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Anonymous Poster

# Weight of air....did you know?

01/18/2007 8:55 PM

If you constructed a cylinder around the base of the eiffel tower, and extended it to the top, the air contained in the cylinder would weigh more than the tower itself?

Perhaps Buckminster Fuller was not so far off when he talked about floating cities contained in hemispheres.He stated that once the diameter exceeded several miles, the weight of the air would dwarf the weight of the structures within it, and a slight increase in air temperature inside would make the city float. The unique airflow pattern generated by the shape would provide free air conditioning. A floating city in California? Why not.

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#1

### Re: Weight of air....did you know?

01/20/2007 12:47 AM

At 0.07#/cu ft for ambient air the cylinder must be rather large to contain a volume of air with weight equal the steel. Floating on water, however, is much easier. Military tanks float in water but not in thin air.

If the above conclusion were true, what keeps the tower from floating in thin air during cold weather when air is heavy?

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#3

### Re: Weight of air....did you know?

01/20/2007 5:39 AM

Actually, with a quick check of the specs on the tower, it is 125 meters square at the base and ~312 meters tall so if you use a cylinder that would just contain the base and rise to 312 meters tall it would contain (at 1kg of air per m^3) ~7.6 million kg of air where as the tower weighs about ~4.9 million kg. You have to remember, although steel is much heavier than air, the volume of the air is much greater than that of the structure.

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#5

### Re: Weight of air....did you know?

01/20/2007 11:55 AM

Why not build a tethered (secured) lightweight framework surrounded by coated Mylar as thee structure and fill it with Helium?

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#8

### Re: Weight of air....did you know?

01/20/2007 8:35 PM

I believe your numbers are off a bit although with all the conflicting information out there who can blame you. I went to the towers official site. http://www.tour-eiffel.fr/teiffel/uk/documentation/structure/page/chiffres.html

Before that I found so many conflicting numbers my head is still spinning!

This statement came from the site. "If the Tower was placed in an air cylinder, its weight would not be more than that of the air cylinder."

The tower is 300 meters tall (without the flagpole or TV tower/antenna)

The weight of air is 1.2kg/cubic meter

The weight of the tower is 7300 metric tons or 7,300,000 kg (just the structure, otherwise it is 10,100,000 kg).

The tower is 125 meters on each side which makes the diameter of a circle encompasing it about 177 meters (176.77)

The volume of air for a cylinder 177 meters in diameter and 300 meters high is approximately 7.36 million cubic meters [(pi(141/2)^2*300) = 7,363,107 cubic meters]

That works out to 8,835,729 kg or about 8836 metric tons or air.

volume of air weight = 8836 metric tons

Weight of tower = 7300 metric tons

The one thing I haven't taken into account is the volume of air displaced by the iron structure itself which is probably where the difference is made to make it so close.

Just as a side note the tower is made of iron not steel.

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#9

### Re: Weight of air....did you know?

01/20/2007 9:18 PM

Yeah I thought about that after I posted. I read 7300 tons and used english units since it didn't say "metric" but then realized that everything else was metric so... Also, I had a figure of 1kg/m^3 and I didn't see the height of the tower without the flag so I used 312m. Not knowing the volume displaced by the tower mass we had no way to figure that but it is probably negligible in the overall picture. I think the main point is to point out that when you are discussing volume enclosed by the space that there's a lot more in the space than the structure. It also applies to matter. Heavy as it may seem and totally counter intuitive but there is far more space within the table on which I am typing that there is actual matter, unless you want to count the space as part of the matter and then of course it may not matter.

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#7

### Re: Weight of air....did you know?

01/20/2007 5:28 PM

This page deliberately left blank, but is reserved for use by philisophunculists such as yourself.

Good day.

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#2

### Re: Weight of air....did you know?

01/20/2007 3:07 AM

right but the cilinder must be totally weightless

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#4

### Re: Weight of air....did you know?

01/20/2007 6:11 AM

"right but the cilinder(sic) must be totally weightless "

No that's not the case. The idea is if you had a cylinder the size of the Eiffel tower and removed all the air from inside it would be capable of lifting a weight of 4.8 Gg or about 5,000 tons.

The question is could you build a structure that size that was capable of withstanding the pressure and weighed less that 5,000 tons? If you can then it would float in the atmosphere.

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#6

### Re: Weight of air....did you know?

01/20/2007 5:18 PM

Do the calculations for a hemisphere, and you will be amazed when the hemisphere approaches several miles diameter, the weight exceeds the common building materials used. No exotic materials needed, as per Buckminster Fuller.He claimed you could float a city in a hemishpere if it exceeded approx. 5 miles diameter. (If I remember correctly) using normal materials.

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#12

### Re: Weight of air....did you know?

01/21/2007 6:54 PM

What if you (hypothetically) could build a very large (20 miles in dia) steel hemisphere and remove most of the air out of it (partly vaccuum) without causing it to collapse.. Wil it have enough boyancy to be able to lift of the ground?

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#13

### Re: Weight of air....did you know?

01/22/2007 2:04 AM

If you could keep the mass of the structure below about 1.28 Tg or 1.28 million tonnes then yes it would float.

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#10

### Re: Weight of air....did you know?

01/21/2007 12:02 PM

I'm not sure I agree with your reasoning. For example, at 20 C, moist air weighs 0.95107 gms per liter. There are 28.3168 l in a cu ft, or 1,000 l in a cu meter.

In a cylinder of 100,000 cu meters, that's 1 MM liters, and 1 MM x 0.95107 gm = 951,070 gm = 2,094.9 pounds....if I did my quick math correctly.

Are you confusing the air pressure in # per cu meter with air weight?

Here's a thought: Suppose you evacuate a 1 lietr fsk, weigh it (tare) and then fill the flask with hydrogen. Will the flask weigh more or less than the tare, with hydrogen itn it? Some would think that the "lifting power" of hydrogen would make the flask weight less, but think about it!

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#11

### Re: Weight of air....did you know?

01/21/2007 1:19 PM

"I'm not sure I agree with your reasoning. For example, at 20 C, moist air weighs 0.95107 gms per liter. There are 28.3168 l in a cu ft, or 1,000 l in a cu meter.

In a cylinder of 100,000 cu meters, that's 1 MM liters, and 1 MM x 0.95107 gm = 951,070 gm = 2,094.9 pounds....if I did my quick math correctly. "

Firstly I got 1.186 gl-1 for the density_of_air and secondly where did the 100,000 m3 come from the volume of the cylinder we are talking about has a volume of 7.363 Mm3.

That gives us a mass of

MassAir = 7.363 Mm3 x 1,000 x 1.186 gl-1 = 8.733 Gg = 8,733 tonnes

MassAir = 7.363 Mm3 x 1,000 x 0.95107 = 7.003 Gg = 7,003 tonnes

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#14

### Re: Weight of air....did you know?

01/22/2007 7:21 AM

Responding to your hydrogen thought here. A volume of hydrogen is lighter than an equal volume of air which gives it the "lifting" quality. The container has been evacuated then refilled with hydrogen. If it has been refilled to the same pressure as before it was evacuated then it would weigh less than when filled with air but more than the tare weight. If the container is very light and depending on the size then it would float. If you force additional hydrogen in thereby pressurizing it then it would weigh more. Think of two ballons one filled with hydrogen and one with air. As you add each gas the ballons inflate or increase in volume. The ballon with air never exhibits any lift while the hydrogen ballon, once filled with enough hydrogen to overcome the weigh of the ballon does begin to lift. We've all seen helium baloons that slowly shrink as the gas escapes dangling from their string/ribbon. They still have helium in them just not enough to overcome the weight of the container. If you have ever had to handle cylinders of hydrogen or helium empty and full then "lighter than air" doesn't mean weightless!

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#15

### Re: Weight of air....did you know?

01/22/2007 2:15 PM

You're neglecting the weight of air inside the building which figures into the total weight of the building. The only way (weigh) this would float in a cylinder of air is if the building was sealed and contained something lighter than air like helium or was under a vacuum. Either way, I don't think the people working there would like it.

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#16

### Re: Weight of air....did you know?

01/24/2007 3:46 AM

For the love of God.....

Get a life

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#17

### Re: Weight of air....did you know?

01/24/2007 7:44 AM

Here's a thought: Suppose you evacuate a 1 lietr fsk, weigh it (tare) and then fill the flask with hydrogen. Will the flask weigh more or less than the tare, with hydrogen itn it? Some would think that the "lifting power" of hydrogen would make the flask weight less, but think about it!

My response to cardio07's "thought" shown above not the original discussion subject. Come on, give me a break!

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#18

### Re: Weight of air....did you know?

02/07/2007 7:35 PM

According to Buckminster F., The lift would be accomplished by the slight differential in temperature between outside and inside.The inside will be hotter, and therefore lighter than outside air. In effect, a hot-air balloon of sorts.When you get into several miles diameter, the weight of the building materials, even common materials, is insignificant compared to the weight of the air.

Do the math for an astrodome of 20 miles diameter.The surface area, vs the volume.It does not work for small diameters, so it is hard to visuallize in everyday objects, such as beakers,tanks, etc.

Then tell me why it won't work.

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#20

### Re: Weight of air....did you know?

02/12/2007 9:32 PM

The eiffel tower statement is true.Buckminster Fuller, however used hemispheres for his calculations.Hemispheres(and spheres) surround the most volume with the least surface area.

Perform the calculations with a 20 KM hemisphere, and you will get , roughly a volume of 2095 cubic KM, and an area of roughly 6283 sq. KM.Now the question boils down to:Will 2095 cubic Kilometers of air weigh less than 6283 Sq .Km of material?

Air weighs approx.1.2 Kg per Cu.Meter.There are 1GM in a cubic Kilometer, hence 1.2^1000000000=12000000000 or 120 million metric tons per cubic KM.Times 2095 KM. = 2514T metric tons of air.

The shell does not have to be solid plate steel.Consider the astrodome roof for example.It is much lighter than a solid steel covering, and much stronger.

I do not know the weight of the building materials, but it would have to exceed 400 M metric tons per square Km to break even, and NOT float with a slight temperature differential.A square kilometer is 100000 square meters, so we are looking at a break-even weight of 40000 tons per square meter.

Someone please check my math, it doesn't look right, and my pencil sharpener just broke.

HTRN

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#21

### Re: Weight of air....did you know?

02/14/2007 5:17 AM

A lot of people are making the fundamental mistake of thinking the total weight is only the steel structure, the total weight includes the gas inside it as well.

Any object that is immersed in fluid or gas will experience an upward buoyancy proportional to the mass of the displaced fluid or gas. So for these enormous structures to float they must displace the air which means they have no air inside. Put simply they must have a vacuum inside to be buoyant.

Lets look at what this means for your structure that has a surface area of 6,283 Km2. The atmospheric pressure is roughly 1,000 Hpa or 100,000 Newtons per square meter so multiplying this out means that force will be around 630 TN.

While in theory one could construct a gigantic evacuated sphere, where the weight of the shell was less than the air that it displaced, trying to get it to withstand the 630 TN crushing force that the atmosphere will cause is a completely different matter.

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#22

### Re: Weight of air....did you know?

02/14/2007 5:39 AM

"Any object that is immersed in fluid or gas will experience an upward buoyancy proportional to the mass of the displaced fluid or gas." Absolutely correct.

"So for these enormous structures to float they must displace the air which means they have no air inside. Put simply they must have a vacuum inside to be buoyant." Not correct! All that is required is that the combined weight of the structure and the gas/fluid inside be less that the gas/fluid that it displaces. Otherwise hot air balloons would not work.

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#23

### Re: Weight of air....did you know?

02/14/2007 6:58 AM

"All that is required is that the combined weight of the structure and the gas/fluid inside be less that the gas/fluid that it displaces. Otherwise hot air balloons would not work."

This is absolutely true and the structure can be filled with anything that has a density less than air. A vacuum filled, or more correctly unfilled, structure will have the smallest volume that could be buoyant. However any added mass will increase the size of the structure that is required.

What I was trying to point out that people were saying that just because the steel in the gigantic structures had a mass less that the air that they encompassed doesn't automatically mean they will float. The keep forgetting about the mass of the air inside them which is analogous to expecting a steel ship full of water to float. The ship only floats because the mass of the water it displaces is equal to the mass of the ship and its contents.

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#24

### Re: Weight of air....did you know?

02/14/2007 7:44 AM

Yeah, I'm not arguing that it is a good idea or even possible, more of just a thought experiment. I'm just a stickler for details, even in the hypothetical. I figured you knew but someone out there might be confused. Scratch the might.

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#25

### Re: Weight of air....did you know?

02/14/2007 8:25 AM

Details are important and I should have included more information about how it could be possible to get these things off the ground. The overlooking of small details has led to many a disaster and there are a lot of people that read the discussions on this site so we owe it to them to be as thorough as possible.

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#19

### Re: Weight of air....did you know?

02/07/2007 8:19 PM

Beam me up Scotty!