Two questions really. What is the expected MAXIMUM pressure you could expect a simple (non hi-tech)
bicycle hand pump to inflate a tire to?

Do you have to put in twice as much energy to double the pressure in the tire. Say from 40psi
to 80psi. Or would it take 3 times or 5 times (or an exponential amount) more effort to double
the pressure?

TJ Sackville-West wrote:
> Do you have to put in twice as much energy to double the pressure in the tire. Say from 40psi to
> 80psi. Or would it take 3 times or 5 times (or an exponential amount) more effort to double the
> pressure?

Every time you double the pressure, you do an equal amount more work, if you do it slowly enough to
work at the constant temperature as you do it. Raising the temperature as you do it works against
you. Raising it a lot works against you a lot. The latter is the usual case, if you feel the end of
your pump now and again for temperature.

The reason that you get only an equal amount more work is that the volume change becomes smaller as
the pressure becomes higher.

To double the pressure of a water-filled tire takes no work at all to speak of, because its volume
doesn't change at all to speak of.
--
Ron Hardin rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.

There are no simple answers to your questions. It depends on the quality and intended pressure
capability of the pump and on the strength and endurance of the pumper. A general expectation would
be that 3 to 4 times the effort would be required to reach 80 psi, as for just 40 psi, considering
that the pump and the pumper had the capacity to reach it at all. Most cheap bicycle pumps in the
sub-$10. range, in U.S. money, top out at about 60 psi. A $20. pump might hit 80 psi and you could
find one capable of 105 psi for $30. These are just rough estimates and apply mainly to small,
hand-held pumps. You may get more pressure capacity for your money from a large floor pump.

Also, do the calculations of effort include starting from 0 psi for going to both 40 and 80 psi
or does the measured effort to reach 80 psi start after 40 psi has been reached?

Steve McDonald

"TJ Sackville-West" <rayxt@hotmail.com> wrote in message
news:5372a77d.0301260227.55c8b490@posting.google.com...
> Two questions really. What is the expected MAXIMUM pressure you could expect a simple (non
> hi-tech) bicycle hand pump to inflate a tire to?

I'm not sure what you mean by a "non hi-tech" pump. There is a direct releationship between the
*force* required and the pressure delivered, that is the pump bore (diameter). You'll have an easier
time reaching high pressures with long, skinny pumps than short fat ones. A good frame pump like the
Zefal HPX series can reach 150 psi, 100-120 is not too hard for most people, these pumps are typical
of those in the $15-25 range.

> Do you have to put in twice as much energy to double the pressure in the tire. Say from 40psi to
> 80psi. Or would it take 3 times or 5 times (or an exponential amount) more effort to double the
> pressure?

Assuming a perfect pump, reaching twice the pressure in a tire would require 4 times as much work,
since each stroke delivers the same quantity of air, and twice the pressure requires twice as much
air, so twice the strokes; and each stroke, on average, would require twice as much force. Twice the
strokes at twice the force is four times as much work.

I could be wrong, as I'm a bit rusty, but I'm pretty sure that for an additional 40psi, you have to
put in 40psi worth of air (at constant temp). Since you have to do it at twice the pressure, it will
probably be approximately twice the work. The PROPORTION of change is smaller. If I recall
correctly, the amount of air relates to n in PV=nRT, but thermo was a long time ago. This assumes
negligible expansion of the tire and an efficient pump. So if the amount of air in the tube is 1
unit when the tube is at 0PSIG (15 psi atmosphere), then it's 3.7 units at 40psi and 6.3 units at
80psig, or approx 2.7 units added each time (psig is pressure reading on the gauge). BTW,
temperature is significant. If I pump it up outside and leave my 1" tires out a couple of days in
overly cold weather I will get a higher reading EVEN ON THE PUMP GAUGE if I let it warm up again.
Normally they'd soften up just a bit in that time.

Ron Hardin wrote:
>
> TJ Sackville-West wrote:
> > Do you have to put in twice as much energy to double the pressure in the tire. Say from 40psi to
> > 80psi. Or would it take 3 times or 5 times (or an exponential amount) more effort to double the
> > pressure?
>
> Every time you double the pressure, you do an equal amount more work, if you do it slowly enough
> to work at the constant temperature as you do it. Raising the temperature as you do it works
> against you. Raising it a lot works against you a lot. The latter is the usual case, if you feel
> the end of your pump now and again for temperature.
>
> The reason that you get only an equal amount more work is that the volume change becomes smaller
> as the pressure becomes higher.
>
> To double the pressure of a water-filled tire takes no work at all to speak of, because its volume
> doesn't change at all to speak of.
> --
> Ron Hardin rhhardin@mindspring.com
>
> On the internet, nobody knows you're a jerk.

--
Lincoln Ross NOTE ADDRESS CHANGE: lincolnr@rcn.com

bigrocketman3@webtv.net (Steve McDonald) wrote in message
news:<24296-3E33DE30-153@storefull-2112.public.lawson.webtv.net>...
> There are no simple answers to your questions. It depends on the quality and intended pressure
> capability of the pump and on the strength and endurance of the pumper. A general expectation
> would be that 3 to 4 times the effort would be required to reach 80 psi, as for just 40 psi,
> considering that the pump and the pumper had the capacity to reach it at all. Most cheap bicycle
> pumps in the sub-$10. range, in U.S. money, top out at about 60 psi. A $20. pump might hit 80 psi
> and you could find one capable of 105 psi for $30. These are just rough estimates and apply
> mainly to small, hand-held pumps. You may get more pressure capacity for your money from a large
> floor pump.
>
> Also, do the calculations of effort include starting from 0 psi for going to both 40 and 80
> psi or does the measured effort to reach 80 psi start after 40 psi has been reached?
>
> Steve McDonald

Conclusion from Steve's statement seems to be that if you use the cheapest hand pumps there's
virtually no (technical) way you COULD pump up your bicycle tire to 60 psi, even if you had the
physical endurance to do it. So to achieve 'easy' road rolling pressures of 60-80+ psi in a tire you
need both a more expensive hi-tech hand pump or use a floor pump.

Meaning as most people only have cheap hand pumps, most are riding on critically under inflated
tires and expensing a lot more pedaling energy than necessary. probably a good thing considering the
genral state of obesity in the developed world.

Lincoln Ross wrote:
>
> I could be wrong, as I'm a bit rusty, but I'm pretty sure that for an additional 40psi, you have
> to put in 40psi worth of air (at constant temp). Since you have to do it at twice the pressure, it
> will probably be approximately twice the work. The PROPORTION of change is smaller. If I recall
> correctly, the amount of air relates to n in PV=nRT, but thermo was a long time ago. This assumes
> negligible expansion of the tire and an efficient pump. So if the amount of air in the tube is 1
> unit when the tube is at 0PSIG (15 psi atmosphere), then it's 3.7 units at 40psi and 6.3 units at
> 80psig, or approx 2.7 units added each time (psig is pressure reading on the gauge). BTW,
> temperature is significant. If I pump it up outside and leave my 1" tires out a couple of days in
> overly cold weather I will get a higher reading EVEN ON THE PUMP GAUGE if I let it warm up again.
> Normally they'd soften up just a bit in that time.

That's possible; I have computed the work in compressing the tire to a higher pressure, rather than
that of adding air.

But then maybe the way to do it is more like mine, compressing the tire from 40 to 80, and filling
another tire to 80 the same way and putting it alongside and removing the barrier. You get a
recursion.

The work in getting to pressure p would be

W(p) = 2 . (W(p/2) + Const)

Wq. the work in filling two half-pressure tires and the Const work in compressing each to double
pressure and then combining them.

So W(p) becomes linear in p. Twice the pressure means twice the work, eventually, because Const
becomes negligible compared to W.

Early in the game, it's less work than linear, p being absolute pressure.
--
Ron Hardin rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.

TJ writes anonymously:

> Two questions really. What is the expected MAXIMUM pressure you could expect a simple (non
> hi-tech) bicycle hand pump to inflate a tire to?

The simplest pump is probably the Silca frame-fit plastic pump, having no features other than a
piston and pump head with a grommet. This pump can get 100psi into a tire for an athletic person as
it did for many years in bicycle racing when racers carried their own spare tubular tires and had no
"spare wheel service".

> Do you have to put in twice as much energy to double the pressure in the tire. Say from 40psi to
> 80psi. Or would it take 3 times or 5 times (or an exponential amount) more effort to double the
> pressure?

If you have tried it, you'll have noticed that 30psi is trivial with the mentioned pump while 90psi
is a bit of work and the last 10psi to 100 are as much effort as all the previous. The Silca has
only a small dead space, that volume of the pump that, when the piston is all the way in, does not
get pushed past the tire valve or pump check valve. Bringing dead space up to pressure occurs with
every stroke but it is not part of the useful effort.

Inflation work is a square law by which doubling pressure requires at least four times the work.
With dead space, that all pumps have, it is more. This means that there is an upper limit to the
pressure a pump can deliver when all air in the cylinder is compressed into the dead space without
any going into the tire that is already at that pressure.

Jobst Brandt jobst.brandt@stanfordalumni.org Palo Alto CA

jobst.brandt@stanfordalumni.org wrote
> Inflation work is a square law by which doubling pressure requires at least four times the work.

Well now this is interesting, because I don't see what's wrong with the plan: start with a tire with
say 4 times the volume and fill with 15 psi (no pressure net), which takes zero work. Then by some
mechanism pull in the sidewalls into the rim to reduce the volume by a factor of two, giving you 30
psi (15 net). Do it again and you get 60 psi (45 net).

Each of these ``doublings'' takes the same amount of work.

Thus you can inflate a tire with only log(p) work.

It must be that most of the work into the pump is theoretically recoverable but not recovered. Or
does it in fact have a check valve that prevents you losing the compressed air that doesn't make it
into the tire, in which case the double force double distance argument is wrong for pumps.

Do everything slowly enough so it's isothermal and that's out of the accounting.
--
Ron Hardin rhhardin@mindspring.com

On the internet, nobody knows you're a jerk.

On Mon, 27 Jan 2003 04:00:00 -0500, TJ Sackville-West wrote:

> bigrocketman3@webtv.net (Steve McDonald) wrote in message
> news:<24296-3E33DE30-153@storefull-2112.public.lawson.webtv.net>...
>> There are no simple answers to your questions. It depends on the quality and intended pressure
>> capability of the pump and on the strength and endurance of the pumper. A general expectation
>> would be that 3 to 4 times the effort would be required to reach 80 psi,

Why? The "effort" involved, as far as it being a problem, is developing the force. Since pressure is
force/area, and the area, the pump plunger, is the same, the force goes up linearly with pressure.
So, twice the pressure, you have to force the handle twice as hard.

Inefficiency of the pump also does not come into play. Whatever inefficiency is there (what, your
pumping goes into heating the pump body??) is also going to at most increase with pressure.

You just don't like cheap pumps.

> as for
>> just 40 psi, considering that the pump and the pumper had the capacity to reach it at all. Most
>> cheap bicycle pumps in the sub-$10. range, in U.S. money, top out at about 60 psi.

Simply not true. I have had cheap pumps that I could use, with difficulty, to get pressures of
100psi. In fact, eventually, any pump could manage this.

> A $20. pump might hit 80 psi and
>> you could find one capable of 105 psi for $30. These are just rough estimates and apply mainly
>> to small, hand-held pumps. You may get more pressure capacity for your money from a large
>> floor pump.

My current "cheap, small" pump, a ToPeak Road Morph, can easily, and I mean easily, pump any tire to
120psi. It takse serveral strokes, but that is not the issue.
>
> Conclusion from Steve's statement seems to be that if you use the cheapest hand pumps there's
> virtually no (technical) way you COULD pump up your bicycle tire to 60 psi, even if you had the
> physical endurance to do it. So to achieve 'easy' road rolling pressures of 60-80+ psi in a tire
> you need both a more expensive hi-tech hand pump or use a floor pump.

Or you need the existence of a gas station pump. But really, if you accept his hypotheses at face
value I have a bridge to sell.

--

David L. Johnson

__o | And though I have the gift of prophecy, and understand all _`\(,_ | mysteries, and all
knowledge; and though I have all faith, so (_)/ (_) | that I could remove mountains, and have not
charity, I am nothing. [1 Corinth. 13:2]

<jobst.brandt@stanfordalumni.org> wrote in message news:1adZ9.62545$Ik.2448944@typhoon.sonic.net...
<mostly snipped>
> Inflation work is a square law by which doubling pressure requires at least four times the work.
> With dead space, that all pumps have, it is more. This means that there is an upper limit to the
> pressure a pump can deliver when all air in the cylinder is compressed into the dead space without
> any going into the tire that is already at that pressure.
>
> Jobst Brandt jobst.brandt@stanfordalumni.org Palo Alto CA

Would most of this dead space be the hose connection the pump cylinder to the tube? Would shortening
the hose = noticably easier inflation?

On Tue, 28 Jan 2003 02:34:00 -0500, Brian Lerner wrote:

> Would most of this dead space be the hose connection the pump cylinder to the tube? Would
> shortening the hose = noticably easier inflation?

Hmm. The best pump (frame or mini) I have ever had is my ToPeak, and it is the first that has had
such a hose. Certainly the effect as Jobst mentioned is there, but that might be overcome by better
design elsewhere. I also do not know whether or not there is a check valve in the pump itself.

The best pumps are all floor pumps, and they all have hoses that are quite long. Probably the
advantage of being able to push down on the handle overcomes the disadvantage of the dead space
in the hose.

--

David L. Johnson

__o | The lottery is a tax on those who fail to understand _`\(,_ | mathematics. (_)/ (_) |

Brian Lerner writes:

>> Inflation work is a square law by which doubling pressure requires at least four times the work.
>> With dead space, that all pumps have, it is more. This means that there is an upper limit to the
>> pressure a pump can deliver when all air in the cylinder is compressed into the dead space
>> without any going into the tire that is already at that pressure.

> Would most of this dead space be the hose connection the pump cylinder to the tube? Would
> shortening the hose noticeably easier inflation?

Most likely not. Pumps that use a hose usually have a check valve in the body of the pump. Dead
space is the volume inside the cup to the pump "leather" of the piston and the clearance of the
piston to the end of the pump cylinder. Add to that the passage from that point to the check valve.
If that passage includes the hose, it's a bad design.

Jobst Brandt jobst.brandt@stanfordalumni.org Palo Alto CA

jobst.brandt@stanfordalumni.org wrote:

> Brian Lerner writes:
>
> >> Inflation work is a square law by which doubling pressure requires at least four times the
> >> work. With dead space, that all pumps have, it is more. This means that there is an upper limit
> >> to the pressure a pump can deliver when all air in the cylinder is compressed into the dead
> >> space without any going into the tire that is already at that pressure.
>
> > Would most of this dead space be the hose connection the pump cylinder to the tube? Would
> > shortening the hose noticeably easier inflation?
>
> Most likely not. Pumps that use a hose usually have a check valve in the body of the pump. Dead
> space is the volume inside the cup to the pump "leather" of the piston and the clearance of the
> piston to the end of the pump cylinder. Add to that the passage from that point to the check
> valve. If that passage includes the hose, it's a bad design.
>
> Jobst Brandt jobst.brandt@stanfordalumni.org Palo Alto CA

Agreed. Due to the effect of the check valve in the pump body, the space inside the hose is not
"dead" space, but pressurized dynamic space. One ought to be able to have a pretty long hose and not
notice any difference. Bernie

"David L. Johnson" <David L. Johnson <david.johnson@lehigh.edu>> wrote in message
news:<b14jor$hl6@fidoii.CC.Lehigh.EDU>...
> On Mon, 27 Jan 2003 04:00:00 -0500, TJ Sackville-West wrote:
>
> > bigrocketman3@webtv.net (Steve McDonald) wrote in message
> > news:<24296-3E33DE30-153@storefull-2112.public.lawson.webtv.net>...
> >> There are no simple answers to your questions. It depends on the quality and intended pressure
> >> capability of the pump and on the strength and endurance of the pumper. A general expectation
> >> would be that 3 to 4 times the effort would be required to reach 80 psi,
>
> Why? The "effort" involved, as far as it being a problem, is developing the force. Since pressure
> is force/area, and the area, the pump plunger, is the same, the force goes up linearly with
> pressure. So, twice the pressure, you have to force the handle twice as hard.
>
> Inefficiency of the pump also does not come into play. Whatever inefficiency is there (what, your
> pumping goes into heating the pump body??) is also going to at most increase with pressure.
>
> You just don't like cheap pumps.
>
> > as for
> >> just 40 psi, considering that the pump and the pumper had the capacity to reach it at all. Most
> >> cheap bicycle pumps in the sub-$10. range, in U.S. money, top out at about 60 psi.
>
> Simply not true. I have had cheap pumps that I could use, with difficulty, to get pressures of
> 100psi. In fact, eventually, any pump could manage this.
>
> > A $20. pump might hit 80 psi and
> >> you could find one capable of 105 psi for $30. These are just rough estimates and apply mainly
> >> to small, hand-held pumps. You may get more pressure capacity for your money from a large floor
> >> pump.
>
> My current "cheap, small" pump, a ToPeak Road Morph, can easily, and I mean easily, pump any tire
> to 120psi. It takse serveral strokes, but that is not the issue.
> >
> > Conclusion from Steve's statement seems to be that if you use the cheapest hand pumps there's
> > virtually no (technical) way you COULD pump up your bicycle tire to 60 psi, even if you had the
> > physical endurance to do it. So to achieve 'easy' road rolling pressures of 60-80+ psi in a tire
> > you need both a more expensive hi-tech hand pump or use a floor pump.
>
> Or you need the existence of a gas station pump. But really, if you accept his hypotheses at face
> value I have a bridge to sell.

Do you take credit cards?