Variation of Temperature with Altitude on Cold Days

[benzie]

Hi Everyone,
I'm currently modelling the effects of external ambient temperatures on an air vehicle. The problem that I have is that I cannot find any data for the variation of temperature with altitude where the sea level temperature is below 0 celcius, apart from a -40 celcius case. As you'll be aware on extreme cold days the temperature actually increases as you increase altitude over the first few thousand feet and then the temp starts decreasing again up to the troposphere.
Does anyone have any suggestions on where this data may be available?
Thanks in advance

Tom

 

[IRstuff]

The US Standard Atmosphere model should also have data for other than standard temperatures.

There are a variety of programs than model the atmosphere. LOWTRAN and MODTRAN, while actually used for modelling electro-optical propagation in the atmosphere, contain simplified models of the atmosphere and do, model the temperature profile of the atmosphere.

TTFN

 

[borjame]

My guide here says that T(degreesR) = sea level ambient(degreesR) - (3.5662 * (altitude(ft) * 10-3)) good up to 36K ft.

 

[davidjh]

Benzie;

Are you looking for (1) some worst rcorded case, or (2)a set of data where temp profiles are plotted versus probability?

FYI: FAA Part 25 airplanes have an allowable operating temperature range versus altitude chart in their Flight manuals. It varies somewhat between manufacturers. I'm not sure of its exact origin, but I do know it goes back a long way and its tweaked a bit every now and then based on input from the airplane operators. So it represents a great deal of real world experience. Some of the "biz" jets are certified to over 50,000ft. Perhaps they are source for you.

 

[IRstuff]

This is what Lowtran predicted for a mid-latitude summer run I made a LONG time ago, first column is altitude in km, temperature in kelvin:

0 294.2
1 289.7
2 285.2
3 279.2
4 273.2
5 267.2
6 261.2
7 254.7
8 248.2
9 241.7
10 235.3
11 228.8
12 222.3
13 215.8
14 215.7
15 215.7
16 215.7
17 215.7
18 216.8
19 217.9
20 219.2
21 220.4
22 221.6
23 222.8
24 223.9
25 225.1
30 233.7
35 245.2
40 257.5
45 269.9
50 275.7
70 218.1
100 190.5


If I can ever find a winter-specific run...

TTFN

 

[benzie]

Guys, thanks for your answers. With the information that you've provided so far I've now got enough to go on. Thanks again

 

[aviat]

The ICAO standard atmosphere (StAl)is only designed to be used in the mid latitudes in spring and fall. It uses a standard temperature of 59 deg. F or 15 deg C at sea level, which is different to what other industries use, hence some of the programs do not work. The StAl uses a dry air lapse rate (average decrease of temperature with altitude) of 3.566 deg F or 2 deg C per 1000 feet. This assumes perfectly dry air and no vertical or horizontal air movement. So the simple formula for temp. at altitude is 59-(3.566*Alt in thousands)eg for 30000 feet (FL30) = 59-(3.566*30)=-48. This lapse rate continues to the tropopause where the temp. stops decreasing. This is about -69.7 deg F at approx. FL35 to FL65 in StAl.

However, the height of the tropopause varies from 28000 feet at the poles to 54000 feet at the equator and it also varies from summer to winter.

At -40 you are 100 deg F below StAl temp., so StAl model will obviously not work. There are two ways to work around the problem. First you can use a different lapse rate. At -40 you are only 30 degrees F from tropopause temp. so if you estimate tropopause to be at 30000 feet then lapse rate will be 30/30 or -1 deg 1000 feet from ambient temp.

A more accurate approach is to contact an aviation weather office in your area. At several location around the world they launch balloons that measure the temp. with altitude. You could obtain prints of these from location (s)where the ground temp. is at which you that you are interested in and then determine a lapse rate.

Cheers