Altimeters and air pressure variation

[jharper aaatttt cisco dddooottt com]

At sea level, the change in atmospheric pressure with altitude is
close to 1"Hg/1000'. Logically, this would mean that the air
pressure would drop to zero somewhere not much above 30000'. It
doesn't, because as the density drops the variation with
altitude also changes.

Which brings to mind the question, how does an altimeter deal
with this? As far as I know, it's just a simple aneroid barometer
with a bunch of linkages and gears to turn its expansion into
pointer movement.

My altimeter is marked "accurate to 20000' ". Is this why? Do
altimeters for higher altitudes have some kind of clever
mechanism to deal with the non-linearity of pressure at higher
altitudes.

I asked my acro instructor (10K+ hrs, airforce instructor pilot,
ex U2 pilot so should know a thing or two about high altitudes).
He explained the non-linearity of pressure to me but was
stumped on how this translates to the altimeter mechanism.

Anyone know?

John

[Icebound]

"jharper aaatttt cisco dddooottt com" <"jharper aaatttt cisco dddooottt
com"> wrote in message news:1105391055.635118@sj-nntpcache-3...
....
> Do
> altimeters for higher altitudes have some kind of clever
> mechanism to deal with the non-linearity of pressure at higher
> altitudes.
>


I am not an expert in the mechanics of barometer/altimeter construction, but
I do not see that it has to be particularly clever.

Typically, the metal "can" (which expands and contracts with air pressure)
is preloaded with a steel-spring against the air pressure. Isn't the force
produced by a steel-spring typically non-linear throughout its expansion...
so could not the spring-steel parameters be chosen such that the
non-linearity matches air pressure non-linearity closely?

[Dean Wilkinson]

"jharper aaatttt cisco dddooottt com" <"jharper aaatttt cisco dddooottt
com"> wrote in message news:1105391055.635118@sj-nntpcache-3...
> At sea level, the change in atmospheric pressure with altitude is
> close to 1"Hg/1000'. Logically, this would mean that the air
> pressure would drop to zero somewhere not much above 30000'. It
> doesn't, because as the density drops the variation with
> altitude also changes.
>
> Which brings to mind the question, how does an altimeter deal
> with this? As far as I know, it's just a simple aneroid barometer
> with a bunch of linkages and gears to turn its expansion into
> pointer movement.
>
> My altimeter is marked "accurate to 20000' ". Is this why? Do
> altimeters for higher altitudes have some kind of clever
> mechanism to deal with the non-linearity of pressure at higher
> altitudes.
>
> I asked my acro instructor (10K+ hrs, airforce instructor pilot,
> ex U2 pilot so should know a thing or two about high altitudes).
> He explained the non-linearity of pressure to me but was
> stumped on how this translates to the altimeter mechanism.
>
> Anyone know?
>
> John

Visit this website and it will answer your questions about the relationship
between pressure, temperature and altitude... altimeters are designed to
take the non-linearity into account...

http://www.lerc.nasa.gov/WWW/K-12/airplane/atmosi.html

[Gig Giacona]

"jharper aaatttt cisco dddooottt com" <"jharper aaatttt cisco dddooottt
com"> wrote in message news:1105391055.635118@sj-nntpcache-3...
> At sea level, the change in atmospheric pressure with altitude is
> close to 1"Hg/1000'. Logically, this would mean that the air
> pressure would drop to zero somewhere not much above 30000'. It
> doesn't, because as the density drops the variation with
> altitude also changes.
>
> Which brings to mind the question, how does an altimeter deal
> with this? As far as I know, it's just a simple aneroid barometer
> with a bunch of linkages and gears to turn its expansion into
> pointer movement.
>
> My altimeter is marked "accurate to 20000' ". Is this why? Do
> altimeters for higher altitudes have some kind of clever
> mechanism to deal with the non-linearity of pressure at higher
> altitudes.
>
> I asked my acro instructor (10K+ hrs, airforce instructor pilot,
> ex U2 pilot so should know a thing or two about high altitudes).
> He explained the non-linearity of pressure to me but was
> stumped on how this translates to the altimeter mechanism.
>
> Anyone know?
>


The following is a WAG but that could be the reason that in the Flight
Levels, above 18k feet everyone sets thier altimeter to 29.90.

[Icebound]

"Gig Giacona" > wrote in message
...
>
> "jharper aaatttt cisco dddooottt com" <"jharper aaatttt cisco dddooottt
> com"> wrote in message news:1105391055.635118@sj-nntpcache-3...

>> Anyone know?
>>
>
>
> The following is a WAG but that could be the reason that in the Flight
> Levels, above 18k feet everyone sets thier altimeter to 29.90.
>
>

Hopefully, 29.92.

[Sriram Narayan]

"Icebound" > wrote in message
...
>
> "Gig Giacona" > wrote in message
> ...
> >
> > "jharper aaatttt cisco dddooottt com" <"jharper aaatttt cisco dddooottt
> > com"> wrote in message news:1105391055.635118@sj-nntpcache-3...
>
> >> Anyone know?
> >>
> >
> >
> > The following is a WAG but that could be the reason that in the Flight
> > Levels, above 18k feet everyone sets thier altimeter to 29.90.
> >
> >
>
> Hopefully, 29.92.
>
>

That still wouldn't help since the pressure change for a 1000ft change in
altitude at 18k would be smaller than at sea level. It would have to have
some non-linear spring compensation as a function of absolute pressure.

[Jose]

> It would have to have
> some non-linear spring compensation as a function of absolute pressure.

It could also be a non-linear gear compensation, such as using
non-circular gears. Lotsaways it =could= be done, but I don't know
how it =is= done.

Jose
--
Money: What you need when you run out of brains.
for Email, make the obvious change in the address.

[Rod Madsen]

I couldn't be done easily with a spring. Springs are very linear except in
very special cases. I think it's done with leaver arms that change
effective length with displacement.

Rod
"Sriram Narayan" > wrote in message
news:1105397045.6c0b9af7d0985bd99dd3e30aa7ae44ee@t eranews...
>
> "Icebound" > wrote in message
> ...
>>
>> "Gig Giacona" > wrote in message
>> ...
>> >
>> > "jharper aaatttt cisco dddooottt com" <"jharper aaatttt cisco dddooottt
>> > com"> wrote in message news:1105391055.635118@sj-nntpcache-3...
>>
>> >> Anyone know?
>> >>
>> >
>> >
>> > The following is a WAG but that could be the reason that in the Flight
>> > Levels, above 18k feet everyone sets thier altimeter to 29.90.
>> >
>> >
>>
>> Hopefully, 29.92.
>>
>>
>
> That still wouldn't help since the pressure change for a 1000ft change in
> altitude at 18k would be smaller than at sea level. It would have to have
> some non-linear spring compensation as a function of absolute pressure.
>
>

[jharper aaatttt cisco dddooottt com]

Dean Wilkinson wrote:
> >
>
> Visit this website and it will answer your questions about the relationship
> between pressure, temperature and altitude... altimeters are designed to
> take the non-linearity into account...
>
> http://www.lerc.nasa.gov/WWW/K-12/airplane/atmosi.html
>

Nice site, thanks. But presumably there is some standard
atmospheric model that altimeters use? After all nobody actually
cares whether FL300 is really 30000' feet above MSL, as
long as everyone flying there is at the same altitude and,
more importantly, not at somebody else's FL290 or FL310.

Which implies that there must be some standard mechanical
way of making the translation? I'll ask next time I visit my
avionics shop, but considering what each visit costs I
quite hope this won't be for a while.

John

[Peter]

jharper aaatttt cisco dddooottt com wrote:

> Dean Wilkinson wrote:
>> >
>> Visit this website and it will answer your questions about the
>> relationship
>> between pressure, temperature and altitude... altimeters are designed to
>> take the non-linearity into account...
>>
>> http://www.lerc.nasa.gov/WWW/K-12/airplane/atmosi.html
>>
>
> Nice site, thanks. But presumably there is some standard
> atmospheric model that altimeters use? After all nobody actually
> cares whether FL300 is really 30000' feet above MSL, as
> long as everyone flying there is at the same altitude and,
> more importantly, not at somebody else's FL290 or FL310.

Yes, there is a standard model and if you click on the first
link on the cited page you get to:
http://www.lerc.nasa.gov/WWW/K-12/airplane/atmos.html
which gives the equations describing that standard model.
>
> Which implies that there must be some standard mechanical
> way of making the translation?

There's a mathematically defined correspondence
between altitude and pressure under the standard
atmosphere assumption. But I doubt if the specific
mechanical means of achieving that correspondence is
specified anywhere. As long as the manufacturer makes
an instrument that is shown to give the right correspondence
to within a specified accuracy why should it matter exactly
how they do it?

> I'll ask next time I visit my
> avionics shop, but considering what each visit costs I
> quite hope this won't be for a while.

[jim rosinski]

Sriram Narayan wrote:

> That still wouldn't help since the pressure change for a 1000ft
change in
> altitude at 18k would be smaller than at sea level. It would have to
have
> some non-linear spring compensation as a function of absolute
pressure.

Yes but the non-linearity is very weak. I coded up the formula for the
US standard atmosphere (described below) and plotted it. See
www.burningserver.net/rosinski/us_std_atmosphere.jpg
Perhaps the non-linearity is so weak that altimeters neglect it? I
don't know.

The formula for US standard atmosphere can be derived from the ideal
gas approximation (p = rho*R*T) and the hydrostatic approximation
(dp/dz = -rho*g). The final equation is:

z = T0/gamma * (1 - (p/p0)**(R*gamma/g)))

where R=287, T0 = 288K, p0 = 1013.25 mb = 29.92 in, gamma = 6.5 deg/km,
g = 9.8.

The formula assumes that temperature decreases linearly with altitude,
an assumption which becomes invalid above the tropopause. The equation
and its derivation can be found in Wallace & Hobbs, "Atmospheric
Science", pg. 60-61.

Jim Rosinski

[jharper aaatttt cisco dddooottt com]

Didn't see that, thanks for pointing it out.
At least that explains the note on my altimeter
saying "certified to 20000' " which I hadn't
understood before.

I wonder how altimeters for airliners work, given
the change that happens at 36152' - or indeed the
U2 altimeter. Must be some interesting stuff inside.

John

Peter wrote:
> jharper aaatttt cisco dddooottt com wrote:
>
>> Dean Wilkinson wrote:
>>
>>> >
>>> Visit this website and it will answer your questions about the
>>> relationship
>>> between pressure, temperature and altitude... altimeters are
>>> designed to
>>> take the non-linearity into account...
>>>
>>> http://www.lerc.nasa.gov/WWW/K-12/airplane/atmosi.html
>>>
>>
>> Nice site, thanks. But presumably there is some standard
>> atmospheric model that altimeters use? After all nobody actually
>> cares whether FL300 is really 30000' feet above MSL, as
>> long as everyone flying there is at the same altitude and,
>> more importantly, not at somebody else's FL290 or FL310.
>
>
> Yes, there is a standard model and if you click on the first
> link on the cited page you get to:
> http://www.lerc.nasa.gov/WWW/K-12/airplane/atmos.html
> which gives the equations describing that standard model.
>
>>
>> Which implies that there must be some standard mechanical
>> way of making the translation?
>
>
> There's a mathematically defined correspondence
> between altitude and pressure under the standard
> atmosphere assumption. But I doubt if the specific
> mechanical means of achieving that correspondence is
> specified anywhere. As long as the manufacturer makes
> an instrument that is shown to give the right correspondence
> to within a specified accuracy why should it matter exactly
> how they do it?
>
>> I'll ask next time I visit my
>> avionics shop, but considering what each visit costs I
>> quite hope this won't be for a while.
>
>

[Blueskies]

"Sriram Narayan" > wrote in message news:1105397045.6c0b9af7d0985bd99dd3e30aa7ae44ee@t eranews...
>
>>
>
> That still wouldn't help since the pressure change for a 1000ft change in
> altitude at 18k would be smaller than at sea level. It would have to have
> some non-linear spring compensation as a function of absolute pressure.
>
>

The USA is just now getting into the RVSM rules which allow vertical separation of 1000 feet. Used to be 2000' minimum
for all of these reasons....

[[email protected]]

On Mon, 10 Jan 2005 18:09:48 -0800, "jharper aaatttt cisco dddooottt
com" <"jharper aaatttt cisco dddooottt com"> wrote:

snip

>I wonder how altimeters for airliners work, given
>the change that happens at 36152' - or indeed the
>U2 altimeter. Must be some interesting stuff inside.

http://www.rockwellcollins.com/ecat/br/ADS-850.html?smenu=109

http://www.cas.honeywell.com/ats/products/airdata.cfm

Typically the DADC's are corrected for known issues/errors in the
pitot/static system of the specific type aircraft it is installed in,
as well as the "change"s you've noted.

TC

[Ash Wyllie]

jharper aaatttt cisco dddooottt com opined

>At sea level, the change in atmospheric pressure with altitude is
>close to 1"Hg/1000'. Logically, this would mean that the air
>pressure would drop to zero somewhere not much above 30000'. It
>doesn't, because as the density drops the variation with
>altitude also changes.

>Which brings to mind the question, how does an altimeter deal
>with this? As far as I know, it's just a simple aneroid barometer
>with a bunch of linkages and gears to turn its expansion into
>pointer movement.

>My altimeter is marked "accurate to 20000' ". Is this why? Do
>altimeters for higher altitudes have some kind of clever
>mechanism to deal with the non-linearity of pressure at higher
>altitudes.

>I asked my acro instructor (10K+ hrs, airforce instructor pilot,
>ex U2 pilot so should know a thing or two about high altitudes).
>He explained the non-linearity of pressure to me but was
>stumped on how this translates to the altimeter mechanism.

A couple of good approximations are

A = 25,000 * ln(30/25000)
and
P = 30 * exp(-A/25000)

For an altimeter, use gears with a varying radius.

-ash
Cthulhu in 2005!
Why wait for nature?

[Sriram Narayan]

"jim rosinski" > wrote in message
oups.com...
> Sriram Narayan wrote:
>
> > That still wouldn't help since the pressure change for a 1000ft
> change in
> > altitude at 18k would be smaller than at sea level. It would have to
> have
> > some non-linear spring compensation as a function of absolute
> pressure.
>
> Yes but the non-linearity is very weak. I coded up the formula for the
> US standard atmosphere (described below) and plotted it. See
> www.burningserver.net/rosinski/us_std_atmosphere.jpg
> Perhaps the non-linearity is so weak that altimeters neglect it? I
> don't know.
>
> The formula for US standard atmosphere can be derived from the ideal
> gas approximation (p = rho*R*T) and the hydrostatic approximation
> (dp/dz = -rho*g). The final equation is:
>
> z = T0/gamma * (1 - (p/p0)**(R*gamma/g)))
>
> where R=287, T0 = 288K, p0 = 1013.25 mb = 29.92 in, gamma = 6.5 deg/km,
> g = 9.8.
>
> The formula assumes that temperature decreases linearly with altitude,
> an assumption which becomes invalid above the tropopause. The equation
> and its derivation can be found in Wallace & Hobbs, "Atmospheric
> Science", pg. 60-61.
>
> Jim Rosinski
>

It doesn't look that linear to me. I found a website with a similar graph
and it appears that at sea level and at 10000ft the slope of the curve is at
least 2x different. Your curve is quite a bit more linear (maybe 20%
increase in slope at 10k). There must some sort of mechanical compensation
involved otherwise altimeters would be off quite a bit even at 10k (even
with your curve). Isn't it something like 75ft accuracy requirement for
altimeters?

http://www.atmosphere.mpg.de/enid/16h.html

[Sriram Narayan]

"jim rosinski" > wrote in message
oups.com...
> Sriram Narayan wrote:
>
> > That still wouldn't help since the pressure change for a 1000ft
> change in
> > altitude at 18k would be smaller than at sea level. It would have to
> have
> > some non-linear spring compensation as a function of absolute
> pressure.
>
> Yes but the non-linearity is very weak. I coded up the formula for the
> US standard atmosphere (described below) and plotted it. See
> www.burningserver.net/rosinski/us_std_atmosphere.jpg
> Perhaps the non-linearity is so weak that altimeters neglect it? I
> don't know.
>
> The formula for US standard atmosphere can be derived from the ideal
> gas approximation (p = rho*R*T) and the hydrostatic approximation
> (dp/dz = -rho*g). The final equation is:
>
> z = T0/gamma * (1 - (p/p0)**(R*gamma/g)))
>
> where R=287, T0 = 288K, p0 = 1013.25 mb = 29.92 in, gamma = 6.5 deg/km,
> g = 9.8.
>
> The formula assumes that temperature decreases linearly with altitude,
> an assumption which becomes invalid above the tropopause. The equation
> and its derivation can be found in Wallace & Hobbs, "Atmospheric
> Science", pg. 60-61.
>
> Jim Rosinski
>

It doesn't look that linear to me. I found a website with a similar graph
and it appears that at sea level and at 10000ft the slope of the curve is at
least 2x different. Your curve is quite a bit more linear (maybe 20%
increase in slope at 10k). There must some sort of mechanical compensation
involved otherwise altimeters would be off quite a bit even at 10k (even
with your curve). Isn't it something like 75ft accuracy requirement for
altimeters?

http://www.atmosphere.mpg.de/enid/16h.html

[Sriram Narayan]

"jim rosinski" > wrote in message
oups.com...
> Sriram Narayan wrote:
>
> > That still wouldn't help since the pressure change for a 1000ft
> change in
> > altitude at 18k would be smaller than at sea level. It would have to
> have
> > some non-linear spring compensation as a function of absolute
> pressure.
>
> Yes but the non-linearity is very weak. I coded up the formula for the
> US standard atmosphere (described below) and plotted it. See
> www.burningserver.net/rosinski/us_std_atmosphere.jpg
> Perhaps the non-linearity is so weak that altimeters neglect it? I
> don't know.
>
> The formula for US standard atmosphere can be derived from the ideal
> gas approximation (p = rho*R*T) and the hydrostatic approximation
> (dp/dz = -rho*g). The final equation is:
>
> z = T0/gamma * (1 - (p/p0)**(R*gamma/g)))
>
> where R=287, T0 = 288K, p0 = 1013.25 mb = 29.92 in, gamma = 6.5 deg/km,
> g = 9.8.
>
> The formula assumes that temperature decreases linearly with altitude,
> an assumption which becomes invalid above the tropopause. The equation
> and its derivation can be found in Wallace & Hobbs, "Atmospheric
> Science", pg. 60-61.
>
> Jim Rosinski
>

It doesn't look that linear to me. I found a website with a similar graph
and it appears that at sea level and at 10000ft the slope of the curve is at
least 2x different. Your curve is quite a bit more linear (maybe 20%
increase in slope at 10k). There must some sort of mechanical compensation
involved otherwise altimeters would be off quite a bit even at 10k (even
with your curve). Isn't it something like 75ft accuracy requirement for
altimeters?

http://www.atmosphere.mpg.de/enid/16h.html

[Sriram Narayan]

"Ash Wyllie" > wrote in message
...
> jharper aaatttt cisco dddooottt com opined
>
> >At sea level, the change in atmospheric pressure with altitude is
> >close to 1"Hg/1000'. Logically, this would mean that the air
> >pressure would drop to zero somewhere not much above 30000'. It
> >doesn't, because as the density drops the variation with
> >altitude also changes.
>
> >Which brings to mind the question, how does an altimeter deal
> >with this? As far as I know, it's just a simple aneroid barometer
> >with a bunch of linkages and gears to turn its expansion into
> >pointer movement.
>
> >My altimeter is marked "accurate to 20000' ". Is this why? Do
> >altimeters for higher altitudes have some kind of clever
> >mechanism to deal with the non-linearity of pressure at higher
> >altitudes.
>
> >I asked my acro instructor (10K+ hrs, airforce instructor pilot,
> >ex U2 pilot so should know a thing or two about high altitudes).
> >He explained the non-linearity of pressure to me but was
> >stumped on how this translates to the altimeter mechanism.
>
> A couple of good approximations are
>
> A = 25,000 * ln(30/25000)
> and
> P = 30 * exp(-A/25000)
>
> For an altimeter, use gears with a varying radius.

Looks good! It is within 2.5% of the actual standard pressure up to 12000
ft. If you change the 25000 to 26000 in the 2nd formula it is within 1% for
the same range. The trick is to build a gear that conforms to this.

[Ash Wyllie]

Sriram Narayan opined

>"Ash Wyllie" > wrote in message
...
>> jharper aaatttt cisco dddooottt com opined
>>
>> >At sea level, the change in atmospheric pressure with altitude is
>> >close to 1"Hg/1000'. Logically, this would mean that the air
>> >pressure would drop to zero somewhere not much above 30000'. It
>> >doesn't, because as the density drops the variation with
>> >altitude also changes.
>>
>> >Which brings to mind the question, how does an altimeter deal
>> >with this? As far as I know, it's just a simple aneroid barometer
>> >with a bunch of linkages and gears to turn its expansion into
>> >pointer movement.
>>
>> >My altimeter is marked "accurate to 20000' ". Is this why? Do
>> >altimeters for higher altitudes have some kind of clever
>> >mechanism to deal with the non-linearity of pressure at higher
>> >altitudes.
>>
>> >I asked my acro instructor (10K+ hrs, airforce instructor pilot,
>> >ex U2 pilot so should know a thing or two about high altitudes).
>> >He explained the non-linearity of pressure to me but was
>> >stumped on how this translates to the altimeter mechanism.
>>
>> A couple of good approximations are
>>
>> A = 25,000 * ln(30/25000)
>> and
>> P = 30 * exp(-A/25000)
>>
>> For an altimeter, use gears with a varying radius.

>Looks good! It is within 2.5% of the actual standard pressure up to 12000
>ft. If you change the 25000 to 26000 in the 2nd formula it is within 1% for
>the same range. The trick is to build a gear that conforms to this.

Oops, a typo... A = 25,000 * ln(30/P)


-ash
Cthulhu in 2005!
Why wait for nature?

[jim rosinski]

Sriram Narayan wrote:

> It doesn't look that linear to me. I found a website with a similar
graph
> and it appears that at sea level and at 10000ft the slope of the
curve is at
> least 2x different. Your curve is quite a bit more linear (maybe 20%
> increase in slope at 10k). There must some sort of mechanical
compensation
> involved otherwise altimeters would be off quite a bit even at 10k
(even
> with your curve). Isn't it something like 75ft accuracy requirement
for
> altimeters?
>
> http://www.atmosphere.mpg.de/enid/16h.html

His graph has more curvature than mine does because his covers a much
greater vertical distance (11000 meters is around 36000 feet). Mine
only goes to 18000 feet. But I agree that a linear assumption will
result in a worst-case error of several hundred feet. Not good enough,
so the nonlinearity must be built into altimeters even if the're only
good to 20000 ft.

Jim Rosinski

[[email protected]]

> Do altimeters for higher altitudes have some kind of clever
> mechanism to deal with the non-linearity of pressure at higher
> altitudes.

NACA (precursor to NASA) from about 1917 on, did a lot of the early
research on this kind of thing. Here's a link with a great explanation
of how they came up with a clever altimeter mechanism:
http://naca.larc.nasa.gov/reports/1930/naca-report-310/

[Sriram Narayan]

"jim rosinski" > wrote in message
ups.com...
> Sriram Narayan wrote:
>
> > It doesn't look that linear to me. I found a website with a similar
> graph
> > and it appears that at sea level and at 10000ft the slope of the
> curve is at
> > least 2x different. Your curve is quite a bit more linear (maybe 20%
> > increase in slope at 10k). There must some sort of mechanical
> compensation
> > involved otherwise altimeters would be off quite a bit even at 10k
> (even
> > with your curve). Isn't it something like 75ft accuracy requirement
> for
> > altimeters?
> >
> > http://www.atmosphere.mpg.de/enid/16h.html
>
> His graph has more curvature than mine does because his covers a much
> greater vertical distance (11000 meters is around 36000 feet). Mine
> only goes to 18000 feet. But I agree that a linear assumption will
> result in a worst-case error of several hundred feet. Not good enough,
> so the nonlinearity must be built into altimeters even if the're only
> good to 20000 ft.


Oops, thanks for pointing that out. Didn't check the Y-scale carefully.
>