So I'm going to step back a bit from fancy math and do some practical experimentation here. I bought the bicycle frame pump above and ran some simple calculations. The basic air mass flow rate for a human being is 6 L/min in a state of rest and 36 as a maximum in an agitated state. Whatever the speed or pressure of the gas, in the end you have to supply 6 Liters of expanded (1 atmosphere) air. How does that feel on your face? How hard is it to push the pump ? Do you need an air tank at all? Are there simple tanks you can make/find for 100 psi or less? Is that possible with a tiny pump like that?
I attempt to answer those questions today.
The frame pump is entirely made from plastic. It is made from a two-cylinder telescopic tube with two settings: low volume - high pressure, and high volume - low pressure. Air comes in through a small opening near the pressure gauge. In the high volume setting, by blocking the outlet of the pump with my thumb, it's actually hard to get much above 30 psi, because the area of the piston inside at that pressure provides a large reaction force. But using the low volume setting (locking the outer cylinder and using only the inner cylinder), I can easily get up to 50 psi momentarily (the piston leaks a little so pressure goes down immediately after the stroke - it's the job of the tyre valve to keep the air in the tyre, so it doesn't matter if the pump's piston leaks a little).
Most importantly, the piston is almost 100% quiet and the operation very smooth with no vibration. It gives me confidence that getting to 60 psi would probably be trivial. Getting to 80 psi looks entirely doable with a simple pulley and electric motor. The pump is rated 120 psi - and it's just a plastic and rubber piston!! The outer cylinder wall is transparent Lexan/Acrylic or similar and no more that 1.2mm thick!
It seems to me that a simple pulley-piston setup would be able to pull it off with a flywheel frequency of a few cycles per second. Let us assume that air enters the cylinder of the pump at ambient pressure and temperature. The travel of the inner cylinder is just 11.5 cm. The inner diameter of the inner cylinder is about 1.7 cm (estimated). This translates to a volume of ~2.61 X10
-5 m
3 of air at 1 atmosphere. Since we have 1000 liters in one cubic meter, then that corresponds to 0.0261 L/stroke. If we divide the minimum flow rate of 6 L/min by the volume of 0.0261 liters per stroke we get the number of strokes per minute to get 6 liters which is ~230 strokes/min, and if we divide again by 60, we get the number of strokes or cycles per second, which is 3.83 strokes per second to pump the 6 liters of air. This does not take into account pressure or temperature at all. The needle in the pressure gauge hardly moves when I pump air through the needle at this rate. These numbers are just for getting the required air supply of expanded air.
Given the physics of the problem, that seems to me to be an entirely achievable goal. Getting a rate 6 times that for the maximum minute respiration rate (36 L / min) seems to me will probably be a challenge, but at least I know I can get the minimum respiration rate with this pump. May no be good for jogging, but if you're riding the bus, shopping in the supermarket, or waiting in line it seems doable. As an experiment I tried pumping 4 cycles per second with my hand - it's not difficult, but your arm will get tired in about 20 seconds, and let me tell you, it's quite a stream of air on your face coming from that needle! The stream of air does come out noticeably cooler, but not much below ambient.
Again I'm not paying attention to cooling at all or pressure at the moment, its all near 1 atmosphere at ambient temperature, because I realize that we are in Fall, and Winter is upon us. It may not matter if by November I don't have a cooling system ready. But my idea is to pursue the development of the system WITH the Bell-Coleman refrigeration cycle, using with a flywheel and piston - its the quietest most efficient setup I can fathom, because other practical compressors are too noisy and rotary compressors are expensive/difficult/non existent yet. All in all it will be a very Victorian setup
I would prefer to get my hands on a screw type compressor, but the water requirement is ridiculous. With more time, I may try to build a Wankel compressor if I can get my hands on a working small-scale die cast model.
I'm actually very disappointed that the engineering community has not given us a quiet, cheap, practical compressor for something as simple as 100 psi. It just sounds ridiculous to me in the 21st century. To give you a feel for the kind of pressures we're talking about, a 2 liter soda bottle packs about 40 psi of pressure at room temperature! That's more than a car tyre which is between 25 and 35 psi !! Actually most sources I researched agree on the 40 psi maximum for a plastic soda bottle when filled with soda, and about 100-150 psi for a maximum failure pressure.
I don't even need to buy a tyre or steel pressure tank! I can just make a pressure vessel out of a soda bottle, or make my own using PVC pipes. But I would much prefer to use PVC pipes as I can adjust the size to what I want, they're much thicker, less prone to puncturing, and one can use tyre valves like these, which I can find at my local Wall of Mart:
So this knowledge save me a lot of complications by allowing me to build stagnation tanks with simple PVC pipes and off the shelf fittings. I would use two valves, one for inflating the tank and another for bleeding the tank.
Do you even need the tank? Well, that depends on how hard the pump needs to work to keep the pressure up to 80 psi. I can tell you it will have to work a lot harder than 4 cycles per second. And for 80 psi the material will probably need to be good enough to deal with the heat generated during compression. The mass flow rate I calculated for a stagnation tank at 80 psi was 10 times that mass flow rate, and that's not paying attention to how much you need in excess to start building up pressure. At 4 cycles per second you will get the basic mass flow rate for respiration, but no cooling at all because the pressure will not increase much throughout the system - speed is close to zero. Likewise with little compression the tank will not heat up by much. If this is Winter and you don't care about choking the needle and expanding a stream of air at Mach 1 or above air to cool, one way to go is to just build a small tank with the sole purpose of stabilizing the air flow coming from the pump, to avoid getting a single puff of air for every cycle in the flywheel/stroke of the cylinder.
I think I will build a small PVC pressure tank and will engineer a pulley system with a DC motor and see what happens... I still need to estimate the electrical consumption and size of batteries, but I imagine one can buy large power tool batteries.
