The 'Ice Budget' Argument

Ross Marsden

Senior Member.
I did a "How much does a contrail weigh?" over at SkyderALERT.com in August.

Suppose the trails are chemspray for what ever purpose...
How much material is there in a trail that is 10 miles long, for the sake of argument. How many pounds of whatever it is, lets say alumina, is required to do that?
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Continuing...
OK, if no one else is going to have a crack at this, I will.
There is a web page that answers "How much does a cloud weigh?"
http://mentalfloss.com/article/49786/how-much-does...

It goes with 0.5 gram per cubic metre for water content. These units are unfamilar to youse in America so I will convert to the Imperial measures of ounces and feet.
At 28.3 grams per ounce and 35.3 cubic feet in a cubic metre, that works out to 0.000499 ounces per cubic foot.
That seems small. How small? Apparently there are 22700 grains in a pound of rice.
That is 1419 grains of rice in an ounce. So 0.000499 ounces is 0.709 of a grain of rice; less than one grain of rice in a cubic foot of air! Very small amount! Crikey... let's press on.

Consider a trail.. let's say its a couple of wing spans wide and deep, and 10 miles long.
At an altitude of 7 miles (36000 feet), and at an elevation of 45 degrees, 10 miles fits between your hands held up with 54 degrees between them; way less than horizon to horizon.
At the cruising speed of 511 mph a A320 covers 8.52 miles per minute which means 1.17 minutes (70 seconds) to cover 10 miles.
So a 10 mile trail is pretty short in the general scheme of things.

Pressing on...
width 200 feet, depth 200 feet, length 10 miles which is 52800 feet.
So the volume of our bit of trail is 2,112,000,000 cubic feet.
The trail contains material at the concentration of 0.000499 ounces per cubic foot.
That is 1054782.8 ounces;
divide by 16 to get 65923.9pounds;
divide by 2240 to get 29.4 tons.
So, 10 miles of trail weighs 29.4 tons.

Many of the planes seen making trails are A320s. According to the Wikipedia on the A320 family ( http://en.wikipedia.org/wiki/Airbus_A320_family )
the operational empty weight is 87000 pounds which is 38.8 tons.
Also the maximum take off weight is 150000 pounds which is 67.0 tons.
So the maximum payload plus fuel of an A320 is 28.1 tons.

But wait! The 10 mile trail contains 29.4 tons of material. That is MORE than the maximum payload total. We have not loaded any fuel, crew, passengers or their luggage and freight!
So the material in the trail is NOT coming out of the plane, is it.
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As it stands the thread has 66 comments (but only 40 are visible for some reason).
Unfortunately it reads a bit disjointed because some commenters deleted their comments.
 

M Bornong

Senior Member.
I really should re-do this in a more artful way, it is somewhat stark, and I should have phrased the second to last sentence to read The basic math is 1.3 lbs water per lb of fuel burned per meter x 10,000 = weight of the persistent contrail per meter. I got rushed near the end of composition. The math will be hard for some people and I wish I had space on one page to show a real life example for a common airliner. If anyone wants to follow my lead and make improvements, especially someone with more artistic graphic design experience, please do so. I know some of you are artists and could improve on my crudity.

PS, also should read, "It is a physical impossibility for the Sabreliner to even carry 66,000 lbs...."

Would the making of Rock Candy be a simple demonstration of the Ice Budget? You start with a super saturated solution, add a seed, drawing the crystals out of the solution resulting in a mass many times the original seed.
 
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Mick West

Administrator
Staff member
It's a reasonable comparison, but not quite the same thing. At a molecular level sugar water is a solution (the water physically separates the sugar molecules via atomic forces), humid air is just a mixture of gasses.

Wikipedia describes the difference:

http://en.wikipedia.org/wiki/Supersaturation
Supersaturation is a state of a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances. It can also refer to a vapor of a compound that has a higher (partial) pressure than the vapor pressure of that compound.
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So while it's a good starting point, ultimately it's not quite the same thing.

Here's the process of dissolving for salt, which goes down to the atomic level (sugar just breaking into individual molecules, not atoms).
 

Ross Marsden

Senior Member.
Actually, I don't think that Wikipedia definition captures the idea.
It does not define what the "normal circumstances" are, and the second sentace should probably read, "It can also refer to a vapor of a compound that has a higher (partial) pressure than the saturated vapor pressure of that compound."

The point with saturation is that there is an equal rate of molecules entering and leaving both phases - there is an equilibrium where those rates are equal. And this is the "normal circumstance" referred to in the first statement in the Wikipedea entry - the close availability of the both phases; a flat water surface in the case of evaporation/condensation, or a flat ice surface in the case of melting/freezing or ablation/deposition (for the phase changes of water substance).

If you can remove the other phase (and have a pristine environment where no other substance can act in it's place, like a condensation nucleus) then you can achive supersaturation by whatever physical process you need to do that; cooling usually.
 

M Bornong

Senior Member.
It's a reasonable comparison, but not quite the same thing. At a molecular level sugar water is a solution (the water physically separates the sugar molecules via atomic forces), humid air is just a mixture of gasses.

Wikipedia describes the difference:

http://en.wikipedia.org/wiki/Supersaturation
Supersaturation is a state of a solution that contains more of the dissolved material than could be dissolved by the solvent under normal circumstances. It can also refer to a vapor of a compound that has a higher (partial) pressure than the vapor pressure of that compound.
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So while it's a good starting point, ultimately it's not quite the same thing.

Here's the process of dissolving for salt, which goes down to the atomic level (sugar just breaking into individual molecules, not atoms).

Isn't it the pressure that allows the 70% humidity and above at those altitudes, and why we rarely see such humidity at ground level at those low temperatures? Isn't the state of matter existing as solid, liquid or gas due to pressure and temperature?
 
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Ross Marsden

Senior Member.
You should edit Wikipedia. :)

Yes, it certaily needs some attention.
For example,
Preparation
Supersaturated solutions are prepared or result when some condition of a saturated solution is changed, for example increasing (or, rarely, decreasing) temperature, decreasing volume of the saturated solvent (as by liquid evaporation), or increasing pressure.
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is well messed up.

Earlier I said, "cooling usually", and that says "or rarely decreasing temperature".
Wha-a-at the ...?

Edit...
to continue

The Supersaturation page is faulty because (in part) the Vapor pressure page is unclear about the difference between Saturation (or Equilibrium) Vapor Pressure and just Vapor pressure.

Where does one start (or stop) editing Wikipedia pages?

I'm a bit disillusioned now. This is the first time I have found serious problems with Wikipedia pages.
 
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Ross Marsden

Senior Member.
Isn't it the pressure that allows the 70% humidity and above at those altitudes, and why we rarely see such humidity at ground level at those low temperatures? Isn't the state of matter existing as solid, liquid or gas due to pressure and temperature?

No. For the liqiud/gas and solid/gas phase interfaces, the saturation vapor pressure only depends on temperature. And the Sat Vap Press with respect to ice and water are different because of the different latent heats of ablation (solid to vapor) and vaporisation (liquid to vapor). In the case of water substance Sat Vap Press with respect to ice is LOWER than that with respect to water.
(See the blue and light blue lines in this diagram.)

These vapor pressures at these low temperatures are very small. The amounts of water we are concerned with is very small - a drop or two per cubic metre of air.

The relative humidity is the ratio between the vapor pressure and the Saturation Vapor Pressure for the temperature. At very low temperature, it is the ratio of two very small numbers.
 

Mick West

Administrator
Staff member
Where does one start (or stop) editing Wikipedia pages?

You can simply click on "Edit", although you might want to create an account first.



There's a lot of help on the help page:
https://en.wikipedia.org/wiki/Help:Contents

It's also good to try to model your contributions on existing ones with regard to formatting, particularly with references, which can be fiddly. However you might want to just wade in and make changes, see what happens.

https://en.wikipedia.org/wiki/Supersaturation
 

Ross Marsden

Senior Member.
Thanks Mick! What I meant by my question was - Eeeek! Am I going to end up editing and correcting every page that vaguely relates to phase changes of materials, as well as a bit of thermodynamics? Nearly every noun has a hyperlink to another Wikipedia page!

As you suggest, I may just wade in. A state of equilibrium will eventually be reached.
 
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