Simple way to demonstrate difference between when a filter and when a respirator.
You wear a filter to remove the stuff you don't want to breath normally - like what a filter for your central air conditioner filter would remove - dusts, pollen's, finally divided powders (like radioactive isotopes), etc. It's a mechanical removal by blocking particles.
A two stage filter system using big box sold A/C filters can be made fairly simply -
first filter - pollen, pet dander, dust/lint, dust mites
second filter - removes everything the first filter does PLUS:
odor, smoke, bacteria, microscopic allergens, mold, virus carriers, smog
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You wear a respirator to remove the stuff that's left. Organic vapors, acid gases, NERVE AGENTS, etc.
IF you have a "well built, well equipped storm shelter you might want to have a 2 stage filter system. It would be a nice design to be able to shut off air intake so you could change the filters elements.
If your storm shelter is an EVEN better equipped shelter, you want to a third element that can remove the stuff that's left like organic vapors, acid gases, NERVE AGENTS, etc.
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IF you can afford it - a PAPR (Positive Air Pressure Respirator) system makes it easier to breath and prevents inspiration issues. An ideal homemade pressure system would have the air pump downstream from the first two filters to prevent contamination and to allow the third element to only have to get rid of "the stuff that's left".