On 8/24/2022 3:06 PM, Frank Krygowski wrote:
> On 8/23/2022 12:49 PM, Frank Krygowski wrote:
>> On 8/22/2022 9:35 PM, Jeff Liebermann wrote:
>>> On Mon, 22 Aug 2022 12:44:29 -0400, Frank Krygowski
>>> <
frkr...@sbcglobal.net> wrote:
>>>
>>>> On 8/22/2022 11:59 AM, Tom Kunich wrote:
>>>
>>>>> You and I are in complete agreement. Though I will add that someone
>>>>> or other made a minipump that clamped into a plastic holder attached
>>>>> under the water bottle holder. It had a reasonably easy use and only
>>>>> 100 strokes to bring a tire to pressure.
>>>
>>>> I'm _very_ curious about a mini-pump that required only 100 strokes, if
>>>> you mean 100 strokes from zero to ~100 psi. What specific pump was
>>>> that?
>>>> 250 to 300 strokes seem to be more common.
>>>>
>>>> We could work on this as a physics problem!
>>>
>>> OK. I'll bite. I get to pick the pump from my collection:
>>> <
http://www.learnbydestroying.com/jeffl/pics/bicycles/misc/bicycle-pumps.jpg>
>>>
>>> Measuring the volume of one stroke is easy. I fill the pump with
>>> water and measure the volume (or weight) of the ejected water. That
>>> takes care of all the volume of valves, cavities, hardware and
>>> oddities inside the pump.
>>>
>>> You get to pick the tube and tire sizes. If you have the actual
>>> dimensions (ID or OD) available that would be handy.
>>>
>>> Calculating the volume of the inflated tube is a bit awkward, but not
>>> impossible. I could probably measure the volume using water
>>> displacement, but I don't have every size tube and tire handy.
>>>
>>> The math is ideal gas law:
>>> <
https://en.wikipedia.org/wiki/Ideal_gas_law>
>>> PV=nRT where:
>>> P=pressure, V=volume, n=number of moles,
>>> R=gas constant, T=temperature
>>> When adding more air N (molecules) and P (pressure) will increase. V
>>> (volume) is constrained by the tire and does not increase. T
>>> (temperature) will increase, but it's assumed that sufficient time or
>>> coolant are available to bring the tire back to room temperature. This
>>> video grinds through the calculations, except it's for deflation and
>>> not inflation. Easy enough to change some signs.
>>
>> OK: My mini pump is a Hurricane HP Air Scepter, 0.669" bore, 7.7"
>> stroke. That's 2.7 in^3 per stroke.
>>
>> I just had a bad experience testing it on my 3 speed's rear tire.
>> That's had a very slow leak, as in several days to need air, so it
>> needed pumping anyway.
>>
>> Tire OD is 1.19", and it's a nominal 27" tire. I'm guessing about 1.1
>> ID. Volume is area times circumference at the centroid of that area.
>> So (Pi * ID^2 / 4) * (27" - 1.19") * Pi gives 77.0 in^3 for the tires
>> volume.
>>
>> To begin, the pump needs to inflate the flat tube to zero pressure.
>> That's just volume to volume at the same pressure. 77 in^3 / 2.7 in^3
>> per stroke = 28 strokes.
>>
>> To pressurize that air, if we ignore temperature effects, all we need
>> is P1*V1 = P2*V2. Condition 1 refers to atmospheric air into the pump.
>> Condition 2 is volume at high pressure - say 100 psi? But both must be
>> absolute pressure, so P1 = 14.7 psi and P2 = ~ 114.7 psi. (Extra
>> significant figures only for clarity.)
>>
>> Pump intake volume = V1 = P2 * V2 / P1 = 114.7 * 77 / 14.7 = about 590
>> in^3
>>
>> 590 in^3/ 2.7 in^3 per stroke = 218 strokes...
>> plus 28 strokes to expand a flat tube to full size, so ~ 250 strokes.
>>
>> ...
>>
>> So, the bad experience: I deflated the already soft tube (slow leak,
>> remember?) and began counting. As I hit 250 strokes I heard a hiss.
>> The leak suddenly transformed from slow to fast. I felt air rushing
>> out of the rim at the valve. I disconnected the pump and watched the
>> tire go dead flat.
>>
>> I'll try again later, maybe with a different bike tire.
>
> Bad news on the 2nd trial, or on the calculation.
>
> I fixed the flat. (Oddly, it looked like a micro-bit of glass went into
> the tube from the spoke side, not the pavement side. I must not have
> cleaned things out properly after the last flat long ago.)
>
> Then I attached the mini-pump and began counting. I stopped at 200
> strokes, felt the tire with my thumb and thought "That feels like about
> 75 psi."
>
> Well, my thumb needs re-calibrating, and so do my calculations. Pressure
> gauges said only 55 psi.
>
> I chose not to do a second trial. I'd already worked on brakes for a
> friend's bike, plus fixed that flat, and I have a wiring project
> awaiting me. I pumped to about 80 psi using my floor pump. But 200
> strokes didn't come close to 100 psi.
>
> Discussion is welcome.
Further followup: I repeated the test of pumping that tire with that
mini pump. I stopped at 200 strokes, measured the pressure, and again
got about 55 psi. I added more air, a total of 300 strokes, and measured
about 75 psi. Again, based on relative volumes and pressurizing the air
in the approximate volume of the tire, I expected 250 strokes to yield
about 100 psi. Obviously that's pretty far off.
Sources of error?
I think the big one is the internal volume of the inflated tire. I
estimated that by measuring the inflated tire's width, subtracting my
guess (TM) at wall thickness of tire plus tube to get ID, assuming a
torus (IOW a circular cross section of the inflated tube) and
multiplying that circular cross section by the circumference of the
cross section's centroid. I think that would be acceptably accurate for
a tubular tire. But the "well" of the clincher rim must add much more
volume than I anticipated. More volume to fill yields less pressure
added per pump stroke.
A second source of error might be the filling of the pump barrel. This
pump has an O-ring piston. I think the intake air has to flow past that
O-ring. It may take a bit of time for that air flow to occur, to fully
fill the pump volume with atmospheric pressure, and when pumping fast
there may be incomplete filling. Also, pumping away quickly I may have
not fully retracted the pump handle some percentage of the time.
There seemed to be negligible air loss in removing the pump (just a
quick, quiet "pop") or in measuring pressure using a tire gauge, so I
don't believe those contributed.
The rim is a Wolber Super Champion Mod 58, in 27" size. The tire is a
Pasela, 27" x 1 1/4. If anyone else wants to take a stab at actual air
volume of the inflated tire, have at it.
--
- Frank Krygowski