One of my old friends in the bicycle science community was Jobst Brandt (RIP), a mechanical engineer at Hewlett-Packard and machine designer. He was the first to document a proper structural analysis of a bicycle wheel, using finite-elements numerical analysis.
He found that rims deflect in normal bending as they pass across the contact patch. As a result, the spoke within the zone of that deflection loses tension. It must therefore be tight enough so that it imparts compressive strength as it loses tension (meaning: tensile stress is never fully relieved). Thus, wheels stand on the bottom spokes. This violates the long-held myth that wheels hang from the spokes at the top.
Biasing a transistor is a useful analogy. We apply enough voltage to keep the transistor in its operating envelope, and we apply enough tension in a spoke to always keep it in tension. It imparts compressive strength only when “biased” by tension; otherwise it would simply buckle.
So, two things determine the strength of a wheel: the bending strength of the rim and the allowable operating tension on the spokes. The allowable spoke tension is constrained by the tangential compressive strength of the rim, and by the strength of the spoke and its attachment points.
So, a thought experiment: an extremely weak, light rim with, say, a hundred spokes. The weak (read: light) rim with too many spokes may not allow the spokes to be tensioned as highly as their own strength might allow—doing so might collapse the wheel—and they are left looser. But there are more spokes near the contact patch to stand on. The biased tension is lower but so is the compressive loading on any one spoke—maybe a wash overall. Adding spokes does not gain the benefit one might expect if the wheel is properly tensioned.
But a strong rim has both greater bending strength and also allows higher spoke tension. This can make a stronger wheel than a lighter rim with more spokes.
Thus, the big change has been heavier, stronger rims. Many are deep to provide a blade shape for reducing aerodynamic drag, which makes them much stronger in bending. And if the cross-section is greater (and it is), it will provide more tangential compressive strength allowing tighter (more heavily biased) spokes.
We used to race on very light box-section rims with no bead, using tires that are sewn together to contain the inner tube and then glued to the rim. Now, we use beaded tires, and the rim has more material to provide the bead. Even without the blade shape, modern rims are heavier and stronger.
Spokes are not much stronger than they used to be. I was using DT stainless steel spokes 50 years ago, and they still sell them. But stronger rims permit heavier gauges and higher tensions. My race wheels in the mid-70’s were 36h, three-cross, 15-17-15 butted Trois Etoiles spokes with brass nipples (which are still much better than aluminum nipples) on Dura Ace hubs. I still have them. Current wheels are 32h, two-cross, 14-15-14 butted DT stainless spokes in Campy Chorus hubs. But the rims on the new wheels are heavier and have twice the section depth.
The key is that spokes must be tight. We did not used to tighten them enough, and many still don’t. They really should be tightened to a high percentage of yield strength—75-80%. The highest stress on a spoke is when the wheel is unloaded, because the bias tension should be higher than compressive stresses, which can only reduce tension in the spoke.
An impact makes a wheel collapse either by buckling the rim or by momentarily unloading enough spokes so that the rim can no longer impart compressive strength and it becomes unstable. When spokes break, it’s because of fatigue, and fatigue cracks are more likely if spokes are not over-tensioned briefly when the wheels are built to force any residual internal stresses to yield. Those internal residual stresses provide roots for fatigue cracks. Good builders always squeeze pairs of spokes together—hard—to perform this function.
We used to think that increasing the number of crosses made a wheel more comfortable, but that’s mostly myth. Increasing the crosses does permit slightly greater spoke tension, however, which makes the slightly wheel stronger.
Rick “fewer spokes are more aerodynamic, too” Denney