Spoke Patterns

Crossings v. Stiffness

One of the issues of lore regarding bike wheels is the relative merits of different cross patterns. You can have anything from no crossings (more commonly termed radial spoking) up to generally around 3 or 4 cross. The limit is a function of the ratio between the rim diameter and the hub diameter. For the geometry as set out on the main analysis page, the limit is four cross.

This page examines the effect on the effective stiffness of the wheel under vertical loads of different spoking patterns.

The analyses

The basic model is as per the main analysis page, with the difference being only that there are variable number of crossings to the spoking. Section properties, spoke numbers and applied loads are all identical, and match those in the main page.

Results

As discussed on the main page, you get most feel for the analysis results by looking at the deformed shapes, so here they are:

0 cross (radial):

1 cross:

2 cross:

3 cross:

4 cross (almost tangential):

Already, it should be apparent that the answer is that different spoking makes very little difference to the stiffness. All the plots have deflection scaled up 100 times, and you'd be struggling to see any difference.

Numerically, I can extract the vertical deflection at the middle of the contact patch:
modeldeflection
mm per 1000N
stiffness
N per mm
0 cross0.1628mm6143
1 cross0.1642mm6090
2 cross0.1654mm6046
3 cross0.1675mm5970
4 cross0.1703mm5872

Conclusions

So, a radially spoked wheel is about 4.6% stiffer than a tangentially spoked one. Alternatively, if you apply 1000N (about 100kg, 220lb) to each of the wheels, the tangential (four-cross) spoked one deflects 0.0075mm (0.0003 inch) more than the radial spoked. Since the tyre is likely to deflect several millimetres at least (if 3mm, that's 400 times more deflection) I conclude the spoking is unlikely to make a discernible difference to the vertical stiffness of the wheel.


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