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```From: jobst.brandt@stanfordalumni.org
Subject: Re: Tension wheel with or without tyre?
Newsgroups: rec.bicycles.tech
Message-ID: <zeZGd.2388\$m31.30571@typhoon.sonic.net>
Date: Tue, 18 Jan 2005 01:02:23 GMT

Philip Holman writes:

>>> You say the mechanism is that cord angle causes constriction but
>>> this is a chicken and egg thing.  Isn't the rim sized to obtain
>>> constriction?  How much constriction would there be for a 700
>>> tubular on a 650 rim? An absurd example but as the rim increases
>>> in size it reaches a point where constriction starts.  Isn't
>>> constriction therefore by design? For a tubular, the rim is a
>>> slightly larger diameter than an inflated tire.  I think the
>>> calculations that determine rim and tire size are being ignored.

>> A used tubular tire fits freely on the rim for which it is made and
>> doesn't come off any easier than one that is a tight fit on the
>> rim, the inflation constriction being the principal retention
>> mechanism.  The cords act similarly to a scissors car jack that as
>> it expands in one axis, becomes narrower in the other.  The same is
>> true for the tire casing and the force relationship between the two
>> axes is likewise.

> Let me pull out this sentence:

> "The cords act similarly to a scissors car jack that as it expands in
> one axis, becomes narrower in the other".

> Thank you Jobst, this epiphany will no doubt fill lots of holes.

Good.  I'm glad that analogy helped.  I was about to invoke Hooke's law
but thought better of it.

> Now onto the clincher. The same mechanism constricts a clincher rim
> which is not quite so obvious. Does circumferential shortening work
> through friction to the inner rim sidewalls?

That is a little more indirect.  As we saw in the discussion, air
pressure pushed inward on the rim and outward on the tire, choosing
the free body diagram conveniently with a separator AT the bead of the
rim.  That is, we look at it as if these were two bodies that touch
at this theoretical cylindrical plane.

Meanwhile, air pressure loads being opposite and equal the tire casing
doesn't see it that way because it has a 45 degree bias ply casing
that adds its constricting force to that interface.  Thus, there is an
imbalance of the otherwise balanced forces at the tire/rim interface
so that the tire does not pull outward as much as the air pressure
pushes inward on the rim.

This effect is less obvious and required a mental exercise when I
rewrote the book for clincher tires, the first edition having tubular
rims in all its diagrams and cover.  Actually nothing changed except
for the pictures.

By the way, I am not happy about the automotive tire folks using the
old junk yard term "tire carcass", the useless body of a worn out
tire, to replace the term tire casing.  It sounds so manly and brutal
in keeping with the times with carcasses here and there.  I am amazed
how fast such language quirks propagate.

Jobst Brandt
jobst.brandt@stanfordalumni.org

```

```From: jobst.brandt@stanfordalumni.org
Subject: Re: Tension wheel with or without tyre?
Newsgroups: rec.bicycles.tech
Message-ID: <0AWGd.2367\$m31.30165@typhoon.sonic.net>
Date: Mon, 17 Jan 2005 22:00:28 GMT

Tim McNamara writes:

>>>> This has puzzled me also. If there is no constrictive force on
>>>> the rim then circumferential stress is only 1/2 hoop stress and
>>>> this would damage tires with 45 deg cords.

>>> Hmmm.  OK, I didn't follow that but I've never properly understood
>>> the issues with hoop stress and 45 deg angles in the cords.  It's
>>> been explained several times, but somehow I don't get it.

>> Quite simply, with any pressurized round tube (straight tube or
>> toroidal) the stress in the wall that tends to make the tube
>> diameter fatter (hoop stress) is twice as high as the stress that
>> tends to make the tube longer.

> Is this true for any proportion of diameter vs length of the tube?
> For example, is it the same for a tube of 1" diameter by 120" length
> compared to 3" diameter by 120" length?

This is not what makes a tire shorten when pressurized.  As was
pointed out, it is the cord angle and when that angle is laid out
other than 45 degrees to the circumference of the tire, the
constriction can be lower or higher.  In the case of air hoses, that
are not supposed to change length with pressure, the angle is the
35.26 degrees previously mentioned.

>> On a pressurized aircraft, the vertical stress in the sidewall skin
>> is double the horizontal stress.  Hence pressure hoses have a cord
>> angle of 37 deg to take a higher hoop stress.  When a tire is
>> stretched around a rim through inflation/constriction, longitudinal
>> (circumferential) stress is doubled and becomes equal to hoop
>> stress.  A 45 degree cord is the optimum angle for this situation.

> The longitudinal stress is increased (doubled) because the tire is
> stretched around the rim?  How does that happen?  Because one side
> of the tube is against the rim rather than flaoting freely and
> unsupported?

You can do this with a tubular tire with no rim and watch it constrict
when inflated.  In fact doing this is not good for the tire because it
shears the inter-ply adhesives that hold the casing together.

Jobst Brandt
jobst.brandt@stanfordalumni.org

```

```From: jobst.brandt@stanfordalumni.org
Subject: Re: Tension wheel with or without tyre?
Newsgroups: rec.bicycles.tech
Message-ID: <awZGd.2391\$m31.30535@typhoon.sonic.net>
Date: Tue, 18 Jan 2005 01:21:10 GMT

Tim McNamara writes:

>> This is not what makes a tire shorten when pressurized.  As was
>> pointed out, it is the cord angle and when that angle is laid out
>> other than 45 degrees to the circumference of the tire, the
>> constriction can be lower or higher.  In the case of air hoses,
>> that are not supposed to change length with pressure, the angle is
>> the 35.26 degrees previously mentioned.

> OK, so in my effort to understand this, I am imagining a cloth tube
> with the warp and weft threads at 45 degrees to the length of the
> tube.  Pressurizing the tube makes it try to expand, which basically
> causes the threads in the casing to "scissor" a bit- the diameter of
> the casing increases, which would then shorten the tube a little.
> Is that about right?

That's it.

>>>> On a pressurized aircraft, the vertical stress in the sidewall
>>>> skin is double the horizontal stress.  Hence pressure hoses have
>>>> a cord angle of 37 deg to take a higher hoop stress.  When a tire
>>>> is stretched around a rim through inflation/constriction,
>>>> longitudinal (circumferential) stress is doubled and becomes
>>>> equal to hoop stress.  A 45 degree cord is the optimum angle for
>>>> this situation.

>>> The longitudinal stress is increased (doubled) because the tire is
>>> stretched around the rim?  How does that happen?  Because one side
>>> of the tube is against the rim rather than flaoting freely and
>>> unsupported?

>> You can do this with a tubular tire with no rim and watch it
>> constrict when inflated.  In fact doing this is not good for the
>> tire because it shears the inter-ply adhesives that hold the casing
>> together.

> I guess that the bit of lore that I was taught years ago about
> inflating tubulars off the rim being damaging was true then.
> However, I'm still wondering why longitudinal stress is doubled- is
> that because the rim actually prevents the tubular from shortening?

Don't mix what that other guy said with what I said.  We aren't
interested in the stress in the tire casing, only the resultant...
which is a shortening of the "hose".  It still annoys me that I didn't
save the pressure hose that I once had that shrunk when the pressure
was turned on.  At the time I didn't realize that these guys didn't
understand pressure.

At some time, you must have seen a clear Tygon hose with reinforcing
cords.  You'll notice that the little "squares" in the cord pattern
are actually parallelograms and have a pressure balancing cord angle.

http://www.biopharm.saint-gobain.com/pdf/Tygon3370IB.pdf
http://news.thomasnet.com/images/large/2003/04/21831.jpg

Jobst Brandt
jobst.brandt@stanfordalumni.org
```

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