Re: spoke lacing and profile crank question
On Thu, 20 Oct 2005, tholub <> wrote:
> I haven’t seen evidence that wheels with fewer crossings are stiffer. I
> don’t see why they would be so, either; certainly radially spoked
> wheels would feel quite loose on a unicycle, due to wind-up.
Fewer crossings are radially stiffer.
Radial spokings are (as you note) tangentially much less stiff than a
tangential (or near-tangential) spoking.
The radial stiffness is almost purely a function of spoke length. As
to evidence, you can read Jobst Brandt ‘The Bicycle Wheel’ which
includes both experimental and theoretical examination. If you’re
prepared to accept purely theoretical work I have some analysis
results at http://www.astounding.org.uk/ian/wheel/patterns.html.
However, the stiffness of the ‘rigid’ parts of the wheel (hub,
spokes, rim) pale into insignificance compared to the behaviour of the
tyre. While the wheel may be stiffer, what you ‘feel’ radially will
be the behaviour of the tyre.
> I also don’t think four-cross is inherently stronger than three-cross;
I think it is, though only slightly - a good three three-cross will
probably be better than a merely average four-cross.
> if four-cross causes weird spoke angles at the hub or rim, it will put
> stresses on the spokes which will be more likely to lead to spoke
No it won’t (or not directly) - spokes rotate at the hub and have a
spherical seating at the rim (on the nipple).
Where there is a problem is that the spokes shouldn’t be beyond
truly tangential at the hub (ie, shouldn’t be tipped over more than 90
degrees from radial). The limiting pattern is a function of rim
inside diameter and hub spoke-hole pitch circle diameter, but for
reasonably foreseeable unicycle geometry, 4 cross doesn’t work.
For example, if the inner diameter if the rim is 490mm, and the hub
ends of the spokes are on a 60mm diameter circle (values taken from my
20" Sem), then 4X would have spokes at 87 degrees from radial - just
If it were built with high flange hub, however, at say 100mm, the
spokes would be at 92 degrees from radial, and that’s generally not
such a good idea.
Admittedly, two degrees, you might get away with it. In fact, for
both these cases, it’s so close to tangential at the hub that the
actual practical issue of whether it will be OK is a function of the
height of the spoke head (because it’s a bad interference between
spoke and the head of the adjacent spoke that’s actually the problem
with going past true tangential).
(The preceding may actually be what you meant by ‘weird spoke angles’,
in which case take my disagreement as an agreement.)
In practice, 3X works for most geometries. 4X sometimes doesn’t.
4X may be very slightly stronger, but it’s a theoretical rather than a
practically useful increase in strength. Similarly, the different
stiffnesses of spoke patterns are not actually likely to be detected
in practice, on a wheel with a tyre fitted.
regards, Ian SMith
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