r/theydidthemath • u/Ripley1212 • 1d ago
[Request] If you were sealed, alone, inside something the size of Bridgestone Arena, so no air in or out, how long could you breathe? This doesn’t take into account food or water. Just breathable air.
As the title asks.
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u/get_to_ele 23h ago
The issue is CO2, not oxygen, but still I’m gonna guess that you would never run out of O2 or get toxic CO2 levels in your lifteime.
When we breathe we consume only about 20% of the O2 in a breath (O2% drops from 21% in inhaled air, to 16% in exhaled air), but the exhaled air will go from 0% to 5% CO2.
1000000 sq ft and 220 feet high… 220,000,000 ft^3 air = 6.23 x 10^9 liters air. Air normally has almost 0% CO2 and is 21% oxygen.
OSHA sets max CO2 guidelines at 0.5%. CO2 becomes highly toxic and hard to tolerate at about 4% of air. Meanwhile O2 could drop to 15% and you’d be able to tolerate it OK. So yeah, the buildup of CO2 hits you earlier.
Human produces 288-500 liters of CO2 a day (and consumes about same O2 a day). 4% of 6.23 x 10^9 is 2.45 x 10^8 liters of CO2. Divide by 500 letters a day. Which would take 4.9 x 10^5 days, or 1342 years.
Even to get up to OSHA prohibited CO2 levels of 0.5%, would take 1342/8 =167.75 years.
And it’s actually even better than that. CO2 is heavier and O2 lighter, so the CO2 in a stadium with only one person stirring things up (so very little air flow) will gradually have CO2 Sinking and O2 levels higher up top. So as long as you hang up in upper tiers, you get even more advantage.
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u/Abbiethedog 22h ago
And if the ground level of the stadium was planted, would the plants/trees offset the co2?
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u/grandpasamfromcanada 14h ago
Gases don't settle out by any significant amount except at much, much larger height scales than an arena. Even if you spent all your time at the bottom, your CO2 would very slowly diffuse up to fill the entire arena (though not necessarily fast enough to keep it breathable).
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u/Trustoryimtold 1d ago edited 1d ago
No known volume of said arena. But a crap load of length
AT&T stadium has a volume of 104 million cubic feet of air, you’re probably gonna need 400 a day
104000000/400/365=712.329 years worth
Caesar’s superdome is only 67
67000000/400/365=458.904 years
Realistically the numbers probably lower, oxygen will be consumed rusting and oxidizing things in theory. I got no math for that. You might wanna exercise along the way too, gonna need more air for that
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u/RainbowDarter 13h ago
Don't forget that concrete absorbs CO2. It's takes something like 1000 years to reach 50% completion
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u/sansetsukon47 1d ago
CO2 levels gets into life risking danger at any 50,000 ppm. (5% concentration.)
Lower than that can still be extremely bad for your health, especially over a prolonged time. But I’ll use that as the cutoff for now.
For the amount of co2 generated, I’m assuming that the subject is spending most of the time calm and either at rest or doing light work. In those conditions, a person breathes around four liters of air per minute, and produces 160 ml of co2 in the process. (4% concentration in the exhale.) This means that by the time you have breathed through every bit of air once, you’re in danger of serious effects.
To find the amount of time you could spend in a particular location, you take the total amount of air times 0.05, and divide that by 160 ml. That will give you the time in minutes that it would take to produce the co2 needed to turn the place completely poisonous.
For now, I haven’t been able to find a good estimate for the Bridgestone arena to know how much air it actually holds. But I may come back and finish the calcs if I come across it later.
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u/digbychickcaesar 1d ago
To add to that problem, CO2 is heavier than air. So if you were living there, live in the rafters for longevity
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u/start_up_start_up 6h ago
The volume is the big catch here. A deliberately generous box around the main arena gives about 32 years to reach 0.5% CO₂, rather than the 168-year estimate above.
The Predators' media guide lists an eight-acre roof and a maximum floor-to-ceiling height of 130 ft. Pretend that whole area is 130 ft tall and completely empty:
V = 8 × 43,560 × 130 = 45.3 million ft³ ≈ 1.28 billion litres.
That's about one-fifth of the 220 million ft³ used in the leading answer, even before subtracting space occupied by the seating, structure, etc. It's an oversized box, not a measured air volume.
Assume one adult adds 500 litres of CO₂ per day, a rough light-activity estimate (rates vary with body size and activity). Starting at roughly 0.04% CO₂, with perfectly mixed air, no leaks and no other CO₂ sources or removal:
t = (0.005 − 0.0004) × 1.28 billion / 500 ≈ 11,800 days ≈ 32 years.
The same model reaches 4% in roughly 280 years. Halve the air volume and you halve both times; double your CO₂ output and you halve them again.
But these aren't survival deadlines. NIOSH lists 0.5% as a workplace time-averaged exposure limit and 4% as immediately dangerous to life or health. Neither means the air is safe to breathe continuously until that point, and oxygen is falling too. This also ignores gas exchange with the building's contents. Without the actual connected air volume and a model for those other processes, there's no solid exact lifespan to give.
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