How wide would my cylinder be to allow air 500m below water surface?

I'd like my (very well funded) group of scientists to conduct an important excavation, in-situ with fully breathable air and comfort. I realize a pipe down to the surface would require a pump and could cause issues.

What I'd like is a cylinder wide enough that there is natural ventilation, and they can continue their excavations, dry, and breathing naturally without any automated pumps, etc.

I'll handle the depth of the cylinder into the seabed later, and of course this is an expensive prospect, but basically want to have a perfectly breathable seabed at 500m depth. How wide would it need to be?

EDIT: I am looking for an open space that allows for the free-breathing of the excavators. Specifically the width of the air-space (I allow a conical shape of course as well). The structural, safety and financial features are a separate question. This is purely about breathe-ability.

• I don't have a good enough visual of what you are looking for. What does width have to do with it? The main limit will be the incredible crushing pressures of the water at 500m, and the extraordinarily high level of risk associated with a failure of the wall. – Cort Ammon - Reinstate Monica Nov 6 '16 at 4:13
• Were you referring to the thickness of the wall, rather than the width of the cylinder? – Cort Ammon - Reinstate Monica Nov 6 '16 at 4:31
• I attempted answering, but it turns out it's more complicated than what I thought. Carbon monoxide and dioxide tends to settle. Flammable vapors might be a problem. Cold walls not helping with convection. And few more issues. Can't help, but I'd like to see a good answer that would talk about these. – Mołot Nov 6 '16 at 6:45
• @CortAmmon - no, I apologize; I aim to find an answer to how wide the airspace diameter is, to allow for natural breathing, not the structural integrity of it (which is another doozie). – Mikey Nov 6 '16 at 7:55
• how much people and equipment(in case combustion engines) there should be. do they work day and night or 8h work day? As I undestand criteria they should not die, and as comfort something like <5000ppm TWA blm.gov/style/medialib/blm/wy/information/NEPA/cfodocs/… Also do u sure to not use some design improvements in you tower of Babylon$^{-1}$? Some kind of heater at bottom could greatly improve air exchange. Also there almost 0 problem to a make airflow in 500m long, 10m wide tube as an example - how big should we start. – MolbOrg Nov 6 '16 at 12:38

Size of Site?

One important factor you have not yet provided us with is the known diameter of the excavation site. Is it miles wide, like a submerged ancient city, or is it a small ship wreck? That information can greatly effect the answer.

However, given the drawing you provided, I'm assuming it's a small site, and hence this is my thought:

Cylindrical Tower with Ventilation Shafts in Walls

You could have a relatively narrow total radius of the tower if your cylinder's walls were hollow with wind-catching vent openings at the top and vent openings at their base:

The amount of wind caught by the ventilation shaft's openings at the top would depend on their height above sea level, since wind speed increases as elevation increases:

(NOTE: 1 knot = 1.15078 mph)

In order to achieve a constant influx of wind, you need to make sure your tower is tall enough to catch a constant breeze--basically a skyscraper. For this, you need to know the atmospheric properties of your site. Although you have stated it will be in the Dead Sea, the amount of wind will be influenced by any nearby geographical features, so you will have to know your exact geographical location.

Once you have this information, you can use wind engineering formulas to determine how high the tower would have to be to achieve a sufficient constant influx of fresh air. You could then calculate:

• tower height
• number of ventilation shafts
• opening size of each vent mouth

Convection-Based Ventilation

This idea would allow you to have a tower only as wide as your dig site. The main concept is to have a solar-heated element running down the central shaft of the tower, heating the air and causing a chimney effect, sucking fresh cool air in from the side ventilation shafts:

Here is an alternate design that doesn't require hollow walls, just a simple partition down the middle of the tower:

The principle of the solar-heated element is basically the same as that used in solar power tower plants, where an array of mirrors focuses sunlight on a central collection tower so that the collection tower becomes quite hot:

I think this type of design would be much more effecient and simple to design than the wind-catching skyscraper idea I proposed earlier. It also allows you to keep the tower quite small, only the size of your excavation site, hence keeping building costs low and increasing real-world feasibility.

By heating air in the center you can draw air down from the sides.

Because of thermal stacking, thermal power generation towers can be as tall as 1000 meters.

just use mine airflow as guide. For heavy exertion humans need a bout 65 liters of fresh air a minute. if they are just walking around they need only 14. the most important factor is what kind of activity level are people doing and how many people are there. But in short no matter what the answer they are probably going to need a few fans.

http://www.molecularproducts.com/pdf/technical-library/A%20Guide%20to%20Breathing%20Rates%20in%20Confined%20Environments%20Technical%20Article.pdf

https://www.cdc.gov/niosh/mining/UserFiles/works/pdfs/bul589.pdf

Really a comment but it won't fit:

1) You're missing a big problem here--you have 5 megapascals of pressure trying to push under your cofferdam. Water is going to seep in pretty quickly playing havoc with your request for dry. (Oops, I originally goofed up and said 50, a zero placement error.)

2) Temperature. It's going to be awfully cold down there, can you say "fog"? And "dew"?

3) Your cylinder need to be at least 540 meters, not 500 meters--it needs to be tall enough to keep the largest rogue wave from going over the top. (Edit: Thinking more about this you need even more height but I don't know how much. The 40 meters was to cover the highest of rogue waves but this isn't a ship designed to cut the water, when the water strikes a wall that wide some of it goes up.)

4) Can you say "sea spray"? Waves are going to hit your cylinder, some of the spray will fall inside. You asked for dry.

Finally

5) If you want your workers comfortable you will need to heat the work area--and that combined with a simple baffle in your cylinder will substantially cut the needed size.

Edit: Why did I get the warning about hard science? This is an oversize comment showing more of the problem, not an attempt to answer it.

As I understand it, you want to work on the seabed, 500 m down, without using either a caisson or divers, so you opt for a cofferdam.

You will have to pump the water out (compare this picture), so pumping air in will be the least of your problems.

If air circulation was your only worry, consider open pit mines like this one in Bingham Canyon as an upper limit on the necessary diameter.

Follow-Up: With a bit of googling I found this article about CO2 emissions from mine shafts. Obviously the shafts have no air scoops, and the emissions depend on outside air pressure. That gives you a lower limit on the diameter of a feasible shaft.

• This does not meet the requirements of the hard-science tag. You would need to compute the result, not just give general pointers. – JDługosz Nov 6 '16 at 9:49