has the effect of lowering pressure, and it is pressure that an altimeter measures. So the altimeter is measuring a low pressure-- which implies a high altitude-- but this is illusory due to the unusually cold air. The plane is not as high as your instrument says it is, look out below.

 

[Alamanach]

Re-reading my last post, I ought to mention--

The equation I cite is the Ideal Gas Law, and it holds for any gas under conditions that are not too extreme and involve enough molecules of gas. (The points at which the law starts breaking down are way beyond anything that the free atmosphere can produce.) The equation is usually written as

PV=nrT

where P=pressure, V=volume, n=number of gas molecules (moles), r is a constant specific to each gas, and T=temperature. Divide both sides by V and we have

P=(nr/V)T

If we multiply (nr/V) by (molar density of gas/ molar density of gas), which equals 1, we can get

Dr'

where D=density and r' is an adjusted constant. Then,

P=DTr'

which is the equation I used in the previous post.

PV=nrT is easy to remember, and I have found it to be handy to know.

 

[GravityHater]

What is the r.o.t. for those canadian approaches when it is supercold?? How and what do we adjust?

 

[A Squared]

As we go up, air density and temperature both go down at linear rates (usually).

Not true. Take a look at a table of the pressure values for the standard atmosphere. It is a long way from being a linear function of altitude, even in the idealized standard atmosphere, to say nothing of the real atmosphere.

From Thermodynamics 101, we know that Pressure = Density x Temperature x (constant r), so pressure is going down as well. Under non-standard conditions, it is possible for temperature to drop faster than usual, while density stays where we expect. This has the effect of lowering pressure, and it is pressure that an altimeter measures. So the altimeter is measuring a low pressure-- which implies a high altitude-- but this is illusory due to the unusually cold air. The plane is not as high as your instrument says it is, look out below.

I think that you are mis-applying the Ideal gas law. Your explanation breaks down when you consider that very low temperatures are more often than not accompanied by "higher* than normal atmospheric pressure and furthermore your explanation fails to explain why an altimeter, when correctly set to valid altimeter setting indicates lower than actual altitude when aloft.


The real reason: The temperature affects the pressure lapse rate, because it changes the density of the air.

Consider this: If you took a waterproof altimeter and submerged it in water, you would see that you would only have to raise it or lower it about 1 foot in the water to make it show a 1,000 ft change in altitude. The difference in air pressure of 1,000 ft is approximately one inch of mercury, and the difference in water pressure of 13.6 inches is also one inch of mercury. This difference is because water is approximately 1000 times more dense than air.

To get back to the original question, when it's colder, the air is more dense, so a 1"hg difference in pressure may only be 900 ft in the actual atmosphere, But if you ewxperience a 1"hg pressure change your altimeter will still display that as 1000 feet.

 

[Alamanach]

Not true. Take a look at a table of the pressure values for the standard atmosphere. It is a long way from being a linear function...

You're right, it's not linear. My bad. Temperature is linear for about the first 30,000 feet, after which it is constant for a while, and after that... well, then it's too high up to matter. The decrease in density is not linear, and this will teach me to be more careful. Page 5 of Aerodynamics for Naval Aviators has a table that spells it out pretty thoroughly.

Page 2 of Aerodynamics for Naval Aviators has an equation toward the end of the page that, I think, supports rather nicely my use of the Ideal Gas Law. By their equation, density is directly proportional to pressure and inversely proportional to temperature; D=P/T, which is saying the same thing as DT=P, which is pretty much what I said.

If, as you point out, lower temperature is associated with higher density, it is because pressure is remaining constant. But constant pressure won't move our altimeter. If temperature changes while density holds constant, then pressure will change, and the altimeter will register that change. It is pressure, not density, that moves the aneroid wafers of the altimeter.

Also, you seem to be saying that cold air makes the altimeter erroneously read a low altitude. If that's the case, (and you would know better than I) then there's some additional phenomenon at work; the basic relationship between temperature, pressure, and density runs in the other direction.

 

[FL420]

New info. for Canadian VNAV approaches

What is the r.o.t. for those canadian approaches when it is supercold?? How and what do we adjust?

From the May, 2006 issue of _Avionics News_ (p.23-24):

Canada

Transport Canada Revises Guidance for FMS Designed for VNAV Approaches

TCCA has published Advisory Circular 500-020 to replace ACPL 75 Issue 1, and provide revised guidance on the criteria for incorporation of temperature compensation in new or updated Flight Management System (FMS) designs for barometric Vertical Navigation (VNAV) approach procedures.

Whereas ACPL 57 called for application of temperature compensation for all temperatures, this AC requires temperature compensation only when below International Standard Atmosphere (ISA) conditions exist at the destination airfield. The requirement for above ISA compensation has been suspended pending resolution of operational considerations, promulgation of an operational requirement, and provision of operational guidance and training material.

Other changes reflected in this AC include a clarification that temperature compensation is to be applied to minimum descent altitude/decision altitude of an approach procedure. This is consistent with the current cold temperature compensation procedure in Nav Canada Air Pilot, Canada Air Pilot General Pages (CAP GEN). In addition, the International Civil Aviation Organization "accurate" method has been included as an acceptable means of temperature compensation.

AC 500-020 can be viewed at

www.tc.gc.ca/CivilAviation/certification/guidance/500/500-020.htm

 

[A Squared]

Page 2 of Aerodynamics for Naval Aviators has an equation toward the end of the page that, I think, supports rather nicely my use of the Ideal Gas Law. By their equation, density is directly proportional to pressure and inversely proportional to temperature; D=P/T, which is saying the same thing as DT=P, which is pretty much what I said.

I didn't say that the Ideal Gas Law was incorrect, nor that it was unrelated. It doen't however, directly explain the phenomenon.

If, as you point out, lower temperature is associated with higher density, it is because pressure is remaining constant. But constant pressure won't move our altimeter. If temperature changes while density holds constant, then pressure will change, and the altimeter will register that change. It is pressure, not density, that moves the aneroid wafers of the altimeter.

What you say isn't incorrect, as far as it goes, but it doesn't account for the phenomenon in question. The question (as I interpret it anyway) is not whether the altimeter of a parked airplane will indicate higher in the morning if the temp drops overnight. It may, or it may not, that depends on what the living breathing atmosphere is doing, and there's a lot more factors than just temp change. True, if that airplane was sitting in a closed container in a laboratory, than it would be just like you say. The atmosphere isn't a closed container in a laboratory.

The question, as I understand it is: why is your true altitude lower than your indicated altitude (on an altimeter correectly set to a valid altimeter setting) when the ambient temp is lower than ISA. Now this is only true when your altitude is higher than the station computing the altimeter setting.

If you are sitting on the ramp at the airport where the altimeter setting is measured, your alitmeter will indicate the correct altitude when set to the altimeter setting, regardless of temp. (if it doesn't there's an error in your altimeter, or there's an error in the setting)

Now the reason there is a difference between true altitude and indicated altitude is because of increased air density. I agree that the altimeter doesn't respond to air density, however than is not what i said (or intended to convey) The colder air is denser, and the denser air increases the pressure *lapse rate*, regardless of whether the atmospheric pressure is higher or lower. And as you move up or down through the atmosphere, the altimeter responds to the pressure lapse rate.

The pressure lapse rate is greater with more dense fluids or gasses. My comparison between the pressure lapse rate in air and water in my previous post shows this. Also, if you look at a table of the standard atmosphere, you will see that the pressure lapse rate decreases with altitude and the air density decreases with altitude. The first is a result of the second.

So, the colder air is more dense, which results in an increased pressure lapse rate, so that on a cold day, an altimeter climbing from sea level to 1000' experiences a pressure change of 1.1" of mercury, so the indicated altitude is 1100 ft while the actual altitude is 1000.

Also, you seem to be saying that cold air makes the altimeter erroneously read a low altitude. If that's the case, (and you would know better than I) then there's some additional phenomenon at work; the basic relationship between temperature, pressure, and density runs in the other direction.

Yeah, My mistake, I said it would read lower, I meant higher, sorry for the confusion.

 

[Alamanach]

What you say isn't incorrect, as far as it goes, but it doesn't account for the phenomenon in question...

Sure it does. If we fly from some ISA air into a body of cold air, but at equal density, then by P=DT, we will see a drop in pressure, which the altimeter will interpret as a gain in altitude, which will be incorrect.

...denser air increases the pressure *lapse rate*...

OK, I see what you're saying, and that could work if it is as you describe. But why would denser air increase the pressure lapse rate? (I'm not saying it doesn't, you're just off into something I'm not familiar with.)

 

[A Squared]

If we fly from some ISA air into a body of cold air, but at equal density, then by P=DT, we will see a drop in pressure,

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.

OK, I see what you're saying, and that could work if it is as you describe. But why would denser air increase the pressure lapse rate? (I'm not saying it doesn't, you're just off into something I'm not familiar with.)

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.

 

[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....