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A pump set up like this, where you move a handle from A to B was my thinking. Who wouldnt want a one-shot tire pump? How long would the lever need to be?
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moocher
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How long would the lever need to be?
There's no need for a lever, you just choose the pump bore to make the product of maximum pressure and piston area equal to the maximum force you can exert on the piston rod.
If you wanted to make a practical device to increase mechanical advantage in order to get the required pressure and volume from a single stroke, you'd use a capstan and a block and tackle, but adding all that friction just so that you can wind a handle multiple turns rather than reciprocating a pump handle multiple times seems silly.
The other alternative is to make the cylinder very long, about 5m should do so your device when extended would be just over 10m long.
Tijmen
gbj_tester
Since there are always 100 ways to skin any particular cat, you can look at the problem from an energy perspective. The energy stored in a pressure vessel (idealised isothermal system) is
In this case:
pA = 0.1MPa (1 bar ambient pressure)
pB = 0.3MPa (3 bar absolute pressure in tyre)
VB = 0.004m³ (4 litres tyre volume)
If we evaluate
0.3 MPa × 0.004 m³ × ln(0.1 MPa/0.3 MPa) + (0.3 MPa − 0.1 MPa) ×0.004m³ = 518J
The pump stroke energy input will have to be a bit more than that to account for losses, but the integral of force over distance must be at least 518J. For the practical maximum stroke for a manual floor pump of about 0.5m, the force will ramp up from zero to just over 2kN. Obviously, if you weigh 2kN you will need more pressure in your 29"×2"tyres that 2 bar gauge, so you end up chasing yourself in a circle 🙂
This leads to a practical guide to #whatpressureyourunning , since the energy stored in your compressed air will always be quite close to the product of your weight and height, e.g. 100kg and 1.85m gives 1800J, compared with 1700J for 2.5 bar gauge in a pair of 55-559 tyres or 1500J in a pair of 25-622 tyres at 6 bar gauge