Also this paper demonstrates ( http://opus.bath.ac.uk/1418/1/Vogwell_P ... _4_563.pdf
" onclick="window.open(this.href);return false;" onclick="window.open(this.href);return false;" onclick="window.open(this.href);return false; ) that the radial stiffness of a wheel is actually dependent of the stiffnes on the rim and not that of the spokes. this i becuase of the way the naths works. See eq 38 in the paper - spokes are alot stiffer than the rim so wheel stiffnes become rim stiffnes divided by approximatley 1 which equals rim stiffness. Counter intuative I know. So a radial wheel has just as much radial complaince as a 3x wheel if the same rim is used, which in reality is almost none.
In fact reading that paper has challanged alot of assumption I had about thicker spokes leading to a radially stiffer wheel.
So spoke count and thickness only makes a difference to lateral stiffness. Count count and thickness has little to do with radial stiffness - that is down to the rim.
I agree that the radial stiffness of any wire spoke wheel is so high that difference between wheels don't matter. However, I wouldn't base that opinion on this paper. I'm afraid to say that this is one of the worst papers I've seen published on this subject, and is full of flawed analyses, faulty assumptions, and one glaringly bad error that invalidates its conclusion. Although the paper lists several references, I don't think the authors read them (or maybe didn't understand them), since many of their analyses and assumptions are contradictory to the referenced publications.
In particular, the largest mistake made in the paper is assuming that the rim and spoke deflections are independent, and that the total wheel deflection is the sum of the rim and spoke deflections (in other words, they treat the rim and spoke stiffnesses as if they are in series). The reality is that the rim and spokes deflect in unison, not independently - when the wheel is loaded at the hub and the hub deflects downward, both the spokes and rim deflect together, which means that the rim and spoke stiffnesses act in parellel (not series). When flexural elements act in parallel, the total stiffness is dominated by the stiffest element. This means that wheel radial stiffness is dominated by the stiffness of the spokes, not the stiffness of the rim.
The relative importance of the rim vs. the spokes on radial stiffness can be seen in the data on a web page that this paper itself references, that of the Grignon wheel test (http://www.sheldonbrown.com/rinard/wheel/grignon.htm
). In this test, the radial stiffnesses of a variety of wheels with different spokes and rim cross sections are measured directly. As can be seen from the data, the stiffest wheel in the test is actually the one with the 12mm tall Mavic GL330 rim, which is the lightest and shallowest (least stiff) rim in the test. This wheel has almost twice the radial stiffness of the Campagnolo Shamal, which has a rim that is more than twice the weight and 3 times the height (40 mm deep) as the GL330. The GL330 wheel is even 50% stiffer than the wheel with the deepest rim in the test, the 58mm carbon fiber Zipp 540. The reason GL330 wheel is the stiffest is because it has the most and thickest spokes of all the wheels in the test - 36 2.0mm straight gauge spokes (vs. 12 3.0x 1.2mm spokes in the Shamal and 18 3.3x1.2mm spokes in the Zipp 540). In other words, the stiffnesses of these wheels is dominated by the spokes, not the rim.
Looking through the paper, there are many other other flaws and poor assumptions in their overly simplified flexural analysis of wheel deflection that should be obvious to anyone who reads some of the other publications that are referenced. I would personally be ashamed to put my name to it, and I'm surprised it got published.