For those with too much time on their hand!
Nerd Alert - Finite Element Analysis of Spoke Lacing Patterns
Williams Cycling commissioned STEM Engineering to study and document the results of finite element analysis of bike wheels with various spoke lacing to sort out the truth and myth.
Link to report: http://www.williamscycling.com/RD_ep_39.html
Keith Williams
yea i got that info in an email… interesting stuff…
'Bout time some spoke the truth.
Excellent article. Just technical enough for me keep reading and just jargon free enough to get me to the end.
The total deflection under power was a lot less than I’d thought it would be, for any wheel. Cool
Of course, the article only dealt with rear wheels thanks to dish and torque. Aeroness of one lacing pattern vs another wasn’t considered an as a rear wheel is in a much more turbulent area, aeroness is less critical. With a front wheel having no dish and not having to deal with torque, but with aero being more important, the very common radial lacing, with bladed spokes seems to be entirely suitable. A radial/radial rear wheel would have been interesting to see. While the article stated that radial lacing was said to NOT deliver torque, I believe a full radial rear wheel WILL deliver torque as all the spokes will become slightly trailing. amd spread the torque over all the spokes, both drive and non-drive side (but that’s just my guess). If a radial/radial wheel delivered no torque, the wheel wouldn’t turn, and the radial/radial wheels I used to have, rode just fine 
Next time I have some wheels made, or make up some myself, for training, I will spec 3x for all with round spokes. For racing it will be radial front with bladed spokes. For rear it will be 3x drive side and radial for non-drive side.
Interesting read.
I admit that I’m not the sharpest knife in the drawer, but part of the conclusion puzzles me. The idea that only the crossed spokes transfer power seems illogical. If both the drive and non-drive side were radial, then no power would get transferred. I don’t understand that. So, obviously I’ve missed something.
The idea that only the crossed spokes transfer power seems illogical. If both the drive and non-drive side were radial, then no power would get transferred. I don’t understand that.
The power isn’t transferred through the radial spokes in this case because there are crossed spokes, the idea being the crossed spokes more appropriately react the applied torque at the hub. In the case of a wheel with only radially laced spokes, which we all know to be perfectly capable of transmitting power, the spokes would be loaded still in tension but through a slightly different vector.
Think if you put down some serious power, and your spokes were made of plastic (so we could see the deflection). As the cassette receives the force applied by the chain, it causes the hub to rotate. Since we have plastic spokes, the hub rotates slightly before the spokes stretch enough to force the wheel hoop to spin up. Now, with our same plastic spoke wheels, if we had crossed spokes (why they’re not named tangent spokes, I don’t understand), upon application of torque to the hub, the crossed spokes immediately react with an axial force before the radial spokes have the opportunity to be stretched far enough by a rotating hub (actually not rotating in this case because the crossed spokes have reacted the torque already)
Of course plastic spokes are a meaningless pursuit, so increase the modulus about 30 times and such is life.
…and if I wrote that paper, my conclusion probably would have been that composite structure analysis is far more challenging and interesting; but I digress. I mean, metal has the same stiffness in every direction; boring.
I think Jobst beat them to it by 30-odd years.
http://www.amazon.com/...dition/dp/0960723668
Edit to add: I’m referring to the conclusion that “In this analysis the 3x/3x wheel provided the best combination of strength, stiffness, power
transfer and reliability.”
Cool report - I enjoyed it.
Thanks for the explanation Shinny. The plastic spoke analogy was easy to understand. I would think that some power would go through the radial spokes, but the lag idea was easy to understand. I knew I couldn’t cut it when I hit 2nd semester freshman physics.
Thanks again.
It seems every wheel manufacturer understands cross-lacing on the drive side for good power transfer - some even advertise that. But what I don’t understand is, a hub, being a pretty solid piece of metal, would transfer power evenly to each flange (sturdy enough not to twist). So why would anyone even consider radial spokes on the non-drive side?
probably as long as you have one nearly tangential spoke you are good to go, and adding any more is of greatly diminishing utility. So other issues like lateral stiffness, weight, durability might be more important.
FAE of spoken tension on a static wheel is interesting but what would seem to be more useful is spoke and rim stresses when the wheel is dynamically moving over a road ( smooth or otherwise ).
Much more complex FAE problem for sure. The driving frequency would be the interesting part. After that it is just number crunching I would think.
Good stuff, Keith! Thanks for doing this and making the results public. I’m still hoping that some day an enterprising college student will do a thesis that explores all sorts of wheel aspects, like the effect of rim and spoke stiffness and number of spokes on wheel stiffness and strength.
A few comments and questions on the study:
-Was the torsional stiffness of the hub modeled?
-A 150lb force at the pedal is definitely higher than normal, but not high enough to be worst case. Even a 150lb rider can easily apply a 300lb load if he completely unloads the pedal first. And of course large riders can exert even more. Thankfully that doesn’t happen often when a rider is in a low gear, and rear wheel traction will be a limiting factor in extreme cases. Also a sinusouidal force with a max of around 100lb is more typical for a strong rider with a steady effort on a steep climb.
-Similarly, the 34/22 gear isn’t worst case either. Rear wheel torque is inversely proportional to the gear ratio, and most mortals will be in a lower gear than that on a very steep climb.
-So depending on what you are interested in (max strength or fatigue strength) the parameters you selected will not be representative of either. For very infrequent stresses you just need to stay below yield, and for common stresses you’d like to be below 50% of yield.
-60% tension in the NDS is not typical. <50% would be average. Also this will vary depending on how the wheel is laced, so assuming the same value for every pattern isn’t correct. On the other hand, 100kg is low for the DS tension.
-I like how you show that using only the NDS to transfer torque (radial DS) can lead to problems if it isn’t done properly. High tension and a large NDS flange will help. The only advantage compared to crossing the DS is that maximum tensile force is reduced which may improve the longevity of a weak rim.
-Do you lace 24h rims 3x? IME that is extreme and exceeds tangent most of the time.
-Last but not least, doesn’t the power “loss” calculation assume that all strain is dissipated as heat? But the spokes and rim are metal parts with low hysteresis, and nearly all the distortion will be returned without loss during low force parts of the pedal stroke. In other words this “loss” is much lower in reality. There was even a company who marketed a hub with a spring inside (eHub?) that would make the windup and release very pronounced, and they claimed a power benefit!
That sounds like a lot of criticism, but I really do appreciate you doing this.
But what I don’t understand is, a hub, being a pretty solid piece of metal, would transfer power evenly to each flange (sturdy enough not to twist).
Hub twist isn’t as small as you think.
*So why would anyone even consider radial spokes on the non-drive side? *
It removes them from the torque entirely which reduces the chance that they will go slack from combined torque, radial, and lateral loading. When tension is lost the strength and stiffness of the wheel plummets.
The idea that only the crossed spokes transfer power seems illogical. If both the drive and non-drive side were radial, then no power would get transferred. I don’t understand that.
Then you’d have a lot of windup and eventually the radial spokes would transfer the power. In a real wheel the crossed spokes carry all the torque with minimal windup and the radial spokes are unaffected.
Also, to answer Tridork’s question, if all the spokes were radial the tensile increase would be very high when torque is applied and the hub flanges, rim, and spokes would need to be extra beefy to survive. It isn’t optimal.
I’m not a physics guy so please forgive my ignorance but what is the downside to 3x lacing on both sides of rear wheel?
Are bladed spokes ok to use on race wheels?