Re: Rim brake heat and clincher blowoff, was Re: Potential good news for Mt. Washington access.



On Mon, 10 Jan 2005 19:53:20 -0500, Frank Krygowski
<[email protected]> wrote:

>
>Several people with strong engineering backgrounds have been following
>this thread. Your "corrections" have grevious factual errors, which is
>why nobody else has brought them up. Comments below:
>


Since I was trying to be nice and add something, and you
were obviously doing the opposite...

Boyles law only works in absolutes. If you use C for the
temp then you must add 273 to your temp on each side, but
only 14.7 for pressure and nothing for volume. You do the
math and see if temp will do anything to the pressure of a
tire in a temperature range that would not first weaken the
tire.

As for friction, you simply do not understand real world
friction applications if you do not think that friction
occurs unless the tire is skiding. Max heating of a tire
occurs at the speed just before the tire stops rotating.
The moment a tire skids friction drops significantly.
Anti-lock brakes?

Mark

PS, Why am I, and bunch of others, double posting
everything to the group tonight?
 
On Tue, 11 Jan 2005 02:01:52 GMT,
[email protected] wrote:

>Carl Fogel writes:
>
>>>> I am coming into this discussion a little late, so if I am
>>>> repeating something that has already been pointed out then I
>>>> appologize in advance. There have been a couple of "factual
>>>> errors" in recent posts. If no one with an engineering background
>>>> has corrected them then...

>
>>>> Expanding air cools, compressing air heats. When you fill a tire
>>>> you are expanding the air (cooling) and then as the...

>
>>> This has got to be a troll, it is so bizarre. Let's not get
>>> carried away by it. This is not the place to review high school
>>> physics for those who missed it.

>
>> It isn't?

>
>> If I'm following the idea, M&C are talking about what happens when
>> air previously compressed to 250 psi and allowed to cool to room
>> temperature is then released into an empty inner tube to a pressure
>> between say 25 and 125 psi--you know, what happens at most gas
>> stations with a compressor.

>
>Hold the phone. The tire is being inflated. That means compressed
>air enters the tire. If that air for one reason or another is colder
>than the tire it is entering then it will warm up and give a little
>more pressure than the gauge on the inflater registers, but not much
>because the surface to volume ratio of a bicycle tire is far smaller
>than a car tire where tires are routinely inflated from zero (ambient
>atmospheric pressure). It's even more so for CO2 cartridges and even
>they don't present a measurable change.
>
>> True, no hairy-chested he-men bent on telling everyone what not to
>> talk about here on rec.bicycles.tech ever use a gas-station
>> air-chuck, but...

>
>> Isn't Nashbar having a sale on CO2 inflators? You know, the kind
>> that get real cold and frosty when you use them to fill empty inner
>> tubes?

>
>I think we get into theoretical effects of insignificant proportions
>here and overlook the practical aspect of what counts. This posting
>remains a troll no matter how you look at it.
>
>> It's all kind of irrelevant to the interesting test that you're
>> working on, but it's still kind of fascinating to see a different
>> point of view on how something as simple as an inner tube gets
>> pumped up.

>
>I am not fascinated.
>
>Jobst Brandt
>[email protected]


Dear Jobst,

You may not be fascinated, but you're certainly fascinating.

Are you suggesting that room temperature 250 psi gas (and
greater in the case of the CO2 fillers) entering an empty
inner tube heats up as it expands and decompresses to 125
psi or less?

Have I misunderstood how refrigerators work all these years?

Carl Fogel
 
On Mon, 10 Jan 2005 21:21:16 -0500, Mark and Christine
<[email protected]> wrote:

[snip]

>Mark
>
>PS, Why am I, and bunch of others, double posting
>everything to the group tonight?


Dear Mark,

If you mean that the posts show up in two different
newsgroups, somewhere along the line a post got cross-posted
to rec.bicycles.misc and rec.bicycles.tech and dragged
subsequent replies along with it.

Some people use services and newsreaders that don't allow
them to confine their replies modestly to a single group.

If you mean that you see everything twice in a single
newsgroup, then your news server is probably wrapped in
white bandadages and not long for this world.

If you mean that you see everything twice in a single
newsgroup, then your news server is probably wrapped in
white bandadages and not long for this world.

Yossarian
 
[email protected] writes:

> On Tue, 11 Jan 2005 02:01:52 GMT,
> [email protected] wrote:
>
>>Carl Fogel writes:
>>
>>>>> I am coming into this discussion a little late, so if I am
>>>>> repeating something that has already been pointed out then I
>>>>> appologize in advance. There have been a couple of "factual
>>>>> errors" in recent posts. If no one with an engineering background
>>>>> has corrected them then...

>>
>>>>> Expanding air cools, compressing air heats. When you fill a tire
>>>>> you are expanding the air (cooling) and then as the...

>>
>>>> This has got to be a troll, it is so bizarre. Let's not get
>>>> carried away by it. This is not the place to review high school
>>>> physics for those who missed it.

>>
>>> It isn't?

>>
>>> If I'm following the idea, M&C are talking about what happens when
>>> air previously compressed to 250 psi and allowed to cool to room
>>> temperature is then released into an empty inner tube to a pressure
>>> between say 25 and 125 psi--you know, what happens at most gas
>>> stations with a compressor.

>>
>>Hold the phone. The tire is being inflated. That means compressed
>>air enters the tire. If that air for one reason or another is colder
>>than the tire it is entering then it will warm up and give a little
>>more pressure than the gauge on the inflater registers, but not much
>>because the surface to volume ratio of a bicycle tire is far smaller
>>than a car tire where tires are routinely inflated from zero (ambient
>>atmospheric pressure). It's even more so for CO2 cartridges and even
>>they don't present a measurable change.
>>
>>> True, no hairy-chested he-men bent on telling everyone what not to
>>> talk about here on rec.bicycles.tech ever use a gas-station
>>> air-chuck, but...

>>
>>> Isn't Nashbar having a sale on CO2 inflators? You know, the kind
>>> that get real cold and frosty when you use them to fill empty inner
>>> tubes?

>>
>>I think we get into theoretical effects of insignificant proportions
>>here and overlook the practical aspect of what counts. This posting
>>remains a troll no matter how you look at it.
>>
>>> It's all kind of irrelevant to the interesting test that you're
>>> working on, but it's still kind of fascinating to see a different
>>> point of view on how something as simple as an inner tube gets
>>> pumped up.

>>
>>I am not fascinated.
>>
>>Jobst Brandt
>>[email protected]

>
> Dear Jobst,
>
> You may not be fascinated, but you're certainly fascinating.
>
> Are you suggesting that room temperature 250 psi gas (and
> greater in the case of the CO2 fillers) entering an empty
> inner tube heats up as it expands and decompresses to 125
> psi or less?


I would be very surprised if M&C's "250 psi" compressor actually
stored air at 250 psi. Far more likely that it is one of those little
numbers without a tank at all. Actually, I would bet my life that she
does not fill her tires from a tank of 250psi air.
 
Carl Fogel writes:

> Are you suggesting that room temperature 250 psi gas (and greater in
> the case of the CO2 fillers) entering an empty inner tube heats up
> as it expands and decompresses to 125 psi or less?


No, but did you ever feel that a tire was noticeably cold after
inflation? Besides, we cant get on a bicycle and ride away before all
this normalizes to the ambient. I go on rides that start below
freezing and end in balmy weather without changing inflation on the
ride.

Let's get practical. This is not a problem or we would see people at
filling stations adjusting tire pressure on cold mornings and again in
the afternoon..

> Have I misunderstood how refrigerators work all these years?


The difference lies in magnitude and time interval. That's why it
takes a bit of feel for the subject to understand which effects are
applicable in which circumstance. Memorizing gas laws does not in
itself make a thermodynamicist.

That's why this is a troll.

Jobst Brandt
[email protected]
 
Mark and Christine write:

> Why am I, and bunch of others, double posting everything to the
> group tonight?


Those of us with intelligent newsreaders can read the response in
either of the two newsgroups and not see it again in the other.
That's the purpose in cross posting instead of re-posting threads
separately to each group.

Apparently your newsreader is not able to do this although many do.

The item became cross posted when some respondents chose to reply in
"rec.bicycles.misc" to the thread in "rec.bicycles.tech". Cross
posting reunited the responses so that they do not require separate
postings for each newsgroup.

Jobst Brandt
[email protected]
 
On Mon, 10 Jan 2005 20:48:22 -0600, Jim Smith
<[email protected]> wrote:

[snip]

>I would be very surprised if M&C's "250 psi" compressor actually
>stored air at 250 psi. Far more likely that it is one of those little
>numbers without a tank at all. Actually, I would bet my life that she
>does not fill her tires from a tank of 250psi air.


Dear Jim,

I'd be envious of a 250 psi tank compressor. Mine is only
125 psi.

But since "she" signs "her" posts "Mark" elsewhere in this
thread, I hope that you don't expect the rest of us to back
your bet without some collateral.

Carl Fogel
 
On Tue, 11 Jan 2005 03:18:09 GMT,
[email protected] wrote:

>Carl Fogel writes:
>
>> Are you suggesting that room temperature 250 psi gas (and greater in
>> the case of the CO2 fillers) entering an empty inner tube heats up
>> as it expands and decompresses to 125 psi or less?

>
>No, but did you ever feel that a tire was noticeably cold after
>inflation? Besides, we cant get on a bicycle and ride away before all
>this normalizes to the ambient. I go on rides that start below
>freezing and end in balmy weather without changing inflation on the
>ride.
>
>Let's get practical. This is not a problem or we would see people at
>filling stations adjusting tire pressure on cold mornings and again in
>the afternoon..
>
>> Have I misunderstood how refrigerators work all these years?

>
>The difference lies in magnitude and time interval. That's why it
>takes a bit of feel for the subject to understand which effects are
>applicable in which circumstance. Memorizing gas laws does not in
>itself make a thermodynamicist.
>
>That's why this is a troll.
>
>Jobst Brandt
>[email protected]


Dear Jobst,

I agree that the temperature effect would be small on the
tire and that it would rise to ambient temperature quickly.

But I think that you miss a lot while boasting of your feel
for everything, dismissing honest posts as trolls, and
backing yourself into frosty corners against rather sharp
teeth on chain rings.

Most people were so busy talking about hand pumps heating up
that they forgot how many people use air compressors and CO2
inflators. I certainly did--and judging by the number of
responses, it is indeed fascinating.

Carl Fogel
 
Mark and Christine <[email protected]> writes:

> As for friction, you simply do not understand real world
> friction applications if you do not think that friction
> occurs unless the tire is skiding.


We understand the real world quite well, however, that
triple-negative is a bit hard to parse.

Your original (incorrect) point was that the friction of the road
against the tire somehow heated up the air in the tube. It doesn't,
essentially all the heat is generated in the brake/rim interface. The
tire friction is significant only in that without we couldn't generate
the braking friction, however, no significant amount of heat is being
generated at the tire/road interface unless the tire is skidding. And
a skidding tire is not of interest to this discussion (for several
reasons).

> Max heating of a tire
> occurs at the speed just before the tire stops rotating.


That makes no sense. There is no given speed at which a tire stops
rotating. Anyhow, the velocity at which maximum power generation
occurs is not the worst-case for temperature rise under steady-state
braking, one has to consider convection cooling at the rim. A
calculation I did some time ago suggests that the worst-case velocity
is Vterm/sqrt(5), where Vterm is the terminal velocity of the rider.

Joe
 
[email protected] writes:

> Tim McNamara writes:
>
>> Hmm, well, if pressure increase from heating is the *only* cause of
>> blow-off, then one would expect to be able to blow off the tire at
>> the same pressure whether in the garage or rolling down the hill.
>> Or at least so it seems to me as a non-engineer. As I recall from
>> the prior discussion, heating the rim to the temperatures normally
>> seen doesn't cause a huge increase in pressure.

>
> As I said, the chafing strip on tire beads is not there for nothing,
> and from observation of aluminum on the strip and cloth marks in the
> aluminum, there is motion. Friction is not a consideration in tire
> retention when moving.
>
>> Or is there some other factor involved- the heat of the rim
>> affecting the coefficient of friction between the rim and tire?
>> There are different designs at the bead- some tires have a fabric
>> chafing strip over the bead, some are just a rubber coating over
>> the casing of the tire- could this make a difference and could it
>> be tested?

>
> Friction is not a consideration in tire retention when moving. I
> don't think rubber coatings last long at high pressure in this
> interface. What HP tires have no chafing strip? I'm considering
> road tires because fat tires have entirely different problems and
> rims.


Well, to answer this I had to look at the pile of tires in my
basement. All appeared to have some kind of chafing strip, although
most (Avocet Duro, Ritchey Tom Slick, Michelin Synergic) appeared to
be coated with the same rubber covering the sidewalls. The
Continental chafing strip seemed to have little or no rubber
coating. That was, I guess, the visual I had in mind when I wrote my
comment- the chafing strip is more visible on the Continentals.

>> Or perhaps the effect of braking causing some kind of pulling on
>> the bead on a line between the contact patch and the rim- drawing
>> the bead tight ahead of the contact patch and loosening it behind
>> the contact patch? Does rim have to be hot or can this happen cold
>> (if the latter is possible, I'd expect to see it happen in
>> criteriums or during panic stops).

>
> This would only be possible with an elastic bead because the entire
> circumference of the bead would have to slip for any of it to move.
> I have not seen any evidence of circumferential tire creep as I
> formerly saw on tubulars.
>
>> And out of this, if the mechanism can be determined, is the
>> question of how to prevent it. Closer tolerances for tire fit on
>> the rim? A change in the materials at the rim-tire interface? A
>> rim strip that insulates the tube?

>
> I think I mentioned that as part of the experiment.


The insulated rim strip, anyway. But I'm puzzled by the utility of
this, given your comments last August:

>> In a thread last August, Jobst stated:

>
>>> The idea that the tire bead gets soft occurred to me but I later
>>> rejected it because I have been in many situations where high rim
>>> temperatures occurred only for a short duration, not long enough
>>> to heat the air in the tube. There was no residual effect over
>>> many miles in which the tires wore out while repeating the rim
>>> heating. I get to review this every summer in riding over many
>>> mountain roads and have reduced the tire blow-off to air
>>> temperature in the tire alone.

>
>> This seems to me to suggest that temperature of the rim and not
>> pressure in the tube may be the culprit. What effect does heating
>> the rim have? The only thing I can think of is that there is some
>> effect on the interface between the tire and the rim- reduction of
>> friction, change in bead position at some point on the rim, etc.
>> And it also seems that the condition must be pretty specific and
>> difficult to achieve, or we'd have this happening on many rides,
>> not just a few..

>
> I don't understand. How do you draw that conclusion, one that is
> exactly the opposite from the one I derive from the cited paragraph
> that I wrote?


I misread, apparently. However, in the context of the thread back in
August it was suggested from the laws of physics that the temperature
increase in the tube would result in a small rise in pressure- from
100 psi to 126 psi with a temperature increase from about 60 F to 250
F, for example, well within the normal capacity of rims and tires to
withstand. This would seem to suggest that there is some other
mechanism other than increased pressure caused by heating the rims
from braking.

However, I'm obviously no physicist nor an engineer, and I'm looking
forward to your findings- one measurement being worth a thousand
opinions.
 
Tom Sherman <[email protected]> writes:

> Tim McNamara wrote:
>
>> Tom Sherman <[email protected]> writes:
>>
>>>Jobst Brandt wrote:
>>>
>>>>... Ride bike. In fact, make a point to ride the Alps. You'll
>>>>love it.
>>>
>>>Unfortunately, most cyclists in North America will never have both
>>>the vacation time and money for an Alpine cycling vacation.

>> Well, many won't have either the time or the money but perhaps not
>> "most." Mostcyclists I know make more than I do. I saved up for
>> it and went, spending two weeks in France and 10 days in the
>> Alps...

>
> How many people in the US can not only accumulate 4 weeks vacation,
> but also be allowed to use it all at once?


That's why I went for two weeks only, ten days of which were in the
Alps (which are in France to a great degree- sorry if that wasn't
clear). A lot of people get four weeks vacation per year, BTW. More
did back before the New Republicans began systematically destroying
the right to collective bargaining... Of course, I should talk, eh?
I don't get paid vacation or paid holidays or paid sick leave...

>> ... The cost total was about $2000 inclusive of air fare, meals,
>> lodging, miscellaneous purchases and one tire. Another week would
>> have only raised the costs about $250. Of course this was 2002
>> when $1 = E1 +/- $0.05. Times have changed, the same vacation
>> today would cost ~$2600....

>
> The lower working classes in the US and Canada could not reasonably
> afford that, nor could the majority of those in Mexico (since the
> original contention involved North Americans).


From what I can see, the lower working classes are pretty mobile as
air fare is subsidized and relatively inexpensive. Whenever I fly, I
see lots of those folks on the plane with me. Somebody making $6.15
an hour is not likely to fly often, to be sure, but I make about $15
an hour- no great shakes for a college graduate with a Master's
degree, is it? Most of my college friends with BA's make 2-4 times
what I make- and I can afford to fly. I dislike flying a great deal
and fly only when there is no other option, but I can afford it.

OTOH, recreational cycling is a rather elitist sport and probably few
non-recreational cyclists would be interested in a trip to the Alps to
ride bike. As I recall from stats published a few years ago,
recreational cyclists tend to be towards the upper end of the range of
income.

>> But I'll warn you- if you go and ride in the Alps once, you keep
>> thinking about how much you want to go back!

>
> I will have to ask my bicycle about this, since it toured the Alps
> with a previous owner.


It wants to go! ;-)
 
Tim McNamara wrote:

> ...
> From what I can see, the lower working classes are pretty mobile as
> air fare is subsidized and relatively inexpensive. Whenever I fly, I
> see lots of those folks on the plane with me. Somebody making $6.15
> an hour is not likely to fly often, to be sure, but I make about $15
> an hour- no great shakes for a college graduate with a Master's
> degree, is it? Most of my college friends with BA's make 2-4 times
> what I make- and I can afford to fly. I dislike flying a great deal
> and fly only when there is no other option, but I can afford it....


So there is a profession that pays worse than engineering (but not by much)!

Somehow it just seems frivolous to spend money on a vacation: "Is this
trip really necessary?"

--
Tom Sherman - Near Rock Island
 
Paul Kopit wrote:
> On Mon, 10 Jan 2005 12:32:09 -0600, Tom Sherman
> <[email protected]> wrote:
>
>>It would be a simple matter to use a tandem (e.g. Arai) drag brake on a
>>single bicycle and/or use adequately sized disc brakes.

>
> It's not that easy to get the components to fit onto a 135 mm spaced,
> threaded hub.


Hmmm... my tandem has 125mm rear spacing (it's old) and with a
five-speed spacing on the right, I've fitted early shimano disks and
Phil Wood disks on the left w/o difficulty. I don't know what the early
Santanas had for rear spacing, but I don't think it was the huge width
we see today, yet they've had Arai drums back there pretty much since
the beginning, IIRC. I think the key is in not expecting to fit 9
speeds on the right side and a drum on the left in 135 mm OLN distance.

> Also, the chain stay needs to hold the brake arm
> somehow. Tandems frequently have the fitting already there and the
> chainstay is sturdy enough to mount a bracket if it's not integral.


I suspect most singles' chainstays are plenty sturdy enough to support a
brake strap back there. (Most tandems now seem to have a braze-on for
the drum "reaction arm", but the norm used to be a strap-and-bolt affair.)

Mark Janeba
"Say, whatever happened to Phil Wood disk brakes? Mine still works
fine, though it's infrequently used."
 
Jim Smith points out that spoke tension is insufficient to
significantly restrain rim diameter from increasing due to thermal
expansion. While contemplating this on my evening walk, I wondered
whether the resulting spoke tension increase could be a significant,
and overlooked, factor affecting spoke life.

A few calculations are in order.

Let
dCr = (delta) increase in rim compressive force
dTs = (delta) increase in spoke tension
n = number of spokes = 36
R = wheel radius
As = spoke cross-sectional area ~ 2mm^2
ks = spoke elasticity ~ 30Mpsi
Fs = ks*As ~ 42,000kgf
a = coefficient of thermal expansion of rim ~ 25e-6/degC
Ar = rim cross-sectional area ~ 80mm^2
kr = rim elasticity ~ 10Mpsi
Fr = kr*Ar ~ 560,000kgf
dT = rim temperature increase
P = rim perimeter
dPt = change in P due to temperature increase in rim
dPc = change in P due to compressive force in rim

(1) dCr = n*dTs/2/pi
(2) dR/R = dTs/Fs
(3) dR/R = (dPt+dPc)/P
(4) dPt/P = a*dT
(5) dPc/P = -dCr/Fr

expanding (3) and plugging in (4) and 5 we get

(6) a*dT - dCr/Fr = dTs/Fs

Using (1) to eliminate dCr gives

(7) a*dT = dTs*(1/Fs + (n/2/pi)/Fr)
(7a) = dTs/Feff

where
1/Feff = 1/Fs + (n/2/pi)/Fr
~ 30,000kgF

From (7a) we find that

(8) dTs/dT = a*Feff ~ 0.75kgf/degC

So a 100degC rise in the rim temperature increases the spoke
tension by 75kgf (165lbf). This is not a trival amount, it
represents about 25% of the ultimate strength of a spoke.

Comments? I have ignored bending in the rim because
I couldn't easily compute its effect. Presumably it
significantly reduces the tension increase in the spokes.


Joe Riel
 
>> Alfred Ryder wrote:
>> I would be interested in knowing whether the blow-off point is
>> affected by
>> whether someone is sitting on the bike or not. The only blow-off I
>> have had
>> was a few seconds after coming to a complete stop.


Frank Krygowski wrote:
> When our tandem was brand new (long, long ago) it suffered two blowouts
> as it sat alone in a bedroom, at least an hour after mounting and
> inflating the tires. I never did figure that out.


Most likely an installation issue.

--
Andrew Muzi
www.yellowjersey.org
Open every day since 1 April, 1971
 
Tom Sherman <[email protected]> writes:

> Tim McNamara wrote:
>
>> ... From what I can see, the lower working classes are pretty
>> mobile as air fare is subsidized and relatively inexpensive.
>> Whenever I fly, I see lots of those folks on the plane with me.
>> Somebody making $6.15 an hour is not likely to fly often, to be
>> sure, but I make about $15 an hour- no great shakes for a college
>> graduate with a Master's degree, is it? Most of my college friends
>> with BA's make 2-4 times what I make- and I can afford to fly. I
>> dislike flying a great deal and fly only when there is no other
>> option, but I can afford it....

>
> So there is a profession that pays worse than engineering (but not
> by much)!


Most of the positions in health care, actually. I am averaging my
income over 2,000 hours because my income and how much time I spend
working are somewhat independent of each other. As a psychologist,
for every hour I work for which I get paid, there is another hour of
work for which I don't get paid. I work slightly less than full time
so that I have more time to ride bike- see the sentiment below for an
explanation. I don't want my epitaph to be "he worked a lot."

> Somehow it just seems frivolous to spend money on a vacation: "Is
> this trip really necessary?"


Sounds like you are a Calvinist. Are vacations necessary? Well, you
won't die without them but on the other hand, the things you end up
regretting are the things you leave undone.
 
On Mon, 10 Jan 2005 20:59:35 -0800, Mark Janeba
<[email protected]> wrote:

>Hmmm... my tandem has 125mm rear spacing (it's old) and with a
>five-speed spacing on the right, I've fitted early shimano disks and
>Phil Wood disks on the left w/o difficulty. I don't know what the early
>Santanas had for rear spacing, but I don't think it was the huge width
>we see today, yet they've had Arai drums back there pretty much since
>the beginning, IIRC. I think the key is in not expecting to fit 9
>speeds on the right side and a drum on the left in 135 mm OLN distance.


My Cannondale Road Tandem is 135 mm spaced and I did get the Arai onto
an XT HF07 tandem hub with an 8/9 sp freehub. You just don't slap it
on. I had to go to the point of shaving down a locknut to get the
tiny amount of room on the NDS.
 
Quoth Mark Janeba:

> "Say, whatever happened to Phil Wood disk brakes? Mine still works
> fine, though it's infrequently used."


Phil Wood disc brakes have been long discontinued, and for very good
reason. They're notoriously dangerous!

The weak point is the disc itself. As it wears, the outer section that
is grabbed by the caliper can break away from the center section that
attaches to the hub.

The thing that makes this particularly nasty is that they fail instantly
with no warning.

You squeeze the brake lever and it feels the same as it always did,
since the caliper is clamping on the rim of the disc as usual, but it
won't slow the bike down even a little bit.

Sheldon "BEWARE!" Brown
+-------------------------------+
| It's never too late to have |
| a happy childhood |
| --Jacek Rudowski |
+-------------------------------+
Harris Cyclery, West Newton, Massachusetts
Phone 617-244-9772 FAX 617-244-1041
http://harriscyclery.com
Hard-to-find parts shipped Worldwide
http://captainbike.com http://sheldonbrown.com
 
On Tue, 11 Jan 2005 06:37:07 GMT, Joe Riel
<[email protected]> wrote:

>
>Jim Smith points out that spoke tension is insufficient to
>significantly restrain rim diameter from increasing due to thermal
>expansion. While contemplating this on my evening walk, I wondered
>whether the resulting spoke tension increase could be a significant,
>and overlooked, factor affecting spoke life.
>
>A few calculations are in order.
>
>Let
> dCr = (delta) increase in rim compressive force
> dTs = (delta) increase in spoke tension
> n = number of spokes = 36
> R = wheel radius
> As = spoke cross-sectional area ~ 2mm^2
> ks = spoke elasticity ~ 30Mpsi
> Fs = ks*As ~ 42,000kgf
> a = coefficient of thermal expansion of rim ~ 25e-6/degC
> Ar = rim cross-sectional area ~ 80mm^2
> kr = rim elasticity ~ 10Mpsi
> Fr = kr*Ar ~ 560,000kgf
> dT = rim temperature increase
> P = rim perimeter
> dPt = change in P due to temperature increase in rim
> dPc = change in P due to compressive force in rim
>
>(1) dCr = n*dTs/2/pi
>(2) dR/R = dTs/Fs
>(3) dR/R = (dPt+dPc)/P
>(4) dPt/P = a*dT
>(5) dPc/P = -dCr/Fr
>
>expanding (3) and plugging in (4) and 5 we get
>
>(6) a*dT - dCr/Fr = dTs/Fs
>
>Using (1) to eliminate dCr gives
>
>(7) a*dT = dTs*(1/Fs + (n/2/pi)/Fr)
>(7a) = dTs/Feff
>
>where
> 1/Feff = 1/Fs + (n/2/pi)/Fr
> ~ 30,000kgF
>
>From (7a) we find that
>
>(8) dTs/dT = a*Feff ~ 0.75kgf/degC
>
>So a 100degC rise in the rim temperature increases the spoke
>tension by 75kgf (165lbf). This is not a trival amount, it
>represents about 25% of the ultimate strength of a spoke.
>
>Comments? I have ignored bending in the rim because
>I couldn't easily compute its effect. Presumably it
>significantly reduces the tension increase in the spokes.
>
>
>Joe Riel


Dear Joe,

Assuming that your calculations are correct, I suspect that
something must have been overlooked. Both the math and the
parameters are beyond me, but here's what makes me dubious.

Jobst Brandt does a lot of downhill braking on very hot
rims.

Jobst builds his wheels by tensioning spokes until the rims
begin to yield locally and then backing off a bit--about
10%, as I recall.

If each of Jobst's spokes, already at 90% of the tension
needed to produce local yield, added 165 pounds more
tension, I think that he'd report that his wheels were
behaving very oddly--wobbling out of true, yielding, and
probably failing.

(A timid question from the mathematically challenged: could
the 165 pounds be for all 36 spokes combined, about a 4
pound per spoke rise?)

Carl Fogel
 

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