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Humans continue to lower the height of the atmosphere… but by how much? PART 1

September 26, 2007

That’s right. It’s all our fault, and I’m not even joking.


Millions of cars, trucks, airplanes, trailers, bicycles, welding shops, and wheelbarrows. What do they all have in common? Compressed air and a bath-tub. Well, not really, but wait… I’m going somewhere with this.


Consider the bathtub effect. Run a bath and watch it fill up with water. Note the level of the water. Take one thimble-full of water out of the tub. By how much did the water level drop? You can’t tell me it didn’t, but trust me when I say, “It did drop”. You might not be able to see it, but it certainly did drop. I’ll prove it:

Bath tub = 80cm long x 150cm wide x 30cm deep = 360,000 cm3 of water.
Thimble = 1cm x 1cm x 1cm = 1 cm3
New bath tub depth = (359,999 cm3
/ 80 cm long / 150cm wide) = 29.999916666666666666666666666667 cm deep.

This represents a 0.00084 mm drop in water. That’s completely indescernable to the naked eye, but you can’t deny that it happened.

Now imagine this bathtub represents the volume of air in our atmosphere. Imagine that the thimble full of water represents the volume of air that humans remove from the atmosphere. How? Simple. We compress air. We humans LOVE compressing air. We take gobs of it and scrunch it down and squeeze it into a space that occupies a fraction of the space that it did before. We take a gymnasium’s volume of air, and put it into a tire.

To figure the mystery of the shrinking height of the atmosphere, we’re going to have to figure out a few things.

  1. What’s the current volume of atmosphere
    • Spherical volume of Earth – Spherical volume of stated atmospheric limits
    • How altitude affects atmospheric densities
  2. What’s the amount of compressed air we have used I think we’ll use a few huge examples:

    • Automobile Tires (cars/trucks/buses)
    • Bicycle Tires
    • Other Tires (wheelbarrows, dolleys, etc. we’ll approx this one to, say, 5%)
    • Compressed air industry (welders/scuba)

I won’t be calculating things that put height into the atmosphere, ie. heat expansion, geo-venting, or vacuum cylinders, cause then these numbers won’t shock and awe… but I wonder how much we “add” to the atmosphere. Oh well, another day perhaps.

I think I’ve just bitten off almost as much as I can chew. The earth will be an easy one. The others, not so much.

Let’s get started! Click More.

PART 1 – Squeezing Earth’s Atmosphere

The FAI defines the world as a sphere exactly 40,000km in circumference. These are the people who define how far you need to fly around the world to beat an aviation world record. The most accurate I could find here is 40,075.16 kilometers at the equator and 40,008 km around the poles.

I know that the earth is a ball which is “bulged” at the equator (squashed like someone is stepping on it). This means that the earth is not a perfect sphere, but for the sake of our numbers, it will be a sphere of 40,000kms in circumference. This makes the calculated volume of the earth 1080759292185.0076 km3 and the calculated radius of the earth 6366.197723675671 km.
That was easy. Next.

We need to find the volume of earth’s atmosphere. Bless wikipedia. It’s a little tricky to determine exactly how tall the atmosphere is. Here’s some interesting facts:

  • 50% of the atmosphere by mass is below an altitude of 5.6 km.
  • 90% of the atmosphere by mass is below an altitude of 16 km.
  • 99.99997% of the atmosphere by mass is below 100 km.

I think what we’re going to have to do is determine first how much volume is missing at sea level, and then determine what the drop would be by “removing that much volume out from underneath the rest of the volume”. That should be easier.

How about when we inflate a tire at sea level? What happens then? Easy. We squeeze the air, which results in the same mass of air being in a tighter space. There’s an equation for that – and it’s simple. Thank you Robert Boyle. You told us that Volume and Pressure are inversely proportional.

P*V=c (c is a magic number that won’t change, no matter how much we squeeze, or stretch out the air).

  • P = For earth’s atmosphere, this is about 101.3 kilopascals (about 14.7 psi) at sea level.
  • V = 1m3
  • 101.3 * 1 = 101.3

Time to re-arrange the equation for a test run. When we inflate a tire, to say, 35psi ( 241.316505 kilopascals), we are actually inflating it to (14.7psi + 35psi) 49.7psi , or (101.3 kpa + 241.3 kpa) 342.6 kilopascals. So it works out that

    • P*V=c
    • V=c/P

The volume of 1 m3 at 35psi is about one third of a cubic metre. Cool. This means that if, say, if a tire has an internal volume of 1 cubic metre, we just stole 2 cubic metres out of the atmosphere to fill it.

Using the calculated volume of the earth (SAearth) and the calculated volume to fill a tire at sea level, we can determine how much inflating 1 million tires lowers the atmosphere.

Why 1 million tires? Beccause 1 is too small for my calculator.

radius (sphere with Volume (Vearth + Vtoinflatemilliontire)) – radius (Vearth) = many zeros followed by a one.

Aw, what the heck:

6366.197723675815 – 6366.197723675671 = 0.000000000144 km.
= 0.000144 mm

Wow. 1 million tires lowers our atmosphere by a fraction of a millimetre! This means, to lower it by 1 mm, we will have to inflate 7 trillion tires, which is 1.75 trillion cars or 1 really long limosine.

hmmmmm… that’s probably more cars than exist today, but as we’re about to find out in the next part, it’s not just car tires that are squeezing air.

Stay tuned for
Humans continue to lower the height of the atmosphere… but by how much? PART 2

3 Comments leave one →
  1. realworldnumbers permalink*
    September 26, 2007 3:48 am

    test comment

  2. pranajules permalink
    September 27, 2007 4:00 pm

    I wonder how much of the atmosphere height decrease is balanced out by global warming (Dense ice, melting into water , warm water evaporating into the sky).

    Is it possible that the earth’s atmosphere is actually getting higher?!?

  3. realworldnumbers permalink*
    September 28, 2007 5:04 pm

    I think *someone* around here is getting higher. My article says it won’t take any kind of expansion into effect. 🙂

    There’s lots of reasons why the atmosphere would expand, yes, creation of gasses, combustion of automobiles (Incredibly expands), thermal heat, farting.

    That’s a subject for another day!

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