Please don’t read further if you are not a spoke engineering nerd.
One of the best examinations of wheel physics and spoke performance is a 1996 paper by Henri Gavin, Bicycle Wheel Spoke Patterns and Spoke Fatigue.
Its findings and predictions stimulate numerous revisits every year in forums and exchanges that explore the principles of bicycle wheels. On page 11 he refers to spoke testing conducted at Stanford in 1984 and 1985 by Wheelsmith. My brother Jon and I were developing a superior spoke at that time and the convenient and friendly presence of Stanford in our neighborhood led to some ground breaking research. Spokes were tested and some conclusions reached. Recently, Charles Ramsey speculated what would be the ideal spoke design, one in which breakage at the elbow was as likely as at the thread.
With a 14 gauge (2.0mm diameter) spoke, breakage at the elbow is much more likely than at the thread. By contrast, with a 15 gauge (1.8mm diameter) spoke, the opposite is true: thread breakage is more likely. Much of this is owed to the ISO thread pitch used on both diameters (56 tip). Jobst Brandt has noted that, in a perfectly rational world, a finer thread pitch would be used on the thinner, 15 gauge spokes, to reduce the stress riser the thread presents. Here is part of Charles’ thinking:
8 of the Wheelsmith spokes tested broke at the threads 68 broke at the elbow. The spokes were also tested at different levels of stress. The HP Gavin paper gives the formula as Log S = -.3 Log N +4.12 the breaks followed a normal distribution with a standard score of .072 If you draw 2 normal distributions separated by 2.5004 standard scores the center where they overlap is 8/76 area on one and 68/76 area on the other. The center is half the possible breaks spokes didn’t break at the threads and the elbow at the same time. Feeding 2.5004 standard scores back into the equation gives Log S = -.3 Log N +4.12 + 2.5004*(.072) solving for any number of cycles gives a stress difference of 1.514 times so a plain gauge spoke is effectively 1.514 times as strong at the threads than at the elbow. If you make a spoke 2.46mm at the elbow and 2.0mm at the threads if will have an equal chance of breaking at the elbow as at the threads. This spoke can be made and I believe it will fit in Shimano hubs. The nipple could be made at 1.36 rather than 1.27 this will let you tighten the spokes an additional 7 percent. I believe a Weinmann 519 rim will take a .156 inch nipple drilled for 14 gauge spokes. I have never been able to crack one of these rims at the spoke hole though I have bent around 10 solid 10mm axles on the rear. With rolled threads the inside of the threads has a diameter of 1.8mm there is of course a stress riser so the center of the spoke could be made thinner perhaps 1.7mm such a spoke would no be stiff enough for me I get a lot of pannier steer so I would stick to a single butted spoke.
His calculations seem valid to me and speculation that a 2.46mm x 2.0mm single butted spoke would be more ideal is also logical.
Helps explain the high success reported with Alpine, DH and Strong spoke models. 2.3mm x 2.0mm may lack some elbow thickness (compared to Charles’ 2.46mm) but they virtually eliminate spoke breakage. Rather than transferring the failure to the thread, in practice they seem to transfer it to the hub (flange crack), rim (hole crack), or time (eventual mishap).
Even so, there is another quirk to this application that deserves mention. Throughout our spoke making careers, the more we tested and watched empirical outcomes, the more we listened to metallurgists, the more it seemed that wire quality trumped all other factors. This is not a scientific observation since the number of variables is so high a reliable deduction process dwarfs my means. Still, we regularly saw outstanding outcomes when the wire was flaw-free. The worst hub, rim, tension, and load situations were easily handled with flaw-free wire. It is more than the absolute mechanical properties of the wire. It’s processing success, making spokes not imbedded with fatigue catalyzing flaws in their microstructure.
So, if there were a wire with 30% lower properties but from which a super consistent spoke could be made, you would have better results compared to wire with greater potential but harder to work. This, of course, is a strike against stainless with its work hardening propensity.
Therefore, my quest for an ideal spoke is driven more by the need for consistency than by geometry. Spoke breakage is a combination of high number of fatigue cycles with a pre-existing metal flaw – a crystal discontinuity, hardness anomaly, impurity, etc. The simple presence of high fatigue is not enough. The wire must offer up a flaw. Spokes that lasted 100,000 miles exist. Their properties are consistent with their ingredients. But flaws they did not present.
A good case in point were tandem wheels built for the budding West Coast scene in the ’80′s. Success came from using the best quality spokes in ANY gauge, not better dimensions in inconsistent wire. Maybe part of the lesson is that bicycle spokes, despite their gossamer appearance, are actually over-dimensioned for the task. If so, 2.0mm wire is more than enough as long as the wire is consistent.
Thanks, Charles, for your predictions, but I’ll continue thinking about superior wire. Of course, upping elbow diameter is an obvious freebie since hub makers have been drilling oversized holes for some time.