B
Ben C
Guest
On 2007-11-07, Peter Cole <[email protected]> wrote:
> Ben C wrote:
>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>> Ben C wrote:
>>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>>> The most a rim can deform before spokes slack is ~1mm. That's not enough
>>>>> to permanently deform.
>>>> That ~1mm is the _change in deformation_, not the total deformation. The
>>>> rim is already precompressed.
>>> Spoke tension causes a circumferential force, load/impact a radial
>>> force, they are orthogonal.
>>
>> But the spokes are pulling radially so isn't that also a radial force?
>
> Yes, but (locally) when the spoke goes slake, that component is gone.
I was talking about the rim yielding due to the radial tension + load,
i.e. yielding that might happen _before_ the spoke above the contact
patch has gone slack.
But I see your point-- the spokes directly above the bit that's
potentially flat-spotting may be slack, but the other spokes are still
contributing a bit of compressive stress because of the circumferential
force. I hadn't even considered that.
[...]
>> Not sure what you mean by ~4x nominal spoke tension.
>
> If you calculate the stress from rim compression, you get somewhere
> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
> 4x to bring the cross section into the region of yield (but the spokes
> would snap, and/or the rim would buckle long before that).
I see.
Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
thinking of the wheel as a cylinder and the spokes collectively as a
sort of gas inside it.
36 spokes, 1500N each: 54000N
Radius (r): 0.3m
Thickness of wall (t): 0.02m
Width of rim: 0.02m
Area of rim: 2*pi*r * 0.02m = 0.037 m^2
Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
hoop stress = pr / t = 21MPa.
Hmm, not quite right, but then the rim is actually a box section, for
one thing.
>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>> it right up to yield, then yes, there is a maximum ~1mm deep
>> deformation.
>
> No rim is that flimsy, not even the old school ones.
Yes, and certainly not if normal spoke tension brings the rim to 1/4
yield.
> Ben C wrote:
>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>> Ben C wrote:
>>>> On 2007-11-07, Peter Cole <[email protected]> wrote:
>>>>> The most a rim can deform before spokes slack is ~1mm. That's not enough
>>>>> to permanently deform.
>>>> That ~1mm is the _change in deformation_, not the total deformation. The
>>>> rim is already precompressed.
>>> Spoke tension causes a circumferential force, load/impact a radial
>>> force, they are orthogonal.
>>
>> But the spokes are pulling radially so isn't that also a radial force?
>
> Yes, but (locally) when the spoke goes slake, that component is gone.
I was talking about the rim yielding due to the radial tension + load,
i.e. yielding that might happen _before_ the spoke above the contact
patch has gone slack.
But I see your point-- the spokes directly above the bit that's
potentially flat-spotting may be slack, but the other spokes are still
contributing a bit of compressive stress because of the circumferential
force. I hadn't even considered that.
[...]
>> Not sure what you mean by ~4x nominal spoke tension.
>
> If you calculate the stress from rim compression, you get somewhere
> around 70MPa, about 1/4 yield, you'd have to increase the spoke tension
> 4x to bring the cross section into the region of yield (but the spokes
> would snap, and/or the rim would buckle long before that).
I see.
Perhaps I can use this: http://en.wikipedia.org/wiki/Pressure_vessel,
thinking of the wheel as a cylinder and the spokes collectively as a
sort of gas inside it.
36 spokes, 1500N each: 54000N
Radius (r): 0.3m
Thickness of wall (t): 0.02m
Width of rim: 0.02m
Area of rim: 2*pi*r * 0.02m = 0.037 m^2
Pressure on inside of rim (p): 54000 / 0.037 = 1430000 N/m^2
hoop stress = pr / t = 21MPa.
Hmm, not quite right, but then the rim is actually a box section, for
one thing.
>> But anyway, if the rim is flimsy enough that 1500N spoke tension brings
>> it right up to yield, then yes, there is a maximum ~1mm deep
>> deformation.
>
> No rim is that flimsy, not even the old school ones.
Yes, and certainly not if normal spoke tension brings the rim to 1/4
yield.