In article <[email hidden]>,
Quoted message said:Luns Tee writes:
There is no difference in lateral casing pull, that portion of casing
tension which is not radial. That same tension pulls on the tire bead
attachment which is what I described as being lost through heating.
Friction will not hold the tire in place, only mechanical interlocking
by its shape. That shape is pressed into the hook of the bead by
inflation pressure, but when heated becomes pliable and can
plastically creep out of engagement.
I'll start with saying that it's still not entirely clear to me
how the clinch works. As I see it, the situation is like a spoke elbow
without a head, but which is somehow still able to pull on a hole in
the hub flange anyway. But a tire casing is more flexible than a
spoke. If the spoke is flexible - imagine the many filaments of silk
you evoke in elbow stress relief discussions - then tension in it is
tension - once you go past where the spoke departs the spoke flange,
it makes no difference what angle you pull it at, that angle being
taken up by wrapping contact of the spoke around the edge of the hub
flange. From that point of contact to the spoke hole, there is only
tension: what's lateral or radial depends only on the path taken by
spoke here, but this is independant of whether the spoke outside the
flange is pulling radially, or directly across to the other
flange, so long as it still touches the hub flange before it heads off.
If we dismiss friction, then the best I can figure is that the
clinch depends on the final bend being stiff, like a fishing
hook tied on the end of a string. Hanging this hook on the corner of a
solid cube, it can support a vertical load, but transfers it to the top
of the cube with a horizontal offset. This offset is a turning moment
which is countered by the eyelet of the hook pressing against the side
of the cube, and something to keep the point of the hook from sliding
off the edge - friction. This is the lateral force that disengages a
clinch, and depends only on the vertical load on the string, and the
geometry of the hook and the corner of the cube, and whatever
deformations the two "rigid" elements experience.
For the tire at the lip of the rim, it's unclear to me whether
the transition from rigid to flexible happens before the tire leaves the
rim or afterwards. If what leaves the rim is flexible, then the only
parameter beyond that point is the tension, regardless of how wide the
tire is relative to the rim.
Quoted message said:Quoted message said:OK, here is a point where we definitely disagree. A clincher tire,
while it does experience constriction effects similar to a tubular,
also experiences a significant outward radial load from the open
bottom of its cavity. This outward force is far greater than the
constriction force, and puts the bead in a net tension.
That outward force is countered by constriction. If you test spoke
tension on a wheel while inflating its tire, you'll see that it
decreases with increasing inflation pressure the same for tubulars and
a clinchers.
It decreases because of air pressure pushing inwards on the rim
bed. The reaction to this inwards force is the outwards force of air
pressure on the tire, a force which is restrained by bearing on the
bead. There's a net constriction if you weld the tire to the casing at
the point of contact and then call the bead a part of the rim. If
they're separate, the rim sees more compression, and the bead more
tension in the casing between where the weld was, and where the bead is
pulls outwards on the bead and inwards on the rim.
Quoted message said:Quoted message said:There's a simple thought experiment that I hope can convince you of
this. Imagine taking two inelastic wire hoops to use as the bead,
and building a tire around it, but with the casing threads free to
slide along the length of the bead. This is still a legitimate
clincher, but what direction do the casing threads pull on the bead?
Outward! There is no mechanism by which the casing can pull the bead
into a smaller diameter. In a tubular tire, the inward pull is
provided by air pressure bearing that segment of casing along the
rim bed that a clincher lacks.
Try the spoke tension test and see how you think about that.
I've already explained how I think about that: air pressure on
the rim bed. In a tubular, this pressure is contained by the tire - this
is why I was giving attention to the span of casing between rim edges
elsewhere in the discussion, the section which you'd wanted to
weld the edges of and forget about.
Try the thought experiment and see how you think about that.
If you want a test, look at the edge of the chafing strip just
above at the lip of the rim as you inflate a tire. I tried this just now.
My tire's edge is only barely visible when inflated at 20 psi, enough
pressure to give the tire its intended shape. Inflating to 100psi, the
strip is pulled out and about 1mm of it is now visible. This is with a
kevlar-bead tire: a steel-bead tire may show less of a difference.
Quoted message said:Quoted message said:If you think of a wheel as an upper and lower half and look at the
forces between the two of them, the forces in a tubular are simple.
There's air pressure on two ~25mm circles pushing them apart, and
casing tension on the periphery pulling them together with twice the
force. The balance is taken up as compression in the rim, which
presses against the tire - this is your constriction.
I think you have the wrong model. Constriction comes from cord angle,
and does not occur in a mylar torus, for instance. Your model assumes
a torus of a homogeneous material with no preferential axis.
No, my model is quite correct. Where the cord angle comes in
is the ratio of the tension per unit length acting along the length
of the sidewalls, to the tension per unit length cross the minor
diameter of the torus. In the mylar torus, these are independant. In
the 45-degree bias ply casing, these unit tensions are equal, being
simply P*r, with P and r being the tire pressure and minor diameter
radius respectively. This acting on the 2*pi*r perimeter of each small
circle is 2P*pi*r^2, which happens to be exactly twice the force of
air pressure on the contained area. I skipped to this end result where I
Quoted message said:Quoted message said:casing tension on the periphery pulling them together with twice the
force [of air pressure].
assuming that you would recognize it, but apparantly not.
Quoted message said:Quoted message said:Clincher tires have their beads in tension. The radial load pulling
on the large major diameter of the bead is much stronger than
constriction effects.
I'm not so sure of that. As I said, before hooked bead rims came
along we rode straight sidewall rims that were nearly as wide as the
tire and these did not blow off at 90psi or so.
These tires had steel beads, yes? If the tires were intended
for straight wall rims, I would expect the bead wires to be somewhat
heavier than typical tires of today, and the radial load of the bead
supported entirely by the wire.
Quoted message said:Quoted message said:Do the calculations: the tension applied to a clincher's beads is on
the order of 15 times the constriction force of a tubular!
So how dies that translate to reduction in spoke tension
Air pressure on the rim, and the pressure of the tire wrapping
around the lip of the rim, the net total of which press inwards on the
order of 16 times the constriction of a tubular.
Quoted message said:or for that
matter, original clincher tires that had no bead wire or Kevlar. In
the days of yore, all clinchers were foldable, having no rigid bead.
I'm not familiar with these tires - how is the edge of the
casing terminated, if not with a bead wire? And if these did work, then
why do we have beads and hooked rims today?
Quoted message said:Quoted message said:However, the above assumed an inelastic bead. A real bead would
stretch under tension, and transfer its tension to the rim instead
by pushing outward radially in the clinch.
I think you have that incorrectly.
Jobst Brandt
I very certain you are mistaken.
-Luns
Quoted message said:Quoted message said:Quoted message said:Isn't that exactly what I said? I'm hearing echos!
Quoted message said:It was unclear to me what you'd meant by 'lateral pull', whether you
were referring to the pull of the casing outside the rim pulling
away from the wheel centerline, or the casing where it's squished
against the rim hook right where the bead reaches into its groove
pulling toward the centerline. I was asserting the latter.
There is no difference in lateral casing pull, that portion of casing
tension which is not radial. That same tension pulls on the tire bead
attachment which is what I described as being lost through heating.
Friction will not hold the tire in place, only mechanical interlocking
by its shape. That shape is pressed into the hook of the bead by
inflation pressure, but when heated becomes pliable and can
plastically creep out of engagement.
Quoted message said:Quoted message said:> The external pull is supported by the rim, and is conveyed to the
> bead like a rope wrapped around a pole. If we assume the friction
> between the casing and rim has failed (no friction), then the
> tension of this pull is just the tension of the casing, which for
> the unloaded part of the tire is the tire width times air pressure
> and some factor involving sqrt(2).
Quoted message said:Quoted message said:Don't make it so cumbersome. Its the horizontal component of
casing tension that does it and this is always present, explaining
why I have had blow offs with less than 100psi after long rim
heating. I don't know what you mean by "external pull", the casing
can only pull in one direction and at its rim contact That means it
is pulling the softened bead around a corner, something it
otherwise resists by its shape.
Quoted message said:If the casing as it goes around the lip of the rim can be treated as
the rope around a pole, then the tension at the bead is the same
tension as the other end of the wrap, whatever angle it may exit at.
It's unclear to me whether we can treat the tire here in this manner
or if there's stiffness in the bead area to be considered: I'm still
pondering it.
That is true, but the net force is only the horizontal component of
that tension because radially constriction balances the radial
component. Since constriction does not have a lateral component, that
portion of casing tension works to disengage the tier.
This problem is as convoluted as the tire supporting the rim because
there are two effects at work, casing tension and constriction.
Quoted message said:Quoted message said:> This is independent of rim width - a 10mm rim, if you could use
> such a thing - with that 20mm tire would be no more susceptible to
> blow offs, and in fact, with more tire wrapping around the rim to
> provide more friction, I would expect it to be less susceptible to
> blow offs than a wider rim.
Quoted message said:Quoted message said:It is not! If the pull were radial it would not lift the tire from
the rim because constriction forces hold that load against the rim.
If you doubt it, do the calculation or try a tubular tire when
inflated. Constriction increases with inflation pressure. I take
it you have not had a tire blow off.
Quoted message said:OK, here is a point where we definitely disagree. A clincher tire,
while it does experience constriction effects similar to a tubular,
also experiences a significant outward radial load from the open
bottom of its cavity. This outward force is far greater than the
constriction force, and puts the bead in a net tension.
That outward force is countered by constriction. If you test spoke
tension on a wheel while inflating its tire, you'll see that it
decreases with increasing inflation pressure the same for tubulars and
a clinchers.
Quoted message said:There's a simple thought experiment that I hope can convince you of
this. Imagine taking two inelastic wire hoops to use as the bead,
and building a tire around it, but with the casing threads free to
slide along the length of the bead. This is still a legitimate
clincher, but what direction do the casing threads pull on the bead?
Outward! There is no mechanism by which the casing can pull the bead
into a smaller diameter. In a tubular tire, the inward pull is
provided by air pressure bearing that segment of casing along the
rim bed that a clincher lacks.
Try the spoke tension test and see how you think about that.
Quoted message said:If you think of a wheel as an upper and lower half and look at the
forces between the two of them, the forces in a tubular are simple.
There's air pressure on two ~25mm circles pushing them apart, and
casing tension on the periphery pulling them together with twice the
force. The balance is taken up as compression in the rim, which
presses against the tire - this is your constriction.
I think you have the wrong model. Constriction comes from cord angle,
and does not occur in a mylar torus, for instance. Your model assumes
a torus of a homogeneous material with no preferential axis.
Quoted message said:The balance is quite different for a clincher. We now have a 14mm
wide rim bed on which the air pressure is pushing inward on the
clincher. On a ~630mm rim diameter, the total pressure over this
area is much greater than for the two little circles of the tubular
tire - about 8x greater! In the meanwhile, the total tension of the
casing cords is still about the same. What balances all this extra
compression? Tension in the bead.
This is a more complex visualization but it boils down to the same
effects. You must draw your FBD carefully not to count forces twice.
Quoted message said:Clincher tires have their beads in tension. The radial load pulling
on the large major diameter of the bead is much stronger than
constriction effects.
I'm not so sure of that. As I said, before hooked bead rims came
along we rode straight sidewall rims that were nearly as wide as the
tire and these did not blow off at 90psi or so.
Quoted message said:It gets worse.
Quoted message said:As the casing wraps around and presses on the lip of the rim, it
also gives a radial compression to the rim. The magnitude of this
compression is equal to air pressure times the difference between
the tire width and the rim width. This is balanced by there being
just as much tension applied to the bead on top of what's air
pressure on the rim bed contributes.
As I said, you must draw your FBD carefully not to count forces twice.
Quoted message said:Do the calculations: the tension applied to a clincher's beads is on
the order of 15 times the constriction force of a tubular!
So how dies that translate to reduction in spoke tension or for that
matter, original clincher tires that had no bead wire or Kevlar. In
the days of yore, all clinchers were foldable, having no rigid bead.
Quoted message said:However, the above assumed an inelastic bead. A real bead would
stretch under tension, and transfer its tension to the rim instead
by pushing outward radially in the clinch.
I think you have that incorrectly.
Jobst Brandt
