Sheldon Brown writes:
> This doesn't surprise me. The usual warnings against radial spoking apply to front hubs, which
> have no torsional loading. The situation is much more serious in the case of rear wheels (or any
> wheel with a hub brake,)
These warnings are given for front hubs because that is usually the only place where people like to
use radial spoking. The custom of left rear radial spoking having come more recently.
> In any spoke pattern, if you extend the spoke line inward until it approaches as close to the
> centerline of the axle as it gets, the distance between the two lines is the "moment arm" of the
> spoke as regards torsional loads.
> The torsional component of the spoke tension is inversely proportional to this moment arm
> distance. That's the reason large flange hubs used to be popular for touring bikes, because back
> in the day of lower quality spokes and lower standards of wheelbuilding, spokes used to sometimes
> break when subjected to high torsional loading.
That was the belief at the time, but you'll notice that the use of large flange hubs has greatly
diminished since then. People saw the analysis of how small these spoke loads are in comparison to
those produced by a vertical load on the wheel. Because torque induced tension is small, the
failures were most likely from poor spoke line at the nipple... and the lack of stress relieving.
We readily forget that spoke failures were formerly attributed to singular events of misuse, pot
holes, or jumping off curbs and the like. The concept of the fatigue failure in spokes was unheard
of. It was much like the belief in Brinell indenting of head bearings, that is actually caused by
fretting motions and lubricant depletion.
> In the case of a perfectly radial spoke, where the moment arm distance is zero, any torsional load
> will theoretically create an infinite amount of tension on the spoke!
That effect is striking because by the time there is practical "wind up" the cosine error (length
change) is significant and the tension increase can easily damage flanges.
> In practice, of course, the spokes will elongate a bit, and the hub will "wind up" a bit until
> there is sufficient moment arm to make the rim turn, but this creates a load which, while not
> "infinite" is still enormous.
The reason "wind up" remains small is that ALL spoke tension, rather than just a differential
tension change of pulling and pushing spokes, acts on the hub to rotate the wheel. This is the
saving grace of rear wheel radial spoking. That is to say, by this force triangle, great torque for
a tiny lever length is generated and makes the wheel feel as torsionally stiff as a cross laced
wheel. Windup remains too small to be felt through the normal drive train ratios.
Jobst Brandt
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