Cloud Base

[Snigs]

I was lecturing PPL Met last night and I was asked a question that I couldn’t answer, I wonder if you could shed any light?

If I know the outside air temperature and the relative humidity, is there any way to calculate the dew point, and hence the expected cloud base. In other words is there a mathematical relationship between % humidity, temperature and dew point?

[homeguard]

No maths just a simple sum.

Use the Dry Adiabatic Lapse Rate (DALR) which is 3 degree C per 1,000ft.

Thus; Surface Temp. 15 degrees C./Dewpoint 9 degrees C. therefore the dew point will be 2000ft., plus allow say 200ft - 300ft, not an exact science, for upward momentum. Answer will be in the region of 2,200-300ft cloudbase.

[Snigs]

Now then, homeguard thanks for that, however, I'm in the situation of knowing the %humidity and the OAT, but not the dew point. So is there a way of calculating the dew point with only the relative humidity and the temp?

It's easy if I know the dew point, the cloud base formula that is used on my syllabus is

Air Temp (C) - Dew Point (C) *400 = Cloud Base.

[FlyingForFun]

Snigs,

I'm not aware of any quick formulae, but someone else might know one. But a quick Google search suggests that what you need is a "Psychometric Chart". Another Google search turns up quite a few of these, but the best one I can find is here (http://ianrpubs.unl.edu/generalag/g626.htm#tpc) .

Unfortunately, it's all in Farenheit, but once you've done the necessary conversions, start by finding the outside air temperature on the bottom scale. Then locate the relative humidity on the top scale. Follow the curved line for the relative humidity down and to the left until it meets the vertical line for the temperature. From this point, locate the nearest diagonal line, and follow this line up and to the left, from where you can read the dew point. Then, use this dew point together with the temperature to work out the cloud base using the rules of thumb you already know.

FFF
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[Edit, because after reading the instructions on the website I've linked to, I discover that I've made a mistake in describing how to use the chart. It is the horizontal lines which represent equal dew point, not the diagonal lines. If you use the diagonal lines, you will get the wet-bulb temperature, not the dew point, and the whole thing stops working! So, once you've found where your vertical line and your curved line meet, you then follow the horizontal line to the left hand side and read off the dew point.]

[homeguard]

Snigs, hope this helps.

Go to the following site. An excellent diagram.


http://hyperphysics.phy-astr.gsu.edu/hbase/hframe.html


in the menu select;

'Heat & thermodynamics' and then next menu;

select 'Relative Humidity';

Scroll down to the Dewpoint Graph. All your questions are answered.

[average bloke]

dew point = relative humidity/100 x air temp

[Snigs]

Excellent, thanks very much.

average bloke that equation is not always accurate, but it seems as though it's a great rule of thumb.

Cheers all.

[funfly]

I think the full answer is
237.3/(1/(LN((HumidityPercentage)/100)/17.27+(AirTemperatureC)/((AirTemperatureC)+237.3))-1)

Easy way to get this result:
If in a spread sheet you put
air temperatureC in H7
relative humidity in H8
Then in H9 put the formula:
=237.3/(1/(LN(H8/100)/17.27+H7/(H7+237.3))-1)
This will give you Dew point
If you then put in H10 the formula:
=((H7-H9)/2.44)*1000
This will give you cloud base (well not far off)

[Atlas Shrugged]

There's one in here and a whole bucnh of other useful stuff too.

http://www.csgnetwork.com/aviationconverters.html

A

[bookworm]

http://williams.best.vwh.net/avform.htm#RH has this and a wealth of other useful stuff. (The formula given appears to be the same as the one given by funfly.)